IEE ELECTROMAGNETIC WAVES SERIES 28 Series Editors: Professor P. J. B. Clarricoats Professor Y. Rahrnat-Samii Professor J. R. Wait
Handbook of
ANTENNAS
Other volumes in this series: Volume 1 Geometrical theory of diffraction for electromagnetic waves G. L. James Volume 2 Electromagneticwaves and CUN& structures L. Lewin, D. C. Chang and E. F. Kuester Volume 3 Microwave homodyne systems R. J. King Volume 4 Radio direction-finding P. J. D. Gething Volume 5 ELF communications antennas M. L. Burrows Volume 6 Waveguide tapers, transitions and couplers F. Sporleder and H. G. Unger Volume 7 Reflector antenna analysis and design P. J. Wood Volume 8 Effects of the troposphere on radio communications M. P. M. Hall Volume 9 Schumann resonances in the earth-ionosphere cavity P. V. Bliokh, A. P. Nikolaenko and Y. F. Flippov Volume 10 Aperture antennas and diffraction theory E. V. Jull Volume 11 Adaptive array principles J. E. Hudson Volume 12 Microstrip antenna theory and design J. R. James, P. S. Hall and C. Wood Volume 13 Energy in electromagnetism H. G. Booker Volume 14 Leaky feeders and subsurface radio communications P. Delogne Volume 15 The handbook of antenna design, Volume 1A. W. Rudge, K. Milne, A. D. Olver, P. Knight (Editors) Volume 16 The handbook of antenna design, Volume 2 A. W. Rudge, K. Milne. A. D. Olver. P. Kniaht (Editors) predichon P. Rohan e Volume 17 ~ u ~ e i l l & cradar Volume 18 Cormaated horns tor microwave antennas P. J. B. Clarricoats and A-D. Olver Volume 19 Microwave antenna theory and design S. Silver (Editor) Volume 20 Advances in radar techniques J. Clarke (Editor) Volume 21 Waveguide handbook N. Marcuvitz Volume 22 Target adaptive matched illumination radar D. T. Gjessing Volume 23 Ferrites at microwave frequencies A. J. Baden Fuller Volume 24 Propagation of short radio waves D. E. Kerr (Editor) Volume 25 Principles of microwave circuits C. G. Montgomery, R. H. Dicke, E. M. Purcell (Editors) Volume 26 Spherical near-field antenna measurements J. E. Hansen (Editor) Volume 27 Electromagnetic radiation from cylindrical structures J. R. Wait Volume 28 Handbook of microstrip antennas J. R. James and P. S. Hall (Editors) Volume 29 Satellite-to-ground radiowave propagation J. E. Allnutt Volume 30 Radiowave propagation M. P. M. Hall and L. W. Barclay . (Editors) Volume 31 Ionospheric radio K. Davies
Handbook of
ANTENNAS
Edited by
J R James & P s Hall
~
Peter Peregrinus Ltd, on behalf of the Institution of Electrical Engineers
Published by: Peter Peregrinus Ltd., London, United Kingdom
o 1989: Peter Peregrinus Ltd.
All rights resewed. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any meanselectronic, mechanical, photocopying, recording or otherwise-without the prior written permission of the publisher. While the authors and the publishers believe that the information and guidance given in this work are correct, all parties must rely upon their own skill and judgment when making use of them. Neither the authors nor the publishers assume any liability to anyone for any loss or damage caused by any error or omission in the work, whether such error or omission is the result of negligence o: any other cause. Any and aii such liability is disclaimed.
Contents
Volume 1
1
Foreword Preface List of contributors Introduction - J.R. James and P.S. Hall 1.I 1.2 1.3 1.4 1.5 1.6
British Library Cataloguing i n Publication Data Handbook of Microstrip Antennas 1. Microwave equipment: Microstrip antennas I. James, J. R. (James Roderick, 1933II. Hall, P. S. (Peter S) Ill. Institution of Electrical Engineers IV. Series 621.381'33
ISBN 0 86341 150 9
Printed in England by Short Run Press Ltd., Exeter
2
Historical development and future prospects Fundamental issues and design challenges Features of microstrip antenna technology 1.2.1 1.2.2 Fundamental problems The handbook and advances presented Glossary of printed antenna types Summary comments References
Analysis of circular microstrip antennas - L. Shafai and A.A. Kishk 2.1 2.2
2.3
2.4 2.5 2.6 2.7
Introduction Formulation of the problem 2.2.1 Matrix formulation 2.2.2 Excitation matrix 2.2.3 Radiation fields Application I: Circular patch antenna 2.3.1 Surface fields 2.3.2 Feed location Effect of the substrate permittivity 2.3.3 Effect of the substrate thickness 2.3.4 Effect of the ground-plane radius 2.3.5 Effect of the ground-plane thickness 2.3.6 2.3.7 Circular polarisation Effect of a central shorting pin 2.3.8 Application 2: Wraparound microstrip antenna Application 3: Reflector antenna feeds Concluding remarks References
xvii xix
xxi 1
Contents
vi Contents 3
Characteristics of microstrip patch antennas and some methods of improving frequency agility and bandwidth - K.F. Lee and J.S. Dahele Introduction Cavity model for analysing microstrip patch antennas 3.2.1 lntroduction 3.2.2 Feed modelling, resonant frequencies and internal fields 3.2.3 Radiation field 3.2.4 Losses in the cavity 3.2.5 Input impedance 3.2.6 VSWR bandwidth 3.2.7 Qualitative description of the results predicted by the model Basic characteristics of some common patches 3.3.1 The rectangular patch 3.3.2 The circular patch 3.3.3 The equitriangular patch 3.3.4 Annuiar-ring patch 3.3.5 Comparison of characteristics of rectangular, circular, equitriangular and annular-ring patches 3.3.6 Brief mention of other patches Some methods of improving the frequency agility and bandwidth of microstrip patch antennas 3.4.1 Introduction 3.4.2 Some methods of tuning MPAs 3.4.3 Dual-band structures 3.4.4 Electromagnetic-coupled patch antenna (EMCP) Summary Acknowledgments References
4
5
Microstrip dipoles - P.B. Katehi, D.R. Jackson and N.G. Alexopoulis Introduction Infinitesimal dipole 5.2.1 Analysis 5.2.2 Substrate effects 5.2.3 Superstrate effects Moment-method techniques for planar strip geometries 5.3.1 Basis functions 5.3.2 Reaction between basis functions 5.3.3 Plane-wave-spectrum method 5.3.4 Real-space integration method 5.3.5 Point-dipole approximation 5.3.6 Moment-method equations Centre-fed dipoles 5.4.1 Single dipole 5.4.2 Mutual impedance EMC dipoles 5.5.1 Methods of analysis 5.5.2 Single dipole 5.5.3 Multiple dipoles Finite array of EMC dipoles 5.6.1 Analysis 5.6.2 Calculation of coefficients 5.6.3 Array design Conclusions References
6
Multilayer and parasitic configurations - D.H. Schaubert 6.1 6.2
Circular polarisation and bandwidth - M. Haneishi and Y. Suzuki Various types of circularly polarised antenna 4.1.1 Microstrip patch antennas 4.1.2 Other types of circularly polarised printed antennas Simple design techniques for singly-fed circularly polarised microstrip antennas 4.2.1 Rectangular type 4.2.2 Circular type More exact treatment for singly-fed circularly polarised microstrip antennas 4.3.1 Analysis 4.3.2 Conditions for circularly polarised radiation 4.3.3 Example Some considerations on mutual coupling Wideband techniques 4.5.1 Design of wideband element 4.5.2 Technique using parasitic element 4.5.3 Technique using paired element References
6.3 6.4 6.5 6.6 7
Introduction Stacked elements for dual-frequency or dual polarisation operation Antennas with separate feeds for each function 6.2.1 Antennas for multiple frequencies and increased 6.2.2 bandwidth Two-sided aperture-coupled patch Parasitic elements on antenna substrate Summary References
Wideband flat dipole and short-circuit microstrip patch elements and arrays - G. Dubost 7.1 7.2 7.3
Flat dipole elements and arrays 7.1.1 Elementary sources Array designs: losses and efficiencies 7.1.2 Short-circuit microstrip patches and arrays 7.2.1 Elementary source 7.2.2 Array designs References
vii
viii
8
Contents Numerical analysis of microstrip patch antennas - J.R. Mosig, R.C. Hall and F.E. Gardiol Introduction 8.1.1 General description 8.1.2 The integral equation model Model based on the electric surface current 8.2.1 Geometry of the model and boundary conditions 8.2.2 Potentials for the diffracted fields 8.2.3 Green's functions 8.2.4 Mixed potential integral equation (MPIE) 8.2.5 Sketch of the proposed technique Horizontal electric dipole (HED) in microstrip 8.3.1 The vector potential 8.3.2 Scalar potential and the fields 8.3.3 Surface waves and spectral plane k 8.3.4 Far-field approximations 8.3.5 Radiation resistance and antenna efficiency Numerical techniques for Sommerfeld integrals 8.4.1 Numerical integration oii the real axis 8.4.2 Integrating oscillating functions over unbounded intervals Construction of the Green's functions Method of moments 8.6.1 Rooftop (subsectional) - basis functions 8.6.2 Entire domain basis functions Excitation and loading 8.7.1 Several microstrip-antenna excitations 8.7.2 Coaxial excitation and input impedance 8.7.3 Multiport analysis Single rectangular patch antenna 8.8.1 Entire-domain versus subdomain basis functions 8.8.2 Convergence using subsectional basis functions 8.8.3 Surface currents Microstrip arrays 8.9.1 Array modelling 8.9.2 Mutual coupling 8.9.3 Linear array of few patches Acknowledgments References
9
Contents Edge-admittance and mutual-coupling networks 9.4.1 Edge-admittance networks 9.4.2 Mutual-coupling network Analysis of multiport-network model 9.5.1 Segmentation method 9.5.2 Desegmentation method Examples of microstrip antenna structures analysed by multiportnetwork approach 9.6.1 Circularly polarised microstrip patches 9.6.2 Broadband multiresonator microstrip antennas Multiport microstrip patches and series-fed arrays 9.6.3 C A D of microstrip patch antennas and arrays Appendix: Green's functions for various planar configurations Acknowledgments References 10
Transmission-line model for rectangular microstrip antennas
- A. Van rle Capelle
Introduction Simple transmission-line model Description of the transmission line model 10.2.1 Expressions for G, and B, 10.2.2 Expressions for the line parameters 10.2.3 Improved transmission-line model Description of the improved transmission-line model 10.3.1 Expression for the self-susceptance B, 10.3.2 Expression for the self-conductance G, 10.3.3 Expression for the mutual conductance G, 10.3.4 Expression for the mutual susceptance B, 10.3.5 Expressions for the line parameters 10.3.6 Application of the improved transmission-line model Analysis and design of rectangular microstrip antennas 10.4.1 10.4.2 Comparison with other methods 10.4.3 Comparison with experimental results 10.4.4 Design application Transmission-line model for mutual coupling 10.5.1 Description of the model Calculation of the model parameters 10.5.2 10.5.3 Comparison with other methods Acknowledgements References
Multiport network approach for modelling and analysis of microstrip patch antennas and arrays - K.C. Gupta 455 11
9.1 9.2
9.3
Introduction Models for microstrip antennas 9.2.1 Transmission-line model 9.2.2 Cavity model 9.2.3 Multiport network model 2-matrix characterisation of planar segments 9.3.1 Green's functions 9.3.2 Evaluation of 2-matrix from Green's functions 9.3.3 2-matrices for segments of arbitrary shape
Design and technology of low-cost printed antennas E. Penard and C. Terret 11.1 11.2
11.3
- J.P. Daniel,
Introduction Analysis of simple patches and slots Rectangular and circular patches 11.2.1 11.2.2 Conical antennas 11.2.3 Linear and annular slots Design of planar printed arrays 1 1.3.1 Design parameters
ix
x
11.4
11.5
11.6 11.7 12
11.3.2 Cavity model analysis of mutual coupling 11.3.3 Linear series array of corner-fed square patches 113.4 Two-dimensional cross-fed arrays Synthesis methods for linear arrays 11.4.1 Relaxation methods 11.4.2 Simplex method 11.4.3 Experimental results New low-cost low-loss substrate 11.5.1 Substrate choice 11.5.2 Fabrication procedure 11.5.3 Electrical characteristics 11.5.4 Environmental tests 11.5.5 Examples of printed antennas on polypropylene substrate Concluding remarks References
Volume 2 14
14.3
Analysis and design considerations for printed phased-array antennas Pozar
12.3 12.4 12.5 12.6
Introduction Analysis of some canonical printed phased-array geometries 12.2.1 Some preliminaries 12.2.2 Infinite-planar-array solutions 12.2.3 Finite-array solutions Design considerations for printed phased arrays 12.3.1 Introduction 12.3.2 Array architectures Conclusion Acknowledgments References
Microstrip antenna feeds - R.P. Owens 14.1 14.2
14.4
- D.M. 12.1 12.2
13
Contents xi
Contents
14.5 14.6 14.7 15
Advances in substrate technology - G.R. Traut 15.1
Circularly polarised antenna arrays - K. Ito, T. Teshirogi and S. Nishimura 13.1
13.2
13.3
13.4
13.5
Various types of circularly polarised arrays 13.1.1 Arrays of patch radiators 13.1.2 Arrays of composite elements 13.1.3 Travelling-wave arrays 13.1.4 Other types of arrays Design of circularly polarised arrays 13.2.1 Arrays of patch radiators 13.2.2 Arrays of composite elements 13.2.3 Design of travelling-wave arrays Practical design problems 13.3.1 Mutual coupling 13.3.2 Unwanted radiation 13.3.3 Limitations and trade-offs 13.3.4 Non-planar scanning arrays Wideband circularly polarised arrays 13.4.1 Arrays of wideband elements 13.4.2 Arrays of dual-frequency stacked elements 13.4.3 Wideband-array techniques References
Introduction Coupling to microstrip patches 14.2.1 Co-planar coupling to a single patch 14.2.2 Series-array co-planar coupling 14.2.3 Probe coupling 14.2.4 Aperture coupling 14.2.5 Electromagnetic coupling Parallel and series feed systems 14.3.1 Parallel feeds for one and two dimensions 14.3.2 Series feed for one dimension 14.3.3 Combined feeds 14.3.4 Discontinuity arrays Direct-coupled stripline power dividers and combiners 4 . 4 Simple three-port power dividers 14.4.2 Isolated power dividers/combiners 14.4.3 Four-port direct-coupled power dividers Other feed systems 14.5.1 Alternative transmission tines 14.5.2 Multiple beam-forming networks Acknowledgments References
15.2
15.3
Considerations for substrate selection 15.1.1 Impact of properties of various substrate systems on microstrip antenna performance 15.1.2 Comparative list of available substrates 15.1.3 Selection of metal cladding for performance 15.1.4 Thermal characteristics of PTFE 15.1.5 Anisotropy of relative permittivity Measurement of substrate properties 15.2.1 Stripline-resonator test method 15.2.2 Microstrip-resonator test method 15.2.3 Full-sheet-resonance test method 15.2.4 Perturbation cavity method 15.2.5 Tabulated evaluation of methods for measuring relative permittivity and dissipation factor Processing laminates into antennas 15.3.1 Handline incoming copper-clad laminates 15.3.2 Handling prior to processing 15.3.3 Safetv considerations for PTFE-based substrates 15.3.4 ~ e d i c i the n ~ effects of etch strain relief 15.3.5 Machining of PTFE-based boards 15.3.6 Bending etched antenna boards 15.3.7 Bonded-board assemblies 15.3.8 Plating-through holes in' microstrip antenna boards
-
xii
15.4
15.5
15.6 16
Contents xiii
Contents
Device attachment on microstrip antenna substrates 15.3.9 Design considerations with selected materials Environmental effects o n antenna substrates 15.4.1 15.4.2 Conductor losses at millimetre-wave frequencies Multilayer circuit-board technology in microstrip 15.4.3 antennas Special features and new materials developments 15.5.1 Substrates clad on one side with thick metal 15.5.2 Low thermal coefficient of K' in fluoropolymer laminates 15.5.3 Microwave laminates with a resistive layer 15.5.4 Thermoset microwave materials 15.5.5 Low permittivity ceramic-PTFE laminates 15.5.6 Very-low-dielectric-constant substrates References
Special measurement techniques for printed antennas - E. Levine
17.3
17.4
Introduction Substrate properties Connector characterisation Measurements of printed lines and networks 16.4.1 Measurement of printed-line parameters 16.4.2 Measurement of printed networks Near-field probing Efficiency measurement Concluding remarks References 17
Computer-aided design of microstrip and triplate circuits - J.F. Ziircher and F.E. Gardiol 17.1
17.2
Introduction, definition of the structure 17.1.1 Outline 17.1.2 Microwaves 17.1.3 Transmission lines for microwaves 17.1.4 Balanced stripline or triplate 17.1.5 Microstrip 17.1.6 Adjustments 17.1.7 Multiple inhomogeneity 17.1.8 Measurement problems Basic relationships for uniform lines 17.2.1 Uniform lines 17.2.2 Conformal mapping 17.2.3 Schwartz-Christoffel transform 17.2.4 Zero-thickness balanced stripline 17.2.5 Finite-thickness balanced stripline 17.2.6 Equivalent homogeneous microstrip line 17.2.7 Characteristic impedance of microstrip 17.2.8 Finite-thickness homogeneous microstrip 17.2.9 Microstrip-line synthesis for b = 0 17.2.10 Dispersion in microstrip 17.2.11 Effect of an enclosure
17.5
17.2.12 Attenuation 17.2.13 Higher-order modes and radiation Discontinuities: bends and junctions 17.3.1 Definition 17.3.2 Models 17.3.3 TEM-line models 17.3.4 Variational techniques 17.3.5 Fourier transform 17.3.6 Dielectric Green's function 17.3.7 Integral equations for inductances Green's function and integral equation 17.3.8 17.3.9 Green's function and electrostatic-inductance computation 17.3.10 TLM (transmission-line-matrix) method 17.3.11 Waveguide model Technological realisation: Materials and manufacturing process 17.4.1 Introduction 17.4.2 Dielectric substrate i7.4.3 Comment 17.4.4 Inorganic substrates 17.4.5 Plastic substrates 17.4.6 Semiconductor substrates 17.4.7 Ferrimagnetic substrates 17.4.8 Metallisation 17.4.9 Circuit realisation 17.4.10 Etching 17.4.11 Metal deposition 17.4.12 Removal of photoresist 17.4.13 Under-etching 17.4.14 Thin and thick film Analysis and synthesis programs 17.5.1 Introduction EEsof: Touchstone CCC: The Supercompact Family CCC: CADEC Acline Thorn '6: Esope RCA: Midas LINMIC High Tech. Tournesol: Micpatch Spefco Software: CiAO Made-it-associates: Mama Ampsa: Multimatch Radar systems technology: Analop Microkop/Suspend Microwave software aoolications Planim DGS Associates: S/Filsyn Webb Laboratories: Transcad Layouts of circuits and cutting of masks 17.6.1 Description 17.6.2 CCC: Autoart 17.6.3 EFSOF: Micad
+
A
17.6
xiv
Contents xv
Contents
20.2.3 Feeding the patch 20.2.4 Theoretical design method 20.2.5 Patch design Dual patch element 20.3.1 Choice of design Location of patch phase centre 20.3.2 20.3.2 Design and optimisation Hybrid feeding network 20.4.1 Overview 20.4.2 Hybrid designs 20.4.3 90' bends 20.4.4 Minimum track distance 20.4.5 Feed-point terminations 20.4.6 Track lengths 20.4.7 Overall design Conical antenna array Substrate fabrication 20.6.1 Overview 20.6.2 Mask drawing and preparation 20.6.3 Etching 20.6.4 Substrate preparation 20.6.5 Triplate bonding Forming the antenna 20.7.1 Bending the substrates 20.7.2 Attachment of components 20.7.3 Final assembly Antenna performance 20.8.1 Grating-lobe suppression 20.8.2 Axial ratio 20.8.3 Antenna gain 20.8.4 Tracking slope Conclusions and future developments References
17.6.4 High Tech. Tournesol: Micros 17.6.5 British Telecom: Temcad 17.7 Insertion of components 17.7.1 Introduction 17.7.2 Discrete components 17.7.3 Mounting procedure Drilling holes in the dielectric substrate 17.7.4 17.7.5 Deposited components 17.8 Examples Design of a broadband amplifier 17.8.1 17.8.2 Bandpass filter design Design of a miniature Doppler radar 17.8.3 17.9 Conclusions 17.10 Acknowledgments 17.11 References 18
Resonant microstrip antenna elements and arrays for aerospace applications - A.G. Derneryd 18.1 18 2 18.3 18.4 18.5 18.6 18.7
19
Introduction Circular antenna element Dual-band circularly polarised antenna element Monopulse-array antenna Dual-polarised-array antenna Concluding remarks References
Applications in mobile and satellite systems -K. Fujimoto, T. Hori, S. Nishimura and K. Hirasawa Introduction Mobile systems 19.2.1 Design considerations 19.2.2 Base stations 19.2.3 Wheeled vehicles 19.2.4 Railways 19.2.5 Pedestrian 19.2.6 Radars Satellite system 19.3.1 Design considerations 19.3.2 Direct broadcasting reception 19.3.3 Earth stations 19.3.4 Satellite borne References
20
Conical conformal microstrip tracking antenna - P. Newham and G. Morris 20.1 20.2
Introduction Single patch element 20.2.1 Choice of array element 20.2.2 Choice of substrate
21
Microstrip field diagnostics - P.G.Frayne Introduction Surface analytical techniques Scanning-network probe Theory of the monopole probe Resonant microstrip discs Resonant microstrip triangles Open-circuited microstriplines Antenna diagnostics 21.8.1 The rectangular patch Linear element patch array Circularly polarised patch antenna Microstrip travelling-wave antenna Acknowledgments References
1155 1155 1158 1161 1161 1161 1162 1163 1163 1166 1168 1168 1171 1171 1172 1172 1175 1175 1175 1176 1176 1177 1177 1177 1178 1181 1181 1182 1185 1187 1188 1188 1191
xvi
22
Contents Microstrip antennas on a cylindrical surface - E.V. Sohtell 22.1 22.2 22.3
22.4
22.5 22.6 23
Introduction Theoretical models for a patch on a cylinder Cavity model of the patch 22.2.1 22.2.2 Surface-currentmodel Single patch application 22.3.1 Mechanical design 22.3.2 Measurements 22.3.3 Radiation-pattern comparisons Array application 22.4.1 General Theoretical treatment of finite and infinite arrays 22.4.2 Design of a phased array on C-band 22.4.3 22.4.4 Measured performance Summary References
Extensions and variations to tho microstrip antenna concept A. Henderson and J.R. James
Foreword
P.S. Hall, 1257
Introduction Radiation pattern control 23.2.1 Reflector feeds 23.2.2 Spherical dielectric overlays Wide-bandwidth techniques 23.3.1 Log-periodic structures 23.3.2 Dichroic dual-function apertures Millimetre-wave hybrid antenna Novel use of materials Foam substrates for large direct-broadcast-satellite 23.5.1 domestic receiving arrays 1288 23.5.2 Magnetic materials and beam scanning 1292 Use of very-high-permittivity substrates in hyperthermia 23.5.3 applicators 1293 Summary comment 1294 References 1295
The Handbook of Microstrip Antennas could not have been written even five years ago, for neither the technology nor the relevant analytical tools were sufficientlydeveloped. This text arrives when the field is at a rush of activity. Fundamental mathematical tools are on hand to solve a variety of the important problems, and practical engineering results are now finding applications. Potential future capabilities and applications now look more optimistic than at any time in the history of this young technology. This new text describes vast developments in theory and practice. In two volumes, and representing the work of over thirty authors, the text is presented with such authority that it is assured a role as a key reference tool for many years. Microstrip antennas are a new and exciting technology. Invented about twenty years ago for application as conformal antennas on missiles and aircraft, the microstrip antenna has found increasing use because it can be fabricated by lithographic techniques in monolithic circuits. Initially, microstrip patch antennas were used as individual radiators, but they soon found use in relatively large fixed beam (non scanning) arrays. More recently, they have progressed to arrays for scanning in one or two dimensions. The advantage of this technology at microwave frequencies is its compatability with large scale printed circuit fabrication. Boards are fabricated lithographically and devices mounted by robotics or automated production line techniques. Microstrip printed circuit arrays are seen as an essential key to affordable antenna technology. At millimeter wavelengths, the benefit of microstrip arrays are enormous and so revolutionary as to create an entirely new technology; the monolithic integrated antenna array. Such an array has transmission lines, amplifiers, phase shifters and radiating elements, all on semiconductor substrates. Beyond this, these monolithic subarrays will be compatible with the integration of various solid state technologies on wafer size substrates. At these integration levels, the antenna array design and monolithic integrated circuit design cannot be separated, for the antenna architecture will need to optimise radiation, solid state device integration, board layout and thermal design. And so is born the antenna system architect!
xviii Foreword
Against this backdrop of energy and creativity, this timely and important book is the first handbook entirely dedicated to presenting a detailed overview of microstrip antenna development and theory. The vast scope of the text does justice to the broad range of research and development being undertaken throughout the world that is addressing a wide variety of microstrip elements and arrays for radiating linearly and circularly polarised waves. The text presents the work of a number of the most prominent and knowledgeable authors and so documents the state of the art at many institutions and in several countries. This monumental handbook is a milestone in the development of microstrip antenna technology.
Preface
Robert J. Mailloux Within two decades Microstrip Antennas have evolved as a major innovative activity within the antenna field and for both of us it has indeed been a fascinating and challenging experience to play a part in this vibrant research. In so doing the opportunity to initiate this International Handbook has arisen and this again has been a stimulating, meaningful objective that has also enriched our personal experiences through contact with numerous colleagues worldwide. It was around 1985 when it was apparent to us that the topic had raced ahead so fast that our previous IEE book "Microstrip Antenna Theory and Design" published in 1981 would soon need up-dating. Such is the vigour in Microstrip Antenna research that neither of us felt that we could do justice to the topic, at least across all its frontiers in a reasonable time scale, and it was at this point that we conferred with colleagues worldwide and this multiauthored Handbook was conceived. As to the subject itself, it has been abundantly clear for years that it is system driven and indeed continues to be so, and that its alarming pace has promoted microstrip antennas from the ranks of a rather specialised technique to a major type of antenna technology in itself. Historically one has always associated low cost, low weight and low profile with Microstrip Antennas but this description is simplistic and inadequate in the industrial atmosphere today where many new systems owe their existence to these new radiators. In reality, the feasibility of a low profile printed radiator has inspired the system creators and there is an abundance of examples, not just in the Defence sector. For instance, we have new generations of printed paper antennas, adaptive conformal antennas sitting on the roofs of automobiles and printed antennas as true ground speed sensors in many transport scenarios. It is indeed a stimulating topic to be associated with and we hope that the Handbook will portray this. For the in-depth researcher, however, the frontiers to push forward carry the familiar headings of bandwidth extension techniques, pattern control, minimisation of losses etc. but the scene has moved on in a decade and industry is now thirsty for significant advances, all at low cost, to meet the demand for higher performance and competitive costs. Research thus
xx
Preface
addresses critical optimisation procedures and advances are hard won. The role of substrate technology is now well appreciated and major developments have taken place to design materials that withstand a wide range of operating constraints, yet are affordable. As to the main thrust in research, it centres around the continual quest for innovative electromagnetic printed structures that satisfy the expanding system demands coupled with the ability to manufacture them and it is in the latter area where computer aided design (CAD) forms the cutting edge. Whether the manufacture of microstrip arrays can be fully automated via CAD in the immediate future is an open question that echoes throughout the Handbook and at present, further research is necessary. In organising the Handbook we have attempted to address all these aspects giving a balanced viewpoint from both industry and research centres and the overlap between chapters is intended to be sufficient to allow meaningful comparisons between contributors to be made. The broad theme adopted is to take the reader through elements and arrays in the first volume followed by technology and applications in the second volume but as may be expected, many authors include material covering more than one aspect. Look-up charts relating items of interest to chapters and a Glossary of over one hundred different types of printed antennas form much of the Introduction to assist the reader to efficiently select those parts that are of immediate interest. Finally, we thank all authors for their creative contributions, splendid cooperation, careful preparation of manuscripts and fellowship in the collective aim to compile a worthy international text with many years9 useful life. In particular we thank Dr David Pozar and Dr Koichi Ito who helped us initially with communications in the USA and Japan respectively. We are also pleased to acknowledge the willing and professional cooperation of the publishers. On a personal note, we have enjoyed the project and in particular the sincere experience of making new friends and acquaintances worldwide. J. R. James P. S. Hall
List of contributors
N. G. Alexopoulos University of California USA A. R. Van de Capelle Katholieke Universiteit Leuven Belgium
J. S. Dahele Royal Military College of Science UK J. P. Daniel UniversitC de Rennes I France A. G. Derneryd Ericsson Radar Electronics Lab Sweden
G. Dubost UniversitC de Rennes I France
F. E. Gardiol Ecole Polytechnique FCdkrale de Lausanne Switzerland
K. C. Gupta University of Colorado USA P. S. Hall Royal Military College of Science UK R. C. Hall Ecole Polytechnique FCdCrale de Lausanne Switzerland
M. Haneishi Saitama University Japan
P. G. Frayne University of London UK
A. Henderson Royal Military College of Science UK
K. Fujimoto University of Tsukuba Japan
K. Hirasawa University of Tsukuba Japan
List of contributors xxiii
xxii List of contributors T. Hori Nippon Telegraph and Telephone Corporation Japan K. It0 Chiba University Japan
D. R. Jackson University of Houston USA J. R. James Royal Military College of Science UK P. B. Katehi University of Michigan USA A. H. Kishk University of Mississippi USA
K. F. Lee University of Toledo USA
E. Levine Weizmann Institute of Science Israel G. Moms Vega Cantley Instrument Co Ltd UK J. R. Mosig Ecole Polytechnique Fkdkrale de Lausanne Switzerland P. Newham Marconi Defence Systems UK
S. Nihimura University of Osaka Japan
R. P. Owens Thorn EM1 Electronics Ltd UK E. Penard Centre National D'Etudes de Elhmmunications France
D. M. Pozar University of Massachusetts USA D. H. Schaubert University of Massachusetts USA L. Shafai University of Manitoba Canada
E. V. SohteU Ericsson Radar Electronics Lab Sweden Y. Suzuki Toshiba Corporation Japan
C. Terret Centre National #Etudes de Elhmmunications France T. Teshirogi Radio Research Laboratories Ministry of Posts and Telecommunications Japan
G. R. Traut Rogers Corporation USA
J. E Zurcher Ecole Polytechnique Fkdkrale de Lausanne Switzerland
Chapter 1
Introduction J.R. James and P.S. Hall
1.1 Historical development and future prospects
The microstrip antenna is now an established type of antenna that is confidently prescribed by designers worldwide, particularly when low-profile radiators are demanded. The microstrip, or printed, antenna has now reached an age of maturity where many well tried techniques can be relied upon and there are few mysteries about its behaviour. The fact that you are now reading an historical review is interesting in itself because all this has happened in a relatively short time span of one or two decades; such is the rate of progress in contemporary antenna technology. To imply that the topic of microstrip antennas is now static would be grossly misleading because the opposite is true with the ever increasing output of research publications and intensifying industrial R and D. The quest now is for more and more innovative designs coupled with reliable manufacturing methods. The driving force is the thirst for lower-cost, less-weight, lowerprofile antennas for modern system requirements. Lower costs, however, rely on the ability of the designer to precisely control the manufacturing process, and this in turn usually demands that the prototype innovative structures can be adequately mathematically modelled and toleranced. It is in these latter respects that the challenge to the antenna expert originates, and the search for the more precise computer modelling of microstrip antennas is now the main preoccupation of designers and researchers alike, as is reflected in this handbook. The invention of the microstrip-antenna concept has been attributed to many sources and the earliest include Greig and Englemann [l] and Deschamp [2]. At that time the emission of unwanted radiation from the then new thin stripline circuits was well appreciated and subsequently the dimensions of the substrate and conducting strip were reduced to inhibit the radiation effects, thus creating 'microstrip'. Whether the advent of the transistor influenced the rapid development of these planar printed circuits is debatable and the main interest was likely to be the development of lower-cost microwave filters etc. Lewin [3] considered
2
Introduction
the nature of the radiation from stripline but there was apparently little or no interest in making use of the radiation loss. Apart from a few references [4, 5, 61 the antenna concept lay dormant until the early 1970s [7,8,9] when there was an immediate need for low-profile antennas on the emerging new generation of missiles. At this point in time, around 1970, the development of the microstrip-antenna concept started with earnest and the research publications, too numerous to itemise, started to flow. The period is perhaps most readily referenced by its workshops and major works. The most significant early workshop was held at Las Cruces, New Mexico, in 1979 [lo] and its proceedings were distilled into a major IEEE Transactions special edition [I I]. At that time two books were published by Bahl and Bhartia [I21 and James, Hall and Wood [I31 which remain in current use today. Another more specialised and innovative development was published as a research monograph by Dubost [14], and here the flat-plate antenna was approached from the standpoint of flat dipoles on subsiraies that generally only partially filled ihe available .;o!ume. The early 1980s were not only a focal point in publications but also a milestone in practical realism and ultimately manufacture. Substrate manufacturers tightened their specifications and offered wider ranges of products capable of working under extreme ambient conditions. Substrate costs were, however, to remain high. It was appreciated that analytical techniques for patch elements generally fell short of predicting the fine pattern detail of practical interest and the input-impedance characteristic to suficient accuracy. It was also appreciated that the connection of feeders to patch elements in a large array was fraught with problems and new approaches were necesary where the feeders and elements are regarded as a complete entity. More recently the term 'array architecture' has come into being as if to emphasise the importance of choice of array topology and the fact that feeders cannot necessarily be freely attached to printed elements, even if the latter are in themselves well optimised. Recent system demands are, as previously mentioned, a dominant factor in the development of printed antennas. Communication systems spanning wider bandwidths are continually emerging and techniques for increasing the bandwidth of microstrip antennas are a growth area. Controlling the polarisation properties of printed antennas is another area of activity arising largely out of the current awareness for making greater use of the polarisation properties of waves, particularly in radar. In defence applications, systems that have an electronic, as opposed to mechanical, beam-scanning facility are attracting much research effort and the concept of 'active-array architecture' is now with us where semiconductor packages and radiating elements are integrated into planar apertures. The cost of such an array is very high and the whole concept is state-of-the-art. This brings us to the present and how we see the immediate future of printed antennas. A seldom mentioned point is the fact that printed substrate technology is readily processed in University laboratories and continues to remain
Introduction
3
a rich source of complex electromagnetic problems; research publications will thus continue to abound, and in parallel with industrial development will most likely be dominated by two aspects: The search for mathematical models that will predict practical antennas more precisely and hence sharpen CAD techniques in manufacture. The creation of innovative antennas to match the demand for new systems. In this latter aspect it must be emphasised that a bulky conventional microwave antenna may well out-perform its thin conformal printed counterpart. Many new systems, however, particularly in aerospace, are only made feasible with the existence of the printed antenna concept, and here lies a major driving force where new systems arise solely from innovative antenna designs. As to the distant future, one can but extrapolate the present trends towards integrated electronically beam-scanned arrays. This leads to a vision of conformal antennas distributed over the surface of vehicles, aircraft, ships, missiles etc., thus replaciiig iiiary convcntional types of iadiatois, but the orgafiisatio:: and control of the radiation pattern co- and cross-polar characteristics is a complex control problem that cannot be solved by software alone and demands innovative physical concepts. Are we thus unconciously converging on the concept of distributed sensors, so common in the insect and animal world, where information is commonly gleaned in a variety of ways to best suit a particular situation? Taking the comparison a step forward, we would therefore expect the distributed conformal apertures to require a significant back-up from signalprocessing techniques, which amount to making use of temporal a priori information on signals and noise. Put this way these ideas are not so far-reaching because many of these adaptive concepts can be recognised in some of our new radar and communication systems, particularly for defence. In this light the printed-antenna concept would therefore appear as a gateway to system compatibility and optimal deployment of sensors, embracing the numerous facets of conformality, low costs, semiconductor integration, electronic radiation pattern control and an opportunity to exploit signal-processing techniques to the full using modern computing power. The prospects are indeed exciting and underline the importance of the microstrip-antenna concept, its continual evolution and impact on electronic systems design.
1.2 Fundamental issues and design challenges
A handbook of this type is intended as an all-embracing treatment that is both diverse and highly specialist. As such it is not possible to include comprehensive background information and we anticipate that readers wishing to recap on basic antenna theory, antenna mesurements and the rudiments of microstrip technology etc. will have no difficulty in obtaining relevant literature. It is our experience, however, that certain fundamental properties of printed antennas
4
lntroduction
lntroduction
have been central to their evolution and limitations, and therefore embody the design challenges of the future as follows. The microstrip antenna has many differences when compared with a conventional antenna. Most of these stem from the planar construction in which for a given substrate in the .uy plane there are only two degrees of freedom, allowing the very thin printed-conductor topology to take any shape within the confines of the .u and y co-ordinate directions. The first and most troublesome property is the issue of loss, principally in the thin conducting strip feeders connecting elements in large arrays. In some applications the loss in the radiating elements also creates dificulties. The radiating elements themselves have a restricted bandwidth arising from the intrinsic high-Q resonator action in the thin substrate. The generation of surface waves is equally important and cannot be avoided unless foam-type substrates are deployed allowing virtual air-spaced operation. The surface waves can corrupt radiation-pattern characteristics, particularly when low sidelobe and cross-polarisation levels are demanded. In many design specifications. problems can only be alleviated by compromising the manufacturing simplicity of the single coplanar printed assembly by employing overlaid element and feed concepts based on multilayer sandwich structures. Microstrip arrays generally require some sort of radome or weather shield, thus increasing the structure depth, but in some cases a degree of radiation-pattern enhancement is obtainable. Last but not least, mention must be made of the relatively high cost of substrates capable of providing the desired electrical and mechanical stability in operation. The substrate cost is often an inhibiting factor in what is otherwise a low-cost manufacturing process. These above issues are of a fundamental nature and we consider it important to highlight current understanding to identify aspects which may offer particular scope for future advancement. Before addressing this we list, for completion, some of the more commonly known properties of microstrip antennas in relation to both contemporary antenna-engineering and modern electronic-systems requirements. 1.2.1 Features of microstrip antenna technology The microstrip antenna is a newcomer to the world of antenna engineering and it is fitting to be reminded of features generally sought after when compiling an antenna specification. A typical checklist is given in Table 1.1 and it is appreciated that it is unlikely that all the performance factors are relevant or indeed critical in any given application. Equally demanding are operational and manufacturing considerations such as those listed in Table 1.2 and these are very dependent on the application in mind. The generation of thermal noise in a receiving antenna is insignificant for most conventional antennas and is clearly a new factor associated mainly with large lossy microstrip arrays. Likewise power-handling and material effects are particularly relevant for microstrip radiators, while the use of new materials such as carbon fibre necessitates careful evaluation of electrical loading, intermodulation effects etc.
5
Table 1.1 Antenna desi.qners' checklist of performance factors Input terminals matched to source feed Matching Main beam
Antenna gain and beamwidth properties
Sidelobes
Constrained to desired envelope
Polarisation
Cross-polar behaviour constrained to desired envelope
Circular polarisation
Constraints on ellipticity
Eficiency
Wastage of power in antenna structure
Aperture eficiency
Relates to illumination distribution, gain and pattern characteristics
Bandwidth
Frequency range over which all above parameters satisfy specification commonly based on input terminal impedance charactericstics
System demands
Size, weight, cost
The commonly upheld properties of microstrip antennas are listed in Table 1.3 and may be usefully compared with the general checklist of Tables 1.1 and 1.2 to ascertain the suitability of microstrip for various operational roles. However, it is important to appreciate that the interpretation of Table 1.3 is very dependent on the intended application. For instance, patch antennas on foam
Table 1.2
O~erationaland manufacturing considerations
Noise effects in receiving antennas Power handling in transmitting antennas Creation of hazards for personnel in near-field Robustness to lightning strikes Electrostatic charge effects in space applications Effects of wind, vibration, ice, snow, rain, hail Ambient conditions on temperature and humidity Exposure to sunlight Aerodynamic constraints, radomes and weather shields Metal corrosion and creep Mechanical and electrical stability of materials Mechanical and electrical tolerances in manufacture Sensitivitiy of design to manufacturing tolerances Generation of intermodulation effects in materials
6
introduction
Table 1.3 Some commonly acknowledged properties of microstrip antennas
Table 1 . 4 ~ Approximate performance trade-offs for a rectangular patch
Requirement
Advantages
Disadvantages
Thin profile
Low efficiency
Light weight
Small bandwidth
Simple to manufacture
Extraneous radiation from feeds, junctions and surface waves
Can be made conformal
Tolerance problems
Low cost
Require quality substrate and good temperature tolerance
Can be integrated with circuits
High-performance arrays require complex feed systems
Simp!e arrays created
Polarisation piiriiy difficuit ro achieve
readily
7
lntroduction
High radiation efficiency Low dielectric loss Low conductor loss Wide (impedance) bandwidth Low extraneous (surface wave) radiation Low cross polarisation Light weight Strong Low sensitivity to tolerances
Substrate height thick thin thick thick thin -
thin thick thick
Substrate relative nermittivitv low low
Patch width wide
-
-
low low
-
low low high low
wide
-
wide
Table 1.46 Approximate performance trade-offs for an array of circular patches
substrates may have a less desirable thick profile but good efficiency and reasonable bandwidth; in contrast a thin overlaid patch assembly with complex feed arrangements on a plastic substrate is likely to be more complicated to manufacture and not necessarily low cost. The modelling and subsequent engineering design of arrays for successful manufacture is often a factor that is originally overlooked and ultimately pushes up development costs. There are many other examples where the commonly quoted properties of Table 1.3 need qualifying, and recent experience from conferences and industrial contacts shows that academics have on occasions failed to convey a realistic impression to industry whereas industry itself has perhaps been too willing to implement the new technology without a sufficient design base that copes with the factors of Table 1.2. We have already stressed the need for advances in CAD techniques for manufacture and will specifically address this again later on, but now we return to the more general features of microstrip antennas such as the trade-offs listed in Table 1 . 4 for ~ rectangular patch antennas. These are very approximate and can be deduced from the basic patch equations [15]. An obvious deduction which is nevertheless significant is that the use of thick low-permittivity substrates, giving essentially air spacing, gives many benefits. When the behaviour of an array of patch elements (Table 1.4b) is considered, feeder radiation is seen to increase for thicker lower-permittivity substrates [16, 171. With this exception, any attempt to compact the antenna using a thin high-permittivity substrate will thus generally invoke all-round penalties in performance. These requirements are thus seen to be contrary to those for optimum operation of MICs, and this imposes restrictions on the integration of antennas and associated front-end circuitry. This perspective is valuable in emphasising the dominant characteris-
Requirement
Substrate height
Substrate relative permittivity
High efficiency Low feed radiation Wide (impedance) bandwith Low extraneous surfacewave radiation Low mutual coupling Low sensitivity to tolerances
thick thin thick thin
low high low low
thick thick
low low
tics of microstrip antennas and the fact that antenna volume-reduction benefits must manifest themselves as cost factors which in turn demand a high standard of engineering design to overcome. Finally we complete our discussion of general features with a list of applications in Table 1.5 that have attracted the use of printed-antenna technology. Almost without exception the employment of microstrip technology arises because of a system demand for thin low-profile radiators. Conventional antennas are clearly disadvantaged in such applications despite their often superior performance over microstrip antennas. In some cases the system has been created around the microstrip concept as mentioned earlier on. 1i2.2 Fundamental problems In our vision of the future we have singled out reliable CAD techniques in array manufacture and the system-led creation of innovative antennas as the major
8
Introduction
Introduction
'i
Table 1.5 Typical applications for printed-antenna technology
Table 1.7 Some generic types of bandwidth-extension techniques Increasing antenna volume by incorporating parasitic elements, stacked substrates, use of foam dielectrics
Aircrafr antennas
Communication .and navigation Altimeters Blind-landing systems
Missiles and telen?etr.y
Stick-on sensors Proximity fuzes Millimetre devices
Creation of multiple resonances in input response by addition of external passive networks and or internal resonant structures
Missile guidance
Seeker monopulse arrays Integral radome arrays
Incorporation of dissipative loading by adding lossy material or resistors
Adaptive arrays
Multi-target acquisition Semiconductor integrated array
Varactor and PIN dlode control grves a wlder effectrve bandwrdth and lrst
Batilefield communications and surveillilnce
Flush-mounted on vehicles
S ATCOMS
Domestic DBS receiver Vehicle-based antenna Switched-beam arrays
$1
I
Mobile radio
Pagers and hand telephones Manpack systems
Reflector feeds
Beam switching
Remote Sensing
Large lightweight apertures
Biomedical
Applicators in microwave cancer therapy
Covert antennas
Intruder alarms Personal communication
9
IS
not Included In the above
thrusts. The problem areas will however centre around the fundamental issues listed in Table 1.6. These issues are un~versallyacknowledged and we will review some of them as follows to emphasise certain aspects which in our opinion are worthy of clarification or perhaps need various points amplified, in particular to bridge the gap between academic research and industrial implementation. 1.2.2.1 Bandwidth extension: The search for new microstrip configurations with wider bandwith has been a dominant feature of the research literature and much effort continues to be expended. No other type of antenna has been so exhaustively treated as regards its bandwidth properties, yet the literature often portrays an incomplete picture by not defining what is meant by bandwidth [18]. The many factors involved are listed in Table 1.7. A common and generally realistic assumption is that the input-impedance characteristic of a resonant patch antenna behaves as a simple tuned circuit, in which case the 3 dB bandwidth B is approximately (100/Q) percent, where Q is the Q-factor of the equivalent tuned circuit. If the antenna is matched at the resonant frequency of the tuned circuit, then away from resonance the input impedance will be mismatched, creating a VSWR(> 1) of S, where
Table 1.6 Fundamental issues that will continue to be addressed Bandwidth extension techniques Control of radiation patterns involving sidelobes, beamshaping, cross-polarisation, circular polarisation, surface-wave and ground-plane effects Reducing loss and increasing radiation efficiency Optimal feeder systems (array architecture) Improved lower-cost substrates and radomes Tolerance control and operational factors
1
1
Use of a thicker and/or lower-permittivity substrate reduces Q and hence increases B. An examination of numerous examples shows that, irrespective of whether the permittivity or substrate thickness is changed, the main effect (Table 1.7) is that B increases with the volume of the antenna, i.e. the volume of substrate between the patch and ground plane. Some examples are shown in Fig. 1.1, which also includes curves of radiation efficiency with and without allowance for the power lost to surface waves. The first point of clarification is to note that there are numerous ways of increasing the volume of a patch element by employment of thicker substrate or stacking several substrates [19] or adding
10
Introduction
parasitic elements 1201, but they all belong to the same generic type of bandwidth extension technique. A second generic technique (Table 1.7) consists of introducing multiple
lntroduction
Table 1.8 Factors constraining the bandwidth of microstrip antenna elements and arrays
Element
Array
-
Fig. 1.I
Patch-antenna efficiency q and bandwidth B versus resonator volume for differen! permittivities (Reproduced from Fig. 2 of Reference 78) -x-x-x- is the radiation efficiency corrected for surface-wave action ( E , = 2 . 0 )
77
Input-impedance characteristic
Surface waves
Side-lobe level
Element mutual coupling
Cross-polarisation level
Feeder radiation
Circular polarisation (axial ratio)
Corporate feed and mismatch
Pattern shape (E- and H-plane symmetry)
Scanning loss
Element gain Efficiency Feeder radition
Fig. 1.2 Patch bandwidth extension using an external passive network a Antenna without network b Effect of matching network.
resonances in the input characteristic, as illustrated in Fig. 1.2 showing the inclusion of a passive network in the input port; the presence of the network invokes additional dissipative losses. The same bandwidth extension effects can be brought about by introducing multiple resonances within the antenna itself [I 81, which usually involves an increase in antenna thickness and hence volume. The important point to note is that a multiple resonance input response does not
obey the simple relationship of eqn. 1.1, and it is difficult to relate the various multiple resonance bandwidth extension techniques that are reported in the literature. Different researchers use different VSWR or insertion-loss criteria to define the bandwidth and the insertion-loss curve shapes are likewise very different. A third much less common technique (Table 1.7) is simply to add lossy material to the microstrip element. This technique would at first sight appear to lead to unacceptable loss, but the manufacturing simplicity has definite appeal and can outweight the other disadvantages. We summarise the above three generic bandwidth extension techniques in Table 1.7, but emphasise that from a system designers' standpoint the definition of bandwidth based on the input-impedance characteristic is just one of many factors listed in Table 1.8 that constrain the bandwidth of an antenna element or array. For instance, the designer may decide to use a rectangular patch accompanied by several parasitic elements to achieve an impedance bandwidth specification, but then finds that the configuration fails to achieve adequate cross-polarisation levels or perhaps E- and H-plane symmetry over the band. In another instance it may be straightforward to meet all the bandwidth criteria for a selected element only to find that, when the latter is connected in an array, the bandwidth specification is not achieved because of mutual coupling or perhaps feeder-line mismatches. Research workers seldom have the opportunity to address the totality of problems in a system design, and it is a natural consequence that they focus on the optimisation of a given property in isolation from other requirements. In contrast, the industrial designer has to optimise many parameters at the same time and bandwidth is a topic area where the gulf
72
Introduction
between isolated research and system design is at its widest. The challenge facing researchers and industrial designers alike is to establish reliable designs for elements and arrays that achieve bandwidth extension under a wide selection of contraints as listed in Table 1.8. It is also highly desirable that the performance of one type of element can be quantified in relation to the performance of any other type of new element; the fact that there are in reality few generic types of bandwidth-extension techniques (Table 1.7) [18] is an important guideline. 1.2.2.2 Pattern control: There is now ample evidence to show that the radiation-pattern control of printed radiators is an order more difficult than with reflector and aperture antennas. Even for modest performance levels of sidelobes and cross-polarisation the printed-conductor topology presents many variables to optimise for a given substrate thickness and permittivity. For sidelobe and cross-polarisation levels of about -20 dB extraneous radiation due to surface waves, feeder radiation and ground-plane edge effects is not insignificant and computer models lose their precision. Surface-wave effects decrease for lower-permittivity substrates but feeder radiation is then more prominent [17]. There is evidence in the literature that much lower levels can be achieved, but generally these are pattern cuts in certain preferred planes or pertain to arrays fitted with lossy material or other special effects. A consensus of opinion is that printed antennas are at present more fitted for applications with less demanding pattern specifications. The challenge for the future thus remains the lowering of the levels of extraneous radiation in printed arrays and improved computer modelling of the overall patterns. Some special mention needs to be made of circularly polarised elements and arrays because considerable progress has been made in this respect and it is likely to be an area for continued exploitation. It is well known that in principle a linearly polarised antenna can be converted to perfect circular polarisation by superimposing upon its radiation characteristics, those of its dual radiator having transposed E- and H-field sources. For instance, a wire dipole (electric source) would need to be combined with a wire loop (magnetic source), but in reality it is physically impossible to construct or feed such an arrangement precisely and compromises are made such as the employment of crossed-wire dipoles which yields circular polarisation in a limited region of the hemisphere and over restricted bandwidth. These and other techniques [21] are well established for conventional antennas, and the point we make here is that they are more difficult to translate to printed elements in view of the constrained planar geometry and feeder requirements. It is therefore inspiring to note the innovation that has been brought about whereby circular-polarisation characteristics have been enhanced by sequential rotation of elements [22], incorporation of finite substrate effects [23], novel feeder arrangements [24] and many more. Creating improved low-cost radiators that provide circular polarisation over wider bandwidths and larger sectors of the radiation-pattern hemisphere is a goal towards which much international effort will continue to be directed.
Introduction
73
1.2.2.3 Eficiency and feeder architecture: The outstanding advantage of microstrip - the simplicity of the printed conductor - is also the source of one of its major disadvantages, which is the relatively high transmission-line loss. The nature of the loss is well understood and arises from the high current density at the strip edge and substrate losses. It is a fact that no worthwhile reductions in transmission loss have been achieved since the inception of microstrip, and the simplicity of the structure offers little scope for innovation in this respect. For patch elements the loss is less significant, and with an appropriate low-loss substrate and strongly radiating patch, antenna efficiencies of 95% are achievable. A conventional wire dipole antenna would have a better efficiency than the patch but the order of loss of the latter is usually very small from a systems standpoint. The main problem arises in large arrays having microstrip or other forms of printed feeder lines because feeder losses limit the gain of the aperture; in fact, beyond a certain critical aperture size the gain will actually reduce. The beamwidth will, or course, also continue to narrow. The critical size is dependent on the feeder topology, substrate etc. and a maximum gain around 35 dB is not uncommon. Fig. 1.3 shows typical computed and measured results efficiency, % 100 50 j 0 /
I
gain
(dB)
u
O1
10 100 array size Dlho
Fig. 1.3 Patch-array gain 0 Calculated [17]; measured. with feed impedance + 100 a, x 120
A 200
[17] and indicates that at maximum gain an efficiency of about 10% can be expected. Travelling-wave antennas show some economy of feeder loss over corporate feeds but the frequency scanning loss for large travelling-wave apertures is then the dominant limitation. Once again the simplicity of a printed feeder system gives little scope for major design changes, and more recently hybrid feeder systems are being considered incorporating more conventional
14
lntroduction
Introduction
cables and waveguides for the longer feeder runs. We have already emphasised in Section 1.2.2.2 the limitations on pattern control enforced by extraneous feeder radiation and any breakthrough in feeder architecture will need to address the latter. However, for some applications the radiation-pattern specifications are less critical than loss of gain and any improvements in feeder loss would be a significant advance. The future challenge is to discover new feeder architectures giving less loss, and if possible less extraneous radiation, with the knowledge that the already simplistic printed configurations offer little scope for fundamental physical change. One possible avenue for advancement lies in the integrated antenna concept whereby transistors are embedded in the feed structure to facilitate beam scanning. This may circumvent the loss problem but exacerbate extraneous radiation effects, and of course escalate costs. 1.2.2.4 Substrate technology: Substrate technology and marketing has been, and will continue to be, a key factor in the acceptance by industry of the printed-antenna concept. Earlier microstrip antennas used plastic substrates or in some cases alumina, but in recent, years the use of lower-permittivity substrates is common. The substrate role thus appears to be mechanical, enabling the printed conductor to be suspended at a uniform height above the ground plane. The use of lower permittivities also reduces surface-wave effects but feeder radiation is then more difficult to suppress. Antenna designers thus require a wide range of substrates available having stable electrical and mechanical properties over the various ambient operating conditions. The major problem has been, and is likely to be in the foreseeable future, a matter of substrate cost because the world demand is relatively small compared with that of some other plastic products. This has encourage some companies to manufacture their own substrates while in other cases the substrate costs have made some large-array projects non-viable, and printed technology is then seen to be costly in contradiction to the commonly upheld properties of Table 1.3. It is also noted that many microstrip antennas will require some sort of weather shield or perhaps a radome, which again is a cost factor. Substrate technology thus offers a challenge to material manufacturers to create lower-cost high-performance stable substrates. Clearly this is a somewhat circular problem which appears to demand a higher-volume market to initiate an immediate advance; conversely such an advance would open up a larger-volume market. Such a situation is not uncommon, and with the considerable manufacturing interest in substrates that is building up (Table 1.9) antenna designers should be optimisitic about the way substrate technology is likely to develop in the next few years. 1.2.2.5 Manufacture and computer-aided design (CAD): The microstrip antenna has been widely mathematically modelled for many years and yet from the manufacturers' standpoint there is a dearth of ready-to-use design equations, and hence reliable CAD packages. This situation has arisen partly owing to the mathematical difficulties associated with practical geometries and partly
Table 1.9 E,
75
Representative substrate list
Material Aeroweb (honeycomb)
Supplier Ciba Geigy, Bonded Structures Div., Duxford, Cambridge, CB2 4QD
Eccofoam PP-4 (flexible low-loss plastic foam sheet)
Emerson & Cumming Inc, Canton, Massachusetts, USA (Colville Road, Acton, London. W3 8BU, UK)
Thermoset microwave foam material
Rogers Corp., Bo 700, Chandler, AZ 85224, USA. (Mektron Circuit Systems Ltd., 119 Kingston Road, Leatherhead, Surrey, UK)
RT Duroid 5880 (microfiber Teflon glass laminate)
Rogers Corp.
Polyguide 165 (polyolefin)
Electronized Chemical Corp., Burlington, MA 01803, USA
Fluorglas 60011 (PTFE impregnated glass cloth)
Atlantic Laminates, Oak Materials Group, 174 N. Main St., Franklin, M H 0323, USA. (Walmore Defence Components, Laser House, 1321140 Goswell Road, London, EClV 7LE)
Rexolite 200 (cross-linked styrene copolymer)
Atlantic Laminates
Schaefer Dielectric Material, PT (polystyrene with titania filler)
Marconi Electronic Devices Ltd., Radford Crescent, Billericay, Essex, CM12 ODN, U K
Kapton film (copper clad)
Dupont (Fortin Laminating Ltd., Unit 3, Brookfield Industrial Estate, Glossop, Derbyshire, UK)
Quartz (fuzed silica)
A & D Lee Co. Ltd., Unit 19, Marlissa Drive, Midland Oak Trading Estate, Lythalls Lane, Coventry, U K
76 Introduction
lntroduction
6.0
RT Duroid 6006 (ceramic-loaded PTFE)
Rogers Corp.,
9.9
Alumina
Omni Spectra Inc, 24600 Hallwood Ct. Farmington, Michigan, 48024, USA (Omni Spectra, 50 Milford Road, Reading, Berks, RGI 8LJ, UK)
10.2
RT Duroid 6010 (ceramic-loaded PTFE)
Rogers Corp.
II
Sapphire
Tyco Saphikin (A & D Lee Co Ltd., Unit 19, Marlissa Drive, Midland Oak Trading Estate, Lythalls Lane, Coventry, UK)
The brief details in the Table are intended to give readers an insight into the range and types of materials available. Mention of any particular product does not imply our endorsement. Likewise exclusion of a material does not imply adverse comment and we presume that some excellent products have been omitted.
17
making and convergence under the designers control. Such an approach has many merits since tolerance and operational effects can be added in gradually to create a reliable manufacturing tool. A disadvantage of the approach is that it must be re-established together with empirical data when a change is made in the design, and furthermore the experience is confined to the particular manufacturer. As we have mentioned already, some manufacturers have been surprised by the need to underpin printed-array manufacture with positive modelling in view of the commonly acknowledge property (Table 1.3) that the antennas are 'simple and low cost'. There is ample evidence, however, showing that the simplicity and low-cost properties are realisable once modelling has been accomplished, and the latter is a one-off development cost and perhaps no more than a few months of a printed-antenna specialist's time. The challenge for the immediate future thus lies in the evolution of reliable interactive CAD packages for printed-array manufacture that are capable of wider usage and of gaining universal acceptance. In the long term one might expect some advances in the rigorous analysis of microstrip-antenna geometries embodying practical features which in turn will translate into more precise manufacturing techniques.
1.3 The handboook and advances presented
to the many varieties of patch antennas and the fact that designs must conform to the vagaries of system requirements. Horn, wire and other conventional metal antennas can be modelled to a high accuracy with well established formulas and this is also true of electrically larger apertures such as the reflector antenna. In contrast to these homogeneous electromagnetic systems the modelling complexity arises largely from the presence of a finite-sized dielectric slab that gives rise to the factors noted in Table 1.8 and elsewhere. This complexity is compounded when the number of elements in an array increases and when the fine detail of patch feeding or complex feed networks is required. Mutual coupling, surfacewave effects and feed radiation manifest themselves as relatively small effects in a small array but they quickly take charge of sidelobe and cross-polarisation levels in the region of - 20 dB as the number of elements increase. When viewed in the light of increasingly tight requirements, modelling accuracy is seen to be the key parameter to successful implementation. As an example, the use of inaccurate CAD may well be more expensive for the manufacturer than design by hand in the long run. Likewise the range of applicability of the package needs to be understood if inherently good models are not to be brought to bear on the wrong problems. However, despite the unlikely possiblity of extending presentday numerical analysis to arrays of patches in the immediate future, the problem is not unsurmountable provided that a close liaison exists between the CAD and antenna designer. Indeed there is a trend for manufacturers to evolve their own CAD packages based on a mixture of simple closed-form expressions for the radiation mechanism backed up by empirical results for the particular array in question. Some degree of iteration is commonly included but with the decision
Many, if not most, of the international community of printed-antenna specialists have contributed to this handbook, which necessarily portrays the state-ofthe-art at the time of going to press. The contributions reflect the authors' specialisation which in some cases is fairly wide ranging. This has meant that it has not always been possible for the editors to maintain a full thematic flow throughout the handbook. However, the chapters have been generally ordered in the following way element analysis and design array aspects microstrip technology applications To assist the reader we have already listed in Table 1.5 the general application areas for microstrip antennas. In Table 1.10 the content of the Handbook is resolved in more detail to identify with the various topic areas within the subject of printed antennas. It can be seen that patch theory and design still concerns many researchers, with current emphasis being on basic characterisation and innovation for controlling in particular bandwidth and polarisation purity. The same applies to arrays, with additional topics such as mutual coupling in scanning arrays gaining more attention. Technology is addressed by several authors with contributions on substrates, connectors, radomes and computeraided design and manufacturing. However, little on environmental factors has
78
Introduction
I
.
Introduction
"I.
79
I
20
Introduction
1
Introduction
21
Table 1.11 Summary o f handbook chapters Element analysis and design
I
2 Shafai and Kishk: Analysis of circular microstrip antennas: An analysis is presented based on the equivalence principle involving both conducting and dielectric boundaries. This allows substrate edges to be accounted for. The method is used to optimise a circular disc on a finite-sized circular ground plane for low cross-polarisation and also a wrap around antenna. 3 Lee and Dahele: Characterisation of microstrip patch antennas and some methods of improving frequency agility and bandwidth: The basic characteristics of patches are reviewed here and conclusions on comparative performance are made. Bandwidth is identified as being- crucial and methods of overcoming the limitations by making the patches frequency agile are presented.
I
I I
4 Haneishi and Suzuki: Circular oolarisation and bandwidth: The methods of obtaining circular polarisation from patches are described in this chapler together with design techniques. Again, as in the previous chapter, bandidth-extension methods are noted and, in particular, element pairing which is described more fully in Chapter 13. 5 Katehi, Jackson and Alexopoulos: Microstrip dipoles: The analysis and design of narrow-strip microstrip dipoles is presented here. For electromagnetically coupled dipoles an improvement in feed radiation is noted together with methods for offsetting mutual coupling in arrays. Bandwidth and superstrate effects are also discussed. 6 Schaubert: Multilayer and parasitic confgurations: This chapter exhaustively reviews multilayer configurations and emphasises advances for wide bandwidth, multiple frequency and dual polarisation. Such structures increase the antenna thickness, and, as a contrast, antennas with coplanar parasitics are also described.
1
7 Dubost: Widebandflat dipole and short-circuit microstrip patch elements and arrays: Elements and arrays developed from the flat dipole concept are described in addition to short-circuited quarter-wavelength patch elements and arrays. The dipole work can perhaps be viewed as a parallel development with microstrip and has produced antennas whose performance is highly competitive. 8 Mosig, Hall and Gardiol: Numerical analysis of microstrip patch antennas: An integral-equation formulation is solved by the moments method to give solutions for arbitrary shaped wide patches, including input impedance, radiation patterns and surface-wave effects.
9 Gupta: Multiport network approach for modelling and analysis of microstrip patch antennas and arrays: Here patches possessing separable geometries in whole or part are analysed using a planar model involving impedance
22
Introduction
Table 1.11 (Cont) matrices. Radiation loading is included by means of edge admittances. The author presents several illustrative examples and discusses the extension of the work to CAD methods. Further progress in the application of analysis such as this and others in this handbook is expected in the near future.
10 Van de Cupelle: Transmission-line model for rectangular microstrip antennas: The application of the transmission-line model to patch analysis is described. Various improvements to the basic model are noted, such as connections for mutual coupling between the radiating edges, that enable good agreement with measurements to be obtained. However, the attraction here is the method's simplicity and easy adaption to CAD, an example of which is given.
Introduction
23
15 Traut: Advances in substrate technology: Microwave substrates are one of the important 'enabling technologies' in printed antennas. Advances in this area are presented which given the reader some insight into manufacturing and environmental factors that affect the antenna's progress from conception to use. Progress here is determined to some extent by the volume of production, and it is hoped that as the applications proliferate substrate technology will continue to imvrove.
Array Aspects
16 Levine: Special measurement techniques for printed antennas: Measurement characterisation of connectors, lines and discontinuities, together with analysis, form an important foundation to good antenna design. Such measurement characteristics are described here with particular emphasis on accuracy and applicability to design. Near-field probing can also form a useful diagnostic tool, and examples are given together with a novel method for efficiency measurement.
I1 Daniel, Penard and Terret: Design and technology of low-cost printed antennas: The design of elements and arrays with the emphasis on low-cost technology is important for successful application in many areas. Design and construction including array sythesis is described here. In addition, some technology and substrate innovations are included which can be compared to materials detailed in Chapter 15.
17 Zurcher and Gardiol: CAD of microstrip and triplate circuits: As noted above, computer-aided design is likely to be an increasingly important factor in printed antenna design. This Chapter is dedicated to CAD of microstrip and triplate systems and highlights some of the important aspects such as characterisation of components, materials, manufacturing, analysis and synthesis.
12 Pozar: Analysis and design considerations for printed phased-array antennas: The effects of scanning of printed phased arrays are derived using moments methods for both infinite and finite arrays of patches. Blind spots due to surface-wave effects are noted to be particularly severe where highdielectric-constant substrates are used for millimetric integrated arrays. Some alternative integration technologies are discussed that mitigate these and other problems.
Applications
18 Derneryd: Resonant microstrip antenna elements and arrays for aerospace applications: Four examples of resonant microstrip antennas and arrays are presented here for various requirements including dual frequency, monopulse radiation pattern and dual polarisation. Important design freatures are noted together with some environmental aspects.
13 Ito, Teshirogi and Nishimura: Circularly-polarised-array antennas; Various types of circularly polarised arrays are reviewed together with the possible feeding arrangements. Some practical problems are considered including pattern control and bandwidth. Some examples of practical arrays are also highlighted.
19 Fujimoto, Hori, Nishimura and Hirasawa: Applications in mobile and satellite systems: Mobile and satellite systems are an important area for lowcost low-profile printed antennas. Various examples of such antennas are given in this Chapter. It is likely that the explosive increase in information systems in the future will accelerate the development of antennas to meet these diverse needs.
Microstrip Technology
20 Newham and Morris: Conical conformal microstrip tracking antenna: A conical conformal microstrip tracking antenna is a severe requirement that involves difficult manufacturing and fundamental electromagnetic problems to be solved. Here the authors have described progress to date in this very challenging area that is likely to require much more research and innovation for some time to come.
14 Owens: Microstrip antenna feeds: Printed antenna feeds are sometimes given insufficientconsideration at the outset of an array design, thus degrading the array performance. Feed design is extensively reviewed here and comparative examples drawn from the literature are used to give engineering direction. Although considerable work has been done, further progress is expected as the importance of good feed design for printed antennas is more widely appreciated.
21 Frayne: Microstripfield diagnostics: The near-field probing technique noted in Chapter 16 is described here in some detail together with extensive results both for microstrip patches and patch arrays with feed networks.
24
22 SoizteN: Microstrip an~ennason a cylitirluiccrl .surfkce: Patch arrays on cylindrical bodies is likely to be an important future application of conformal concepts. Modifications to the basic patch-design expressions due to the curvature are presented here together with design and performance of a representative cylindrical array. 23 HUN, Henderson and Junzes: E.uretzsions and variations to the microstriptrntenncr concept: There are a wide variety of specialist applications that spawn innovative concepts in the use of microstrip antennas. This final Chapter highlights some of these, including applications where microstrip is combined with other radiating or transmission structures to form hybrid antennas. Operation over multi-octave bandwidths or at millimetric frequencies are also design challenges that are covered, together with applications involving very high and very low dielectric-constant materials. Such specialised requirements are likely to continue to lead antenna designers to further innovative progress in the microstrip field.
Relevant Chapter numbers are given together with References in brackets.
(a) Patches The generic microstrip patch is an area of metallisation supported above a ground plane and fed against the ground at an appropriate point or
Principal shapes The freedom in the xy plane gives rise to the possibility of a multiplicity of possible shapes. Only a few have been seriously examined such as the rectangular or square patch and disc [25], ellipse [26], equilateral[27],or rightangled isosceles [28] triangle, annular ring [29] and pentagon [30].
appeared in the literature and Chapter 15 contains one of the few appraisals of this area of printed technology. A diverse range of applications is also noted that mirror the list given in Table 1.5. In terms-of printed-antenna techniques microstrip is the predominant one discussed in the handbook although some contributions on printed dipoles and ground-plane slots are presented. Although both these elements are likely to have similar electromagnetic properties to microstrip radiators, the increased complexity involved in manufacture seems to have been the overriding factor that has influenced designers away from them. This is particularly true for slot antennas in triplate stripline where shorting pins or holes are needed to prevent parallel-plate mode excitation. It is thus clear that the conceptual simplicity of microstrip remains one of its most attractive features. As a final aid to the reader Table 1.1 1 highlights the advances described in each chapter with particular reference to the fundmental issues and challenges identified in Section 1.2.
1.4 Glossary of printed antenna types The various forms of printed elements and arrays are very numerous and it is useful for designers to have a check list at hand. With this in mind we have composed the glossary giving an outline sketch, some key references and a few supporting comments and an indication of which chapter in the handbook deals with each type. Although the glossary is by no means exhaustive, the 70 entries on radiating elements and the 37 on arrays reflect the wide range of flexibility and scope for innovation that microstrip offers.
25
Introduction
Introduction
2, 3, 4, 8,
9, 10, 11, 18, 21, 22
Characteristics of these principal shapes are generally similar [Chapter 31 with fundamental modes having broadside beam. Bandwidth and physical area vary between shapes. The annular ring gives increased bandwidth, gain and sidelobe levels for higher-order modes but becomes physically large.
a
l3ll
Patches can be short-circuited along a null voltage plane to form the shorted patch or hybrid microstrip antenna [31]. Impedance and resonant frequency remain the same as for a full-size patch but for low dielectric constant the bandwidth is increased.
7, 1 I , 20
26
Introduction
Introduction
Variants on principal shapes
Circularly polarised patches Single-point feeding gives circular polarisation with constructional simplicity. The feed excites two orthogonal degenerate modes [35]. The 90" excitation phase difference is obtained by detuning the two modes by a variety of geometrical distortions giving the following types: rectangular patch [36] notched square patch [37] slotted square patch [38] notched disc [39] truncated corner square [40] ellipse [26] penragon j3Fj
Single point feeds
Circular sector and annular-ring-sector [32] patches have been analysed using the cavity model. Expressions for impedance and resonant frequency, but no indication of likely bandwidths or pattern performance are given.
[331
Star microstrip patches have been theoretically investigated [33] as a radiator of higher-order modes with good symmetry. Rectangular-ring and H-shaped patches have been investigated by Palanisamy & Garg [34] and found to give performance similar to principle shapes.
Other possible shapes
27
4, 9
The input VSWR bandwidth is wider than that of an isolated mode but the axial-ratio bandwidth is much narrower with axial ratio rising to about 6 dB at the edge of the 2: 1 VSWR bandwidth. The above technique is shown for the fundamental mode. Use of internal slots in discs for higherorder modes has also been shown [41].
9
Many uninvestigated variants have been suggested [28]. They are expected to give performance similar to the principal shapes. A selection is given here. Multiple-point feed
135, 421
Circular polarisation can be produced using multiple-point feeding by: . Two offset rectangular patches [35], which is also used in arrays [42]. Here the offset phase centre leads to a more rapid degradation of axial ratio off boresight than the following
4, 1 I , 13, 18, 19, 21
Introduction
Introduction
28
- - - - - - -. 90' couplor -. -
-- -
-.
Single parches fed at two points [43, 44, 251
-,
[43, 44, 251
m
[ o...
4
5
1
[521
ZBZZZ
1531
Parasitics
110.
Short-circuit patches arranged to produce a crossed slot [46] which
270'
Patch shaping such as steps [521 or conical depression [53] also yields wide bandwidths
Shaped patches
Four-point feeding [45], which suppresses cross-polarisation generated by higher-order modes within the patch and this improves axial ratio
29
Multiple stacked patches with the upper patches acting as electromagnetically coupled parasitics can be designed for extended bandwidths. Examples using coaxial-probe feeding [54] and microstrip-line feeding [55] have been made with the latter designed for an alumina (E, = 10) base substrate.
3
Parasitics can also be mounted coplanar as thin resonators [56], as additional patches either gap or line coupled to square [57] or triangular patches [58]. Alternatively many thin parasitics [59] can be gap coupled to form a wideband patch. Some of these configurations exhibit variations in the radiation pattern with frequency.
3
1551 A patch in a corrugated ground plane [47], which also improves low-angle performance
\ \
.:-- -- -- _-- ----
/
0 0 0 n
I
'--_ - ,' _ [47] -
[561
Wideband patches Thick patches
Use of low-dielectric-constant (E, = 1.0), thick (h/& > 0.1) substrate results in bandwidths > 10% [48]. Alternatively patches on thinner substrates can be broadbanded (up to 30%) by e.uterna1 matching circuits [49]. Use of thick substrates leads to impedance-matching problems that can be overcome by use of matching gaps in the probe [SO] or patch [51].
2, 4, 6, 7, 11, 18
Short-circuited quarter-wavelength parasitic~have also been applied to square [60] or circular [61] patches. A band-width increase of 2 is obtained in the square-patch case. In the circular case cross-polarisation is substantially reduced.
30
Introduction
Introduction
Other wdeband forms
The m~crostripspiral [62] gives about 40% bandwidth with limited efficiency. The spiral 1s limited to less than one turn, as further turns give rise to radiation-pattern degradation.
p
p
* .
xledband patch notch
,
Dual-frequency patches Multiple layers
Multiple-layer patches having two- [I91 and three- [63] frequency operation use direct probe connection to the top patch and gap coupling to the lower ones. Direct connections to both patches in two-frequency designs [64, 651 have also been made. Tuning of the two frequencies is also possible by an adjustable-height upper patch using discs [66] and annular rings [67].
[731
2, 3, 4, 5, 6, 18,
[741 Other patch variants
'm. [761
Single-layer two-frequency patches with orthogonal polarisations [68] using two feed points. Use of shorting pins [69, 701 allows operation with the same polarisation. The use of tabs in rectangular [71] or circular [72] patches also permits dual-frequency operation.
3, 4, 6
1771
I /681
[69, 701
High-frequency patches have been located within low-frequency patches to give orthogonal polarisation [73] or same circular polarisation [74] using frequency-sensitive coupling stubs
19
751
Single layers
31
z
In the coplanar stripline patch [75] the input line is fed against the upper ground plane. The overall performance is similar to conventional patches with reduced cross-polarisation and mutual coupling. The electromagnetically coupled patch [76] allows reduction in feed radiation bv locating it closer to the -ground plane than the patch. The effect of dielectric covers (superstrates) is noted [77], where, in addition to element protection, enhanced gain can be obtained.
-
The use of superimposed dielectric spheres [78] on patches result in improved gain and reduced crosspolarisation.
patch resonator
23
32
Introduction
Introduction
The groundplane dot [79] fed by a microstrip line can be used as a bidirectional element or as a unidirectional one by the addition of a reflec tor.
ground plane
11n0
Outputs\
33
comparator ,ekments
grwnd plane
[791 Folded dipoles can be operated close to a ground plane by means of appropriate matching circuits [14]. Many variants are possible giving wide bandwidth and low cross-polarisation. Construction is more complex than the basic microstrip patch although, owing to the use of rr atching circuits, wider impedance bandwidths may be possible.
maon r~tlecto,
\
SUppMt
Microstrip patches and arrays can be combined with the reflector concept. Their use as feeds [80, 811 allows integration with microwave integrated circuits, but with lower bandwidth and cross-polarisation compared to conventional feeds.
substrate
Paiches have aiso been used in the reject array configuration [82] where beam scanning is achieved by varying the phase of the reflected wave by pin diodes. A single element is shown here. Phase shift in the circularly polarised system is obtained by varying the angle of the short-circuit plane.
2, 23 Conformal antennas
4°F ground plane
The flexibility of the microstrip concept allows use in conformal applications. Examples are: - Spiral slot [83]
2, 7, 19, 20, 22
34
Introduction
Introduction - Wrap-around antenna [84]: a single wide-quarter wavelength patch wrapped around a cylindrical body
(b) Arrays
Feed structures
- Cylindrical 185, 861 or spherical [87] patch arrays
Putch connection
Patch elements for arrays can be connected by through the substrate pin connections (through hole plating or via holes), to one or more layers [89] of feed circuits located behind the ground plane in microstrip or triplate. Mechanical simplification can be achieved by aperture coupling to a parallel [90] or a perpendicular [91] microstripline. Feeding can also be from a coplanar microstrip circuit [92] which involves pattern perturbation due to feed radiation. This can be reduced by electromagnetic coupling to overlaid patches [76]. Connector effects give rise to fundamental limits to array action [93] due to radiation from the discontinuity in the guiding structure. Pin connections to patches give rise to higher-order modes [94] that perturb the radiation pattern and increase cross-polarisation levels.
Feed circuits
Feed structures for many elements 4, 5, take various forms. Corporate feeds 7, I I, [95, 961 for either one- or 12, 13, two-dimensional arrays give wideband 14, 18, action, whilst series-fed arrays give - 19, 20, 22 narrow bandwidth with broadside beam when resonant or wide bandwidth with a scanning beam when travelling wave.
wide patch
P I corporate feed kcd
35
pomni
5, 6, I I, 12, 14, 16, 18, 19, 20, 22
--
Active patch
Active devices can be integrated into patches. An example with a Gunn diode [88] demonstrated the principle, but had high cross-polarisation and low patch efficiency.
LJ LJ LJ LJ [951
'4+"4-,-4'
36
lntroduction
Introduction
37
Dual polarisarion is obtained by dual series interconnection of patches [99]. Chain type structures for linear polarisation having rectangular [I001 and triangular or honeycomb shapes [loll. Both the series array of patches and chain arrays are resonant and thus have a narrow bandwidth.
Wideband squintless operation is obtained with the series-compensated feed [97] One-dimensional arrays: linear polarisation
feed oolnt
The cross-fed arrangement [98] gives narrowband action with a tapered distribution and hence low sidelobes with equal-width feed lines
Early microstrip antennas were series fed one-dimensional arrays of Gutton and Bassinot [4] and Dumanchin [I021 in 1955 and 1959, respectively. Since then many forms of series-fed array have been developed. Arrays can be formed using resonant elements or meandering microstrip lines, in which the radiation is determined by radius of curvature or line width. Examples of arrays using resonant elements are:
Sequentially rotated feeding [22] gives wide-bandwidth axial ratio and input VSWR for circularly polarised patch arrays
comb line [I031 parasitically coupled patch array [ 1041 series-connected patches [I051
-
-
Array structures Two-dimensional arrays
[921
Microstrip patch arrays can be fed by any of the feed structures noted above. A typical linearly polarised parch array [92] fed by a coplanar microstrip corporate feed is shown here.
7, 1I, 12, 13, 14, 18, 19, 20, 22
9, 10, I I, 13, 14, 18, 19
38
lntroduction
lntroduction
Other array forms
- - Pv X
i
*
Examples of arrays using meandering U06, 1071 microstrip lines are:
y
[I 061
Various other forms of series fed linear arrays exist: A A,/2 wide line can be made to radiate by feeding with an asymmetric step [I 131. Alternatively angled slots can also force the line to radiate.
serpent line 1106, 1071 triangle or tiapeioidi line 11061 rampart line [I081 chain line [I091 Franklin line [i l O]
A combination of strip dipoles and slots can be used to form a circularly polarised linear array [I 141. The high losses in long microstrip series arrays can be reduced by replacing the line by a dielectric rod [llj]; radiation occurs by coupling the line energy to microstrip patches.
An omni-directional array has been made by forming alternating resonators in the line and ground plane [I 161.
Circular polarisation is obtained from the rampart line [108], chain line [I 1I] and herringbone line [I 121.
Circular polarisation --.-<% L--.J
[lo71
13, 14, 18
Multi-octave bandwidth operation can be obtained by a series-fed log-periodic arrangement of patches [I 171.
39
13. 23
40
Introduction
lntroduction
1.5 Summary comments The historical development and future prospects of the microstrip antenna are reviewed to portray a n invention that is now reaching maturity while its supporting research and development continues to expand unabated, driven by system demands for conformal low-cost radiators. Future activity will be dominated by both the creation of innovative designs to match system demands and the search for improved CAD techniques in array manufacture. The concept of distributed conformal sensors with integral signal processing is one projection for the distant future. For completeness the more common features of microstrip antennas, their applications and typical antenna design criteria are listed and briefly described prior to critically reviewing the outstanding design problems that are fundamental to microstrip antennas. The viewpoint of both researcher and antenna manufacturer is usefully taken to identify knowledge gaps and challenging issues that are vital to the advancement of the printedantenna concept. The importance of the contributions in the present handbook in advancing the state-of-the-art is emphasied and each chapter briefly highlighted. Finally a glossary of microstrip antenna types is presented as an initial guideline for the designer.
1.6 References
16
HALL, P. S., and JAMES, J. R.' 'Cross polarisation behaviour of series fed microstrip linear arrays', IEE Proc., 1984, 131H, pp. 247-257 17 HALL, P. S., and HALL, C. M.: 'Coplanar corporate feed design effects in microstrip patch array design', IEE Prac., 1988 135, H. 18 HENDERSON, A., JAMES, J. R., and HALL, C. M.: 'Bandwidth extension techniques in printed conformal antennas'. Military Microwaves, MM 86, Brighton, June 1986, pp. 329-334 19 LONG. S. A., and WALTON, M. D.: 'Dual frequency stacked circular disc antenna', IEEE Trans., 1979, AP-27, pp. 270-273 20 KUMAR, G., and GUPTA, K. C.: 'Non radiating edge and four edges gap coupled multiple resonator broad band microstrip antennas,' IEEE Trans., 1985, AP-33, pp. 173-177 21 RUDGE, A. W., MILNE, K., OLVER, A. D., and KNIGHT, P.: 'Handbook of antenna design' (IEE, Peter Peregrinus, 1982) pp. 24-28 22 TESHIROGI, T., TANAKA, M., and CHUJO, W.: 'Wideband circularly polarised array with sequential rotation', Proc ISAP, Tokyo, Japan, Aug 1985. pp. 117-120 23 KISHK, A. A., and SHAFAI, L.: 'Effect of various parameters of circular microstrip antennas on their radiation efficiency and the mode excitation', IEEE Trans., 1986, AP-34, pp. 969-977 24 HORI, T., TERADA, N., and KAGOSHIMA, K.: 'Electronically steerable spherical array antenna for mobile earth station'. IEE Conf. on Ant. and Prop.. ICAP 87, York, pp. 55-58 25 HOWELL, J.Q.: 'Microstrip Antennas', IEEE Trans, 1975, AP-23, pp. 90-93 26 SHEN, L. C.: 'The elliptical microstrip antenna with circular polarisation', IEEE Trans, 1981, AP-29, pp. 90-94. 27 LUK, K. M., LEE, K. F., and DAHELE, J. S.: 'Theory and experiment on equilateral triangular microstrip antenna'. Proc 16th European Microwave Conference, 1986 28 Reference 12, pp. 139-153 29 CHEW, W. C.: 'Broadband annular ring microstrip antenna', IEEE Trans, 1982,AP-30, pp. 41 51-07? 30 WEINSCHEL, H. D.: 'Cylindrical array of circularly polarised microstrip antennas'. IEEE AP-S Int. Symp. Dig., 1975, pp. 177-180 31 PENARD, E., and DANIEL, J. P.: 'Open and hybrid microstrip antennas', IEE Proc., 1984, 131, H, (1) 32 RICHARDS, W. F., OU, J. D., and LONG, S.A.: 'Theoretical and exoerimental investieation of annular, annular sector and circular sector microstrip antennas, IEEE Trans, 1984, AP-12. .oo. . 864-866 33 PARASNIS, K., SHAFAI, L., and KUMAR, G.: 'Performance of star microstrip as a linearly and circularly polarised TM,, mode radiator', Electron. Lett., 1986.22, pp. 463-464 34 PALANISAMY, V and GARG, R.: 'Rectangular ring and H-shaped microstrip antennas: Alternatives to rectangular patch antenna', Electron Left., 1985, 21, pp. 874-876 35 Reference 13, pp. 194-224 36 SANFORD, G. G., and MUNSON, R. E.: 'Conformal VHF antenna for the Apollo-Soyuz test project'. IEE Int. Conf. on Antennas for Aircraft and Spacecraft, London, pp. 130-135 37 OSTWALD, L. T., and GARVIN, C. W.: 'Microstrip command and telemetry antennas for communications and technology satellites'. IEE Int. Conf. on antennas for Aircraft and Spacecraft, London, pp. 217-222 38 KERR, J.: 'Microstrip antenna developments'. Workshop on Printed Antenna Technology, New Mexico State University, 1979, pp. 3.1-3.20 39 HANEISHI, M., et al.: 'Broadband microstrip array composed of single feed type circularly polarised microstrip element'. IEEE AP-S Int. Symp. Dig, May 1982, pp. 160-163 40 SHARMA, P. C., and GUPTA, K. C.: 'Analysis and optimised design of single feed circularly polarised microstrip antennas', IEEE Trans. 1983, AP-31, (6) 41 MARTIN PASCUAL, C., FONTECHA, J. L., VASSAL'LO, J., and BARBERO, J.: 'Land mobile antennas for satellite communications'. IEE Conf. on Mobile Satellite Systems, 1984, pp. 145-149
,."
GREIG, D. D. and ENGLEMAN. H. F.: 'Microstrip - a new transmission technique for the kilomegacycle range', Proc. IRE, 1952, 40, pp. 1644-1650 DESCHAMPS. G. A,: 'Microstrip microwave antennas'. 3rd USAF Symposium on Antennas, 1953 LEWIN. L.: 'Radiatton from discontinuities in stripline'. Proc. IEE. 1960,107C, pp. 163-170 GUTTON. H. and BAISSINOT, G.: 'Flat aerial for ultra high frequencies'. French Patent No. 7031 13, 1955 FUBINI. E. G. er a/.: 'Stripline radiators'. IRE Nat. Con. Rec., 3, 1955, pp. 51-55 McDONOUGH. J. A,: ' ~ k c e n tdevelopments in the study of pr~ntedantennas'. IRE Nat. Conv. Rec., 5, Pt. 1, 1957, pp. 173-176 DENLINGER. E. J.: 'Radiation from microstrip resonators', IEEE Trans, 1969. MTT-17, pp. 235-236 HOWELL, J. Q.: 'Microstrip antennas'. IEEE AP-S. Int. Symp. Digest, 1972, pp. 177-180 MUNSON, R. E.: 'Conformal microstrip antennas and microstrip phased arrays', IEEE Trans., 1974. AP-22. pp. 74-78 Proc. of Workshop on Printed Circuit Antenna Technology, 17-19, Oct. 1979, New Mexico State Univ., Las Cruces. New Mexico IEEE Trnns, 1981, AP-29, (I) BAHL. I. J. and BHARTIA. P.: 'Microstrip antennas' (Artech House, Dedham. Mass, 1980) JAMES. J. R.. HALL. P. S. and WOOD, C.: 'Microstr~pantenna theory and design' (IEE. Peter Peregrinus. 1981 ) DUBOST, G.: 'Flat radiating dipoles and applications to arrays' (Research Studies Press. Antenna Series No 1, 1980) JAMES, J. R., HENDERSON. A,, and HALL, P. S.:'Microstrip antenna performance is determined by substrate constra~nts',M i u u ~ ~ ~ oSwr. v e ,Ve~en,s,1982, 12, (X), pp. 73-84
47
42
Introduction HUANG, J.: 'Technique for an array to generate circular polarisation with linearly polarised elements'. IEEE Trans, 1986, APZ-34, (9) BRAIN, D. J., and MARK, J. R.: 'The disc antenna - A possible L band aircraft antenna'. IEE Conf. Publ. 95, Satellite Systems for Mobile Communications and Surveillance, 1973, pp. 14-16 MUNSON, R. E.: 'Conformal microstrip antennas and microstrip phased arrays,' IEEE Trans, 1974, AP-22, pp. 74-78 CHIBA, T., SUZUKI, Y., MIYANO, N., MIURA, S., and OHMORI, S.: 'Phased array antenna using microstrip antennas'. 12th European Microwave Conference, Finland, 1982, pp. 475-477 SANFORD, G. G., and KLEIN, L.: 'Recent developments in the design of conformal microstrip phased arrays'. IEE Conf. Publ. 160, Maritime and Aeronautical Satellites for Communication and Navigation, London, 1978, pp. 105-108 BAILEY, M.C.: 'A broad beam circularly polarised antenna'. IEEE AP-S Symp. Stanford, USA, 1977 CHANG, E., LONG, S. A,, and RICHARDS, W. F.: 'Experimental investigation of electrically thick rectangular microstrip antennas', IEEE Trans, 1986, AP-34, (6) GRIFFIN, J. M., and FORREST, J. R.: 'Broadband circular disc microstrip antenna', Electron. Lett., 1982, 18, pp. 26-269 FONG, K. S., PUES, H. F., and WITHERS, M. J.: 'Wideband multilayer coaxial fed microstrip antenna element', Electron Lett. 1985, 21, pp. 497-499 HALL, P. S.: 'Probe compensation in thick microstrip patches', Electron. Lett., 1987,23, pp. 606-607 PODDAR, D. R., CHATTERJEE, J. S., and CHOWDHURY, S. K.: 'On some broad band microstrip resonators', IEEE Trans, 1983, AP-31, (I) CHATTERJEE, J. S.: 'Conically depressed microstrip patch antenna', IEE Proc, 1983, 130, H, pp. 193-196 SABBAN, A,: 'New broadband stacked two layer microstrip antenna'. IEEE AP-S Symp., Houston, 1983, pp. 63-66 HALL, P. S., WOOD, C., and GARRETT, C.: 'Wide bandwidth microstrip antennas for circuit integration', Electron Lett. 1979, 15, pp. 458-460 SCHAUBERT, D. H., and FARRAR, F. G.: 'Some conformal printed circuit antenna designs'. Proc Workshop of Printed Antenna Technology, New Mexico State University, 1979, pp. 5.1-5.21 KUMAR, G., and GUPTA, K. C.: 'Non-radiating edge and four edges gapcoupled multiple resonator broad band microstrip antennas', IEEE Trans., 1985, AP-33, pp. 173-177 BHATNAGAR. P. S., DANIEL, J. P., MAHDJOUBI, K., and TERRET, C.: 'Hybrid edge, gap and directly coupled triangular microstrip antenna', Electron Lett., 1986.22, pp. 853-855 AANANDAN, C. K., and NAIR, K. G.: 'A compact broad band microstrip antenna', Electron Letl., 1986, 22. pp. 1064-1065 WOOD, C.: 'Improved bandwidth of microstrip antennas using parasitic elements', IEE Proc., 1980, 127H, pp. 231-234 PRIOR, C., and HALL, P. S.: 'Microstrip disc antenna with short circuit annular ring, Electron Lett., 1985, 21, pp. 719-721 WOOD, C.: 'Curved microstrip lines as compact wideband circularly polarised antennas', IEE J. MOA, 1979. 3, pp. 5-13 MONTGOMERY, N. W.: 'Triple frequency stacked microstrip element', IEEE AP-S, Boston, MA, June 1984, pp. 255-258 SENSIPER, S., WILLIAMS, D., and MCKONE, J. P.: 'An integrated global positioning satellite antenna low noise amplifier system'. ICAP 87, York, IEE Conf. Publ. 274, 1987, pp. 51-54 JONES, H. S., SCHAUBERT, D. H., and FARRAR, F. G.: 'Dual frequency piggyback antenna', US Patent No 4 162 499, 24 July 1979
Introduction
43
DAHELE, J. S., and LEE, K. F.: 'Dual frequency stacked microstrip antenna'. IEEE AP-S Int. Symp. Dig. 1982, pp. 308-311 DAHELE, J. S., LEE, K. F., and WONG, D. P.: 'Dual frequency stacked annular ring microstrip antenna', IEEE Trans, 1987, AP-35, GRONAU, G., MOSCHURING, H., and WOLFF, I.: 'Input impedance of a rectangular microstrip resonator fed by a microstrip network on the backside of the substrate'. 14th European Microvwave Conference, Liege, Sept. 1984, pp. 625-630 ZHONG, S. S., and LO, Y. T.: 'Single-element rectangular microstrip antenna for dual frequency operation', Electron Lett., 1983, 19. pp. 298-300 KUBOYAMA, H., HIRASAWA, K., and FUJIMOTO, K.: 'Post loaded microstrip antenna for pocket sue equipment at UHF'. Int. Symp. on Ant. &Prop., Japan, 1985, pp. 433-436 RICHARDS, W. F., DAVIDSON, S. E., and LONG, S. A,: 'Dual band reactively loaded microstrip antenna'. IEEE Trans, 1985, AP-33, pp. 556-561 McILVENNA, J., and KERNWEIS, N.: 'Modified circular microstrip antenna elements', Electron Lett., 1979, 15, pp. 207-208 KERR, J.: 'Other microstrip antenna applications', Proc 1977 Antenna Applications symposium, Illinois, USA SANFORD, G. G., and MUNSON, R. E.: 'Conformal VHF Antenna for the Apollo-Soyuz Test Project'. IEE Conf. Publ. 128, Antennas for Aircraft and Spacecraft, 1975, pp. 130-135 GREISER, J. W.: 'Coplanar stripline antenna', Microwave J., Oct. 1976, pp. 47-49 OLTMAN, H. G.: 'Electromagnetically coupled microstrip dipole antenna elements'. 8th European Microwave Conference, Paris, Sept. 1978, pp. 281-285 ALEXOPOULUS, N. G.. and JACKSON, D. R.: 'Fundamental superstrate (cover) effects on printed circuit antennas', IEEE Trans, 1984, AP-32, pp. 807-816 JAMES, J. R.. HALL, C. M., and ANDRASIC, G.: 'Microstrip elements and arrays with dielectr~coverlays' IEE Proc., 1986, 133, H. (6) YOSHIMURA, Y.: 'A microstrip slot antenna', IEEE Trans, 1972. MTT 22, pp. 760-762 HALL. P. S., and PRIOR, C. J.: 'Microstrip feeds for prime focus red reflector antennas', IEE Proc. 1987, 134, H, pp. 185-193 OLTMAN, H. G., WEEMS, D. M., LINDGREN, G. M., and WALTON. F. D.: 'Microstrip components for low cost millimeter wave missile seekers', AGARD Conf. Proc. 245, Millimeter and Submillimeter Wave Propagation and Circuits, Munich, 1978, pp. 27.1-27.9 MONTGOMMERY, J. P.: 'Microstrip reflect array antenna element'. Proc 1978 Antenna Applications Symposium, Illinois, USA SINDORIS, A. R., SCHAUBERT, D. H., and FARRAR, F. G.: 'The spiral slot - A unique microstrip antenna'. IEE Conf. Proc. Ant. & Prop., London, 1978, pp. 150-154 MUNSON. R. E.: 'Conformal microstrip antennas and microstrip phased arrays', IEEE Trans. 1974. AP-22. pp. 74-78 SOHTELL, E. V., and STARSKI, J. P.: 'Cylindrical microstrip patch phased array antennaChalscan C'. Military Microwaves Conf., Brighton, June 1986, pp. 317-322 LUK. K. M., LEE. K. F., and DAHELE, J. S.: 'Input impedance and Q factors and cylindrical-rectangular microstrip patch antennas', ICAP 87, York, IEE Conf. Publ. 274, 1987. pp. 95-99 SEEHAUSEN, G: 'Polarisation control of conformal arrays consisting of linerly polarised elements', ICAP 83, Norwich, IEE Int. Conf. on Ant. & Prop., 1983, pp. 154-157 THOMAS, H. J.. FUDGE, D. L., and MORRIS, G.: 'Active patch antenna';Proc. Military Microwave Conf., June 1984, pp. 246-249 OWENS, R. P., and SMITH, A. C.: 'Dual band, dual polarisation microstrip antenna for X band satellite communications', Military Microwaves Conf., Brighton, June 1986, pp. 323-328 POZAR, D. M.: 'Microstrip antenna aperture coupled to a microstrip line', Eleclron Lett.. 1985, 21. pp. 49-50 BUCK, A.C., and POZAR, D. M.: 'Aperture coupled microstrip antenna with a perpendicular feed, Electron Lett., 1986, 22, pp. 125-126
Introduction HALL, P. S., and PRIOR, C. J.: 'Radiation control in corporately fed microstrip patch arrays'. JINA 86, Journeees Internationales de Nice sur les Antennes, 1986, pp. 271-275 HENDERSON, A,, and JAMES, J. R.: 'Design of microstrip antenna feeds - Pt 1: Estimation of radiation loss and des~gnimplications', IEE Proc, 1981, 128H, (I), pp 19-25 LO. Y. T., SOLOMON, D., and RICHARDS, W. F.: 'Theory and experiment on microstrip antennas', IEEE Trans, 1979, AP-27, pp. 137-145 Reference 13, pp. 116 and 161 HALL, P. S., and JAMES. J. R.: 'Design of microstrip antenna feeds - Pt 2: Design and performance limitations of triplate corporate feeds', IEE Proc., 1981, 128H. pp. 26-34 ROGERS, A,: 'Wideband squintless linear arrays', Marconi Rev., 1972, 187, pp. 221-243 WILLIAMS, J. C.: 'Cross fed printed aerials'. Proc 7th European Microwave Conference, Copenhagen, Sept 1977, pp. 292-296 DERNERYD, A. G.: 'Linearly polarised microstrip antennas', IEEE Trans., 1976, AP-24, pp. 846-85 1 TIURI, M.. HENRIKSSON, J., and TALLQUIST, S.: 'Printed circuit radio link antenna', 6th European Microwave Conference, Rome, Sept 1976, pp. 280-282 HILL, R.: 'Printed planar resonant arrays', [CAP 87, York, IEE Int. Conf. on Ant. &Prop., 1987, pp. 473-476 DUMANCHIN. R.: 'Microstrip aerials'. French Patent Application 855234, 1959 JAMES, J. R., and HALL. P. S.: 'Microstrip antennas and arrays - Pt. 2: New design technique'. IEE J. MOA 1977, 1, pp. 175-181 CASHEN, E. R., FROST, R., and YOUNG, D. E.: 'Improvements relating to aerial arrangements'. British Provisional Patent (EM1 Ltd) Specification 1294024. METZLER, T.: 'Microstrip series arrays', IEEE Trans., 1981, AP-29, pp. 174-178 TRENTINI, VON G,: 'Flachantenna mit periodisch gebogenem leiter', Freyuenz, 1960 14, pp. 230-243 SKIDMORE, D. J., and MORRIS, G.: 'Design and performance of covered microstrip serpent antennas'. ICAP 83, Norwich, IEE Int. Conf. on Ant. and prop., 1983, pp. 295-300 HALL, P. S.: 'Microstrip liner array with polarisation control'. IEE Proc., 1983, 130H, pp. 2 15-224 TIURI, M., TALLQUIST, S., and URPO, S.: 'The chain antenna', IEEE SP-S Int. Symp., Atlanta, USA, pp. 274-277 NISHIMURA, S., NAKANO, K., and MAKIMOTO, T.: 'Franklin-type microstrip line antenna', IEEE AP-S, Int. Symp., Seattle, pp. 134-137 HENRIKSSON, J., MARKUS, K., and TIURI, M.,: 'Circularly polarised travelling wave chain antenna'. Proc 9th European Microwave Conf., Brighton, 1979 JAMES, J. R., and WILSON, G . J.: U K Patent Specification N o 1529361, 18 Oct. 1978 MENZEL, W.: 'New travelling wave antenna in microstrip', Proc. 8th European Microwave Conference, Paris, 1978, pp. 302-206 ITO, K., ITOH, K., and KOGO, H.: 'Improved design of series fed circularly polarised printed linear arrays', IEE Proc., 1986, 133, H , pp. 462466 JAMES, J. R., JOHN, G., and HALL, C.M.: 'Millimetric-wave dielectric-microstrip antenna array', IEE Proc., 1984, 131, H, pp. 341-350 HILL. R.: 'Twin line omni-directional aerial configuration', Proc. 8th European Microwave Conference, Sept. 1978, pp. 307-31 1 HALL, P. S.: 'Multi-octave bandwidth log periodic microstrip antenna array', IEE Proc. 1986, 133, H , pp. 127-137
Chapter 2
Analysis of circular microstrip antennas L. Shafai and A. A. Kishk
2.1 Introduction
Microstrip antennas are finding increasing popularity owing to their advantages in size, cost, conformity to the supporting structure and ease of fabrication [I] [2], [3]. To analyse their impedance and radiation properties many elaborate analytical techniques are proposed and used. Numerical methods are also developed and have received increasing attention in recent years, these being primarily based on Sommerfeld-type integral equations. All these methods, which are discussed in following Chapters of this handbook have one important assumption in common: they assume that the dielectric substrate and the supporting ground plane are infinite in extent. The solutions are therefore valid for infinite geometries, or when the substrate and ground-plane dimensions are relatively large. The assumption does not introduce a severe difficulty in impedance calculations since microstrip geometries are inherently resonant structures and their impedance characteristic is primarily controlled by the printed elements. However, difficulty arises in predicting the radiation patterns, where, for small antenna dimensions, diffraction effects alter the side and back radiations. Consequently, the Geometrical Theory of Diffraction is occasionally used in conjunction with other methods to improve the radiation-pattern predictions [4, 51. Accurate formulation of the electromagnetic problem of microstrip antennas is feasible. But, for finite substrate and ground-plane sizes the formulation must be solved numerically. In this Chapter we present a general formulation which is based on the concept of equivalence principle, and provides integral equations for the field distribution on the surfaces of the conductors and dielectric substrate. The formulation is exact and satisfies all boundary conditions. However, since it involves the field distributions on the substrate and ground plane, the numerical solution of the resulting integral equations is efficient only for small antenna dimensions. The problem is considerably simpler for axisymmetric geometries, where the surface distributions can be expanded in terms of the azimuthal modes representing the physical modes of the structure. Consequent-
46
Analysis of circular microstrip antennas
ly, since microstrip antennas support only a limited number of modes, the numerical solutions for accurate field representations are readily obtainable. In addition, the modal expansion of the fields reduces the problem to the solution of matrix equations for each individual mode and simplifies computation considerably. For this reason, all computed results in this Chapter are presented for circularly symmetric configurations. The formulations can, however, be used with additional labour for the investigation of other microstrip configurations as well. For instance, when the microstrip geometry is non-circular, or even arbitrary in shape, one can use a surface-patch segmentation over the conducting and dielectric surfaces. The current and surface distributions can then be represented by appropriate basis functions over these patches to convert the integral equations to a matrix equation using a moment method. The solution of the resultingmatrix equation gives the surface distributions over the conducting and dielectric surfaces. However, since the segmentation is over the entire surface the matrix size is normally large. In addition, the method gives numerical results for the surface distributions and fails to provide information on the modal excitation. This difficulty can be overcome by expanding the current distributions in terms of patch eigen functions, in which case the procedure becomes similar to the case of axisymmetric configurations discussed previously. Since the existing solutions in the literature predict microstrip-antenna impedance properties accurately, no attempt is made here to investigate the antenna impedances. Instead, emphasis is put on predicting the radiation patterns and investigating the effects of microstrip dimensions on them. Consequently, to simplify the analysis, excitation sources are replaced by simple electric dipoles. No significant effect is anticipated by this source simplification, since the resonant nature of microstrip antennas controls their mode excitation, and thus radiation patterns. The generated equations are used to investigate the radiation properties of three different antennas; namely, a circular microstrip patch antenna, a wraparound antenna and the reflector feeds. They are fundamentally different antennas and selected to provide complementary analysis and design information. For instance, the circular patch is one of the basic microstrip antennas. Its radiation characteristics and mode excitations are studied in length and the effect of the ground-plane size and other dimensional or material parameters on its radiation patterns are investigated. The results, although computed for a circular patch geometry, provide information for precise understanding of the radiation properties of resonant patch antennas. The wrap-around antenna is selected to show that the formulation can be used to investigate any axisymmetric antenna configuration. It is also shown that multiple source excitation can be used to control mode excitation, and consequently the radiation patterns. The last example, i.e. the reflector feed, is included to indicate the usefulness of the method for design of precision antennas. The reflector feeds should not only provide an efficient illumination function, but their cross-polarisation and the
Analysis of circular microstrip antennas
47
phase-centre location must also be controlled precisely. The numerical method provided in this Chapter enables accurate and efficient generation of pattern data, which, when coupled with optimisation algorithms, gives antenna-design parameters to meet stringent performance requirements. 2.2 Formulation of the problem
The electromagnetic problem involving microstrip antennas deals with determination of the field components in the presence of conductors and dielectrics. The boundary conditions to be satisfield are therefore of mixed type. This requires vanishing of the tangential electric-field components on the conductors and continuity of the tangential electric and magnetic components over the dielectrics. Because practical geometries are finite h size, an exact analytical solution cannot be found to satisfy all boundary conditions. A numerical solution must therefore be utilised. In this regard, two formulation types can be developed. One involves volume integral equations for the polarisation currents in the dielectrics and the induced surface currents on the conductors. This type of formulation is not convenient to work with, but is general enough to handle inhomogeneous dielectrics. For homogeneous dielectrics a convenient formulation can be developed in terms of the tangential field components over the boundary surfaces. The resulting integral equation includes all boundary conditions and the formulation is therefore an exact one. Thus the solution accuracy will depend on the management of the problem thereafter and on the numerical algorithms used to determine the unknown surface distributions. In the following Sections we shall provide integral-equation formulations only for the surface distributions, and present numerically generated data for several known antenna configurations. The formulations may be derived from the use of the equivalence principle [6, 71. To proceed we select a general electromagnetic problem shown in Fig. 2.la, where a homogeneous dielectric material is sandwiched between two conducting layers. The surfaces S,,, S,, and Sckrefer, respectively, to the boundaries between the conductors and the exterior region, the conductors and the dielectric, and the exterior region with the dielectric. Similarly, Ed, Rdand E', I;i' refer to the field vectors within the dielectric and exterior regions, respectively. The dielectric region has a volume V,, bounded by surfaces S, and S,, and its material parameters are td and p,. The exterior region has a volume V, and its permittivity and permeability are defined by E, and p,, respectively. The excitation sources are provided by impressed electric and magnetic currents J', and within the dielectric. We now may invoke thd equivalence principle to reduce the complex original problem to two simpler ones [8], involving the exterior and interior regions. Fig. 2. I b shows the external equivalence. The combined volume of the conductors and the dielectric is bounded by S,, and S,,, and supports equivalent currents I,,
ad,
48
Analysis of circular rnicrostrip antennas
Analysis of circular rnicrostrip antennas
:I 1 1
'ce Fig. 2.1 a
Original problem
'ce
-
I Jce -e y H-e
'
49
m.
7, and These currents radiate in a homogeneous medium (E,, p,) and produce (E',R')in V, and zero field within the bounded region. Here, J,, is the electric current on S,, and Jdeand A? are the electrlc and magnetic currents on S,. The internal equivalence is shown in Fig. 2.lc, where the volume V, is enclosed by S,, and S,,. The equivalent currents are - I,,, - 1, and -A? and radiate in a homogeneous medium ( E,, p,) to produce together with J', and ( E d , I?,) in V, and zero field elsewhere. Again, -3, is the electric current on S,,, and - J, and -A? are the electric and magnetic currents on S,. Since, in the original problem of Fig. 2. l a the surfaces S , and S , are perfectly conducting, they support only equivalent electric currents in Figs. 2.lb and 2 . 1 ~ The . negative-sign relationship between the aperature currents of Figs. 2. l b and 2.lc is dictated by the zero-field stipulations and the continuity of the tangential electric and magnetic field components across the aperature surface S, of Fig. 2.la. However, the selection of the negative sign for -Jcd in Fig. 2.lc is not mandatory and is made to match the negative sign of the aperature currents. In the above example, the application of the equivalence principle reduced a complex multi-region problem to two simpler ones involving homogeneous regions. The field components in each region can therefore be found readily from the equivalent currents. However, these equivalent currents are still unknown and must be determined. This can be achieved by enforcing the boundary conditions on the field vectors of the original problem in Fig. 2.la. The boundary conditions to be satisfied are:
zero field
and the surface equivalent currents are Fig. 2.1 b
External equivalence
Again, the currents I,, I,, and 1, are the equivalent electric currents on each respective surface and lii is the magnetic current on the interface surface between the dielectric and the exterior region. The field components in eqns. 2.1 can be determined from these equivalent currents and provide the following field relationships:
Fig. 2.1 c Internal equivalence
50
Analysis of circular rnicrostrip antennas
Analysis of circular microstrip antennas
- &""(J,,
+ J,,
m - flP,(J',
= - R&(Jid,0 )
+ J,,
m
on S,,
(2.6)
51
formulations involve the surface distributions on the dielectric, their numerical solution for arbitrarily shaped geometries may require excessive computer time and storage. The problem is considerably simpler for axisymmetric geometries,
where E'(J, && and Ed(J,A?) represent the electric fields due to the currents 3 and A?, radiating in media characterised by E,, p,, and E,, p,, respectively. R' (3, h?) and R q J , 12;1) are the associated magnetic fields. Note that, since the equivalent currents are still unknown, the field eqns. 2.3 - 2.6 represent integral equations for these currents. These integral equations can be generated using appropriate vector potentials, in terms of which the field vectors are given by
where
and
The function Gv is the scalar Green's function and is given by
where R = (r - r'l is the distance between the field point r and the source point the surface, k, = w ( ~ , p , ) "is~the propagation constant of the region and q represents e or d.
Fig. 2.2 Geometry of the body of revolution
r' on
2.2.1 Matrix formulation The above formulations provide integral equations valid for any combination of dielectric and conducting bodies of arbitrary shape. They can be solved for the unknown currents by a non-linear optimisation routine or after linearisation of the relationships by an application of a moment method. However, since the
where the field vectors can be expressed in Fourier series of the azimuthal co-ordinate. A solution can therefore be generated separately for each Fourier component, resulting in reduced computation time and storage. This is particularly important in microstrip antennas, which are highly resonant and often support only one of the azimuthal modes. For this reason, we shall restrict the remaining material of this Chapter to the development of solutions for axisymmetric geometries.
52
Analysis of circular microstrip antennas
Analysis of circular microstrip antennas
Fig. 2.2 shows a simple representation of an axisymmetric object, generally known as a body of revolution. The surface tangents can be defined along the generating curve I and the azimuthal co-ordinate 4. They are shown in Fig. 2.2 and form an orthogonal curvi-linear co-ordinate system on the surface of the body. Because the geometry is rotationally symmetric the surface co-ordinates can be represented conveniently in terms of p, 4 and z co-ordinates in a cylindrical system, with the origin on the axis of the body. We define the orthogonal surface tangents by their unit vectors ii, and ii, and the outward normal by the direction of its unit vector ii given by A = ii,xri,
(2.16)
On the surface of the body we define a field point by its co-ordinates ( I , 4) or (e, 4 , z ) and a source point by (t', 4') or (Q', $', 2 ' ) . Their respective unit tangent vectors are (i,, ii,) and (ii;, G).The unit vector ii, is orthogonal to the z-axis, but ii, and i are at an angle v. This angle is assumed to be positive if ii, points away from the z-axis. Similarly, v' is the angle between ii', and the z-axis at (t', 4'). The relationships among these unit vectors can be determined by an inspection of Fig. 2.2, and are given by 12, = sinv ii,
+ cow 2, -
+)ii,
+ sinv'sin(4'
+ cos(4'
- 4)ii,
+ cosv'ri,
- d)ii,
(2.18) (2.19)
In addition, if the positional vectors of points ( t , 4) and (1', 4') are r and r ' , respectively, then
@ a , + zii,
P
=
F'
= Q'
and Co~(4'- 4)
J (7)= i,.S(1', 4')
+ k,J@ (t', 4')
-
1I] (2.25)
where S , and M', Mb are the current components along ii,. and ii,., respectively. The electric current J exists on both conducting and dielectric surfaces, but A? exists only on the dielectric. If the electric and magnetic surface currents are expanded into N, and N,,expansion functions, respectively, the surface currents can be represented by
+ M$ K,$ ( t ' , $')aq
(2.28)
where Ji,, J$, Kh, K$ are expansion functions defined by
(2.17)
ii,, = sinv' cos(4' - 4)ii, ii,, = -sin(@
along the unit vectors ii, and i i , and expressed in the form [9
53
+ p'sin(4'
- 4)i, + zf6;
(2.21)
where
Also, by definition, the surface gradient of a scalar function @ on the body of revolution is given by
and the surface divergence of a vector function @' is defined as
The unknown currents J a n d A? can now be decomposed into two components
The range - M , to + M , gives the total number of azimuthal modes. The coefficients I;,, I$, MAl, M$ are the current coefficients to be determined by solving the matrix equation which results when eqns. 2.27 and 2.28 are substituted via eqns. 2.25 and 2.26 into the integral eqns. 2.3 - 2.6. The procedure involves taking the inner products of the field equations with certain testing functions and integrating them over the surface. The testing functions are defined by
tTf
=
d4A (t)
(2.31)
The inner product of two vectors P and is defined by their scalar product and integrated over the surface of the body; that is
The expansion and testing functions, i.e. [J,,,, R,,,]and [@,;I, as defined by eqns. 2.29,2.30 and 2.31 are orthogonal over the period 0 to 2a in 4. This means that the inner products of k?;' and J{ ( p = t or 4) vanish for I # n and the contribution of different azimuthal mode separates. The resulting equations therefore involve only a particular mode of index n. This is the major simplification that is introduced by the mode orthogonality in axisymmetric objects. Accordingly we obtain a separate matrix equation for each mode. For explicit evaluation of the matrix elements, one must choose f;(t). It is known that subsectional expansions, using flat pulse or triangle pulse functions,
54
Analysis of circular microstrip antennas
Analysis of circular microstrip antennas
give rise to well conditioned matrices. Flat-pulse current expansions with point matching were first used to solve the scattering problems of conducting spheres. However, with such expansions the moment-method solutions of the surface currents do not converge rapidly to the exact solutions. The triangular-function expansions, on the other hand, converge satisfactorily and provide accurate solutions. For this reason triangular pulse functions are used here to represent both current expansions and the testing functions [9]. A minor deviation from the literature is to use d ( t ) instead ofJ;(t), which is defined by four impulses given by
55
and are shown in Fig. 2.4, where the coefficient T', for i = 1, are given by
Now, all information needed to proceed with transferring the integral equations to a system of linear matrix equations is known. Following procedures well known in the application of moment methods the matrix equation for the nth Fourier component of currents can be written as
r,
is a square matrix representing the impedance and the admittance where sub-matrices, 1, is a column matrix for the unknown expansion coefficients of and fi,and p,,is the excitation column matrix. Each mode has a matrix Fig. 2.3
Triangle function approximation
where 6(t) is the unit impulse function and its coefficients Tare defined in Fig. 2.3, which for i = 1 are given by
Similarly, the derivative of ef;(t) is approximated by four impulses as d
;ii[ d ( a
z 4
=
p =
l
T;+4;-46(t
-
1,+21-2)
(2.35)
where q, = q,/q,; and V,d is the excitation sub-matrix due to the electric-field sources in the dielectric and I ,is the excitation due to the magnetic-field sources in the dielectric region, respectively. The sub-matrices Z and Y with superscripts e and d denote the impedance and admittance matrices for the exterior and interior media, respectively. The first pair of suffixes identify field surface and the second pair of suffixes identify the source surface where the Fourier mode n is implied. I,,,,I ,,,,, Icle,,and M,, are the unknown expansion coefficients of the electric and magnetic currents on S,,, S,, and S,,, respectively. In the above
56
Analysis of circular microstrip antennas
equations, each sub-matrix by
Analysis of circular microstrip antennas
Y:: or Z::consists of four submatrices. They are given
( Y 3 ) , = &(z, - z,)G, (Y4)ij =
and
and p' = p + 4 i - 4
Fig. 2.4 Derivative of the triangle function approximation
where
and their elements have the form
with
r
= I+4j-4
f
= p + 2 i - 2
f
= I+2i-2
57 (2.44)
58
Analysis of circular microstrip antennas
Analysis of circular microstrip antennas
59
and hf' is the spherical Hankel function of the second kind and zero order and is the dipole moment in the =-direction. If the Hankel function is represented by at t = t ' , R is approximated by with
G,,, 2.2.2 Excitation matrix Microstrip antennas are normally excited by a transmission line or a coaxial probe. To solve the problem numerically one must model the exciting source, from which the elements of the excitation matrix can be determined. However, a precise modelling of either source, i.e. the junction between the transmission line or the coaxial probe with the microstrip patch, although feasible is a difficult task. On the other hand, microstrip antennas are highly resonant structures and within their operating frequency band one of the Fourier components, i.e. the modes, dominates. This means, one can represent the excitation source with a simple elementary source, such as an electric dipole, without affecting the solution accuracy. The representation of the source by a single electric dipole is quite adequate if the substrate thickness is small, or the width of the transmission-line feed is not excessively large. Otherwise, multiple dipole sources must be used. For instance, when the substrate thickness is so large that the current distribution along the coaxial probe is not constant, a linear array of electric dipoles along the probe length may be used. In such a case, the excitation of dipoles must correspond to the current distribution of the probe. Similarly, for simulating wide transmission-line junctions, multiple dipole exciations may be used, where their excitation must be weighted by the field distribution under the line. In the following analysis we consider only the case of thin substrates or transmission lines, and represent the excitation source by a single electric dipole. This simple form of source representation simplifies the excitation matrix considerably. Simulating the excitation by an electric dipole, its electric and magnetic fields can be computed from Erncq
= - j m ,$
- v ~q
(2.61)
I
=
G-,
=
a,, hi2' (kqr')j,,(kqr)P~(cos9)P~(cosB'), r' > r
I, F 0,
f- a,, hL2' (kqr)j,,(kqr')P~(cos9)P,"(cosO'), r' <
(2.66) r
1, = "l
where a,, = (2n + 1) (n - m)!/(n + m)!; then using eqn. 2.61 for I?, excitation matrix elements can be calculated from
its
where 1, is the t co-ordinate of the upper end of the generating curve. Similarly, using eqn 2.62 for A'"',its matrix element can be calculated from
2.2.3 Radiation fields Once the induced currents J and A? on the surface are determined after the solution of the matrix equation, the field components E, and E4 at a far-field point (r,, O,, 4,) can be determined [I21 as
and
60 with
i,
Fl(Oo,4,) = L(.l
1 +A - i4)e-"'o" %
and ds
(2.73)
+ -1 K ~ , [ s i n v ' c ~cos(4' s~~
where S is the exterior antenna surface, Po is a unit vector in the direction from the origin of the co-ordinates to the field point, P' is the positional vector of the source point (x', y', 2 ' ) on the antenna, and C and i, are unit vectors in the , direction of increasing 0 and 4 , respectively. Referring to the field point, these vectors can be written as
+ cos 8, sin 4,6?
i, = cos 0, cos 4,cir i, = - sin q5,ci,
-
sin B0cir
+ cos 4,4
'I
= (x'cos =
+ y' sine,) sine, + z'cos 8, - 4,) sine, + z'cos0,
4,
~ ' c o s(4'
(2.76)
jn
jn(@) =
- cosv sine,]
2n
le-jeco-e-~nada
2~
(2.84)
0
I
(2.77)
- 4,)
Changing the order of summations and integrations and using the integral representation for the Bessel function of the first kind, namely
(2.75)
and,the dot product in the exponential term of eqns. 2.73 and 2.74 can be shown to be to P'
61
Analysis of circular microstrip antennas
Analysis of circular microstrip antennas
the integration in eqns. 2.82 and 2.83 involving the azimuthal co-ordinate 4' can be evaluated as ~ l r ~ - ~~o~coseo ~ ~d ~4' ( = 4 ~2 i ~ j " d "J, ~~ (kef sine,) (2.85)
where (Q', d', z') are the cylindrical coordinates of the point (x', y', 2'). If we now substitute for J a n d fiin eqns 2.73 and 2.74, and evaluate the dot products (fi,. i,), (fi,, i4) as
.
6,. i, = sinv' cos0, cos(4' - 4,) - cosv sine,
(2.78)
fi,. i, = sinv' sin(& - 4,)
(2.79) The far-field functions can then be represented by
and fi4
fi4
5
=
. i4 =
- sinO,sin($' - 4,)
+ cos 4'cosq5,
sin&
= cos(4'
- 4,)
then F,(flO,4,) and F,(B,, 4,) take the form
+ (R$,~M),k,?,j] where 4
-12) cos &sin (4' - 4,)
+-v1 KAlsinv'sin(@
-
+-I?1 k$, COS(@- 4,)
(R?)j
C [j(J,
=
+
, - Jm- ,)sin v'cosOo - 2 cos v'
sin eoJ,]
Y-I
(2.89) 4,)
I
~ ' 4' d dt'
62
Analysis of circular microstrip antennas
Analysis of circular microstrip antennas
63
can be generated from the above symmetric property. The second property is the mode symmetry. This enables one to generate the Y and Z submatrices of the modes with negative indices from the positive ones, as
with
z?,
=
zp
The same relations are valid for the Y submatrices. Similarly, the elements of the excitation for an electric dipole, generated using eqns. 2.67 - 2.70, satisfy the following relationships:
The far-field component can finally be put in a compact form as Thus the solution of the matrix equations, given by eqns. 2.38, gives the following symmetric relationships satisfield by the current coefficients:
M", This completes the formulation of the problem and determination of the radiated fields from the computed equivalent currents. The external field near the antenna or the field within the dielectric substrate can also be determined, but are omitted here for brevity. Two different properties of the Y and Z submatrices are used to reduce the computation time and cost. One is the matrix symmetry. This property is evident from eqns. 2.42 - 2.49 and gives
(Z1l) . m B
=
(Z')g
= -
=
M!
Accordingly, one only needs to compute the coefficients of the positive modes, i.e. one half of the mode coefficients. This results in a major reduction of computation time and cost. The mode symmetry can also be used in calculating the far-field components from eqn. 2.98. The needed relationships are
(Z1').. m 11 (-Z!)ji
(Z?,, = (Y").. = m v
- (Y,y).,
(y3v
=
- (y?)Ji
(Y;,)v
= - (Y;@)ji
(Z9ji
This means that only one half of the matrix needs to be created. The other half
@hJ
=
p.J m
which can reduce the summation over the modes to one from m = 0 to
+ M.
2.3 Application 1: Circular patch antenna The circular patch antenna is one of the fundamental microstrip geometries and its impedance and radiation characteristics have been investigated extensively.
64
Analysis of circular microstrip antennas
Analysis of circular microstrip antennas
However, the methods used so far assumed an infinite size for the ground plane and substrate. The solutions are therefore approximate and lack the influence of the finite substrate and ground-plane dimensions. Their accuracy therefore depends on the type of application. For instance, because microswp patch geometries are highly resonant, their impednace characteristics are dominated by the patch dimensions. The ground plane size, provided it is reasonably larger than the patch, has a negligible effect. Similarly, the radiation near the broadside direction is determined primarily by the patch itself. Th finite size of the
I=
65
The geometry of a circular patch microstrip antenna is shown in Fig. 2.5, where the excitation is simulated by an electric dipole immersed in the dielectric substrate under the conducting patch. The radius is selected as [2]
a,
=
a[l
2h na +(In - + 1.7726]'12 xu&, 2h
c i r c u l a r patch
/--
dielectric
/ '
,
finite ground p l a n e Fig. 2.5
Microstrip antenna geometry
substrate or ground plane influences the radiation at wide angles, and particularly behind the antenna. Thus, when radiation patterns along the broadside direction are necessary or their approximate form is adequate, the analytic solutions can provide sufficient information. The numerical method presented in this Chapter enables one to determine the radiation characteristics in all space. In addition, the accuracy of the generated results can be very high. Thus it is a useful method for generating solutions for high-precision work, such as in a reflector-antenna feed design. In this Section we present a few representative results for a circular patch antenna.
Fig. 2.6
The computed electric and magnetic surface currents of the 7M,, mode on the outside boundary (Reproduced from Reference 14 @ 1986 IEEE)
where a is the radius of the conducting patch, a, is the effective radius due to the spread of the fringing field from the patch edge to the ground plane, h is the dielectric thickness and E, is the relative permittivity of the dielectric substrate.
66
Analysis of circular rnicrostrip antennas
The effective radius is calculated from
where K,,,,, is the mth zero of the derivative of the Bessel function of order n. The effective patch radius is therefore a function of substrate height, the dielectric permittivity and the order of the excited mode. The effects of these parameters, as well as the ground-plane size, o n the radiation characteristics of the patch are investigated in the following Sections [14].
Fig. 2.7
The computed electric and magnetic surface currents of the TM,, mode on the outside boundary (Reproduced from Reference 14 @ 1986 IEEE)
Analysis of circular microstrip antennas
67
2.3.1 Surface fields In microstrip antennas the radiation is normally from the periphery of the patch, where the fringing field is maximum. However, since the exciting dipole launches guided modes of the parallel-plate region under the patch, it is desirable to compute the surface-field distributions on the conducting and dielectric surfaces of the antenna to understand their behaviour. These distributions are given by the equivalent currents 1 and A?. For two selected modes, i.e. the dominant TM,, and the higher TM,, modes, the computed results are shown in Figs. 2.6 and 2.7. In Fig. 2.6 the patch radius is a = 0.181I, where I is the wavelength in free space and the patch resonates in the dominant T M , , mode. The horizontal axis shows the length of the contour along the generating curve. Since the geometry is rotationally symmetric only one half of the surface contour is shown. The external surface currents are plotted with respect to their locations on the surface, where points A to B correspond to the ground plane, points B to C represent the dielectric substrate which supports both electric and magnetic currents and points C to D correspond to the patch surface. An examination of this Figure reveals that the electric current is the strongest on the patch surface and has a negligible value o n the ground plane. Its equivalent distribution on the dielectric, i.e. the tangential magnetic field on the dielectric, is also small. However, it shows some slight increase near B, on the substrate termination, which is an indication of surface-wave excitation. The distribution of the magnetic current &?, i.e. the tangential electric field on the substrate, is shown on the right side of the Figure. It increases progressively from B to C, indicating strong fringing field near C. The contributions to the antenna radiation are therefore mainly from on the patch and M4 on the substrate. The surface distributions for the TMl, excitation are shown in Fig. 2.7. Again, the currents on the ground plane are small, but J' shows stronger values on the substrate termination near B. Here, both J' and J 4 are strong on the patch and have rapid variations. The magnetic current A? again increases rapidly from B to C, near the patch edge. The main radiation zones are similar to the T M , , mode case, being the upper patch surface, the dielectric surface near the patch and its truncated end near the ground plane. 2.3.2 Feed location For coaxial feeds, the location is usually selected to provide a good impedance match. Since, we simulate the excitation by an electric dipole we ignore the impdenace of the feed and investigate the effect of its location on the excitation efficiency of various modes. Also, different modes have different radiation patterns and affect the overall antenna pattern at different angular regions. For this reason, rather than computing the magnitude of the Fourier coefficients of the currents we compute the peak intensity of their radiation fields. Fig. 2.8 shows the effect of the feed position elon the excitation of the first three modes, when the patch is resonant at the T M , , mode. The dominant mode has the strongest excitation efficiency of the other modes, i.e. TM,, and TM,, modes,
68
increase progressively as the feed moves to the patch edge, but their peak radiation level is always below - 15 dB. These modes radiate conical beams and their effect will manifest a t a n angular range near 45' off the z-axis. However, the T M , , mode has a broad beam and its pattern roll-off is about 4 d B near the 45" angle. Thus, other modes will not affect significantly the radiation of the T M , , mode for 0 < 0 ,< 45O, and the co-polar patterns will be decided primarily by the dominant mode. Their contributions will be significant for 0 > 45" and, in particular, for determining the cross-polarisation which, from Fig. 2.8, shows a peak at about - 25dB range. Here the cross-polarisation is computed in 4 = 45' plane, in which it maximizes. The results also show that increasing the substrate height generally increases the excitation efficiency of the other modes
Fig. 2.8
Analysis of circular microstrip antennas
Analysis of circular microstrip antennas
69
at = 0 . 7 5 ~Again, . their contributions are below the - 25 d B range. However. since the TM?, mode has a null along the z-axis, the contribution of the T M , , mode will cause a minor peak at this location. The results of Figs. 2.8 and 2.9 indicate that the resonance nature of a microstrip patch controls the excitation of the azimuthal modes, and the resonant modes can easily be excited significantly above the adjacent modes simply by selecting an appropriate location for the feed. With this type of excitation the contributions of the adjacent modes manifest themselves mainly in the cross-polarisation. They may be ignored if the antenna cross-polarisation is not the main concern. Also, the substrate permittivity seems to have a small effect on the mode excitation.
The effect of the feed position on the excitation efficiency of TM,, mode (Reproduced from Reference 74 @ 7986 IEEE)
The excitation efficiencies for a patch dominant a t the T M 2 , mode are shown in Fig. 2.9. The results are plotted for two different substrate permittivities, and show similar excitations. Again the dominant mode has the strongest excitation, but its peak radiation increases for Q, > 0 . 6 8 ~and decreases thereafter. The peak radiations of the other modes have more complex behaviour and minimise
Fig. 2.9
The effect of the position on the excitation efficiency of TM,, mode (Reproduced from Reference 14 @ 1986 lEEE)
We now present a few results for the radiation patterns. Fig. 2.10 shows the computed patterns for the T M , , mode and Fig. 2.1 1 for the TM,, mode. In both cases the feed location is selected to maximise the excitation of the dominant
70
Analysis of circular rnicrostrip antennas
Analysis of circular rnicrostrip antennas
mode. In Fig. 2.10, the T M , , mode is dominant and the radiation pattern is computed by including four modes, i.e. the T M , , mode along with adjacent TM,, , TM,, and TM,, modes. The radiation peak is in the broadside with a significant radiation level behind the ground plane, owing to its finite size. In Fig. 2.1 1 the TM,, mode is resonant and the radiation patterns are generated by including the first five modes, i.e. TM,, to TM,, modes. T o examine the accuracy of the computed results, sample calculations are also compared with experi-
77
2.3.3 Effect of the substrate permittivity Increasing the substrate permittivity reduces the patch size and consequently the size of the radiation zone. One therefore expects to see a broadening of the radiation pattern. This is shown in Figs. 2.14 and 2.15 for a T M , , mode patch and in both E and H-planes. Since the ground-plane sizes are all the same, the antennas have equal sizes. The results show that the broadening is taking place only in the E-plane. The H-plane patterns are independent of the substrate permittivity, but show an increase in the level of the back radiation, which is also evident in the E-plane patterns. Note that, for the selected antenna dimensions,
Fig. 2.10 The radiation patterns of a circular patch for the dominant mode excitation t = 0,021 Ground lane thickness = 0.01 1
ment. Figs. 2.12 and 2.13 show the comparison for the T M , , mode. The computed and experimental patterns are identical in the upper half plane and deviate slightly thereafter, owing to the coupling between the antenna and its support structure.
Fig. 2.11
The radiation patterns of a circular patch for the TM,, mode excitation; data same as Fig. 2.10
the small permittivity of E, = 2.32 gives nearly symmetric radiation patterns with small cross-polarisation, Since increasing e, broadens only the E-plane pattern, the pattern symmetry deterioriates by increasing the substrate permit-
72
Analysis of circular microstrip antennas
Analysis of circular microstrip antennas
-180.00
-135.00
-SB.00
-45.08
0.00
45.00
90.00
135.00
73
180
Angle, degrees Fig. 2.1 2
Measured and computed data in H-plane of a circular patch excited with a coaxial probe (Reproduced from Reference 1 4 @ 1986 IEEE) E, = 2.54, g = 4.5crn, h = 0.159cm, f = 3.2GH,, feed at edge -measured . . . . computed
Fig. 2.1 4
E-plane radiation patterns of a circular patch with different substrate permittivities (Reproduced from Reference 14 Q 1986 IEEE)
Fig. 2.15
H-plane and cross-polarisation patterns of Fig 2.14 (Reproduced from Reference 1 4 @ 1986 IEEE)
Angle, degrees Fig. 2.13
Measuredandcomputed data in E-plane of the case in Fig. 2.12 (Reproducedfrom Reference 14 @ 1986 IEEE) ---measured. data same as Fig. 2.1 2 ' ' ' ' computed
74
Analysis of circular microstrip antennas
Analysis of circular microstrip antennas
75
tivity. This means the antenna cross-polarisation will increase, which is evident from the results presented in Fig. 2.15. Here, the cross-polarisations are computed in the 4 = 45" plane, where it has the maximum magnitude.
--
-32
1
-(rh,
-- ---( ---(
-40
-180
=2.3:4A a, pi) ( h . a . f ,) h, a, pi) h . a . p,)
-135
-90
,
( = ( = ( = ( =
0.02. 0.04. 0.06. 0.10.
-45
0.1806. 0.1732. 0.1675. 0.1590. 0
8 Fig. 2.1 6
,
0.045 0.044 0.041 0.039 45
)A )A )A )A
E-plane
90
11
135
' 9 Fig. 2.17
H-plane and cross-polarisation patterns of Fig. 2.16 (Reproduced from Reference 14 @ 1986 IEEE)
180
E-plane radiation patterns of a circular patch with different substrate heights (Reproduced from Reference 14 @ 1986 IEEE)
2.3.4 Eflect of the substrate thickness The bandwidth of microstrip antennas increases by increasing the substrate height. It is therefore desirable to study its effect on the radiation patterns. For the TM,, mode patch, representative results are shown in Figs. 2.16 and 2.17. For h < 0.061 the beamwidth of the H-plane patterns decreases slightly by increasing h, but increases to some degree in the E-plane. The relationship reverses for h > 0.06 1. Consequently, the cross-polarisation increases initially with h, but tends to decrease afterwards. Also, it is interesting to note that the effect of the substrate may resemble a thinner one with a higher substrate permittivity, which, from Fig. 2.14 may affect the E-plane patterns significantly. However, the results of Fig. 2.16 show otherwise, where E-plane patterns are relatively independent of h. This can be understood by considering the effect of these two parameters. A higher permittivity reduces the patch size and the extent of the fringing fields. Consequently, the radiation is due to a narrow magnetic current ring around the patch periphery, which normally gives asymmetric radiation patterns. A thicker substrate, on the other hand, does not reduce the patch size significantly, but extends the zone of the fringing fields, thus resulting in a broad radiation ring.
Fig. 2.1 8 E-plane radiation patterns of a circular patch with different ground plane diameter for the dominant TM,, mode (Reproduced from Reference 14 @ 1986 IEEE)
76
Analysis of circular rnicrostrip antennas
Analysis of circular rnicrostrip antennas
77
2.3.5 Efect of the ground-plane r a d i u ~ Since the ground plane controls the back radiation, its size has a pronounced effect on the patch radiation pattern. For the T M , , mode case, sample computed patterns are shown in Figs. 2.18 and 2.19. Again, cross-polarisation are computed in the 4 = 45" plane. In the H-plane, shown in Fig. 2.19, pattern beamwidth decreases by increasing the ground-plane size. Consequently, the infinite ground plane has the most rapid pattern roll-off. In the E-plane, on the other hand, the beamwidth decreases initially by increasing the ground-plane radius g, but increases for g > 0.71. The infinite ground plane gives the broadest beam, which approaches -6 dB a t the horizontal plane. The crosspolarisation therefore increases rapidly by increasing the ground-plane size from its optimum radius. These results show that the assumption of an infinite ground plane in approximate analysis of microstrip antennas will have a serious effect on the correct prediction of the radiation patterns, particularly for angular ranges beyond 45' off the main beam. The prediction of the cross-polarisation will, in fact, be an impossible task.
Fig. 2.20 E-plane radiation patterns of a circular patch with different ground-plane diameter for the dominant TM,, mode (Reproduced from Reference 1 4 @ 1986 IEEE)
Fig. 2.19 H-plane and cross-polarisation patterns of Fig. 2 . 7 8 (Reproduced from Reference 14 @ 1986 IEEE)
For a TM2, mode excitation the corresponding computed results are shown in Figs. 2.20 and 2.21. The effect of the ground-plane size on the radiation patterns is similar to the T M , , mode case. The beamwidth in the H-plane decreases progressively with the ground-plane size, and for the infinite ground plane the pattern roll-off is the largest. The angle for the peak radiation, which is around 45O off the z-axis, is, however, almost independent of the ground plane. The E-plane patterns also show similar behaviour to those of the T M , ,
Fig. 2.21 H-plane and cross-polarisation radiation patterns of Fig. 2.20 (Reproduced from Reference 14 @ 1986 IEEE)
78
Analysis of circular microstrip antennas
Analysis of circular microstrip antennas
mode, and their beamwidth initially decreases by increasing g, but increases for larger ground planes. For an infinite ground plane the pattern remains relatively constant beyond the peak of the pattern at about 45'. It is therefore evident that the assumption of an infinite ground plane will not provide a meaningful pattern shape for the TM,, mode, where the main feature of the patterns manifest itself beyond the 45'.
Fig. 2.23 H-plane radiation patterns of the cases in Fig. 2.22
Fig. 2.22 E-plane radiation patterns of TM,,. T M , , and TM,, modes of a circular patch a = 0.1806 1. g = 0.31, Q, = 0.051, t = 0.021, E, = 2.32,and the ground plane thickness is zero.
The above results indicate that, the radiation characteristics of various modes can easily be controlled by the ground-plane size. So far, the total patterns are shown. It may be desirable to examine the effect of the ground-plane radius on the mode-excitation efficiencies. To investigate this, the case of the TM,, mode patch is selected and the mode patterns are computed for two ground-plane radii of 0.31 and 0.42. This range of ground-plane radius gives the most symmetric co-polar patterns, with minimum cross-polarisations. The computed patterns for the 0.32 antenna are shown in Figs. 2.22 - 2.24. The E-plane patterns in Fig. 2.22 are all in the 4 = 0 plane. The H-plane patterns are, however, in the H-plane of each mode, being 4 = 90" and 4 = 45' for the TMII and TM2, modes, respectively. The corresponding results for the 0.41 ground plane are shown in Figs. 2.25 - 2.27. These results indicate that the small ground plane, with g = 0.31, all non-resonant modes are well below the
Fig. 2.24
Total radiation patterns of the case in Fig. 2.22 -E-plane
--- H-plane cross-polarisation.
79
80
Analysis of circular rnicrostrip antennas
Analysis of circular rnicrostrip antennas
81
dominant T M , , mode and their peak amplitudes are less than - 30 dB. Increasing the ground-plane radius to 0.41 increases the excitation of both TM,, and TM,, modes, and their peak amplitudes approach - 17 dB range. The generated cross-polarisation is therefore larger in magnitude and increases from the - 25 dB level of 0.31 ground plane to more than - 20 dB for the 0.41 case.
0 Fig. 2.25 E-plane radiation patterns of TM,,, TM,,, TM,, and TM,, modes of a circularpatch a = 0.18061.g = 0.41.p, = 0.051.t = 0.021.6, = 2.32,and the ground plane th~cknessis zero
Fig. 2.27
Totalradiation patterns of the case in Fig. 2.25 -E-plane
---
H-plane Cross-polarisation
Fig. 2.26
H-plane radiation patterns of the cases in Fig. 2.25
2.3.6 Effect of the ground-plane thickness The results of the previous Section indicate that the size of the ground plane affects the excitation efficiency of non-resonant modes. In some applications such as reflector feeds, the ground plane may not be infinitesimally thin but may have a finite thickness. Since the thickness of the ground plane affects the reflection coefficients of various modes, at its terminal edge, it may also affect their excitation efficiency. This is investigated here for the TM,, excitation of the patch and a ground-plane radius of 0.4 1.The results are shown in Figs. 2.28 2.30. Again, each of the modes of the patterns are generated in their respective E- and H-planes. The overall patterns for the co-polarisation are in the q5 = 0" and 90' planes, the principal planes of the TM,, mode and the cross-polarisation are in the 45" plane. Comparing these results with those in Figs. 2.25 - 2.27 for zero ground-plane thickness, one notes that increasing the thickness of the ground plane to 0.05 1has reduced the excitation efficiencies of the higher TM2, and TM,, modes. The excitation of the TM,, mode, on the other hand, has
82
Analysis of circular microstrip antennas
I
I
Analysis of circular microstrip antennas
83
remained the same. One therefore concludes that the thickness of the ground plane can also be used to modify the mode excitation. In other words, in designing microstrip antennas with small ground plane and for a high degree of mode purity, one must optimise not only the resonant patch size but also the size and thickness of the ground plane. This is, of course, valid for a given location of the excitation source, which in practice is determined by the impedance requirements. However, as shown earlier, the feed location has its own effect on the mode excitation and can be used as a parameter if warranted.
B Fig. 2.28 Same as Fig. 2.25 with the ground-plane thickness of 0 . 0 5 1
2.3.7 Circular polarisation Many techniques have been proposed in the literature to generate circular polarisation with a microstrip patch antenna. In most methods a geometrical deformation is used to generate both symmetric and asymmetric modes to cause a circularly polarised radiation. These methods are convenient to generate circular polarisation when only one sense of polarisation is needed, and can be implemented by a single feed. However, when a polarisation diversity is required, one must use two separate feed arrangements. In such a case, a symmetric patch with two separate feed points and an appropriate phase switch will be sufficient. Also, to generate circularly polarised radiations with a low axial ratio, one needs an antenna with a nearly symmetric radiation pattern. The results of previous anlaysis indicated that the pattern symmetry can be controlled by
84
Fig. 2.31
Analysis of circular microstrip antennas
Radiation patterns of a circular patch fed by two dipoles for circular polarisation a = 0.18061, g = 0.4i.. e, = 0.051, t = 0.021, E, = 2.32, and the ground plane thickness of 0.1 1 ----- E-plane - - - H-plane
Analysis of circular microstrip antennas
85
modifying the ground-plane size and thickness. To investigate the quality of the circularly polarised radiation we present a few computed results for circular patches, fed at two locations, with a 90' phase difference. The antenna selected is resonant at the TM,, mode and has a ground-plane radius of 0.41. The circularly polarised E, and E4 components, and their difference as the cross-polarisation, are shown in Fig. 2.31. These principalplane electric vectors represent the envelopes of measurement data with a rotating linearly polarised test antenna. The actual right- and left-handed circular polarisation vectors are shown in Fig. 2.32. The peak of the left-hand vector, which is the cross-polarisation, is below - 20 dB level in the upper half plane, which is the main region of concern. Its pattern shape is identical to the difference pattern of Fig. 2.31 and indicates a fairly good circular polarisation. The computed data for the case of 0.3 1ground plane of zero thickness or for the 0.41 ground plane of 0.05 2 thickness are not shown here. However, their results can easily be determined from the co-polar and cross-polar patterns already. . provided. Since they have lower non-resonant mode excitations with reduced levels of cross-polarisation, their generated circular polarisations will also be more superior. Thus, the foregoing results indicate that, by a proper selection of the feed-point location or the size or thickness of the ground plane, circularly polarised patch antennas with extremely low axial ratio can be designed. One only needs to optimise the antenna dimensions properly.
Cross-polarisation.
2.3.8 Effects of a central shorting pin
So far the computed results were presented for a standard circular patch geometry. The patch dimension is therefore selected to resonate at a particular mode. However, it is reported in the literature that, by using a central pin to short the upper patch to the ground plane, one may improve the purity of the resonant mode. The previous results show that this may not be the case. Since, with a finite ground-plane size and thickness, the mode excitation can easily be controlled by modifying their dimensions. An addition of a shorting pin acts as an extra parameter to control the mode excitation. For a given antenna dimension, one can readily find a pin radius that minimised the non-resonant mode excitations. This can be done easily with the current method, provided that the pin does not destroy the rotational symmetry of the configuration. Since the introduction of the pin increases the resonance size of the patch, perhaps the most important property of the pin is to control the antenna gain by increasing the patch size. This may be a useful parameter to use in the design of higher-gain patch antennas.
2.4 Application 2: Wrap-around microstrip antenna 6' Fig. 2.32
Co-polar and cross-polar circularly polarised radiation patterns of the example of Fig. 2.37
The wrap-around antenna refers to a microstrip-ring conformal antenna that is embedded in a missile or cylinder body. Its various configurations are con-
,
86
Analysis of circular microstrip antennas
Analysis of circular microstrip antennas
sidered in literature and investigated [I 51, [3]. Analytic solutions, using cylindrical Green's functions, can be obtained [I61 by assuming that the cylinder length is infinite, so that boundary conditions on its surface can be satisfied. In practice, however, the missile shape and the location of the antenna on the body influence
87
mode number. Thus, when a particular mode must be excited, the exciting source must eliminate others, which can be achieved by the axial symmetry of multiple source excitations. For each excited mode, the radiation patterns then depend on the shape of the cylindrical surface. In most practical applications the zero-order mode is used and the present study will provide the computed data for its radiation patterns.
-B
-
Fig. 2.34 Rad~at~on patterns of wrap-around antennas for the zero and 4th order modes. Zero mode - - - 4th mode W, = 1,/4, L, = 4 11, Wd = 0.61. L, = 0.1 A, a = 30', 6, = 2 32, a = 0.2571, t = 0.021
Fig. 2.33
Cross-section geometry of wrap around antenna for missile geometry
the antenna radiation patterns. The accurate determination of the radiation patterns must again be determined numerically. Since the configuration is rotationally symmetric, it can be analysed readily by the current method. In this section, the radiation patterns for some of useful geometrical shapes are computed. We have selected this antenna because of its complex shape. Although it is a microstrip antenna, the conducting patch and the ground plane, i.e. the cylinder, are not planar and the mode configuration are different. Here, the modes under the patch form the azimuthal modes of the cylindrical zone and their excitation is dependent on the cylinder radius. In practice, for a single exciting source all modes are present, but their magnitudes decrease with the
Fig. 2.33 shows the cross-section of the antenna geometry that is investigated. It consists of a conducting ring conformal to the cylinder surface and is supported by a dielectric substrate, which is embedded in the cylinder. The radius of the cylinder is selected to be a = 0.257 1,which represents that of a typical small rocket. The excitation is due to four dipoles at the lower edge of the ring, which are angularly separated by 90". Since the cylinder radius is small, the selection of four excitations ensures that the azimuthal pattern is omnidirectional. The azimuthal symmetry of the excitation means that only 4Kn modes are allowed to be excited, where K is an integer. All intermediate modes cancel out. To investigate the mode excitation we select a geometry and compute the radiation patterns of the first two modes, i.e. K = 0 and 4. The results are shown in Fig. 2.34, where the dominant mode is for K = 0, the zero-order mode. The next mode for K = 4 is weakly excited and its contribution is below - 30 dB range. The next higher mode for K = 8 is far too weak to be shown on the plot. These
88
Analysis of circular microstrip antennas
results indicate that, for the selected radius of the cylinder, only the zero-order mode has a significant value and all other modes can be neglected. Also, since E, is zero for the zero-order mode, all radiation patterns in this section will show the plots of the E,, component only. Here, we present the dependance of E, o n the antenna parameters. Fig. 2.35 shows the computed patterns when the radiating ring is located at the base of the cone, i.e. L,, = 0. The computed patterns show the effect of the cone angle o n the radiation patterns, where cc is the halfcone angle and cc = 90' refers to the geometry of a finite cylinder. Since the patterns are all similar, they are progressively shifted down by 4 dB to improve the clarity. The results show that, although the antenna is located at the upper end of the cylinder, the main beam is in the backward direction and the radiation towards the cone tip is small. Also, for the selected cone angles, the effect of the cone is not significant. In this example, the substrate permittivity is 2.32 and the width of the ring is 0.51,; i.e. one half wavelength in the substrate. Other dimensional parameters are shown o n the Figure.
Analysis of circular microstrip antennas
89
same. This means that the separation distances of the antenna from the cylinder ends can be used to control the radiation intensities in the forward and backward directions. In the above examples the width of the ring was selected to be one half wavelength in the substrate. The effects of ring width on the radiation patterns are shown in Fig. 2.37, where the ring widths are 0.51,, 0.41, and 0.251,, respectively. Reducing the ring size reduces the broadside radiation.
e Fig. 2.35 Radiation patterns of wrap-around antennas with different nose angle a -a= 90" --- a = 60" a = 45" . . . . a = 30"
L, = 4.1 i, Wd = 0 . 6 L L,
=
0.0. W,, = 1 d / 2 ,E, = 2.32, a = 0.2571
For G( = 30°, Fig. 2.36 shows the effects of moving the antenna away from the cone tip and changing the cylinder length, by retaining all other parameters constant. It is evident that increasing the separation from the cone base improves the forward radiation. Also reducing the antenna separation from the cylinder base reduces the back-lobe level. Otherwise, the pattern shape stays the
6 Fig. 2.36 Radiation patterns of wrap-around antennas with different tail lengths From up to down: L, = 5.1 1. L, = 3.1 1 and L, = 2.1 1, respectively. W, = 0.61, L, = 0.1 1. W, = 1,/2, E, = 2.32, a = 0,2571. a = 30"
Here, patterns are normalised by the main beam peaks. The quarter-wavelenth ring is a n end-fire antenna and radiates mainly in the back direction. The effect of the substrate permittivity is shown in Fig. 2.38, where the width of the ring is again0.5 1,. Increasing the permittivity rapidly reduces the broadside radia-
90
Analysis of circular microstrip antennas
tion. Finally, Fig. 2.39 shows the effects of moving the antenna towards the cylinder base. It indicates that, by increasing the antenna separation from the cone, the forward radiation increases.
Analysis of circular microstrip antennas
97
symmetric and radiates mainly near the broadside direction, but the beam peak is around 70'. Increasing the cylinder radius moves the beam peak initially towards 90' and then towards the back direction. The effect of the substrate thickness is also studied and shown in Fig. 2.42. Decreasing the substrate thickness moves the beam peak towards the broadside and improves its symmetry. The effect of the substrate permittivity is shown in Fig. 2.43. Larger permittivities broaden the radiation pattern, which is partly . . due to the reduction of the effective ring width.
Fig. 2.38 Radiation patterns of wrap-around antennas with different dielectric constants
-E,
--- E, . E , =
Fig. 2.37 Radiation patterns of wrap-around antennas with different patch widths -w, = 1,/2 --- W, = 0.4 1, W, = 1,/4 L, = 4.1 1, a = 30'. E, = 2.32. a = 0.2571, t = 0.021
To complete this study, the radiation characteristics of the ring antenna on a dielectric-coated cylinder with the antenna located symmetrically from two ends. Fig. 2.41 shows the effect of the cylinder radius on the patterns. The exciation is again due to four dipoles. For a small cylinder radius the pattern is
=
4
= 2.32
-10
Since the analytic solution of wrap-around antennas on infinite cylinders is known, it is useful to generate their numerical solutions as well for comparison. To handle the problem, the image theory of infinite cylinders is applied to modify the originual geometry. Fig. 2.44 shows the original and equivalent problems. In the originual problem a ring antenna, excited by four dipoles, is supported on a dielectric-coated infinite cylinder. Applying the image theory one can determine the image of dipoles and the conducting ring inside the cylinder. The equivalent problem, in the cross-section of the cylinder, thus has eight dipoles and additional central ring representing the image of the original ring inside the cylinder. The two rings are separated by the dielectric substrate and excited by eight dipoles. The numerical solution is obtained for the finite geometry, i.e. a truncated cylinder of height 0.61, and the corresponding radiation patterns are shown in Fig. 2.45 for different dielectric permittivities. The
92
Analysis of circular microstrip antennas
Analysis of circular microstrip antennas
computed results agree well with the published analytical data [16]. The radiation is in the broadside direction, for the selected ring width of 0.5 l,, and the pattern broadens by increasing the permittivity. These results show that the
Fig. 2.40 Geometry of a wrap-around antenna on a finite dielectric-coated cylinder
e Fig. 2.39 Radiation patterns of wrap-around antennas with different L, and L, From up to down (L, = 2.1 1, L, = 3.21). (L, = 1.1 1, L, = 4.1 1 ) and (L, L, = 5.1 1 ) . respectively W d = 0 . 6 1 ,W p = 1 , / 2 . ~ , = 2 . 3 2 , a = 0 . 2 5 7 1 , a = 3 0 '
=
0.1 1,
numerical method presented here can also be used to investigate infinite structures and the accuracy of the generated results is satisfactory. The usefulness of the method, however, is in handling finite geometries where analytic methods fail.
Fig. 2.41 Effect of the radius on the radiation patterns = 0,451 -a a = 0.351 --- a = 0.25L. w, = 1,/2, t = 0.021
93
94
Analysis of circular rnicrostrip antennas
e Fig. 2.42
Effect of coating thickness on the radiation patterns -t = 0.051 . . . . . t = 0.031 - - - t = 0.021
Analysis of circular microstrip antennas
Fig. 2.44 Geometry of wrap-aroundantenna of an infinite cylinder Left cross-section indicates the original problem with four dipoles for excitation; right is the cross-section using the image theory.
8 Fig. 2.43 Effect of dielectric constant on the radiation patterns -a, = 10 ---- E, = 4
a,
=
2.32
w, = &I2 a = 0,251,t = 0.021
95
Fig. 2.45
Effect of the dielectric constant on the radiation patterns
a, = 2.32 --- a, = 4.0 -8, = 10 a = 0.2571,t = 0.021
96
Analysis of circular rnicrostrip antennas
2.5 Application 3: Reflector antenna feeds In high-gain applications microstrip antennas may be used as feeds for ryflector antennas [I7 - 201. The merits of microstrip feeds, however, depend oq the type of application. In symmetric prime focus systems, the feed nomrally blocks the central region of the aperture and causes reductions in aperture Jiiciency and gain factor, raises the sidelobe levels and causes undesirable diffraction effects. The rise of the antenna sidelobes also increases the antenna ~ o i s etemperature. Because the size of the feed depends on the operating frequc .,y and the reflector f / D , where f and D are the reflector focal length and diameter, the aperature blockage is most severe in small paraboloid reflectors. A larger feed blocks a larger portion of the reflector central region and also requires heavier support structures. The latter further blocks the aperture, reducing the reflector performance and limiting the cross-polarisation performance. A microstrip feed is normally smaller and reduces the central blockage and its subsequent degrading effects. Furthermore, it is low cost and light weight. which reduces the complexity of the supporting structure, and can be integrated readily with its associated electronics. The simplicity of microstrip elements also offers additional features with other reflector configurations. In offset paraboloids and dual reflector systems a small array can be used to control the reflector illumination and provides a limited scan capability with reduced sidelobes and coma lobe difficulties. Such arrays can also be used in non-paraboloidal reflectors, such as spherical reflectors, to improve the aperture efficiency and reduce the abberation. Their main advantage, however, is in the reduction of the system complexity. Microstrip feed arrays can be integrated readily with their associated circuitry and electronics, such as the power dividers, phase shifters and amplifiers. Here, we will only address the design approach and determine the performance levels for wideangle feeds that are used with symmetric paraboloids. The array designs and their associated problems are beyond the scope of this Chapter and are discussed in subsequent Chapters. In symmetric paraboloid reflectors the system performance is controlled primarily by the feed [21, 221. A desirable feed must illuminate the reflector efficiently and cause small spillover. This means that the feed pattern must be broad within the cone of the reflector and roll off rapidly thereafter. It should also have negligible back radiation. The shape of the feed pattern controls the reflector efficiency, but with a symmetric system does not affect the reflector cross-polarisation. Thus, for low cross-polarisation the feed must also have a good polarisation property. From Ludwig's third definition, for minimum cross-polarisation. the feed pattern must be symmetric and have a unique phase centre [23]. A circular patch antenna is a good candidate as a feed for a symmetric reflector. Its pattern shape can be controlled readily by the size and thickness of the ground plane. Fortunately, symmetric patterns are achievable with small
Analysis of circular microstrip antennas
97
ground planes, which reduces the blockage. There are, however, a few problems to be overcome. The back radiation of a microstrip antenna with a small ground plane is high and its bandwidth is normally narrow. The level of the back radiation can be reduced by incorporating peripheral chokes. Generally, adding a single quarter-wavelength choke on the periphery of a waveguide feed reduces its back radiation by about 10 dB [24]. Such a reduction of the back radiation in microstrip antennas is also expected. Additional chokes can further reduce the back-lobe level, but at the expense of increased aperture blockage. In microstrip feeds one should select one or perhaps two chockes, since a large number of chokes will increase the feed size. Microstrip antennas are small in size and peripheral chokes will increase their relative size considerably, thus eliminating one of their main advantages. The limitation in the microstrip antenna band-width can also be overcome by using any of the many methods which are avaiable in literature. However, broadening the bandwidth should not affect the pattern symmetry and shape.
8 Fig. 2.46 Radiation patterns of a circular rnicrostrip patch, covered by a dielectric thickness ofO.11 a = 0.171. g = 0.41, Q, = 0.17 1 and E, = 2.32 -E-plane --- H-plane - .- .- Cross-~ o l a r
Here, we present a design example. The previous results for a circular microstrip patch indicated that the ground-plane size and thickness can be used as parameters to equalize the E- and H-plane patterns. It was also shown that, for a ground plane radius around 0.4 1, the pattern symmetry is satisfactory. This
98
Analysis of circular microstrip antennas
Analysis of circular microstrip antennas
99
A
m
a
-180
e Fig. 2.47
Radiation patterns of a circular parch covered by a dielectric g = 0.31,other data same as Fig. 2.46 -E-plane --- H-plane Cross-polar
-135
-90
-45
0
45
BO
135
180
B Fig. 2.49
Radiation patterns of a covered circular patch with a conducting collar g = 0.31; other data same as Fig. 2.48 -E-plane --- H-plane Cross-polar
8 Fig. 2.48
Radiation patterns of a covered circular patch with a conducting collar Data same as Fig. 2.46 -E-plane --- H-plane Cross-polar
Fig. 2.50 Radiation patterns of a two-layer stacked rnicrostr~p(Reproduced from Reference 20 @ 1986 IEEE Diameters: 0.321.(up); 0,341(bottom; g = 0.4A)
100
Analysis of circular microstrip antennas
Analysis of circular microstrip antennas
results in a feed of diameter less than one wavelenth, which is considerably smaller than commonly used waveguide feeds with chokes. To retain the geometrical symmetry and to increase the bandwidth one may use a stacked patch configuration [25]. This means the resonant patch will be covered by another dielectric-substrate which will alter its resonance frequency and the radiation pattern. To investigate the latter we have shown the radiation patterns of the new structure for ground-plane radii of 0.4 and 0.3 i in Figs. 2.46 and 2.47. The symmetry of the patterns is satisfactory, but not perfect. To improve the geometrical rigidity we then incorporate a peripheral collar around the substrate and compute the new radiation patterns. They are shown in Figs. 2.48 and 2.49 for the previous configurations. The addition of the collar limits the radiation from the substrate termination and considerably improves the pattern symmetry. The cross-polarisation is thus improved. Finally, we add the upper patch to the configuration. The radiation patterns of the final design are shown in Figs. 2.50 and 2.51, respectively for 0.4 /1 and 0.3 1 ground planes. It is interest-
707
the ground-plane radius is 0.42 and compute the cross-polarisation of different modes. Fig. 2.52 shows the contribution of the first four modes,to the crosspolarisation. As expected, the TM,, and TM,, modes have the main contributions. However, since they have different azimuthal dependenmces their combined cross-polarisation is asymmetric. Note that the feed cross-polarisation is maximum in the 4 = 45" plane and all presented data are in this plane. Fig. 2.52 also shows that adding the contribution of the higher-order modes reduces the cross-polarisation of the TM,, and TM,, modes. The overall cross-polarisation is high at about - 24 dB, but within the small angular region of + 45" is below the - 30 dB range.
-56
-90
-45
0
45
90
0 Fig. 2.52 Effect of different modes on the cross-polarisation of antenna in Fig. 2.48. (Reproduced from Reference 20 @ 1986 IEEE) . . . TM, + TM,,
.
0 Fig. 2.51
Radiation patterns of a two-layer stacked microstrip (Reproduced from Reference 20 @ 1986 IEEE) g = 0.31;other data same as Fig. 2.50 -E-plane H-plane
---
Cross-polar
ing to note that the pattern characteristics remain unchanged and excellent pattern symmetries are found for both antenna geometries. The cross-polarisations for both cases are below - 24 dB, but the back radiations are high. The latter will be reduced later by incorporating chokes. For the present, we investigate the sources of the cross-polarisation. We select the case of Fig. 2.48 where
TMo, + TM,, + TM,, ---- TMol + TMl, TM,, + TM,,.
To reduce the back radiation we have used two different choke configurations. In Figs. 2.53 and 2.54 the antennas of Figs. 2.50 and 2.51 are incorporated with a choke behind the ground plane. Their pattern characteristics in the forward directions remain unchanged, but the back radiation decreases to around - 24 dB. This type of choke geometry is not as efficient as the peripheral chokes in reducing the back radiation, but does not increase the feed diameter. The results with a peripheral choke are shown in Fig. 2.55, where the back radiation decreases to about - 30 dB range. Adding a second choke behind the ground plane reduces the back lobe by an additional 2 dB. A second peripheral
102
Analysis of circular rnicrostrip antennas
Analysis of circular rnicrostrip antennas
-40 -180
-135
-90
0 Fig. 2.53 Radiation patterns of antenna in Fig. 2.51 with a 214 back choke (Reproduced for Reference 20 @ 7986 IEEE) -E-plane --- H-plane
Cross-polar
0
45
90
135
A
ID0
0 Fig. 2.55
Cross-~olar
Fig. 2.54 Radiation patterns of antenna in Fig. 2.50 with a 114 back choke (Reproduced for Reference 2 0 @ 7986 IEEE) --- E-plane --- H-plane
-45
103
Radiation patterns of antenna in Fig. 2.50 with a 114 side choke (Reproduced from Reference 2 0 @ 7986 IEEEJ -E-plane - - - H-plane Cross-polar
9 (degrees) Fig. 2.56
Measured patterns of feed shown in Fig. 2.55 -E-plane --- H-plane Cross-polarisation at 45" plane
104
Analysis of circular microstrip antennas
Analysis of circular microstrip antennas I
choke can also be incorporated, but may not be necessary since the back lobe is already low and a new choke will enlarge the feed size. The feed with the peripheral choke was also fabricated and tested. Its measured E- and H-plane patterns, as well as the cross-polarisation in the 4 = 45" plane shown in Fig. 2.56, which are at the band centre frequency of 4.6GHz. The principal plane patterns agree with the computed data, but the cross-polarisation is higher. The measured peak cross-polarisation is about - 21 dB, which is about 7 dB higher than the computed one. It also shows a central peak at the boresight, which indicates the misalignment of the test set up. Also, within a bandwidth of 500 MHz, i.e. 11%, the co-polar patterns remained nearly symmetric. We expect that, by improving the fabrication tolerances and a proper alignment of the test range the measured cross-polarisation should approach the computed ones. The return loss of the feed was also measured and is shown in Table 2.1. Further improvement of these return losses can be achieved by modifying the feed-point location.
Table 2.2a Feed characteristics at the resonant frequency f, Case of Fig.
Peak cross-pol. 0 < 0 < 900 (dB)
Gain (dB)
Beamwidths., dee '2
3 dB
10 dB
Table 2.1 Mearurpd return lower o f l e e d ~ Feed 2, Fig. 2.55
Feed 1, Fig. 2.51 Frequency, GHz
Return loss, dB
Frequency, GHz
Return loss, dB
4.10 4.15 4.20 4.25 4.30 4.35 4.40 4.45 4.50 4.55 4.60
9.5 11.0 13.0 14.0 17.0 18.0 16.0 15.5 14.0 11.0 9.0
4.30 4.35 4.40 4.45 4.50 4.55 4 60 4.65 4.70 4.75 4.80
10.0 11.0 11.5 12.0 12.5 12.5 12.5 12.5 12.0 11.5 10.0
Table 2.2 summarises the performance of the above antennas, where the beamwidths at 3 dB and 10 dB levels, as well as the peak cross-polarisation, are provided. To evaluate the performance of these feeds on a reflector antenna the data on the gain factor, spill-over efficiency and the corresponding aperture angles must be known. They are calculated and shown in Table 2.3. It shows that the aperture angle varies from 60" to 71° and the gain factor rises from 72.5% to 74.24%. The feed performance is therefore reasonable. The computed gain factors are somewhat smaller than those of waveguide feeds with a corrugated flange. However, their aperture blockage is small owing to their small size. Thus, when used on small reflectors, they should provide comparable performance. These microstrip feeds are, on the other hand, light weight and easy to fabricate and can readily be integrated with receiving electronics.
Table 2.2b Data of Table 2.2 at f = 1.05f, Case of
Peak cross-pol.
Gain
Beamwidths. deg
Table 2 . 2 ~Data of Table 2.2 at f = 0.95f, Case of Fig.
Peak cross-pol. 0 < 0 < 90' (dB)
Gain (dB)
Beamwidths, den3 dB
10 dB
105
106
Analysis of circular microstrip antennas
Analysis of circular microstrip antennas
Table 2.3 also shows the location of the phase centre of each antenna calculated over its aperture angle, given in column 2 [26]. Their location is measured from the ground plane, i.e. z = 0, and are all positive, indicating that the phase centres are above the ground plane. However, it is interesting to compare
Table 2.3a Reflector aperture angles, gain factors, spill-over eficiencies and phase-centre locations above the ground plane for various feeds, f = f , Case of Fig. Aperture angle, Gain factor, Spill-over efficiency,phase centre, O h Yo I deg 2.46 68 72.93 85.43 0.075 2.47 71 73.85 86.70 0.0675 2.48 66 73.14 85.23 0.1 127 2.49 71 73.37 85.50 0.1167 2.50 66 72.86 84.16 0.1202 2.51 71 73.47 85.48 0.1212 24 66 74.29 86.24 0 1186 2.55 60 73.83 84.67 0.1827
Table 2.3b Data of Table 2.3 a t f = 1.05f, Case of Fig. Aperture angle, Gain factor, Spill-over efficiency, phase centre, deg Yo % I 2.46 67 72.1 84.9 0.08 2.47 71 73.9 88.1 0.09 2.48 67 72.3 86.6 0.144 2.49 71 73.50 85.5 0.121 2.54 71 73.0 87.0 0.142 2.55 60 73.83 84.67 0.174
Table 2 . 3 ~Data of Table 2.3 at f = 0.95 f, Case of Fig. Aperture angle, Gain factor, Spill-over efficiency, phase centre, % % I deg 2.46 69 73.2 85.8 0.065 2.47 71 74.1 86.2 0.068 2.48 68 73.34 87.1 0.085 2.49 71 73.53 85.6 0.071 2.54 66 74.34 86.8 0.1 14 2.55 66 71.2 83.9 0.416 the cases of Figs. 2.46 and 2.47 with the remaining ones, which have the peripheral conducting collar. In the former cases the phase-centre location is just above the ground plane. Since the total thickness of the dielectric is 0.1 1,
707
the phase centres are inside the dielectric and under the lower patch. In the remaining cases, all phase centres are outside the dielectric. From these results the following important conclusion can be drawn: In microstrip antennas, in Figs. 2.46 and 2.47, the radiation is mostly from the aperture between the patch and the ground plane. Incorporating the side collar raises the radiation zone to the periphery around the upper patch. The performance of the above antennas listed in Tables 2.2a and 2.3a is also studied as a function of frequency. Within 5% frequency variation the computed results are shown in Tables 2.26, 2 . 2 ~ and 2.36,2.3c. An examination of these results reveals that the feed performance remains relatively constant within the band, in the magnitude of the peak cross-polarisation and the reflector gain factor. The feed gain, however, decreases to some degree, regardless of increasing or decreasing the frequency. This is primarily due to the increased excitation of the modes adjacent to the TM,, mode.
2.6 Concluding remarks
In this Chapter a general numerical method has been presented that enables one to solve antenna problems involving conductors and dielectrics. While the formulation is applicable to arbitrary antenna shapes, the matrix formulation was provided only for axisymmetric configurations. The method was then used to investigate the radiation properties of three distinctly different antenna types. The circular microstrip patch antenna was selected to study the radiation mechanism of a typical microstrip antenna element. The wraparound antenna was chosen to show that the method can be used to design or analyse complex antenna candidates. The last example, i.e. the reflector feed, was included to show the design steps involving high-precision antennas, with stringent amplitude and phase-pattern requirements. The circular patch antenna was studied in some detail to show the effect of various material and dimensional parameters on its radiation patterns. For instance, the results showed that the ground-plane size has a significant influence on the radiation patterns beyond 45' off the symmetric axis. In addition, it was shown that, by selecting an appropriate ground-plane size, nearly symmetric radiation pattern with very low cross-polarisation can be obtained. On the other hand, the feed-point location was shown to influence the excitation of nonresonant modes, which also contribute to the cross-polarisation. The information provided in this Chapter is intended to help the reader in understanding the radiation mechanism of microstrip antennas and use of various parameters to control them. While the results are computed for circular patch antennas, they can also be used for square-patch configurations, and with judicious qualifications, for other patch geometries as well. Also, the results are valid only for single, i.e. isolated microstrip antennas. When antenna elements in a practical array environment are considered, their radiation characteristics will be affected
708
Analysis of circular microstrip antennas
by their mutual coupling and the element location within the array. The main effect of the mutual coupling will manifest itself in the mode excitation, which is considered in a later chapter. The element location within the array affects its ground-plane size, and thus its radiation patterns. For large arrays the ground plane is large and its effect can be neglected. For small arrays the peripheral elements will 'see' a smaller ground plane than the central ones and their radiation patterns will be affected accordingly. However, the ground-plane effect in array applications becomes significant mainly in phased arrays, where the beam must be scanned for low elevation angles.
2.7 References I 2 3 4 5 6 7 8 9
10 11
12
13 14
15 16
17
JAMES, J.R.. HALL, P.S., and WOOD, C.: 'Microstrip antenna, theory and design' (Peter Peregrinus, 1981) BAHL, I.J., and BHARTIA, P.: 'Microstr~pantennas' (Artech House, 1980. Dedham, Mass.) JOHNSON. R.C., and JASIK, H. (Eds.): 'Antenna engineering handbook' (McGraw-Hill, NY, 1984) 2nd edn., chap. 7 HUANG, J.: 'Finite ground plane effect on microstrip antenna radiation patterns,' IEEE Trans., 1983, AP-31, 649-653 LIER, E.: 'Rectangular microstrip patch antennas.' Ph.D. Dissertation, University of Trondheim, Norway, June 1982 MAUTZ, J.R., and Harnngton, R.F.: 'Boundary formulation for aperture coupling problem,' Archivfur Elekronik & Ubertrangungstechnik, 1980, 34, pp. 377-384 MEDGYESI-MITSCHANG, L.N., and PUTNAM, J.M.: 'Electromagnetic scattering from axially inhomogeneous bodies of revolution,' IEEE Trans., 1984, AP-32, pp. 797-806 HARRINGTON, R.F.: 'Time harmonic electromagnetic fields' (McGraw-Hill, NY, 1961) Sec. 3-5 MAUTZ, J.R., and HARRINGTON, R.F.: 'H-field, E-field and combined field solutions for conducting bodies of revolution,' Archiv fur Elekrronik & ubertragungstecltnik, 1978, 32, pp. 175-164 MAUTZ, J.R., and HARRINGTON, R.F.: 'Electromagnetic scattering from a homogeneous material body of revolution, Archiv fur Elektronik & Ubertragungstechnik, 1979,33, pp. 71-80 ISKANDER, K.A., SHAFAI, L., FRADSEN, A., and HANSEN, J.E.: 'Application of impedance boundary conditions to numerical solution of corrugated circular horns,' IEEE trans., 1982, AP-30, pp. 366-372 KISHK, A.A.: 'Different integral equations for numerical solution of problems involving conducting or dielectric objects and their combination.' Ph.D., Dissertation, University of Manitoba, Winnipeg, Canada, I986 YAGHJIAN, A.D.: 'Augmented electric and magnetic-field integral equations,' Radio Science, 1981, 16, pp. 987-1001 KISHK, A.A., and SHAFAI, L.: 'The effect of various parameters of circular microstrip antennas on their radiation efficiency and the mode excitation,' IEEE Trans., 1986 AP-34, pp. 969-977 MUNSON, R.E.: 'Conformal microstrip antennas and microstrip phase arrays,' IEEE Trans., 1974. AP-22, pp. 74-78 FONSECA, S.B.A., and GIAROLA, A.J.: 'Pattern coverage of microstrip wraparound antennas.' Int. Conf. on Antennas and Propag., ICAP 83, Norwich, England, P. 1, 1983, pp. 300-304 KERR, J.L.: 'Microstrip antenna developments,' Proc. Workshop on Prmted Circuit Antenna Technology, New Mexico State University, USA, Oct. 1979, pp. 3.1-3.20
Analysis of circular microstrip antennas
709
18 HALL, P.S., and PRIOR, C.J.: 'Wide bandwidth microstrip reflector feed element.' 15th European Microwave Conference, Paris, 1985, pp. 1029-1044 19 PRIOR, C.J., and HALL, P.S.: 'Microstrip disc antenna with short circuit annular ring,' Electron. Lett. 1985, 21, pp. 719-721 20 KISHK, A.A., and SHAFAI, L.: 'Radiation characteristics of a circular microstrip feed,' Conference on Antennas and Comm., Montech 86, Montreal, Canada, 1986, pp. 89-92 21 CLARRICOATS, P.J.B., and OLVER, A.D.: 'Corrugated horns for microwave antennas.' IEE Electromagnetic Wave Series 18 (Peter Peregrinus, 1984) 22 RUDGE, A.W., MILNE, K., OLVER, A.D., and KNIGHT, P., (Eds.): 'The hand-book of antenna design' Vol. 1. IEE Electromagnetic Wave Series 15 (Peter Peregrinus, 1982) 23 LUDWIG, A.C.: 'The definition of cross-polarisation,' IEEE Trans., 1973, AP-21, pp. 116119 24 SHAFAI, L., and KISHK, A.A.: 'Coaxial waveguides as primary feeds for reflector antennas and their comparison with circular waveguides,' Archiv Fur EIektronik & Ubertragungstchnik, 1985, 39, pp. 8-15 25 OLTMAN, H.G.: 'Electromagnetically coupled microstrip dipole antenna,' IEEE Trans., 1986, AP-34, pp. 467-50 26 SHAFAI, L., and KISHK, A.A.: 'Phase centre of small primary feeds and its effect on the feed performance,' IEE Proc., 1985, 132, pp. 207-214
Chapter 3
Characteristics of microstrip patch antennas and some methods of improving frequency agility and bandwidth K.F. Lee and J.S. Dahele
3.1 Introduction
The develuptnerit of microstrip antennas arose from the idea of utilising printedcircuit technology not only for the circuit components and transmission lines but also for the radiating elements of an electronic system. The basic geometry of a microstrip patch antenna (MPA) is shown in Fig. 3.1. A conducting patch is printed on the top of a grounded substrate. The shape of the patch can in principle be arbitrary. In practice, the rectangular, the circular, the equitriangular and the annular ring are common shapes. The feed can be either a coaxial cable (Fig. 3.la) or a strip line (Fig. 3.lb), which guides the electromagnetic energy from the source to the region under the patch. Some of this energy crosses the boundary of the patch and radiates into space. The MPA is a relatively new form of radiator. In addition to compatibility with integratedcircuit technology, it offers other advantages such as thin profile, light weight, low cost and conformability to a shaped surface. The main disadvantage is its inherent narrow bandwidth (typically a few percent) arising from the fact that the region under the patch is basically a resonant cavity with a high quality factor. The MPA was first proposed by Deschamps in 1953 [I]. However, it was only in the past 15 years or so that extensive research was devoted to this type of antennas. This was motivated by the advantages mentioned above, which make the microstrip antenna an attractive candidate for use in high-speed moving vehicles such as aircraft, missiles, rockets and communication satellites. By 1981, two textbooks [2, 31 and a special journal issue [4] containing two review articles [ 5 , 61 were devoted to the subject. A wealth of information is now available about the microstrip patch antenna as a radiating element, primarily for the case when the substrate thickness is much smaller than a wavelength. This Chapter attempts to present some of this information, including some developments since 1981. The plan of the Chapter is as follows. In Section 3.2, the cavity model method of analysing MPAs is described. The basic characteristics of common patch
7 72
I
i
Characteristics of microstrip patch antennas
shapes are presented in Section 3.3. Some methods of improving frequency agility and bandwidth are discussed in Section 3.4. Section 3.5 contains concluding remarks. i
3.2.1 Introducrion Let us consider the basic geometry of a microstrip patch antenna shown in Fig. 3.1, where the z-axis is perpendicular to the plane of the patch. Electromagnetic waves are first guided along the coaxial or stripline and then spread out under the patch. When they reach the boundary of the patch, some are reflected and some radiate into open space. There are two lines of approach to deduce the radiation fields. One is to find the current distributions along the antenna structure and then obtain the radiation fields from these current sources. The other is to find the fields at the exit region. These fields act as equivalent sources, from which the radiation fields are obtained.
I
-
113
results accurate enough for many engineering purposes. Our discussion will be restricted to the thin-substrate case. At the time of writing, the extension of the model to thick substrates is still in the early stage of exploration.
3.2 Cavity model for analysing microstrip patch antennas
A
Characteristics of microstrip patch antennas
I
3.2.2 Feed modelling, resonant frequencies and internal fields The simplicity of the cavity model can be traced to the assumption that the thickness of the substrate is much less than a wavelength, i.e. t < A. The following observations then follow from this assumption:
(i) The electric field E has only the z component and the magnetic field H has only the transverse components in the region bounded by the conducting patch and the ground plane. (ii) The fields in the aforementioned region do not vary with z. (iii) Since the electric current in the microstrip must not have a component normal to the edge, it follows from Maxwell's equations that the tangential component of H along the edge is negligible. As a result of (i)-(iii), the region between the patch and the ground plane can be considered as a cavity bounded by electric walls on the top and bottom, and by a magnetic wall on the side. The fact that assumption (i) does not hold near the edge because of the existence of fringing fields is taken into account by extending the edge slightly. This model has long been used in the analysis of microstrip resonators. However, the application to microstrip patch antenna appears to be due to Lo et al. (71, Richards e t al. [8] and Derneryd [9, 101. Writing Maxwell's equations for the region under the patch, we have
conductma
ground biane feed
a Fig. 3.1
Microstrip patch antenna with (a) coaxial feed and (b) stripline feed
Under the two approaches mentioned above, a number of methods of analysis have been developed. The main ones are the transmission-line model, the cavity model and the integral equation method. The transmission-line model in its original form is limited to rectangular or square patches; however, extension to other shapes is possible. The integral-equation method is perhaps the most general: it can treat arbitrary patch shapes as well as thick substrates. However, it requires considerable computational effort and provides little physical insight. Both the transmission-line model and the integral-equation method are treated elsewhere in this Handbook. In this section, we shall introduce the cavity model. Most of the results obtained using this model are for electrically thin substrates. For this case, the cavity model offers both simplicity and physical insight. It also appears to yield I
E in eqns. 3.2 and 3.3 is the permittivity of the substrate, the permeabtlity of whlch is assumed to be p,. The current density J in eqn. 3.2 is due to the feed, which is usually in the form of a coaxial cable or a stripline. The advantages of the coaxial feed are that the desired impedance characteristic can be obtained by proper location of the Inner conductor (see Section 3.3) and that the cable can be placed under the ground plane to minimise coupling between the feed and the antenna patch. The disadvantage is that the structure is not completely monolithic and becomes more difficult to produce. This advantage is avoided in a stripline feed, which, however, introduces some radiation of its own and offers less flexibility in obtainmg the proper impedance. Usually, a quarter-wave line with a proper characteristic impedance 1s necessary to transform the antenna impedance to that of the stripline. It is appropriate at this point to discuss the modelling of a feed current which
174
Characteristics of microstrip patch antennas
has been used in the development of the cavity model. Consider first a coaxialline feed. It can be represented by a cylindrical band of electric current flowing from the ground plane to the patch, plus an annular ring of magnetic current at the coaxial opening in the ground plane [ l 11. The latter can be neglected with little error, and the former can be idealised by assuming that it is equivalent to a uniform current of some effective angular width 2w, centered on the feed axis. For example, for a circular patch fed at a distance d from the centre, it is illustrated in Fig. 3.2 and described by
I
1
Characteristics of microstrip patch antennas
115
be modelled by a :-directed equivalent current source of some effective width 2w. For the circular patch, it is of the same form as eqn. 3.5 except that d is replaced by the patch radius a. In both the coaxial and the stripline feed, the z-directed current is assumed to be independent of z on account of the thinness of the dielectric region. Hence V .J = -jwe = 0 and eqn. 3.3 reduces to V.E = 0
(3.7)
From eqns. 3.1, 3.2, 3.7 and 3.4, we obtain where is the wavenumber in the dielectric. The electric-wall conwhere k , = dition is automatically satisfied since E = Ezfwhile the magnetic-wall condition implies that
on the sides of the cavity. To solve eqn. 3.8 subject to the boundary conditions, we first find the eigen functions of the homogeneous wave equation
I
subject to the same boundary conditions. Let the eigen functions of eqn. 3.10 be $I,, and the eigen values of k , be km,. Assuming the eigen functions to be orthogonal, the solution to eqn. 3.8 is
where
, Fig. 3.2
Modelling of a coaxial feed by a current ribbon for a circular patch
The effective angular width 2w is a parameter chosen so that good agreement between the theoretical and experimental impedances is obtained. Usually, the arc length 2wd is several times the physical dimension of the inner conductor. If the feed is a stripline, it can be replaced by an equivalent current source obtainable from the transverse fields in the plane where the stripline connects the patch [12]. From uniqueness concepts, only the tangential magnetic field H backed by a perfect magnetic conductor is needed. Hence the stripline feed can
* denotes complex conjugate and
In eqns. 3.12 and 3.13, integration is over the domain of the patch. The resonant frequencies are obtained from setting k: - k i n = 0 and are given by
fmn =
kmn/2dZ.
(3.14)
3.2.3 Radiation field To calculate the radiation field, consider a closed surface S shown in Fig. 3.3. The top face of S lies just outside the patch and the bottom face lies just outside the ground plane. The vertical face of S coincides with the magnetic wall of the
7 76
Characteristics of microstrip patch antennas
cavity. The fields exterior to S c a n be calculated from the equivalent sources on Sand their images; the latter is necessary to account for the ground plane, which is assumed to be infinite in extent for the purpose of analysis. Since the tangential electric fields on the top and bottom faces, as well as the tangential magnetic field on the vertical surface, are zero, the only contribution to the equivalent sources are the tangential electric field E, on the vertical surface of the cavity. Together with its image, the total equivalent magnetic current is
Characteristics of microstrip patch antennas
1
1
7 17
given by Wood [I41 is more quantitative: t / l o < 0.07 for E, = 2.3 and t / l o < 0.023 for E, = 10 if the antenna is to launch no more than 25% of the total radiated power as surface waves. More recent work by Fonseca et al. [I51 showed that the size of the patch is also a parameter. For simplicity, we shall use Wood's criterion and assume that it is satisfied in subsequent discussions. The dielectric loss P, and the conductor loss P, are calculated from the electric field under the cavlty, while the radiation loss P, is calculated from the far-zone electromagnetic field. They are given by
where ri is the unit outward normal.
P, =
gro;nd
1
lo loIEI2 ? sin OdO d 9 2n
n
The quantity 6 In eqn. 3.20 is the loss tangent of the dielectric and R, in eqn. 3.21 is the surface resistivity of the conductors. The radiation or antenna efficiency is the ratio of radiated power to input power:
plane
coax feed
Fig. 3.3 Application of the equivalence principle to calculafe the radiation from a microstrip patch antenna
If the substrate thickness t is much less than the wavelength 1,its effect on the radiation field is small and M can be assumed to radiate in free space. Using the free-space Green's function, the electric potential F a t a point r is given by
In calculating the losses, it is usual to make use of the resonance approx~mation [8].This arises from the observation that, if the frequency is close to the resonant frequency of a particular mode, the factor l/(k: - k i n )in eqn. 3.11 is very large and the contribution to Ez, and hence to the radiation field E, is due mainly to the resonant-mode term. The electric energy stored at resonance is
where integration is over the perimeter of the patch. The fields in the far-zone are given by
and the total stored energy at resonance is
H(r) =
-joF(r)
E d r ) = IoHd(r) =
where
io=
The effective loss tangent of the cavity, taking into account the three losses P,, PCand P,, is given by
- IoHdr)
a.
8,
3.2.4 Losses in the cavity The losses in the cavity under the patch comprise dielectric loss P,, conductor loss PC,radiation loss P, and surface-wave loss James et al. [I31 estimated that surface-wave excitation is not important if t / & < 0.09 for E , = 2.3 and t/& < 0.03 for E , 10, where lois the free-space wavelength. The criterion
-
e,,..
= P T / ( ~ ~ T )
(3.26)
where PT = Pd
+ PC + P,.
(3.27)
A number of quality Q factors are defined as follows: Dielectric Q: Q, = o WT/Pd = 116
(3.28)
118
Characteristics of microstrip patch antennas
Characteristics of microstrip patch antennas
Conductor Q: Q,
=
wW,/P,
Radiation Q: Q,
=
w WT/P,
(3.30)
=
wWT/P, = 1/6,8
(3.31)
Total Q: QT
=
e
t
(3.29)
In eqn. 3.29, a is the conductivity of the patch and the ground plane. 3.2.5 Input impedance The input impedance at the feed of the antenna is given by Z = R
+ jX
=
V/I
=
E,t/I
119
specific standard. In the case of the microstrip patch antenna which is basically a strongly resonant device, it is usually the variation of impedance, rather than pattern, which limits the standard of performance. If the antenna impedance is matched to the transmission line at resonance, the mismatch off resonance is related to the VSWR. The value of VSWR which can be tolerated then defines the bandwidth of the antenna. If this value is to be less than S, the usable bandwidth of the antenna is related to the total Q-factor by [I I] Bandwidth (BW)
(3.32)
-
=
%
(s 2
1)
QT$
where E, is the average value of the electric field at the feed point and I is the total current. For example, if the feed is modelled by eqn. 3.5, we have
and I = -J(2wd)
(3.34)
Unlike the calculations of 6@, it was found that non-resonant modes must be included in the calculation of input impedance if good agreement between theory and experiment was to be obtained. The appropriate equation for EZis therefore eqn. 3.1 1, which contains the factor I/(k: - kin). To keep this term finite at resonance, the permittivity of the dielectric must be considered complex. If only the dielectric loss is considered, we have E
k:
=
E ~ E , (I j6)
= a 2 & & = k$z,(1 - js),
(3.35) (3.36)
However, Richards et al. [16] found that better agreement with experiment was obtained if, instead of the loss tangent of the dielectric, the effective loss tangent is used. Thus, in calculating the input impedance, eqn. 3.1 1 is modified to read
Fig. 3.4
Typical impedance characteristics around the resonant frequency of a mode
For S = 2, which is a common standard, the above equation reduces to
where
A typical impedance versus frequency curve is illustrated in Fig. 3.4. There is usually some reactance at the resonant frequency of a mode due to the contributions from the non-resonant modes. 3.2.6 VSWR bandwidth The bandwidth of an antenna is the range of frequencies within which the performance of the antenna, with respect to some characteristic, conforms to a
While eqn. 3.39 is the most commonly used definition for bandwidth and is the one we use in this Chapter, it should be pointed out that this is not a universal definition. For example, some authors define the bandwidth as l/Q,. 3.2.7 Qualitative description of the results predicted by the model
In Section 3.3, the equations presented above will be used to obtain the specific results for a number of microstrip patch antennas. It is perhaps instructive to describe here the qualitative features which are common to MPAs. These features follow naturally from viewing the MPA as a leaky cavity.
720
Characteristics of microstrip patch antennas
Characteristics o f microstrip patch antennas
(i) There are an infinite number of resonant modes, each characterised by a resonant frequency. (ii) Because of fringing fields at the edge of the patch, the patch behaves as if it has a slightly larger dimension. Semi-empirical factors are usually introduced to obtain these effective dimensions. These factors vary from patch to patch. (iii) Each resonant mode has its own characteristic radiation pattern. The lowest mode usually radiates strongest in the broadside direction. The pattern of this mode is broad, with half-power beamwidths of the order of 100". (iv) For coaxial-fed antennas, the input impedance is dependent on the feed position. The variation of input resistance at resonance with feed position essentially follows that of the cavity field. For the lowest mode, it is usually large when the feed is near the edge of the patch and decreases as the feed moves inside the patch. Its magnitude can vary from tens to hundreds of ohms. By choosing the feed position properly, an effective match between the antenna and the transmission line can be obtained. jvj Since the cavity under the patch is basicaily a resonaror, the rorai Q and the impedance bandwidth are dependent on the thickness of the substrate t and its permittivity E . For low values of E,, the bandwidth generally increases with increasing t and decreases with increasing E,. This is presumably due to the fact that the stored energy W, decreases with t and increases with E, while the total loss P, is insensitive to these changes. However, detailed analysis (Section 3.3) shows that the bandwidth and Q are complicated functions of frequency, substrate thickness and the permittivity. (vi) For thin substrates, the impedance bandwidth varies from less than one to several percent.
121
width b. The electric field of a resonant mode in the cavity under the patch is given by (3.41) Er = E,,cos (mnxla) cos (nnylb) where m, n = 0, 1, 2 . . . The resonant frequency is where
In the next Section, the results obtained by applying the formulas of this Section to rectangular, circular, equitriangular and annular-ring patches will be presented.
3.3 Basic characteristics of some common patches Fig. 3.5
Geometry for the rectangular patch
-c47
A number of canonical patch shapes can be analysed by straightforward application of the cavity model. Of these, the rectangular, the circular, the equitriangular and the annular ring are the common shapes used in practice. They will be considered in detail in this Section. An example comparing the characteristics of these patches will be given in Section 3.4, while other patch shapes will be briefly mentioned in Section 3.5.
Eqn. 3.42 is based on the assumption of a perfect magnetic wall. To account for the fringing fields at the perimeter of the patch, the following empirical formula can be used for the effective dimensions [7]:
3.3.1 The rectangular patch
b, = A more accurate but lengthy formula, suggested by James et al. [3] is
3.3.1.1 Introduction: The rectangular patch (Fig. 3.5) is probably the most commonly used microstrip antenna. It is characterised by the length a and the
+ 112 b + 112
a, = a
(3.44) (3.45)
122
Characteristics of microstrip patch antennas
Characteristics of microstrip patch antennas
123
where
where f, is the resonant frequency given by eqn. 3.42. Eqn. 3.46 is found to yield resonant frequencies which are within 3% of experimental values, while the perfect magnetic-wall model gives errors up to 20%. The far-field, losses and Q, and input impedance can be calculated by applying the equations of Section 3.2. Since for the rectangular patch they are well documented [ 3 , 7 , 8 ] ,they will not be reproduced here. In what follows, we shall present numerical results based on these equations to illustrate the basic characteristics of the rectangular patch. Experimental results will also be given.
TMol mode
3.3.1.2 Illustrative results: We present in this Section numerical, and in some cases experimental, results illustrating the basic characteristics of the rectangular patch antenna. (a) Magnetic-current distribution The electric-field and magnetic-surface-current distributions on the side wall for TM,,, TM,, and TM, modes are illustrated in Fig. 3.6. For the TM,, mode, the magnetic currents along b are constant and in phase while those along a vary sinusoidally and are out of phase. For this reason, the b edge is known as the radiating edge since it contributes predominantly to the radiation. The a edge is known as the non-radiating edge. Similarly, for the TM,, mode, the magnetic currents are constant and in phase along a and are out of phase and vary sinusoidally along b. The a edge is thus the radiating edge for the TM,, mode. (b) Radiation patterns The modes of the greatest interest are TM,, and TM,, . However, the TM,, mode has also received some attention. These three modes all have broadside radiation patterns. The computed patterns for a = 1.56 and two values of E, are shown in Figs. 3 . 7 ~ - fIn . the principal planes, the TM,, and TM,, modes have similar polarisations while that of the TM,, mode is orthogonal to the other two. As will be discussed in Section 3.4.3.2,the TM,, and TM,, modes can be utilised to operate the rectangular patch as a dual-frequency antenna. The patterns do not appear to be sensitive to alb or t. However, they change appreciably with E,
.
TMIO mode b
TMZO mode
Fig. 3.6 Electric field and magnetic-surface-current distributions in walls for several modes of a rectangular microstrip parch antenna a TM,, mode b TM,, mode c TM,, mode
124
Characteristics of rnicrostrip patch antennas
Characteristics of rnicrostrip patch antennas -9
OdB
,
L,
,
, ,J,or
-80' -30 -90'
OdB
-10
-20
-30
-30
-20
b
-8
l Eel
-10
OdB
-10
-20
-30
-30
-20
-10
OdB
125
126
Characteristics of rnicrostrip patch antennas
Characteristics of microstrip patch antennas
127
a = 1.5b. For E, = 2.32 and E , = 9.8, the results for three thicknesses are given. In general, the efficiency increases with the thickness of the substrate and decreases with increasing E, . In using these curves, the criterion given by Wood for the avoidance of excessive surface-wave excitation mentioned in Section 3.2.4 should be kept in mind. For E, = 2.32 and E, = 9.8, the cut-off frequencies (below which the surface wave is less than 25% of total radiated power) are 21/t and 6.9/t GHz, respectively, where t is in millimetres. These correspond to 6.60 GHz for E, =
OdB
Fig. 3.7
-10
-20
-30
-30
-20
-10
OdB
Helatlve fleld patterns for a rectangular patch with alb = 1.5, f,, = 1 GHz, and (I) 2.32, t = 0.318, 0.159, 0,0795cm; (ii) E, = 9.8, t = 0.127, 0.0635, 0.0254 cm ( a ) TM,,. 4 = O' ( b ) TM,,. = 90" ( c ) TMOl , 4 = 90" ( d ) T M , , . 4 = 0" ( e ) TM,,, 4 = 90' ( f ) TM,,.4 = 0" ( g ) TM,, , 6, = 2.32
E, =
+
The patterns of most of the other modes have maxima off broadside. For example, those of the T M , , mode are illustrated in Fig. 7g. Fig. 3.8 shows the computed and measured radiation patterns of the TM,, and TM,, modes obtained by Lo et al. [7] for a rectangular patch with a = 11.43cm, b = 7.6cm, E, = 2.62 and t = 0.159 cm. Both Eo and E4 were measured in each of the two cuts, q5 = 0" and q5 = 90". It was found that one component of polarisation was negligible when compared to the other in each case and is not shown. (c) Radiation eficiency Let us first obtain some idea of the relative magnitudes of the power dissipated in the metal, the power dissipated in the dielectric, and the antenna radiation efficiency. These are described by the quantities P,/P,, P,/P, and P,/P,, respectively. The cases of (i) a = 1,5b, E, = 2.32, t = 0.159 cm and (ii) a = 1.56, E, = 9.8, t = 0.0635cm are illustrated in Fig. 3.9 for the TM,, mode. It is seen that, for both E, = 9.8 and E, = 2.32, the loss due to the conductor is larger than the loss due to the dielectric. The ratio P,/P, decreases rapidly as frequency increases. The radiation efficiency e = P,/P, of the TM,,, TM,, and TM,, modes as a function of resonant frequent is shown in Figs. 3.10~-c for a patch with
Fig. 3.8 Theoretical (x) and measured (solid or dashed line) radiation patterns in 4 = 0' and C $ = 90' planes of a rectangular patch antenna with a = 17.43 cm, b = 7.6 cm, E, = 2.62, t = 0.159 cm. (Reproduced from Reference 7 p. 140 @ 1979 IEEE) ( a ) and ( 6 ) at resonant frequency 8 0 4 MHz of (1, 0 ) mode ( c ) and ( d ) at resonant frequency 1187 MHz of (0, 1) mode
2.32, t = 0.318cm and 5.43GHz for E, = 9.8, r = 0.127cm. For the other cases, the cut-off frequencies occur beyond 10 GHz. (d) Directivity and gain The directivity D of an antenna is defined as the ratio of power density in the main beam to the average power density while the gain G = eD. For a rectangular patch with a = 1.5b, the directivities as a function of resonant frequency
128
Characteristics of microstrip patch antennas
Characteristics of microstrip patch antennas
129
for the three broadside modes are illustrated in Fig. 3.1 1. The directivity of the TM,, mode is largest and that of the TM,, mode the smallest. It is not sensitive to substrate thickness and resonant frequency. The gain, on the other hand, increases with resonant frequency in the manner shown in Figs. 3.12L~-c.
"., resonant frequency (GHz)
a
resonant frequency (GHz)
F i g . 3.9
Metallic (P,), dielectric (P,) and radiation (P,) losses for the TM,, mode as a function of resonant frequency for (a) a = 1.56. c, = 2.32,t = 0.159cm and (6) a = 1.56, e, = 9.8, t = 0.0635cm
(e) Total Q and bandwidth For the three broadside modes, the variation of total Q with resonant frequency is shown in Figs. 3.13~-c for the case a = 1.56. The bandwidth, as defined by eqn. 3.43, is shown in Figs. 3.14~-c.It is seen that the TM,, mode has the lowest Q and therefore the largest bandwidth compared to the other two modes. For E, = 2.32, the bandwidth for a given mode increases with substrate thickness except for frequencies below about 0.7 GHz. The behaviour is more complicated for E, = 9.8. For this case, there appears to be a range of frequencies for which a thinner substrate actually yields a larger bandwidth. (f) Input impedance Richards et al. [8] have reported calculated and measured values of the input impedance of a coaxial-fed rectangular patch with e, = 2.62 and t = 0.159cm. The Smith chart plot for the TM,, mode is shown in Fig. 3.15 for three feed positions. The variation of the input resistances at resonance of the TM,, and TM,, modes is shown in Fig. 3.16. It is seen that the input resistance is largest
resonont frequency (GHz)
Fig. 3.10 Radiation efficiency as a function of resonant frequency for a rectangular patch witho = 5 . 8 x 107S/m,6 = 0.0005, a = 1.5band(i) e, = 2.32,t = 0.318.0.159, 0.0795 cm; (ii) 8, = 9.8, t = 0,127, 0,0635, 0,0254 cm
130
Characteristics of rnicrostrip patch antennas T"03
Characteristics of rnicrostrip patch antennas
137
a-1 5 b
resonant frequency (GHz) C
when fed at the edge of the patch, but it can attain the convenient value of 50 R when the feed position is chosen properly. More detailed theoretical results for the input resistance at resonance are shown in Figs. 3.17~-c for the TM,,, TM,, and TM,, modes for E , = 2.32, t = 0.159cm and a/b = 1.5. The resistances are plotted as a function of feed position parametric in the resonant frequencies. It is seen that the values vary somewhat with the resonant frequency. It should also be noted that, for the TM,, mode, the variation with feed position is not a monotonically decreasing function, which is the case for the TM,, and TM,, modes. It is clear from these illustrations that, for a coaxial feed, matching the antenna impedance to the transmission-line impedance can be accomplished simply by putting the feed at the proper location. There is less flexibility in the case of a stripline feed. In this case, a quarter-wave transformer may be added to effect matching. Alternatively, an insert into the patch can be made. To conclude this Section, we point out that a rectangular patch with a single feed produces linearly polarised radiation. If circular polarisation is desired, the most direct approach is to use two feeds located geometrically 90' apart and with a relative phase shift of 90". This arrangement excites two orthogonal modes, each providing a linearly polarised wave at right angles to each other and at phase quadrature. Circular polarisation can also be produced by a nearly square patch, where one pair of sides resonates at a slightly higher frequency than the other pair. If the phase difference at the centre frequency between the pairs of sides is 4 2 , circular polarisation results. Lo and Richards [17, 181 have shown that the sides
0
2
L
6
8
10
resonant frequency (GHz)
Fig. 3.11 Directivities (absolute value) of the TM,,, TM,, and TM,, modes as a function of resonant frequency for a rectangular patch with a = 7.56 and (ii) 6, = 2.32, t = 0,318, 0.159, 0.0795crn; (ii) E, = 9.8, t = 0.127, 0.0635, 0,0254 cm
a and b must satisfy a/b = 1 + l/Q and the feed must be located along the line y = f bxla. The plus and minus signs produce left-hand and right-hand circular polarisations, respectively, in the direction normal to the patch.
Characteristics of microstrip patch antennas
Characteristics of microstrip patch antennas
I
133
a11.5b
T"l~
resonant frequency (GHz) a
resonant frequency
(GHz)
C
Fig. 3.12
Gain (absolute value) as a function of resonant frequency for a rectangular patch witho = 5.8 x 1O7Slm.6= 0.0005.a = 1.5band(i)c, = 2.32, t = 0~318.0.159, 0.0795cm; (ii) c, = 9.8, t = 0.127. 0,0635, 0.0254cm (a) TM,, ( 6 ) TMo, ( c ) TMo3
resonant frequency
b
(GHz)
134
Characteristics of microstrip patch antennas
Characteristics of microstrip patch antennas T"03
resonant frequency (GHz)
735
a=1.5b
resonant frequency (GHz)
a Fig. 3.13
Total Q factor as a function of resonant frequency for a rectangular patch with x 107Slrn, S = 0.0005, a = 1.56 and (i) E, = 2.32, t = 0.318, 0.159, 0.0795cm; (ii) E, = 9.8, t = 0.1 17, 0.0635, 0,0254crn ( a ) TWO ( b ) TMOI ( c ) TM03
rr = 5.8
3.3.2 The circular patch
0.318 crn
3.3.2.1 Introduction: The geometry of the circular patch or disc (Fig. 3.18) is characterised by a single parameter, namely, its radius a. In this respect, it is perhaps the simplest geometry since other shapes require more than one parameter to describe them. The mathematical analysis, however, involves Bessel functions. The electric field of a resonant TM, mode in the cavity under the circular patch is given by
E, = E,,J, (k,, Q)cos n$ resonant frequency (GHz) b
(3.49)
where Q and I) are the radial and azimuthul co-ordinates, respectively. E, is an arbitrary constant, J, is the Bessel function of the first kind of order n and
k,
= Xm/a
(3.50)
136
Characteristics of microstrip patch antennas
Characteristics of microstrip patch antennas
resonant frequency (GHz)
resonant frequency (GHz) C
a
30
TMOI
137
a:l
Fig. 3.14 Bandwidth as a function of resonant frequency for a rectangular patch with a = 5 . 8 x 107Slm. 6 = 0,0005. a = 7.56 and (i) E, = 2.32, t = 0.378, 0.759, 0.0795cm; (ii) E, = 9.8, t = 0.1 17, 0.0635, 0,0254 cm ( a ) TMto ( b ) TMo, ( c ) TMo3
5b
In eqn. 3.50, &, are the roots of the equation where differentiation is with respect to x. The first five non-zero roots of eqn. 3.51 are shown in Table 3.1. The resonant frequency of a TM,,, mode is given by
where c is the velocity of light in free space. Eqn. 3.52 is based on the assumption of a perfect magnetic wall and neglects the fringing fields at the open-end edge of the microstrip patch. To account for these fringing fields, an effective radius a,, which is slightly larger than the physical radius a, is introduced [19]:
10 resonant frequency (GHz)
b
10
138
Characteristics of rnicrostrip patch antennas
Characteristics of microstrip patch antennas
Eqn. 3.53 is obtained by considering the radius of an ideal circular parallel-plate capacitor which would yield the same static capacitance after fringing is taken into account. Although the result is borrowed from the static case, it appears to yield theoretical resonant frequencies which are within 2.5% of measured values.
3.3.2.2 Illustrative results: In this Section, we present graphical illustrations of the circular microstrip patch antenna. They include the magnetic-current distribution, radiation patterns, efficiency, directivity and gain, bandwidth and Q,and input impedance.
x
T6
739
x measurement
- theory feed polnts
w
-
N
C
rectangular microstrip antenna substrate rexolite 2200 1116"nominal th~ckness
o measured locus x computed locus x increment: 5 M H z (increasmg frequency is clockwise)
o
0
0.2
0.3
0.4
0.5
y'lb for x'=5.33cm for (0.1) mode x'lb for y'=3.81 cm for (1.0) mode (x'y') IS location of feed point
b
a
0.1
Fig. 3.15 Impedance of the TM,, mode of a rectangular patch antenna of a = 1743cm. b = 7.6 cm, 6, = 2.62, t = 0.759 cm. (Reproduced from Reference 8 p. 3 9 @ 198 1 IEEE) a Feed placement for impedance measurements b Comparison of measured (0) and computed (x) impedance loci
Table 3.1 The first five non-zero roots of J, ( x ) = 0
Fig. 3.1 6
As with the rectangular patch, the expressions for the far field, losses and Q, input impedance etc. are well documented [2] for the circular patch and will not be reproduced here. The characteristics obtained from these equations will be illustrated in the next Section.
Variation of resonant resistance with feed position of the TM,, and TM,,, mode in a rectangular patch antenna with a = 17.43cm. b = 7.62cm. &, = 2.62, t = 0.159cm. (Reproduced from Reference 8 p. 42 @ 1987 IEEE)
(i) Magnetic current distribution The magnetic-current distribution around the edge of the disc for the nmth mode is proportional to cosn($ - a).This is illustrated in Fig. 3.19 for n = 0, 1, 2 and 3. It is independent of I(/ for modes with n = 0 and undergoes three sinusoidal periods for modes with n = 3.
140
Fig. 3.1 7
Characteristics of microstrip patch antennas
Characteristics of microstrip patch antennas
74 1
Variation of resonant resistance with resonant frequency for a rectangular patch antenna with alb = 7.5,E, = 2.32,t = 0.159cm ( a ) TMlo ( b ) TMoi
( c ) TM03 y'lb
(ii) Radiation patterns Lo and co-workers [7] were among the first to obtain theoretical and experimental radiation patterns of the circular disc. Some of their results are shown below. In their experiment, a disc with a radius of 6.7cm and a dielectric thickness of 1.5 mm was used. The relative permittivity was 2.62. For this disc, the first resonance, i.e. that of the TM,, mode, was at 794MHz. The second
resonance, i.e. that of the TM,, mode, was at 1324MHz. The calculated and measured radiation patterns in the Q, = 0" and Q, = 90" planes are shown in Fig. 3.20. Qualitatively, the calculated and measured results showed reasonable agreement. No attempt was made to take into account the effects of a finite
142
Characteristics of microstrip patch antennas
Characteristics of microstrip patch antennas
143
(iv) Directivity and gain The directivity versus resonant frequency is plotted in Fig. 3.22. A circular patch on an alumina substrate has a directivity of about 3.5, which is almost independent of substrate thickness and resonant frequency. If the substrate is Duroid, it has a maximum directivity of about 5.3, which decreases with increasing resonant frequency and dielectric thickness. The gain of the lowest mode is illustrated in Fig. 3.23.
Fig. 3.18
Geometry of the circular patch antenna
ground plane in the theory, which was about 12 wavelengths on a side for frequencies near 794 MHz. The radiation patterns of the higher-order modes (0,2) and (3,O) also exhibit nulls in the broadside direction. Since the higher-order modes are seldom used in practice, only the characteristics of the lowest mode will be illustrated in subsequent sections.
(v) Total Q and bandwidth The variation of total Q with resonant frequency for the lowest mode is shown in Fig. 3.24. The bandwidth, as defined by eqn. 3.40, is shown in Fig. 3.25. Its dependences on substrate thickness and E, are similar to the rectangular patch.
(iii) Eflciency The radiation efficiency for the lowest mode TM,, as a function of resonant frequency for various dielectric substrate is shown in Fig. 3.21. It is seen that the efficiency increases with increasing substrate thickness and decreasing dielectric constant.
(vi) Input impedance Richards et al. have reported calculated and measured values of the input impedance of a coaxially fed circular patch as a function of radial feed position. This is shown in Fig. 3.26 for the TM,, mode. It is seen that the input resistance is largest when fed at the edge of the patch, but it can attain the convenient value of 50R when the feed location is chosen properly.
744
I
Characteristics of microstrip patch antennas
Characteristics of microstrip patch antennas
745
Dahele and Lee [20] have studied experimentally the effect of substrate thickness on the input im~edanceof a coaxially fed circular patch. Their results are shown in Fig. 3.27.
Fig. 3.20
Theorettcal (x) and measured radtatlon patterns tn the q5 = 0' and q5 = 90' planes of a circular patch w ~ t radius h a = 6 . 7 5 ~ 1E,, = 2.32 (Reproducedfrom Reference 7 p. 141 @ 1979 IEEE) (a) and ( b ) At 794 MHz of mode ( 1 . 1 ) ( c ) and ( d ) At 1324 M H z if mode ( 2 , l )
Fig. 3.21
Radiatton efficiency versus resonant frequency for the TM,, mode of the ctrcular patch with g = 5.8 x 1O7Slm, 6 = 0.0005 and (I) E, = 2.32, t = 0.318, 0.159, 0.0795cm; (;I) c, = 9.8, t = 0.127, 0.0635, 0.0254cm
Fig. 3.19 Surface magnetic-current distribution of the nmth mode in the circular patch antenna resonant frequency (GHz)
TO conclude this Section, We point out that, as in the case of the rectangular patch, feeding the circular patch at a single point results in linearly polarised radiation. Circular polarisation on boresight can be obtained using two feeds at
i
146
Characteristics of rnicrostrip patch antennas
Characteristics o f rnicrostrip patch antennas
147
1
resonant frequency (GHzI
Fig. 3.22 Directivity versus resonant frequency for the TM,, mode of the circular patch: (i) e, = 2.32, t = 0~318,0~759,0~0795cm;(ii) e, = 9.8, t = 0~127,0~0635,0~0254cm
0.1
Fig. 3.24
resonant frequency ( G H ~ )
Total Q versus resonant frequency for the TM,, mode of the circular patch with a = 5.8 x 107S/m, 6 = 0.0005 and (i) E, = 2.32, t = 0.318, 0.759, 0.0795cm; (ii) e, = 9.8, t = 0.727, 0.0635, 0.0254cm
0.1 01
10
resonant frequency (GHzl
1 resonant frequency (GHz)
Fig. 3.23 Gain versus resonant frequency for the TM,, mode of the circular patch with a = 5 8 x 707S/m, 6 = 0,0005 and (i) E, = 2.32, t = 0,318, 0.159, 0,0795cm; (ii) 6, = 9.8, t = 0.127, 0,0635, 0.0254cm
Fig. 3.25 Bandwidth versus resonant frequency for the TM,, mode of the circular patch with a = 5.8 x 107S/m,6 = 0.0005 and (ii) E, = 2.32, t = 0.318, 0.159, 0~0795cm: (ii) e, = 9.8, t = 0.127, 0.0635, O.0254cm
748
Characteristics of microstrip patch antennas
-
Characteristics of microstrip patch antennas
749
+
x x computed p a n t 2 5 M H z Increment measured locus 5.0 MHz Increme
(1, = t+b, and (1,, 90' and excited in phase quadrature. Alternatively, a slightly elliptical patch with the right amount of ellipticity and fed at theappropriate location can produce circularly polarised waves. This will be discussed further in Section 3.3.6.
u computed polnt Increment 5 OMHr
260r 2~0.
0
measured
P
+ Calculated 220 -
--
200 -
/
/
C 180-
-
-,a5
i
P
120-
/ /
loo-
/
0
; 8060
-
/
d
/
,
,
,
,
6 radlal source locat1on.d
Fig. 3.26
,
,
Fig. 3.27
8 ial8
(a) Calculated and measured TM,, mode input impedance loci for several radial feed locations. (6) Variation of TM,, resonant input resistance with radial feed position for a circular patch with a = 6.7~171 on Rexolite 2200 substrate (E, = 2.62) of thickness O.159cm (Reproduced from Reference 8 p. 41, @ 1987, IEEE)
Measured real part (R) and imaginary part (X) of input impedance as function of frequency for the TM,, mode of a circular patch with a = 6.8cm. 8, = 2.32 and three dielectric thicknesses. The feed is at d = 6.5 cm (Reproduced from Reference 20 p. 359 @ 1983 IEEE)
3.3.3 The Equitriangular patch Several triangular patch shapes are amendable to analysis by the cavity model. These include the 45"-45"-90°, 30'-60"-90°, and the 60"-60"-60" equitriangular
150
151
Characteristics of microstrip patch antennas
Characteristics of microstrip patch antennas
(equilateral triangular) patches. However, unlike the rectangular and circular patches which have been studied extensively, there are only a handful of investigation on the triangular patches [2, 21-24]. In this Section, the equitriangular patch is treated in detail. The geometry, for the case of a coaxial feed, is shown in Fig. 3.28. The presentation follows closely that of Luk et al. [24].
There were two suggestions for accounting for non-perfect magnetic wall effects. Helszain and James [I71 suggested that the side length a in eqn. 3.55 be replaced by the effective value a, = a
+ t(~,)-'"
(3.56)
On the other hand, Bahl and Bhartia [2] proposed that, in addition to a, replacing a in eqn. 3.55, E, should also be replaced by the effective value
-x
top vlew
z patch,
Fig. 3.28
t
Geometry of the equitriangular patch antenna
3.3.3.1 Formulas based on the cavity model: The solutions for the fields in an equitriangular waveguide with perfect electric walls have been described by Schelkunoff 1251. It follows from the duality principle of electromagnetism that the TM modes with perfect magnetic walls are the same as those of TE modes with perfect electric walls. Starting with the solutions given in Schelkunoff, we obtain the following results for the equitriangular patch antenna.
The question of which suggestion is appropriate can only be determined by comparison with experiment. It was shown by Dahele and Lee [23] that the suggestion of Helszajn and James [21] yielded much better agreement, and consequently, in the cavity-model theory of the equitriangular patch, the side length a will be replaced by its effective value a, but E, will not be replaced by E,. This is similar to the correction used in circular patch antennas. (ii) Internal and radiation fields of the coaxial-fed antenna In this Section, we present the formulas for the internal and radiation fields of the coaxial-fed equitriangular patch antenna. These take the form of doubleinfinite series comprising the various modes excited. If the characteristics of a particular resonant mode are desired, they can be obtained by examining the term corresponding to this mode. Let the coaxial feed be located on the bisector line at a distance d from the tip of the triangle (Fig. 3.28). The x and y co-ordinates of the tip are - a/,and 0, respectively. Following usual practice, the feed is modelled by a uniform current ribbon of some effective width 2w along the x-axis:
where
The internal field for TM modes inside the cavity is assumed to be z-directed and is given by m
E, = jog
m
"=om="
(i) Resonant frequencies The formula for the resonant frequencies of z-independent TM modes satisfying the perfect magnetic wall boundary condition is
X COS
2nIx' cos ,acos
[
1 1 C,,,,,
2n(n - 1)y 3a
2n(m - n)y 3a
2nmx' + cos $0
I
2nnx' 2741 - m)y + cos COS 3a
where the integers rn, n and I satisfy
a,
(3.60)
752
Characteristics of microstrip patch antennas
Characteristics of microstrip patch antennas
753
and x' = x
+ a/$ 4a 3a
k,,
= - (m2
+ mn + n2)'l2
(3.63b)
sin
C",, =
I
1
ifm=n=O
6
if ( m = 0 and n # 0 ) or ( m # 0 and n = 0 ) or ( m = n # 0 )
-
+ cos
3
3
""I 111 -
12 i f m # n # O (3.65~)
jo(x) = sin x/x
(3.656)
In eqn. 3.60, the conditions on the indices m , n are m > n 3 0 because the eigen functions ,$ = $, . The far-zone electric field at a point P(r, 0, 4 ) is given by Eo =
-jw(,(FX cos 0 cos 4
E,
-jwl;,(-FXsin4
=
+ Fycos 0 sin 4 )
(3.66a)
+ Fycos$)
(3.666)
where F, and Fy are the electric potential components given by
+ cos
J X ~
+jfi(a/2)z2
,pi(/- m)2b2(1 - m)b sin 2(1 - m)n + cos 3 3
+ COS
3
3
&%/2)x2
+ cos 2(m 3x
T[
( m - n)b
n)nl 11 -
sin
-
2(m - n)n 3
JXZ
~fi(012)~~
$[(m - n)2b2-
+ cos
3
x:]
754
Characteristics of microstrip patch antennas
X
( m - n)n (m - n ) sin ---cos ( 7 4 3 ) - v 3 ( m - n)n (- 1)"3a COS sin (nv/3) + 3 n[(n - 1)' - vZ]
-
I
(n x
Characteristics of microstrip patch antennas
-
(n - I)n I ) sin --- cos ( 7 4 3 ) - v 3
I
( n - I)n . cos ----- sin (nv/3) 3
1)"3a + n[(l (- m)* - v2]
I cos (nv/3) - v (I - m ) sin ( 3 x cos -----(' - m)n sin (nv/3)]}]
(3.68)
3
In eqns. 3.67 and 3.68,
XI
= kosin 0(cos $
+ sin $/$)
x2
=
kosin O(cos $
- sin dl$)
(3.73)
(iii) Input impedance The input impedance seen by the coaxial feed located at a distance d from the tip of the triangle is given by Z = R+jX=
+ cos
-jwhCC- 4
[
' cos ( 2n l d ) lo , ( . R ; ) fia
rzd)(T) (z) (%)I jo
where deA.is the effective loss tangent.
27a2
+ cos
jo
755
3.3.3.2 Illustrative results (i) Radiation patterns The radiation patterns are not sensitive to the resonant frequency or the size of the patch. The results to be presented are obtained using sidelength a = 10cm. For this length, the resonant frequencies of the first five modes for E, = 2.32, t = 0.159 cm and E, = 9.8, t = 0.635 mm are shown in Table 3.2. The fieldstrength patterns are shown in Figs. 3.29~-j.Notice that, in the $ = 0" plane, only the component E, is present. In the 95 = 90" plane, however, both the Ee and the E+ components are present, except in the broadside direction (0 = 0"). This feature is different from the circular and the rectangular patches, for which the principal-plane patterns contain only either E, or E+, but not both.
Characteristics of microstrip patch antennas
Characteristics of microstrip patch antennas
-0
OdB -10 -20
-20
-10
OdB
OdB -10
-20
-10
OdB
-20
157
158
Characteristics of microstrip patch antennas
Characteristics of rnicrostrip patch antennas
-e
159
For the TM,, and TM,, modes, radiation is strongest .in the ,broadside. Although there is a slight dip at the broadside for the TM,, mode, the radiation is still very strong in this direction. For convenience, we shall refer all three modes as broadside modes. Reference to the Figures shows that the polarisations of the three modes are the same at 6 = 0". This suggests that the equitrian-
Table 3.2
Theoretical resonant frequencies of an equitriangular patch with sidelength a = 10 crn
fm,GHz (W n) (1, 0) (1, 1) (2, 0) (2, 1) (3, 0)
Fig. 3.29 Radiation patterns of the equitriangular patch at,,,f t = O.159crn; (ii) e, = 9.8, t = 0.0635crn (a) TM,,. d = 0' (b) TM,,, 9 = 90' ( c ) TMii, d = 0' ( d ) TM,,,+ = 90' (e) TM ., d = 0' ( f ) TM, = 90' (9)TMa d = 0' ( h ) TM,, , 9 = 90' ( i ) TM, 4 = 0' ( j ) TM,. d = 90'
=
1GHz and (i)
E, =
E, =
2.32, t = 0.159cm 1.3 1.84 2.6 3.44 3.9
E, =
9.8, t = 0.0635cm 0.64 0.90 1.28 1.66 1.91
2.32.
2
4
6
resonant frequency
8
10
(GHz)
a
Fig. 3.30 Radiation efficiency versus resonant frequency for an equitriangular patch with 0 = 5.8 x 1O7S/rn,d = 0.0005 and (i) E, = 2.32, t = 0.318, 0.159, 0.0795crn; (ii) E, = 9.8, t = 0.127, 0.0635, 0,0254crn (a) TMlo (b) ( c ) TM21
Characteristics of microstrip patch antennas
Characteristics of microstrip patch antennas
-.,
-g
761
4-
-
t -1.275rnrn. 0.635rnrn.0.254rnrn
?
er:9.8
U
u
321-
7
0
2
4
6
8
10
resonant frequency (GHz)
resonant frequency (GHz)
b
resonant frequency (GHz)
Fig. 3.31
l
I
'
2
"
'
"
4
b
t
6
8
resonant frequency (GHz) C
10
Directivity versus resonant frequency for an equitriangular patch with: (i) E, = 2.32, t = 0,318, 0.159. 0,0795cm; (ii) E, = 9.8, t = 0.127. 0,0635, 0,0254cm ( a ) TWO ( b ) TM,o ( C ) TMz
162
Characteristics of microstrip patch antennas
Characteristics of microstrip patch antennas
Tho 31
0
2
6 6 8 1 resonant frequency (GHz)
0 0 0.1
C
1 resonant frequency (GHz)
b
0 0.1.
1
10
resonant frequency (GHz)
Fig. 3.32 Gain versus resonant frequency for an equitriangular patch with a = 5.8 x lo7 Slm. 6 = 0.0005 and (i) e, = 2.32,t = 0.318, 0.159, 0.0795cm; (ii) E, = 9.8, t = 0.127. 0.0635, 0.0254cm ( a ) TM,, ( b ) TMm ( c ) TMn
resonant frequency (GHz) C
10
163
164
Characteristics of microstrip patch antennas
Characteristics of microstrip patch antennas
TMZO
I
gular patch can be operated at the resonant frequencies of the three broadside modes with similar pattern and polarisation characteristics. We shall further show in the next Section that it is possible to find a position for a coaxial feed such that the input impedance of all three modes are in the range of 50-100 R. (ii) Radiation eficiency, directivity, gain, total Q and bandwidth The radiation efficiency, directivity, gain, total Q and bandwidth as a function of resonant frequency for the three lowest broadside modes, i.e. TM,,, TM,,, and TM,, are shown in Figs. 3.30-3.34. The results of e, Q,and BWare similar. However, the directivities and gains are significantly different.
resonant frequency (GHz) b 1'421
6,.9.8
0'
resonant frequency
(GHz)
6,-2.32 1 59 mrn
3.18 mrn
Fig. 3.33 Total 0 factor versus resonant frequency for an equitriangular patch with o = 5 . 8 x 107Slm. S = 0.0005 and (i) 8, = 2.32, t = 0.318, 0.159. 0,0795cm; (ii) E, = 9.8, t = 0.127, 0,0635, 0.0254cm ( a ) TMlo ( 6 ) TM*, ( c ) TM21
10
"
'2
k
"
j
m6
m
8
resonant frequency (GHz)
10
165
166
Characteristics of microstrip patch antennas
Characteristics of microstrip patch antennas
Compared to the rectangular and the circular patches, major differences are found in the Q, and B W curves. While these parameters depend on E,, t and f in a complicated manner for the rectangular and circular patches, their behaviour for the equitriangular patch is simple: Q , decreases (BW increases) with decreasing E, and increasing t irrespective of frequency. (iii) Input impedances and their variations with feed position The input impedances and their variations with feed positions are important characteristics of patch antennas. In the cavity-model theory for the equitriangular patch, the coaxial is modelled by a current ribbon of effective width 2w along the x-axis. Usually this is several times the physical diameter of the coaxial inner conductor and the input impedance is not a sensitive function of 2w. For a patch with a = IOcm, E, = 2.32 and t = 0.159cm, the input impedances of the three broadside modes, TM,,, TM2, and TM2, are shown in Fig. 3.35. The value of 2w used in the computation is 6 mm.
2
8 4 6 resonant frequency (GHz)
resonant frequency G H z ) a
Fig. 3.34
Bandwidth versus resonant frequency for an equitriangular patch with a = 5.8 (ii) e, = 9.8, 107S/m,6 = 0.0005 and (i) &, = 2.32, t = 0~318,0~159,0~0795cm; t = 0.127, 0,0635, 04254cm ( a ) TMlo (b) W o ( c ) TMz1
c (GHz) resonant frequency
10
167
168
Characteristics of microstrip patch antennas
Characteristics of microstrip patch antennas
169
The variations of R and X at resonance with feed position d a r e shown in Fig. 3.36. It is seen that R decreases with increasing d only up to a certain value of d. The distance d can be chosen so that, for a particular mode, it assumes the value necessary to match the characteristic impedance of the feed. If the antenna is to be used for more than one mode, it is desirable that the input impedances for these modes are not too different, in addition to having the same polarisation and similar radiation patterns. In this connection, it is interesting to point out that, by placing the feed at an appropriate location, the input resistances at
Fig. 3.36 Resonant resistance versus feed position of the three broadside modes of the equitriangular patch with sidelength a = 10cm. 6, = 2.32,t = 0.159crn I 0
8
0 0
u
0
,;I
..-.
r
0
0
u
resonance of the three broadside modes can be made to fall in the range of 50-100R. For example, if d is equal to 4,7cm, we obtain R = 100,50 and 60R for modes TM,,, TM,, and TM,,, respectively. Comparison of theory and experiment for the equilateral triangular patch is relatively scarce in the literature. In Reference 24, a comparison was made on resonant frequencies and input impedances, and reasonable agreements were obtained.
3.3.4 Annular-ring parch 3.3.4.1 Introductory remarks: While the rectangular and the circular patches are probably the most extensively studied patch shapes, the annular ring has also received considerable attention [26-341. There are several interesting features associated with this patch. First, for a given frequency, the size is substantially smaller than that of the circular patch when both are operated in the lowest mode (see example in Section 3.3.5). In application to arrays, this allows the
7 70
I
Characteristics of microstrip patch antennas
Characteristics of rnicrostrip patch antennas
777
I
elements to be more densely situated, thereby reducing the grating-lobe problem. Secondly, it is possible to combine the annular ring with a second microstrip element, such as a circular disc within its aperture, to form a compact dual-band antenna system [26]. Thirdly, the separation of the modes can be controlled by the ratio of outer to inner radii. Finally, it has been found that, by operating in one of the higher-order broadside modes, i.e. TM,,, the impedance bandwidth is several times larger than is achievable in other patches of comparable dielectric thickness. The annular ring has been analysed using the cavity model [2, 26, 301, the spectral-domain technique in Fourier-Hankel transform domain [28] and the
3.3.4.2 Cavity-model theory (i) Resonant frequencies, internal and radiation jields Consider an annular ring patch with outer radius b and inner radius a, as shown in Fig. 3.37. Assuming that only TM modes exist, the resonant frequencies are determined by
where k,,,, are the roots of the characteristic equation
J:, ( k b )Y', ( k a ) - J:, ( k a )Y:,( k b ) = 0 I
I I
(3.77)
In eqn. 3.77, J,,(x) and Y,(x) are Bessel functions of the first and second kind, order n, respect~vely,and the prime denotes derivatives with respect to x. Letting C = hla, eqn. 3.77 takes the form
1y:,(4,",1 - J:,(Kt",1Y'(c&,,,, 1 =
J:, (c4,,,,
0
(3.78)
where
X,",
=
k,,d
(3.79)
For the case C = 2, the roots of eqn. 3.78 are given in Table 3.3.
Table 3.3 Roots of the characteristic equation J',,(X,,C)Y,(X,,) (X,,)Y',,(X,,,C) = 0,where C = bla = 2 m
1
2
3
4
- J',,
5
s ~ d evlew
eed
Fig. 3.37
The cases when n = 1 and n = 2 are also of particular interest. The roots are shown in Figs. 3.38 and 3.39. Note that the spacings between the roots are dependent on alb. This parameter can therefore be used to control the frequency separation of the modes. For the general equation 3.77, solutions presented in the form of a mode chart are given in Reference 33. To account for the fact that a small fraction of the field exists outside the dielectric, it is customary to use an effective permittivity E, in place of F, in eqn.
Geometry of the annular-ring patch antenna
use of the method of matched asymptotic expansion [27].In what follows, the results obtained using the cavity model will be presented, together with some comparisons with experiment. V
7 72
Characteristics of microstrip patch antennas
Characteristics of microstrip patch antennas
3.76. The formula for E, as given by Schneider [31] is
173
To account for the fringing fields along the curved edges of the ring, it has been suggested that the outer and inner radii be modified according to
where W = (b
-
a)
where
po is the permeability and zo is the quasi-static characteristic impedance of a microstrip line of width W. A pair of empirical formulas for the modified radii, sufficient for many engineering purposes, are given by [33] C Fig. 3.38
The roots X, of eqn. 3.78, for n = 7, as a function of
C
= bla
For the glven values of a and b, a, and b, are calculated. Then the characteristic equation is solved by replacing a and b by a, and b,. After solving the characteristic equation for k,,,, the resonant frequencies are determined from
It should be pointed out that the correction to the resonant-frequency formula involves both the effective permittivity and the effective radii. This is somewhat different from the cases of the circular, the rectangular, and the equitriangular patches, which involve the effective dimensions only. Lee and Dahele [30] had shown that, in the case of the annular ring, good agreement between theory and experiment can be obtained only if both effective quantities are used. The electric field under the patch is given by I
Fig. 3.39
The roots, X, of eqn. 3.78, for n = 2, as a function of C = bla
The far-zone electric field is
776
Characteristics of microstrip patch antennas
Characteristics of microstrip patch antennas
7 77
The effective loss tangent, comprising the three kinds of losses, is given by
The total Q factor is the inverse of the effective loss tangent.
(iii) Coaxial-fed annular ring For an annular ring fed by a coaxial line at a distance d from the centre, which we modelled by a uniform current ribbon of effective width 2w (eqn. 3.9, the expression for E in the cavity is
where Rum =
and
Fig. 3.41 Sketches of the rad~at~on patterns of the TM,, and TM,, modes of the annular-r~ng patch antenna w ~ t hbla = 2 ( a ) 9 = 0' ( b ) lp = 90'
where the quantity I, is the integral: =
jo
~ 1 2n2cos20
J,,(koasin 0) - J,,(kob sin 0) J',(k,,,,, a) a
E,,
~ Z sin X (2nw) cos nn[J,(k,d)Y',(k,,a)
=
- Jk (k,a)
Y,(knmd)]
1 forn # 0 2 for n = 0
The 0 and C$ components of the far-zone electric field are E,
= j"+l
e-Ikor 2tk0up,, J X
r
n
m
cosnd knm
J,(koa sin 0) - J',(k0 b sin 0) -T--Jn (k,,rnb) E4 = -j""--- 2twp0J e-jkorcos e x r sin 8
.,
(3.101)
knm sinn)
-I
J,,(koa sin 8) - J,,(kob sin 8) J',,(k,,a) b J'"(k",b)
(3.102)
7 78
Characteristics of microstrip patch antennas
Characteristics of microstrip patch antennas
The input impedance is
7 79
addition to larger bandwidth, the TM,, mode also has a larger directivity. Similar results were obtained in Reference 35. The input impedance and bandwidth of the annular ring patch antenna have also been determined by modelling the antenna as a section of radial line loaded with wall admittances [36]. The results are in qualitative agreement with the other methods mentioned above.
where
3.3.4.3 Broadside modes T M , ,and TM,,: The most interesting finding for the annual ring patch is perhaps the relatively wide-band property of the TM,, mode. This was first predicted theoretically by Chew [27] and by Ali et al. [28] using the matched asymptotic expansion technique and the vector Hankel transform, respectively. Experimental verification of the theoretical prediction was first reported by Dahele and Lee [29]. Lee and Dahele [30] also obtain this theoretically within the framework of the cavity model, i.e. using the formulas of Section 3.3.4.2. For an annular ring patch with bla = 2, a = 3.5cm, E, = 2.32, t = 0.159cm, the variation of input impedance with frequency of the TM,, and TM,, modes is illustrated in Figs. 3.42 and 3.43 for two feed positions, one near the inner edge (d/a = 1.05 and the other near the outer edge (dl a) = 1.95. It is seen that, for the TM,, mode, the impedance is not sensitive to the feed position and the impedance bandwidth is very narrow ( < 1%). On the other hand, the input impedance of the TM,, mode is very sensitive to the feed position. With the feed near the outer edge, the value at resonance is only about 20R. With the feed near the inner edge, it attains the convenient value of about 60R at resonance. The bandwidth is about 4%, which is several times that of the TM,, mode. This is also larger than the bandwidth achievable with the rectangular, the circular, or the equitriangular patches with the same dielectric constant and thickness, as reference to the corresponding Figures in Sections 3.3.1-3.3.3 shows. The theoretical results agree with the conclusion of Chew [27], and Ali et al. 2][! who analysed the problem using considerably more complicated methods. ~ x ~ e r i r n e n tthe ~ l above ~ , predictions had been verified by Dahele and Lee [29] and Lee and Dahele [30]. Detailed theoretical results based on the cavity model for the characteristics of the TM,, and TM,, modes are shown in Figs. 3.44-3.48. Note that, in
-5001
590
600
610
620
630
640
650
f (MHz)
Fig. 3.42
Theoretical input impedance of the TM,, mode of an annular-ring patch with b = 7.0cm. a = 3.5cm. 8, = 2.32,t = 0.159cm. fed at two radial locations
3.3.5 Comparison of characteristics of the rectangular, circular, equitriangular and annular ring patches It is instructive at this point to present an example comparing the characteristics of the rectangular, the circular, the equitriangular and the annular ring patches. Let us take the operating frequency to be 2 GHz and fabricate the patches on a substrate material of thickness t = 1.59 mm and E, = 2.32. If the patches are designed to operate in the lowest mode, a rectangular patch with an aspect ratio 1.5 has dimensions b = 3.28 cm, a = 4.92 cm; a circular patch has radius 4.92cm; an equitriangular patch has side length 6.57cm; and an annular ring
180
Characteristics of rnicrostrip patch antennas
Characteristics of rnicrostrip patch antennas
with b / a = 2 has b = 1.84 cm, a = 0.92 cm. The characteristics of the lowest mode for the four patches are shown in Table 3.4. It is seen that all are broadside modes. The circular patch has the smallest beamwidth in both planes. The annular ring patch has the smallest physical area. The circular patch has the largest physical area but it also has the largest bandwidth, efficiency and gain.
I
I
a -0
a
2 -0 -%op
G a w
X
-30~7'5~'
"
a
2800 '
*
a
'
2850 ' 4
2900
f (MHz)
Fig. 3.43
Theoretical input impedance of the TM,, mode of an annular-ring patch with b = 7.0cm. a = 3.5crn. e, = 2.32, t = 0.159cm. fed at two radial locations
The picture changes somewhat if the annular ring with b = 2a is designed to operate in the TM,, mode. This is shown in the last column in Table 3.4. The beamwidth is much narrower while both the gain and the bandwidth are considerably larger. However, these improvements are achieved at the expense of increasing the size of the patch. For the TM,, mode to resonate at 2 GHz,
181
782
Characteristics of microstrip patch antennas
Characteristics of microstrip patch antennas
783
b = 8.9 cm and a = 4.45cm, yielding an area of 249cm2. This turns out to be a specific example of a general principle: increase in bandwidth can only be achieved at the expense of increasing the volume of the resonator.
resonant frequency ( G H z )
a
0
2
4
6
8
10
resonant frequency ( G H z ) Fig. 3.45 D~rect~v~ties of the T M , , and TM,, modes for the annular-rlng patch wlth b = 2a. (i) E, = 2.32, t = 0.318cm, 0.159 cm, 0.0795 cm, (ii) 8, = 9.8, t = 0.127 cm, 0,0635 em, 0.0254cm
0L 0.1
1
10
resonant frequency ( G H z ) b
Fig. 3.44
Radiation efficiency versus resonant frequency for the annular-ring patch with E, = 2.32, t = O.318cm. O.l59cm, 0.0795cm (ii) 6, = 9.8, t = 0.727 cm, 0,0635 cm, 0.0254 cm ( a ) TMll ( 6 ) TM12
b = 2a: (i)
3.3.6 Brief mention of other patches Besides the rectangular, circular, equitriangular and the annular ring, a number of other patch shapes have been studied in the literature. They include the right-angled isosceles triangular patch [2, 7, 371, the annular sector [7, 371, the circular sector [37], the rectangular ring [38], the H-shaped patch [38] and the elliptical patch [38-411. The analysis of the rectangular ring and the H-shaped patch requires the segmentation method, while the other patches mentioned above can be analysed using the simple cavity model. However, except for the elliptical patch which offers the'possibility of generating circularly bolarised waves using a single feed, the other shapes do not appear to contain any features which are not obtainable from the rectangular, circular, equitriangular or annular ring patches. For this reason, only the elliptical patch will be briefly discussed below. The geometry of the elliptical patch is shown in Fig. 3.49. Experimental study
184
Characteristics of microstrip patch antennas
0
'
~
~
~
~
Characteristics of microstrip patch antennas
~
6
;
~
h
l
185
b
resonant frequency (GHz) 0
resonant frequency (GHz)
2
6
3'
10
resonant frequency ( G H z )
resonant frequency (GHz)
b
Fig. 3.46
Gain versusresonant frequency for the annular-ring patch with b = 2a. a = 5.8 x 707Slm. d = 0,0005, and (i) E, = 2.32, t = 0.318em. 0.759 cm, 0,0795 cm, (ii) E, = 9.8, t = 0.727 cm, 0.0635 cm, 0.0254 cm ( a ) TMl, ( b ) TM12
Fig. 3.47
Total O factor versus resonant frequency for the annular-ring patch with b = 2a. a = 5.8 x 107Slm,6 = 0,0005and (i) E, = 2.32, t = 0.318cm. 0.159cm. 0,0795 em, (ii) E, = 9.8, t = 0.127em. 0.0635cm. 0.0254cm
(a) TMll ( 6 ) TM12
-
Characteristics of microstrip patch antennas
Characteristics of microstrip patch antennas
187
of this antenna was reported by Yu [39] and later by Long et al. [41]. Theoretical studies were carried out by Shen [40] using the cavity model, by LovandRichards [I81 using a perturbation method, and by Despande and Bailey [42] using moment method. The main conclusions of these studies are summarised as follows: (a) The radiation in the direction perpendicular to the patch is in general elliptically polarised. However, with proper selection of both the feed position and the eccentricity of the ellipse, circular polarisation can be obtained. (b) The desired circular polarisation is best achieved by limiting the eccentricity of the ellipse to a range of 10-20%. This corresponds to a (semi-major axis) and b (semi-minor axis) differing by only a few percent. The perturbation method of Lo et al. [18] yields the formulas
1
0.1 0.1
1.0
10
semimajor axis a semlmlnar axbs b
resonant frequency (GHz) a TMIZ
foci : x = bs2a
t
c
c=(a2-b21' eccentricity e,:+
Fig. 3.49
Geometry of the elliptical patch
where the quality factor Q can be assumed to be that of the circular patch of radius a or b. For example, if Q = 46.35, b/a = 0.976. (c) The feed point should be on a radial line making 45' relative to the semimajor axis, i.e. 4, = 45". The positive sign yields left-hand while the negative sign yields right-hand circular polarisation. ( d ) To achieve an operating frequencyf, the semi-major axis should be chosen to be
+ I
0.10.1
1.0
10
resonant frequency (GHz)
Fig. 3.48
Bandwidth versus resonant frequency for the annular-ring patch with b = 2a. o = 5 . 8 x 107Slm,6 = 0.0005 and (i) E, = 2.32, t = 0.318cm, 0.159cm, 0.0795cm. (ii) E, = 9.8, t = 0.127cm. 0.0635cm. 0.0254cm ( a ) TM,, ( b ) TM,,
where p is a constant ranging from 0.27 to 0.29.
188
Characteristics of microstrip patch antennas
Characteristics of microstrip patch antennas
( e ) To achieve an impedance of 50R, the feed point should be at a distance from the centre on the 4, = +45" line, where Q, 2. 0 . 2 8 ~ .
frequency agility of MPAs. One line of approach is to consider methods whereby the operating frequency of the antenna can be tuned over a range of values so that the same antenna can be used for several adjacent channels. This is the single-band tunable case illustrated in Fig. 3.50d. In another scheme, dualfrequency antennas with resonant frequencies separated by a certain range have
Q,
3.4 Some methods for improving the frequency agility and bandwidth of microstrip patch antennas 3.4.I Introduction As mentioned in Section 3.1, the microstrip patch antenna (MPA), being basically a leaky cavity, is inherently narrow band. The pattern bandwidth is usually many times larger than the impedance bandwidth, which therefore is the parameter controlling the frequency response of the antenna. For this reason, our subsequent discussion on bandwidth will refer to impedance. For a single patch operating at the lowest mode, typical bandwidth is from less than 1% to 2.3 several percent for thin substrates satisfying the criteria t / l , < 0.07 for E, and t l l , < 0.023 for E , 2: 10. When these inequalities are satisfied, the effect of surface wave is assumed to be unimportant. For comparison purposes, a halfwave dipole with a radiusllength ratio equal to 0.01 has a bandwidth of about 16%, while a medium-length helix operating in the axial mode has a bandwidth of about 70%. One way of obtaining a relatively wide bandwidth is to use an annular ring patch and operate it in the TM,, mode, as the results of Section 3.3.4 indicate. The price one has to pay is that the size of the patch is considerably larger than that of the rectangular, circular, equitriangular or the annular ring operated in the lowest mode. In this Section, we discuss a number of other methods which have been developed for overcoming the bandwidth problem. Let us illustrate our discussion of bandwidth with a series of frequency response characteristics depicted in Fig. 3.50. Let the response in (a) represent the ideal characteristics, in which the input resistance is constant over a wide range of frequencies. A typical MPA response, however, is that shown in (b). Since this is not satisfactory for most purposes, a great deal of attention has been devoted in recent years to improving the bandwidth characteristics of MPAs. One line of attack is to widen the absolute bandwidth of the antenna as much as possible, as illustrated in (c). This in principle can be achieved simply by increasing the thickness of the substrate. However, this introduces several problems. First, a thick substrate supports surface waves, which will produce undesirable effects on the radiation pattern as well as reducing the radiation efficiency of the antenna. Secondly, as the thickness of the substrate increases, problems associated with the feeding of the antenna arise. Thirdly, higher-order cavity modes with fields depending on z may develop, introducing further distortions in the pattern and impedance characteristics. It is therefore of interest to develop more sophisticated methods of improving the absolute bandwidth of MPAs, and a great deal of research has been devoted to this effort. There has also been a substantial amount of effort devoted to increasing the
789
1
j
\
a
deal
b
typ~cal MPA response
C
increased absolute bandw~dth
f
-
f
Rl
f
,,!7p '\
.'
f
d single band, tunable
n n
c
dual band non -tunable
f
dual band tunable
Fig. 3.50 Illustrating the various frequency-response characteristics
been developed (Fig. 3.50e). These duaLfrequency structures are useful in situations where the antenna is required to operate in two distinct frequencies which may be too far apart for a single antenna to perform efficiently at both frequencies. Related to this is the dual-band tunable configuration, in which one or both of the resonances are tunable. The case for which only the upper resonance is tunable is illustrated in Fig. 3.505
190
Characteristics of microstrip patch antennas
In the next two Sections, some of the methods that have been developed to provide the characteristics illustrated in Fig. 3.50 will be described.
3.4.2 Some methods of tuning MPAs We shall describe four methods of tuning the resonant frequencies of MPAs. These utilise (i) varactor diodes, (ii) shorting pins, (iii) optically controlled pin diodes and (iv) adjustable air gap. The advantages and disadvantages of these methods will be discussed.
Characteristics of microstrip patch antennas
the ground plane. These shorting posts present an inductance, and therefore alter the effective permittivity of the substrate. In the context ,of microstrip antennas, the method was first introduced by Schaubert et al. [44] in 1981. It is illustrated in Fig. 3.53. Using two posts, the experimental results obtained are shown in Fig. 3.54. It is seen that the resonant frequency is dependent on the separation of the two posts and a tuning range of some 18% is obtained as the separation varies between 0 and the whole width of the patch.
9l
Fig. 3.51
191
alpha D V H 6733-168-001 varactors
Illustrating the use of varactor diodes for tuning
3.4.2.1 Varactor diodes: For a given set of patch dimensions, the resonant frequency is primarily governed by the value of the relative permittivity E, of the substrate. If some means is available to alter E,, the resonant frequency will change. One method of achieving this is to introduce varactor diodes between the patch and the ground plane, as shown in Fig. 3.51. The diodes are provided with a bias voltage, which controls the varactor capacitance and hence the effective permittivity of the substrate. Bhartia and Bahl [43] performed an experiment on this method and the results are shown in Fig. 3.52. The resonant frequency f , of the lowest mode of the rectangular patch increases with the bias voltage, owing to the increase of the diode capacitance. It is seen that, in this experiment, a tuning range of some 20% was achieved with a 10V bias. The range increased to about 30% with a 30 V bias. Note that the curve ofj; versus bias voltage is not a linear one. Since the paper by Bhartia and Bahl [43], there appeared to be no further reports in the literature on this method, either experimentally or theoretically.
3.4.2.2 Tuning using shorting posts (pins): The value of E, can also be changed by introducing shorting posts (pins) at various points between the patch and
b ~ a svoltage ( V )
Fig. 3.52 Resonant frequency versus bias voltage for a varactor-loaded rectangular patch antenna (Reproduced from Reference 43 p. 306 @ IEEE 1982)
Schaubert et al. [44] developed a theory of shorting pins based on the transmission-line model, and the predictions (shown in Fig. 3.54) agree reasonably well with experimental data. However, because the transmission line model is not capable of predicting the variations in the inductive component of a load as its position is varied within the element, it fails to predict certain trends in the resonant frequency of a short-loaded patch as the shorting pin approaches the patch edge. This model also cannot predict the impedance of the element very accurately because the field distribution between the ground plane and the patch of a loaded element is much too complicated to be adequately represented by a single-mode transmission-line model. It should be noted, however, that the transmission-line model has been further developed for rectangular as well as for circular patches with shorting pins by Sengupta and co-workers [45, 461.
192
Characteristics of microstrip patch antennas
Characteristics of microstrip patch antennas
193
Lo and coworkers [47] have developed the cavity model for MPAs with lumped linear loads in general and shorting pins in particular. They have also applied the shorting-pin method to design dual-frequency structures. This will be discussed in Section 3.4.3.2. led
Fig. 3.55
Fig. 3.53
Illustrating the use of shorting posts for tuning the resonant frequency of a patch antenna
Tuning using optically controlled pin diode
3.4.2.3 Optically tuned patch antenna: A method of tuning the resonant frequencies of patch antennas utilising optically controlled pin diodes was recently reported [48]. The scheme is illustrated in Fig. 3.55. A stub is connected to the patch by means of an optically controlled pin diode. When the diode is reversed biased, it acts as an open circuit and the patch resonates at the frequency for which it is designed, say f,. When the diode is forward biased, it acts as a short circuit and the resonant frequency becomes that of the patch and the stub, i.e. f, - AJ In the experiment, f, was 10.285 GHz and f, - Af was 10.207GHz. These are the limits in the range of tuning. By illuminating the diode with light, the diode impedance can be varied from a high value to a low value. As a result, the resonant frequency is optically tuned. It was found in their experiment that an illumination of 1 w/cmZ resulted in a 15 MHz downward shift in the frequency. This method clearly needs further development as the range of tuning reported was extremely limited. Discussion: The three methods described so far suffer from the following disadvantages:
Fig. 3.54 Resonant frequency versus separation of posts for a 6 . 2 x 9.0 cm rectangular patch antenna with E, = 2.55,t = 1.6mrn (Reproducedfrom Reference 44p. 7 19 @ IEEE 79811
(i) The design of the patches is complicated by the added components such as varactor diodes, optically controlled pin diodes and their associated biasing circuit. In the case of shorting pins, their precise positions are also important. (ii) For high frequencies (say > IOGHz), the patch sizes are small and it is difficult to accommodate the diodes and shorting posts underneath each patch. (iii) The added complications in design multiply for an array consisting of a large number of elements.
194
Characteristics of microstrip patch antennas
The potential advantage of the three methods is the possibility of electronic tuning. For example, there were suggestions that the shorting pins could take the form of switching diodes so that the frequency can be changed by electronically switching the diodes on and off. However, to the authors' knowledge, a real demonstration of such electronic switching applied to MPAs has yet to be reported in the literature. In Section 3.4.2.4, we describe a somewhat different method of tuning the resonant frequency of an MPA, i.e. utilising an adjustable air gap between the substrate and the ground plane.
195
Characteristics of microstrip patch antennas
Experimental results: The first configuration studied by Dahele and Lee was the circular patch. The radius of the patch was 5cm fabricated on Duroid material of thickness 0.159 cm and relative permittivity 2.32. The width of the air gap is controlled by using spacers between the substrate and the ground plane. In the experiment, spacers of 0.5 mm and 1.Omm were used. The antenna was provided with a coaxial feed near the edge of the disc at a distance d = 4.75 cm from the centre. This feed position is chosen as it is well known that it yields a larger resistance at resonance compared to a feed which is closer to the centre. The
3.4.2.4 Tuning using an adjustable air gap Introduction: By introducting an air gap between the substrate and the ground plane in a microstrip patch antenna the effective permittivity of the cavity will change. This can be used to tune the resonant frequency of a microstrip patch antenna as discussed below.
substrace
I
I
conductma ~ a t c h
I
I A airgap
spacer
;;50'
I
II
/-coaxial
Fig. 3.57
1350
1400
Measured input impedance of the T M , , mode of a 5 c m circular-disc microstrip antenna for three values of air-gap width A. E, = 2.32,t = 0.159cm (After Reference 51 pp. 455-460)
feed
Table 3.5 Fig. 3.56
' 1300 '
'
f (MHz)
T ground'plane
'
Geometry of a microstrip patch antenna with air gap
Measured resonant frequencies and impedance bandwidths of the first few modes of a 5cm-radius circular-disc microstrip antenna for three values of the air-gap width --
The geometry of a microstrip antenna with an airgap is shown in Fig. 3.56. Consider the cavity under the conducting patch. It is made of two layers: a substrate of thickness t and an air region of thickness A. Compared to the case with no air gap the effective permittivity of the cavity is evidently smaller. As a result the resonant frequencies of the various modes will increase. Since the, effective permittivity decreases as A increases, tending towards the free-space value E,, as A -+ a,it follows that the resonant frequencies can be tuned by adjusting the air-gap width A. As a by product the bandwidth will also increase partly due to the increase in the height of the dielectric medium and partly because the effective permittivity is smaller. Based on the above idea, Dahele and Lee [49-521 have carried out a series of experimental and theoretical studies on the microstrip antenna with air gaps. Some of their results are presented below.
TM,, TM,, TM,, E,
fm
% BW
1128MHz 1879MHz 2596MHz
0.89 0.85 0.77
f,,,, 1286MHz 2136MHz 2951MHz
%BW 1.48 2.15 1.63
f,,
% BW
1350MHz 2256MHz 3106MHz
2.07 2.61 2.02
= 2.32, t = 0.159~111; fed at 4.75cm from the centre
measured resonant frequencies are shown in Table 3.5. For the lowest mode TM,,, there is a tuning range of about 20% in frequency and a more than twofold increase in the bandwidth as A goes from 0 to 1.0mm. Similar behaviour is recorded for the other modes. The measured input impedances of the TM,, mode as a function of frequency are shown in Fig. 3.57. The upward shift in the resonant frequency and the widening of the bandwidth are clearly seen.
196
Characteristics of microstrip patch antennas
Characteristics of microstrip patch antennas
As for the radiation pattern it was found that the air gap did not have a significant effect on the pattern. Another antenna studied was the annular-ring patch. The effect of an air gap on the two broadside modes TM,, and TM,, are shown in Table 3.6 for an annular ring of outer radius 7.0 cm and inner radius 3.5 cm fabricated on Duroid material of thickness 0.159cm and E, = 2.32. As in the circular patch there is an upward shift in the resonant frequencies and a widening of the bandwidths. It is significant that, for the TM,, mode, the bandwidth attains a value of 8.6% when A is equal to 1.0 mm. Table 3.6
Measured resonant frequencies and impedance bandwidths of the TM,, and TM,, modes of an annular-ring microstrip antenna for three values of the air-gap width A
A = 0 TM,, TM,,
626MHz 2757MHz
A 0.6 4.0
=
720MHz 3040MHz
Inner radius a = 3.5cm. outer radiur b = 7,0cm, 6, d/a = 1.05 where d is the distance from the centre
A
0.5mm
=
0.7 8.0 2.32, r
=
=
l.Omm
778MHz 3240MHz
0.8 8.6
197
effective permittivity of the two-layered medium:
Eqns. 3.108 and 3.109 are valid for any patch shape. Note that, as the air gap width A increases, E," decreases and the resonant frequency increases. The dependence ofJ;,,,(A) on A, however, is not a linear one.
Discussion:As in the other methods the adjustable air gap as a means of tuning the resonant frequencies has advantages and disadvantages. The advantages are: (i) No costly components are added. (ii) It can be applied to patches of any shape. There is no need to know the details of the fields in the cavity. (iii) The method is particularly attractive for an array made up of a great number of elements as illustrated in Fig. 3.58. If the elements are fed by striplines, the resonant frequencies of all the elements, and therefore of the array, can be tuned by a single adjustment of the air gap width A.
0.159cm. The feed is placed a t
Theory: Lee and Dahele has developed the theory of the two-layered microstrip antenna using the cavity model. The original assumptions of the model are modified to account for the two layers as follows: (i) Owing to the close proximity between the conducting patch and the ground plane only transverse magnetic (TM) modes are assumed to exist. The z-component of the electric field, however, is a function of z since the cavity is two-layered. (ii) The cavity is assumed to be bounded by perfect electric walls on the top and on the bottom and by a perfect magnetic wall along the edge. (iii) Across the dielectric-air interface the tangential electric field and the normal electric flux density are continuous. Based on the above assumptions detailed analysis for the circular and annularring patch were carried out and good agreement between theory and experiment was obtained. In the interest of brevity, except for the resonant frequencies, the theoretical formulas will not be included here. The formula for the resonant frequency, however, is a very simple one and is given by
where Jrf;,,(0)is the resonant frequency when there is no air gap and
is the
spacer alr gap
Fig. 3.58
Tuning a microstrip antenna array by using an adjustable airgap
Stripline feeds are assumed
The disadvantages are: (i) The width of the air gap has to be changed mechanically. Electronic tuning appears to be difficult. (ii) The antenna is slightly thicker. This however is compensated for by an increase of the bandwidth.
198
Characteristics of microstrip patch antennas
Characteristics of microstrip patch antennas
199
To end this Section we point out that it is possible to alter the resonant frequency by inserting a piece of dielectric in the air region, as illustrated in Fig. 3.59. The relative permittivity of the inserted dielectric can be either the same as that of the substrate or different. Both the thickness and the permittivity of the inserted dielectric will determine the resultant resonant frequency. ,conduct~ng
patch
s u b s t r a t e -spacer
resonant frequency cdn be tuned by Inserting a piece of dielectric In alr region (plug In u n ~ t )
Fig. 3.59 Altering the resonant frequency by inserting a piece of dielectric in the air gap
' . I 20, - 3 78cm
3.4.3 Dual-band structures There has been considerable interest in the development of dual-frequency microstrip antennas. The characteristics of this class of antennas is illustrated in Fig. 3.50e. They are useful when the antenna is required to operate in two distinct frequencies which are too far apart for a single antenna to perform efficiently at both frequencies while the behaviour of the antenna in the range of intermediate frequencies is of little or no concern. Several methods of obtaining the dual-frequency characteristics have been developed. We begin with the method of simply stacking two patches together. \ d l
Kconducting
1.0
,
3.2
frequency (GHz)
patch
?/
frequency ( (
Fig. 3.60 Non-tunable dual-frequency stacked microstrip antenna
3.4.3.1 Stacked circular-disc antenna: The first experimental report on a dual-frequency structure using two stacked circular patches was that of Long and Walton [53]. The geometry is shown in Fig. 3.60. The discs were photo-etched on separate substrates and aligsxd so that their centres were along the same
Fig. 3.61 Real and imaginary parts of impedance of stacked circular patches etched on a dielectric with E, = 2.47 ( a ) 2a, = 3.70ci-n ( b ) 2a, = 3.78cm ( c ) 2a, = 3.85 cm (Reproduced from Reference 53 p. 271 @ lEEE 1 9 7 9 )
200
Characteristics of microstrip patch antennas
Characteristics of rnicrostrip patch antennas
line. The sizes of the two discs and their spacings were varied and the resultant behaviour of the antenna characteristics measured. The antenna was fed by means of a coaxial line. The centre conductor passed through a clearance hole in the lower disc and is connected electrically to the upper disc. If one considers the two regions under the patch' as two resonant cavities it is clear that the system behaves as a pair of coupled cavities. Since the fringing fields are different for the upper and lower cavities, two resonant frequencies are expected even if the diameters of the two discs are the same. While the qualitative explanation is relatively simple the quantitative theory for this structure is still lacking. In what follows the experimental results of Long and Walton are described.
I
I
207
Walton which showed that they were similar to the radiation pattern of the lowest mode for the single circular patch. While the results of Long and Walton [53] showed that it is possible to design for the separation of the resonant frequencies by choosing the diameters of the upper and lower discs, this is not very convenient in practice because of the lack of formulas to predict the frequencies. Also once they are designed and etched, it is not possible to alter or tune the separation of the two resonant frequencies. The configuration as presented by Long and Walton was therefore a dual-band non-tunable antenna of the type illustrated in Fig. 3.50e.
-
I
conduct~ngpatch
!
ground 'plane
--I -I Fig. 3.63 Tunable dual-frequency stacked microstrip antenna utilising the air-gap idea
upper d~scdlameter 2al (mm)
Fig. 3.62 Resonant frequencies versus upper disc diameter of stacked circular patches etched on a dielectric with E, = 2.47, 2a2 = 3.78~171,t, = t, = 0.75mm. (Reproduced from Reference 53 p. 271 @ IEEE 1979)
Fig. 3.61 shows the real and imaginary parts of the input impedance for ?a, = 3.78 cm, t , = t2 = 0.075 cm and three values of 2a,. The resonant frequencies as a function of the upper disc diameter are shown in Fig. 3.62. Also shown is the resonant frequency of the lowest mode for a single disc of diameter 2a and substrate thickness t = 0.075cm, taking into account the fringing field through the effective diameter. It is seen that the lower resonant frequency is relatively constant, remaining near the value of a single disc with 2a = 3.78 cm and d = 0.075 cm. The upper resonance, on the other hand, is highly dependent on the size of the upper disc. Radiation patterns were also taken by Long and
Dahele and Lee 1541 have applied the air gap idea to study dual-frequency stacked discs. The geometry is shown in Fig. 3.63 in which air gaps between the lower substrate and the ground plane and/or between the two substrates are introduced. Either of the air gap widths can be set to zero. Their experimental results performed with two stacked discs of 7 cm radii, each etched on substrates with E, = 2.32 and thickness 0.159cm are shown in Fig. 3.64 and 3.65. In Fig. 3.64, with the lower air gap set to zero the upper air gap is seen to increase the resonant frequency of the upper resonance. In Fig. 3.65 the upper air gap is set to zero and the effect of the lower air gap is studied. It is seen that the effect is more complicated since it shifts not only the lower but also the upper resonance. In both cases the bandwidth of the lower resonance is substantially broadened. Dahele and Lee [55] have also studied a structure consisting of two stacked annular ring patches as shown in Fig. 3.66. This structure was also found to exhibit dual-frequency behaviour. As in the case of circular discs an upper air gap was found to be a convenient method of altering the separation of the frequency bands. 3.4.3.2 Single-element dual-frequency microstrip untenna: It is possible for a single-element microstrip antenna to operate at many frequencies correspond-
202
Characteristics of microstrip patch antennas
Characteristics of microstrip patch antennas
ing to the various resonant modes pertaining to the structure. However, for most applications it is required that the radiation pattern, the polarization and the impedance be similar if not identical in all the frequency bands of operation. T M l r mode; d-6.5cm; A1=O 400
-R
I
substrate
Fig. 3.64 Measured input impedances of the TM,, mode of a pair of stacked circular discs of 7 c m radius for three values of the upper air gap: d = 6.5cm. A, = 0, e, = 2.32, t = 0.159cm (After Reference 57 pp. 455-460)
Fig. 3.65
kb ground plane
conducting patches
,
Ill 11
/-coaxial
Fig. 3.66
feed
Geometry of the stacked annular-ring antenna
Measured input impedances of the TM,, mode of the stacked circular discs of Fig. 3.63 for two values of the lower air-gap. d = 6 5 c m . A, = 0, e, = 2.32, t = 0.759cm (After Reference 57 pp. 455-460)
This immediately rules out many modes. Furthermore, for a given geometry all the resonant frequencies are related in fixed ratios, providing no flexibility for the designer.
Fig. 3.67 Geometry of a rectangular patch antenna with six possible shorting pins anda short matching stub. (After Reference 56 pp. 298-300) All dimensions in centlmetres
204
Characteristics of microstrip patch antennas
If for a particular patch shape two modes can be found which produce similar radiation patterns with the same polarisation, dual frequency is possible with a single patch. For the rectangular patch the two modes (0, 1) and (0, 3) satisfy this requirement. However, their resonant frequencies are related by a fixed ratio of approximately 3, the exact value being dependent on the edge effect. Suppose now shorting pins are placed on the nodal lines of the (0,3) model field, there will be little effect on the (0, 3) mode but a strong effect on the (0, I) mode. This offers a way of altering the separation of the two frequency bands. The insertion of pins at proper locations can also be used to tune the input impedance for the (0, I) mode while the feed location is chosen first for the desired impedance for the (0, 3) mode. The above idea has been successfully demonstrated experimentally by Zhong and Lo [56]. A multiport-cavity-model theory has also been developed by Lo and coworkers which appears to predict the effects of shorting pins on frequency and impedance well. We limit here to a summary of the experimental results of Zhong and Lo.
Characteristics of microstrip patch antennas
205
directivities of the two modes are quite different. By increasing the number of pins the two frequencies can be brought to a ratio of about 1.8. If a smaller ratio is desired it is found that it can be achieved by introducing slots in the patch. This, however, makes the fabrication of the patch somewhat complicated.
H - plane
Table 3.7 Resonant frequencies for (0, 1 ) and (0, 3 ) modes against shorting pins used (After Reference 56)
E - plane -70"
-80"
80'
90'
-90"
---- low-band. f - 8 8 3 M H z -hlgh-band;f: 1848 MHz Fig. 3.68
The geometry of the rectangular patch in their experiment is shown in Fig. 3.67. It is made of 118 in copper-cladded Rexolite 2200 with six shorting-pin positions. The effects of successively adding more and more pins (each approxmately 0.05 cm in diameter) at the positions indicated in Fig. 3.67 are shown in Table 3.7. It is seen that the ratio of the two operating frequenciesf,,/f,, can be varied approximately from 3 to 2. Since all these pins are located on the (0, 3) nodal lines f,, remain constant at approximately 1865 MHz whilef,, is varied from 613 to 891 MHz. In order for the impedances of the two bands to be close to 50R at resonance it is necessary to attach a short capacitive stub of 0.6cm x 2.1 cm. With the stub added, the bandwidth with reference to 3:l VSWR is about 2% for the low band and almost 8% for the high band. Typical low- and high-band patterns in both E and H planes are shown in Figs. 3.68. It is seen that, while the two modes radiate strongest in the broadside, the
Typical radiation patterns in H- and E-planes for antennas shown in Fig. 3.67with six pins inserted (After Reference 56 pp. 298-300)
The rectangular patch is not the only geometry capable of providing dualfrequency operation. In Section 3.3.3, it was shown that the TM,,, TM,, and TM,, modes of the equitriangular patch are all broadside modes with similar polarisations in the broadside direction. Moreover, by choosing the location of the feed properly, the impedances of these modes do not vary greatly. It thus appears that it is possible to utilise the equitriangular patch for dual- or even triple-frequency operation. 3.4.3.3 Dual-band microstrip antennas with reactive loading: A dualfrequency microstrip antenna can also be obtained simply by loading it with a reactive load. If the reactive load takes the form of a short-circuited length of microstrip transmission line the low-profile characteristic of a microstrip patch
206
Characteristics of microstrip patch antennas
-
antenna is retained. Such a structure was suggested by Davidson et al. [57] and was demonstrated to work experimentally. Fig. 3.69 shows the dual-band rectangular microstrip patch antenna with a monolithic load studied in the experiment of Davidson et al. The patch was of
sut
Characteristics of microstrip patch antennas
The separation of the resonances can be varied by (i) changing the length of the microstrip line and (ii) introducing an inset dimension S with an accompanied gap spacing G between the line and the radiator, as shown in Fig. 3.71. The results for the resonant frequencies are shown in Table 3.8.
ground 'plane
str rate
Fig. 3.69 Dual-frequency rectangular patch antenna with monolithic reactive loading (After
Fig. 3.71 Geometry incorporating an insert dimension S and a gap spacing G (After Re-
Reference 57 p. 936-937)
ference 5 7 pp. 936-937)
Table 3.8 W cm 0.33 0.33 0.33 0.33 0.33
-501
2200
207
2400 2600 frequency ( M H z )
Fig. 3.70 impedance of edge-loaded, 4
2800
6cm patch antenna with 1 = 4,Ocm. W = 0.33 cm, E, = 2.77, t = 0.079 cm; coaxially fed near the edge and at the centre of the 6cm side (After Reference 5 7 pp. 936-937) x
dimension 6cm x 4cm etched on a substrate with E, = 2.17 and thickness 0.079 cm. It is coaxially fed near the edge and at the centre of the 6cm side. For a line length of L = 4.0cm and width w = 0.33 cm, the impedance characteristics is shown in Fig. 3.70. Good pattern performance was observed at each of the resonant frequencies (2.275 GHz and 2.666 GHz, respectively).
Resonant frequencies of monolithic microstrip elements (after Reference 57)
L cm 4.0 4.0 8.4 4.0 4.0
G cm 1.O 0 0 0.7 0.3
S
f~
fu
cm 1.5 0 0 1.5 1.5
GHz 2.356 2.275 2.339 2.437 2.47 1
GHz 2.494 2.666 2.628 2.494 2.514
Discussion: In summary three methods of obtaining dual-frequency characteristics for microstrip patch antennas have been described. The method using shorting pins use two different modes. As such the radiation patterns, while similar in the broad sense, do vary in detail as well as in directivity. The separation of the resonances can be controlled by the number of pins, but it is difficult to have them close together unless additional features such as slots are introduced in the patch. These additional design features appear to be difficult to accommodate at high frequencies where the patch size is small. The advantage of using shorting pins to realise dual-frequency characteristics and to control the frequency separation is that it is a single-patch geometry,
208
Characteristics of microstrip patch antennas
thereby retaining the low profile characteristic of microstrip antennas. This advantage is also shared by the monolithic reactive-loading method. In the reactive-loading method the two frequencies are separated by 10-20%. The separation can be controlled by several parameters associated with the reactive load. However, once a design is etched it is not possible to tune the antenna. For the case when the separation is in the range of 10-20% it appears that the stacked geometry discussed in Section 3.4.3.1 offers the advantages of operating in the same mode and the flexibility of tuning the separation by means of an air gap. This structure, however, is thicker than the single patch and the low-profile characteristics of the microstrip antenna is slightly compromised. 3.4.4 Electromagnetic-coupled patch antenna ( E M C P ) 3.4.4.1 Introduction: As mentioned in Section 3.4.1, a great deal of research has been devoted to increasing the absolute bandwidth of MPAs. The methods fall into three categories: electromagnetic-coupled patches (EMCP), use of parasiticelements and log-periodic arrangement of an array of patches. We shall discuss in this Section only the EMCP since it is related to the tunable stacked geometry of Section 3.4.3.1. The use of parasitic elements and log-periodic arrangement are covered in other Chapters of the Handbook. As mentioned in Section 3.4.1 it is possible to increase the absolute bandwidth of MPAs by simply using thicker substrates. This, however, introduces several problems. The first is the excitation of surface waves, which distorts the normal radiation pattern and introduces additional loss; the second is the excitation of higher-order modes with z dependence, which introduces further distortions on the pattern and impedance characteristics. The third is that the application of common feeding techniques, i.e. direct feeding by either a coplanar microstrip line or a perpendicular coaxial line, becomes increasingly difficult for the following reasons. Consider first a coaxial feed. Since the probe (extension of inner conductor of the coaxial line) introduces a series reactance almost proportional to the substrate thickness, the lead inductance will become significant with respect to the antenna radiation resistance for thick substrates and will therefore prevent proper matching. Consider next a patch which is edge-fed by a coplanar microstrip line. For a fixed impedance level the line width is almost propo~tional to the dielectric thickness. Since the patch dimensions for a fixed resonant frequency are only weakly dependent on the dielectric thickness (through the fringing field) the width of the feed line will become non-negligible as the substrate reaches a certain thickness. As a result the radiation pattern of the antenna will be disturbed partly due to the covering of the radiating patch edge by the line and partly due to increased radiation from the feed line. In view of the above problems, electromagnetic coupling (instead of direct coupling) has been studied as a possible feed technique for electrically thick MPAs. In particular, promising results have been obtained for the stacked dual-patch geometry which we now discuss.
Characteristics of microstrip patch antennas
209
3.4.4.2 Stacked dual-patch geometry: The basic geometry of the ,stacked dual-patch electromagnetic-coupled microstrip antenna is shown in Fig. 3.72. Each conducting patch is fabricated on an electrically thin substrate and separated by a region of air or foam with E, 2: 1. The structure looks similar to the tunable dual-frequency antenna of Section 3.4.3.1, but is different in two aspects. First, the thickness of the air region is several times the substrate thickness, while in the tunable version discussed earlier, it is a fraction of the substrate thickness. Secondly, rather than being fed directly by a transmission line, the top element is excited via electromagnetic coupling from the lower element, which is located closer to the ground plane and is connected directly to a feed line. The top and bottom patches are referred to as the radiating and the feeding patches, respectively.
radlatlng patch
spacer----A
I
O L r reg10nt
e
e
d
l
n
g patch
ground plane
Fig. 3.72
Electromagnetic-coupled patch antenna
When the air region is small two resonances are expected, as in the case discussed in Section 3.4.3.1. Experimental studies showed that, as the air region exceeds a certain thickness, the lower resonance disappears and only one resonance remains. The single resonance condition can also be obtained by designing the diameter of the radiating element to be larger than the feeding element. Electromagnetic-coupled patches appeared to be first discussed by Sabban [60]. Circular, annular-ring, rectangular and square patches in the S band (2-4GHz), etched with substrates about 0.01 1 thick, were reported to yield bandwidths ranging from 9% to 15%. His paper contained very little information on the air-gap width and the relative sizes of the elements, other than the statement that the radiating element was larger than the feeding element and that the antennas exhibited a single resonance rather than dual resonances. A more detailed experimental study was carried by Bhatnagar et al. [61]. The elements were triangular patches operating in the S band, and foam material with E , = 1 was introduced as the air gap between the dielectric layers (Fig. 3.73). The side lengths of both the top and bottom equitriangular patches were 37 mm fabricated on a substrate of thickness 1.6 mm and relative permittivity 2.55. The lower patch was provided with a coaxial feed at a distance
Characteristics of microstrip patch antennas
Characteristics of microstrip patch antennas
270
F, = 13.5 mm. The width A of the air gap is controlled by using foam material of uniform thickness. The functional behaviour of the impedance characteristics is given in Table 3.9. The results for A = 3 mm showed an increase in the bandwidth at lower resonance and a sizable radiation resistance at the second resonance. so that the structure may be operated as a dual-frequency antenna. Separation of the resonances was about 12% at A = 0 and 18% at A = 1.5 mm. For A > 3 mm the first resonance disappears. The second resonant frequency increased and the real and imaginary parts of the impedance increased with A. At t = 5mm the bandwidth was 595MHz, which was about 17.5% at the centre frequency of 3.407 GHz.
-,
27 7
and 20dB in the E-plane. It is interesting to note that the directivity of the antenna was larger than that of an ordinary microstrip patch, the beamwidth of which was greater than 85'-90'. The configurations of EMCP studied by Sabban and Bhatnagar et al. can be
p a r a s i t ~ cpatch
Fig. 3.73 Geometry of electromagnetic-coupled triangular patch antenna (After Reference 67 pp. 864-865)
Table 3.9
Characteristics of the stacked triangular patch antenna (after Reference 61)
First resonance
Second resonance
A
f
% BW
Maximum resistance
f
% BW
Maximum resistance
mm 0 1.5 3 4 5 6 9
GHZ 3.1 3.12 3.135
a 3.5 4.8 6.4
150 150 75
-
-
-
GHZ 3.54 3.8 1 3.77 3.72 3.61 3.56 3.45
2.5 3.1 3.2 10.5 17.46 14.8 8.6
90 55 48 52 55 62.5 105
-
a
The radiation patterns in both the E-plane and the H-plane at various frequencies within the impedance bandwidth are shown in Fig. 3.74 and Fig. 3.75, respectively. The beamwidth varied from 75" to 85" in the H-plane and 55" to 65" in the E-plane. The cross-polar level was better than 16 dB in the H-plane
angle (degree)
Fig. 3.74 E-plane radiation patterns of the antenna of Fig. 3.73 with L = 37mm. t , = t, = 7.6mm. A = 5 m m andF, = 73.5mm (After References 67 pp. 864-865) -3.1 GHz --- 3.3 GHz 3.5GHz 3.7 GHz
212
Characteristics of microstrip patch antennas
Characteristics of microstrip patch antennas
2 73
described as the 'normal' type. If the upper patch is fabricated on the underside of the substrate an 'inverted' configuration is cobtained. Fig. 3.76 illustrates these two types of configurations. The advantage of the inverted type is that there is a protective dielectric cover for the upper conducting patch. It has been studied by Chen et al. [62] and by Dahele et al. [63]. Further studies of the EMCP antenna were carried out by Lee et al. [64], using rectangular patches etched on Cuflon substrates ( E , = 2.17). Exciting the TM,, mode at about IOGHz, they recorded the variation of pattern shape, 3dB beamwidth and bandwidth with the separation A, for A between 0 and 0.37 1,. This is beyond the range studied by previous authors. It was found that, depending on A, the characteristics of the antenna can be separated into three
radlatlng patch
coax probe normal conf~guratlon 0
Fig. 3.76
angle (degree)
Fig. 3.75
H-plane radiation patterns of the antenna of Fig. 3.73 with L = 37mm. t , = t, = 1.6mm. A = 5mm and F, = 73.5mm (After Reference 61 pp. 864-865)
-3.1 G H z --- 3.3 G H z
3.5G H z 3.7 G H z
~ n v e r t e dconflguratlon
b
Normaland inverted configurations of the electromagnetic-coupledpatch antenna
regions. Region 1 is associated with bandwidths exceeding 10%; region 2 has abnormal radiation characteristics and region 3 is associated with narrow beamwidth and high gain. The value of A separating these regions depends on the dielectric material between the two layers. The gain in region 3 is 9-1 0 dB, compared to 5.3 dB for the single patch. It begins at A = 0.3 1 2, for air dielectric and at A = 0.21 1, for Teflon. The bandwidth in region 3, however, is only about 1.3% for air and 0.85% for Teflon. It is evident from the experimental results of the authors cited above that, by operating in region 1, the EMCP offers a promising way of achieving bandwidths in excess of lo%, while reducing the problems encountered by simply increasing the substrate thickness. If high gain rather than large bandwidth is desired, the EMCP can be operated in region 3. Although analytical methods are available [65], little work has been done to apply them to this interesting antenna. As such, the experimental results described above have not been quantitatively explained, nor are there formulas available which would aid the design in terms of resonant frequency, impedance, bandwidth and gain. Such theoretical research is urgently needed.
214
Characteristics of microstrip patch antennas
Characteristics of microstrip patch antennas
3.5 Summary
II
This Chapter begins with introducing the simple cavity model for analysing microstrip patch antennas with thin substrates. The formulas obtained from this model for rectangular, circular, equitriangular and annular-ring patches are then presented. The radiation pattern, efficiency, directivity, gain, quality factor and imvedance of these. antennas are illustrated. mainlv for the broadside modes. Experimental results are included or referenced where available. After a brief mention of some other geometries, notably the elliptical patch, the Chapter proceeds to discuss some methods of improving the frequency agility of microstrip patch antennas. They include the use of varactor diodes, shorting pins, optically controlled diodes, adjustable air gap, stacked geometries and reactive loading. The advantages and disadvantages of these methods are discussed. Finally, the method of increasing the absolute bandwidth by electromagnetic coupling of a fed and a parasitic patch in a stacked geometry is discussed.
12
13 14 15 16 17 18 19 20 21
3.6 Acknowledgments The authors wish to acknowledge the assistances of Dr. K.M. Luk and Mr. T. Huynh. Dr. Luk provided the numerical data for the majority of illustrations for the rectangular, equitriangular and annular-ring patches, while T. Huynh contributed to some of the computations for the rectangular and circular patches.
22 23 24
25 26
3.7 References 1 DESCHAMPS, G. A.: 'Microstrip microwave antennas'. Presented at the 3rd USAR Symposium on Antennas, 1953 2 BAHL, I. J., and BHARTIA, P.: 'Microstrip antennas' (Artech House, Mass., 1980) 3 JAMES, J. R., HALL, P. S., and WOOD, C.: 'Microstrip antenna theory and design' (Peter Peregrinus, 1981) 4 IEEE Trans., Jan. 1981, AP-29 5 CARVER, K. R., and MINK, J. W.: 'Microstrip antenna technology', IEEE Trans., 1981, AP-29, pp. 2-24 6 MAILLOUX, R. J., McILEVENNA, J. F., and KERNWEIS, N. P.: 'Microstrip array technology', IEEE Trans., 1981, AP-29, pp. 25-39 7 LO. Y. T., SOLOMON, D., and RICHARDS, W. F.: 'Theory and experiment on microstrip antennas', IEEE Trans., 1979, AP-27, pp. 137-145 8 RICHARDS, W. F., LO, Y. T., and HARRISON, D. D.: 'An improved theory for microstrip antennas and applications', IEEE Trans., 1981, AP-29, pp. 38-46 9 DERNERYD, A. G.: 'Analysis of the microstrip disk antenna element', IEEE Trans., 1979, AP-27, pp. 660-664 10 DERNERYD, A. G.: 'Extended analysis of rectangular microstrip resonator antenna', IEEE Trans., 1979, AP-27, pp. 846-849
27 28 29 30 31 32 33 34 35 36 37
2 15
DERNERYD. A. G.: 'Microstrio. array. antenna'. Proc. 6th European Microwave Conference, 1976, pp. 339-343 RICHARDS, W. F., LO, Y. T., and SOLOMON, D.: 'Theory and application for microstrip antennas'. Proc. Workshop on Printed Circuit Antenna Technology', New Mexico University, Las Cruces, 1979, pp. 8.1-8.23 JAMES, J. R., and HENDERSON, A,: 'High-frequency behaviour of microstrip open-circuit terminations', IEE J Microwaves, Optics & Acoustics, 1979, 3, pp. 205-218 WOOD, C.: 'Analysis of microstrip circular patch antennas', IEE Proc., 1981 128H. pp. 69-76 FONSECA, S. B. A,, and GIAROLA, A. J.: 'Microstrip disk antennas. Pt. I: Efficiency of space wave launching', IEEE Trans., 1984, AP-32, pp. 561-567 RICHARDS, W. F., LO, Y. T., and HARRISON, D. D.: 'Improved theory of microstrip antennas', Electron. Lett., 1979, 15, pp. 42-44 RICHARDS, W. F., LO, Y. T., and SIMON, P.: 'Design and theory of circularly polarized microstrip antennas'. IEEE AP-S International Symposium Digest, June 1979, pp. 117-120 LO, Y. T., and RICHARDS, W. F.: 'Perturbation approach to design of circularly polarized microstrip antennas'. Electron. Lett., 1981, 17, pp. 383-385 SHEN, L. C., LONG, S. A,, ALLERDING, M. R., and WALTON, M. D.: 'Resonant frequency of a circular disc, printed-circuit antenna', IEEE Trans., 1977, AP-25, pp. 595-596 DAHELE, J. S., and LEE, K. F.: 'Effect of substrate thickness on the performance of a circular-disk microstrip antenna', IEEE Trans., 1983, AP-31, pp. 358-360 HELSZAJN, J., and JAMES, D. S.: 'Planar triangular resonators with magnetic walls', IEEE Trans., 1978, MlT-26, pp. 95-100 KEUSTER, E. F., and CHANG, D. C.: 'A geometrical theory for the resonant frequencies and Q factors of some triangular microstrip patch antennas', IEEE Trans.,1983, AP-31,27-34 DAHELE, J. S., and LEE, K. F.: 'Experimental study of the triangular microstrip antenna'. IEEE AP-S International Symposium Digest, 1984, pp. 283-286 LUK, K. M., LEE, K. F., and DAHELE, J. S.: 'Theory and experiment on the equilateral triangular microstrip antenna'. Proc. 16th European Microwave Conference, 1986, pp. 661666 SCHELKUNOFF, S. A,: 'Electromagnetic waves' (Van Nostrand, New York, 1943) Chap. 10 MINK, J. W., 'Circular ring microstrip antenna elements'. IEEE AP-S Int. Symp. Digest, June 1980, pp. 605-608 CHEW, W. C.: 'A broad-band annular-ring microstrip antenna', IEEE Trans., 1982, AP-30, pp. 918-922 ALI, S. M., CHEW, W. C., and KONG, J. A,: 'Vector Hankel transform analysis of annularring microstrip antenna'. IEEE Trans., 1982, AP-30, pp. 637-644 DAHELE, J. S., and LEE, K. F.: 'Characteristics of annular-ring microstrip antenna', Electron. Lett., 1982, 28, pp. 1051-1052 LEE, K. F., and DAHELE, J. S.: 'Theory and experiment on the annular-ring microstrip antenna', Ann. des Telecomm., 1985, 40, pp. 508-515 SCHNEIDER, M. V.: 'Microstrip lines for microwave integrated circuits', Bell Syst. Tech. J., 1969.48, pp. 1421-1444 OWENS, R. P.: 'Curvature effect in microstrip ring resonators', Electron. Lett., 1976, 12, pp. 356-357 WU, Y. S., and ROSENBAUM, F. J.: 'Mode chart for microstrip ring resonators', lEEE Trans., 1973, MlT-21, pp. 487-489 DAS, A., DAS, S. K., and MATHUR, S. P.: 'Radiation characteristics of higher-order modes in microstrip ring antenna', IEE Proc., 1984, 131, pp. 102-106 EL-KHAMY, S. E., EL-AWADI, R. M., and EL-SHARRAWY, E-B. A,: 'Simple analysis and design of annular ring microstrip antennas', IEE Proc., 1986, 133H. pp. 198-202 BHA'ITACHARYYA, A. K., and GARG, R.: 'Input impedance of annular ring microstrip antenna using circuit theory approach', IEEE Trans., 1985, AP-33, pp. 369-374 RICHARDS, W. F., OU, J. D., and LONG, S. A,: 'A theoretical and experimental investiga-
2 76
Characteristics of microstrip patch antennas
tmn of annular, annular sector, and circular sector microstrip antennas', IEEE Trans., 1984. AP-12, pp. 864-866 PALANISAMY, V., and GARG, R.: 'Rectangular ring and H-shaped mlcrostrip antennas Alternatives to rectangular patch antenna', Electron. Lett., 1985, 21, pp. 874-876 YU. I. P.: 'Low profile circularly polarized antenna', NASA Report N78-15332, 1978 SHEN, L. C.: 'The elhptical microstrip antenna with circular polarization', IEEE Trans., 1981, AP-29, pp. 90-94 LONG, S. A., SHEN, L. C., SCHAUBERT, D. H., and FARRAR, F. G.: 'An experimental study of the circular-polarized elliptical printed circuit antenna', IEEE Trans., 1981, AP-29, pp. 95-99 BAILEY, M. C., and DESHPANDE, M. D.: 'Analysis of elliptical and circular microstrip antennas using moment method', IEEE Trans., 1985, AP-33, pp. 954-959 BHARTIA, P., and BAHL, I.: 'A frequency agile microstrip antenna', IEEE AP-S Int. Symp. Digest, 1982, pp. 304-307 SCHAUBERT, D. H., FARRAR, F. G., SINDORIS, A. R., and HAYES, S. T.: 'Microstrip antennas with frequency agility and polarization diversity', IEEE Trans., 1981, AP-29, pp. 118-123 SENGUPTA, D. L.: 'Resonant frequency of a tunable rectangular patch antenna', Electron. Lett., 1984, 20, pp. 614-615 LAN, G. L., and SENGUPTA, D. L.: 'Tunable circular patch antennas', Electron. Lett., 1985, 21, pp. 1022-1023 LO, Y. T., and RICHARDS, W. F.: 'Theoretical and experimental investigations of a microstrip radiator with multiple linear lumped loads', Electromagnetics, 1983, 3, pp. 371-385 DARYOUSH, A. S., BONTZOS, K., and HERCSFELD, P. R.: 'Optically tuned patch antenna for phased array applications'. IEEE AP-S Int. Syrn. Digest, 1986, pp. 361-364 DAHELE, J. S., LEE, K. F., and HO, K. Y.: 'Mode characteristics of annular-ring and circular disc microstrip antennas with and without airgaps'. IEEE AP-S Int. Sym. Digest, 1983, pp. 55-58 LEE, K. F., HO, K. Y., and DAHELE, J. S.: 'Circular-disk microstrip antenna with an air gap', IEEE Trans., 1984, AP-32, pp. 880-884 DAHELE, J. S., and LEE, K. F.: 'Theory and experiment on microstrip antennas with airgaps', IEE Proc., 1985, 132H, pp. 455460 LEE, K. F., and DAHELE, J. S.: 'The two-layered annular ring microstrip antenna', Int. J. Electronics, 1986, 61, pp. 207-217 LONG, S. A., and WALTON, W. D.: 'A dual frequency stacked circular disc antenna', IEEE Trans., 1979, AP-27, pp. 270-273 DAHELE, J. S., and LEE, K. F.: 'A dual-frequency stacked microstrip antenna'. IEEE AP-S Int. Sym. Digest, 1982, pp. 308-31 1 DAHELE, J. S., LEE, K. F., and WONG, D. P.: 'Dual-frequency stacked annular-ring microstrip antenna', IEEE Trans., 1987, AP-35 ZHONG, S. S., and LO, Y. T.: 'Single-element rectangular microstrip antenna for dualfrequency operation', Electron. Let?., 1983, 19, pp. 298-300 DAVIDSON, S. E., LONG, S. A., and RICHARDS, W. F.: 'Dual-band microstrip antennas with monolithic reactive loading', Electron. Lett., 1985, 21, pp. 936-937 DAHELE, J. S., and LEE, K. F.: 'Top-loaded single and coupled microstrip monopoles'. IEEE AP-S Int. Sym. Digest, 1983, pp. 47-50 MclLVENNA. J., and KERNWEIS, N.: 'Modified circular microstrip antenna elements', Electron. Lett., 1979, 15, pp. 207-208 SABBAN, A.: 'A new broadband stacked two-layer microstrip antenna'. IEEE AP-S Int. Sym. Digest, 1983, pp. 63-66 BHATNAGAR, P. S.. DANIEL, J.-P., MAHDJOUBI, K., and TERRET, C.: 'Experimental study on stacked triangular microstrip antennas', Electron. Lett., 1986, 22, pp. 864-865
Characteristics of microstrip patch antennas
2 17
62 CHEN, C. H., TULINTSEFF, A,, and SORBELLO, R. M.: 'Broadband two-layer microstrip antenna'. IEEE AP-S Int. Symp. Digest, 1984, pp. 251-254 63 DAHELE. J. S., TUNG, S. H.. and LEE, K. F.: 'Normal and inverted configurations of the broadband electromagnetic coupled microstrip antenna'. IEEE AP-S Int. Sym. Digest, 1986, pp. 841-844 64 LEE, R. Q., LEE, K. F., and BOBINCHAK, J.: 'Characteristics of a two-layer electromagnetically coupled rectangular patch antenna', Electron. Lett.. 1987, 23, pp. 1070-1072; also IEEE AP-S Int. Sym. Digest, 1988, pp. 948-951 65 RIVERA, J., and ITOH, T.: 'Analysis of an electromagneticallycoupled patch antenna'. IEEE AP-S Int. Sym. Digest, 1983, pp. 170-173
Chapter 4
Circular polarisation and bandwidth M. Haneishi and Y. Suzuki
Microstrip antennas are widely used as an efficient radiator inmany communication systems [I]. One of the most interesting applications is their use for transmitting or receiving systems ,required for circular polarisation [2-51. A circularly polarised microstrip antenna can be classified into two categories, e.g. single- or dual-fed types. The classification of an antenna is based upon the number of feeding points required for circularly polarised waves. The singly-fed antenna is useful, because it can excite circular polarisation without using an external polariser. Therefore, it is important to understand the radiation mechanism of the antenna. However, one of the most serious problem in such an antenna is the considerable narrowness of the bandwidth compared to ordinary microwave antennas. This is a serious problem for the practical application of this antenna. For this reason, it is also important to study some wideband techniques. In this Chapter, the various types of circularly polarised antennas are first briefly introduced in Section 4.1. In Section 4.2, a simple design method for a singly-fed antenna is described together with some useful design data. This method is useful in understanding its radiation mechanism and to roughly design it. However, if the general radiation mechanism and an accurate design method are required, then the more exact treatment, developed in Section 4.3, is necessary. In Section 4.4, some considerations of mutual coupling are described. Finally, three kinds of wideband techniques are introduced in Section 4.5.
4.1 Various types of circularly polarised antennas There are many types of circularly polarised (CP) printed antennas, which are widely used as efficient radiators in many communication systems. Fig. 4.1 shows basic arrangements for various types of CP-wave printed antennas. In this Section, we describe briefly techniques for designing such CP printed antennas.
220
Circular polarisation and bandwidth
4.1.1 Microstrip patch antennas A microstrip antenna is one of the most effective radiators for exciting circular polarisation. A circularly polarised microstrip antenna is categorised into two types by its feeding systems: one is a dual-feed CP antenna with an external polariser such as 3dB hybrid, and the other is a singly-fed one without a polariser. The classification of antennas is based upon the number of feeding point required for CP excitation.
Circular polarisation and bandwidth
221
both the input VSWR and ellipticity bandwidth are broad, since a 3 dB hybrid, in general, has a broadband nature. The other category is the offset-feeding CP antenna. Here, offset feeding lines, with one quarter wavelength longer than the other, are set at the edges of the patch, as shown in Fig. 4 . 2 ~One . of the most serious disadvantages of this type of antenna is the narrow bandwidth, since the frequency dependency of an offset-feeding line is greater than that of the usual hybrid.
(a-1) Dual fed patch
(a-2) Singly fed patch
hybrid
-
8
-
RHCP LHCP
RHCP LHCP
RHCP ( d l Microstrip printed slot
( a ) Dual f e d CP patches Fig. 4.1
( b ) Singly f e d CP p a t c h e s
Various types of circularly polarised printed antennas
Fig. 4.2
(a) Dual-fed CP patch antenna: The fundamental configurations of a dualfed CP patch antenna are shown in both Fig. 4.1 (a-1) and Fig. 4.2 (a). The patches are fed with equal amplitude and 90' out of phase by using an external polariser. As shown in the Figure, these antennas are also divided into two categories by the shape of an external polariser: one is the 3 dB hybrid type and the other is an offset-feeding one. As is well known, a 3 dB hybrid such as a branch-line coupler produces fields of equal amplitude but 90' out of phase at its centre frequency. Therefore, setting the outputs of such a hybrid to the edges of the patch, the antenna acts as a CP radiator. It is necessary to note that each input terminal of a hybrid, however, gives an opposite sense of circular polarisation. In the present case,
Typical arrangements for circularly polarised microstrip antennas LHCP: Left-hand circular polarisation RHCP: Right-hand circular polarisation
(b) Singly-jed CP patch antenna: A singly-fed CP antenna may be regarded as one of the simplest radiators for exciting circular polarisation. The typical configurations of this antenna are shown in Fig. 4.2b. It is important to note that the generated mode in this case is usually excited in an electrically thin cavity region of the microstrip antenna. Accordingly, the operational principle of this antenna is based on the fact that the generated mode can be separated into two orthogonal modes by the effect of a perturbation segment such as a slot or other truncated segment [6-7,10-1 I]. Consequently, by setting the perturbation segment to the edge of the patch, the generated mode is separated into two
222
Circular polarisation and bandwidth
orthogonal modes 1 and 2. The typical amplitude and phase diagrams after perturbation are shown in Fig. 4.3, together with typical samples of antennas. The radiated fields excited by these two modes are, in general, perpendicular to each other, and orthogonally polarised in the boresight direction. When the amount of perturbation segment is adjusted to the optimum value, modes 1 and 2 are excited in equal amplitude and 90' out of phase at the centre frequency, as shown in the Figure. This enables the antenna to act as a CP radiator in spite of single feeding. This antenna has several advantages compared to dual-fed ones and can excite CP radiation without using an external polariser. Design techniques will be described in detail in Sections 4.2 and 4.3.
Circular polarisation and bandwidth
223
the present case, on setting the radiating elements such as the strip and the slot to the maximum positions of V, and I,,these radiating elements radiate transverse and longitudinal electric fields E,, and E,,, respectively, in the boresight direction. The fields E,, and E,, can be excited in equal amplitude and at 90° out
-
input
microstrip l i n e M :
;C%+
l1
(a) Radiating element for composite-type circularly polarised printed antennaI81
( polarity)
input
E
matched
input i-----
i
Frequency Fig. 4.3 Amplitude andphase diagrams for singly-fed circularly polarisedmicrostripantennas
E
matched
input
4.1.2 Other types of circularly polarised printed antennas In this section, we describe briefly the fundamental design procedures for others types of CP antennas.
Fig. 4.4
( a ) Composite type of CP printed antenna: Fig. 4 . 4 shows ~ the fundamental configuration of a composite-type CP antenna [8]. The antenna is composed of the combination of a half-wavelength-long strip conductor and a slot in the ground plane. If the microstrip feeding line is short-circuited at 1 = 0, a standing-wave voltage V, and current I, occurs along the microstrip feeding line. In
of phase, if the strip and the slot are spaced one-quarter wavelength apart and the coupling between the radiating element and feeder is controlled to be identical in value. Therefore, this type of antenna acts as CP radiator without using any external polariser. Details of design techniques for this antenna will be discussed in Chapter 13.
(b) Various arrangements of rampart line antennas[6] Typical arrangements for travelling-wave-type printed antennas
224
Circular polarisation a n d bandwidth
Circular polarisation a n d bandwidth
(b) Discontinuity type of C P printed antenna: A rampart-line antenna is a typical radiator for the discontinuity type [6,9]. Fig. 4.4b shows typical rampart line antennas that act as CP and LP radiators. Each radiator consists of a microstrip meander line having a series of corner bends. The antenna also has a matched load at the open end of the meander line. In this system, radiation occurs mainly from the discontinuity section of the meander line such as a corner bend. Therefore, both C P and LP rampart line antennas can be easily fabricated by controlling the length L, width Wand period P of the meander line. If L, Wand P a r e adjusted to 412, 3$/4 and ,Ig, respectively, for a unit cell of the meander line (As is the wavelength of the travelling wave along the meander line), the antenna acts as a CP radiator. When L = 2A8/3, W = 413 and P = 2Ag/3, the antenna radiates horizontal polarisation, while L = W = 414, P = 1,/2 excites vertical polarisation, as shown in Fig. 4.46. Details of the design procedure will be discussed in Chapter 13.
225
equations. while a perfect magnetic wall is assumed as a boundary condition at the antenna peripheries (x = fa/2,y = 4 b/2); 4" = V, sin k x
4h = VOsin k y where Vo = $/a and k = z/a. The eigen function 4, is concerned with the field distribution of TM,, mode, and 4, with that of TMo,, mode. By setting the perturbation segment As at an appropriate position of the antenna, as shown in Fig. 4.5, two orthogonally polarised modes are excited in a cavity region of the antenna.
4.2 Simple design techniques for singly-fed circularly polarised microstrip antennas
This Section gives a brief description of design techniques for singly-fed radiators together with some useful experimental results. The approach is based on the variational method, and is useful for understanding the mechanism of CP radiation from such singly-fed radiators.
( a ) Standard patch
4.2.I Recfangular type In general, microstrip antennas are divided into two types by the shape of radiating element: rectangular type and circular type. However, since the rectangular patch antenna is considered to be a fundamental device for exciting CP radiation, the design techniques for this type are discussed first. (a) Fundamental configuration of rectangular CP-wave antenna: The fundamental configurations of the antenna and its co-ordinate system are shown in Fig. 4.5. In type A, the feeding point F is placed on the x- or y-axis, whereas in type B, F is placed on the diagonal axis. In both cases, the perturbation segment As is set at an appropriate location in the patch element to excite CP radiation. Here, we describe briefly the sense of direction for the CP-wave. Right-hand or left-hand CP radiation can be achieved by setting feeding points at appropriate locations such as F(f Q,, 0) and F(0, -+eo), as shown in Fig. 4.6. (b) EfSecf of perturbation segment: The effect of perturbation segment As for the type-A antenna is described first, since this type of radiator is a basic device for exciting CP radiation. The eigen functions 4 , and &,, which are excited in an electrically thin cavity region of the square patch, are generally given mathematically by the following
(b) Singly fed circularly polarised patch Fig. 4.5
Fundamental configurations of singly-fed rectangular patches (From Reference I I )
The new eigen function 4' and the new eigen value k', after perturbation by the segment, are determined by the following equations [I 1, 12, 151:
4'
=
P4, + Q 4 b
I
where P and Q are unknown expansion coefficients of the new eigen function 4'.
226
Circular polarisation and bandwidth
Circular polarisation and bandwidth
The new eigen value k' of the antenna can be derived by employing the following matrix, since eqn. 4.2 is a variational-expression form: det
I
k2
+ 41 - k 2 ( 1 + P I )
q12 - K2PI,
+ 92
- kf2(1 + PI)
q12 - V2 P i 2
In case of the type-A antenna, the parameters in eqn 4.3, such a s p , , p2, q , , q,, p , , and q,,, are expressed by the following equations [I I]:
227
The eigen values used in eqn. 4.6 are assumed to be k,' = k,,' = k by means of first-order approximation. Furthermore, the turn ratios N,' and Nb', which correspond to the energy distribution ratios for both the 4,' and 4,' modes after perturbation, are defined as [I I]
Nb
=
($?/a)(sin kx - sin ky)
Nb = (@/a)(sin kx
(4.7)
+ sin ky)
In the case of the type-B antenna shown in Fig. 4.5, the eigen functions & ,
$6 and other parameters can also be derived by similar calculations employed for type A. The equations obtained by these calculations are as follows: Substituting eqn. 4.4 into eqn. 4.3, the new eigen values k,' and k,' for type A are given as
where k,' and k,' correspond to the eigenvalues of the new orthogonal eigen functions, 4,' and 4,', respectively. modes are Using eqn. 4.5, new sets of resonant frequencies for the 4,' and easily obtained as follows: f, =
for + Af: = h , ( l - 2 W S ) f b = hr + AfL. = A,
wheref,, is the resonant frequency for a normal square patch before perturbation, and Af,' and Afb' are the shifts of resonant frequencies for the 4,' and 4,' modes after perturbation. Normalising the new eigen functions for the 4,' and 4,' modes, the unknown expansion coefficients P and Q are determined as follows [I I, 121: For 4,' mode,
P,
=
(I/$)
(1 - 2As/S)
Qa = ( - 1 1 4 ) ( I
For
-
2As/S)
2.
(I/$)
2.
(-I/$)
4,' mode P,
=
Q,
=
where V, = I/a and k = nla. Using eqns. 4.1-4.7, we can derive the equivalent circuit for the type-A antenna. Furthermore, the equivalent circuit of the type-B antenna after perturbation can also be derived using the relations given in eqns. 4.8. The circuit for both the types of antennas is shown in Fig. 4.7. In this circuit, T', and T', represent ideal transformers having turn ratios Nb and &, and is input voltage applied to the 1-1' terminal.
5
(%'5)
Finally, using eqns. 4.1, 4.2 and the expansion coefficient, the new eigen functions 4,' and 4,' are given in a closed form by
(c) Condition requiredfor CP-wave radiation: In this Section, conditions for exciting CP-wave radiation are determined by use of the preceding equivalent circuit. As is well known, the equivalent conductances Gh and Gb in the circuit are expressed as the sum of the radiation, dielectric and copper losses. However, in normal patches having adequate radiation efficiency above 90%, radiation loss is dominant compared with the other losses.
228
Circular polarisation and bandwidth
Circular polarisation and bandwidth
Consequently, the equivalent conductances Gb and G ; are mainly caused by the radiated fields resulting from the patch antenna. In other words, the induced voltages and generated on G:, and Gb can be assumed to correspond to the radiated fields caused by the orthogonal 4: and 4; modes.
c,
(Ijblt,) = + j is satisfied. Accordingly, these antennas act as a CP radiator by setting the relative amplitude and phase between the two orthogonal modes at I &/?,I = I and arg ( & I t ) = f90°, respectively. Applying the above conditions to eqn. 4.9, turns ratios are required to satisfy the relation INf,/N:,I = 1. In addition, when this restriction is applied to the type-A antenna, it is necessary to place the feeding point F on the x-axis for (Nb/N:,) = 1. Contrariwise, the feeding point F is required to be placed on the y-axis by another restriction (N',/K)= - 1. 1
( b l LHCP Fig. 4.6
229
Nb:l
dA- mode
(1r.l ~ a / 2 1
Feeding locations required for circular polarisation RHCP: Right-hand circular polarisation LHCP: Left-hand circular polarisation eo = feed location
1-;
L(1-1
%=-2.ds t,,
~'=Klsinkx -sin kyl sink* + i n k K=fi/a
*)N;=l
I
N ~ = K l r i n k xI
I;=b1(l-9+)
{
4, - d s i
N;*KI
$inky)
f =~
I.,
Applying network analysis to the equivalent circuit, the complex amplitude in the two orthogonal modes is given as follows: ratio
t/c
Fig. 4.7
Equivalent circuit for rectangular circularly polarised patch antennas
Setting the feeding point at each location, the expression for the complex amplitude ratio is shown as follows:
t,
where and 6 are input admittances for the orthogonally polarised 4: and 4: modes, respectively. In addition, the unloaded Q factors in the above equation are expressed as Q,, = Qob = Q, to first-order approximation, where Q,, and Q,, are the unloaded Q factors of the 4: and 4: modes. From eqn. 4.9, radiation of CP waves by these radiators may be expected if
230
Circular polarisation and bandwidth
Circular polarisation a n d bandwidth
By application of the CP conditions satisfying I ~ / E=I 1 and a r g ( c / < ) = - 90" to the above equation, an important relation between Q, and (As/S) is obtained as follows:
+
237
(e) Radiation characteristics of CP antennas: In order to verify the validity of the above design procedures, typical samples of CP antennas were fabricated and tested at X-band. These antennas were fed with a coaxial probe to avoid the influence of unwanted radiation from the feeding networks. The radiation
where M = (1 + mAs/S), N = (1 + nAs/S), and m and n are the constants in = fo,(l mAslS) andf, = fo,(l nAs/S). In case of the type-A radiator, constants m and n are shown as m = - 2 and n = 0, as mentioned previously. Substituting these values into eqn. 4.10, and carrying out some modifications of the equation, the most important expression for designing purposes is easily obtained as follows:
+
f;,
+
This expression is simple in form but very useful for actual design of the type-A -*a,+.:-.
I'LUL'ZLUI
.
Furthermore, in case of the type-B antenna, a basic equation for design can also be derived by the use of similar techniques, and the expression is as follows: I
I
0
The relations for both basic expressions are illustrated in Fig. 4.86 by solid lines. They help to provide important design parameters such as the amount of perturbation (As/S) required for CP radiation.
2
I
I
I
L
4 6 substrate th~ckness(t/ho)
' 0
I
8 (X~O-~)
(a) Unloaded Q(Qn) and radiation efficiency
(d) Basic design procedures for CP-wave antennas: In designing CP-wave antennas, it is necessary to estimate the value of unloaded Q(Q,) as a function of substrate thickness t for an antenna. Therefore, theoretical values of Q, were calculated for a typical sample (a = 9.14mm, t = 0.6 mm, E, = 2.55). employ- ing a commonly used technique [6, 101. The theoretical values agreed well with the experimental ones, as shown in Fig. 4 . 8 ~After . determining the value of Q,, the design of an antenna can be achieved by the following procedures: (i) Using the relations shown in Fig. 4.8a, the unloaded Q(Q,) of the square patch is chosen so as to ensure that the radiation efficiency q of the patch will exceed 90%. (ii) The amount of perturbation (AsjS) required for CP-wave excitation is determined using the relation between Qo and (As/S) shown in Fig. 4.86. (iii) Finally, the input impedance of the test antenna is matched to that of the feed network by the offset loading technique of coaxial probe or using a quarter-wavelength transformer. The approaches described above are performed without considering the effect due to fringing fields. However, when the fringing effect is taken into consideration [6], the procedures help to provide more accurate design parameters required for CP radiation.
01
0
I
I
I
20 30 Unloaded Q(QO)
I
40
I
50
(b) Relations between Q0 and amount of perturbation segment ( A S I S ) Fig. 4.8 Fundamental design chart for singly-fed circularly polarised patch antennas
patterns measured by a spinning dipole are shown in Fig. 4.9. As seen from the Figure, the ellipticity of the test antenna is less than 0.5dB in the boresight direction. Furthermore, the ellipticity is within 1.5dB in the desired angular region of 45'.
232
Circular polarisation and bandwidth
Circular polarisation and bandwidth
233
Fig. 4.10 shows the measured impedance characteristics of the typical CPwave antenna. From these results, it is found that loop 1 in the impedance-plot locus depends on the degree of mode separation; namely, loop 1 becomes larger in area with an increase in mode separation, and converged to a point when the mode separation is reduced. In any case, however, the best ellipticity can be obtained at or near the peak of loop 1 in the impedance locus.
Fig. 4.10
la)
Typical measured impedance characteristics for rectangular singly-fed circularly polarised patch antennas (From Reference 7 I ) t/& = 0.018, E, = 2.55, tan6 = 0.0018 and ( e 0 l ( a / 2 ) )= 0.3
P a t t e r n of t y p e - A circularly polarlsed p a t c h
substrate
I
180
135
90
45
0 45 (deg.)
90
135 180
(a) Ibl
Fig. 4.9
S~LLFCII
Standard patch
of t y p e - 0 c ~ r c u l a r l y polarlsed patch
Typical radiation patterns of rectangular singly-fed circularly polarised patches, (From Reference 11) [ t / i o= 0,018, E, = 2.55, tang = 0.0018. ( p o / ( a / 2 ) )= 0.3, !A( = W, = io (Fig. 4.5a), and X-band
4.2.2 Circular type This Section gives a brief description of a design technique for a circular antenna. The geometry and feed system of the antenna are shown in Fig. 4.1 1. In this antenna, the perturbation segment As is also located a t a specific location. The degenerate mode is also separated from the dominant mode (TM,,,) in the antenna into two orthogonal modes by the effect of the perturbation segment.
( b ) c i r c u l a r CP elements
( c l Feeding s y s t e m
Fig. 4.1 1 Fundarnentalconfigurationsfor circular singly-fed circularly polarised patch antennas
234
Circular polarisation and bandwidth
The equivalent circuit after perturbation is useful for network analysis of the radiator. Fortunately, the equivalent circuit for the antenna can easily be obtained by employing the same procedures as in the previous Section. The equivalent circuit for the antenna after perturbation is shown in Fig. 4.12 [7].
Circular polarisation and bandwidth
235
provide important design parameters such as the amount of perturbation required for CP-wave radiation. In actual design, however, it is important to note that the Qo of the circular patch becomes equivalent to that of the rectangular one, if both the patches are designed to have the same resonant frequencies. For this reason, the circular CP antennas can be designed as easily as rectangular antennas by employing the relations shown in Fig. 4.8. However, the fringing effect is disregarded in above approaches. If the effect of fringing fields is taken into consideration [6], the experimental results agree well with theory, as mentioned below. In order to verify the validity of the design procedure, some circular CP patches were fabricated and tested at X-band. These samples were fabricated using a substrate consisting of copper-clad 0.6mm-thick Teflon glass fibre with a dielectric constant of 2.55 and a loss tangent of approximately 0.0018. The boresight ellipticity of the test antenna was about 0.5dB or less, and the radiation patterns revealed as a high a level of performance as those of the rectangular patch. In addition, the ellipticity bandwidth within 3 dB was about 1% with a substrate thickness of (t/lo) = 0.019, and about 2% with a thickness of (tll,) = 0.037. These results indicate that, as the substrate thickness increases, the ellipticity bandwidth also increases. Furthermore, the trend of the impedance locus plot of the antenna coincided with that of the rectangular one shown in Fig. 4.10. 4.3 More exact treatment of singly-fed circularly polarised microstrip antennas
Fig. 4.1 2
Equivalent circuit for circular singly-fed circularly polarised patch antenna (From Reference 7)
The CP-radiation condition for the circular patch can be determined using the above equivalent circuit. Namely, by application of the design procedures employed for the rectangular patches, the CP-wave condition for the circular one is obtained as where (ASIS), Qo and x,, correspond to the amount of perturbation, the unloaded Q and the eigen value of the dominant TM,,, mode, respectively. Using the above equation, the relation that gives a CP-radiation condition for the antenna is indicated by the dotted-line in Fig. 4.8b. This Figure helps to
The patch radiator can easily be modified from a circular, square or rectangular shape so as to excite circularly polarised waves with a single feed as mentioned previously. In addition to these shapes [4, 51, a specially shaped pentagonal [2], triangular [I31 or elliptical radiator [3] can also radiate circular polarisation. Furthermore, it has been known that the polarisation and resonant frequency can be conveniently controlled by inserting posts at suitable locations within the patch boundary [14]. However, it is not generally easy to analyse such antennas accurately, so designers are often forced to use cut-and-try methods to realise the desired characteristics. In this Section, an analysis, based on variational method [IS] and modal expansion technique [16], is briefly summarised for an arbitrarily shaped microstrip antenna with multi-terminals before starting the discussion concerning a singly-fed circularly polarised antenna. Using the results of analysis the conditions for producing circularly polarised waves are derived, and then it is shown that a microstrip antenna, in general, can radiate circularly polarised waves at two kinds of frequencies with a single feed. Finally, one design example is given in order to confirm experimentally the several theoretical predictions concerning the feed points and the operating frequencies to radiate them.
236
Circular polarisation and bandwidth
Circular polarisation and bandwidth
4.3.1 Analysis [ I 71 The present method is based on the variational method applied to arbitrarily shaped microstrip planar circuits with multi-terminals [I51 and the modal expansion technique [16]. The following approach is more suitable and useful in the analysis, and the design of a singly-fed circularly polarised microstrip antenna than that based on the moment method [19]. In the present method, the eigen values and orthonormalised eigen functions are derived from the Rayleigh-Ritz method under the Neumann boundary conditions [20]. The formula for the mutual impedance is derived using the relations between the terminal voltages, stored energies and radiated and dissipated powers. Also the equivalent circuit applicable to the microstrip antenna with multi-terminals is obtained.
237
to this problem may be given by where G(x, ylx,, yo) is a Green function generally expressed using the eigen values and eigen functions as
In this equation, k"' and cp(') are the eigen value and eigen function for the I th mode, respectively, and can be derived by employing the Rayleigh-Ritz method [20] for an arbitrarily shaped microstrip antenna. ( b ) Mutual impedance and equivalent circuit: In a multi-terminal microstrip antenna, if the power is supplied only to the 9 t h terminal and the other terminals are all open. the electric field Elq(x, y ) associated with the terminal current I, located at (x,, y,) can be expanded in terms of series of eigen functions as N
El,(& Y) = 1,
(a) Green function: The geometry of an analytical model and the co-ordinate system employed are shown in Fig. 4.13. The arbitrarily shaped patch is located on the surface of the grounded dielectric substrate with thickness t and the dielectric constant 6,. Usually, the patch is fed either by microstrip feed lines or coaxial probes. However, microstrip feed lines lead to problems of coupling with the patch radiator and problems of radiation, though there is an advantage in that they can be etched together with the patch radiator. Accordingly, the following discussion is restricted to the case of coaxial-probe use, because we want to separate the problem of the antenna itself from that of the feed network. In this Figure, C denotes a boundary line for the patch radiator, S is its area and A is a unit vector normal and outward to the boundary C . In many practical applications, the substrate is electrically thin, so that only a Zcomponent of the electric field and the X and Y components of the magnetic field exist in the region bounded by the patch radiator and ground plane. Assuming e'"' time variation, the electric field E: associated with a current source Jz located at (x,, yo) must satisfy
+ k2)E:
= -jw&J:(x,,y,)
(4.15)
I= I
where the unknowns F(1, x,, y,) are functions of the mode number I and the terminal location (xq, y,). Eqn. 4.15 implies that a mutual impedance can be expressed as a superposition of that for each mode as follows:
Fig. 4.13 Structure of analytical model and co-ordinate system
(V:
C F(l, X,, Y,)CP'"(X,Y)
N
z,.,
Y,)/I,
=
Cz 1! I- I
(4.16)
where Zz) is the mutual impedance between the p th and q th terminals for the I th mode and can be expressed by
In the above equation, V$) and Vf) are the terminal voltages, W$) and W i: are the time-averaged electric and magnetic stored energies, Pj:' is the radiated power, and PSf and P$ are the powers dissipated in the conductor walls and the dielectric, respectively. These parameters can be derived from the fields within the patch boundary according to the perturbation theory. As a result, the mutual impedance can be expressed as
(4.12)
where V, is the transverse part of the del operator with respect to the Z-axis, w signifies angular frequency, and k2 = ~ , k &with k, being a free-space wave number. If the perfect magnetic wall is assumed on the boundary, the solution
= E,(x,,
where
238
M:'
=
239
Circular polarisation and bandwidth
Circular polarisation and bandwidth
impedance'. When viewed from each feed point, it is generally defined as
flcp")(x,, y,)
C = -E, SEO t
with R,being the real part of the surface impedance of the conductor walls and tan 6 being the loss tangent of the dielectric substrate. Also, P,$'is written as
where
exp { jko(xcos
+ + y sin 9 )sin 6)dl
(
0 G 0 G
3
-
(4.29)
and R is unit vector of R-axis direction in polar co-ordinate, the asterisk means complex conjugation and Re{.) means real part in the brace. Eqn. 4.18 implies that an equivalent circuit for a multi-terminal microstrip antenna can be represented by the network model shown in Fig. 4.14, where the first resonant circuit, for I = 1, has a(')= 0 and thus corresponds to the mode resonating at zero frequency. This equivalent circuit is useful for network analysis of the microstrip antennas. (c) Input impedance: When the microstrip antenna has multi-terminals, the coupling among the terminals in the cavity must be considered in order to derive the accurate input impedance. Such input impedance is called an 'active input
Fig. 4.1 4
Equivalent circuit for multi-terminal microstrip antenna (From Reference 17)
where Vy) is the input voltage to the q th terminal and Zo, is the characteristic impedance of the q th terminal. I, is the current flowing in the q th terminal and found as a solution of the following matrix equation: [I] = [Z1]-' [v""']
(4.32)
240
Circular polarisation and bandwidth
where [V'"']is the input voltage vector whose typical term is Vp' and [Z'] is the impedance matrix whose typical term is given by
to the conductor and dielectric losses, and can be written as
tW 2
P,, = - E,E, tan 6
In practice, when using coaxial probes as feed lines, the correction is approximated by adding the following terms [21] to the self-impedance terms:
jx,
= j
&
tan (kot)
247
Circular polarisation and bandwidth
(4.34)
However, when using striplines, such a correction is not needed as the striplines are regarded as a part of the patch radiator, and the eigen values and eigen functions are derived for the patch boundary including the striplines. (d) Radiation field, directive gain and radiation &icie.~cy: The total radiatior. field can be calculated as a superposition of that for each mode. The radiation field for the lth mode can be represented by
4.3.2 Conditions for circularly polarised radiation [I81 In general, ideal circularly polarised waves are obtained when the ratio of the two orthogonally polarised radiation-field components is equal to &j. Solving this relationship with respect to the frequency, two kinds of frequencies at which the circularly polarised waves are radiated can be derived through an iterative process. Also, all the corresponding optimum feed locations can be determined numerically.
So the total radiation field is obtained from
(a) Radiation field from singly-fed circularly polarised microstrip antenna: If the contributions from the non-resonant modes are very weak and may be ignored, except those for the two strongest orthogonal modes necessary to radiate the circularly polarised waves, the total radiation field may be written as
where Qt' is an unknown coefficient, and can be determined for each mode from the boundary condition with respect to the voltage at the q t h terminal as follows:
where (x,, yo) is a feed point. In the above equation, the vth and (v I)th modes are chosen as the two wanted orthogonal modes. If a co-ordinate system can be fixed for convenience so as to align the X-axis with the direction of the vth field vector Et'(0, o)and the Y-axis with the direction of the (v + 1)th field vector EC+l)(B,w) on the boresight, then the far field given by eqn. 4.44 can be expressed on the boresight as
+
where Next, the directive gain U at O = 0 and the radiation efficiency q are defined by E,
=
E(0) . j = R('+l'(xo,yo)Etf "(0,0 ) . j .
(4.47)
Eqn. 4.45 can also be modified as E(0) = EL(f where P,, P,. and P, are the total radiated power and the dissipated powers due
+ j j ) + ER(3 - j j )
(4.48)
where E, and EL denote the right-hand and left-hand circularly polarised
242
Circular polarisation and bandwidth
Circular polarisation and bandwidth
equations can be derived:
components, respectively, and they are written as
g'"(w) =
+ ---
for RHCP for LHCP for RHCP
1 ER = - (JE, 2~ +
-
Ey) =
2 { Q ( " ) ( Xyo)E$'(O, ~, a) f a).$I
(4.54) (4.55)
for LHCP
1
,a@+ 1 ) ( x 0 ,Y ~ ) E $ + I ) ( O ,
243
where (4.50)
Therefore, from EL = 0 or ER = 0, the following equation can be obtained: Q("+')(X Y ~ ), E $ + I ) (wO) ., j = T j R(')(xo,yo)E$)(O, o ) . f
for EL
=
0
for ER
=
0
(4.51)
'#hen cqn. 4.5i is satisfied, the resultant fieids become the circuiar poiarisations and are expressed as E(0) = Q(")(xo, yo)[E$)(O,o).f ] ( f T j j )
RHCP
By eliminating + Bjfi from eqns. 4.54 and 4.55, a biquadratic equation with respect to the CP operating angular frequency can be obtamed as follows: w4 + u 2 [ U 2 ( o )- { ( w ( ' + ' ) )+~ ( w ( ' ) ) ~ + }]
{ W ( ~ ) . O ( " + ~= ) } ~0
(4.58)
where
where RHCP and LHCP mean right-hand and left-hand circular polarisation, respectively. In this case the significant roots of eqn. 4.58 are given by ( b ) CP operatingfrequency and optimum feed location: A microstrip antenna may become singly-fed circularly polarised antenna when its dimensions are adjusted to suitable values as mentioned previously. In addition, when the operating frequency and feed point are chosen correctly, good circularly polarised waves can be radiated. The frequency at which the ideal circularly polarised waves are excited is called the CP operating frequency. This Section indicates how the CP operating frequency and the corresponding optimum feed location are derived. Substituting eqns. 4.20 and 4.38 into eqn. 4.51, the following expression can be derived for the CP operating conditions:
Through comparison between the coefficients of the real parts and the imaginary parts on both sides of the above complex equation, the following simultaneous
where D(w) = [{w") - w('+"I2 - U 2 ( o ) .] [{a(") +
&+I)
}2 - u 2 ( a ) ] 2 0
(4.61)
Eqn. 4.60 shows that eqn. 4.58 has two significant roots, provided that the following CP operating condition, derived from an inequality of eqn. 4.61, is satisfied: low - w ( v + I ) ,1 > (4.62) Physically, this implies that the microstrip antennas can produce circular polarisation at two kinds of frequencies with a single feed. But, if the inequality of eqn. 4.62 is not satisfied, good circularly polarised waves cannot be produced from such antennas. However, eqn. 4.60 is not a closed-form expression, because the conductance components are, in general, a function of operating frequency. So it is difficult analytically to find out the CP operating frequencies. Accordingly, they are determined approximately through an iterative process;
244
Circular polarisation and bandwidth
namely, the (p
+ I)th iterative solution is approximated by
using the pth iterative solution o,.Fortunately, satisfactory convergence for eqn. 4.63 is usually obtained by about three iterations. Correct choice of the feed point however, is, also very important for good circularly polarised radiation. All the feed-location loci, consisting of obtimum feed points, are determined numerically by substituting the convergence results of eqn. 4.63 into eqn. 4.54. Next, let us consider the case when the equality in eqn. 4.62 is satisfied. Then instead of eqn. 4.60, only one CP operating frequency is given by rn = Jw(y)wo (4.64)
Circular polarisation and bandwidth
245
Now, let us consider the patch radiator shown in Fig. 4.15. This Figure shows a plan view of the patch radiator whose angles L E and L Fare right angles. The shape of such a pentagon can be prescribed completely by two parameters c/a and bla; i.e. the pentagon becomes a rectangle when cla = 0, an isosceles triangle when c/a = 1, and it becomes a special pentagon proposed by Weinschel[2] when bla = 1.0603 and c/a = 0.3061. So it is interesting to investigate the variation of CP operating frequency with respect to the aspect ratio cla in the case of bla = 1.0603. This can be derived iteratively from eqn. 4.63; the solid lines in Fig. 4.16 show the theoretical relations. In this Figure, the two chain-dotted lines denote the resonant frequencies for the two orthogonal modes contributing to the circular polarisation and the pair of dots indicate the experimental results for the pentagon proposed by Weinschel. These results show that antennas having dimensions satisfying the condition of eqn. 4.62 can
The theory developed here is quite adequate for obtaining initial design data on the, CP operating frequencies and the corresponding feed-location loci. However, if one wants to realise a near-perfect singly-fed circularly polarised antenna, then experimental trimming may be necessary in the final design stages to revise the errors due to the material-tolerances effects of the substrate used. Examples of calculations based on this theory are presented in the following Section.
Fig. 4.1 5 Plan view of pentagonal microstrip antenna Fig. 4.16
4.3.3 Example (13, 181 In this Section, an example is given of a singly-fed circularly polarised microstrip antenna designed on the basis of the theory developed in the previous Section. Several measured results are also presented for comparison with the calculated ones. The antenna used in the experiments was made of copper-clad 3.2 mmthick Teflon glass fibre with a nominal dielectric constant E, = 2.55 and a loss tangent of approximately 0.0018; it was fed by a coaxial probe to avoid the degradation of ellipticity by unwanted radiation from the feed network.
Relations between CP operating frequencies and aspect ratio cla of pentagonal microstrip antenna with bla = 7.0603, a = 700mm. t = 3.2mm. &, = 2.55,and tan6 = 0.0018 (From Reference 18) -calculated, a measured
always radiate circularly polarised waves at two frequencies. However, when eqn. 4.62 is not satisfied, i.e. cla approaches 0 or 0.5 in this example, such antennas cannot radiate any pure circularly polarised waves. In addition to the above condition concerning patch dimensions and CP operating frequencies, in order practically to obtain good circular polarisation, the antenna must be fed
246
Circular polarisation and bandwidth
Circular polarisation and bandwidth
247
at a location so that the two orthogonal radiation fields, contributing to the circular polarisation, are excited with equal amplitude. Such a feed location can be determined numerically by substituting the corresponding CP operating frequency into eqn. 4.54. The numerical results for several aspect ratios are shown as feed-location loci in Figs. 4.17~-f[37]. These Figures show the various pairs of feed-location loci when the aspect ratio cla is varied with bla = 1.0603 and a = 100mm. In these Figures, T, and T, show the loci when the CP operating frequency isf;, and T,and T, show the loci when it isf,,, noting that T, and T,, indicated by the solid line, correspond to the LHCP and T2 and T,, indicated by the broken line, correspond to the RHCP. It is found from these results that the triangular microstrip antenna can also radiate circularly polarised waves at two frequencies. The triangular microstrip antenna has the attraction that the area necessary for the patch radiator can be small; namely one half to three quarters that of the nearly square one. Fig. 4.18 Plan view of isosceles triangular microstrip antenna and feed-location loci in case of bla = 0.98, a = 76mm. t = 3.2mm. 6, = 2.55, and tan6 = 0.0018 (From Reference 13) -RHCP, ---- LHCP
Fig. 4.17
Variation of feed-location loci with respect to aspect ratio c/a for pentagonal microstrip an:enna with bla = 1.0603, a = 100mm. t = 3.2mm. E, = 2.55, and tan6 = 0,0018 (From Reference 37) ---- RHCP, -LHCP
0
Let us therefore consider the triangular microstrip antenna in detail. Fig. 4.18 shows a plan view of the isosceles-triangular patch radiator with the loci T,to r, of the theoretical feed location for each CP operating frequency, where a = 76 mm and bla = 0.98. In this Figure, T,and T2indicate the loci when the
0
d2 ! ig60
aspect ratio bla
,A6
Fig. 4.19 Relations between CP operating frequencies and aspect ratio for isosceles triangular microstrip antenna with a = 76mm. t = 3.2mm. E, = 2.55 and tan 6 = 0.0018 (From Reference 13) calculated, 0 measured
-
248
Circular polarisation and bandwidth
Circular polarisation and bandwidth
CP operating frequency is 1583.8 MHz and T, and T, indicate the loci when it is 1564.2MHz. In general, the shape of the isosceles-triangular patch shown in Fig. 4.18 can be prescribed completely by introducing the aspect ratio bla as a parameter. The solid lines in Fig. 4.19 show the variation of CP operating frequency when bla is varied, with a =,76mm; the pair of dots represent the measured results when the aspect ratio is 0.98. From these results it can be noted that the circularly polarised waves are always excited at two different frequencies when bla is smaller than about 0.985 or greater than about 1.015 in this case. Next, let us consider the axial-ratio characteristics. Fig. 4.20 shows the boresight axial ratio with respect to frequency, when bla = 0.98 and a = 76mm. The
249
good circularly polarised waves are excited at two different frequencies and that their bandwidths for 3dB axial ratio are about 0.5-0.6%. Although there are frequency differences of about 20-25 MHz and slight different of feed point between theory and experiment, both agrees well and also yield the excellent circular polarisation.
(a) Isolated patch
.o 2
a
1550
6
1560
-
1570 1580 1590 frequency. MHz
1600
1610
b \
m
-D6 4 . 2-
d
& \
TI
I
7
t f! i'
d (b) Two elements array
\
a
Fig. 4.21 0 1570
1580
I
I
1590 1600 1610 frequency. MHz
I
1620
Co-ordinate systems for circular patch and its array
J
1630
Fig. 4.20 Axial-ratio characteristics for isosceles triangular microstrip antenna with b / a = 0.98.a = 76mm, t = 3.2mm. &, = 2.55,and tan h = 0.0018 (From Reference 131 a Calculated results for point B-fed case in Fig. 4.18 and measured results for point 6, -fed case b Calculated results for point A-fed case in Fig. 4.1 8 and measured results for point A, -fed case
solid line in Fig. 4 . 2 0 ~represents the calculated results when selecting point B in Fig. 4.18 as a feed point, and the broken line the measured results with B, as a feed point. In Fig. 4.20b, the solid line represents the calculated results when selecting point A in Fig. 4.18 as a feed point and the broken line the measured results with A, as a feed point. From these Figures it can be appreciated that
4.4 Some considerations on mutual coupling In the design of an array, it is important to estimate the mutual coupling between microstrip patch antennas [22-231. In this Section, we present a simple method for calculating the mutual coupling of patch antennas. The technique based on the EMF method is simple and very effective for estimating the mutual coupling and the mutual admittance of antennas [22]. The geometry of the analytical model and the co-ordinate system employed here are illustrated in Fig. 4.2 1. Two patches are located on the same surface of a grounded dielectric substrate having thickness t and the dielectric constant 8,. Using this co-ordinate system, and considering the field distribution of the dominant mode (TM,,,) excited in a cavity region of the patch, the magnetic current J, due to the dominant mode is given by
250
Circular polarisation and bandwidth
Circular polarisation and bandwidth
where J, corresponds to the z-component of the electric field at the periphery of the antenna, and J, is the maximum amplitude of an equivalent magnetic current due to the dominant mode. Also, rT is an effective radius that contains a fringing effect [6], S(z) is the delta function and i,. is the &-directed unit vector at the point N(d, 4', 0) in the spherical co-ordinates. In order to simplify the following estimations, the equivalent magnetic current J, is assumed to exist only in the xy-plane, as shown in Fig. 4.21. Then the vector potential A, and the magnetic field H at P(e, 4, z) generated by this magnetic current J, are given mathematically by
251
where rn, (d, 4', +", JI) = dsin (4' - $) m2(d, 4', &", $) = dcos(4' - $) R, = RI,=,, K,
e
=
+ iisin (4' - 4") + acos(4' - 4")
= Jml(j4n)
{dZ+ 6'
cos (4)
=
+ 2ddcos($ - 4")}1/2 {dcos (JI) + ii cos (4")}/~
sin (4) = {dsin ($)
+ ri sin(d")}le
and H: and H$are the components of the magnetic field Hqat the point Q. By application of the EMF method to eqn. 4.67, the mutual admittance Y12 between the two patches can be easily obtained as follows:
-
is the where J,($') = 2Jmcos(4'), o is the angular frequency, ko(= a=) free-space propagation constant and E , and po are the free-space permittivity and permeability, respectively. R is the distance between the magnetic current J, and the observation point P, and is given by Using eqn. 4.66 and the co-ordinate system shown in Fig. 4.216, the magnetic field Hqat the point Q can be derived analytically by the following equation [22], while it corresponds to the magnetic field at the periphery of patch antenna 2:
s
rn7{e sin (4')
= (K~I~P~)
-
(
d,
4,
- 2a Jmi(0)
dsin (JI - 4")
(4.68)
JUO)
where J*,,(@) is the complex conjugate of m J@ 2()' and i+.is the 4" directed unit vector at the point Q. Substituting eqn. 4.67 into eqn. 4.68, and carrying out numerical integration for eqn. 4.68, the values of mutual admittance ( = G I , + B,,) can be determined numerically, as shown by the solid lines in Fig. 4.22. It is important to note that the results shown in Fig. 4.22 are expressed in term of the normalised admittance PI,(= Yl,/G,,) between the two patch antennas. Here, GI, denotes the self conductance for an isolated patch antenna, and is shown as GI, = GI,/,,,. In order to verify the estimates of PI:,,,experimental work was carried out at S-band using typical samples. The theoretical values based on eqn. 4.68 agree well with the experimental ones within the desired range, as shown in the Figure. In the design of an array, the mutual coupling IS,,I for a patch antenna is also an important factor. The mutual coupling for an antenna is therefore described here, together with the experimental results. Using the normalised admittance and the scattering S-matrix, we can express the mutual coupling by the following equation:
c,
z2
where Poand respectively.
g, correspond to the normalised
self and mutual admittances,
252
Circular polarisation and bandwidth
Circular polarisation and bandwidth
0.4/-
10.4
253
The mutual coupling ISl2)for a circular patch was estimated here using eqn. 4.69. The calculated values of coupling for a circular patch are shown in Fig. 4.23. As shown in the figure, the theoretical coupling for a rectangular patch obtained by the same calculation coincides fairly well with that for a circular patch. The samples of both rectangular and circular patches are designed to have the same resonant frequency. In this Section, we have presented a simple method for estimating the mutual coupling of patch antennas. After estimating the coupling, the calculated values were compared with the experimental ones. The calculated values agree well with the experimental results in spite of neglecting the effects of dielectric substrate.
4.5 Wideband techniques
Fig. 4.22
Normalised mutual admittance ?, A, = 0.078 (From Reference 22)
between two microstrip antennas, where t/
r;=
9.375 GHz
n
1---
circular ~atch
element spaclng (dl+,) Fig. 4.23
Comparison of IS,,I between circular and rectangular microstrip antennas
As is well known, the handwidth of microstrip antennas c m basical!y be increased by increasing the thickness of the substrate and decreasing its dielectric constant [24, 271. Also, it is well known that it is quite effective to mount a parasitic element on the original patch radiator [25]. On the other hand, in the case of an array, the bandwidth can also be increased collectively by arranging the antenna elements in a certain way [26]. In the following Sections, the wideband techniques for the first two methods are described fully, and finally the last method is also described. 4.5.1 Design of wideband elements The bandwidth of a microstrip antenna depends on the patch shape, the resonant frequency, and the dielectric constant and thickness of the substrate. In this Section, the relations between these parameters are derived and a design method is described for the wideband microstrip antenna. The wider bandwidth is usually obtained by employing a thick substrate with low dielectric constant [24, 271. However, such an antenna, in general, has two major problems which should be considered. One concerns the surface-wave radiation and the other concerns the unwanted mode generation. The former may impose a limiting factor on the maximum usable thickness of any substrate, because a practical microstrip antenna is usually designed so as not to radiate any surface waves. However, the latter problem cannot be ignored for microstrip antennas having a bandwidth greater than about 6%. Although a wideband microstrip antenna has these problems, it has the advantage that no balun (or balanced-to-unbalanced transformer) is required, so that the bandwidth can be accurately and analytically estimated. This advantage makes it possible to design the microstrip antenna taking into account not only the resonant frequency but also the bandwidth. In this Section, the relations between the design parameters are briefly summarked first. Next, in order to make it easy to understand the design procedure, a design example is given for a circular microstrip antenna whose bandwidth for
254
Circular polarisation and bandwidth
Circular polarisation and bandwidth
a VSWR less than 2.0 is 8.75% [28]. Finally, two methods of cancelling out the higher-order modes caused by lowering the antenna Q-factor is briefly described. (a) Relations between parameters necessary for design [ 2 9 ] : The antenna bandwidth is, in general, represented as a function of the unloaded Q factor and the input VSWR [24]. Accordingly, if the requirements of the input VSWR and the bandwidth are specified, the desired value for the unloaded Q factor can be determined. In this Section, the relation between them is first derived and it is also shown that the product of the bandwidth and unloaded Q takes the maximum value for the special characteristic impedance of feeder used. Generally, the input admittance of the microstrip antenna may be approximated, using the relative bandwidth denoted by B, and the unloaded Q denoted by Q,, as follows:
Y,
=
g('y{l
+ jQoBr}
255
when the following condition is satisfied for the coupling coefficient: The results of eqns. 4.74 and 4.75 are illustrated by the broken and solid lines in Fig. 4.24, respectively. Using this Figure, the unloaded Q necessary for the design of the antenna can be determined graphically if the requirements for the bandwidth and input VSWR are specified. Also, the chain-dotted line in Fig. 4.24 indicates the result obtained from eqn. 4.76. This relation is useful in determining the position of the feed point and the characteristic impedance necessary for thefeeder used.
(4.70)
where g(')' = g ( O j ~ W
and g(') is the conductance component given by eqn. 4.24. Mg) is the turns ratio for the 1th resonant circuit in Fig. 4.14, and is given by eqn. 4.19 or 4.20 for any feed point. If the transmission line with characteristic admittance of Go is connected to this antenna, the input VSWR is given by
Substituting eqn. 4.70 in the above, the equation giving the relation between the bandwidth, unloaded Q, and input VSWR can be obtained by QOB, =
dPe -
1)(1
- Pie)
(4.72)
where p is the coupling coefficient and is defined by
P
=
VSWR
GO/g(ly
Eqn. 4.72 implies that, if an input VSWR of < Q is required, the product of the Q factor and bandwidth necessary for the antenna is related only to the coupling coefficient. As a special case, let us consider the case of P = 1, i.e. Go = g('); then eqn. 4.72 results in [24]
However, it should be noted that eqn. 4.74 does not usually give the maximum value for the product of the bandwidth and Q factor. It can be obtained from
Q,B, = J(eZ
-
1k1
-
1/e2>/:!
(4.75)
(P)
Fig. 4.24 Relationship between 0,.6,. Po and input VSWR (From Reference 29)
Next, the relation between the resonant frequency, the dimension of the patch radiator, and the thickness and dielectric constant of the substrate used is derived. Let S be the physical area of the patch radiator and t be the substrate, thickness. Now, if @ / t is introduced as a parameter, the product of the can generally be expressed as a function of f i t resonant frequencyf (') and and the substrate dielectric constant 8,. Fig. 4.25 shows the relations between f@' @ and @/Iwith E, as a parameter for a circular microstrip antenna. The dots in the Figure show the measured results. On the other hand, if the radiation conductance can be regarded as a domi-
4
256
Circular polarisation and bandwidth
Circular polarisation and bandwidth
nant factor compared with the other conductance components, the unloaded Q denoted by Q, can also be approximated as a function of E, and f i t . Fig. 4.26 shows the relation between Q, and f i / t with E, as a parameter, for the circular microstrip antenna. In this Figure the dots show the measured results.
257
In eqn. 4.77, the second-order mode (TM,,,) is chosen as a dominant mode. From Fig. 4.24, the product of the maximum bandwidth and Q,, when Q = 2.0, is QoBr
=
0.75
(4.79)
From the above equation and eqn. 4.78, it is found that Q, necessary for this antenna is Qo = 8.6
(4.80)
It follows from Fig. 4.26 that when a substrate of E,
Fig. 4.25
t/S
Relations between ff2) and @t antenna (From Reference 29)
= 1.21
(4.81)
with E, as a parameter, for circular microstrip
Although only one example of a circular microstrip antenna is given here, the relationships shown in Figs. 4.25 and 4.26 are typical, and the above approach is applicable to any shape of antenna including rectangular and triangular microstrip. ( b ) Design example (291: In this Section, the specific design procedure is given for the example of a wideband circular microstrip antenna. Let us assume the following requirements for the frequency range and input VSWR: Frequency range: 1530-1670 MHz Input VSWR: less than 2.0 In this case, the centre or resonant frequency and the relative bandwidth are f'2' = 1600MHz (4.77)
Fig. 4.26 Relations between unloaded 0 and $ I t with E, as a parameter for circular microstrip antenna (From Reference 29)
is used, the &?/t
f i r value necessary to get the Q, value of eqn. 4.80 is = 5.84
Accordingly, in the case of a circular microstrip antenna whose equal to the above, it can be seen from Fig. 4.25 that
fly2' =
114.86
(4.82) fi/t
value is (4.83)
258
Circular polarisation and bandwidth
Circular polarisation and bandwidth
Eqns. 4.77 and 4.83 show that
fl
=
71.79mm
and the radius of the patch radiator is 40.5 mm. From the above result and eqn. 4.82, the thickness of the substrate to be used is calculated as In summary, the circular microstrip antenna to meet the proposed requirements has the following specifications: Dielectric constant of substrate: 1.21 Thickness of substrate:
12.3mm
Patch radius:
40.5 mm
-
259
mode, and their influence may become a serious problem, when the bandwidth is expanded without careful consideration. In this Section, the influence of lowering the quality factor is described. For example, the antenna shown in Fig. 4.27 is a fairly wideband antenna whose relative bandwidth is 8.75%, and the influence of the unwanted modes can no longer be ignored. The mode closest to the wanted one is the TM,,, mode in this case. The influence of the TM,,, mode may be most prominent when the antenna is used as a circularly polarised one with dual feeds. In that case, the TM,,, mode gives rise to some coupling between two terminals. The measured results for this coupling are shown, together with the calculated ones, in Fig. 4.29, where the solid line shows the measured results and the broken line shows the calculated ones. Also the chain-dotted line shows as a reference measured results for an antenna having a fairly high quality factor. In this Figure, the coupling is less
Such a microstrip antenna can be made using paper honeycomb materials as a substrate. Fig. 4.27 shows a circular microstrip antenna manufactured according to the above specification. Also, Fig. 4.28 shows the return-loss characteristics for this antenna, where the calculated and measured results are indicated by the solid and broken lines, respectively. Both results show the wideband performance of about 8.75% for VSWR 5 2.0, which agrees well with the requirement in eqn. 4.78. Circu l o r disk
Frequency
I/ V
I/
(
GHz )
Fig. 4.28 Return-loss characteristicsfor circular microstrip antenna shown in Fig. 4.27 (From Reference 29) a = 40.5 mm, t = 12.3mm, and E, = 1.21 Paper honeycomb core
C o a x i a l probes
Epoxy fiberglass skins Fig. 4.27 Structure of circular microstrip antenna consisting of epoxy Fiberglass skins and paper honeycomb core (From Reference 29)
( c ) Injhences of unwanted modes and countermeasures against them [28]: The bandwidth of a microstrip antenna can be increased by employing a
thick substrate with low dielectric constant, as shown in Fig. 4.28. However, it is expected that some unwanted modes will be generated as well as the wanted
than - 50 dB at the resonant frequency, which is small enough for the antenna with a high quality factor, and the coupling increases to about - 28 dB for an antenna with a low quality factor. These results suggest that the axial ratio may be degraded owing to the influence of this coupling when the latter antenna is used as a dual-fed circularly polarised antenna, although it is fed by a perfect 90' hybrid. Fig. 4.30 illustrates the axial-ratio characteristics for such an antenna, where the solid line shows the calculated results and the dots show the measured ones. This Figure shows that the best axial ratio is only of the order of 1.3 dB. In order to improve the axial ratio it is necessary to investigate the mechanism of the degradation. When a microstrip antenna has a low quality factor, the
260
Circular polarisation and bandwidth
Circular polarisation and bandwidth
261
Frequency (MHz) Fig. 4.29
Coupling characteristics between orthogonal ports for circular microstrip antenna with dual feeds (From Reference 28)
Frequency ( M H z ) Fig. 4.30 Axial-ratio characteristicsfor dual-fed circularly polarised circular microstrip antenna a = 40.5 mm, t = 12.3 mm, and E, = 1.21
Fig. 4.31 Equivalent circuit for dual-fed circular microstrip antenna having low-quality factor and the corresponding inner-surface current flows on the patch radiator a Equivalent circuit b Current flows (e signs denote the feed point)
equivalent circuit can be approximated by Fig. 4.31~.This Figure implies that the coupling may arise between two orthogonal terminals through the 4th resonant circuit, in which the current due to the unwanted mode flows. Therefore, the current flowing in the 4th resonant circuit must somehow be ,suppressed. Fig. 4.32 shows one method of cancelling out such a current by adding more two terminals to the original two, and feeding from four terminals 90" out of phase with equal amplitude. Fig. 4.33 shows the axial-ratio characteristics with such a method of feeding, where the solid line represents the calculated results and the broken line the measured ones. As expected, the axial ratio is improved remarkably compared with Fig. 4.30 for the case of the antenna fed from only two terminals. The above is particularly useful when the antenna is used only as a single element. When it is used as an element comprising an array antenna, it is also possible to cancel out the cross-polarised component radiated from each element at any observation point in free space. For convenience, let us consider a two-element array radiating elliptically polarised waves from each element, as shown in Fig. 4.34. If they are both RHCP and the excitation ratio is l : ~ e ' the ~, total electric field radiated from them can be determined from Fig. 4.34 as E = {a,
+ ydA(/?,C O S ~+ j/?,sinS)}f
262
Circular polarisation and bandwidth
Circular polarisation and bandwidth 1
& , =
1
5 [@I
- a21
263
+ yBAe-j6(8l - PI)]
(4.89)
with E, denoting the RHCP component. Therefore, in order to make the reverse polarised components cancel out on the boresight direction, the following complex excitation condition between two elements must be satisfied:
* Fig. 4.32 Actual feeding methods for circularly polarised circular microstrip antenna with four feed point (From Reference 28) a Right-hand circular polarisation b Left-hand circular polarisation
-
-:1.c 0 .+ "a. .-0
Fig. 4.34
d
-
2
Col.
I
f 30
1550
1600 Frequency
1650
1700
(MHz)
Two kinds of elliptically polarised waves radiated from two-element array a Polarisation ellipse of no. 1 element b Polarisation ellipse of no. 2 element
LHCP: left-hand circular polarisation RHCP: right-hand circular polarisation
Fig. 4.33 Axial-ratio characteristics improved by feeding from four terminals as shown in Fig. 4.32a (From Reference 28) a = 40.5rnrn, t = 1 2 . 3 rnrn, and e, = 1.21
on the boresight direction, where 6 indicates the physical rotation angle of the polarisation ellipse of the no. 2 element against that of the no. 1 element on an XY plane as shown in Fig. 4.34. Dividing the above field into the two components of co-polarisation and cross-polarisation, it can be expressed as
E where
= U
f
-
+ E,,,df + 9)
Frequency
(4.87)
[MHz)
Fig. 4.35 Axial-ratio characteristicsimprovedby employingpairedelemenrs (From Reference 28) a = 40.5 mm, t = 12.3 mrn, and
E, =
1.21
264
Circular polarisation and bandwidth
Circular polarisation and bandwidth
I
Since an ordinary array antenna consists of the same elements, the above relationship can be reduced to
265
tions, using an impedance matrix known as a matrix Green's function, as follows:
because it can be assumed that a, = p, and a, = B,. The radiation field for the RHCP, being a co-polarised component in this case, can be expressed as Em
=
ER
=
- j(a,
+ a,)d6sin6
(4.92)
parostic element
The above equation implies that the co-polarised component takes the maximum value
IEmI
=
lERl
=
la! +
(4.93)
when the following condition is satisfied for the rotation angle 6: 6
=
90"
(4.94)
On the other hand, the excitation condition for LHCP, instead of RHCP as above, can be similarly derived and is given by y p = - e-jd = &("-6) (4.95)
?(a)
when a , = p, and a, = B,. The resultant LHCP component is represented as a function of 6, as in the case of RHCP. So the same maximum value as in RHCP case can be obtained, when the same condition (eqn. 4.94) is satisfied for 6. It is concluded from the above discussion that the axial ratio may be improved, in case of an array antenna, by arranging for the paired elements to have a rotation angle 6 = 90". Fig. 4.35 shows the measured results for the axialratio characteristics of such paired elements. As expected, the resultant axial ratio is improved remarkably compared with the results of Fig. 4.30, and is of the same order as that obtained by the previous four terminal-fed cases. 4.5.2 Technique using parasitic element [34] The bandwidth of a microstrip antenna can also be increased by employing a parasitic element [25, 30-321. In this Section, the type shown in Fig. 4 . 3 6 ~is analysed using the Hankel-transformed domain-analysis method [33], and it is shown from theory and experiment to achieve an increase in the bandwidth. In this Figure, the two substrates are stacked so that they are parallel and the two circular etched disc conductors are concentric. The upper one is used as a parasitic element. (a) Characteristic equation in the Hankel-transformed domain: In general, Green's function in the real domain is a very complicated convolutional integral or summation form, as shown in eqn. 4.14. However, it is known that Green's function becomes of simple algebraic form if it is expressed in the Hankel-transformed domain. In this domain, it can be deduced from Reference 33 that the electric fields on the boundary are related to the corresponding current distribu-
air
short for E- wove
for H- wove
(b) Fig. 4.36
Circular microstrip antenna with parasitic element and its spectral-domain equivalent circuit (From Reference 34) a Structure of analytical model and co-ordinate system b Equivalent circuit for E- and H-waves
where the sub-vectors [E(a)],,, and [i(cc)],,, consist of two elements, respectively, and are
266
Circular polarisation a n d bandwidth
Circular polarisation a n d bandwidth
The tilde means the quantities in the Hankel-transformed domain, and each element is defined from its tangential components, which consists of both E-wave and H-wave, as
with F,(r) and F6(r) being the tangential components and J,,,(x) being the Bessel function of the first kind with (n + 1) or (n - I) th order. Also the subscripts 1 and 2, being the order of elements in each sub-matrix of eqn. 4.97, are referred to the lower and upper conductors. The sub-matrices in eqn. 4.96 can be represented by
for 1
= e
for 1
=
267
(E-wave)
h (H-wave)
for I
= e
for I
=
(E-wave)
h (H-wave)
These elements can be derived from the spectral-domain equivalent circuit shown in Fig. 4.366. Next, the unknown current distributions are expanded on each circular conductor in the real domain as follows:
where the matrices [Z(a)], and [Z(a)], denote the impedance matrices for E-wave and H-wave, respectively, and are written as where A, and B, are expansion coefficients with i = 1 and 2 being referred to the lower and upper conductors, whilef,,(r) and &(r) are basis functions. In this case, the Hankel-transformed current distribution $*)(a) in eqn. 4.976 is expressed as They can be easily determined from the corresponding admittance matrices, which consist of the following elements:
(4.101~)
- Ysin (pd) sin ( r t ) ]
Y:2(a)
=
Y:! (a) =
-jYY1 Ycos (pd) sin (B't) Y'cos (p't) sin (pd)
where [A,] and [B,] are unknown vectors with A;, and B,,, and [x(a)],,, and [&(a)](+, are the transformed basis function vectors with x!:)(a) and &'(a). Substituting eqn. 4.104 into eqn. 4.976 and then substituting the resulting equation and eqn. 4 . 9 7 ~into eqn. 4.96, the following matrix equation can be obtained:
+
[ A ~ l [ h f a ) l ( ++) j[~11[.?41fa)I(+)
(4.1016)
[A2l[X2fa)l1+, + i[~21[342fa)lc+) [ A l l [ ~ l f a ) l ( -) j[~~l&~fa)l(-)
- Y' sin (pd) sin (Pt)]
with I
=
(4.101~)
EJ-I (a)
[A21[.f,2fa)l(-) - j [ ~ ~ l t f 4 ~ f a ) l ~ - )
e or h and
p = ,/8. = J W ~ ~ , E , E ,
- a2
Taking inner products of eqn. 4.105 with all the transformed basis functions fi;)(a) and]$:'(a) according to Galerkin's method, the left-hand sides of all the resulting equations vanish owing to the boundary conditions. Thus it is possible
268
Circular polarisation and bandwidth
269
Circular polarisation and bandwidth
to choose the following combinations in order to avoid divergence of integrals appearing in the characteristic equation:
to exist. Therefore, the characteristic equation for this problem can be written as Q(w)
=
det[P] = 0
(4.1 12)
where w is the complex resonant angular frequency whose real and imaginary parts correspond to the resonant angular frequencies and the damping factors, respectively. where a bracket ( . ) in the above equations is employed for the following infinite integral:
Finally, eqn. 4.106 can be rewritten in a matrix form and is given by
p111
0.0
where the matrix [PI is defined as follows:
0.85
0.90
0.95
real port
Fig. 4.37
and the elements of the sub-matrices [P!]
I 0.80
through [ P a ] with i
=
1 or 2 and
j = I or 2 are given by
with
From eqn. 4.108, the determinant of [PI must vanish for a non-trivial solution
1 .OO
1.05
Dr
Contour of complex resonant frequencies of circular microstrip antenna with parasitic element (From Reference 34) t = 1.6 mm and E, = 2.55.b = w/wo = b, + jh,
( b ) Electrical characteristics: In this case, two basis functions for each current component provide satisfactory accuracy, so that the characteristic equation results in a form of determinant of size 8 x 8. Fig. 4.37 shows numerical results for the complex resonant frequencies solved from eqn. 4.1 12, where the thickness and dielectric constant for the substrate used are t = 1-6mm and E, = 2.55, respectively. The Figure shows the contour map for the real and imaginary parts of normarised complex resonant frequencies with a,/a, and d/al as parameters. From this Figure, it is found that two dominant resonant modes, which exhibit a double-tuned characteristic, exist in this antenna. So the input VSWR characteristics can be calculated by considering a double-tuned performance. In this case, two resonant resistances R, and R, can be determined uniquely as follows:
270
Circular polarisation and bandwidth
Circular polarisation and bandwidth
because
277
in some special applications [36]. In this Section, we briefly describe design procedure of such a paired element. Fig. 4 . 3 9 ~shows the fundamental arrangement of a microstrip paired-element unit. The patch elements are rotated orthogonally on the coplanar plane and are fed in uniform amplitude but 90' out of phase through the sequentially rotated feeding points F, and F,. w0 = 1441c in Fig. 4.37
(-n12) phase shifter
a,
where w,, and w,, are resonant angular frequencies for two dominant modes and cis the velocity of light in vacuum. Fig. 4.38 shows the calculated and measured input VSWR characteristics for the antenna with d = IOmm, a , = 20+3mm, a, = 21.0 mm, t = 1.6 mm, and 6, = 2.55. In this Figure, the results for the antenna without a parasitic element are also shown as a reference, and it is seen that the effect of the parasitic element is considerable.
( a ) Paired element
EY
>
1.1
I
2.4
2.5
2.6
2.7
2.8
frequency ( G H r )
Fig. 4.38
Calculated and measured VSW R characteristics for circular microstrip antenna with parasitic element (From Reference 34) d = 1 0 m m , a, = 2 0 . 8 m m . a , = 2 1 . 0 m m . t = 1.6rnm. a n d & , = 2.55
4.5.3 Technique using paired element Circularly polarised microstrip antennas including single-fed patches are widely used as effective radiators in many communication systems [6, 101. However, the most serious problem with such antennas is the narrowness of the ellipticity and impedance bandwidth compared with ordinary microwave antennas. Several techniques for the expansion of bandwidth have been reported in the literature [29-341. However, most of these broadband techniques, including double-stacked CP patches, are applicable to isolated CP patch antennas. Hence, other wideband techniques using sequential arrangements of antenna elements have been developed in recent years [26,35]. The simplest device for such a sequential array is a paired element, and it is used as an effective radiator
( b ) Principle of wideband
Fig. 4.39 Paired element and its polarisation pattern
A sub-array composed of such paired elements demonstrates the broadband nature in spite of using narrow-band patch elements [26]. In order to evaluate the performance, the polarisation pattern of an antenna is briefly described. In general, individual elements of a pair show elliptical patterns of polarisation, as shown in Fig. 4.396. The polarisation ellipses marked A and B correspond to those of each element of a pair, while the Ex- and E,-axes correspond to the horizontal and vertical components of the radiated electric field. The polarisation ellipses for an individual CP patch vary rapidly with change of frequency. However, if the CP patch of a pair is arranged orthogonally and is fed uniformly in amplitude but 90' out of phase, the resultant polarisation pattern due to the pair can be shown as a trace of perfectly circular polarisation over a wide frequency range, as shown in the figure.
272
Circular polarisation and bandwidth
In order to verify the performance, a 2 x 2 element sub-array unit having two pairs was constructed and tested at X-band. With regards the feeding system, the input impedance for each element of the pairs was matched to that of the main feeder M, by means of A,/4 impedance transformers, T,, T,,T, and T,, where 1, is the wavelength in stripline. Fig. 4.406 shows the typical measured ellipticity bandwidth for the sub-array unit. The ellipticity bandwidth for an isolated CP-patch antenna is also shown for comparison in the Figure. It is shown that the sub-array unit using the paired element contributes enormously to the improvement of the ellipticity bandwidth compared with a single CPpatch element. The 3 dB ellipticity bandwidth obtained by this sub-array unit is about five times the value obtained by an ordinary CP-patch element, as shown in the figure. A more detailed description of the sequential array is given in Chapter 13.
Circular polarisation and bandwidth 2
3 4 5 6 7 8 9 10 I1 12 13 14
15 16 17 18 19 20 21 22
23 24 Fig. 4.40 Sub-array unit and its ellipticity bandwidth
25
4.6 References 1 MAILLOUX, R. J., McILVENNA, J. F., and KERNWEIS, N. P.: 'Microstrip array technology', IEEE Trans., 1981, AP-29, pp. 25-37
26
27
273
WEINSCHEL, H. D.: 'A cylindrical array of circularly polarized microstrip antennas'. In!. Syn7p. Dig. Antennas Propagat. Soc., June 1975, pp. 177-180 SHEN, L. C.: 'The elliptical microstrip antenna with circular polarization', IEEE Trans., 1981, AP-29, pp. 90-94 RICHARDS, W. F., LO, Y. T., and HARRISON, D. D.: 'An improved theory for microstrip antennas and applications', IEEE Trans., 1981, AP-29, pp. 38-46 KERR. J. L.: 'Microstrip polarization techniques'. Proc. Antenna Applications Symp., Allerton Park, IL, Sept. 1978 JAMES, J. R., HALL, P. S., and WOOD, C.: 'Microstrip antenna'. (Peter Peregrinus, 1981) chap. 7 HANEISHI, M., NAMBARA, T., and YOSHIDA, S.: 'Study on elliptical properties of singly-fed circularly polarised microstrip antennas', Electron Lett., 1982, 18, pp. 191-193 ITOH, K.: 'Circularly polarised printed array composed of strip dipole and slot', Microwave J., April 1987, pp. 143-153 JAMES, J. R., HALL, P. S., WOOD, C., and HENDERSON, A,: 'Some recent developments in microstrip antenna design', IEEE Trans., 1981, AP-29, pp. 124-128 CARVER, K. R., and MINK, J. R.: 'Microstrip antenna technology*,IEEE Trans., Antennas & Piopagi., :98:, AP-29, pp. 2-24 HANEISHI, M., and YOSHIDA, S.: 'A design method of circularly polarised rectangular microstrip antenna by one-point feed', Electron & Commun in Japan, 1981, 54, pp. 46-54 OKOSHI, T., and MIYOSHI, T.: 'Planar circuits', (Ohm Publishing (in Japanese), 1973) SUZUKI, Y., MIYANO, N., and CHIBA, Y.: 'Circularly polarised radiation from singly-fed equilateral-triangular microstrip antenna', IEE Proc. 1987, 134, pp. 194-198 SCHAUBERT, D. H., FARRAR, F. G., SINDORIS, A,, and HAYES, S. T.: 'Microstrip antennas with frequency agility and polarization diversity', IEEE Trans., 1981, AP-29, pp. 118-123 OKOSHI, T., and MIYOSHI, T.: 'The planar circuits - An approach to microwave integrated circuitry', IEEE Trans., 1972, MlT-20, pp. 245-252 CARVER, K. R.: 'A modal expansion theory for the microstrip antenna', Int. Symp. Dig. Antennas Propagal. Soc., June 1979, pp. 101-104 SUZUKI, Y., and CHIBA, T.: 'Computer analysis method for arbitrarily shaped microstrip antenna with multi-terminals', IEEE Trans., 1984, AP-32, pp. 585-590 SUZUKI, Y., and CHIBA, T.: 'Improved theory for a singly-fed circularly polarized microstrip antenna', Trans. IECE Japan, 1985, E68, pp. 76-82 For example, NEWMAN, E. H., and TULYATHAN, P.: 'Analysis of microstrip antennas using moment methods', IEEE Trans., 1981, AP-29, pp. 47-53 MORSE, P. M., and FESHBACH, H.: 'Methods of theoretical physics: Pt. 11. (McGraw-Hill, NY, 1953). pp. 1112-1 119 CARVER, K. R.: 'Input impedance to probe fed microstrip antennas', In!. Symp. Dig. Antennas Propagat. Soc., June 1980, pp. 617-620 HANEISHI, M., YOSHIDA, S., and TABETA, M.: 'A design of back-feed type circularly polarised microstrip antenna having symmetrical perturbation segment', Electron & Commun. in Japan, 1981, 2, pp. 52-60 POZAR, D. M.: 'Input impedance and mutual coupling of rectangular microstrip antennas', IEEE Trans., 1982, AP-30, pp. 1191-1 197 DERNERYD, A. G., and LIND, A. G.: 'Extended analysis of rectangular microstrip resonator antennas', IEEE Trans., 1979, AP-27, pp. 846-849 ITAMI, H., and HORI, T.: 'Broad band circular polarized microstrip antenna'. In!. Conv. Rec. lECE (in Japanese), 1982, p. 642 HANEISHI, M., YOSHIDA, S., and GOTO, N.: 'A broadland microstrip array composed of single-feed type circularly polarized microstrip antennas', in In!. Symp. Dig. Antennas Propagal. Soc., May 1982, pp. 160-163 MURPHY, L.: 'SEASAT and SIR-A microstrip antennas', Proc. Workshop on Printed Circuit Antenna Technology, Oct. 1979, paper 18
274
Circular polarisation a n d bandwidth
28 CHIBA, T., SUZUKI, Y., MIYANO, N., MIURA, S., and OHMORI, S.: 'A phased array antenna using microstrip patch antennas', 12th European Microwave Conference, Sept. 1982, pp. 472-477 29 SUZUKI, Y.,and CHIBA, T.: 'Designing method of microstrip antenna considering the bandwidth', Trans. IECE Japan, 1984, E67, pp. 488-493 30 WOOD, C.: 'Improved bandwidth of microstrip antennas using parasitic elements', IEE Proc., 1980, 127, pp. 23 1-234 31 LONG, S. A., and WALTON, M. D.: 'A dual-frequency stacked circular disc antenna', Int. Symp. Dig. Antennas Propagat. Soc., June 1978, pp. 260-263 32 SANFORD, G. G.: 'Multiple resonance radio frequency microstrip antenna structure', US Patent 4070676, Jan. 1978 33 ARAKI, K., and ITOH, T.: 'Hankel transform domain analysis of open circular microstrip radiating structures', IEEE Trans., 1981 AP-29, pp. 84-89 34 ARAKI, K., UEDA, H., and TAKAHASHI, M.: 'Numerical analysis of circular disk microstrip antennas with parasitic elements', IEEE Trans., 1986, AP-34, pp. 1390-1394 35 TESHIROGI, T., TANAKA, M., and CHUJO, W.: 'Wideband circularly polarised array antennas with sequential rotations and phase shift of elements'. Proc. Int. Symp. on Antennas & Propagt., Japan, Vol. 1, Aug. 1985, pp. 117-120 36 HANEISHI, M., HAKURA, Y., SAITO, S . , and HASEGAWA, T.: 'A low-profile antenna for DBS reception'. Int. Symp. Dig. Antennas Propagat. Soc., June 1987, pp. 914-917 37 SUZUKI, Y.: 'Analysis of microstrip antennas based on the planar circuit theory and its applictions (in Japanese)'. Doctoral dissertation, Tokyo Inst. Technol., Nov. 1984
Chapter 5
Microstrip dipoles P.B. Katehi, D.R. Jackson and
N.G. Alexopoulos
5.1 Introduction
Microstrip dipoles have been studied extensively during the last 20 years. Tlley are planar elements which consist of a pair of collinear thin-strip conductcrs printed on the surface of a dielectric slab (Fig. 5.1). They resemble the free-space cylindrical dipoles in the sense that radiation results from a harmonically varying dipole moment. Microstrip dipoles are attractive elements owing to their desirable properties such as simplicity, small size and linear polarisation.
1
I
I
1
Coaxial Excitation
Fig. 5.1 Excitation mechanisms for a microstrip dipole
They are well suited for higher frequencies in particular, where the substrate may be electrically thick. In this case the bandwidth of the dipoles may be quite significant. For thicker substrates it is also possible to alter the radiation properties by the use of a superstrate layer, making dipoles a possible candidate in a substrate-superstrate geometry. When designing microstrip dipoles, the choice of feed mechanism is very
276
Microstrip dipoles
Microstrip dipoles
important and should be made taking into consideration the following two factors: theoretical modelling and practical implementation. Fig. 5.1 shows the most commonly used mechanisms: the coaxial feed, the twin-line feed and the coupled-line feed (EMC dipole). In the twin-line feed a voltage is applied directly to the arms of the dipole. In the coaxial feed the two dipole arms are shorted together, with the dipole becoming essentially a narrow patch antenna with a probe feed. The EMC dipole excitation is realised through electromagnetic coupling to the feed line, with no direct contact. Because of its simplicity, the EMC feed represents the most desirable way to feed a dipole from a microstrip line. Even if practical excitation mechanisms are employed in the design of microstrip dipoles, more ideal ones may be considered for their analysis. The reason lies in the fact that most of their radiation properties are independent of the excitation (i.e. bandwidth, efficiency, radiation pattern etc.). Throughout this Chapter the iiiiciosirip dip& is siiidied extensiveiy as a single radiator as well as an array element. Furthermore, infinitesimally small, centre-fed and EMC dipoles are presented separately, and the dependence of their properties on the electric characteristics of the dielectric layers is discussed. The study of microstrip dipoles is concluded by presenting a design technique for a n array of EMC dipoles which accounts for the mutual interactions between dipole elements.
277
complicated functions of 1, z, z', and are given in Reference 2. The time dependence is ef'"", and is suppressed here. The functionsf and g are of the form
where a and b are analytic functions of 1except for the branch-type singularity due to the wavenumber k
112
=
(G -2)
which appears in the expressions [2]. The functions D,(1) and Dm@)have zeros on the real axis at A,, producing poles in the integrand. The zeros of D,(1) are
5.2 Infinitesimal dipole The simplest dipole structure which can be studied is the infinitesimal dipole. An analysis of the infinitesimal dipole is important because all the radiation characteristics of full-size dipoles may be obtained simply from this solution. Only for near-field (impedance) calculations is it essential to analyse the full-size dipole with a moment-method technique.
5.2.1 Analysis A horizontal electric dipole (HED) is shown in Fig. 5.2. In general, the dipole may be embedded within an arbitrary number of layers, although two layers are sufficient to cover most cases of practical interest, including microstrip dipoles with a protective top (superstrate) layer, or EMC dipoles with a transmission line at the interface (z = b). In the classical Sommerfeld solution, components of the magnetic vector potential at x, y, z due to a source at x', y', z' are written as
with
Q,
q5 describing cylindrical coordinates [I]. The functions f and g are
Fig. 5.2 Substrate-superstrate geometry with horizontal electric dipole (HED) embedded
the TE-mode surface-wave propagation constants, while those of D,(1) correspond to the TM-mode surface waves. These poles are in the region where k, = max (k,, k,). The path of integration goes k, < A, < k,, around the poles, as shown by contour C in Fig. 5.3. By using symmetry properties [I] the integrations may be extended to (- co, + co) and the path deformed to an integral around the branch cut (contour C b ) plus integrals around the poles in the right-half plane. The potentials may then be written as
Microstrip dipoles
279
with P,a, and P,, the radiated and total surface-wave powers, respectively. 5.2.2 Substrate effects The effect of substrate thickness on the efficiency of an infinitesimal dipole on top of a single layer is shown plotted against the electrical substrate thickness b / A d (where Ad = A,/JE,) in Fig. 5.4 for various substrates. Note that the efficiencydecreases for increasing substrate thickness, and is lower for higher E , .
Fig. 5.3 Contours of integration
The residue contributions at the poles give the surface-wave fields. A steepestdescent method may be used to find the far-zone radiation field, although a reciprocity method is simpler [2]. The Poynting vector from the far-zone radiation field may be integrated over a hemisphere to find the radiated power. This reduces to a one-dimensional numerical integration [2]. The surface-wave Poynting vector may be integrated over a large cylinder to find a closed-form expression for the power in a surface wave. The surface waves are orthogonal with each other and with the radiation field in the lossless case [3], so the total power is simply the sum of all the powers. The radiation efficiency is defined in the lossless case as
Fig. 5.4 Efficiency of HED versus substrate thickness for dipole on top of single substrate layer
The efficiency approaches 1.0 for thin substrates, but the radiated power of the dipole then becomes very low, as seen from Fig. 5.5. This points toward one of the practical limitations of using resonant-length dipoles on thin substrates, namely low input resistance. A patch antenna does not have this disadvantage since the resonant resistance is fairly independent of substrate thickness [4].
280
Microstrip dipoles
,& Tad
Microstrip dipoles
Normalized by 10 ' 1 1%
281
Another limitation of resonant-length dipoles on thin substrates is a very small bandwidth -much lower than that of a patch (this is discussed in Section 5.4.2). Because of these limitations, dipoles find best application for thicker substrates where bandwidth and resistance are no longer serious limitations, and where the patch antenna becomes non-resonant [5]. 5.2.3 Superstrate effects
It is interesting to note that a superstrate (cover) layer on top of a microstrip dipole may significantly influence the radiation properties. For example, if the substrate is thin enough, a superstrate layer may be used to eliminate surfacewave excitation, resulting in an efficiency of 100% [2]. An example of this is shown in Fig. 5.6 for a GaAs superstrate over a Teflon substrate. In a different application, a substrate-superstrate geometry may be used to produce 'radiation into the horizon', a phenomenon in which the far-zone radiation field
-E-PLANE
PATTERN
blXd
Fig.
Radiated power of HED (Watts) versus substrate thickness for unit-strength dipole on top of single substrate layer
Fig. 5.7 Radiation pattern of HED demonstrating the radiation into the horizon effect (Reproduced from Reference 6,@ 1985 IEEE) The dipole is embedded within a single substrate layer here
Fig. 5.6 Efficiency of HED versus superstrate thickness, showing 100% efficiency at tlL, = 0.233 (Reproduced from Reference, 2, @ 1984 IEEE) The dipole is at the interface (z, = b )
remains non-zero down to the layer surface. One result is the possibility of producing very nearly omnidirectional patterns [6].An example of this is shown in Fig. 5.7 for a dipole embedded within a single substrate layer of thickness b (or, equivalently, the superstrate material is the same as the substrate). A third application of a superstrate layer is in the production of high-gain patterns about any desired angle 0, in space. By using one or more superstrate layers of the proper thickness, narrow-beam patterns may be produced as the superstrate E , ~becomes large [7].An example of this for 0, = 45" is shown in
282
Microstrip dipoles
Microstrip dipoles
Fig. 5.8 using a superstrate with E,, = 100. This narrow-beam effect is produced by weakly attenuated leaky waves which exist on the structure [a]. All the above effects pertain to any type of microstrip element in a substratesuperstrate geometry. However, except for the first effect (increased efficiency), these methods all require electrically thick layers, making dipoles an attractive candidate.
283
domain piecewise-sinusoidal basis functions of the form Bky)
= J,
= ~ 0 1 5(x) )
lyl < w / 2
(5.8)
1x1 < d where
E-PIANE PATTERN
Fig. 5.8 Radiation pattern of HED demonstrating the high-gain effect (Reproduced from Reference 7, @ 1985 IEEE) The dipole is embedded within the substrate with a superstrate layer on top
5.3 Moment-method techniques for planar strip geometries The analysis of geometries comprising dipoles and transmission lines involves strips which are usually narrow compared to a wavelength ( w 4 4). The geometry of a strip is shown in Fig. 5.9. Because the strip is narrow, current may be assumed in the f direction only. The narrow-strip assumption also allows for certain techniques to improve the computational efficiency of the analysis. In this Section methods for analysing strip structures are discussed. 5.3.1 Basis Functions For the moment-method solution of strip geometries, including dipoles and transmission lines, the current on the strips may be represented using sub-
Fig. 5.9 Planar strip in a layered geometry, divided into subsections. Also shown is the basis function variation in x
Three useful choices for the transverse variation are the pulse function, the modified Maxwell function [9] and the Maxwell function:
284
Microstrip dipoles
The normalisation constants here are chosen to give a unit current at x = 0. The Maxwell function more closely represents the true current on a narrow strip. The modified Maxwell function is similar to the Maxwell function except near the edges. Because it lacks the singular behaviour at the edges, the Fourier transform of the modified Maxwell function decays faster for large values of the transform variable, which makes it computationally more efficient for spectraldomain analysis techniques. 5.3.2 Reaction between basis functions The fundamental step in a Galerkin moment-method solution of strip problems is the computation of reaction between two basis functions:
Microstrip dipoles
285
5.3.3 Plane-wave spectrum method Two distinct methods have been used in the literature for the calculation of reaction: the Fourier transform (plane-wave spectrum) method and the realspace integration technique. In the spectral method, eqns. 5.1 and 5.2 are first transformed into rectangular (Fourier) transform form, and substituted into eqns. 5.12 - 5.14. The resulting integrations in x, y, x', y' result in Fourier transforms of the current [10,1I]. The result is
- z:
(I,, A,) cos &A,) cos
(44) d1d4
(5.15)
where
with and with S, and S, the basis-function surfaces. G,, is the f f component of the dyadic Green's function for E,(x, y, 2,) due to a source at x', y', z,. This is given by
a2n + 2. a2n + -+ ax axa~
ag A1 az h(1, z,, z,) = -
G,, = k Z n x
If more than one strip is involved in the problem under consideration, it is convenient to choose the x-axis offset between strips as an integral multiple of the subsection length d, so that the impedance submatrices will all be Toeplitz. Depending on the particular problem, d is typically in the range 0.01 A, < d < 0.05 A,. In this case 5(x) is close to a piecewise linear function, and the value of k, in eqn. 5.8 is not critical. The choice of transverse distribution ~ ( y has ) some influence in the reaction values obtained, especially for the self-term (no offset between basis functions). Experience has shown, however, that the current amplitudes, obtained from the moment-method matrix solution, are fairly independent of the choice of qb). For the solution of the strip problems, the starting point is the calculation of arrays Z,(m) where the mth element is reaction between basis functions separated by (m-l)d between centres in the %direction. The index i refers to the particular submatrix in the Galerkin impedance matrix, corresponding to basis functions on different strips. The y-directed offset may be different for each submatrix if the strips have transverse offset. z, and z, may be different for each submatrix as well.
The separation between basis-function centres is denoted as Ax, Ay here. For the basis function choices (eqns. 5.9 - 5.1 1) the transforms may be evaluated in closed form [lo]. The integral on (0, co) in eqn. 5.15 is along the Sommerfeld contour C in Fig. 5.3. A pole-extraction technique may be used to account for the poles on the real axis [I 11. A simpler way is just to deform the contour to go around the poles as shown by contour C, in Fig. 5.3 [12]. An advantage of the spectral approach is that self-term problems are avoided. However, the convergence of the Sommerfeld integral in eqn. 5.15 becomes worse as the separations Ax, Ay become large compared to the respective basis function dimensions, for the case z, = z,. This is because the functions f and h tend to constants as 1 + co in this case, resulting in a rapidly oscillating, slowly converging integral. For z, f z,, as is possible for the reaction between currents on different strips, the termsf and h decay exponentially in 1, and there is relatively little trouble for most values of Ax, Ay. T o speed up the computation for the case z, = z, = z, several numerical techniques may be employed. The first is the use of a Filon integration method to account for the oscillatory cosine terms [13]. A second technique is to subtract from the integrand a limiting-beha.viour term with constantsflco, z , z), h(co, z, z), so that the integral converges much faster. The integral of the extracted term may be evaluated by identifying
286
Microstrip dipoles
it as the reaction between currents in a grounded homogeneous half-space of effective wave number k, [14]. This reaction may be evaluated using a free-space Green's function with a real-space integration. In this case the pulse choice of q b ) (eqn. 5.9) is most convenient, since the resulting real-space reaction integral reduces to a one-dimensional integral [14]. Another type of extraction may be employed for the case z = z, = z, when z is sufficiently far from a layer boundary, as for a strip embedded within a layer. In this case, a term corresponding to the incident field in a grounded homogeneous space of wave number k, is extracted [15], where k, is the wave number of the layer. The resulting integrand then decays exponentially. The reaction in the grounded homogeneous half-space is computed as before. This extraction fails for a strip at the interface of different media, and is therefore of more limited use than the first type of extraction. Another method for improving the convergence of eqn. 5.15 is to asymptotically approximate the transform Jxfor large 2 in a sufficiently simple form so that the tail integral over ( A , co) may be performed analytically, for some large number A. This is the most straightforward technique, but the tail integral must be reformulated for each specific choice of qb). Finally, as an alternative to trying to accelerate the convergence of eqn. 5.15 for large separation between basis functions, the reaction may be computed by a different technique, as discussed in Sections 5.3.4 and 5.3.5. 5.3.4 Real-space integration method
The reaction Z,, may also be computed by integrating the electric field directly in the spatial variables. To avoid a prohibitive amount of calculation, a 6-function testing procedure is used at the strip centre instead of a Galerkin method, so that impedance elements are defined as
A technique due to Katehi and Alexopoulos [16,17] computes this impedance term by directly applying the electric-field operator (eqn. 5.14) to the Sommerfeld form of potentials (eqns. 5.1 and 5.2). An integration by parts is used to shift the derivatives to the current function J,, (x', y'), and various algebraic manipulations are employed, including an analytical tail integral evaluation. The resulting expression involves a single Sommerfeld-type integral of a rapidly converging series. This formulation does not suffer from convergence difficulties to the same degree that eqn. 5.15 does. Although a comprehensive comparison of computational efficiency has not been performed, it is felt that the real-space method is somewhat comparable to the spectral method when one of the accelerating techniques mentioned previously is used. Both methods have been used to generate the results of this Chaptei.
Microstrip dipoles
287
5.3.5 Point-dipole approximation The reaction between widely separated basis functions may often need to be computed, especially for mutual-impedance problems. In this case, the most efficient technique is to approximate the currents as point dipoles located at the basis-function centres. Computing reaction is then equivalent to finding the Ex field of an I-directed point source, which may be obtained efficiently. One way to perform this calculation is by directly applying the electric-field operator (eqn. 5.14) to eqns. 5.1 and 5.2. It is well known that the resulting Sommerfeld integrals are nonconvergent when z = z', however, and therefore cannot be evaluated directly. One technique for overcoming this difficulty is to extract terms from the integrand to give convergence [18]. Another way is to extend the integration contour to ( - co, + co) and deform around the branch cut, as described in Section 5.2.1. The numerical integration around the branch cut converges very rapidly for large radial separation @ between dipoles, owing to the exponmtia! decay of the Hankel functions in eqns. 5.5 and 5.6 along the imaginary axis. For separations larger than 0.25& this is usually the most efficient of the two methods.
5.3.6 Moment-method equations Consider an arbitrary set of x-directed strips having a 1V &gap voltage source at some point on one of the strips. Let the basis functions be numbered 1, ...N with the source at the centre of basis-function numbers, at x = x,. The current representation is then
with BJx, y) = B(x - x,, y - y,). Because q k ) in eqns. 5.9 - 5.11 is normalised, I,, represents the current in amperes at x = x,. Enforcing Ex = 6 (x - x,) on the strips by applying Galerkin's method using eqn. 5.17 results in the set of equations
which is then solved to find the currents on the strips. 5.4 Centre-fed dipoles
5.4.1 Single dipole The analysis described in Section 5.3.6 may be applied to find the current distribution for a centre-fed dipole, shown in Fig. 5.10. A variational expression for the input impedance is [I91
288
Microstrip dipoles
Z,
=
-
1
- j3Js, 4;
Microstrip dipoles CENTER
J,(i) G, (i,7 )Jr(?') dsds' .
-
289
FED DIPOLES
w = .05
LO
Using eqn. 5.17 this reduces to
z,
=
I -xz 1; ,""
4--
I I
mn
PATCH RESONATOR WITH Er= 2.45
"
/
\
\
which, in view of eqn. 5.18, reduces further to simply Z,"
Fig. 5.10
=
1 I",
-.
Centre-fed strip dipole
This simple formula for input impedance is thus accurate to second order owing to the relation between Galerkin's method and the variational method [20]. From input impedance, the resonant length and bandwidth may be determined. Approximate formulas for resonant dipoles may also be used [lo]. A dipole on a substrate layer has a resonant length
provided h 9 w and w 4 1,. At resonance the resistance is Fig. 5.11
where P, is the total power (watts) produced by a unit-strength point dipole on the substrate. Owing to the behavior of P, (see Fig. 5.5) R, is very small for thin substrates.
Bandwidth (%) of centre-fed dipole versus substrate thickness for two different substrates. The dashed lines indicate that no frequency is found for which X , = 0. In this case f, was chosen to minimise )Xj,,I, with X , (f,) then subtracted from all values. A patch resonator is shown for comparison for h l l , < 0.1
290
Microstrip dipoles
Microstrip dipoles
29 1
The substrate thickness has a dominant effect on bandwidth. The bandwidth for different substrates with a dipole width of 0.05 1, is shown in Fig. 5.11. Here the bandwidth is defined as
Fig. 5.12a
Real part of the input impedance of a centre-fed strip dipole with e, = 2.45 and h = 0.21,
with f, the resonant frequency ( X , = 0) and f,, f, the frequencies at which SWR = 2.0 on a feed line having a match at fa.The maximum bandwidth occurs for h/& z 0.30, and increases for larger E , . For substrates thinner than this, the bandwidth is relatively independent of E, for a given physical thickness h/&. For comparison, the bandwidth of a microstrip patch resonator is shown for the E, = 2.45 case. The patch has a much higher bandwidth for thin substrates, a conclusion reached previously by Pozar [5]. The effect of dipole width is seen in Figs. 5.12a, and b for a substrate with E, = 245. The resonant input resistance is insensitive to width, as is the resonant length. The slope dXi,,/dL a t f , is lower for wider dipoles, indicating a greater bandwidth. However, the slope is not extremely sensitive to width. Only when the substrate becomes thin does the width have a dramatic effect on bandwidth, owing to the cavity-resonator effect. 5.4.2 Mutual impedance
Mutual impedance between centre-fed dipoles may be calculated in different ways. In the moment method, dipole no. 1 is excited with no. 2 short-circuited. After solving eqn. 5.18 for the currents, the formula [lo] Xln
(Ohms) 800
.
- - 0.0002 w
1,
with may be employed. Alternatively, the classical reciprocity formula [21]
Fig. 5.1 2b
Imaginary part of the input impedance of a centre-fed strip dipole with e, = 2.45 and h = 0.2 1,
-1 Z,, = Jx2 ds Il(O)I*(0) J-s2 may be used, with piecewise-sinusoidal currents assumed on the dipoles. The reaction may be evaluated using eqn. 5.15. For narrow strips, the dipoles may be assumed filamentary and the integral (eqn. 5.26) evaluated directly using the real-space technique, or by using the point-dipole approximation to find Ex (Section 5.3.5). Results for filamentary dipoles obtained in this way are shown in Figs. 5.13a,b for broadside and endfire dipoles on a substrate with E, = 10. The slow decay of Z12in the endfire case is due to the dominant TMo mode, which is strongest at 4 = 0 [22].
292
Microstrip dipoles
Microstrip dipoles
2.0
I
(Ohms)
1.5
1.5
1.0 (Ohms)
1.0
.5
.5
0 0
-. 5
-.5
I
I
0
0.2
I
0.4
I
0.6
I
I
I
I
I
I
0.8
1.0
1.2
1.4
1.6
1.8
s IX, Y
Fig. 5.1 3a
Mutual impedance versus separation for resonant-length filamentary dipoles in broadside configuration with E, = 10.0 (Reproduced from Reference 10, @ 1986 IEEE)
-1.0
Fig. 5.13b Mutual impedance versus separation for resonant-length filamentay dipoles in endfire configuration with 8, = 10.0 (Reproduced from Reference 10, @ 1986 IEEE)
294
Microstrip dipoles
Microstrip dipoles
295
5.5 EMC Dipoles
5.5.1 Methods of analysis Fig. 5.14 shows several ways in which one or more dipoles may be electromagnetically coupled to a transmission line. In each case the analysis involves a moment-method solution together with simple transmission-line theory [23]. The transmission line is assumed close to the ground plane, so that a TEM-like field propagates on the line. A 6-gap source is taken near the end of the line farthest from the coupled end. The exact location is not critical. The source sets up a standing-wave current on the line which is essentially a sinusoidal current, except within a small region near the coupled end where the current is perturbed by the dipoles. Away from this coupling region, the line may be regarded as terminated by a equivalent self-impedance Z, = R, + j X, at some arbitrary value of x, where
with r(x)
Top v i e w
=
SWR - 1 e+,28(" SWR + 1
- X,,")
In eqn. 5.28 x,, is the position of a minimum and is the propagation constant on the line, which may be determined from the distance between current minima on an isolated line or by separate analysis [9,10]. In this formulation only the reaction between piecewise-sinusoidal-basis functions is required. An alternative formulation using traveling-wave-basis functions on the line may also be developed [24]. An advantage of this latter formulation is the use of fewer unknowns for the line current, although it requires different types of basis functions. For the results of this Chapter, only piecewise-sinusoidal basis functions were used.
Top v i e w Fig. 5.14
Various configurations of dipoles electromagnetically coupled to a microstrip line
5.5.2 Single dipole A single EMC dipole can be either overcoupled, matched, or undercoupled according to the amount of coupling to the feed line (Fig. 5.15). Of all the possible parameters which affect the coupling, the most critical is the distance t between the line and dipole. If t is too large, then no choice of dipole length or offset will yield an input match, and the dipole is said to be undercoupled. If the line is sufficiently close to the dipole, an input match may be achieved by varying the dipole length and either the longitudinal (x-axis) or transverse (y-axis) offset, or both. The dipole is then said to be overcoupled. In this case the locus of points for the centre of the matched dipole is somewhat elliptical in shape, roughly centered about the end of the line [25]. For a given substrate, this implies a maximum distance t,,, for which an input match may be achieved,
296
Microstrip dipoles
Microstrip dipoles
297
where the locus collapses to a single point [25]. In this case the dipole may be said to be critically coupled. Figs. 5.16 and 5.17 show how an input match may be achieved for the overcoupled case by varying either the longitudinal or transverse offset, respectively, for E, = e,, = E,, = 2.35. ~
-
-
-
matched
undercoupled overcoupled
Fig. 5.1 5
Current amplitude on the strip dipole ( I , ) andmicrostrip line (I,) (Reproducedfrom Reference 2 3 @ 1984 IEEE) 1; is the incident current amplitude. The three cases correspond to h = 0.079& (overcoupled) (matched), h = 0.084A0(undercoupled), and h = 0,070d,,
Fig. 5.17 Z,/Z, as a function of dipole length L, and transverse offset (Reproduced from Reference 23, @ 1984 IEEE The longitudinal offset is 50% of the dipole length. The impedance reference plane is at the position of a current maximum on the line Fig. 5.16
Z,/Z, as a function of dipole length L, and longitudinal offset (Reproduced from Reference 2 3 @ 1984 IEEE) Offset is measured by percent overlap as KO, = (AXIL,) x 100. The impedance refaranre nlana is at the nnsitinn nf a cllrrant maxirn~~rn nn the linn
298
Microstrip dipoles
Microstrip dipoles
299
The bandwidth of an EMC dipole is almost identical to that of a centre-fed dipole on the same substrate, provided the EMC dipole is matched. Hence, it is desirable to keep the dipole significantly above the ground plane to obtain a reasonable bandwidth. On the other hand, it is also desirable to keep the line as close as possible to the ground plane, to minimise line radiation. However, for a given substrate thickness h l l , corresponding to a prescribed bandwidth, the line height should be chosen so that b > h - t,, to avoid being undercoupled, which will reduce bandwidth. Hence, the height b = h - t,,, is a good trade-off between bandwidth and line radiation. An improved coupling may be achieved by using a top layer with E, > E , between the line and dipole. This improves coupling by increasing the capacitance in between [lo]. However, a more pronounced improvement is possible by using multiple dipoles.
53.3 Miiliipk d&i'~~ The bandwidthlline-radiation trade-off may be improved by using multiple dipoles. A dominant theme in these schemes is the introduction of additional capacitance between the line and the main radiating dipole. This is usually accomplished by placing one or two coupling dipoles (parasitics) either in a stacked fashion between the line and top dipole (Fig. 5.146) or coplanar to, and near the end of, the line (Fig. 5.14~)[26]. For the stacked configuration, the bandwidth for SWR < 2.0 is shown plotted against t p / t in Fig. 5.18 for two different values of h (3 mm and 4.5 mm) with corresponding dipole lengths of 8.4mm and 8.7mm, respectively, at a frequency of 10 GHz. These lengths are close to the input-match values for a single EMC dipole. The transmission-line height b is constant a t 0.72 mm. Also shown is the minimum achieved SWR as the frequency is varied for each value of t,. From this Figure it can be seen that the thinner substrate has a lower optimum bandwidth. Also, 'as the substrate thickness changes from 3 mm to 4.5 mm the range of tpfor SWR < 2.0 becomes smaller and shifts toward higher values. Therefore, like the case of a single dipole, there is a maximum value h,, such that, for h > h,,, the SWR is always larger than 2.0 for this value of b. The addition of another dipole between the top dipole and line may further reduce the SWR and increase the bandwidth in this case. When the parasitics are on the same level with'the line and of comparable length to the radiating dipole, the bandwidth may be improved as shown in Fig. 5.19. Appropriate positioning of the parasitics may improve the bandwidth even more. An advantage of this configuration is possibly fewer alignment difficulties during fabrication. However, the improvement in bandwidthlline-radiation is much more dramatic for the case of stacked dipoles.
.
300
Microstrip dipoles
Microstrip dipoles
30 1
5.6 Finite array of EMC dipoles
5.6.1 Analysis A finite array of EMC dipoles IS shown in Fig. 5.20. Away from the coupled ends, the current o n the mth line may be written as the sum of incident and backward waves, of the form J,,(x,y) =
Jh,(x,y )
=
4,?Cv)e-'P' t,vb)e+'"'
SIDE-VIEW
Fig. 5.20 Finite array of EMC dipoles
(5.29)
OF ELEMENT #n
302
Microstrip dipoles
Microstrip dipoles
with x = 0 at the line end. The current on the mth dipole may be assumed sinusoidal as J;(x, Y) = I , d ? ( ~ ) m )
(5.30)
303
To calculate B, and D m ,dipole n may be excited with a &gap source (line n may be absent), with line-dipole pair m passive. Then
Here <(x) is given by eqn. 5.8 with d replaced by Lm/2.Because of linearity, the line and dipole current amplitudes may be written as
where B,,, Dm,are back-scattering and dipole coefficient accounting for mutual interaction between dipoles. To, is the voltage reflection coefficients at the end of line m when all dipoles except number m are absent. E,, is similarly an excitation coefficient in the isolated case. These equations may be written in matrix form as
where [r], [El are diagonal matrices and [B], [Dl are zero on the diagonal. [Ib] and [Ti] are column vectors. Eqn. 5.34 yields
[fl = [El-' ([ul - [Dl) [PI with [ V the identity matrix. Substituting into eqn. 5.33 yields Eqn. 5.35 gives the incident currents required to produce the desired set [PI (which determines the radiation pattern). Eqn. 5.36 gives the resultant backscattered currents. From this the scattering matrix is found to be [Sl = [ r l - [BI([UI - [DI)-'[Kl for the case of identical lines.
(5.37)
5.6.2 Calculation of coefficients The transmission-line analysis used to calculate r in Section 5.5.1 may be extended to calculate E, as well as B,,,,, Dm,,between two line-dipole pairs. The formula for E is
with I, the line current at a maximum (x discussed in Section 5.5.1.
= x,,).
The line may be excited as
1-
Fig. 5.21
Input Match
Excitation coefficient E versus longitudinal offset for a single EMC dipole E , = 2.2. E , = 2.35, b = 0.03 in, t = 0.06 in, L, = 0.367 in, and w = 0.059 in with f = 1OGHz
where I, = j I, e-'8' is the incident-current amplitude, with I the line length. As for the calculation of r, a formulation using traveling-wave-basis functions could also be used here.
304
Microstrip dipoles
Microstrip dipoles
Results were calculated for the case E,, = 2.2, E,, = 2.35, b = 0,03in., t = 0.06in, w = 0.059in at a frequency of 10GHz. The dipole lengths are taken as 0.367in, the value required for an input match in the isolated case with only longitudinal offset. In Fig. 5.21 the excitation coefficient E is shown plotted
.
305
used as an EMC dipole excited by line no. 1. The results for the EMC case depend on the feed-line length (TL,) to some extent owing to spurious coupling between line no. 1 and dipole no. 2. The agreement is fairly good, however. In Fig. 5.23, S,, results [27] are shown for the case measured by Stern and Elliott
0.25
T-IL
1-1 experimental
-
: theoretlcz
Ld-
k-
k
0 . 3 8 4 5 rnch
Broadside Dipoles
............................ ....................................................
-
JDIZ
I
-
Source o n L i n e Feed .............. C e n t e r - F e d D i p o l e ....................................................................................
1-
-
I B12 1
-
Fig. 5.22
Mutual coupling coefficients Dl,, E l , for two line-dipole pairs Coefficients are calculated with dipole no. 1 excited in two ways: with a centre feed (no line) and by coupling to a line of length TL, . Dimensions are the same as in Fig. 5.21 with dipole offsets chosen to give a match in the isolated case
against offset for a single line-dipole pair. The magnitude of E is a maximum close to the input-match point (A, = 0.1 14in). In Fig. 5.22 results for B , , , D,, between two pairs are shown. Dipole no. 1 is excited as a source in two different ways: first, by a &gap feed at the centre (line no. 1 absent), and secondly, when
Fig. 5.23 Comparison o f theoreticalandmeasuredS,, for two line-dipole pairs. (Reproduced from Reference 27, @ 1987 IEEE) The two dipoles are broadside with separation S, between centres. Measured values taken from Reference 29: E, = 2.35, b = 0.037in. t = 0,0485in. w = 0.059 in with f = 10GHz. The reference planes have been placed at the first current maximum from the end of the lines
[28,29]. The dipoles were taken to be slightly shorter than the experimental lengths since rounded dipoles were used in the measurement. 5.6.3 Array design There are two possibilities for an array design: to have an input match on each line in the active state, or to relax the match condition and simply put matching transformers or stubs on each line. The second case is simpler because all dipole lengths and offsets may be chosen the same (L,, = L,). Eqns. 5.35 and 5.36 give the line currents, with the active reflection coefficient for line m given by
306
Microstrip dipoles
Microstrip dipoles
From this the matching network may be designed. In particular, knowing determines the distance from the end of each line at which the impedance is purely real. At this point quarter-wave transformers may be placed to impedance match to the desired feed-line impedance. The input power on line m is P, = ZomIf,12(1 - lr;l2) where Z,,, is the impedance of line m, which couples to the mth dipole. The phase of fmdetermines the necessary phase delay, and hence line length, of line m. In the first case, an iterative procedure may be used to solve for each dipole length and offset to give Tm= 0. This could be achieved by starting with an initial length and offset to give an input match in the isolated case, and then using eqn. 5.35 to find fm.The new length and offset are chosen to satisfy
+
307
As an example, a 4-element linear array with a 0.5 12, element spacing was designed to give a broadside beam with a dipole excitation ratio of 0.65: 1.0: 1.0:0.65. The board materials and line-dipole widths were the same as those in Figs. 5.21 - 5.22. The dipoles were chosen to be of resonant length at the design frequency of 10.0GHz with an offset chosen to give a match in the isolated case. A summary of the coefficient values and results obtained from the equations in Sections 5.6.1 and 5.6.2 is given in Table 5.1. Based on these results the ratio of powers into the feed lines is calculated as P2/Pl = P3/P4= 2.55. Because LT; = Lrt in this particular design, the
The process then repeats. This is similar to the iteration scheme used by Elliott [28] to design an array of EMC dipoles, which was based on an experimental evaluation of coupling. By utilising one of the design techniques described above, a complete array of EMC dipoles may be designed, which will have prescribed dipole currents in the presence of mutual coupling. The dipole currents directly determine the array pattern, neglecting line radiation. The design equations 5.33,5.35 and 5.41 permit the direct design of the array feed network using standard corporate-feed power dividers once the coupling coefficients have been obtained. Table 5.1 Summary of coefficient values and results
W i l k i n s o n Power S p l i t t e r s
r = o
Fig. 5.24 Diagram of the feed network for a four-element array (not actual size) The dipoles are shown displaced from the feed network for clarity
impedance is purely real and a minimum at approximately the same distance from the end of the line on each feed line, at a distance s = 4.43 cm (A8 on the feed lines is 2.02cm). At this location the active impedance is approximately 40Cl (from simple transmission line calculation). Hence, a feed network which gives the required power split into impedances of 40Cl is required. Such a feed network was designed using standard Wilkinson power splitters [30], and is shown in Fig. 5.24 [31]. After a 1: 1 power split, each Wilkinson splitter further
308
Microstrip dipoles
Microstrip dipoles
splits the power to a 2.55: 1.0 ratio. The 4 0 0 lines coming out of each Wilkinson splitter meet the 62 !2 lines of width 0.05 1, at a distances from the ends, allowing each Wilkinson splitter to feed into a matched load. The inner two lines were made slightly shorter than the outer lines to account for a small unbalanced phase shift through the Wilkinson splitters, which was observed experimentally. The theoretical and measured radiation patterns for this array are shown in Fig. 5.25. The theoretical pattern is found from a reciprocity method [2].The H-Plane 9.9 GHz
Fig. 5.25
Theoretical (dashed line) and measured (solid line) patterns for the four-element array The theoretical pattern is at 10.0 GHz while the measured pattern is at 9.9 GHz. E,, = 2.2. E,Z = 2.35, b = 0.03 in. t = 0.06 in. L, = 0,367 in and w = 0.059in. The
offsets are Ax
=
0.1 1 4 in
measurements were performed at a frequency of 9.9 GHz since this was found experimentally to be the optimum frequency for the array. At this frequency the SWR on the 50R input feed line was approximately 1.4. Finally, it should be mentioned that in large arrays of EMC dipoles, accurate results may be obtained by using an infinite array analysis, involving a summation of Floquet modes [32]. Results for an infinite EMC dipole array have recently been obtained [33].
5.7 Conclusions Microstrip dipoles are generally characterized as being narrower than patch antenna elements, and are not usually probe-fed like the patch. These features
309
allow the microstrip dipole to be a useful radiating element in many applications. In particular, due to the small size, the dipole may be useful when space limitations are important. Dipoles have low radiation resistance and narrow bandwidth for thin substrates, in comparison with the patch antenna. However, the dipole may be used as a resonant element for thicker layers, for which the bandwidth may be quite considerable, and the input resistance no longer a limitation. Dipoles thus find best application for thicker substrates. In this chapter a general method has been presented for analyzing strip configurations, which include the microstrip dipole as well as the feeding microstrip lines. The analysis technique discussed is flexible, allowing for a wide variety of different configurations, including the single dipole, the mutual coupling between two dipoles, or the electro magnetically coupled (EMC) dipole. One of the most practical methods for feeding a microstrip dipole is by electromagnetic coupling to a microstrip line. If the dipole is sufficiently close to the iine, an input match can always be achieved by varying the dipole length and the offset from the line, in either the longitudinal or transverse directions. In the EMC dipole it is usually desired to minimize the line radiation as much as possible, while maintaining an input match. This implies a line height above the ground plane for which the dipole is critically coupled. T o improve the bandwidth-line radiation trade-off, multiple dipoles may be coupled to the line, either in a stacked configuration, or coplanar with the line. The stacked configuration gives the best improvement in bandwidth, for a given line height. A design procedure for a finite array of EMC dipoles may be developed using a matrix description of the line and dipole currents, together with a momentmethod solution for the necessary mutual coupling coefficients. Two design procedures were discussed. One is an iterative procedure which yields an input match on each line, but requires each dipole length and offset to be different. The other design procedure allows each dipole length and offset to be the same, but requires matching transformers on each line. This procedure is simpler, not requiring any iterations. In both cases, the design equations allow for the direct determination of the necessary feed network.
5.8 References I SOMMERFELD, A,: 'Partial differential equations' (Academic Press, 1962) 2 ALEXOPOULOS, N. G., and JACKSON, D. R.: 'Fundamental superstrate (cover) effects on printed circuit antennas', IEEE Trans., 1984, AP-32, pp. 807-816 3 COLLIN. R. E.: 'Field theory of guided waves' (McGraw-Hill. 1960) 4 CARVER. K. R. and MINK, J. W.: 'Microstrip antenna technology', IEEE Trans., 1981, AP-29, pp. 2-24 5 POZAR. D. M.: 'Considerations for millimeter wave printed antennas', IEEE Trans., 1983, AP-31, pp. 740-747 6 ALEXOPOULOS, N. G., JACKSON, D. R., and KATEHI, P. B.: 'Criteria for nearly omnidirectional radiation patterns for printed antennas', lEEE Trans., 1985, AP-33, pp. 195-205
3 10
Microstrip dipoles
7 JACKSON, D. R. and ALEXOPOULOS. N. G.: 'Gain enhancement methods for printed circuit antennas', IEEE Trans., 1985, AP-33, pp. 976-987 8 JACKSON, D. R. and OLINER, A. A.: 'A leaky-wave analysis of the high-gain printed antenna configuration', IEEE Trans., 1988, AP-36, pp. 905-910 9 DENLINGER, E. J.: 'A frequency dependent solution for microstrip transmission lines', lEEE Trans.. 1971. M'IT-19. DD. 30-39 10 JACKSON, D. R., and ALEXOPOULOS, N. G.: 'Analysis of planar strip geometries in a substrate-superstrate configuration', IEEE Trans., 1986, AP-34, pp. 1430-1438 I I UZUNOGLU, N. K., ALEXOPOULOS, N. G., and FIKIORIS, J. G.: 'Radiation properties of microstrip dipoles', lEEE Trans., 1979, AP-27, pp. 853-858, 12 NEWMAN, E. H., and FORRAI, D.: 'Scattering from a microstrip patch', IEEE Trans., 1987, AP-35, pp. 245-251 13 FILON. L. N. G.: 'On a quadrature formula for trigonometric integrals', Proc. Roy. Soc. Edin., 1928, 49, pp. 38-47 14 POZAR, D. M.: 'Improved computational efficiency for the moment method solution of printed dipoles and patches', Electromagnetics, 1983, 3(3-4), pp. 299-309. 15 YANG, H. Y.: 'Frequency dependant modelling of passive integrated circuit components' Ph. D. dissertation, University of California, Los Angeles, 1988 16 KATEHI, P. B., and ALEXOPOULOS, N. G.: 'Real axis integration of Sommerfeld integrals with applications to printed circuit antennas', J . Math. Phys, 24, (3). pp. 527-533 . .. 17 KATEHI, P. 8.: 'A generalized solution to a class of printed circuit antennas' Ph.D. Dissertation, University of California, Los Angeles, 1984 18 JACKSON, D. R. and ALEXOPOULOS, N. G.: 'An asymptotic extraction technique for evaluating Sommerfeld-type integrals,' IEEE Trans., 1986, AP-34, pp. 1467-1470 19 RUMSEY, V. H.: 'Reaction concept in electromagnetic theory', Phys. Rev., 1954, 94, pp. 1483-1491 20 JONES, D. S.: 'A critique of the variational method in scattering problems', IRE Trans., 1956, AP-4, pp. 297-301 21 HARRINGTON, R. F.: 'Time harmonic electromagnetic fields' (McGraw-Hill, 1961) 22 ALEXOPOULOS, N. G. and RANA, I. E.: 'Mutual impedance computation between printed dipoles', IEEE Trans., 1981, AP-29, pp. 106-111 23 KATEHI, P. B., and ALEXOPOULOS, N. G.: 'On the modeling of electromagnetically coupled microstrip antennas - The printed strip dipole', IEEE Trans., 1984, AP-32, pp. 1179-1186 24 JACKSON, R. W. and POZAR, D. M.: 'Full-wave analysis of microstrip open-end and gap discontinuities,' IEEE Trans., 1985, MTT-33, pp. 1036-1042 25 OLTMAN, H. G. and HUEBNER, D. A.: 'Electromagnetically coupled microstrip dipoles', IEEE Trans., 1981, AP-29, pp. 151-157 26 KATEHI, P. B., ALEXOPOULOS, N. G. and HSIA, I. Y.: 'A bandwidth enhancement method for microstrip antennas', IEEE Trans., 1987, AP-35, pp. 5-12 27 KATEHI, P. B.: 'A generalized method for the evaluation of mutual coupling in microstrip arrays', IEEE Trans., 1987, AP-35, pp. 125-133 28 ELLIOTT, R. S. and STERN, G. J.: 'The design of microstrip dipole arrays including mutual coupling Part I: Theory', IEEE Trans., 1981, AP-29, pp. 757-760 29 STERN, G. J. and ELLIOTT, R. S.: 'The design of microstrip dipole arrays including mutual coupling. Part 11: Experiment', IEEE Trans., 1981, AP-29, pp. 761-765 30 HOWE, H.: 'Stripline circuit design' (Artech House, 1974) 31 DINBERGS, A.: 'Analysis and design of an array of electromagnetically coupled microstrip dipoles'. Masters thesis, University of Houston, 1988 32 POZAR, D. M., and SCHAUBERT, D. H.: 'Scan blindness in infinite phased arrays of printed dipoles', lEEE Trans., 1984, AP-32, pp. 602-610 33 CASTANEDA, J. and ALEXOPOULOS, N. G.: 'Infinite arrays of microstrip dipoles with a superstrate (cover) layer', IEEE Intl. Symp. Digest, 1985, Vol 2, pp. 713-718
Chapter 6
,..
Multilayer and parasitic configurations D.H. Schaubert
6.1 Introduction
A standard configuration for a microstrip antenna is a single patch of conductor supported above a ground plane by a simple dielectric substrate and directly contacting an appropriate transmission line in order to couple power between the resonant patch antenna and the transmitter or receiver circuit. This is a simple configuration that is rugged and relatively easy to fabricate, but it is limited in its functional capabilities. The focus of this Chapter is antennas that consist of two or more metallic patches supported by one or more dielectric layers, or that consist of one metallic patch that is not directly contacting the transmission line that feeds it. These configurations are more complicated to design and fabricate, but they offer performance features that are not usually obtainable from the single-patch, single-dielectric configuration. These features include increased bandwidth, multiple frequency operation, dual polarisation, lower sidelobe levels, and ease of integration. The examples presented here do not represent all of the configurations that have been successfully demonstrated, but they do represent many of the fundamental methods that have been successful. One method often employed is to stack patch radiators one above the other with intervening dielectric layers. This allows two or more resonant patches to share a common aperture area. The patches may be fed individually from microstriplines or coaxial probes, or only one or two may be fed directly while the others are coupled parasitically. Several examples are presented in Section 6.2. Another method that is employed utilises a single resonant patch that is coupled electromagnetically to a microstrip feed line. This form of parasitic coupling usually involves two layers of substrate, which may be on the same or opposite sides of the ground plane. If the feedline and patch are on opposite sides of the ground plane, a small aperture can be used to efficiently couple power through the ground plane. This configuration is presented in Section 6.3. The final method presented here consists of one or more patches on the surface of a single substrate layer. These patches may be coupled parasitically
312
Multilayer and parasitic configurations
Multilayer and parasitic configurations
313
to each other, and possibly to the feed line. These configurations are generally easier to fabricate than the multilayer configurations, buithe often is not as desirable. Some examples are presented in Section 6.4.
efficiency of antennas designed for increased bandwidth. Decreased efficiency has been reported for some configurations, but available experimental and analytical data are not sufficient to quantify the relationship between bandwidth and efficiency for the many configurations that have been demonstrated.
6.2 Stacked elements for dual-frequency and dual-polarisation operation
6.2.1 Antennas with separate feeds for each function Stacked patches with separate feeds can take a variety of forms. Two of these are shown in Fig. 6. lb and c. Another form is depicted in Fig. 6.2. In all these configurations, the outer conductor of the upper feed connects the lower patch to the ground plane (Fig. 6.ld). This short-circuit connection, which actually presents a small inductive load to the antenna, can often be placed to have minimal effect on the antenna performance. However, it also can be placed to achieve desirable tuning effects, which will be described below. The use of one-half-wavelength and one-quarter wavelength elements in the stacked configurations offers the designer considerable flexibility in selecting the operating frequencies of the antenna. Of course, the use of one-quarterwavelength elements restricts the radiated field from that element to be linearly polarised, and requires the fabrication of via connections to form a short circuit along one side of the antenna. Nevertheless, this configuration is desirable for many applications and the designer can stack a one-quarter-wavelength patch and a one-half-wavelength patch of comparable sizes in order to obtain operating frequencies that are separated by approximately one octave. Independent control of E,,,,, and q,,,, (Fig. 6. Id) provides another means of adjusting the two operating frequencies. The piggy-back antenna depicted in Fig. 6.lb and described below is one example of an antenna that uses a one-half-wavelength lower element and a smaller one-quarter-wavelength upper element that is tuned to operate at a frequency moderately close to that of the lower element. This configuration leads to different beamwidths at the two closely spaced operating frequencies. (Care must be exercised if extremely close operating frequencies of the same polarisation are required because the stackedklements can exhibit strong mutual coupling, as described in Section 6.2.2.) As noted above, one of the principal disadvantages of the one-quarter-wavelength antennas is the need to fabricate a short-circuit boundary by plated-through holes, rivets or soldered pins. The shapes of the patches that are stacked is somewhat arbitrary, although most designs that have been reported use similar shapes for the upper and lower patches. Square (or rectangular) and circular patches are the most commonly used shapes, but the wedge shape depicted in Fig. 6.lb is useful for conformal antennas on small conical bodies.
Stacked elements have the advantage of providing two or more metallic patches within the same aperture area. This allows the antenna designer to obtain multiple frequencies with or without dual polarisation. Three typical configurations are depicted in Fig. 6.1, where case a represents a triple-frequency dualpolarised antenna [I], case b represents two linearly polarised elements operating at different frequencies [2], and case c represents two circularly polarised elements operating at different frequencies. These examples are representative of stacked configurations, which may use a single feed for multiple frequencies and different feeds for each polarisation (case a) or separate feeds for each frequency and polarisation (cases b and c). The dielectric substrates may differ in thickness or permittivity in order to control the bandwidths and sizes of the metallic radiator. This Section is organised into two Subsections. The first describes antennas that utilise separate feeds for each frequency and polarisation. The second describes antennas that utilise a single feed to obtain multiple frequencies. Before presenting details of these stacked antennas, it is desirable to list some of their general advantages and disadvantages.
Advantages
Disadvantages
Multiple functions share common aperture.
Stacked substrates must be aligned and bonded.
Stagger tuning increases bandwidth.
Increased thickness and weight of the antenna structure.
Separately tuned radiators benefit from frequency and/or polarisation isolation
Fabrication of feed can be difficult, particularly when upper feed must attach to lower antenna.
Many configurations are possible to meet a variety of needs
Increasing total substrate thickness increases excitation of surface waves, resulting in lowered efficiency.
Different substrates may be selected for upper and lower antennas.
Most of these advantages relate to increases in performance, whereas most of the disadvantages relate to fabrication and mechanical concerns. One performance parameter that has not received sufficient attention in the literature is the
Two-frequency antennas: The piggy-back antenna in Fig. 6. lb, or any similar configuration, has been found to work well for radiating or receiving two independent, linearly polarised signals at different frequencies from a common aperture. The input impedance and radiation patterns of the piggy-back antenna
374
Multilayer and parasitic configurations
Multilayer and parasitic configurations
3 15
are typical of those obtained from ordinary patch antennas, although any asymmetries of the stacked geometry may lead to slight asymmetries in the patterns. Some asymmetries are evident in the E-plane patterns of Fig. 6.3. The ground plane for the antenna is modest in size, so that some diffraction effects
_shortmg pin
feed points
section A A'
Fig. 6.1
top view
cross sectional vlew (AA)
Typical stacked-patch configurations a Triple-frequency, dual-polarised antenna [After Reference 11 b Piggy-back antenna for two linearly polarised frequencies c Two-frequency, circularly polarised antenna d Cross-section of stacked patches that utilise upper feed as inductive post in lower Wtch
are also evident. The operating frequencies and impedance bandwidths of each element are approximately the same as they would be in the absence of the other, except that the lower element must be considered as a post-tuned antenna [3]. The feed for the upper element may not, in general, pass through the lower element at a point where the electric field between the lower patch and the ground plane is zero. Then, the effect is similar to an inductive post in a
37 6
Multila yer and parasitic configurations
Multilayer and parasitic configurations /
Fig. 6.2
A
377
rectangular waveguide cavity. Several papers have analysed the post-tuned antenna [4-61 and have succeeded in predicting quite accurately ,the resonant frequency and input impedance. However, a first-order approximation is easily obtained by using the transmission-line model [7] for a rectangular antenna as
Orthogonally polarised version of piggy-back antenna with low-frequency, onequarter-wavelength patch on bottom
E-plane
narmalised post spacing (sla)
H-plane quarter wave ---- 1140MHz
-
patch 990 MHz
Fig. 6.4
(a) Transmission-linemodel of patch symmetrically loaded with inductiveposts. (b) Operating frequency (upper curves) and VSWR (lower curves) of post-tuned antenna on 1.6 mm Teflon fibreglass substrate calculated. -measured [taken from Reference 31
---
is done in Reference 3. Typical results taken from Reference 3 are shown in Fig. 6.4. The values used in the calculations for the post reactances were obtained from Fig. 6.3 Radiation patterns of piggy-back antenna
xp
=
x 377
tan
2zt n
( t = substrate thickness)
(6.1)
318
Multila yer and parasitic configurations
Multilayer and parasitic configurations
which is Carver's estimate 181 that the post's reactance should be the same as the input impedance to a piece of short-circuited transmission line. The use of only one inductive post yields similar results, but the amount of frequency increase caused by the post is approximately one-half that caused by two posts (Fig. 6.5).
horizontal feed,
near feed
\.
LH
3 19
C
+
opposlte feed
Fig. 6.6 Rectangular patch antenna with feeds for horizontal and vertical polarisation at different freyueritiies
post location (2dla)
Fig. 6.5
Measured operating frequency and VS WR of antenna with one post near the feed or one post opposite the feed
Two-Polarisation Antennas: A simple rectangular patch antenna with two feeds located along perpendicular centre lines of the antenna is an easy choice for radiating or receiving two independent, orthogonal, linearly polarised signals. However, this antenna has the disadvantage that the width of the patch for the horizontal mode is fixed by the desired operating frequency of the vertical mode, which determines L, (Fig. 6.6). Therefore, the H-plane beamwidth of the horizontal mode is fixed by the vertical frequency, and vice versa. This limitation can often be overcome by using a stacked configuration such as the one in Fig. 6.7. The upper feed of the model shown passes through the lower element at a voltage null so that the primary effect on the lower antenna is some loading due to the upper substrate, but this effect is easily compensated in the design. Thus, the patch widths and H-plane beamwidths can be controlled as long as the performance requirements allow the designer to fit the upper vertically polarised antenna within the boundaries of the lower, horizontally polarised antenna. If the use of differing permittivities for the two substrates is permissible, a higherpermittivity upper substrate helps to reduce the size of the upper patch. The radiation patterns and input impedances of the individual antennas are similar to those of comparable antennas operating in an isolated environment. Some typical radiation patterns are shown in Fig. 6.8. The impedances of the
Fig. 6.7
Stacked patches for orthogonal linear polarisation at two independent frequencies
320
Multilayer and parasitic configurations
Multilayer and parasitic configurations
32 1
two elements, when both are tuned to operate at 3.465 GHz, are shown in Fig. 6.9. The isolation between the feeds for the two orthogonally polarised elements is greater than 18 dB over the operating band. E plane
Fig. 6.8
E plane
Typical radiation patterns of stacked orthogonal patches on a small ground plane a Upper patch b Lower patch
start 3.000000000 GHz
stop 4.000000000 GHz
6.2.2 Antennas for multiple frequencies and increased bandwidth One form of the stacked patch antenna for multiple frequencies is depicted in Fig. 6 . 1 0 ~This . antenna is similar to the one in Fig. 6. l a [I], where three patches permit three separate operating frequencies to be obtained at each of the orthogonally polarised feed ports. This form is typical of that used for multiplefrequency antennas where the feed probe passes through a clearance hole in the lower patch and connects to the upper patch. This method of feeding couples strongly to the resonance of each patch, even though the resonant frequencies may be far part. This strong coupling is probably the result of currents on the feed probe directly exciting the cavity of each patch antenna through which it passes. A second form of the stacked patch antenna is depicted in Fig. 6.10b, where only the lower patch is fed directly and the upper patch is coupled parasitically. This form of the antenna is widely used for increased bandwidth at a single operating frequency [9-111, and it can be used for dual polarisation by inserting a second, orthogonally polarised feed similarly to the multiple-frequency antenna in Fig. 6 . 1 ~ . The characteristics of both forms of the stacked, single-feed patches have been investigated and compared to a single patch. For the data presented below, the patches were circular and fabricated on separate sheets of Duroid 5870
Fig. 6.9 Input impedance of stacked orthogonal patches Each substrate is 1.6 mm thick, 8, = 2.2; upper patch is 2 9 x 23 mm and is fed 11.6 rnm from edge; lower patch is 27 x 36 mm and is fed 8.0 mm from edge
b Fig. 6.1 0 Single feed configurations for multiple frequencies or increased bandwidth a Top-feed model b Bottom-feed model
322
Fig. 6.11
Multilayer and parasitic configurations
Input impedances of dual-frequency, top-fed circular discs a Dimensions of the model b DUD,, = 3.3 cm. c D,,, = 3.45 cm d D,,, = 3.55 cm
Multilayer and parasitic configurations
Fig. 6.1 1
Cont.
323
324
Multilayer and parasitic configurations
Multilayer and parasitic configurations
( E , = 2.3) substrate and then carefully aligned in the stacked configuration. The input impedance of the multiple-frequency form is shown in Fig. 6.1 1 for three different diameters of the upper patch. These and additional data are summarised in Table 6.1, which tabulates the maximum value of input resistance and the associated frequency and Q. As noted by Long and Walton [12], the resonant frequency and resistance of the lower patch are relatively unaffected by changes in the diameter of the upper patch. However, the resonant frequency and resistance of the upper patch both decrease as the patch diameter increases. In fact, increasing the upper patch diameter to 3.6cm results in an upper resonance at 3.277 GHz with a resistance of 16ohms. It appears that the upper patch in this configuration should always be smaller (or only slightly larger) than the lower patch.
F i g . 6.12
Equivalent circuit to model input impedance of Fig. 6 . 1 1 ~
D
Table 6.1 Impedance characteristics of multiple-frequency stackedpatches Upper patch diameter cm
R,.,, ohms
3.3
75 93
f.. GH7
.,,,
3.185 3.465
Q 61 60
Lower patch diameter: 3.5 cm
= 8 P P " = 2.32 d""" = durnr = 04.79 cm = 0.030 in
@"'
Feed is 0.6crn from centre
An equivalent circuit has been used successfully to model the input impedance of the stacked, dual-frequency antenna. This circuit, depicted in Fig. 6.12, consists of two coupled parallel resonant circuits and a series inductor to model the feed inductance that is usually observed in probe-fed patches. The values shown in Fig. 6.12 are for the 3.45 cm-diameter upper patch. These values were obtained by optimising the fit between the impedance of the measured data and the model. The mutual inductance represents electromagnetic coupling between the two discs. The wide-bandwidth form of stacked patches (Fig. 6.10b) has also been studied and three typical results are shown in Fig. 6.13. The best results for increased bandwidth are obtained when the two patches are nearly the same
325
b
Fig. 6.13 Input impedance of wide-bandwidth bottom-feed circular discs a Dimensions of the model b D,,, = 3.45 cm c D,,, = 3 . 5 0 cm d DUDp,= 3 . 5 5 cm
326
Multilayer and parasitic configurations
Multilayer and parasitic configurations
327
size. Since the feed probe does not pass through the cavity of the upper patch, the coupling to that patch is very weak unless it is comparable in size, or larger than the lower patch. Thus, the preferred configuration for multiple frequencies is to feed the top disc and use a larger bottom disc, while the preferred configuration for increased bandwidth is to feed the lower disc and use an equal or slightly larger top disc. By properly adjusting the feed distance from the patch centre, the impedance loop in Fig. 6 . 1 3 ~can be made to encircle the centre of the Smith chart. This has produced a model fabricated from two sheets of 0.076 cm-thick (0.030 in) Duroid 5870 (E, = 2.3) having a VSWR < 2 bandwidth of 5% at 3.3 GHz. This compares with approximately 3% bandwidth for a single patch on 0.15 cm-thick substrate.
Fig. 6.14 Stacked discs for increased bandwidth [After Reference 101 a Antenna structure b Return loss
Fig. 6.13 Cont.
Chen et al. [lo] have provided data on the operation of antennas in the form of Fig. 6.10b for either wide bandwidth or dual frequencies. By using a relatively thick, low-permittivity foam substrate between the patches, they have achieved a 20% bandwidth for VSWR < 2 and a 10% bandwidth for VSWR < 1.22. A typical result is shown in Fig. 6.14. They measured a gain of 7.9 dB at 4.25 GHz for the 10% bandwidth antenna. They also noted that stacked patches with the lower patch on a relatively thin substrate exhibit lower crosspolarised radiation than a single patch fabricated on a thick substrate to achieve comparable bandwidth. This result is consistent with observations that direct radiation from feed probes can be significant for antennas on thick substrates [13]. For dual-frequency operation, Chen et al. present a graph showing the relationship between the patch diameters, separations and operating frequencies. However, they do not indicate if the results are limited to their particular choices of dielectric substrates. An analysis of stacked, circular patch antennas has been conducted by Araki et al. by using the spectral domain Green's function [14]. They solve the eigenvalue problem to find the complex resonant frequencies of the structure, and they calculate the input impedance. Their results are compared to measure-
328
ments in Fig. 6.15, which shows good agreement for a wide-bandwidth example. No results are presented for a dual-frequency example, but their analysis should be valid for this case, as well.
329
create a series capacitance, which adds a degree of freedom that can be used in conjunction with the inductance of the feed probe and the resonant patch impedance to obtain increased bandwidth in the manner of Griffin and Forrest [IS]. Alternative configurations suggested by Paschen are shown in Fig. 6.17.
ground plane-
I----
Multilayer and parasitic configurations
Multilayer and parasitic configurations
-_----\
/
/-
wlthout parasttic antenna patch
m 1.2
with parasitic element
>
-1
----
1 2.4
2.5
measured
x x xJ calculated
2.6 frequency .GHz
2.7
2.8
(a) Geometry of stacked circular patches for spectral domain computations ( 6 ) VSWR characteristics for h = 10.0, a, = 20.8 mm, a, = 2 1 . 0 mm, d = 1.6 mm, 6, = 2 . 5 5 [After Reference 141
Fig. 6.16 Proximity coupling by means of series capacitance between patch and feed probe a Paschen's design [After Reference 151 b Hall's design [After Reference 171 c Fong et a1 design [After Reference 161
Another antenna configuration that resembles those of Fig. 6.10 has been proposed by Paschen [15]. However, this antenna actually functions more like that of Fong et al. [16], as is apparent from alternative configurations shown by Paschen. Three antenna configurations (from Paschen [I 51, Hall [17], and Fong et al. [16]) are shown in Fig. 6.16. The objective of these configurations is to
The cylindrical form of the capacitor has been used to fabricate an L-band antenna covering the global-positioning satellite frequencies of 1227 MHz and 1575 MHz as well as the NDS frequency of 1381 MHz. Air dielectric was used and a quadrature feed network for circular polarisation was implemented on a thin circuit at the bottom of the antenna cavity (Fig. 6.18). By adjusting the
b
Fig. 6.1 5
330
Multilayer and parasitic configurations
Multilayer and parasitic configurations
probe diameter to control probe inductance and also adjusting the cylindrical capacitor, the antenna was tuned to provide VSWR less than 2 for a bandwidth of 25%. A typical radiation pattern is also shown.
331
radtotlng element
ground p l m e
quadrature feed network 'spherlcol orray (dome1
stand-off
/
connector ptn
Fig. 6.17 Alternative configurations for coupling by means of cylindrical capacitors
6.3 Two-sided aperture-coupled patch Microstrip antennas have been popular elements for planar and conformal arrays. A traditional means of fabricating these arrays that takes maximum advantage of the economies of printed-circuit fabrication involves the layout of radiating elements and a feed network on a single surface of a grounded substrate. This minimises the size and weight of the total array and requires the installation of only one coaxial connector to feed the array, thus reducing the cost. However, the microstrip feed network radiates small amounts of power that can degrade the sidelobe and polarisation characteristics of the array. Also, the radiators and feed lines occupy much of the available area, leaving little space for the phase shifters that are required for beam steering. Furthermore, for monolithic phase shifters, the substrate must be GaAs or another appropriate material, which is not a desirable substrate for the radiators [19]. Most of these problems can be alleviated by using a two-layer structure that has the radiating elements and their substrate on one side of a ground plane and
b
Fig. 6.18
Circularly-polarised L-band antenna utilising air dielectric and cylindrical capacitor coupling [After Reference 151 a Antenna for use on spherical surface b Typical radiation pattern at 1381 MHz
332
Multilayer and parasitic configurations
Multilayer and parasitic configurations
the feed network and its substrate on the other. In the past, arrays fabricated in this fashion have utilised a via connection probe at each element in order to transfer power from the feed network to the radiators (Fig. 6.19). However, these via connections are increasingly difficult to fabricate as the frequency increases and excess probe inductance makes the antenna difficult to match. Also, the use of GaAs as a feed substrate complicates the fabrication because it is more difficult to drill the via hole. r a d i a t h g patch via connect
\
333
new design, the via connection is replaced by an electrically small aperture (Fig. 6.20) that couples power efficiently to the patch and is easy to manufacture. An open-circuited length of the microstripline extending beyond the aperture provides an additional degree of freedom to be used for impedance matching and bandwidth enhancement. This stub, together with the aperture length, can be used to control the input impedance over a wide range of values, as illustrated in Fig. 6.21. The calculated results were obtained by using the moment-method technique of Reference 21, and have been found to be in good agreement with measured results.
/,.
rad~atmgpatch
E:-L
Fig. 6.19
Two-sided design with via connection between feed line and radiating patch
A useful alternative to the via connection probe is aperture coupling [20, 211. In this configuration, power is coupled from the microstripline feed to the radiating patch through an electrically small aperture in the ground plane (see Fig. 6.20). No electrical connection is required and the performance is relatively insensitive to small errors in the alignment of the two circuits. Single elements have performed well at frequencies as high as K,-band [22]. Several additional advantages are obtained by the use of a two-sided configuration. These include isolation of the feed network from the radiating aperture of an array, which eliminates the spurious-feed-network radiation that can degrade polarisation and sidelobe levels [13]. Also, the two-sided configuration provides two distinct microstripline media so that the antenna substrate can be chosen to optimise the performance of the radiating patches (e.g. low 6, to improve radiation, increase bandwidth, and move scan blindness further from broadside), and the feed substrate can be chosen independently to optimise feed performance (e.g. high E, to reduce circuit size or the use of GaAs for active integrated feeds). Furthermore, the feed substrate may be composed of many diced wafers without introducing substrate discontinuities into the radiating side of the array. The aperture-coupled patch antenna resembles a traditional microstrip-array element with a microstrip patch antenna on a substrate with relative permittivity $ and a feed network on a substrate with relative permittivity These are separated by a common ground plane. In the traditional configuration, a via connection carries power from the feed network to the radiating patch. In the
4.
Fig. 6.20
Microstrip radiator electromagnetically coupled to microstripline feed in two-sided configuration [After Reference 2 11
The performance illustrated in Fig. 6.21 can be understood in terms of the equivalent circuit [23] in Fig. 6.22, which is a two-port representation of the microstrip feed line as it passes the aperture. The effect of the aperture and patch is approximately a lumped series load on the microstripline of characteristic impedance Z,. The input impedance of the patch, Z,n, can be obtained by evaluating the series combination of the aperturelpatch circuit and a short stub terminated in an open circuit. The series inductance represents the effect of the electrically small (below resonance) aperture, and the impedance Z,, represents the open-end effects of the microstrip stub. As the stub increases in length, the input impedance at a fixed frequency approximately follows a constant-resistance circle in Fig. 6.21a, with the reactance increasing according to the reactance of the open-circuited stub. The effect of increasing the aperture size is
334
Multilayer and parasitic configurations
Multila yer and parasitic configurations
335
similar to that of increasing the size of a hole coupling power from a waveguide to a resonant cavity. When the aperture is small, the patch is undercoupled and the resonant resistance is less than the characteristic impedance of the feed line. As the aperture size increases, the coupling and the resonant resistance increase. A wide range of resistance and reactance values can be achieved by adjusting the aperture length and the stub length (It has been found that narrow slot apertures offer the most effective coupling in this configuration.)
Fig. 6.21
Fig. 6.21 lmpedance of aperture coupled patch E! = E: = 2.54,d, = d, = 0.16cm; patch length = 4 cm; patch width = 3 cm, aperture width = 0.16 cm a lmpedance for various stub lengths with aperture length = 1 . 1 2 cm 6 lmpedance for various aperture lengths with stub length = 2.0 cm [Reproduced from Reference 211
Cont.
The bandwidth and radiation patterns of the aperture-coupled patch antenna are essentially the same as those of a probe-fed antenna on the same substrate. The peak radiation from the aperture on the feed side of the ground plane has been computed and measured to be at least 20 dB below the peak of the patch radiation for the antennas that have been tested. This is an important characteristic of the antenna that makes it useful in planar arrays, as compared to a simple microstripline-fed slot that has a bidirectional radiation pattern. Arrays of aperture-coupled patches can be built by using series feeding or corporate feeding. Examples of E-plane arrays are illustrated in Fig. 6.23. Both types of arrays have been built at C-band. An eight-element corporate-fed array with patches on 0.159 cm E: = 2.2 and feed lines on 0.064 cm = 10.2 has performed favourably, demonstrating the feasibility of using a substrate like GaAs for the feed network and a lower-permittivity substrate for the radiating
336
Multilayer and parasitic configurations
Multilayer and parasitic configurations
elements. The use of a low-E,antenna substrate will increase the angle at which scan blindness occurs due to surface waves on the antenna substrate. However, a blindness also will occur due to surface waves on the feed substrate, and methods may be needed to control this phenomenon at very short wavelengths where the substrate thickness may exceed 0.02-0.03&.
modification in the dimensions and would allow nionolithic phase shifters to be integrated with the feed network. Mutual coupling levels in the array are given by the S parameters in Table 6.3, and the input impedance of a typical interior element is shown in Fig. 6.24. Radiation patterns of the array, fed by an external coaxial power divider and appropriate lengths of line to steer the beam, are shown in Fig. 6.25. These patterns agree well with expected results and the radiation behind the ground plane is 20 dB below the main beam, despite the relatively small ground plane (approximately 212, x 41,). Table 6.2
Eight-element, E-plane array
Element spacing = 3.0cm Stub length = 0.42 cm Slot width = 0.056cm pd= 10.2 dfwd= 0@j4cm
Patch length = 1.78cm Patch width = 2.54cm Slot length = 0.83 cm &y' = 2.22 8"' = g.:5F i i ~ i
stub
Zin
Fig. 6.22
337
Equivalent two-port network for aperture backed by a patch antenna and fed by a microstripline
Table 6.3
Mutual coupling in array with d0/2spacing IS,l, dB
m~crostr~p feed ltne on lower substrate
aperture ~n ground plane
resonant patch on upper substrate
s4,
- 30.7
SQ
- 24.8 -21.6 -22.1 - 27.0 - 30.3 -31.8
s 4 3 s45 s46
s4, s4,
li------------ij
1I :-----I
L------
L Sij, deg
- 79 102 - 46 - 52 103 -110 70
A variation of the aperture-coupled patch is shown in Fig. 6.26 [24]. This configuration permits the feed network to occupy as much space as is needed in the depth dimension. This use of depth has been essential in most microwave phased arrays that have been fabricated. Other variations with perpendicular feed substrates have been built with non-contacting feeds [25], which offer significant advantages in fabrication.
b
Fig. 6.23 Aperture-coupled microstrip antenna arrays a Series feed b Corporate feed
The array dimensions in Table 6.2 could be scaled to yield operation at 25 GHz, which would lead to a feed substrate thickness of 0.005 in. The use of 0.005-in GaAs (E, = 12.8) for the feed substrate would require only a slight
'6.4 Parasitic elements on antenna substrate The microstrip antenna design is so appealing that engineers are inclined to capitalise on its conformability, manufacturability, and ruggedness for applications that are contrary to its inherent electrical characteristics. In particular, considerable effort has been devoted to increasing the operating bandwidth of the microstrip antennas. Several of these efforts have been described in previous
338
Multilayer and parasitic configurations
Sections of this Chapter. However, a recent study [26] has shown that the bandwidth obtainable from a microstrip antenna is approximately proportional to its volume measured in 1;. This phenomenon is consistent with accepted antenna theory [27]. Therefore, the bandwidth of a simple microstrip antenna
Fig. 6.24 Input impedance of element 6 in corporately fed E-plane array having dimensions in Table 6.2.All other elements terminated in 50 R
can be increased by increasing its length, width, or substrate thickness. However, the length of a fundamental-mode antenna must be approximately onehalf wavelength in the dielectric substrate, so the antenna can be lengthened only if the substrate permittivity is lowered. Unfortunately, feed lines and probes radiate more on low-~,substrates, so this technique must be used with care when cross-polarisation and sidelobe levels are important. Increasing the antennas's width is fairly straightforward, but higher modes of the antenna can be excited if the width is increased to one or two wavelengths. Also, elements larger than approximately 1,/2 cannot be used in scanning arrays owing to undesirable grating lobes. In this Section, some alternatives to multiple-layer structures and to increasing the substrate thickness, which can lead to increased feed radiation and surface wave excitation, are presented. The fundamental approach here is to
Multilayer and parasitic configurations
339
340
Multilayer and parasitic configurations
Multilayer and parasitic configurations
create a double-tuned resonance by adding parasitic resonators on the same substrate surface as the primary microstrip antenna. Many of the elements described here have two disadvantages that must be weighed against the benefits of increased bandwidth: (i) the physical area of the element is increased, and (ii) the radiation pattern exhibits asymmetries that may change with frequency.
method [32] has been used to accurately predict the input VSWR. Examples of these antennas are depicted in Fig. 6.29. All of the structures described in References 29-31 exhibit multiple tuning, and an element like the one in Fig. 6 . 2 9 ~has been measured to have 25% impedance bandwidth (VSWR < 2) at /
rnicrostr~p patch on front s ~ d e
antenna substrate feed substrate
coupl~ng aDerture
1
resonant d~rect~on of patch
,',/ J,/ X
/ ,of
I
contacts top aperture
34 1
length of parasltlcs 13.0 crn and 13.l crn
Teflon fiberglass (3.2rnrn thick)
2.5Gcrn w ~ d e
/ / spacing = 08 crn
plane
Fig. 6.26 Aperture-coupled patch with perpendicular feed network. (Reproduced from Reference 24)
The first example (Fig. 6.27) utilises narrow conducting strips adjacent to the driven radiator [28] in order to alter its impedance and radiation properties. These strips couple to the non-radiating edges of the antenna and significantly modify its impedance. A square, edge-fed microstrip antenna with VSWR = 4 can be matched to VSWR = 1.2 by using the parasitic strips. The antenna works best when the parasitic strips are slightly longer than the patch. The performance of the antenna is strongly affected by the separation between the strips and the patch, and the best performance has been obtained when the separation is 2.5 to 3 times the substrate thickness. The interaction between the strips and the patch changes the resonant frequency of the patch by a few percent. However, it is possible to broaden the impedance bandwidth of the antenna by stagger-tuning the strips. Fig. 6.276 shows the VSWR of the antenna with and without the strips. Radiation patterns of the parasitic-tuned antenna are shown in Fig. 6.28. The H-plane radiation pattern is slightly skewed by the asymmetry of the stagger-tuned strips. The coupled-resonator approach has been extended to include up to four parasitic elements [29] and to provide for direct as well as electromagnetic coupling to the parasitic elements [30]. Parasitic elements coupled to the radiating edge of the antenna are described in Reference 29, where the segmentation
11 700
725
750 frequency (MHz)
775
I
800
b
Fig. 6.27 Parasitically tuned antenna with narrow strips adjacent to nonradiating edges [After Reference 281 a Dimensions for U H F model b VSWR w i t h and without parasitics
3.16 GHz on 0.125411 substrate, E, = 2.55. In order to achieve this bandwidth, the total element area is approximately one wavelength square. Also, the radiation pattern changes with frequency within the band of operation as the segments contribute with differing amplitudes and phases. This is illustrated in the
342
Multilayer and parasitic configurations
Multilayer and parasitic configurations
E-plane patterns of Fig. 6.30, which shows the reported performance of the antenna in Fig. 6.31. The VSWR < 2 bandwidth is 24% (about seven times that of a single patch on the same substrate). However, the radiation pattern changes appreciably at the four frequencies shown in these plots. No data on cross-
----
Fig. 6.28
kEe \.-
I \
E-plane H- plane
Radiation patterns of parasitically tuned antenna [After Reference 281
\
(in
-90' OdB
+ ..plane),'
\ /
\
10
3.72 1' '
20
30
30
20
I 10
90' OdB
Fig. 6.29 Antennas with four parasitic elements a Electromagnetically coupled parasitics [After Reference 291 b Directly coupled parasitics [After Reference 301
polarised radiation are presented. The usefulness of this, or the other parasitically coupled antennas, will depend on the designer's ability to accept increased element area and pattern asymmetries and variations across the operating band.
Fig. 6.30 Measured performance of antenna in Fig. 6.31 [After Reference 301 aVSWR , b E, in @ = 0' plane c E+ in @ = 90' plane
343
344
Multilayer and parasitic configurations
Multilayer and parasitic configurations
345
An extension of parasitically coupled elements leads to a parasitically coupled array [33]. In this configuration, a single driven patch is coupled to closely spaced adjacent patches, which are coupled to additional patches to form a linear or planar array (Fig. 6.32). Arrays of this type have been developed experimentally to producelinear or circular polarisation. The distance between patches is reported to be 0.1 to 2 times the substrate thickness and can be
Fig. 6.31 Dimensions of antenna used to obtain results of Fig. 6.30 L = 3.0cm W,, = W,, = 0.025 cm W = 2.0cm W,, = W,, = 0.44cm I, = 2.85cm 6, = 6, = 0.71 cm I, = 2.635 cm a = 0.48 cm 1, = I, = 2.35cm e, = 2.55cm h = 0.31 8cm
F i g . 6.33 Three parasitically coupled arrays [Reproduced from Reference 331
F i g . 6.34 Measured performance of 7-element, E-plane linear array of parasitically coupled patches [Reproduced from Reference 331 patch radiator
Fig. 6.32 Planar array of parasitically coupled microstrip elements [Reproduced from Reference 331
adjusted to control the power distribution in rows and columns for sidelobe minimisation. This distance also affects the input impedance, which is approximately equal to the impedance of a single patch divided by the number of patches.
346
Multilayer and parasitic configurations
The performances of the three antennas in Fig. 6.33 are reported in Reference 33. The linear array operates at 10.8 GHz and has the characteristics shown in Fig. 6.34. The 5 x 3 array is reported to have 9 dB gain at 8.55 GHz and - 26 dB sidelobes. The 2 x 2 array is designed to produce circular polarisation by feeding the driven patch at a corner. The ellipticity was measured to be less than 2 dB over a bandwidth of 130MHz at 5.83 GHz. Another antenna that consists of a driven element and additional metallisation on the substrate surface is the microstrip disc antenna with a short-circuited annular ring [34]. The antenna (Fig. 6.35) can be considered as a microstrip disc
Multilayer and parasitic configurations
347
(taken at band centre) illustrate the wide beamwidth and low cross-polarisation levels obtainable with the antenna. Maximum cross-polarisation within the 10 dB beamwidth is reported to be -21 dB over the band 5.00-544 GHz.
Fig. 6.35 Microstrip disc antenna with annular ring Centre frequency = 5.21 GHz, h = 3.18 mm, d = 19.5 mm, g = 2.25 mm. r = 9 mm, E, 2.5 [Reproduced from Reference 341
with a parasitic annular ring, or as a cylindrical cavity with an annular slot. The dimensions of the cavity produce a resonance at approximately the same frequency as the resonance of the microstrip disc. The element produces a circularly symmetric radiation pattern with 10 dB beamwidth equal to 160°, which is appropriate for illuminating a reflector with F/D = 0.3. By adjusting the slot width g, VSWR < 2 bandwidths of 10% have been obtained, but significant gain reduction is experienced at the upper portions of the operating band. It is speculated in Reference 34 that the losses are due to a second resonance that is contributing to the increased bandwidth. The radiation patterns in Fig. 6.36
Fig. 6.36 Radiation patterns of disc antenna with short-circuited annular ring [Reproduced from Reference 341 a Principal planes b Diagonal planes
9
Table 6.4 Antenna characteristics Antenna type
Section
Performance characteristics
Fabrication requirements
Piggy-back
6.2.1
Independent antennas share aperture Multiple frequency and/or polarisation Upper feeds form tuning posts in lower antennas
Align and bond multiple layers Coaxial feed lines soldered to ground plane and to lower patches
6.2.2
Multiple frequencies Can be dual polarised
Align and bond multiple layers Upper patches smaller
Stacked patches with lower patch fed
6.2.2
Increased bandwidth Can be dual polarisation Reduces cross-polarisation May reduce efficiency Increased bandwidth May reduce efficiency No effect on pattern
Align and bond multiple layers Upper patch larger or same size Precise control of capacitor gap
Feed network isolated from radiation More parameters to control impedance Can be used in most cases where probe could be used
No via connection Microstrip stub occupies space on substrate Independent choice of substrates Alignment not critical, but bonding is required
6.2.2
Aperture coupling
6.3
3
% 3
2
2 o 3
Q
Stacked patches with upper patch fed
Capacitive feed tuning
U)
2 a2. 2. 0
o
% G.
Sg. 2
Patch radiation and bandwidth not affected Some radiation from stub and aperture Parasitic beside driven patch
6.4
Increased bandwidth Usually some pattern asymmetry Pattern may change with frequency Large bandwidth requires greater than 1,/2 size
Single-layer fabrication Direct or electromagnetic coupling to parasitics
fB
P
7
4,
3
Q
P
2
2. P 0
ra
0
3 3
c
3
3 2
350
Multilayer and parasitic configurations
6.5 Summary Microstr~pantennas composed of multiple conducting patches or feed lines electromagnetically coupled to the resonant, radiating patch offer several advantages over the traditional single patch connected to a feed line or feed probe. These advantages include increased bandwidth or multiple frequency operation, dual polarisation, and control of input impedance. However, the antennas are often more complicated to fabricate or they may require more surface area, so that the designer may be required to sacrifice one desirable feature in order to obtain another one. Table 6.4 contains a summary of several key features of the antennas described in this Chapter, and can be used as a guide in choosing the best configuration for a particular purpose. Most of the structures in this Chapter have been modelled by using either the cavity model or moment methods, and the segmentation method has also been applied to some of the configurations. Ir? genera!, the analysis techniques provide a good qualitative model for the antennas, thus providing the designer with the insights needed to develop a functional antenna. Many of the existing analyses also have shown good quantitative agreement for the cases appearing in the literature, but the ranges-of validity are not generally known, and the computed results may not be sufficiently accurate for many practical values of substrate permittivity and thickness or for variations in patch geometry. Nonetheless, multiple-layer microstrip antennas and antennas utilising parasitic coupling to the feed or to other resonant patches offer distinct advantages for many systems applications, and are likely to be used in antenna systems that require the specialised features available from these antennas.
6.6 References I 2 3
4 5 6 7 8 9
MONTGOMERY, N. W.: 'Triple-frequency stacked microstrip element.' IEEE Ant. and Prop. Intl. Sym., 1984, Boston, MA, pp 255-258 JONES, H. S. Jr., SCHAUBERT, D. H. and FARRAR, F. G.: 'Dual-frequency piggyback antenna.' US Patent 4 162 499, 24 July 1979 SCHAUBERT, D. H., FARRAR, F. G., SINDORIS, A. R., and HAYES, S. T.: 'Microstrip antennas with frequency agility and polarization diversity.' IEEE Trans. 1981, AP-29, pp. 118-123 RICHARDS, W. F., and LO, Y. T.: 'A wide-band, multiport theory for thin microstrip antennas.' IEEE Ant. and Prop. Intl Syrn., 1981, Los Angeles, CA, pp 7-10 RICHARDS, W. F., and LO, Y. T.: ;Theoretical and experimental investigation of a microstrip radiator with multiple lumped linear loads.'Electromagnetics,1983, 3, pp. 371-385 SENGUPTA, D. L.: 'Transmission line model analysis of rectangular patch antennas,' Electromagnetic~,1984 4, pp. 355-376 MUNSON, R. E.: 'Conformal microstrip antennas and microstrip phased arrays,' IEEE Trans., 1974, AP-22, pp. 74-78 CARVER, K. R.: 'Input impedance to probe-fed microstrip antennas.' IEEE Ant. and Prop. Intl. Syrn., 1980, Quebec, Canada, pp. 617-620 SABBAN, A.: 'A new broadband stacked two-layer microstrip antenna.' IEEE Ant. and Prop. Intl. Sym., 1983, Houston, TX, pp 63-66
Multila yer and parasitic configurations
35 1
CHEN, C. H., TULINTSEFF, A,, and SORBELLO, R. M.: 'Broadband two-layer microstrip antenna.' IEEE AP-S Sym. Digest, 1984, Boston, MA, pp. 251-254 HOLZHEIMER, T., and MILES, T. 0.: 'Thick, multilayer elements widen antenna bandwidths,' Microwaves & RF, Feb. 1985, pp. 93-95 LONG, S. A,, and WALTON, M. D.: 'A dual-frequency stacked circular-disc antenna,' IEEE Trans., 1979, AP-27, pp. 270-273 HALL, P. S., and PRIOR, C. J.: 'Radiation control in corporately fed microstrip patch arrays.' Digest of 1986 Journees Internationales de Nice sur les Antennes (JINA '86), Nice, France, pp. 271-175 ARAKI, K, UEDA H., and TAKAHASHI, M.: 'Hankel transform domain analysis of complex resonant frequencies of double-tuned circular disc microstrip resonators/radiators,' Electron. Lett., 1985, 21, pp. 277-279 PASCHEN, D. A,: 'Practical examples of integral broadband matching of microstrip antenna elements,' Antenna Applications Syrn., Univ. of Illinois, Urbana, IL, I986 FONG, K. S., PUES, H. F., and WITHERS, M. J.: 'Wideband multilayer coaxial-fed microstrip antenna element,: Electron Lett., 1985, 21, pp. 497-499 HALL, P. S.: 'Probe compensation in thick microstrip patches,' Electron lelt., 1987, 23, pp. 606-607 GRIFFIN, J. M., and FORREST, J. R.: 'Broadside circular disc microstrip antenna,' Elecwon. Lett., 1982, 18, pp. 266-269 POZAR, D. M., and SCHAUBERT, D. H.: 'Comparison of architectures for monolithic phased arrays,' Microwave J. 1988, 29, pp. 93-104 POZAR, D. M.: 'A microstrip antenna aperture coupled to a microstripline,' Electron Lett., 1985, 21, pp. 49-50 SULLIVAN, P. L., and SCHAUBERT, D. H.: 'Analysis of an aperture coupled microstrip antenna,' IEEE Trans., 1986, AP-34, pp. 977-984 SCHAUBERT, D. H., JACKSON, R. W., and POZAR, D. M.,' 'Antenna elements for integrated phased arrays,' Antenna Applications Sym., Univ. of Illinois, Urbana, IL, 1985 SULLIVAN, P. L., and SCHAUBERT, D. H.: 'Analysis of an aperture coupled microstrip antenna,' RADC-TR-85-274, Rome Air Development Center, Feb. 1986 BUCK, A. C., and POZAR, D. M.: 'Aperture coupled microstrip antenna with a perpendicular feed,' Electron Lett., 1986, 22, pp. 125-126 POZAR, D. M., and JACKSON, R. W.: 'An aperture coupled microstrip antenna with a proximity feed on a perpendicular substrate, IEEE Trans., 1987, AP-35, pp. 728-731 HENDERSON, A., JAMES, J. R. and HALL, C. M.: 'Bandwidth extension techniques in printed conformal antennas,' Proc. Military Microwaves '86, Brighton, England, 1986, pp. 329-334 HARRINGTON, R. F.: 'Time harmonic electromagnetic fields' (McGraw-Hill, NY 1961) pp. 307-31 1 SCHAUBERT, D. H. and FARRAR, F. G.: 'Some conformal printed circuit antenna designs.' Proc. Printed Circuit Ant. Tech. Workshop, New Mexico State Univ., Las Cmces, 1979 KUMAR G. and GUPTA, K. C.: 'Nonradiating edges and four edges gap-coupled multiple resonator broad-band microstrip antennas,' IEEE Trans., 1985, AP-33, pp. 173-178 KUMAR G. and GUPTA, K. C.: 'Directly coupled multiple resonator wide-band microstrip antennas,' IEEE Trans., 1985, AP-33, pp. 588-593 KUMAR G. and GUPTA, K. C.: 'Broadband microstrip antennas using additional resonators gap-coupled to the radiating edges,' IEEE Trans., 1984., AP-32, pp. 1375-1379 GUPTA, K. C. and SHARMA, P. C.: 'Segmentation and desegmentation techniques for analysis of planar microstrip antennas,' IEEE Intl. Sym. on Ant. and Prop., June 1981, pp. 19-22 ENTSCHLADEN, H. and NAGEL, U.: Microstrip patch array antenna,' Electron Lett., 1984, 20, pp. 931-933 PRIOR, C. J. and HALL, P. S.: 'Microstrip disc antenna with short-circuited annular ring,' Electron. Lett., 1985, 21, pp. 719-721
Chapter 7
Wideband flat dipole and shortcircuit microstrip patch elements and arrays G . Dubost
This chapter comprises of two sections. Section 7.1 discusses a flat dipole which is a wide- bandwidth hybrid radiating source, originated and developed i n , France, and used in flat arrays having several hundred or more of such elements. Its low radiation resistance is advantageously matched to the characteristic resistance of the stripline used to feed it. In each array, spurious radiation is avoided because the feed network is completely shielded. Section 7.2 describes the short-circuited patch acting at quarter-wave resonance. Its large beamwidth in the E-plane and weak coupling in the H-plane are characteristics particularly suitable for use in microstrip-phased arrays with beam steering over a large angular sector. Because of their small thickness compared with wavelength they can be used with advantage in flat arrays having omnidirectional radiation or a directional deflected beam. These two radiating dipoles are studied theoretically by means of models which are equivalent to several lossy coupled transmission lines operating in the quasi-transverse electromagnetic mode.
7.1 Flat dipole elements and arrays Fig. 7.1 shows several models of the usual wide-bandwidth flat dipoles. The specific properties of each model are given in Table 7.1. 7.1.1 Elementary sources The flat dipole is used as a folded slot dipole symmetrically fed across a gap. When isolated in Fig. 7.1 (2) or used in a large array in Fig. 7.1 (3), it is fed by means of a Lecher line or a stripline network, respectively. It has already been described in References 2 - 5. Fig. 7.2 shows the flat dipole which is linearly polarized, parallel to, and at a distance H from, a reflector. A dielectric sheet is placed between the radiating structure and the reflector, so that it can be fabricated by means of printed circuits. The analysis and synthesis are presented in sections 7.1.1.1 and 7.1.1.2. The first model Fig. 7.1 (I), which was asymmetrical, has been described previously [I] and is used in arrays [3]. A broadband
Wideband flat dipole and short-circuit microstrip
Wideband flat dipole and short-circuit microstrip
Fig. 7.1
Usual wide-bandwidth flat dipoles
radiating slots
/
d~electric (Er)
Fig. 7.2
'\
reflector plane
Geometry of directional flat folded dipole
355
356
Wideband flat dipole and short-circuit microstrip
circularly polarised flat radiating source is shown in Fig. 7.1 (4) and described in Reference 3. A dual polarised model in Fig. 7.1 (5) is described next. We present a flat radiating source which is able simultaneously to receive or transmit two frequencies of orthogonal linear polarisations, and subsequently a circularly polarised wave of either the right-hand or left-hand sense. It is a new flat dipole arrangement [(5) in Fig. 7.11, [9, 101. Circular polarisation can be obtained from a trivial patch antenna when using two orthogonally phased feeds, but it has a narrow circularly polarised bandwidth [l I] when non-isolating power splitters are used. To broaden the bandwidth, we can make use of a thick substrate of low dielectric constant, with a thickness of approximately one-tenth of a wavelength, and isolating power splitters (Wilkinson) as in Reference 18. The higher modes must be suppressed [12, 3, 13, 141 when symmetrical feed structures are used. The radiating source (Fig. 7.3) is an enlargement of the linear wide-bandwidth fiat symmetrica! folded dipole [4, 51. The radiating structure is composed of two symmetrical crossed and overlapped flat folded dipoles with orthogonal electric moments. Each dipole is composed of two metallic plates which are fed in opposite phase. The two dipoles, nos. 7, 8 and nos. 9, 10, are etched onto one of the two metallic faces of the first printed circuit (1). The radiation in one half-space is possible when the whole metallic face (1 1) of an identical second printed circuit (2) is used. The other metallic faces of the two printed circuits, (1) and (2), support the two stripline central conductors, (5) and (6), which are insulated with a thin dielectric sheet (3). Each dipole is coupled by its feeding line through a gap by means of an open quarter-wave stripline section, so that the two edges are fed in opposite phase. The model operates between 3.45 and 3.85 GHz [15] with a VSWR of less than 2, when directors are used to broaden the bandwidth.
Wideband flat dipole and short-circuit microstrip
357
The input impedance is due to the transformation of two impedances; namely the radiation impedances of the two radiating slots. This transformation is achieved along a non-radiating slot line. Each half slot can be considered as two
7.1.1.1 Analysis in quasi-TEM approximation: Self and mutal impedances, and far fields are next studied. We have shown previously that the symmetrical flat dipole operates with the widest bandwidth at its third resonance [4], when a model equivalent to several lossy and uncoupled transmission lines, operating in a quasi-transverse electromagnetic mode, is taken into account. Radiation impedance and bandwidth: Fig. 7.2 shows the flat dipole parallel to, and at a distance H from, a reflector plane. A dielectric sheet is placed between the radiating source and the reflector, so that it can be realised by means of printed circuits. The stripline feeding network is shown. The coupling between the radiating element and the feeding stripline is realised by means of a quarterwavelength open stripline. The two large plates are fed in opposite phase from a gap AB. Thus the symmetrical plane perpendicular to the xx' axis and to the reflector plane is at zero potential. It is then possible, but not necessary, to short-circuit middle points of the folded arm at the reflector plane without disturbance to the electromagnetics properties.
Fig. 7.3 Wide-bandwidth dual polarised microstrip antenna
transmission lines. To explainctheoretically the wider bandwidth, in conformity with experimental work, it was necessary to introduce coupling between the two transmission lines [5]; ie., across the two radiating slots (Fig. 7.2). The input impedance Z, relative to the middle AB of the gap is due to the transformation of two impedances 2Z', which are the radiation impedances of the two radiating
358
Wideband flat dipole and short-circuit microstrip
Wideband flat dipole and short-circuit microstrip
slots. This transformation is carried out along a non-radiating slot line of total length Wand characteristic resistance R,.Each half slot, having a radiation impedance equal to Z',, can be considered as two coupled transmission lines of length I with characteristic impedances Z and Z', and C,, being the coupling capacitance per unit of length. The length 1 is given by the expression
359
iMutua1 impedance and coupling: Fig. 7.5 shows the configuration of two coupled f l a ~dipoles in a parallel position (or in the H-plane) separated by a distance D and located above a perfectly conducting ground plane at a height H. The mutual coupling may, in principle, be due to either guided waves, or
with Ah, = 0.41 H
+
(E, 0,3)(s/H (E, - 0.26)(s/H
+ 0.26) + 0.81)
where s is the width of the slot of total length 2h0,Ah, the increase in length due to an end effect. The characteristic resistance Z and Z' are those of microstriplines of equal H a n d thickness and widths, respectively, of W / 2 and (W-W)/2 - s. The conducting currents are strictly located on the edges of every slot. Radiation is taken into account by introducing, for equivalent coupled lines, attenuation constants per unit length cc and cc' given by the following equations:
where f is the frequency and tanh is the hyperbolic tangent. The two coupled transmission lines are divided into N equal four-port sections. When the boundary conditions are applied, the potential and the electriccurrent distributions, and the input impedance Z, are deduced. Fig. 7.4 shows the theoretical input admittance l/Z,, obtained with N = 250, and experimental points in a wide frequency band with the following parameters (in millimetres):
Fig. 7.4
Theoretical input admittance Y, = folded dipole (Y, = G, + jB,)
IIZ,and experimental points of a directional flat
We deduced:
substrate
'
I
reflector plane
Fig. 7.5 Configuration of two flat folded dipoles in H-plane
Owing to the coupling capacitance across the two slots, a fourth resonance (1 1.2 GHz) was observed not far from the third one (10.3 GHz), which explains the increased bandwidth. From another model [6] a bandwidth of 16% has been measured between 11.25 and 13.2 GHz for a VSWR lower than 2. The radiation resistance is always located at about lOOR whatever the model parameters.
space waves, or both. In our theory, guided waves will be neglected. Then the mutal impedance Z , , and the coupling coefficient C(dB) are given by the following expressions [7,8]:
360
Wideband flat dipole and short-circuit microstrip
Wideband flat dipole a n d short-circuit microstrip
361
Fig. 7.6 shows, for h, = 4.35mm, H = 3.2mm, W = 3.8 mm, s = 0.9 mm, 2.2 and f = 9.5 GHz, the theoretical mutual impedance and coupling factor in terms of their distance D, together with some experimental points. It was seen that, for microstrip patches, the E-plane coupling always exceeds that of the H-plane coupling. It is the opposite for the flat dipole. Nevertheless the coupling levels encountered, which are more critical for the H-plane (parallel position as in Fig. 7.5), should not involve any difficulty of array design. The main coupling effect is via space waves [7, 81. In effect, for the arrays which are described in Section 7.1.2, the ratio of the mean distance between two adjacent flat dipoles to the wavelength in free space is greater than 0.8. Then the coupling factor is always lower than - 25 dB. E, =
where R, is the normalisation resistance and E, is the equivalent relative dielectric constant with k, = 2n/& and K = k,&.
Radiatedfields andpolarisation: We assume the flat-dipole reflector plane to be infinite. The flat-dipole moment vector is parallel to the xx'-axis (Fig. 7.2). By using electric l a n d polarization I, current distributions and applying the volume equivalence theorem we can calculate the far field radiated by the antenna in the E-plane from the following expressions [5]:
I,(x)
=
+
~O(E - E,) W(COS~X tgkl sinklxl)V, i ? 1x1
(7.8)
2V, is the potential which is applied between the two gap edges. In the E-plane and after integration the co-polar pattern is deduced from eqn. 7.7: s i n k (-i n ) sink,l(& + sin$) E, = cos$ sin(k,Hcos4) kOl(J~,- sin$) k,l(&, sin4)
+
sin - cots(k0 bc')
- (&
-
sin$)
+
2 kol sin - (& 2 ko 1 - (& 2
+
+ sin$)
+ sin$)
In the H-plane, the polarisation current distribution due to the substrate has no effect, and the normalised far field radiated is given by the equation:
E" Fig. 7.6
Mutual impedance Z,, = R,, + j XI, f = 9.5GHz in H-plane
and coupling factor in terms of D l i , at
The validity condition of eqns. 7.4 and 7.5 is:
=
sin(k, Hcos0) W + s . cos [k, -s m ~ ] sin k o H 2
In eqns 7.9 and 7.10 no effect of the mutal coupling are taken into account, since the equations apply to an isolated source and an infinite reflector plane. 7.1.1.2 Synthesis in quasi-TEM approximation: A theoretical model equivalent to several lossy coupled transmission lines was used in section 7.1.1.1 to
362
Wideband flat dipole and short-circuit microstrip
Wideband flat dipole and short- circuit microstrip
363
explain the bandwidth and the radiation resistance of the flat dipole. Conversely it is useful to find the geometrical parameters of such an antenna and its radiation resistance when the frequency band is known. The number of parameters is reduced, and to obtain an attractive bandwidth their values are bounded. From Fig. 7.2 we take [16]: W/L0 = 2(W/, sll,), g/L, = 0.014,
+
Fig. 7.7 Optimal resistance R,,,
= 2.2. As 2h, ,< 21 ,< 2h we take 21 = 2h, with I given by eqn. 7.1. Then the variable parameters are H/&, W/& and s/&, and using Figures. 7.7 - 7.9, we can define the size of the whole antenna and its optimal resistance R,, when the frequency band is given. In Fig. 7.8 the optimised bandwidth (B %) is due to the input impedance Z,, related to R,, for a VSWR below 2; an example is given. The frequency band is equal to 11.3 - 13.2GHz (B = 15.5%). With a normalised thickness H = 3.2mm ( E , = 2.2), we obtain, for the mean frequency (1, = 24.5mm), H/1, = 0.13. In Figs 7.8 and 7.9 we deduce, for sll, = 0.02, that W/& = 0.1 (then W/I, = 0.24) and I/& = 0.204. Fromeqn. 7.1 we deduce that Aholio = 0.029 and 2ho/l, = 0.33. The final antenna dimensions are: W = 2.45mm, W = 5.9mm, 2h = IOmm, s = 0.5mm, 2h, = 8 mm, H = 3.2 mm, g = 0.34mm. For these parameters and from Fig. 7.7 we obtain R,, = 140Q. Synthesis resulting (Fig. 7.7 and 7.8) indicate that the E,
Fig. 7.8 Optimised bandwidth B(%) of input impedance 2, related to R,, VSWR < 2 W'/& = 2(W/L0 + s / i o ) ,g/&, = 0.014 8, = 2.21 - - - flat dipole is acting at the 3rd and 4th resonances -flat dipole is acting at the 3rd resonance
(Fig. 7.7) for a
364
Wideband flat dipole and short-circuit microstrip
antenna bandwidth increases and radiation resistance decreases as its transverse area (in relation to the square wavelength) and coupling between the two equivalent radiating lines of each slot increase. Elsewhere, it was observed that the flat dipole performs best when a substrate of low dielectric constant is used [I 71, this is a general property [I 81. For these reasons we obtained, using e, = 1, H = 5 mm, W' = 9.2mm, W = 7mm, g = 1,2mm, 2h = 9,6mm, 2h, = 7mm, s = 0,6mm, the correct behaviour for an experimental model acting within one actave, i.e. between 8 and 16GHz [19, 251.
Wideband flat dipole and short-circuit microstrip
365
meshes. Each mesh is composed of four segments which are crossed cylindrical conducting wires. The influence of the conducting-wire diameter on the radiation impedance and bandwidth is considerable. The diameter chosen is equal to one quarter of the mesh dimension. The scattering problem is reduced to a flat-shaped bi-dimensional structure. In Fig. 7.11 we present the complete
j,,
IA
/
ref lector plane
cut AB
'
Fig. 7.10 Very large bandwidth flat folded dipole configuration
Fig. 7.9 Half-slot effective length I/>.,
7.1.1.3 Moments-method analysis: Recently we have studied a wide-bandwidth flat dipole, fed through the gap by means of a Lecher line which is located on a thin printed circuit parallel to a reflector plane and isolated by a sheet of air (Fig. 7.10). The general scattering problem of an arbitrary shaped tri-dimensional antenna solved by the moments method and the finite-difference approach applied to integral equations has explained the antenna behaviour. The wire-grid model is suitable for expressing the boundary conditions along the various edges of the antenna, which are, in fact, the boundary conditions on the thin wire surfaces. The antenna is equivalent to an array of conducting square
Fig. 7.11 Average surface-current vector distribution
distribution, which corresponds to the average surface current vector for each mesh. The length vector is proportional to the current amplitude. In Fig. 7.12 we present the theoretical and experimental input impedance related to the
366
Wideband flat dipole and short-circuit microstrip
Wideband flat dipole and short-circuit microstrip
367
middle of the gap in terms of frequency (GHz). The impedance is normalised to IOOQ, which is the Lecher-line characteristic resistance.: Table 7.2 gives the parameters used in Fig. 7.12 (in mm)..
Fig. 7.12
Theoretical ( 1 ) and experimental (2) input impedance of the large bandwidth flat folded dipole in terms of frequency (GHz) 1 = 100R
7.1.2 Array designs. Losses and eficiencies
A number of flat arrays with several hundred or more flat dipoles have been designed and constructed. In every array each source radiates through a window cut in one of the two metallic shields of the stripline feeding network (Fig. 7.2). 7.1.2.1 Large gain: Fig. 7.13 shows an array of 1024 radiating sources operating between 11.7 and 12.4GHz with a measured isotropic linear maximum gain of 37dB [20]. This high-gain array has been designed to receive radio-broadcasting signals sent out by geostationary satellites. It is composed of 1024 (32 x 32) flat dipoles (section 7.1.1.1) fed by a stripline network (Fig. 7.14). Like the elementary source, the array is constructed using two large compressed printed-circuit sheets with no direct connection between the feed network and the radiating sources. The symmetrical feed network comprises unequal stripline power splitters joined by stripline transmission lines, the
368
Wideband flat dipole a n d short-circuit microstrip
characteristic impedance of which is 7 5 0 . The distance between two adjacent where >., is the wavelength in air a t the mean frequency sources is 0.89 i,,, ( 12. I GHz). The square array of a 0.5 m' area was manufactured using two printed-circuit sheets ( E , = 2.1 7) I .6 mm thick. Circular polarisation is produced by a polariser embedded in a radome. Fig. 7.16 shows an exanlple of the measured patterns in one diagonal plane at 12.1 GHz. Between 11.7 and 13.5GHz the experimental maximum linear isotropic gain was equal to 36.9 F 0.3 dB, and the efficiency is better than 48% between I 1.7 and 12.4 GHz.
Wideband flat dipole and short-circuit microstrip
369
0.85 x 0-40 x 0 4 5 m . The linear isotropic maximum measured gain a t 5.25 GHz is 26.5 dB. the efficiency is about 40% and the measured sidelobe level is lower ~ h a n- 29 dB for a theoretical level of - 39 dB. Fig. 7.17 shows an example of radiation patterns in E- and H-planes at 5.25GHz for an array covered with a radome. The second array [23] (Fig. 7.18) is incorporated in a
Fig. 7.13 High-gainarray (11.7- 12.4GHIj offlatfoldeddipole.
The feeding arrangement is shown in Fig. 7.14 and the feeder dielectric a n d metallic losses are equal to 2.5 dB. The cross-polarisation level o n the axis is lower than -30dB, and, together with the polariser, the measured array ellipticity ratio along the principal axis is better than I.5dB over the frequency range. Fig. 7.15 shows the radiation patterns in E- and H-planes measured a t 12.1 GHz. 7.1.2.2 Low sidelohe level: Two passive arrays with flat dipoles showed a sidelobe level lower than - 30dB. The first array [21, 221 operates between 5.25 and 5.45 GHz in a system used to detect natural resources, and is carried o n a n aircraft. It is composed of 128 symmetrical flat dipoles which are fed by lines a n d splitters realised using stripline technique by means of two printed-circuit sheets, as has been shown for the high-gain array (Fig. 7.14); the dimensions a r e
Fig. 7.14 High-gain array (7 1.7 - 12.4GHz): feeding arrangements
Table 7.3 Measured values for the array in Fig. 7.18 9.6 9.3 f, G H z 9.1
9.9
31.3 31.9 2'30' 2'40' < - 36 < -30
10.1 31.4 2'30' < -29
26.9 Max. gain, d b 30.9 2'35' 3dBbeamwidth,deg(H-plane) 2'40' First sidelobe, dB (H-plane) < - 28 < -28 The efficiency at 9.6 GHz is equal to 33.3% (or - 4.78 dB). The cross-polar~sationlevel is lower than - 35 dB.
system used o n ground-surveillance radars. It is composed of 512 flat dipoles, it uses stripline technology and features low sidelobe radiation: it operates between 9.4 and 10.1 GHz. The distance between two adjacent sources equals
370
Wideband flat dipole and short-circuit microstrip
Wideband flat dipole and short-circuit microstrip
371
Fig. 7.16 Large-gain array (see Figs. 7.13 and 7.14) (Reference 2 0 ) Pattern in a diagonal plane at 12.1 GHz
-
e (DEGREES)
Fig. 7.17 Low-side lobe-level array. Patterns in E- and H-planes at 5.25 GHz
Fig. 7.15 Patterns at 12.1 GHz. Large gain array (see Figs. 7.13 and 7.14) (From Reference
A
e (DEGREES)
372
Wideband flat dipole and short-circuit microstrip
0.9 E., in the H-plane and 0.8 E,, in the E-plane. Some measured values are given in Table 7.3. 7.1.2.3 Vuriable r/irc.ctiiities: A flat array with four fixed beams of different directivities and gains is considered [24]. This array supports 256 flat dipoles separated by a distance of 0.85 /., together with 60 electronic switches, integrated in a stripline structure (Fig. 7.19). The global efficiency is about 50%. For each and difference (A) patterns in the two of the four states we can form sum
(z)
Wideband flat dipole and short-circuit microstrip
airborne communication systems, electronic warfare systems or ECM. We show [25]cylindrically shaped radiating elements working in octave bandwidth (Fig. 7.21). In azimuth, the theoretical angular-sector coverage can be equal to 360'. In the different meridian planes or site planes, the beamwidth and sidelobe level may be of any proportion. The antnenna consists of radiating elements arranged in vertical arrays photo-etched on a printed circuit which is wrapped around a cylindrical dielectric lens of 2a diameter. Each radiating element is a flat dipole, used as a folded slot dipole symmetrically fed. When the substrate has air as the
Fig. 7.19
Fig. 7.18 Low-side lobe-level array of flat folded dipoles (9.4 - 10.1 GHz)
orthogonal principal planes of the array. which acts between 11.7 and 12.4GHz. Fig. 7.20 shows the ratio A / x for each of the four states in terms of the deviation angle 8. The various beamwidths obtained at the mean frequency are 4"3', 7'7', 12'6' and 27', and the cross-polarisation level is always lower than - 25 dB. The efficiency is given by the formula q% = 100 1'G,w/4ns, where s is the geometrical area (0.12 m2)and G,, is the maximum isotropic linear gain. With a measured value GM = 31 dB. we obtained y = 50%. For each of the four states the mean switching losses are about 1.6dB. 7.1.2.4 Very large bunrtwidrh: This section discusses broad-angular-coverage and wide-bandwidth antennas, which are increasingly used, for example in
373
Multiple-beam flat array ( 1 1.7 - 12.4GHIJ
medium and if the thickness is increased, the flat dipole acts over wide bandwidth (sction 7.1.1.3). Thus, when it is fed symmetrically with a Lecher line, the operating range covers one octave. Each array, which is aligned along a generating line of the cylindrical lens, can be considered as a separate channel. In a plane perpendicular to the axis the antenna acts as a Luneberg lens. In effect, the n constant-index-of-refraction surfaces are cylinders of radius r such that n ( r ) = [2 - ( r / ~ ) * ] "The ~ . dielectric lens was machined from a cylindrical Teflon rod. It has longitudinal grooves which are uniformly distributed around the lens axis and which are small compared with the vacuum wavelength [26]. In the meridian section of the lens, which contains one array the optical path is deduced, by means of integration, from the continuous refraction law. Applying an asymptotic development of the Kottler formula, the radiated far field is calculated from the electromagnetic field distribution along the lens outside surface, as has been done previously, but for a small bandwidth using shortcircuited flat dipoles at quarter-wave resonance [27, 281. The antenna is composed of 64 folded flat dipoles arranged in eight vertical
374
Wideband flat dipole and short-circuit microstrip
Wideband flat dipole and short-circuit microstrip
arrays, and it acts in the 8 - 16 GHz range. The diameter of the cylindrical lens is equal to 86mm. The beamwidth in the frequency range lies between 24" and 10" in the azimuth plane, and between IS0 and 7" in the site planes. Whatever the azimuth direction, the minimum isotropic linear gain which can be expected over an angular coverage of 1lo0, and in the 8 - 16 GHz frequency range, is 18 dB. The maximum isotropic linear measured gain G,(dB) is compared with the theoretical maximum directivity D,(dB) in Fig. 7.22. The impedance matching of each array is given in Fig. 7.23. Fig. 7.24 shows the measured ratio A / C between difference (A) and sum patterns expressed on a linear scale.
(I)
Fig. Fig. 7.20 Ratio A / C of sum (CI and difference (A) patterns for the four states (F, to 12.7 GHz (see Fig. 7.19)
F,)
wad-angular-coverage and wide-bandwidth antenna
at
7.2 Short-circuit microstrip patches and arrays 7.2.1 Elementary source
Self impedance and bandwidth: Fig. 7.25 shows the half short-circuited patch configuration. It looks like a half short-circuited flat dipole acting at a quarterwave resonance. The relation between radiation conductance G, and Go can be determined from [29] Fig. 7.22 Maximum measured gain GM and maximum directivity DM
376
Wideband flat dipole and short-circuit microstrip
Wideband flat dipole and short-circuit microstrip
Eqn. 7.11 expresses the development of the input impedance of a lossy shortcircuited line whose length is assumed equal to H' = H + h. The losses comprise the radiation resistance of the patch. The main problem lies in determining the line attenuation constant. In order to do this, the radiation resistance of the half short-circuited patch, parallel to the perfect reflector plane, is identified with that of a loop constituted by the half short-circuited dipole and its electrical image in relation to the reflector plane [3]. When finite conductivity a and lossy dielectric substrate are taken into account, as has been done for the opened flat dipole acting at half-wave resonance (Patch) [30], the input conductance G, is given as follows:
377
r
r -20 degrees
-10
0 10 20 degrees
F= 8 GHz 0.05fdegree
o$ ; -
degrees
(I)
patterns in terms of Fig. 7.24 Measured ratio A / x between difference ( A ) and sum frequency. Broad-angular-coverage and large bandwidth antenna
shorting pins or electric wall
Fig. 7.23 Broad-angular-coverage and wide-bandwidth antenna Impedance matching of each array
where d, (nfha)-'I2 is the skin depth, 6 is the dielectric loss angle, 1, = and Go = ( ~ ~ / p ~ ) " ~ The bandwidth B% related to VSWR is given by
-
Lastly, the radiating source efficiency at resonance is given by
_I
The quarter-wave resonance condiction is h
+ H 1. 114.
sub;trate (E,) Fig. 7.25 Half short-circuitedmicrostrip antenna configuration
378
Wideband flat dipole and short-circuit microstrip
Mutual impedance and coupling: Explicit formulas are presented for the mutual impedance and coupling between two parallel or co-linear shortcircuited flat dipoles at resonance in air medium in terms of three dimensions with respect to wavelength [31]. Experimental and theoretical results are in good agreement and show that these small microstrip antennas are particularly well uncoupled, and therefore suitable for incorporation in a phased array with a steering beam inside a large angular sector. Thus, for the following values (Fig. 7.25):
Wideband flat dipole and short-circuit microstrip
379
Feedthrough is used to excite each radiating element from the output of the associated phase shifter by means of a short coaxial line. This 3 bit digital phase shifter was recently described [34]. A total of only eight PIN diodes is required
the coupling factor in t h e E- and H-planes is lower than - 20dB between short-circuited flat dipoles separated by a distance 0.5 i,. Radiatedfields andpolarisation: The far field radiated by this source has been calculated [32j. With the w m e notation as in Fig. 7.25 we ~btaincd: The Normalised electric field in the E-plane (4 = 0)
The normalised electric field in the H-plane (0 = n/2)
7.2.2 Array designs These short-circuited patches acting at a quarter-wave resonance (section 7.2.1) have been used in several arrays. 7.2.2.1 Phased array with steering beam: Eflect of mutual coupling: This section concerns a Ku-band phased array acting in a large angular [33] at around 15 GHz. The array has 64 short-circuited patches in air medium, located on a 8 x 8 square lattice. The element spacing is lOmm (0.5 A,), such that the coupling coefficient in the E- and H-planes is lower than - 20 dB. The measured results on each radiating element at around 15 GHz are as follows: Bandwidth for a VSWR < 2: 17% Pattern in E-plane: 1dB in an angular sector of 160" Beamwidth in H-plane at 3 dB:80°
+
Fig. 7.26 3bit digitalphase shifter with eight PIN diodes in Ku band
for the whole phase shifter (Fig. 7.26) instead of ten for a conventional type. It is arranged in such a way that no series capacitance is necessary to separate the different bias [35]. So only three wires are used to apply the DC bias to the eight PIN diodes. For each of the eight states, the phase-shifter insertion losses is equal to 3 i I dB in a bandwidth of 15% at about ISGHz. The 64 phase shifters are photo-etched on four fused-quartz substrate plates each of 5.08 x 5.08 cm (Fig. 7.27). So for every deflected beam we can form sum and difference patterns. The feeding structure, which is composed of splitters,
380
Wideband flat dipole and short-c~rcuitmicrostrip
Wideband flat dipole and short-circuit microstrip
branch lines, corporate feeds and DC bias. is also photoetched according to a microstrip technique. Four plugs are connected by pliant and thin conductors to the etched wires for DC bias feeding. The square feeding R F network is divided into four parts. The adjacents parts are deduced from each other by rotation symmetry (RS) so that the four outputs 1 , 2 , 3 . 4 are located on the four array sides (Figs. 7.29 and 7.27). This rotation symmetry is only related to the four parts of the square feed R F network, and does not concern the short-
Fig. 7.28
Phased array with steering beam i n Ku band; 6 4 radiating sources
Fig. 7.27 Phased array with steering beam i n Ku band: 6 4 3 b i t digital phase shifters and feeding arrangements
circuited radiating dipoles which are linearly polarised (Fig. 7.28). The parasitic signals at the input of the four quadrants, which are due to the radiating-dipole aerial alternately coupling in the E o r H planes, are out of phase. This concept
Fig. 7.29 Square feeding network (From Reference 3 6 ) S: output towards source ?:source electrical moment
381
382
Wideband flat dipole and short- circuit microstrip
Wideband flat dipole and short-circuit microstrip
[36] has advantages as compared with an axial-symmetry network (AS). For instance, in Fig. 7.30 we show the theoretical sum patterns in the H-plane deflected by 45' and related to (RS) and (AS). Furthermore, because of the compensation of aerial mutual coupling, the risk of scan blindness is reduced when the (RS) concept is used. Fig. 7.31 shows measured sum gains in the E, H or diagonal planes and Fig. 7.32 shows the ratio A / C between the difference and sum patterns for different deflection angles a. The measured efficiency q% is
383
8 (degrees) -60
-3 0
0
30
60
8 (degrees) Fig. 7.30
Deflected sum patterns in H-plane at f = 15GHz (From reference 36)
-(RS) - - - (AS)
deduced from the following expressions:
Fig. 7.31
Measured sum gains G ( d 8 ) for different deflection angles or (degrees)
G , is the measured maximum isotropic linear gain (dB) and A is the antenna geometrical area. In conclusion, major advances have been made in lowering side-lobe level [36], in the reduction of phase-shifter complexity [35] as well as in the manufacturing procedures developed for building the array. 7.2.2.2 Omnidirectional radiation array for a mobile telecommunication station: This section discusses a very flat antenna with circular or elliptical polarised directional radiation over a large conical angular sector, and linear omnidirectional radiation in the reflector plane [37,38]. It can be advantageously used for communication between mobile stations. The antenna comprises four short-circuited half dipoles (section 7.2.1) acting at quarter-wavelength resonance and fed in phase quadrature (Fig. 7.33 a and b). The ends of the four short-circuited half dipoles (1, 2, 3, 4) are screwed (7) on the edges of a cavity
AIC between
Fig. 7.32 measured ratio deflection angles a 1 : E-plane 7. U-nlann
difference (A) and sum
(u
patterns for different
384
Wideband flat dipole and short- circuit rnicrostrip
Wideband flat dipole and short-circuit rnicrostrip b
,
tw
Fig. 7.33 Omnidirectional radiation array configuration
Fig. 7.34 Linear directivity in E-plane (f = 1.2GHz) 11 ): , GTD ( 2 ) : GO ( 3 ) : Measurements ( m m ) 2h = 115/W = 5 0 / H = 7,5/e = 1.6 \
-I
1 I
386
Wideband flat dipole and short-circuit microstrip
in air medium (6). A printed circuit (8) of thickness e supports, on one face, the four half dipoles and, on the other face, the feed microstrip lines (lo), with quarter-wave transformers (9) which are connected to coaxial lines (1 I). The four quarter-wave-transformer ends are joined and short-circuited to the bottom of the cavity by 12. Another feed concept is possible (Fig. 7.33 c) by which the feed-point location is chosen to match the radiation resistance of the coaxial line. With the following dimensions (in mm): 2h = 115, W = 50, H = 7.5, e = 1.6,2 d = 300 (2 d is the dimension of the square reflector); the bandwidth is equal to 4.35% for mismatch losses lower than 0.5 dB, while the theoretical bandwidth given by eqn. 7.13, is equal to 4.3% for a VSWR < 2 and E, = 1. The mean frequency is equal to 1.2 GHz. Fig., 7.34 shows the linear directivity in the E-plane. The E-plane is the symmetrical plane related to the two opposite short-circuited half dipoles (Fig. 7.33 b ar cf which Ire !inear!y po!arised. Curve (!) gives the directivity when GTD on the reflector edges is taken into account. Fig. 7.35 shows the linear isotropic gain measured for different site angles 0, with horizontally or vertically polarised waves. We can see that the antenna is circularly polarised along its axis (0, = 0°), which is perpendicular to its plane, and quasi-linearly polarised in all directions (8, = 90") of the reflector plane. Another configuration is shown in Fig. 7.36. The antenna, which is vertically polarised with omnidirectional radiation, is composed of four short-circuited half-dipoles acting at quarter-wavelength resonance in air medium and fed in phase [39]. To match the radiation resistance of each half-dipole, a correct feed-point location along the symmetrical axis is found [40] and soldered to the central conductor of a coaxial line. The four coaxial lines are fed in parallel by means of a standard divider. A model was calculated and tested with the following parameters (in mm): 6, = 1, I = 40.5, W = 52, H = 2.6, h = 34.5, 2 d = 400. The measured resonance frequency was found to be 1.90GHz while the theoretical one (f, given by eqn. 7.17) is equal to 1.93 GHz.
f;' =
4ph'2~A'2 [h
Wideband flat dipole and short-circuit microstrip
387
7.2.2.3 Log-periodic array: This antennas is a microstrip travelling-wave antenna of large bandwidth [19,41,42,43]. The log-periodic array is composed of flat short-circuited half dipoles acting at quarter-wave resonance and fed in series by means of a high-characteristic-resistance microstrip line, R, (Fig. 7.38).
half short-circuited
cut AB Fig. 7.36
Vertically polarised antenna with omnidirectional radiation
+ H + 0.72H(W/H + 0.26)(W/H + 0.81)-'1
(7.17) The measured bandwidth for a VSWR of less than 2 is equal to 4.7% while the theoretical bandwidth, given by eqn. 7.13, is 4.62%. Fig. 7.37 shows the measured E-plane, co-polar and cross-polar gain patterns, and the theoretical one when diffraction corrections, obtained with GTD applied to the square reflector edges, are taken into account. Maximum isotropic linear directivity of 6.46dB occurs for 0 = 37", while the measured maximum gain of the antenna with its divider is equal to 54dB. For a constant angle 0 around the antenna, the measured radiated far field is practically constant, with variations of f l dB when 0 < 0 < 90'. The bandwidth can be improved when the height H is increased, and the maximum site directivity angle may be altered by when adjusted the I parameter. This model is particularly thin since H/1, is equal to 0.017.
8 (degrees) Fig. 7.37
Measured E-plane directivity pattern (copolar and cross-polar) 4 = n / 2 . O: variable E, = 1 , I = 40.5mm, W = 5 2 mm, H = 2.6 mmlh = 34.5mrn, 2d = 400 mm
Each half dipole has a large E-plane pattern and weak coupling, especially in the parallel position (H-plane), and so the log-periodic array can be used for a progressive wave, when a squinted beam in the H-plane and large pattern
388
Wideband flat dipole and short-circuit microstrip
-
coverage in the E-plane are suitable. Fig. 7.39 shows the geometrical parameters W,,,H,,.and /I,, for the half-dipole (D,,)of the nth order. acting at a quarter-wave (4hv%)-', where f;, is the reresonance in air medium with /I,, + H,, sonance frequency. The various radiating parts are located on one metallic face
Wideband flat dipole and short-circuit rnicrostrip
389
of a printed circuit (I). They are fed in series across a gap (G,,) by means of a stripline (M) etched on a second printed-circuit sheet (J). The classical logperiodic parameters are:
,
I,, being the distance along the stripline between the gaps (G,,) and (G, + ,) of (D,,) and (D,,, ,) separated by a distance 4+,. To limit the variation of the VSWR in the frequency band, it is necessary to increase the expansion parameter T. The distance I,, must be lower than As/2 to compensate for the various reflections appearing at each gap. The following parameters have been adopted: r = 0.95, a = 0.4, 4,/A, = 0.2, H,,/A, = 0.1, I,,/i, = 0.32, W,/1, = 0.166, R,,= 180R. With these parameters, a 50" 3 dB beamwidth and 45" deflected beam are calculated. With 50 radiating sources the antenna dimensions are 1.1 x 0.1 x 0.07m, which corresponds to a theoretical frequency band of 0.9 - 6GHz bounded by a VSWR < 2 and an efficiency of 95%. +
LA
cut AB
Fig. 7.39 Geometrical parameters of the log-periodic structure
Fig. 7.38 Log-periodic array of short-circuited patches ( 1 ) : Printed circuits and complete array (2): Cross-sect~on
The antenna performs well between 0.75 and 4.5 GHz. Fig. 7.40 shows the measured H-plane radiation patterns at three frequencies. The average values are 42" for the deflection angle and 50" for the 3dB beamwidth over all the experimental bandwidth.
390
Wideband flat dipole and short-circuit rnicrostrip
Wideband flat dipole and short-circuit microstrip
391
7.3 References I
2
3 4 5 6 7
g
9 0 . degrees
10
(A) 11 12 13 14 15 16 17 18 19 20 21 8 . degrees
22 23
Fig. 7.40 A Measured H-plane directivity patterns a t 4.5 GHz
B
Measured H-plane directivity patterns
-.-.-
Copolar at 0 4 GHz
-Copolar at 2.9GHz
---- Cross-polar at 2.9 GHz
24 25
DUBOST, G., and ZISLER, S.: 'Antennes a large bande. Theories et applications' (Masson. Paris, 1976) DUBOST, G., and VINATIER, C.: 'Doublet replie symetrique en plaques fonctionnant a t*s hautes frequences et a large bande'. Brevet Europeen 0044779 BI, 13 Nov. 1985; USA, 284702, 20 July 1981; Japan, 114526, 23 July 1981 DUBOST, G.: 'Flat radiating dipoles and applications to arrays' (John Wiley, 1981) DUBOST, G. BEAUQUET, G., and VINATIER, C.: 'Theoretical radiation admittance of a , pp. 252-253 large bandwidth flat symmetrical folded dipole', Elec~ron.L e ~ t 1984.20, DUBOST, G., and RABBAA, A.: 'Analysis of a slot microstrip antenna', IEEE Trans., 1986, AP-34, pp. 155- I63 DUBOST, G.. and VINATIER, C.: 'RCseau dedoublets replies symetriques en plaques, a large bande autour de 12GHz'. L'Onde Electrique, 1981, 61, pp. 34-41 DUBOST. G., and GUEHO, S.: 'Impedance mutuelle et couplage entre deux doublets repli6s plans paralleles en fonction de leur ecartement', CR Acad. Sci. Paris, 1985, 301, ser. 11, pp. 79-82 DUBOST, G.: 'Mutual ooupling between flat folded dipoles in terms of frequency'. Int. Symposium Antennas and EM Theory, Beijing, China, Aug. 1985, pp. 706-711 DUBOST, G., and FRIN, R.: 'Antenne plaque a double polarisation croisee'. (Brevet 36 05 990, 23 April 1986 DUBOST. G.: 'Large bandwidth dual polarized multilayer microstrip antenna'. AP-S Intern. Symp., Philadelphia. USA, June 1986, pp. 455-458 PALANISAMY, V., and GARG, R.: 'Analysis of circularly polarized square ring and crossedstrip microstrip antennas', I E E E Trans., 1986, AP-34, pp. 1340-1345 DUBOST, G.: 'Broadband circularly polarized flat antenna'. Int. Symp. Ant. &Prop., Japan, 1978, pp. 89-92 CHIBA T., et ai.: 'Suppression of higher modes and cross polarized component for microstrip antennas'. IEEE AP-S, 1982, p. 285 HUANG, J.: 'CP microstrip array with wide axial ratio bandwidth and single feed LP elements*. IEEE AP-S, 1985, pp. 705-708 DUBOST, G., FRIN, R.: 'Antenne a double polarisation associee des directeurs'. Brevet Europe, USA and Japan, April 1987 DUBOST, G., and RABBAA, A,: 'Synthbe de I'antenne plaque a double fente', L'Onde Electrique, 1987, 67, pp. 72-79 DUBOST, G., and RABBAA, A.: 'Substrate influence on flat folded dipole bandwidth', Electron. Lett., 1985, 21, pp. 426-427 JAMES, J. R., HALL, P. S., and WOOD, C.: 'Microstrip Antenna' (Peter Peregrinus 1981) IEE Electromaghehe Waves Series 12. DUBOST, G.: 'Comparison between flat radiating source bandwidth'. IEE Coloquim on Antenna bandwidth extension techniques, London, 28 Oct. 1985. DUBOST, G., and VINATIER, C.: 'Large bandwidth and high grain array of flat folded dipoles acting at 12GHz' 3rd Int. Conf. on Ant. and Ptopag. ICAP, Norwich, April 1983 DUBOST, G.: 'Improvements in printed-circuit radiating sources and arrays'. IEE Colloquim on receiving antennas for satellite broadcasting', London, April 1984 DUBOST, G., BEGUIN, D., CHAPUIS, E., AURIOL, A.: 'Reseau plat a grand gain et a faibles lobes secondaires a 5 GHz'. Conference Internationale sur le Radar, Paris, May 1984 MARCHAND, M.: 'Antenne plane a reseau en bande X', Rev. Tech. Thornson-CSF (France), 1985, 17, pp. 83-109 DUBOST, G., POTIER, P.: 'Rkseau plat a commutation tlectronique de faisceaux dans la bande des IZGHz', L'Onde elecwique, 1985, 65, pp. 56-61 DUBOST, G.. and NICOLAS M.: 'A braod angular coverage and large bandwidth antenna'. 17th European Microwaves Conf., Rome, Sept. 1987
392
Wideband flat dipole and short-circuit microstrip
26 DUBOST G.. NICOLAS, M., VALLEE, P.: 'Antenne a pas de balayage reduit dans un large secteur angula~re'.Brevet 85 07 348, 15 May 1985 27 DUBOST, G.: 'Antenne symetrie de revoloution associant une lentille dielectrique a une source plaque'. IEEE Symposium AP-S, Vancouver, Canada, June 1985, pp. 587-590 28 DUBOST, G.: 'Flat linear radiating array applied on a cylindrical lens'. Melecon'85 Mediterranean Electrotechn~calConference, Madrld, Oct. 1985, pp. 215-218 29 DUBOST, G.: 'Short-or open-circuited dipole parallel to perfect reflector plane and embedded in substrate and acting at resonance', Electron. Lett., 1981, 17, pp. 914-916 30 DUBOST. G.: 'Transmission-line model analysis of a lossy rectangular microstrip patch' Electron. Lett. 1982, 18, pp. 282-282 31 DUBOST. G.. and RABBAA, A.: 'Mutual impedance between two short-circuited flat resonant dipoles'. IEEE Trans., 1981. AP-29, pp. 668-671 32 DUBOST. G.: 'Far field radiated by short-circuited microstrip antenna acting at a quarter wavelength resonance' Electron. Lett. 1983, 19, pp. 737-739 33 DUBOST, G., GUEHO, S., and BEGUIN, D.: 'Ku band phased array in a large angular sector', 5th Int. Conf. on Antennas and Propag., ICAP 87, 1987, University of York 34 DUBOST, G., and GUEHO, S.: 'A 3 bits digital phase shifter in Ku band for microstrip ,.**.d 'r,:"v ~ --.., A..7m y..,,,, ,".,,..'.-., Q , h ,-,,I,.",.:buAuquu~a vu x r ~ r u n c a vr ~ r ~ r ~ :... u r u c d r r unug. u, ~ 7< 8".. uuddpe~i, ~ . Hu~rya~y 35 DUBOST, G., GUEHO, S., BEGUIN, D.: 'Dephaseur Clementaire en ligne microruban et dephaseur a commande numerique en faisant application', Brevet 86 11 923. 21 Aug. 1986 36 DUBOST, G . , GUEHO, S., and BEGUIN, D.: 'Antenne reseau carrk, monopulse a balayage C.lectronique'. Brevet 8720774, 13 Jun. 1987 37 DUBOST, G., ALEXIS, R.: 'Antenne formee a partir d'une cavitt resonnante comportant une face rayonnate'. Brevet 8408.392, 19 May 1984 38 DUBOST, G.: 'Antennes plaques pour les te1&communications entre stations mobiles' L'Onde Electrique, 1985), 65, pp. 41-49 39 DUBOST, G.: 'Vertically polarized flat antenna with omnidirectional radiation". Int. Symposium on Antennas and Propagation, ISAP, Aug. 1985, Kyoto, Japan, pp. 109-112 40 DUBOST, G.: 'Influence of feed-point location on radiation resistance of a short-circuited flat dipole', Electron. Lett., 1984, 20, pp. 980-981 41 DUBOST, G., BIZOUARD, A,: 'Antenne periodique plane'. Brevet 83.19.924 13 Dec. 1983 42 DUBOST, G., GUEHO, S., and BIZOUARD, A,: 'Log-periodic short-circuited dipole array with a squinted beam', Electron. Lett., 20, pp. 41 1-413 43 DUBOST, G., and GUEHO, S.: 'Theory of a large bandwidth microstrip plane array with a deflected beam'. IEEE Int. Symposium on Ant. Prop., June 1984, Boston, Mass., USA
--
A:-..
Chapter 8
Numerical analysis of microstrip patch antennas J.R. Mosig, R.C. Hall and F.E. Gardiol
8.1 Introduction 8.1.1 General description Microstrip patch antennas are thin and lightweight radiating elements, formed by a substrate, including one or several dielectric layers, backed by a metallic sheet (the ground plane). Thin metallic patches (the radiating elements) are located on the air-substrate interface and, possibly, between the dielectric layers. Microstrip antennas are manufactured by the photolithographic process developed for printed circuits. Their low profile, low weight and mechanical ruggedness make them an ideal choice for aerospace applications. They can be mass-produced, and could thus provide inexpensive receiver antennas for direct reception of microwave signals from satellites (television, mobile communications). Finally, they are ideally suited to be combined in large arrays, the individual patches sharing the same substrate. Thus directive antennas can be obtained in spite of the inherent low directivity of a single patch. The remarkable practical advantages offered by microstrip antennas are offset, to some extent, by their inhomogeneous nature, and a rigorous analysis was long considered to be a hopeless task. An accurate model should take into account the three inhomogeneities of a microstrip structure (Fig. 8.1): ( a ) The presence of at least two dielectrics (often air and substrate) ( 6 ) The boundary conditions on the interfaces between different layers are inhomogeneous since thin metallic plates making up the radiating elements and feeding the structure can partially fill the interfaces (c) Any microstrip structure is finite in dimensions; i.e. its ground plane and its dielectric substrate are bounded in the transverse directions. The edges may, however, be located at a very large distance, in which case this third inhomogeneity may be neglected (the structure is then assumed, mathematically, to extend to infinity).
394
Numerical analysis of microstrip patch antennas
Models used to study microstrip patch antennas range from very simplified ones, such as the transmission-line model, through cavity models, planar circuit analysis, segmentation techniques, and up to quite sophisticated approaches based on an integral-equation formulation. In the framework of the integralequation model, many different approaches exist, depending on the use of spectral or space quantities and on the geometries to be included.
Fig. 8.1
The three inhomogeneities of a microstrip structure. a Dielectric media of unequal permittivity, b Infinitely thin conductors introducing surface current between the dielectric media c Finite transverse dimensions of substrate and ground plane
Detailed surveys of these models are available (e.g. Reference I), and several of them are treated elsewhere in this book.
8.1.2 The integral equation model The purpose of this Chapter is to provide a rigorous treatment of microstrip antennas, free from over-simplifying assumptions. Among its principal features, the proposed model is able to handle patches of arbitrary shapes where no educated guess of the surface-current distribution is possible. Also there is no limitation in frequency and substrate thickness. The model automatically takes into account mutual coupling between elements and can predict the performance of a patch embedded in an array environment. Surface waves are included as well as dielectric and ohmic losses. Thus the model allows accurate prediction of quasistatic behaviour, dominant and higher modes of resonance, and input impedances, coupling coefficients, radiation patterns, gain and efficiency at any frequency. The model relies upon the identification of a microstrip antenna as a particular case of a stratified medium. The pioneer work on electromagnetic-wave propagation in stratified media must be ascribed to A. Sommerfeld, who investigated the radio-wave propagation above a lossy ground as early as 1909. The microstrip antenna is modelled by an integral equation where the main unknown is the electric surface current density on the patches. The Green's functions forming the kernel of this equation include the effects of the layers, and are obtained in the form of inverse Hankel transforms by the systematic use
Numerical analysis of microstrip patch antennas
395
of stratified media theory. The first Sections of this Chapter are devoted to the construction of the integral equation and of the pertinent Green's functions. Considerable attention is paid to the development of efficient numerical techniques for evaluating the Green's functions. The integral equation is directly formulated in the space domain using a vector and a scalar potential. The resulting mixed potential integral equation (MPIE), similar to that obtained for wire antennas, is better suited for numerical analysis than the customary electric-field integral formulation. The MPIE is solved by a method of moments. In the general case, rooftop subsectional-basis functions are used. For particular geometries, it can be more efficient to use entire domain-basis functions corresponding to the eigenvalues of the equivalent cavity. Finally, standard circuit analysis is used to deal with multiport antennas, loaded antennas and arrays. The final Sections of the Chapter present numerical results for the input impedance, coupling coefficients and radiation patterns of several microstrip antennas and arrays of practical interest. 8.2 Model based on the electric surface current 8.2.1 Geometry of the model and boundary conditions In order to present the theory in the clearest possible manner, the electric surface-current model will be developed for the simple microstrip structure of Fig. 8.2 with a single dielectric layer and a metallic patch. The generalisation to multilayer antennas and to multiple patches (arrays) will be considered later. The substrate is assumed to extend to infinity in the transverse directions and is made of a nonmagnetic, isotropic, homogeneous material which can be lossy. The ground plane also has infinite dimensions, and the upper conductor (the metallic patch) has zero thickness. Both the ground plane and patch are allowed to have ohmic losses. The direction perpendicular to the ground plane is selected as the z-axis (Fig. 8.2). The patch extends over part of the z = 0 plane, denoted by the surface So. The remainder of the z = 0 plane, i.e. the surface separating the two dielectric media, is denoted S and called hereinafter the interface. Indexes 1 and 2 are associated, respectively, with the infinite dielectric extending above the substrate, usually the air, and with the substrate itself. Thus, we have El
=
Eo,
E~
=
E~E,
Z
=
> 0
~ ~ ~ i ( I - j t a n 6 )- h < z < O
where h is the substrate thickness and everywhere.
(8.1)
396
Numerical analysis of microstrip patch antennas
The excitation is provided by a time-harmonic electromagnetic field. Complex phasor notation is used throughout this Chapter. Any complex scalar quantity C represents an instantaneous quantity C(t) given by: c(t)= J2 Re [Cexp (jwt)]
Numerical analysis of microstrip patch antennas
397
The induced currents in turn create diffracted or scattered electromagnetic fields. These fields, denoted E" Hd, add to the excitation fields to yield the total fields E, H existing in the entire space. On the air-dielectric interface (the plane z = 0, excluding the surface of the patch So)the boundary conditions are: ez x (El - E l )
= 0
(8.4)
e r x (HI-Hz)
= 0
(8.5)
On the metallic surfaces the boundary conditions will be inhomogeneous owing to the presence of the currents. Assuming that the patch and the ground plane are perfect conductors (this restriction will be removed later) we have on the upper side of the patch S,(z = 0+): e Z x El = 0;
e, x H, =
4,
(8.6)
and, similarly on the lower side z = Ow: e, x El = 0; e, x Hz = - J,2 Combining the above pairs of equations, we obtain e, x (El - E,)
(8.8)
= 0
e, x (HI - Hz) = J,,
+ J,
= J,
(8.9)
which apply to the fields on both sides of the patch. Eqns. 8.4-8.9 are written in terms of the total fields. However, since the excitation fields are assumed to be continuous, the boundary conditions (eqns. 8.4-8.5) and (eqns. 8.8-8.9) also hold for the diffracted fields. Hence the diffracted tangential electric field is continuous across the patch, while the jump in the diffracted tangential magnetic field equals the total surface current on the patch. Finally, the boundary conditions on the ground plane z = - h are Fig. 8.2
General view of a microstrip antenna and vertical cut in the y = 0 plane Superscripts e and d refer to the incident fields (excitation) and to the scattered (diffracted) fields. For a infinitely thin patch the currents J, and J,, can no longer be distinguished and the meaningful quantity is the total current J, = J,,+ J,, flowing on the patch.
The excitation fields are denoted by Ee and He. They can be the fields of a plane wave coming from infinity (receiving antenna) or the local fields created by a finite source located within the microstrip structure (transmitting antenna). In either case, the excitation fields induce surface currents on the upper side of the ground plane and on both sides of the metallic patch. However, since the patch is assumed to have zero thickness, the model cannot differentiate between the currents flowing on its upper and lower side. Indeed, the patch is modelled as a sheet of current 4 whose value at any point is the algebraic sum of the upper and lower surface currents 4, and 4, existing at z = 0+ and z = 0- (Fig. 8.2).
ez x El = 0 e, x Hz =
4
(8.10) (8.1 1)
It must be pointed out that the microstrip antenna problem can be completely solved without actually knowing the exact distribution of surfacepxrent on the ground plane. In fact, image theory can be used to remove the ground plane and the boundary conditions (eqns. 8.10-8.11) will then be included automatically in the Green's functions. 8.2.2 Potentials for the diffracted field Since no volume sources are considered in this model, the diffracted fields satisfy the homogeneous Maxwell's curl equations:
V V
x E L-jwp,,Hd
(8.12)
x Hd = j w ~E d
(8.13)
398
Numerical analysis of microstrip patch antennas
The resolution of antenna problems can in many cases be simplified by introducing the scalar and the vector potentials for the diffracted fields:
subject to Lorentz's gauge:
Numerical analysis of microstrip patch antennas
399
effects of the dielectric substrate and of the ground plane. Therefore, the Green's functions must satisfy the boundary conditions (eqns. 8.4-8.5) and (eqns. 8.108.11). Moreover, the boundary condition for the magnetic field (eqn. 8.9) is automatically built into the formulation of the Green's functions. These functions are dyadics, and unfortunately do not have a closed analytical expression. However, once they are formulated and numerically evaluated, the only unknown which remains is the true electric surface-current distribution on the conducting patch.
Introducing the above expressions into Maxwell's equations 8.12 and 8.13 and combining, we obtain two homogeneous Helmholtz's equations for the potentials:
where k, = ~ ( j i ~ is~the , ) wavenumber "~ in medium i. It must be recalled here that the choice of the couple A , V is not unique [2]. Indeed, any vector A* = A gradY can be used as a new vector potential provided that the scalar potential is replaced by V * = V - joy. Moreover, if Y is a solution of the homogeneous Helmholtz's equation, the new potential will still satisfy Lorentz's gauge (eqn. 8.16). We shall discuss later some convenient choices for the potentials.
+
8.2.3 Green's functions Let us consider an arbitrarily oriented Hertz dipole of moment I dl located at the point r' (Fig. 8.3). In general, the vector potential a t the point Y due to this dipole is given by the linear relationship
w h ~ E, e is a three-dimensional dyadic Green's function. The physical meaning of G, is evident: the scalar component Git gives the s-component of the vector potential existing at the point r created by a t-directed Hertz dipole located at the point r'. If the source and the observer are surrounded by an infinite homogeneous medium, the dyadic G, is diagonal and can be exp~essedas the product of a scalar Green's function GA times the unit dyadic In this case, the vector potential is always colinear with the source dipole. For a microstrip antenna it is possible to use a scalar free-space Green's function of the vector potential. However, if we do, we then need to use fictive electric and magnetic surface currents on the air-dielectric interface in order to satisfy the boundary conditions. These currents are also unknowns in the integral-equation formulation of the problem and add to the complexity of the numerical solution. The preferred solution is to include in the Green's functions
Fig. 8.3 Horizontal electric dipole ( H E D ) o n a microstrip substrate T h e fields and potentials of such an elementary source give the Green's functions associated with a microstrip antenna.
Keeping in mind the linearity of Maxwell's equations, the vector potential of a given current distribution can be written as a superposition integral involving the corresponding dyadic Green's function
The scalar potential V is obtained by introducing the above expression in the Lorentz gauge with the result:
a.
The Green's function G, associated with the scalar potential must be carefully defined. In fact, the uniqueness of G, is guaranteed only if the divergence of GA is an irrotational vector. Thus we can write [3]
where V' acts on the primed co-ordinates. Expression 8.21 is now easily transfor-
400
Numerical analysis of microstrip patch antennas
med into
where dS, is the perimeter of the patch and n is the outwards-pointing normal unit vector (Fig. 8.2). The edge condition guarantees that the normal component of the surface current vanishes on the perimeter of the patch. Hence, the line integral in eqn. 8.23 can be eliminated. We can now introduce the associated surface-charge density q, via the continuity equation:
Finally, we can express the scalar potential as:
It is worth mentioning that the edge condition can be applied even if So is a portion of a larger patch. Such a situation may arise when solving the problem with a method of moments using subsectional-basis functions. In this case the line integral in eqn. 8.23 can still be eliminated, but since 4 does not necessarily vanish on the boundary of So, the continuity equation must be interpreted according to the theory of distributions, and delta functions corresponding to line charges in the boundary of So, will appear in the expression for q,. The Green's function G,can be viewed as the scalar potential created by a point charge, even if isolated time-varying point charges do not exist in the real world. Thus, owing to the lack of a sound physical interpretation, it is better to consider G, only as a useful mathematical device. Only when the frequency goes to zero, does this function become the familiar electrostatic potential of a point charge. 8.2.4 Mixed potential integral equation ( M P I E ) The diffracted fields derived from the potentials of eqns. 8.20 and 8.25 satisfy Maxwell's equations and the boundary conditions of the problem (eqns. 8.48.5) and (eqns. 8.8-8.9). The last step is now to relate these fields to the excitation fields via conditions (eqns. 8.6-8.7). If the total tangential electric field is forced to vanish on the patch surface, we get the standard electric field integral equation. This equation can be slightly modified to account for the ohmic losses on the patch. The total tangential electric field is now proportional to the total surface current, and we can write
or, introducing the potentials
where the proportionality constant Z, is a surface impedance (measured in
I
Numerical analysis of microstrip patch antennas
407
ohms) which accounts for the finite conductivity of the patch. An accurate value for Z, can only be obtained by measurement since Z, must include technological data such as the thickness and roughness of the metallic patch. However, in most cases the patch is thick compared with the skin depth 6, and the classical expression (8.27) Z, = (1 + j)/a*6 represents a good approximation. In the above expression a* is an effective conductivity that includes roughness effects and can be several times lower than the values of conductivity found in standard tables. Finally, introducing the integral form of the potentials (eqns. 8.20-8.21) in eqn. 8.26 we get the final expression for the mixed potential integral equation (MPIE):
The validity of this equation depends on the possibility of defining the Green's function G, by eqn. 8.22. Eqn. 8.28 is a Fredholm integral equation of the second kind. However, the term Z, J, is usually small and the iterative techniques commonly used for Fredholm integral equations of the second kind that arise, for example, when using the magnetic field integral equation [4], do not apply here. The unknowns in the integral equation 8.28 are the surface current J, and the surface charge q,. However, they are not independent, and are related through the continuity equation. 8.2.5 Sketch of the proposed technique The successive steps in solving the microstrip antenna problem are now clear. We start with the theoretical determination of the required Green's functions GA and G,. In general, the Green's functions are available as definite integrals over semi-infinite intervals and they must be numerically evaluated for distances ranging from zero to the maximum linear dimension of the patch. The construction of accurate numerical integration algorithms to evaluate the Green's functions is a crucial step of the overall problem. Once the Green's functions are computed, the unknown surface current is expanded over a set of basis functions and the integral equation is tested against a set of test functions using the so-called method of moments (MOM). Here, the correct choice of these sets of functions is essential for the quality of the final results. In this way, the integral equation is discretised and transformed into a set of linear equations. The complex eigenvalues of the matrix equation provide the unperturbed resonant frequencies of the patch and its unloaded quality factor. The next step is the construction of the excitation fields. These fields depend strongly on the physical nature of the excitation. In many cases (coaxial pin, microstrip line) the computation of the excitation fields calls for the same or
.
402
Numerical analysis of microstrip patch antennas
Numerical analysis of microstrip patch antennas
related Green's functions that were calculated for the MOM matrix. Testing the excitation fields yields the independent vector of the matrix equation. The solution of the matrix equation gives a numerical estimation of the unknown surface current. Computing the voltages at the excitation points allows the determination of the impedance and scattering matrices of the antenna. Standard circuit analysis may be used to account for any load or for multiple excitations. Resonant frequencies and loaded quality factors are easily derived from the input impedance. Table 8.1 Essential steps (-) and main results (*) of the proposed numerical technique
from the boundary conditions -construct the pertinent
I
J
-find the pole and the residue associated to the GFs when expressed in the spectral domain
I
1 I
A DIPOLE
)
I
I
-evaluate numerically the GFs for the potentials in the near field region
I
GFs for the fieldsin the far field region
1 AND UNLOADED a
to the intearol eountion
complex determinant
+SURFACE CURRENT DISTRIBUTIONsINPUT IMPEDANCE AND LOADED Q
4-
4
solve the matrix equation] I -
*RADIATION PATTEF POLARIZATION. DIRECTIVITY. GAIN AND EFFICIENCY
To calculate the radiation pattern we need to go back to the Green's functions and obtain their asymptotic forms in the far field. This can be done analytically and the radiation pattern of the antenna, including polarisation and phase information, is obtained by using a superposition integral over the patch.
403
Finally, integration of the far fields over the upper half-space will give the directivity of the antenna and an estimation of its efficiency and gain. These steps are summarised in Table 8.1. 8.3 Horizontal electric dipole (HED) in microstrip The construction of the Green's functions requires the determination of the fields created by a horizontal electric dipole (Hertzian dipole) located on the air-dielectric interface of a microstrip structure (Fig. 8.3). The first investigations of a HED embedded within a stratified medium are due to Sommerfeld, who published in 1909 the exact solution for a dipole over an imperfect ground. The Hankel integral transforms which appear within such a problem are often known as Sommerfeld integrals. The vertical dipole over a conducting plane covered with a dielectric layer was studied by Lo and Brick in two articles which appeared almost simultaneo~sly 15, 61. The problem is quite similar to the one arising in microstrip antenn, s, except for the dipole orientation. However, even though the first microstrip lines were introduced around the time these articles were pubIished, no connection between the two fields was made - microstrip antennas were to be developed some 20 years later. This may explain the different approaches to the two problems, in particular the absence of a detailed study of the near field, which is essential when the source and the observer are both located on the surface of the substrate. The general theory of dipoles - either electric or magnetic, horizontal or vertical, located within an arbitrary stratified medium - was developed later, mainly by Brekhovskikh [7], Wait [8], Felsen and Marcuvitz [9], and Kong [lo]. However, as was done in previous publications, the emphasis was put on the study of radiated fields, for which approximate asymptotic analysis is sufficient. For the accurate study of microstrip radiation, however, precise knowledge of the surface currents on the patch, and hence of the near fields on the dielectric interface, are required. For this reason, the fields created by a HED located on the air - dielectric interface will be determined. 8.3.1 The vector potential Let us consider a HED of moment Idx equal to unity placed at the point r' = 0 as indicated in Fig. 8.4. In order to ease the mathematical development required for solving the Helmholtz equation 8.17 satisfied by the vector potential, we will replace the space variables x , y by their spectral counterparts k,, ky according to the double Fourier transform:
404
Numerical analysis of microstrip patch antennas
Numerical analysis of microstrip patch antennas
405
If the dipole is embedded in an infinite homogeneous medium of permittivity E,, the vector potential is parallel to the dipole and exhibits a spherical symmetry: 1 -jfmmf(kX, 2n k,)exp(jk,x +jk,y)dk,dk, (8.30) In the spectral domain the homogeneous Helmholtz equation becomes: =
where
On the other hand, it is well known [I I] that two cartesian components of A are needed to satisfy the boundary conditions in an inhomogeneous structure such as a microstrip antenna. Here, we shall adopt Sommerfeld's choice and postulate an additional vertical component for the vector potential. Hence A = e,A, ezA,. Choosing now for A, and A, general expressions of the form of eqn. 8.32, we obtain after satisfying the boundary conditions the expressions:
+
2
Fig. 8.4 Co-ordinate system for the study of an x-directed horizontal electric dipole (HED) on a microstrip substrate The air-dielectric interface is at z = 0 and the ground plane is at z = -h. The continuity equation implies that there are two point charges of value * I dxljw at both extremities of the dipole
According to eqn. 8.1 we shall adopt from now on the shorthand notation u: = U: = ki - % a n d ui = u2 = ki - E,%. The general solution of eqn. 8.31 for a cartesian component of A is (s = x, Y, 2): where the unknown factors a, b may be functions of the spectral variables. The fields are obtained by usingeqns. 8.14-8.15 and the Lorentz gauge, which also holds in the spectral domain. Since no external excitation fields are considered here, the fields of eqns. 8.14-8.15 are total fields. These fields must satisfy the boundary conditions eqns. 8.4-8.5 on the interface and eqn. 8.10 on the ground plane. In particular, the HED is equivalent to a surface current density in the plane z = 0 given by:
=
PC (,
2n
- 1) J
i
+
cosh u(z h) (DmD, cosh uh)
+
u tanh uh, and the upper and lower where D, = u, + ucoth uh, D, = E,U, expression inside the symbol { ) correspond, respectively, to the upper semiinfinite medium (z > 0) and to the substrate (- h < z i0). It can be easily shown that if er = 1 and h 4 co, the vertical component A, vanishes and A, becomes the free-space vector potential given by eqn. 8.34.
8.3.2 Scalar potential and the fields The continuity equation applied to an electric dipole implies the existence of two point charges q = Ijjw at both ends of the dipole. Since the product Idx has been assumed to be equal to unity, the moment of this pair of charges is qdx = l/jw. The scalar potential associated with the dipole is given directly by the Lorentz gauge. Introducing eqns. 8.35 and 8.36 in eqn. 8.16 we get:
+
p
j ~~xP(-w)/(DTEDTM) = -2 ~~JW Nsinh I u(z h)/(DrEDTM sinh uh)
+
(8.37)
with N = u, + u tanh uh. In the space domain, the scalar potential V of an electrostatic dipole of moment lljw is related to the scalar potential V, of a single unit point charge by the well known expression:
v
I av, jw ax
= ---
406
Numerical analysis of microstrip patch antennas
Numerical analysis of microstrip patch antennas
407
or, in the spectral domain by
Comparing eqn. 8.39 with eqn. 8.37, we can deduce by analogy that the potential of a unit point charge on the air-dielectric interface of a microstrip antenna is given by Nsinh u(z + h) DTEDTM sinh uh
i
Now, the construction of the fields is straightforward, for we have in the spectral domain:
Hence, the surface waves appear as poles of the integrands in the complex plane k, = 1 + j v . It can be shown [I31 that D , has no zeros if kOh(c;- 1)1'2< 4 2 and D , has only one corresponding to the dominant zero-cutoff TM surface wave. This condition is equivalent to the restriction:
For the sake of simplicity we shall assume from now on that this inequality holds. Higher frequencies would add new poles, but the analysis made for the single-pole case remains qualitatively valid. For substrates with moderate losses the pole 1, + jv, lies slightly below the real axis (v, < 0) and its real part is bounded by 1 < Ap/k0 < ~ f " (Fig. 8.5).
It can be easily demonstrated that the vertical component E, shows the expected jump discontinuity when crossing the air-dielectric interface. 8.3.3 Surface waves and the spectral plane k, It can be shown [I21 that the equations DTE = 0, D , = 0 are the characteristic equations for the TE and TM surface-wave modes propagating on a dielectriccoated conducting plane. Hence the zeros of D , and DTM give the phase constant of the surface waves existing on a rnicrostrip structure. The terms D, and DTMdepend on k, and k, only through the radial spectral variable $ = k2, $. For functions exhibiting such a kind of dependence, the inverse Fourier transform 8.30 can be written as
+
g-'[.&)l
=
jom~
d ~ ~ ddkQ~ ~ 3 ( ~ ~ )
(8.42~)
Pole (lossless)
Fig. 8.5
Topology of the complex plane k, with the original integration path from zero to infinity The Figure also shows the geometrical locus of the pole as a function of dielectric losses.
and More precisely, a good approximation for electrically thin substrates [I41 is where Q, 4 are polar co-ordinates and Jois the Bessel function of zeroth order and first kind. The replacement of the double Fourier transform by Hankel transforms is of great utility when performing the numerical evaluation of the fields and potentials. For instance, if the observation point is also on the interface ( z = 0) we have: The integration path of the Sommerfeld integral eqn. 8.43-8.44 is, in general, the real positive axis 1. But, if we consider the theoretical case of a lossless substrate, then v, = 0 and the pole is on the real axis. Since, by continuity, the integration path must remain above the pole, the integral from zero to infinity in the lossless
408
Numerical analysis of microstrip patch antennas
Numerical analysis of microstrip patch antennas
case is interpreted as:
409
On the other hand, it can be shown [9] that this replacement will give correct results even for the broadside direction Q = 0". The final expression of the integral in the w-plane is
where the symbolfstands for Cauchy's principal value and R is the residue of the integral at the pole k, = Finally, it should be mentioned that the function u; = ki - ki introduces a branch point at k, = ko (Fig. 8.5). However, the integral remains bounded here and no deformation of the integration path is needed.
4.
8.3.4 Far-Jield approximations Far-field approximations are essential for the evaluation of the radiation pattern of a microstrip antenna. They can be obtained by using standard asymptotic techniques, such as the steepest-descent method [9]. We shall outline briefly the application of these techniques to Sommerfeld integrals. We begin by replacing the Bessel functions in these integrals by Hankel functions. This is done recalling the identity F i g . 8.6 The integration path C closing at infinity in the k, plane and the new branch cut introduced by the Hankel function A portion (dotted line) of the path C is in the lower Riemann sheet
which holds if.f'is an even function of k, [ll]. In this way, the integration path C in the complex plane k, closes at infinity (Fig. 8.6) while the topology of the plane remains unchanged except for an additional branch point introduced by the Hankel function (Fig. 8.6). For the sake of clarity, the pole k, = is located on the real axis (lossless substrate, see Fig. 8.5). Let us consider now a typical integral in the air:
5
where C is the path shown in Fig. 8.6. To obtain an asymptotic expansion for I, the plane k, is transformed into a new complex plane w defined by the relation
The transformed path C* in the plane w is shown in Fig. 8.7. The pole is now located at w, = 4 2 jarcosh (lp/ko)and the branch cuts associated with the points k, = $. ko disappear owing to the new choice of variables. Introducing spherical co-ordinates r, 8 (z = r cos 8, Q = r sin 8) the argument of the Hankel function becomes
+
Since we want an expression useful in the far field (k,r p l), we can replace the Hankel function by its first-order asymptotic expression. The integration path can be deformed far from the origin w = 0 in order that sin w never vanishes.
= k,sin w ) showing the transformed path C*,the steepest descent path , C and the new location of the pole Also the correspondence with the four quadrants of the plane k, is given, either in the upper (U)or in the lower (L) Riemann sheet.
Fig. 8.7 The new complex plane w (k,
F(W) = j"
(
nR sin" 0 sin w )'I2 k, cos w/(ko sin w)
with R = kor and q(w) = -jcos(w - 8).
410
Numerical analysis of microstrip patch antennas
Numerical analysis of microstrip patch antennas
The saddle point w, of function q is given by w, = 0. The steepest-descent path CsD through w, is defined by Im(q) = - 1. Its particularities are easily derived (Fig. 8.7): (i) Cm is at a 45" angle with the real axis. (ii) Cs, intersects the line Re(w) = n/2 at the level Im(w) = cosh-'(l/sin 0). (iii) As a result, the pole w, is located between CsDand the positive real axis only when 0 > 0, = sin-'(k,/&). n/2. (iv) CsD possesses two vertical asymptotes at Re(w) = 0
+
Contributions from the integrals joining the two paths C* and CsD at infinity can be eliminated since the term exp (Rq) vanishes in these regions. The path C* can then be deformed into the path CsD, provided the contribution of the pole is added for angles greater than the critical angle 0,. This is written symbolically as
where U is the Heaviside unit step function and Cp is a patch surrounding the pole wp (Fig. 8.7). The first-order approximation for the integral along CsD can now be obtained by standard techniques [9]. The integral around the pole is evaluated using the residue theorem and is expressed in the original k, plane. Finally, the asymptotic expression of the integral I(eqn. 8.49), valid in the far field region, is
I
=
2j"+l cotan 0f (k, sin 0) exp(-'kor)
[I
+ ~ ( r - I ) ]- U(B - B,)
where the residue R is given by
-
R = lim (k, kg
4)f(k,)
(8.55)
AP
and the Landau notation O(f) indicates the behavior at infinity of the first term neglected in the asymptotic expansion. It must be noted here that the asymptotic approximation eqn. 8.54 is only valid if the pole rZ, is located far enough from the saddle point 1 = k,, sin 0, i.e. (k, sin O - AP)r % I. Otherwise, the contributions of the saddle point and of the pole cannot be separated and a modified saddle-point method must be used [9]. From the asymptotic point of view, the fields and potentials are the sum of two terms. The first term, due to the saddle point, represents a spatial wave with a complex factor depending on angle 0 and corresponds to the geometrical optical fields. The second term, due to the pole at Ap, represents a cylindrical wave decreasing exponentially away from the substrate that corresponds to the surface wave.
41 1
The surface wave is only relevant for angles 0 > OP, i.e. near the interface. However, its field dependence on e-'I2 can make it the dominant term of eqn. 8.54 when fields on the substrate surface at z = 0 are evaluated. Radiated electricjeld: An immediate application of the asymptotic relationship eqn. 8.54 is the computation of the radiated field. It is assumed here that 0 < OP,so that the surface wave can be neglected. In a real situation, a substrate always has finite dimensions and the surface wave can be observed directly only close to the substrate. For angles near 0 = n/2 (grazing angles) but far from the substrate, diffraction effects of the surface wave on the edges become significant. The radiation field is obtained by transforming, for z > 0, the rectangular components of E (eqn. 8.41) into spherical components and then applying eqn. 8.54 to the resulting integrals. The final expressions are
where 2, is the free-space impedance, I , the free-space wavelength, not to be confused with the spectral variable 1 = Re[k,], and go(@
=
g,(0)
= cos 0/(cos0 - jTcotank,hT)
Tcos 0/(T - j&,cosOcotan k,hT)
These asymptotic expansions have also been derived, with a different approach, by several other authors [15, 161. The result for E, shows that this component decreases faster with distance than Ilr, and is thus not a radiated component. Figs. 8.8 and 8.9 give the polar radiation patterns, respectively, in the E-plane and H-plane. In each Figure, four substrate thickness k,h = 0.05,0.1, 0.2 and 0.5 have been considered, and, for each thicknesses, curves corresponding to four dielectric constants E, = 1, 2, 5 and 10 have been plotted. The presence of a dielectric layer increases, in general, the half-power beamwidth in the E-plane, especially for thin substrates. On the other hand, the H-plane pattern is almost independent of the substrate parameters, except for very thick substrates just on the threshold for the generation of a second surface wave. Potentials at the interface: The Green's functions appearing in the integral equation 8.28 can be obtained from the potentials A, and V,. Solving the integral equation requires the knowledge of these potentials only at the interface. If we apply eqns. 8.54 to eqns. 8.43 and 8.44, transformed according to eqn. 8.48, we obtain with z = 0 and O = x/2:
472
Numerical analysis of microstrip patch antennas
4m0 %
-
-2zjRHi2)(&~)
Numerical analysis of microstrip patch antennas
(8.58)
where the residue R is given by eqn. 8.55 with f = k,N/DTEDTM.It is here apparent that the Q - ' contribution of the saddle point vanishes in both expressions. If higher-order terms in Q-' are desired for A,, which has no surfacewave component, the whole C,, integration path in the complex plane k, must be considered. E plane: kh=0.05
in all situations, but the calculations are rather complex, requiring error functions of complex arguments [9],and they will not be carried out here. Asymptotic expressions 8.58 and 8.59 will be used in the following development to check the results obtained using numerical integration of the potentials. H plane: kh=0.05
H plane: kh=O.l
E plane: kh=O.l
H plane: kh-0.2 E olane: kh=0.2
413
H plane: kh=0.5
E plane: kh=0.5
Fig. 8.8 Polarplot of the E-plane radiation pattern (in dB) of a HED on a microstrip substrate for four normalised substrate thicknesses ( a ) k,h = 0.05 ( b ) koh = 0.10 ( d ) koh = 0.50 ( c ) koh = 0.20 A:E,= 1 B:E,= 2 C:c,= 5 D : t , = 10
It can be shown that the asymptotic behaviour of the integral is mainly determined by the discontinuity of the derivative of the integral at the point k, = k,,. The dominant term in the asymptotic expansion is
with the parameter A defined as A = k , h ( ~ ,- 1)'''. It is possible to replace eqn. 8.58 by a uniform asymptotic development valid
Fig. 8.9 Polarplot of the H-plane radiation pattern (in dB) of a HED on a microstrip substrate for four normalised substrate thicknesses (6)koh = 0.10 ( a ) koh = 0.05 ( c ) koh = 0.20 ( d ) koh = 0.50 A: 8, = 1 B:E, = 2 C: &, = 5 D: E,= 10
8.3.5 Radiation resistance and antenna efficiency
If the cylindrical components of the fields are expressed in terms of the potentials by transforming eqns. 8.41, it can be shown that the term DTMappears only in the denominator of components E,E, and H 4 . Therefore, these are the components that include a surface-wave term, and thus the Poynting vector S associated with the surface wave has a radial and a vertical component, respectively, S, = - E,H4 and Sz = E,H4. Consideration of the general expression 8.54 shows that the vertical component decreases exponentially with z , and consequently does not contribute to the radiated power. On the other hand, the
414
Numerical analysis of microstrip patch antennas
radial component can be written according to expression 8.54 as
Numerical analysis of microstrip patch antennas
415
and we get
S, = (Zo/2nko)(~, - 1) ~ o s ~ ~ ~ ~ ( l d l ) ~ L ~ F ( z ) / @ (8.60)
with F(z)
=
exp (- uO~)/~TE cosh u(z
+ h)/D,cosh
uh
where the asymptotic expansion of the Hankel function has been used, and R is the residue of l/D, at the pole. It can be shown that the integral of this component over a cylindrical surface of radius Q extending from z = - h to infinity has a non-zero value independent of Q Hence, there is a net amount of power carried away by the surface wave. The surface integral must, in general, be numerically evaluated, essentially because there is no analytical formula for computing the pole Ap. However, for thin substrates we can use the approximation given in eqn 8 46 and estimate the residue appearing in eqn. 8.60 as:
Here again, the above formula becomes for E, = 1 the well known radiation resistance of a horizontal dipole above a ground plane [40]. It is worthwhile to compute numerically the integral 8.64 and plot the values of the radiation resistance R,, normalised to n ~ ~ ( d l / l , as ) ~a, function of the parameter A = koh which is proportional to the substrate thickness and to the frequency. This has been done and the results are given in Fig. 8.10 for three values of the dielectric constant. Initially, the radiation resistance increases with the square of the thickness, as predicted by eqn. 8.66. But as the normalised thickness increases, the values of the resistance oscillate and show a discontinuous derivative at the points where A is an odd multiple of 4 2 . These values correspond to the generation of higher-order surface waves [17].
m,
Then we define a radiation resistance R,,,, associated with the surface wave as
In a similar fashion, we can introduce the radiation resistance R, associated with the space wave. Starting with the asymptotic expansions 8.56 for the fields and using the fact that in the far-field zone we have Z o H = e, x E we can demonstrate that the Poynting vector is radial, its modulus being given by
Integrating this expression over the upper (z > 0) half-sphere of radius r and equating the resulting power to 1 2 R , we obtain the expression of the radiation resistance of the space wave:
0
0.2
0.4 0.6 0.8 normalized thickness
Fig. 8.10 Normalised radiation resistance O = R,l[nZo(dl/io)Z] of a HED on a rnicrostrip substrate as a function of the parameter A = kohJ(E,- 1). Z, % 120n is the free-space wave impedance.
As before, this surface integral cannot be analytically evaluated except for the case E, = 1 and h = co,where we recover the classical result for the radiation resistance of a Hertzian dipole radiating into free space. However, for thin substrates we can again estimate the surface integral 8.64 by using the approximations: jk0h(a, - sin20) g, = ; g, = jk,h cos 0, (8.65) E,
A: E, = 2 8:E, = 3 C: E, = 4
We can now evaluate the ratio between the power carried away by the surface wave and the power radiated by the space wave as: Power (surface wave) = n2 (a, - 1)'h/& (8.67) = Power (spatial wave) 2 4 -E;(E, - 1) -E, 3 15
+
476
Numerical analysis of microstrip patch antennas
Numerical analysis of microstrip patch antennas
which is proportional to the normalised thickness and shows a rather complicated dependence on the permittivity of the substrate. Finally, the radiation efficiency of a HED on a thin lossless microstrip substrate is given by
a
=
l/(l
+ 4)
(8.68)
Numerical tests have shown eqn. 8.67 to be accurate for h C 0.05 Lo. Fig. 8.1 1 gives the theoretical values of the efficiency for several dielectric constants.
Fig. 8.11
Radiation efficiency (space- wave radiated-powerltotalradiated-power) of a HED on a lossless microstrip substrate as a function of the normalised substrate thickness
A: E, = 2 8: E, = 5 = 10
C:E ,
Finite sizepatches: The above considerations refer to an elementary Hertzian dipole, but can be easily extended to finite-size microstrip patches by using superposition. The patch is excited by a unit current, and the input impedance Z,, of the antenna is obtained with techniques to be described in the following Sections. Once the radiated fields are known, a radiation resistance R, is calculated using the techniques outlined in this Section. The overall antenna If the antenna has been analysed efficiency is given by the ratio R,,/Re (Z,,,,). assuming a lossless substrate and a perfect conductor, the conservation of power R,,, = Re (Z,,,,). This is a useful check on the accuracy of the implies that R, R,, and the numerical calculations. Otherwise Re (Z,N) is greater than R, difference gives the power dissipated in the antenna in the foim of ohmic and dielectric losses.
+
+
47 7
The gain of the patch can now be defined in a customary way, as the product of the efficiency times the directivity.
8.4 Numerical techniques for Sommerfeld Integrals
When a microstrip antenna is analysed by an integral-equation technique, it is necessary to evaluate the interaction between points separated by distances ranging from zero to several wavelengths. For most of these distances the accuracy of near- and far-field approximations is not sufficient and the potentials must be numerically evaluated. For a single-layer microstrip antenna the source and the observation point are both on the interface. Hence z = 0 in the integral expressions for the fields and the potentials, and the exponential function which ensures convergence of the integrands disappears. This is the most difficult case numerically, and we will concentrate on it in this Section. Even though many deformations of the original path C of Fig. 8.6 have been tried [14, 181, we feel that the integration along C (the real positive axis A of the complex plane k,) provides the most efficient algorithm for evaluating the Sommerfeld integrals appearing in microstrip problems. 8.4.1 Numerical integration on the real axis The functions to be integrated oscillate on the real axis due to the Bessel functions. The square root uo = (A2 - k;)'l2 introduces a discontinuity of the derivative at 1 = k, that corresponds to a branch point in the complex plane. If the integrand contains D, in the denominator there is a pole just below the real axis (or on the axis itself for a lossless substrate) that produces very strong variations of the integrands. Finally, many of the oscillating integrands have an envelope which converges very slowly (A,, V,) or even diverges at infinity (A,, V). When the envelope diverges, the integral diverges in the Riemann sense since the area under the curve representing the integrand fails to converge to a finite value as the upper bound goes to infinity. However, the integral can be interpreted in the Abel sense as
lomF(1) d l
= lim Z-o
lomF(1) exp ( - u, z) d1
and the exponential guarantees convergence. This means, physically, that the potentials at the interface can be considered as the limiting case of the potentials in the air when the height of the observation point above the interface goes to zero. All these facts are clearly depicted in Fig. 8.12, which shows the integrand of the scalar potential V, for E,, = 2.55, tan6 = 0, k,h = 0.3 x, and k,e = 3. In this Figure, the substrate has been chosen quite thick for the sake of pictorial clarity. Electrically thinner, more common substrates will exhibit a pole very close to the branch point.
478
Numerical analysis of rnicrostrip patch antennas
The integration interval is decomposed into three subintervals [O, k,], [ko, koJE,] and [k,J&,, co]. In the region [0, k,] the infinite derivative in ko is eliminated with a change of variables 1 = k,cos t. The resulting smoother function is integrated numerically. In the interval [k,, k,,/~,], the singularity is first extracted if the integrand has D , in the denominator. By writing the function under the integral sign in the form F(1) = J.(~Q)f(L), we have
Fig. 8.12 Normalised values of the integrand associated with the scalar potential V of a HED on rnicrostrip ~ , = 2 , 5 5koh=0.3x k o e = 3 A: Discontinuities in the derivative 8 : Sharp peaks due to the pole C: Oscillatory and divergent behaviour at infinity -Real part ---- Imaginary part
where Here 4 + jvp is the complex pole (v, < 0) and R the residue of F at the pole. The function F,,, is integrated analytically as
Numerical analysis of microstrip patch antennas
419
It is worth mentioning that, in the lossless case (v, = O), the above integral becomes
and therefore the principal-value formulation (eqn. 8.47) of the lossless case is included' as a limiting case in this numerical technique.
Fig. 8.13 Realpart of the integrand of Fig. 8.12 for the lossy case in the interval[k,, k, J(E,)] A: Before the extraction of the singularity 8 : After the extraction of the singularity C: After the change of variables: 1 = k,cosht
Fig. 8.13 depicts the real part of the original function F(l) (solid line, A) and the difference F(1) - Eing(l)(dotted line, B) after the singularity has been extracted. There is still an infinite derivative in the curve B at I = k,; however, with a change of variables 1 = k,cosh(t) one finally obtains a very smooth integrand (the dashed line C in Fig. 8.13), which is integrated by a Gaussian quadrature. The same procedure is applied to the imaginary part of F(1) to eliminate in a similar way the sharp peak and the infinite derivative. Finally, in the region [~,JE,, co] we first extract the static term defined by F(d, ko = 0). Fig. 8.14 depicts the integrand F(1, k,) (curve A) and the difference F(1, k,) - F(d, 0) (curve B). It can be shown that the static term has the form and hence it can be integrated analytically.
420
Numerical analysis of microstrip patch antennas
Numerical analysis of microstrip patch antennas
The remaining part is a slowly convergent oscillating function over a semiinfinite interval that is integrated with specially tailored techniques.
8.4.2 Integrating oscillating functions over unbounded intervals Sommerfeld integrals, as given by eqn. 8.42, can be grouped in a more general class of integrals defined by: I(@) =
Jom
g @ d f( 4 d l
42 7
required - two features which are difficult to incorporate in an automatic computation routine. (b) Another approach applies if g(lp) is a strictly periodic function. The following decomposition is then used:
(8.74)
where (a) g(i@)is a complex function whose real and imaginary parts oscillate with a strictly periodic behaviour (sin, cos), or behave asymptotically as the product of a periodic function and a monotonic function. A typical example of this class of functions, which will be termed from now on as quasi-periodic, are the Bessel functions of the first kind. (b) f (A) is a smooth, non-oscillating function which behaves asymptotically as 2 exp (- lz). Therefore, for points on the interface (z = O), the function f ( i ) decreases very slowly or even diverges at infinity if a > 0. Here, we shall discuss the most interesting case, z = 0, which is also the most difficult from a numerical point of view. For the sake of simplicity, f(A) is assumed to be real. Complex functions can be handled by working alternately with their real and imaginary parts. (c) The lower integration bound a has been chosen conveniently to ensure that the interval [a, co) is far enough from any possible singularities of f(L). For instance in our problem, we shall take a = JE,. It is worth mentioning that the general expression 8.74 includes many integral transforms such as Fourier and Hankel transforms. Hence, the following techniques can be applied to many other problems in numerical analysis. The classical problem involving Sommerfeld integrals is the problem of radio-wave propagation above a lossy ground, where the comprehensive monograph of Lytle and Lager is the classical reference [19]. These authors have found an iterative Romberg integration satisfactory, since here the integrand displays an exponential convergence and its poles have been removed from the real axis. In microstrip problems, Romberg integration has also been used, but its effectiveness decreases considerably in the absence of a well-behaved integrand. In recent years, there has been a considerable amount of work published on the numerical evaluation of Fourier transforms, which are included in eqn. 8.74 as a particular case. The involved techniques can be classified in three groups. (a) The decomposition [a, co] = [a, A] + [A, co]. Here, Filon's algorithm is applied to the finite interval [a, A], while an asymptotic expression of the integrand is used to estimate the integral's value over [A, co] [20]. The most serious drawbacks of this approach are the choice of A and the analytical work
where P is the period of the function g. The infinite sum under the integration sign can be evaluated using standard techniques such as Euler's transformation. Recently, a more involved technique using theoretical Fourier-transform concepts has been described in connection with a problem on quantum-mechanics impact cross-sections [21]. These methods work very well for large values of Q and an exponentially decreasing integrand. Unfortunately, their extension to quasi-periodic diverging integrands seems problematic. (c) The third group of techniques, introduced by Hurwitz and Zweifel[22], are defined by the decomposition
The integration over each half-cycle is performed prior to the series' summation. As before, an accelerating device, such as the nonlinear transformations of Shanks [23] and Sidi [24] can be used to sum the infinite series. We feel that the decomposition 8.76 is particularly well suited for the Sommerfeld integrals encountered in microstrip problems and we have used it extensively throughout this work. However, instead of the sophisticated nonlinear techniques mentioned above, we have devised a new simple technique based on the concept of a weighted average between the half-cycle integrals [14]. This accelerating device has proved to be faster and more accurate for these kind of integrals.
8.5 Construction of the Green's functions Once the potentials of a HED are known, the potentials created by an arbitrary surface current J, existing on the plane z = 0 can be determined by using the superposition integrals 8.20 and 8.25. The Green's functions arising in these expressions are closely related to the potentials of a HED and can be easily obtained if the symmetry properties of microstrip structures are taken into account. We shall restrict ourselves here to the case where the source and observer are both on the air-dielectric interface (z = z' = 0). Then, according to the translational invariance of the microstrip structure in any plane perpendicular
422
Numerical analysis of microstrip patch antennas
Numerical analysis of microstrip patch antennas
to the z-axis (eqn. 8.43), we have
423
dipole. However, since only horizontal surface currents are considered we do not need to compute these expressions. It is now a matter of straightforward algebra to show that the transverse divergence of the dyadic
is given by where the angle a is given by a = tan-'{0, - yf)/(x - x')). In short, we can say that the components G F and GF are given by the Sommerfeld integrals 8.43 with the polar co-ordinates Q, cp replaced by R = lr-r'l and a. 0.4
and, correspondingly, is derived from a scalar potential according to eqn. 8.22. Therefore, provided that no vertical currents are considered, it is possible to define a Green's function associated with the scalar potential as
A
G,(rlrf) I
=
eqn. 8.44 with
Q
replaced by Ir - r'l
=
R.
(8.81)
This concludes the derivation of the Green's functions needed to solve the integral equation 8.28. A method-of-moments solution, described briefly in the next section, is used to numerically solve the equation and calculate the microstrip antenna parameters of interest. 8.6 Method of moments
Fig. 8.1 4 Real part of the integrand of Fig. 8.12 for the lossy case in the interval [k,J(&,), m] A: Before the extraction of the static term B: After the extraction of the static term
In a similar way, since a microstrip substrate shows a symmetry of revolution around the z-axis, we can write
I GP (rlr')
=
G7(rlr1)
To evaluate G;', G r , Gy we would need the potentials of a vertical electric
The integral equation 8.28 will be numerically tackled with a method of moments (MOM). This technique [25] transforms the integral equation into a matrix algebraic equation which can be easily solved on a computer. The method of moments is among the most widespread numerical techniques in electromagnetics and a detailed account of the underlying principles will not be given here. For the problem of the microstrip antenna two particular versions of the MOM deserve attention: the subsectional-basis functions approach and Galerkin's method with entire domain-basis functions. 8.6.1 Rooftop (subsectional)-basis functions If no a priori assumptions about the shape of the patches are made, a successful technique must decompose the patch into small elementary cells and define simple approximations for the surface current on each cell. The most commonly used shapes for the elementary cells are the triangle [26] and the rectangle. Even though the triangular shape is more flexible, rectangular cells involve simpler calculations and suffice for many microstrip antenna problems. Concerning the basis functions to be defined on these rectangular cells, a comparison of available possibilities [13] led to the selection of rooftop functions for the surface current J,, that have been successfully used in similar problems [27]. To implement these functions, the patch's boundary is replaced by a Manhattan-type
424
Numerical analysis of microstrip patch antennas
polygonal line (Fig. 8.15). As most commonly used antennas exhibit this kind of geometry anyway, this requirement is easily satisfied. The patch's surface is then divided into rectangular cells, called charge cells, which, for the sake of clarity, will be assumed to be of identical size. This is not an essential requirement for the theory of the algorithm, but the use of different cell sizes considerably increases the computation time.
Numerical analysis of microstrip patch antennas
4
=
Decomposition of the upper conductor in elementary cells showing the discretisation of the current and the test segments. After [38].
Two adjacent charge cells, sharing a common border perpendicular to the x-direction (y-direction) will form an x-directed ( y-directed) current cell (Fig. 8.16). An automatic overlapping of current cells is obtained in this manner so that a particular charge cell may belong to up to four different current cells. The number of charge cells is thus related to the number of current cells, though the relationship is not a simple one, since it depends on the shape of the patch. However, for rectangular patches with m x n charge cells, the number of x-directed current cells is M = (m - l)n, and there are N = m(n - 1) y-directed current cells. Every current cell supports one rooftop basis function and there is one associated test segment joining the centres of the two charge cells making up the current cell. The centre of the segment C,r, associated with the j t h x-directed current will be denoted by the vector r,,, and its ends by r,; and r; (Fig. 8.16). These three vectors are related through A similar relationship is written for y-directed segments C,(j = 1, 2,. . . N ) .
Basis functions: The Cartesian components of the surface current are expanded over a set of basis functions T,, T,:
f Z I,,T,(r - r,]) /=I
where the basis funct~onsare rooftop-type funct~onsshown In Flg 8 16:
T,( 4
F i g . 8.15
425
Fig. 8.16
-
Ixl/a
=
1x1 r a, I yl < b/2 elsewhere
Subsectional basis functions defined over pairs of adjacent cells (a), associated constant charge distribution on each cell (6). and razor testing functions (c)
A similar expression is obtained for T, by interchanging a tt b and x ++ y in the above equation. The introduction of factors I/a and llb in eqn. 8.83 yields unknown coefficients I, and I,,having the dimensions of a current. Moreover, every coefficient gives the total current flowing across the common boundary of two charge cells. The associated surface charge density is obtained from eqn. 8.83 by using the continuity equation, yielding
N
+ 2I I t J [ n ( r- r;)
- n(r - r i
)I
(8.85)
J=
where H(r) is a two-dimensional unit pulse function defined over a rectangle of dimensions a x b , centered at r = 0. The charge density within every elementary cell remains constant, justifying the name charge cell. For the charge cell of Fig. 8.15, with four test segments ending at its centre, the surface charge density is simply given by
426
Numerical analysis of microstrip patch antennas
The charge density is discontinuous on the borders between charge cells. However, the scalar potential remains bounded, while the electric field becomes singular, since q, does not satisfy a Holder condition [13]. This means that the test functions must be selected carefully, avoiding the locations where the electric field is singular. Discrete Green's functions: The notation and the computational task can be simplified by introducing 'discrete Green's functions', that have as a source a complete basis function, rather than the traditional elementary point source. The vector potential T, is created by a rooftop distribution of surface current, whereas rvis the scalar potential resulting from a rectangular distribution of unit surface charge. In practice it is convenient to deal with dimensionless quantities and in a normalised space where physical lengths are replaced by electrical lengths. The following dimensionless expressions are therefore introduced that define the discrete Green's functions:
A similar expression may be written for T:?. In these formulas rq(ro,) denotes the centre of a test segment and S,(Soj) the surface of a current (charge) cell. The discrete Green's functions exhibit the same properties of translational invariance and symmetry as the conventional Green's functions. In general, the surface integrals in eqns. 8.87 and 8.88 must be evaluated numerically. When the observation point r belongs to the source cell, some difficulties arise in the integration process. It is then recommended that the singular part of the Green's function which corresponds to the dominant term of their static value be extracted, i.e. G = G, + (G - G,) where the static value G, is given by:
Numerical analysis of microstrip patch antennas
427
When the observer is located many cells away from the sources, the sources can be concentrated at the centre of the cell. The following approximations may then be used:
Test functions: The last step of the solution with the moment method is the selection of a suitable test function. Previous work [I31 has shown that the best choice, compatible with the basis functions selected, is the use of unidimensional rectangular pulses. The use of these test functions, also called razor test functions (see Fig. 8.16), is equivalent to integrating the boundary condition (eqn. 8.26) along the segments linking the centres of adjacent cells (test segments), and therefore the testing procedure yields equations of the type:
where C,v,is the x-directed test segment extending from r,; to :r and VE1 is the excitation (impressed) voltage along the segment. A similar relationship is obtained for y-directed test segments. It is worth mentioning that this choice eliminates the need for computing field values near the edges where field singularities can adversely affect the performance of the moment method. Eqn. 8.93 is well suited for numerical treatment since all derivatives have been removed. The integration of J,, can be done easily using the expansion given by eqn. 8.83 with the result
for the vector potential and The last approximation is valid for a reasonably smooth current distribution. for the scalar potential. The singular part G, can be analytically integrated over the cell's surface. For instance, the singular part of eqn. 8.88 is 2n(e,
+ l)Tv(OIO)
with tan cr = bla.
-
2k0a In tan
(; + 3
- - 2k0b In tan ( 4 2 ) (8.91)
The matrix equation: Introducing the expansions 8.83 and 8.85 in eqn. 8.93 and using the discrete Green's functions defined above, the following matrix equation is obtained:
428
Numerical analysis of microstrip patch antennas
The elements in the submatrices are given by
where 6, is the Kronecker delta. The expression for C$yis obtained by interchanging the couples ( x , y), (a, b) and (M, N ) within eqn. 8.96. Finally, it is easily shown that C? = CT. For distances Ir,, - r,l much greater than the dimensions of a cell, the integrals in eqn. (8.96) can be replaced by
In principle, this approximation is not valid for short distances between cells. For these situations, however, the contribution of the vector potential is overshadowed by that of the scalar potential, so that the approximation of eqn. 8.98 still suffices. As a matter of fact, eqn. 8.98 may be used everywhere but on the diagonal terms. This approximation has been confirmed by extensive numerical tests. A last point worth mentioning concerns the number of discrete Green's functions that must be calculated. For a rectangular patch with rn x n charge N)2, with M = ( m - 1)n and cells, the number of matrix elements is (M N = (n - I)m. When all the cells have identical sizes, only rn x n values of T,, M values of Py and N values of Ti;Y are needed in order to completely fill the matrix. This is the great advantage of using cells of equal size, and it is generally more convenient to use a larger number of identical cells rather than fewer cells of different sizes.
+
Interpolation among Green's functions: The evaluation of the matrix in eqn. 8.95 requires a large amount of computation. For a rectangular patch divided into 10 x 10 cells, the order of the matrix is 180; hence the number of elements in the matrix is 1802 = 32400. Even when a simple 4 x 4 Gaussian quadrature is used to evaluate the discrete Green's functions, the number of Sommerfeld integrals that need to be evaluated would exceed half a million.
Numerical analysis of microstrip patch antennas
429
Fortunately, for a given structure these integrals depend only upon the distance from source to observer. It is thus possible to tabulate the integrals for a small number of distances, and then to interpolate between the tabulated values. The distances to be considered range from zero to the maximum linear dimension of the patch. Several interpolation schemes have been tried [13]. The best solution was obtained by separating the Green's functions according to eqn. 8.89, and then using a simple parabolic Lagrange interpolation for the regular part. For a square patch with 10 x 10 cells, at frequencies for which the patch's length is less than a free-space wavelength, the error obtained when interpolating from 25 tabulated values is hardly noticeable: less than 0.5%, even though the computation time was reduced by a factor of loo! 8.6.2 Entire domain basis functions If the microstrip patch has a simple regular shape (circular or rectangular) we can consider the equivalent electromagnetic cavity obtained when the patch is enclosed by a lateral magnetic wall. If the eigen modes have a simple analytical expression it is reasonable to use them as a set of entire domain basis functions. For thin substrates, the surface-current distribution on a microstrip patch at resonance follows closely the behaviour of the corresponding eigenmode except for a slight disturbance due to the antenna's excitation. Therefore, meaningful results can frequently be obtained by using a very small number of entire domain basis functions. This fact enables the analysis of microstrip arrays having hundreds of elements. The size of the linear system to be solved will be equal to two or three times the number of patches. It is clear that if only one basis function is allowed per patch, we cannot use a poor testing procedure such as point matching and match the boundary condition only at the centre of the patch. The best alternative is provided by Galerkin's method where the test functions are identical to the basis functions and the inner product includes a surface integration over the patches [25]. To be clear, let us consider a single rectangular patch of dimensions L, W. The eigen modes of the corresponding cavity are [28]
1;
=
mxx e,sin-cos-
L
nny W
mnx + e,cos-sinL
. nxy W
where the co-ordinate origin is in the lower left corner of the patch. The vectors correspond to the modes TM,,, of the equivalent cavity. The choice of the modes TM,,no in the expansion of J, is rather arbitrary and depends on the problem considered. For instance, they can be ordered according to their resonant frequencies, or we can consider only the TM,, subset if variations along the co-ordinate y can be neglected. In any case, the relation between the integers m, n and the ordinal number j in eqn. 8.99 should be clearly defined. We assume now for the unknown surface current density the following
430
Numerical analysis of microstrip patch antennas
expansion:
Numerical analysis of microstrip patch antennas
437
The above techniques can easily be generalised to the analysis of an array of patches. In this case, the domains of the ith and j t h modes do not necessarily coincide. If the distance between the centres of the patches is greater than the largest linear dimension of a single patch, we can use the approximation
and consequently
Notice that here the unknown coefficients a, are interpreted as being amplitudes of the surface current distribution [A/m] while, when using subsectional basis, the unknowns were the total currents [A] flowing across contiguous cells. If we test now the boundary condition 8.26 in the Galerkin sense, we get the set of equations
where vi, rj denote the centres of the patches. More accurate approximations can be obtained by expanding the Green's functions in a Taylor series. These mathematical tools and powerful numerical integration routines enable the total computation time to be kept within reasonable limits. 8.7 Excitation and loading
The integral involving the scalar potential can be rewritten as
+
W .f; has been used. where the identity V . ( f ; V ) = f; . V V Finally, introducing expansions 8.100 and 8.101 into eqn. 8.102 we get the linear system
where
and
The last term in the expression of c, vanishes if i # j due to the orthogonality of the eigenmodes f;. It can be seen that, essentially, each matrix element requires the computation of two fourfold integrals. Fortunately, two of the four integrations can be performed analytically, by introducing the new variables u = x - x', U' = x x', v = y - y', v' = y y'. As in the subsectional basis case, the elements c,, will include a singularity when r = r' in the Green's functions. Again, a decomposition of the type of eqn. 8.89 or a change to polar co-ordinates may be used to eliminate the singularity.
+
+
In practice, microstrip antennas are excited by many different techniques. A good survey of these has been recently given by Pozar [29]. This Section will present a brief description of those most commonly found, keeping in mind that the method of moments will be used to analyse the antenna. 8.7.1 Several microstrip-antenna excitations A very common technique used for feeding a microstrip antenna consists of a microstrip line directly connected to the patch. A thorough treatment of this excitation requires the analysis of the incident and reflected quasi-TEM current waves existing on the line, which is assumed to extend from the patch to infinity. A more realistic model assumes that the microstrip line has a finite length and introduces a mathematical excitation (for instance, a filament of vertical current or a series voltage generator) at the end of the line. The vertical filament of current is a good model for the coaxial excitation and on a physical basis is preferred to the series voltage generator. The microstrip line is then cut at a point where uniform line conditions can be assumed. In this way the discontinuity created by the line-patch junction, and possibly discontinuities of the line itself, are included in the analysis. If a vertical filament of unit current is used as excitation, the input impedance is simply the voltage at the insertion point. When using other mathematical excitations, the section of line included in the analysis must be long enough to support a standing-wave pattern that can be used to estimate the input impedance of the patch. Finally, it is worth mentioning that replacing the microstrip line by a coaxial probe at the edge of the patch is a first-order approximation that gives surprisingly good results in many practical cases. Microstrip line under the patch: A more sophisticated excitation, designed to minimise the spurious radiation coming from the feed line, uses a microstrip line under the patch to couple energy to it electromagnetically [29, 301. The presence
432
Numerical analysis of microstrip patch antennas
Numerical analysis of microstrip patch antennas
of two dielectric layers adds an additional degree of freedom to the design. The comments made above for the line directly connected to the patch also apply here. The microstrip line can be cut far from the patch and terminated in a coaxial probe or excited by some other mathematical device. Slot in the ground plane: A slot in the ground plane can be used to couple energy to the patch from, presumably, a triplate transmission line [31]. The mathematical treatment replaces the slot by an equivalent distribution of surface magnetic current. The excitation field E''' results from this current. In the numerical procedure, this modifies only the independent terms b, (eqn. 8.106). 8.7.2 Coaxial excitation and input impedance A coaxial line attached to the bottom of the patch (Fig. 8.17) is also a practical way of feeding microstrip patches. From a theoretical point of view, the coaxial excitation is of great interest because simple yet accurate mathematical models are available. While the models presented here are constant current or voltage sources and not constant power sources, that are actually used in practice, the calculated values of the input impedance agrees closely with measured results.
433
between the inner and outer conductors of the coaxial line on the ground plane (Fig. 8.17). For thin substrates, however, replacing the coaxial probe by a vertical filament of current gives results accurate enough for engineering purposes. If the Galerkin technique is used, we can model the probe as a filament of zero diameter ending in a point charge at the junction with the patch. The calculation of the excitation fields would normally require a knowledge of the fields created by vertical electric dipoles embedded in the substrate; however, the reciprocity theorem allows the evaluation of the terms bi (eqn. 8.106) using only formulas related to horizontal electric dipoles. Thus, we have
where E, is the field created by the surface current density J, = f, of eqn. 8.99 and E' is the field produced by the excitation current density Je [A/m2]entering the feed point (x,, y,). The total excitation current is normalised to IA, i.e.
Je
=
e,6(x - x,)6(y - y,)
-h < z < 0
(8.109)
and its domain V, reduces to a segment of length h in the case of zero-diameter filament. Consequently:
Finally, in terms of the Green's functions we have
an expression which can be cast in an easier form as
with the modified scalar Green's function being given by G*, = u,tanhuh/u DTM. Now, once the vector of excitation terms b = (b,) is known, the amplitudes of the basis functions are obtained by solving the linear system of equations (eqn. 8.104). The input impedance is finally given by Fig. 8.1 7 Microstrip patch antenna excited by a coaxial probe The most rigorous model of this configuration considers the probe as belonging to the patch and the whole structure excited by a frill of magnetic current. Simpler models reduce the coaxial line to a filamentary current entering the patch.
The most accurate treatment of a coaxial probe [32, 331 assumes that the portion of the inner coaxial conductor embedded in the substrate belongs to the patch. The whole structure is then excited by a frill of magnetic current existing
When the subsectional basis functions are used together with razor test functions, the coaxial probe must be modelled more carefully in order to avoid mathematical singularities in the excitation terms. The total current entering the probe must be spread over a region of the patch surrounding the insertion point. A simplified attachment mode in which the current is spread over a cell with a linear dependence has been developed and successfully tested [38]. In the frame-
434
Numerical analysis of microstrip patch antennas
Numerical analysis of microstrip patch antennas
work of this model, the expression 8.108 for the excitation terms is still valid but the excitation Ee is created by the currents belonging to the probe and to the attachment mode. Also, the expression 8.1 13 for the input impedance can still be used, but the effect of the attachment mode on itself must be added in order to obtain accurate predictions for the reactance values. Finally, owing to the discretisation inherent in this approach, the excitation point (x,, y e ) can only be located at the centre of a charge cell. The reactance of theprobe: Expression 8.11 3 gives the impedance at the patch level, i.e. z = 0. To obtain the impedance at the ground plane level, z = - h, we need to add in series the self-impedance of the coaxial probe. Assuming now that the inner conductor of radius r, carries a current I evenly distributed on its surface, we have
435
of the M-port. Therefore, the complete determination of the impedance matrix requires the solution of M linear systems, but, fortunately, the matrix C of the system remains unchanged when exciting each port. The elements Z, have been termed 'input impedances' previously (eqns. 8.1 13 and 8.117); however, it must be pointed out that these are input impedances corresponding to a single-port excitation since the remaining M-1 ports are open-circuited. These impedances may be quite different from the true input impedances for which an expression will be given now. Let us consider that each port is connected to a voltage generator U,with an internal impedance Z, (Fig. 8.18). This arrangement includes the case of a passive load Z,, by allowing U, = 0.
I
For thin substrates, we can approximate the magnetic potential due to these currents by u1
array or multiport patch
and the self impedance is given by
Ui
UZ - a m
This term is mainly inductive. Thus, finally, a better estimate of the input impedance of a coaxial-fed antenna is
Z,
=
eqn. 8.113
+ Z,,,
(8.117)
8.7.3 Multipart analysis In many practical situations the microstrip antenna is excited simultaneously at M points, for instance, in the case of a microstrip array. In this case the antenna can be considered as an M-port device and standard circuit theory may be applied to completely characterize the antenna. The first step is to solve the linear system Ccc = b, obtained by application of the method of moments, M times for M different excitation vectors bi. These vectors correspond to a physical situation in which a unit current is entering the j t h port while the remaining M-1 ports are open-circuited. After solving the matrix equation, we get the vector a, = C-I b, containing the amplitudes of the N basis functions. Then, by computing the voltage at each port we get the quantities Zv,i = 1, 2 . . . M, which is the j th column of the impedance matrix
Fig. 8.18 Equivalent circuit of a microstrip antenna array considered as a multiport device The voltage generators are replaced by short circuits at the ports terminated with a passive load
We define a vector U with elements U, and a diagonal load matrix Z , with elements Z,,. The equations relating currents I, and voltages v a t each port (Fig. 8.18) are (8.1 18) u = Z,I + v = ( Z , Z ) I
+
where Z is the matrix of impedances previously calculated. The vector of port currents is then given by (8.1 19) I = (Z, + z)-'U
436
Numerical analysis of microstrip patch antennas
and the vector of port voltages is V
=
Z(ZL
+ z)-I
U . The new vector
N
a* =
1 I'ai ,=I
Numerical analysis of microstrip patch antennas
,
437
input-impedance loci on the Smith chart, the surface current distribution at several resonances and the far-field radiation pattern.
(8.120)
contains the amplitudes of the basis functions for the real working conditions of the antenna, i.e., with all the loads and excitations simultaneously present. This is the vector to be used in the computations of the radiation pattern and when studying the surface current distribution. Finally, the input impedance at each port is
It is clear that, for a single-port antenna, this input impedance equals the parameter Z , , which is directly given by eqns. 8.1 13 or 8.1 17.
8.8.1 Entire-domain versus subdomain basis functions Section 8.6 presented several choices of basis functions that could be used in a MOM procedure. Among the choices were wide-triangle or rooftop subdomain basis functions used with razor testing and entire-domain cosine basis functions used in a Galerkin procedure, i.e. tested with cosine testing functions. Computer programs have been written using these two choices of basis and testing functions, and a comparison of the results obtained will be presented in this Section. The calculation of the far-field radiation pattern will be considered first. If subdomain basis functions are used the patch is reduced to an array of horizontal electric dipoles (HED). In this sense, each rooftop basis function is equivalent to a HED whose moment is given by the product of the total current flowing across the common border of two cells times the distance between the centres of the cells. Now, the far field for a horizontal dipole, which can be thought of as the element pattern in this procedure, is multiplied by the array factor resulting from the segmentation of the patch to give the total far field pattern. Mathematically, the far field is thus given by M
Em
=
GF(rI0)
aIx,exp(jk0e;g~) i=I N
+ GY(40) C bI, exp Woe,. Q;)
(8.122)
j= 1
Fig. 8.1 9 Geometry of a single rectangular patch 6, = 2.55 tan 8 = 0.002 h = 1.28 mm 2, = 0.9e-7
8.8 Single rectangular patch antenna In previous Sections the mathematical theory and numerical procedures have been developed for the analysis of general microstrip structures. This Section will concentrate on a single, rectangular, coaxial-fed patch to illustrate how the theory is applied, present computed results for a simple common structure and answer some of the questions that remain. Remaining questions include the convergence of the method-of-moments procedure and the advantages and disadvantages of the various choices of basis functions presented in Section 8.6. Results will be presented for a single patch as shown in Fig. 8.19 showing the
where a = 0, cp, Li and I, ark the MOM current coefficients and G, represents the far fields due to a HED. The pattern can then be integrated to calculate the directivity, gain and efficiency. When properly chosen entire domain basis functions are used, the far field for each basis function can be calculated analytically, and the total far field is a simple sum of the fields generated by each basis function. For other choices of basis functions costly numerical integration techniques may be required. Fig. 8.20 shows the far-field pattern for a single rectangular patch. The subdomain rooftop and entire-domain cosine basis functions yield identical co-polar patterns at resonance while only the rooftop basis functions yield an estimate of the cross-polar pattern. The cross-polar pattern is due mostly to currents on the patch in phase with the excitation spreading out from the coaxial probe, and to the currents in the probe. In general, the cross-polarised pattern is very difficult to calculate accurately and is sensitive in practice to the size of the ground plane; an item not included in the numerical model. The model can be used, however, to study the effect of the placement of the coaxial probe on the cross-polar pattern. Figs. 8 . 2 0 ~and 8.206 show the far-field pattern of a single patch when excited by a coaxial probe located at different points.
438
Numerical analysis of microstrip patch antennas
Numerical analysis of microstrip patch antennas
439
The entire domain functions could, in theory, model accurately the patch at frequencies away from resonance and its cross-polar behaviour, however, in practice, this is costly. Near resonance only one or two entire domain functions are needed to model surface current, and are therefore very well suited to standard geometries near resonance. The cost to include additional basis functions needed away from resonance or to calculate the cross-polar pattern is, however, relatively high compared to the subdomain basis functions. Thus it may be more efficient to use subdomain basis functions when studying a single patch or small array away from resonance or when cross-polar pattern is needed.
10
,
theta (degrees)
Fig. 8.21 Input impedance for the single rectangular patch shown in Fig. 8.19. Frequency range: 1.52-1.58 GHz. Frequency increases clockwise with a 0.01 GHz step Rooftop basis functions 0 Entire-domain cosine basis functions
theta (degrees) Fig. 8.20 Radiation pattern for the single rectangular patch shown in Fig. 8.19. Frequency = 1.565GHz. A Coaxial feed at x = 16.66 mm. y = 16.66 mm B Coaxial feed at x = 16.66 mm. y = 20 mm . . . . .E-plane co-polar H-plane co-polar
---- E-plane cross-polar --- H-plane cross-polar
The input impedance for a single patch is given on the Smith chart of Fig. 8.21. The two choices of basis functions yield approximately the same results with a slight shift in frequency. The resonant frequencies obtained differ by 0.77%, which is often much less than what arises due to uncertainties in the manufacturing process and material parameters. Fig. 8.22 shows the variation of the real part of the input impedance as a function of position for three choices of widthlaspect ratios. In each case, the coaxial line was centered in the nonresonant direction on the patch and then moved inward from the edge of the patch to the centre. Note that the results were calculated at the resonant frequency for each patch.
440
Numerical analysis of microstrip patch antennas
8.8.2 Convergence using subsectional basis functions The question of convergence must always be dealt with when using a moment method. If a numerical result has not converged there is virtually no hope of its being correct. The factors affecting convergence include: the choice of basis and testing functions, frequency, antenna shape, the dielectric used and even the numerical precision of the computer. Since this list includes nearly all the parameters of the antenna and affects nearly all of the decisions made during the development of the computer program to some degree, it is difficult to give rules that guarantee that a particular result has converged. However, several rules of thumb are applicable and can be used as a base when studying convergence. This Section will briefly demonstrate how the MOM solution using subsectional basis functions converges.
Numerical analysis of microstrip patch antennas
441
direction transverse to the resonance direction, i.e. parallel to the H plane at the first resonant frequency, may be reduced without a significant penalty, resulting in large savings in computation time. Fig. 8.23 shows how the input impedance of a rectangular patch converges when the number of basis functions in the H-plane direction is varied at frequencies near the first resonance. Note the resonant frequency changes by only 0.3% when using three basis functions in the transverse direction as opposed to using 7, however, the input impedance changes by approximately 20%. Thus, a rough study of the antenna's resonant frequency and radiation pattern can be performed quickly at low cost. The final analysis can then be performed using additional basis functions.
10
Fig. 8.22 Real part of the input impedance as a function of the position on the patch. The coaxial is centered along the non-resonant direction and moved from the edge of the patch ( x l L = 0 ) to the centre of the patch ( x l L = 0.5). For case ( a ) the antenna parameters are given in Fig. 8.1 9 where L = 60mm and W = 40mm. For cases ( 6 ) and ( c ) the width W is varied. ( a ) . . . . . L I W = 1.5 f,,,,,, = 1.555 GHz (6)----LIW=l.O f,,,,,,=1.543GHz ( c ) --- L I W = 0.667 f,,,,,, = 1.535 GHz
The general rule of thumb given in the published literature is that, when using subsectional basis functions, of the order of 10 basis functions per wavelength are needed to obtain good results. This rule also holds for microstrip antennas operating near the first few resonances when calculating the input impedance. It is interesting to note, though, that the number of basis functions in the
Fig. 8.23 Input impedance for the single rectangular patch shown in Fig. 8.19 with the coaxial centered vertically (y = 20mm) and at x = 76.66mm versus the number of basis functions in the H-plane direction, i.e. along the y-axis Frequency range is from 1.52 GHz increasing clockwise to 1.60 GHz with a step of 0.01 GHz +: 9 by 7 cells 0: 9 by 5 cells ': 9 by 3 cells
8.8.3 Surface currents The subsectional basis functions can be used to model virtually any current distribution owing to their flexibility. As an example, a rectangular patch was analysed and measured at the first four resonances, TM,,, TM,,,, TM,,, and TM,,. The patch dimensions are 60 x 40mm and the dielectric is a standard low-frequency printed-circuit substrate with high losses in the microwave range (E, = 4.34 and tans z 0.02). The excitation point has been selected at
444
Numerical analysis of microstrip patch antennas
induces currents in its neighbours affecting the element's radiation pattern and input impedance. Thus, elements in an array environment have to be studied in the actual array environment to properly account for mutual coupling [34, 351. However, when the coupling between array elements is less than 20 or 30dB, it may be possible to neglect mutual coupling and still obtain acceptable results.
Numerical analysis of microstrip patch antennas
445
current distribution on the elements. The method of moments is well suited for the task because any current distribution can be calculated to the desired precision and coupling coefficients are easily calculated. However, practical limitations exist when applying the MOM to anything but small arrays. The use of subsectional basis functions, while very flexible in modelling arbitrary geometries and current distributions, comes with a high price in the number of unknowns. To accurately model an element of the array approximately 50 unknowns are needed; thus for a linear array 10 elements long, 500 unknowns are needed. It can be seen that the capacity of even the largest currently available computer is quickly surpassed. There are, however, several techniques that can be used to study larger arrays without simply using a larger computer or more computer time. These techniques include: (a) Entire domain basis functions
(b) Infinite array techniques Additionally, specialised numerical techniques may be applied with success in certain cases. The method of conjugate gradients has been proposed as a method that would allow the solution of larger systems of linear equations [36, 371. However, normally the MOM matrix is not sparse and the slow convergence of iterative routines applied to fully populated linear systems precludes their use. Of the two techniques discussed above only the use of entire-domain basis functions will be discussed since infinite array techniques are included as a full Chapter of this handbook. Using entire-domain basis function only one or two basis functions are typically needed at resonance per element; so arrays having up to several hundred elements can be studied easily with today's computers. However, the study of circularly polarised elements or the cross-polarised fields requires the use of additional higher-order basis functions. This considerably increases the computation time and reduces the size of largest array that can be studied.
Fig. 8.25 Input impedance near the two first resonances of the patch of Fig. 8.24.After [38]. 0 Theory (9 x 6 cells) Measurements.
This section will present results for several small arrays and show how the element factor and input impedance are affected when an isolated element is incorporated in an array. 8.9.1 Array modelling To accurately model an array the model should not assume any particular
8.9.2 Mutual coupling A 2 x 2 element array was build on a lossy, inexpensive substrate and the four elements of the scattering matrix were measured and compared with the results obtained using the numerical procedures presented previously in this Chapter. The scattering matrix is defined by
where Z i s the impedance matrix with elements calculated using eqn. 8.1 17 and I is the unit dyadic. The array consisted of four identical patches, each 60 mm along the E-plane and 40 mm along H-plane. The substrate thickness was 0.8 mm and the dielectric constant was 4.34 with a loss tangent of 0.02. The elements were coaxially fed with the coaxial line centered along the H-plane and located lOmm from the
446
Numerical analysis of microstrip patch antennas
Numerical analysis of microstrip patch antennas
-1 8 1.10
1.10
1.14
1.14
1.18 1.22 frequency (GHz)
1.26
1.18 1.22 frequency (GHz)
1.26
1.30
-44
1 1.10 1.14 1.18 1.22 1.26 1.: frequency (GHz)
1.30
Fig. 8.26 Scattering parameters for a 2 x 2 microstrip array: measured versus theory Patch size: 60 mm by 40mm, h = 0.8 mm E, = 4.34 tan 6 = 0.02 E-plane separation 20mm between patch edges H-plane separation 1 6 mm between patch edges (8) S I ~ ( 6 ) s12 ( c ) S13 ( d ) Sll ---- Measured . . . . .Theory
-60
447
I
1.10
,
, 1.14
,
,
,
,
1.18 1.22 frequency (GHz)
,
, 1.26
, 1.:
448
Numerical analysis of microstrip patch antennas
edge. The separation between the patches was 20mm along the E-plane and 16 mm along the H-plane, corresponding, respectively, to 0.08 and 0.064 freespace wavelengths at the isolated patch's resonance of 1.2 GHz. The reslllts are shown in Fig. 8.26. The two algorithms, which use different basis fmctions, yield nearly identical results across the frequency band. As can 'se seen, the agreement between the measured and calculated results is good.
Numerical analysis of rnicrostrip patch antennas
449
H-plane coupling decreases faster than the E-plane coupling, which is sustained by the surface wave and becomes dominant for greater separations. It must be finally pointed out that the values of the coupling (s,, parameter) are dependent on the input impedance (z,, parameter) and are usually given for a couple of patches matched to 500. The small differences with measurements in Fig. 8.27 can be due to a slight mismatch of the patches. 8.9.3 Linear array of four patches The last example in this Chapter will illustrate, from a theoretical point of view, the relevance of mutual coupling in the computation of input impedances and mutual coupling, The selected configuration is shown in Fig. 8.28 and consists of four rectangular identical patches fed by coaxial probes and working in the lowest-order mode. The substrate parameters are h = 0.787 mm, and E, = 2.23. The patches are coupled by their non-resonant sides (H-plane coupling) and they are excited uniformly. On the other hand, their spacing is non-uniform in order to obtain a lower first-sidelobe level [39].
H
3rnm
t 4 4;;1 t 10.3
rn rn
10.3 rnrn
-
h= 0.787rnrn f = 11.9GHz relative perrnitivity=2.23 Fig. 8.27
Measured (Jedlicka, Poe and Carver [35]) and calculated mutual coupling between two coaxial-fed rnicrostrip antennas versus the separation between the patch centres D measured in free-space wavelengths W = 105.7mm L = 65.5mrn h = l . 6 m m E, = 2.53 f, = 1.414GHz Measured E-plane (From Reference 35) 0 Measured H-plane (From Reference 35) . . . . . Calculated E-plane ---- Calculated H-plane --- Calculated 45' plane
Fig. 8.27 gives the E- and H-plane coupling results as a function of the distance between two patches measured by Jedlicka, Poe and Carver [35], and compares these results with those calculated using the theory presented above. Entire-domain basis functions were used. In addition, the calculated coupling results between two antennas located along a diagonal are also presented. It is readily apparent that the H-plane coupling is stronger for small separations. This is the kind of coupling found in standard microstrip coupled line filters, and it is mainly due to quasi-static terms and to the space wave. However, the
Fig. 8.28
Linear array with four identical patches and nonuniform spacing The substrate has a permittivity of E, = 2.23 and a thickness of h = 0.787mm. The nominal resonant frequency is f,, = 11.9GHz.
Fig. 8.29 shows the normalised real and imaginary parts of the input impedance presented by an inner patch. For each of the quantities, two curves are given, corresponding to theoretical calculations without mutual coupling (the patch is considered as an isolated element) and with mutual coupling (the patch is embedded in an array environment with the three other patches terminated by 50R loads). It can be seen that, for this array, mutual coupling raises the maximum resistance from 130R to 154R. This significant change (18%) shows clearly that mutual coupling should be taken into account for properly matching a microstrip array. The influence of mutual coupling on radiation patterns is even stronger. Fig. 8.30 shows the H-plane radiation patterns of an isolated patch and of an inner patch in an embedded configuration. The asymmetries in the geometrical environment of an inner patch (coupled to two patches on one side but only to one
450
Numerical analysis of microstrip patch antennas
o! 11.0
,
, 11.4
,
,
,
,
,
11.8 12.2 frequency (GHz)
, 12.6
Numerical analysis of microstrip patch antennas
I
,
13.0 Fig. 8.30
-0.75
Calculated isolated-element and embedded-inner-element far-field radiation patterns for the array of Fig. 8.28 I n the embedded case all the other elements are loaded with 50R --- Isolated element . . . . . Embedded element
i---7-TT , , , , , , 11.0
Fig. 8.29
45 7
11.4
11.8 12.2 frequency (GHz)
12.6
13
Calculated isolated-element and embedded-inner-element input impedance versus frequency for the array of Fig. 8.28. Values are normalised to 50R a Real part b Imaginary part . . . , . Isolated element --- Embedded element
theta (degrees) Fig. 8.31
Calculated H-plane far-field pattern of the array shown in Fig. 8.28 with and without mutual coupling . . . . . With mutual coupling (MOM result) First sidelobe = -1 3 S d B coupling First sidelobe = - 18.6 dB
--- Without mutual
452
Numerical analysis of microstrip patch antennas
on the other side) are clearly reflected in the asymmetrical pattern for the embedded situation. Finally, Fig. 8.31 gives the overall radiation pattern of the array in the H-plane. A first theoretical prediction neglects mutual coupling and computes the array pattern as the product of the isolated element pattern times the array factor. The first-order sidelobe is then at - 18.6dB, well below the value of - 13.2dB which can be obtained with four equally spaced, uniformly fed elements [40]. However, if the integral-equation model presented in this Chapter is used, mutual coupling is automatically taken into account. Theoretical predictions show then how mutual coupling deteriorates the radiation pattern, raising the first-sidelobe level to only - 13.8dB.
8.10 Acknowledgments
The authors would like to thank the members of the Laboratoire d'ElectromagnQisme et dlAcoustique (LEMA) for their aid and support. Specifically, Anja Skrivewik, Lionel Barlatey and Bertrand Roudot performed many of the calculations and measurements presented in this Chapter. Also special thanks are due to Mrs. Mary Hall for typing the manuscript. 8.11 References 1 BAHL, I. J., and BHARTIA, P.: 'Microstrip antennas' (Artech House, 1980). 2 STRATTON, J. A,: 'Electromagnetic theory' (McGraw-Hill, NY, 1941). 3 MICHALSKI, K. A.: 'On the scalar potential of a point charge associated with a timeharmonic dipole in a layered medium', IEEE Trans., 1988, AP-36. 4 POGGIO, A. J., and MILLER, E. K.: 'Integral equation solutions of three-dimensional scattering problems', In M1TTRA;R. (Ed.), 'Computer Techniques for Electromagnetics' (Pergamon Press, 1973). 5 LO, Y. T.: 'Electromagnetic field of a dipole source above a grounded dielectric slab', J. Appl. Phys., 1954, 25, p. 733. 6 BRICK, D. B.: 'The radiation of a Hertzian dipole over a coated conductor', Proc. IEE, 1955, 102C, pp. 103-121. 7 BREKHOVSKIKH, L. M.: 'Waves in layered media' (Academic Press, NY, 1960). 8 WAIT, J. R.: 'Electromagnetic waves in stratified media', (Pergamon Press, 1962). 9 FELSEN, L. B., and MARCUVITZ, N.: 'Radiation scattering of waves', (Prentice Hall, New Jersey, 1973). 10 KONG, J. A,: 'Theory of electromagnetic waves', (Wiley, NY, 1975). I I SOMMERFELD, A.: 'Partial differential equations in physics' (Academic Press, NY 1949). 12 HARRINGTON, R. F.: 'Time harmonic electromagnetic fields' (McGraw-Hill, NY, 1961). 13 MOSIG, J. R., and GARDIOL, F. E.: 'A dynamical radiation model for microstrip structures'. in HAWKES, P. (Ed.) 'Advances in electronics and electron physics', (Academic Press, NY, 1982) pp. 139-237. 14 MOSIG, J. R., and GARDIOL, F. E.: 'Analytic and numerical techniques in the Green's function treatment of microstrip antennas and scatterers', IEE Proc., 1983, 130H, pp. 175-182. 15 SHASTRY, S. V. K.; Ph.D. Dissertation, Indian Institute of Science, Bangalore, India, 1979.
Numerical analysis of microstrip patch antennas
453
UZUNOGLU, N. K., ALEXOPOULOS, N. G., and FIKIORIS, J. G.: 'Radiation properties of microstrip dipoles', IEEE Trans., 1979, AP-27, pp. 853-858. MOSIG, J. R., and GARDIOL, F. E.: 'Dielectric losses, ohmic losses and surface wave effects in microstrip antennas.' Int. URSI Symposium, Santiago de Compostela, Spain, 1983, pp. 425-428. MICHALSKI, K. A,: 'On the efficient evaluation of integrals arising in the Sommerfeld halfspace problem', IEE Proc., 1985, 132H, pp. 312-318. LYTLE, R. J., and LAGER, D. L.: 'Numerical evaluation of Sommerfeld integrals'. Report UCRL-52423, Lawrence Livermore Lab., Univ. of California, 1974. PANTIS, G.: 'The evaluation of integrals with oscillatory integrands', J. Comp. Phys., 1975, 17, pp. 229-233. BORIS, J. P., and ORAN, E. S.: 'Evaluation of oscillatory integrals', J. Comp. Phys., 1975, 17, pp. 425-433. HURWITZ, H., and ZWEIFEL, P. F.: 'Numerical quadrature of Fourier transform integrals', Math. Tables Aids Cornput., 1956, 10, pp. 140-149. ALAYLIOGLU, A., EVANS, G., and HYSLOP, J.: 'The evaluation of oscillatory integrals with infinite limits,' J. Comp. Physics, 1973, 13, pp. 433-438. SIDI, A,: 'The numerical evaluation of very oscillatory infinite integrals by extrapolation', Math. Comp., 1982, 38, pp. 517-529. HARRINGTON, R. F.: 'Field computation by moment methods' (MacMillan, NY, 1968). RAO, S. M., WILTON, D. R., and GLISSON, A. W.: 'Electromagnetic scattering by surfaces of arbitrary shape', IEEE Trans., 1982, AP-30, pp. 409-418. GLISSON, A. W., and WILTON, D. R.: 'Simple and efficient numerical methods for problems of electromagnetic radiation and scattering from surfaces', IEEE Trans., 1981, AP-29, pp. 593-603. COLLIN, R. E.: 'Foundations for microwave engineering', (McGraw-Hill, NY, 1966). POZAR, D. M.: 'New architectures for millimeter wave phased array antennas', Journees Internationales de Nice sur les Antennas (JINA), Nice, 1986, pp. 168-179. KATEHI, P. B., ALEXOPOULOS, N. G.: 'On the modelling of electromagnetic coupled microstrip antennas - The printed strip dipole,' IEEE Trans. Antennas Propagat., AP-32, pp. 1179-1 186, 1984. SULLIVAN, P. L. and SCHAUBERT D. H., 'Analysis of an aperture coupled microstrip antenna,' IEEE Trans. Antennas Propagat., AP-34, pp. 977-984, 1986. POPOVIC, B. D., DRAGOVIC, M. B., and DJORDJEVIC, A. R.: 'Analysis and synthesis of wire antennas', (Wiley, NY, 1982). HALL, R. C., MOSIG, J. R., and GARDIOL, F. E.: 'Analysis of microstrip antenna arrays with thick substrates', 17th European Microwave Conf., Rome, Italy, 1987. ALEXOPOULOS, N. G., and RANA, I. E.: 'Mutual impedance computation between pr~nted dipoles', IEEE Trans., 1981 AP-29, pp. 106-1 11. JEDLICKA, R. P., POE, M. T.. and CARVER, K. R.: 'Measured mutual coupling between microstrip antennas', IEEE Trans., 1981, AP-29, pp. 147-149. JACOBS, D. A. H.: 'A generalization of the conjugate-gradient method to solve complex systems', IMAJ of Numerical Analysis, 1986, 6, pp. 447-452. PETERSON, A. F., and MITTRA, R.: 'Method of conjugate gradients for the numerical solution of large-body electromagnetic scattering problems', J. Opt. Soc. Am. A, 1985, 2, pp. 971-977. MOSIG, J. R., and GARDIOL, F. E.: 'General integral equation formulation for microstrip antennas and scatterers', IEE Proc., 1985, 132H, pp. 424-432. GRONAU, G., and WOLFF, I.: 'Spectral domain analysis of microstrip antennas', Proc. of Workshop 'Analytical and numerical techniques for microstrip circuits and antennas', Montreux, Switzerland, March 1988. BALANIS, C. A,: 'Antenna theory: analysis and design', (Harper & Row, NY, 1982). -
-
Chapter 9
Multiport network approach for modelling and analysis of microstrip patch antennas and arrays K. C. Gupta
9.1 Introduction
The multiport network approach for microstrip patch antennas is based on the use of segmentation and desegmentation methods for analysis of planar structures. Segmentation and desegmentation techniques were developed originally for analysis of two-dimensional (planar) circuit components [I-7.Since microstrip patch antennas on thin substrates can be treated as two-dimensional planar components, segmentation and desegmentation techniques have been employed for the analysis of microstrip antennas also [8, 91. This approach has been used successfully for the analysis and design of several types of microstrip patch antennas [lo-171 and arrays [18], and promises to be an appropriate methodology for computer-aided design [19,20] of microstrip patch antennas and arrays in hybrid as well as in monolithic configurations. This Chapter describes the multiport network approach, segmentationdesegmentation techniques, and their applications to design of microstrip antennas. Relevant aspects of various models for microstrip antennas are presented in Section 9.2. The multiport network model [19], which is an extension of the well known cavity model [21,22] for microstrip patches, is discussed. Evaluation of multiport impedance matrices from the Green's functions for various types of segments is described in Section 9.3. Modelling of external fields (including fringing, radiation and surface wave) by edge-admittance networks is detailed in Section 9.4. Segmentation and desegmentation methods for analysis of planar electromagnetic structures (and for multiport networks) are discussed in Section 9.5. Various examples of microstrip antenna configurations, which have been analysed and designed using multiport network approach, are reviewed in Section 9.6. These include various types of single-feed circularly-polarised microstrip patch configurations, such as a diagonally-fed nearly square patch, .a square patch with truncated comers, a square patch with a diagonal slot, a pentagonal-shaped patch, a square ring patch, and a cross-shaped patch. The second group of antennas analysed by the multiport network approach consists
456
Multiport network approach for modelling
of broadband multi-resonator microstrip antennas. Three-resonator and fiveresonator configurations (coupled to a central patch either by a capacitive-gap coupling or by short sections of microstrip lines) are included in this group. The third category of microstrip antenna configurations, discussed in Section 9.6.3, consists of two-port rectangular, two-port circular patches, and series-fed arrays making use of these two-port patches. Discussion related to the development of CAD procedures for microstrip patches and arrays is contained in Section 9.7. It is pointed out that multiport network modelling and segmentation/desegmentation methods of analysis are ideally suitable for implementation of CAD procedures for microstrip antennas.
Multiport network approach for modelling
457
ports are located along the non-radiating edges, transmission from port 1 to port 2 can be controlled by suitable choices of distances x, and x,. Again, the two models shown in Figs. 9.2a and b do not incorporate the parasitic reactances associated with the feed-line-patch junctions.
9.2 Models for microstrip antennas The transmission-line model [23, 241 and the cavity model [21, 221 are the two most widely used network models for analysis of microstrip antennas. We will discuss these models briefly before introducing the multiport network model suitable for implementing segmentation/desegmentation methods. 9.2.1 Transmission-line model In this model, a rectangular microstrip antenna patch is viewed as a resonant section of a microstrip transmission line. A detailed description of the transmission-line model is given in Chapter 10. The basic concept is shown in Fig. 9.1 which illustrates the transmission-line models for (a) and unloaded rectangular patch; (b) a rectangular patch with a feed line along the radiating edge; and (c) a rectangular patch with a feed line along the non-radiating edge. Z,, is the characteristic impedance of a microstrip line of width W,, and E , is the corresponding effective dielectric constant. Be and G, are capacitive and conductive components of the edge admittance Y,. The susceptance B, accounts for the fringing field associated with the radiating edge of the width W,, and G, is the conductance contributed by the radiation field associated with each edge. Power carried away by the surface wave(s) excited along the slab may also be represented by a lumped loss and added to G,. In Fig. 9. lb and c, Zof and are the characteristic impedance and the effective dielectric constant for the feeding microstrip line of width Wf. In both of these cases, the parasitic reactances associated with the junction between the line and the patch have not been taken into account. Transmission-line models may also be developed for two-port rectangular microstrip patches [14]. These configurations are used in the design of series-fed linear (or planar) arrays [25, 181. Models for two types of two-port rectangular microstrip patches are shown in Fig. 9.2. Fig. 9.2a illustrates the equivalent transmission-line network when the two ports are located along the radiating edges, and Fig. 9.26 shows the transmission-line model [26] when the two ports are along the non-radiating edges. It has been shown [14,26] that, when the two
a unloaded patch
b feedline along the radiating edge
rn
c feedline along the non-radiating edge
Fig. 9.1 Transmission-line models for three rectangular microstrip patch configurations
There are several limitations inherent to the concept of the transmission-line model for microstrip antennas. The basic assumptions include: (i) fields are uniform along the width W, of the patch; and (ii) there are no currents transverse
458
Multiport network approach for modelling
to the length I of the patch. Detailed analysis of rectangular patches has shown [27] that, even at a frequency close to the resonance, field distribution along the radiating edge is not always uniform. Also, the transverse currents are caused by the feeding mechanism and are invariably present. Moreover, the circularly polarised rectangular microstrip antennas (whose operation depends upon the excitation of two orthogonal modes) cannot be represented by the transmissionline model discussed above. Clearly, a more accurate method for modelling of microstrip antennas is needed.
a feedlines olong radioting edges
b feedlines olong non-radioting edges
Fig. 9.2
Transmission-line modes for two-port rectangular microstrip patch antennas
9.2.2 Cavity model A planar two-dimensional cavity model for microstrip patch antennas [21, 221 offers considerable improvement over the one-dimensional transmission-line model discussed in the previous Section. In this method of modelling, the microstrip patch is considered as a two-dimensional resonator surrounded by a
Multiport network approach for modelling
459
460
Multiport network approach for modelling
Multiport network approach for modelling
461
perfect magnetic wall around the periphery. The fields underneath the patch are expanded in terms of the resonant modes of the two-dimensional resonator. This approach is applicable to a variety of patch geometries. These geometries, the corresponding modal variations denoted by $ ., and the resonant wave numbers k,, are shown in Table 9.1 (from Reference 21). E and H fields are related to ,$, by
Ern" =
(9.1)
*d
K . = i x V,rCl,liw (9.2) where i is a unit vector normal to the plane of the patch. Resonant wave numbers k,,, are solutions of (Vf
+ en)*,=
0
(9.3)
with
on the magnetic wall (periphery of the patch). V, is the transverse part of the del operator and p is perpendicular to the magnetic wall. The fringing fields at the edges are accounted for by extending the patch boundary outwards and considering the effective dimensions to be somewhat larger than the physical dimensions of the patch. The radiation is accounted for. by considering the effective loss tangent of the dielectric to be larger than the actual value. If the radiated power is estimated to be P,,the effective loss tangent 6, may be written as
where Pd is the power dissipated in the dielectric substrate and 6, is the loss tangent for the dielectric medium. The effective loss tangent given by eqn. 9.5 can be modified further to incorporate the conductor loss. The modified loss tangent 6, is given by
The input impedance of the antenna is calculated by finding the power dissipated in the patch for a unit voltage at the feed port, and is given by where P = P, + PC + P,, + P,.WEis the time-averaged electric stored energy, and W, is the time-averaged magnetic energy. The voltage V equals Ezd averaged over the feed-strip width (d is the substrate thickness). The far-zone field, and radiated power are computed by replacing the equivalent magnetic-current
462
Multiport network approach for modelling
Multiport network approach for modelling
ribbon on the patch's perimeter by a magnetic line current of magnitude Kd on the ground plane (xy plane). The magnetic current source is given by
463
respectively. Green's function G is usually a doubly infinite summation with terms corresponding to various modes of the planar resonator (rectangular or circular or triangular) with magnetic walls.
where ii is a unit vector normal to the patch's perimeter and iE(x, y) is the component of the electric field perpendicular to the ground plane. A cavity model for microstrip patch antennas may also be formulated by considering a planar two-dimensional resonator with an impedance boundary wall all around the edges of the patch. A direct form of network analogue (DFNA) method for the analysis of such a cavity model has been discussed in Reference 28. 9.2.3 Multiport network model The multiport network model of microstrip patch antennas [19, 291 may be considered as an extension of the cavity model discussed above. Electromagnetic fields underneath the patch and outside the patch are modelled separately. The patch itself is analysed as a two-dimensional planar network [I], with a multiple number of ports located all around the edges as shown in Fig. 9.3. Each port represents a small section (of length v ) of the edge of the patch. is chosen so small that the fields over this length may be assumed to be uniform. Typically, for a rectangular patch, the number of ports along each radiating edge is taken to be 4, and along each non-radiating edge the number is taken to be eight.
Fig. 9.3
Multiport representation of a rectangular patch
Thus, a 24 x 24 matrix is typically adequate for the characterisation of the interior fields of a rectangular patch. For patches of regular shapes (rectangles, circles, rings, sectors of circles and of rings, and three types of triangles), this multiport planar network model can be analysed by using two-dimensional impedance Green's functions available for these shapes [I]. A multiport Z-matrix characterisation representing the fields underneath the patch can be derived from the Green's function as: Z, =
w1y [&JY
~ ( x lY, ~ I ~j)dsids, X~,
where x,,, y,, denote the locations of the two ports of widths
(9.9) and
y,
Fig. 9.4
(a) A cross-shaped microstrip patch. (6) Multipart-network model of the crossshaped microstrip patch
For patches of composite shapes (such as a cross shape shown in Fig. 9.4a), a multiport network model can be written by treating the composite shape as a combination of the elementary shapes for which Green's functions are available. The cross shape of Fig. 9 . 4 ~can be considered as a combination of three rectangular segments as shown in Fig. 9.46. Segmentation and desegmentation methods [I] are used for finding the 2-matrix of a composite shape from those of the elementary segments. If the patch or one of the segments of a composite patch is of an irregular shape for which Green's function is not available, a technique called the contour integral method [I] can be used to evaluate the Z-matrix. In the multiport-network modelling of radiating microstrip patches, the fields (namely, the fringing fields at the edges, the surface-wave fields outside the and the radiation field) are incorporated by adding equivalent edge admittance networks (EAN) connected to the various edges of the patch. This representation is shown in Fig. 9.5 for the case of the rectangular patch shown in Fig. 9.3. EANs are multiport networks consisting of parallel combinations of the capacitances C (representing the energy stored in the fringing field) and the conductances G (representing the power carried away by radiation and surface waves) as shown in Fig. 9.6a. Each capacitance-conductance pair is connected to a port of the planar equivalent circuit of the patch. EANs at the non-radiating edges may be simplified to consist of capacitances only, as shown in Fig. 9.6b. Values of capacitance and conductance in the edge-admittance networks may be obtained from the various analyses reported in the literature [30-321. The flexibility of the multiport network model leads to several advantages when compared with the conventional cavity model discussed in Section 9.2.2. For example, the parasitic reactances at the junction between the feed line and the patch can be incorporated in the multiport network model by considering
464
Multiport network approach for modelling
Multiport network approach for modelling
a small section of the feed line as an equivalent planar circuit connected to the patch at a finite number of (typically five) ports. Solution of this network problem (depicted in Fig. 9.7) is equivalent to the expansion of the fields (in the feed line as well as in the patch) in series of eigen - functions and matching the fields at the interface.
465
current sources at the two corresponding sections of the edges. Similar MCNs may also be included between the non-radiating edges, between a radiating edge and a non-radiating edge, or between two edges of different patches in an array.
NR-EAN
NR-EAN
NR-EAN
Fig. 9.7 lncorporation of feed-junction reactance in multipart-network model of a rectangular patch
Fig. 9.5
Edge-admittance networks (EANs) connected to the multiport representation of a rectangular patch
Fig. 9.6 Edge admittance networks for (a) radiating edges; (b) non-radiating edges
R-EAN
Also, the multiport network model discussed above can be extended to incorporate the effect of mutual coupling between the two radiating edges [33] by inserting a mutual coupling network (MCN) as shown in Fig. 9.8. The edge-admittance terms associated with various ports at the edges constitute the diagonal terms of the admittance matrix for MCN. The non-diagonal terms of this matrix are obtained from the 'reaction' between the equivalent magnetic
I
Fig. 9.8 Incorporation of mutual coupling in multipart-network model of a ~ectangularpatch
It may be noted that, in the multiport network model, the characterisation of fields underneath the patch is conceptually similar to that used in the conventional cavity model [21, 221. In both of these models, the fields under the patch
466
Multiport network approach for modelling
Multiport network approach for modelling
are considered two-dimensional with no variations of fields perpendicular to the substrate. For this reason, the limits of the applicability of the technique in terms of substrate permittivity and thickness are similar to that for the cavity model. Also, both of these methods will not be accurate when applied to narrow-width microstrip dipoles rather than to the wide microstrip patches discussed in this Chapter. y
4
Y
A
467
9.3 Z-matrix characterisation of planar segments
9.3.1 Green's functions For practical microstrip antennas, the thickness of the substrate is much smaller than the wavelength. Therefore fields underneath the patch do not vary in the z-direction (perpendicular to the substrate). Electric field has a z-component only. Since aE,/az = 0, we may define a voltage V(x,y) given by (9.10) V(x,Y ) = - Ez(x, y)d where d is the substrate thickness. When a magnetic-wall boundary condition is assumed at the edges of the patch, V(x,y) satisfies the boundary condition given by eqn. 9.4, i.e.
If we consider a z-directed electric current source Jx(xo,yo) located at (xo,) ,), the voltage V(x,y) is related to the source current through a two-dimensional impedance Green's function G(x, ylx,, yo) defined by
microstrip patch antenna
I
I
top view
&coax connector side view Fig. 9.10 Microstrip patch antenna with a probe feed perpendicular to the substrate Fig. 9.9 Various geometries of the planar segments for which Green's functions are available
Green's functions used for evaluating impedance-matrix characterisation for patches of various shapes are discussed in Section 9.3. Derivation of the Z-matrix is also included therein.
where the source current J, is distributed over a region D in x, y plane. These Green's functions are known [I] for several regular shapes shown in Fig. 9.9. Expressions for these Green's functions are listed in Appendix 9.8. When a microstrip antenna is excited by a probe feed perpendicular to the
468
Multiport network approach for modelling
Multiport network approach for modelling
substrate, as shown in Fig. 9.10, the current density may be related to the axial current through the z-directed probe. For patches excited by a microstrip line feed, the current J,,flowing into the patch can be expressed as an equivalent z-directed electric current sheet J, as follows. At the magnetic wall surrounding the patch (as shown in Fig. 9.1 I),
-
J, =
B
x H,
(9.13)
469
and involves integration of G(x, ylx,, yo) over the extent of the two-ports corresponding to the specific element of the Z-matrix. For a microstrip line feed with an effective width y, the integral is carried out over the width 4. For a probe-feed type of external port, the integration is carried out over a circular path corresponding to the cylindrical surface of the probe. Alternatively, the circular probe maybe replaced by an equivalent strip and the integration carried over this equivalent width. Z-matrix for rectangular segments: Green's functions for various geometries, discussed in Appendix 9.8, appe8r as double-infinite summations. In numerical computations of the 2-matrix elements, order of integration and summations could be interchanged. For rectangular segments, the integrals involved may be carried out analytically. When sides of the rectangle are oriented along x- and y-axes and for the two ports (say, port p and port q), the impedance-matrix element Z,, may be written in the following form [37]:
. dJm,(~q,~,)l(k2x+ Jin
feedline
H,
4' :!tj,
k: -
where, for ports oriented along the y-direction,
6,
(x, y)
=
cos (k,x) cos (kyy) sinc
patch
and for ports oriented along the x-direction dJmn(x,y) = cos ( k p ) cos (k,,y) sin Fig. 9.11 Equivalence between the port current and the z-directed fictitious current density at the junction between a microstrip-line feed and a patch
and for the planar waveguide model of the microstrip line feeding the patch
Jm
= LxH,
Thus (J,I = I Ji,J.If the effective width of the microstrip line is port), the input current at the port j may be written as
4
=
TI JzI
(Y)
(v)
\ L / The function sinc (z) is defined as sin (z)/z, and nn mn k = - k = I a ' Y b
(9.14) (for the j t h (9.15)
9.3.2 Evaluation of 2-matrix from Green's functions Green's functions discussed above may be used to find the 2-matrix characterisation of various planar segments of the shapes shown in Fig. 9.9 with respect to specified locations of external ports. These external ports may be either of the probe-feed type (Fig. 9.10) or the microstrip-feed type (Fig. 9.11) or a combination of these. Evaluation of the Z-matrix is based on relation 9.9
6 = loss tangent of the dielectric The length of rectangle is a, its width is b, and height of the substrate is d. The points (x,, y,) and (x,, y,) denote the locations of thep and q ports, respectively. It has been shown [37] that the doubly infinite series in (eqn. 9.16), along with eqns. 9.17 and 9.18, can be reduced to a singly infinite series by summing the inner sum. The choice of summation over n or m depends on the relative locations of the ports p and q, and also on the aspect ratio of the rectangular segment. We consider two different cases
470
Multiport network approach for modelling
Multiport network approach for modelling
Case I: When both the ports ( p and q) are oriented along the same direction (x or y). We may write Z,, as
477
The sign of yl is chosen so that Im (y,) is negative. w, and w, are widths of ports p and q, respectively. Also, we use Y > = max(y,, Y,)
Y < = min(yp9 Y,)
and a similar notation for x, and x, when I = n. The choice of the integer L in eqn. 9.19 becomes a trade-off between fast computation and accuracy. A compromise is to select L so that (y,F) is less than or equal to 100. Case 2: When the two ports ( p and q) are oriented in different directions (x and y), various elements of the Z-matrix may be
.
f
cos (k,u,) cos (kp,) sinc
I=L+I
Z,
(F)
-CF-
=
1
1a,cos(k,u,)cos(k,u,)cos(y,z,)
'I /=o
where
1 " -CF cos (kp,) cos (k,u,) 'I l = L + I
and
. sinc
2
(y) ( -.iyl exp
C
=
jopd/(ab)
When the two ports are oriented in the y-direction we choose I they are along x-direction I is put equal to m. Also,
=
n, and when
(v> - v < -
T)) (9.20)
dwj
Choice of Iis made by noting that, for convergence of the last summation in the above equation, we need (v, -
V,
- wj/2) > 0
(9.21)
We choose the index of the inner summation so that this condition is satisfied. This condition may be written more explicitly as I
=
m,
if {max(y,, y,) - min ( y,, y,) - wj/2) > 0
(9.22)
and I = n,
and
if {max (x,, x,)
- min (x,,
x,)
-
w,/2} > 0
(9.23)
When both of these conditions are satisfied, any choice of I will ensure convergence. If I = n, wi corresponds to the port oriented along y-direction and w, corresponds to the port along the x-direction. On the other hand if I = m, wi is for the port along the x-direction and wj for the port along the y-direction. Z-matrix for circular segments: For circular-shaped patches, the impedance Green's function is given by eqns. (A9.10) and (A9.11) in Appendix 9.8. When ports are located along the circumference of the circle (as shown in Fig. 9.12),
472
Multiport network approach for modelling
Multiport network approach for modelling
various elements of the Z-matrix [38] may be written as follows. For any port i, the Z-matrix element Z,, may be written as
473
where HA') is the zeroth-order Hankel function of the second kind and r is the straight-line distance between the point M(s) and the source point on the periphery (given by L(so)). The integral on the right-hand side of eqn. 9.26 is carried out over the entire periphery. The RF voltage at any point just inside the periphery can be derived from the above relationship. We obtain 2jv(s)
= fc
{k cos OH$ (kr)v(so)
+ jopdJ,, (so)~h2)(kr)} ds,
(9.27)
Fig. 9.12 Various parameters for ports located at the circumference of a circular segment Fig. 9.1 3
Off-diagonal terms of the impedance matrix are found to be
{COS[n(Ai - A,)]
-
cos ["(Ai
+ A,]} cos (n+d)
(9.25)
where Similar expressions for computation of the Z-matrices for planar segments of other geometries shown in Fig. 9.9 have not been reported so far. 9.3.3 Z-matrices for segments of arbitrary shape When we come across segments of arbitrary shapes, for which Green's functions do not exist, the impedance matrix can be found by a method known as contour integral method [39]. The contour integral method is based on the Green's theorem in cylindrical co-ordinates. The R F voltage at any point M(s) inside the periphery of an arbitrarily shaped planar segment shown in Fig. 9 . 1 3 ~is given by
(a) Configuration of a planar segment for analysis by contocr integralmethod; (b) Division of the periphery in N sections for the analysis
where HI2)is the first-order Hankel function of the second kind, and J, denotes line current density flowing into the segment at so.The variables s and sodenote distances along the contour C and r is the distance between the two points M and L (specified by s and so) as shown in Fig. 9.13~.The angle 0 is the angle made by the straight line joining points M and L with the normal to the periphery at L. Line current density J,, flowing into the segment at a coupling port, is given by
For the numerical calculation of the impedance matrix, we divide the periphery into N sections having arbitrary widths W, , W ,. . . W, as shown in Fig. 9.13b. The periphery is divided in such a manner that each coupling port contains an integral number of such sections. For greater accuracy, wider coupling ports may be divided into a multiple number of sections. We set N sampling points, one at the centre of each section, and assume that each section is a straight edge. It is further assumed that the widths of the sections are so small that magnetic and electric fields can be considered constant over each section. Under the assumptions outlined above, the line integral in eqn. 9.27 can be replaced by
474
Multiport network approach for modelling
Multiport network approach for modelling
summation over the N sections. The resulting expression is given by N
2jv,
= ",=I
{kv,G,
+ jwpd i,&,}
where v, is the voltage over the Ith section and i,(= J, W,) is the total current flowing into the m th section. The matrix elements G, and fi,,, are given as
to>
otherwise
475
be deleted from ZN.If each coupling port covers only one section, the matrix thus obtained (after deleting rows and columns corresponding to the open sections from Z,) is the required impedance matrix. If some coupling ports extend to more than one section, the sections in these coupling ports are like sub-ports and the procedure detailed in Reference 1 can be used to obtain the overall admittance matrix at the coupling ports (and hence impedance matrix, if desired). 9.4 Edge-admittance and mutual-coupling networks
and
In eqn. 9.31, y(= 0.5772.. .) denotes the Euler's constant. In the above discussion we assume that the current can be fed into the planar circuit from all the N sections and ,i denotes the current fed from the m th section. This yields the impedance matrix for the N-port circuit. This matrix can be used to obtain the impedance matrix for any specified number and location of ports on the planar circuit being analysed. Eqn. 9.29 is written for each section I on the periphery of the planar circuit. All these equations combined together in matrix form become where v and i are the voltage and the current vectors at each section. A and B denote N by N matrices, determined by the shape of the circuit. The elements of these matrices, obtained from eqn. 9.29, are a , = - k G , for I
f
m
a , = 2j and bh = j w d & (9.34) From eqn. 9.32, the impedance matrix for the N sections, considered as ports, is obtained as
In practice, the coupling ports are connected to onlv a few of the N sections . .. - ..- . Rows and columns corresponding to the sections which are open-circuited can -
-
As discussed in Section 9.2.3, the multiport network modelling approach assumes that the fields outside the patch may be represented by an equivalent network model. The concept of edge admittance associated with the radiating edges has been widely used in conjunction with the transmission-line model [23, 24,261. The same concept can be extended to the multiport network modelling approach. For the multiport network model, the two-terminal edge admittance (used in the transmission-line model) is replaced by the multiport network shown in Fig. 9 . 6 ~or b. If an edge of the patch is divided into n sections, the edge-admittance network (EAN) is an n-port network with the common terminal being the ground return. In this Section, we discuss various methods for evaluating parameters of edge-admittance networks. Also, the network modelling approach can be extended to incorporate the effect of mutual coupling between the radiating edges of a single patch, as well as among the edges of adjacent patches in an array environment. 9.4.1 Edge-admittance networks Edge admittance associated with a radiating microstrip patch consist of two components: (i) a susceptance representing the energy stored in the fringing field associated with the edge; and (ii) a conductance G representing the power transmitted to the radiation field as well as the power carried away by the surface waves excited along the dielectric substrate. For incorporating edgeadmittance networks in the multiport network model for microstrip patch antennas, a capacitance-conductance pair is connected to each of the ports of the equivalent planar multiport representation of the patch. The conductance G consists of two parts: a radiation conductance G,and a surface-wave conductance G,.Radiation conductance associated with an edge of a microstrip patch is defined as an ohmic conductance (distributed or lumped), which, when connected to the edge (continuously or at discrete ports), will dissipate a power equal to that radiated by the edge (or by an equivalent magnetic current source) for the same voltage distribution. If the edge has width W and the power radiated for a uniform voltage distribution is P,,, the radiation conductance per unit length of the edge is given by 2PJ W, where P,,,is calculated for a unit
478
Multiport network approach for modelling
Two other formulas, useful for design and based on Wiener-Hopf characterisation of an infinitely wide microstrip patch edge, are given by Kuester et al. [32] and Gogoi et al. [30]. The formula of Kuester et a[. (32) for electrically thin substrates (kod < 1) may be written as
Multiport network approach for modelling
479
e, < 2.65. Accuracy of formula 9.42 is 2.6% for 0.2 < kod < 0.6 and 2.45 More rigorous formulations for edge conductance of open-ended microstrips have been reported by James and Henderson [41], and more recently by Katehi and Alexopoulos [42] and by Jackson and Pozar [43]. Analysis techniques and numerical results for a limited set of parameters have been given in References 41-43. James and Henderson [41] have pointed out that their rigorous results agree with eqn. 9.37a and a previous estimation by Lewin [44] for d/Ao < 0.09 when E, = 2.32, and for d/& < 0.03 when e, = 10. Results based on full-wave analysis using the method of moments [43] agree with results in Reference 41 for substrate thicknesses up to 0.1 &.
Edge susceptance: As in the case of edge conductance, several different results are available for edge susceptance also. One of the formulas for edge susceptance B is based on the parallel-plate waveguide model of a microstrip and is given by Reference 45 as:
y = 0.57721 (Eurler's constant)
The formula given by Gogoi et al. [30] is as:
Accuracy of eqn. 9.41 is 1.1% for 0.05 < k,d < 0.6 and 2.45 < e, < 2.65. These two formulas are accurate for wide patches (large value of b in Fig. 9.11). Results based on these formulas are also plotted in Fig. 9.14. Fig. 9.14 shows a comparison of the formulas 9.37-9.41 for the following set of data: frequency f = 7.5 GHz; dielectric constant e, = 2.48; and thickness of substrate, d = 1/32 in. It is inferred from Fig. 9.14 that formulas 9.37 and 9.38 yield close results as expected. The difference between formulas 9.37 and 9.41 increases with decreasing value of the width. This is because of the fact that formulas 9.40 and 9.41 are valid only for wide patches. Formulas 9.40 and 9.41 are both based on the Wiener-Hopf formulation and therefore yield identical results for all values of the width. From this limited discussion, it seems reasonable to use formula 9.37 owing to its simplicity. Although the power coupled to surface waves is very small compared to the radiated power, the conductance corresponding to the surface waves should be added to GR.This conductance may be expressed as [30]
where Z, and e, are the characteristic impedance and effective dielectric constant of a microstrip line of width a. Expressions for Zoand e, are well known [I]. cis the velocity of waves in free space ( = 3 x 108m/s).Another formula for B, which is based on open-end capacitance of a microstrip line [46] is given by
where
Other formulas, which are based on the Wiener-Hopf formulation and which can be used for wide patches, are given in References 30 and 32. From Reference 32,
where ~ ( 0 is) as given earlier for eqn. 9.40. According to Reference 30,
where
480
Multiport network approach for modelling
Multiport network approach for modelling
The accuracy of expression 9.48 is 2% for 0.1 < kod < 0.6 and 2.45 < E, .: 2.65. Formulas 9.43-9.48 are compared in Fig. 9.15. Expressions 9.43, 9.44 and 9.47 give close results for all practical values of the resonator width (0.25 1, < w < 0.6 1,). Eqn. 9.44 predicts an end-susceptance value of one-half of that computed using other formulas. For all practical values of interest, formula 9.43 may be used, since there is no restriction on the width of the patch for this formula. When the width is large, both expressions 9.46 and 9.47 can be used.
481
with
53
=
l +
0.5274 arctan [0.084(w/d)l94"'52] &0.9236
re
T4
=
1
+ 0.0377 arctan [ 0 . 0 6 7 ( ~ / d ) " ~ ~ ~ ]
x ( 6 - 5exp(0.036(1 - 8,)))
(,
=
1 - 0.218exp(-7.5w/d)
(9.49)
Expressions in eqns. 9.49 make use of the effective dielectric constant formula of keference 50, ;.e.
where u = wld. Accuracy df results given by eqn. 9.49 is claimed to be better than 2.5% for the range of normalised widths 0.01 < wld < 100 and E, < 50. I
0.5
I
I
1.0
1.5
normalised width ( b / h o ) Fig. 9.15
Edge susceptance of a rectangular microstrip antenna versus normalised width (From Reference 27)
More rigorous characterisation of microstrip open-edge susceptance has been reported in [41, 43, 47, 481. Results of the analysis in References 47 and 48 are available [49] as a closed form expression obtained by curve fitting of numerical data. Normalised outward extension of the radiating edge (Auld in eqn. 9.44) is given by
Non-radiating edges: For rectangular patches radiating linearly polarised electromagnetic waves, radiating and non-radiating edges can be distinguished clearly. As shown in Fig. 9.66, the non-radiating edges can be modelled by EAN consisting of capacitances only. An equivalent approach is to extend the width of the patch by moving the non-radiating edges outwards so that the edge capacitance is accounted for by the increased capacitance of the wider patch. The concept of radiating and non-radiating edges has been studied [59] by studying the total and partial reflections from the end of a parallel-plate waveguide with an extended dielectric slab. It has been pointed out [60] that the radiating or non-radiating nature of the edge depends on the angle at which the wave underneath the patch is incident on the edge. For grazing incidence there is no radiation, whereas for normal incidence the edge radiates. In between there is a critical angle where the transition from non-radiation to radiation takes place. It has been recognised that the so-called non-radiating edges of a rectangular
482
--,
Multiport network approach for modelling
Multiport network approach for modelling
patch (operating at the resonance of 1,O mode) do contribute to a crosspolarised radiation field. Compared to a single radiating edge, cross-polarised radiation from a single non-radiating edge is typically 10-15 dB lower. When we combine the radiated fields (in the broadside direction) from the two non-radiating edges, the total field is much smaller. This is caused by the fact that equivalent magnetic currents corresponding to the fringing fields at the two non-radiating edges are in the opposite direction and tend to cancel each other. However, the non-radiating edge-admittance network (NR-EAN), shown in Fig. 9.6b can be used only in cases where approximate results (obtained by ignoring the cross-polarised radiation from NR edges) are considered satisfactory. In more general cases, especially when the antenna operation is not at 1, 0 mode resonance (as for the circular polarised radiator discussed in Section 9.6.1), the EANs at all edges are similar to that shown in Fig. 9 . 6 ~ . In spite of the numerous results for edge admittance that have been reviewed in this Section. the lack of an accurate characterisation for the edne admittance is one of the major shortcomings in the design information required for precise design of microstrip patches and arrays. u
483
patch
,
E 1('
i
I
I
L-,
I
X
E1
0I I I I
'tL'
10 \
iE '%-
E-f ield distribution
-4+ I I
Fig. 9.1 6 Modelling of the fringing field at the patch edges in terms of magnetic-current line sources
9.4.2 Mutual-coupling network As shown in Fig. 9.8, the mutual interaction between the fringing fields associated with any two edges can be expressed in terms of a network model. The basis idea of using an admittance element to represent mutual coupling between two radiating edges was initially presented in Reference 51 in co&n&on with the transmission-line model of microstri~antennas. The reader is referred to Chapter 10 for details of this concept. The multiport mutual-coupling network shown in Fig. 9.8 is an extension of this concept suitable for incorporating in the multiport network model of microstrip patch antennas discussed in this Chapter.
Evaluation ofmutual-coupling networks: For computation of external mutual coupling between various edges of a microstrip patch antenna on a thin substrate, the field at the edge may be modelled by equivalent line sources of magnetic current placed directly on the ground plane at the location of the edges. This is illustrated in Fig. 9.16. Magnetic currents M are given by
where d is the height of the substrate. Product ( - E d ) is the voltage V(x, y) defined in eqn. 9.10. 4 denotes a unit vector normal to the ground plane as shown. For the E-field in the direction indicated in this Figure, both magnetic current sources M a r e in y-direction, i.e. directed out of the plane of the paper. The coupling between two magnetic current line sources is evaluated by dividing each of the line sources in small sections, each of length dl. The magnetic field produced by each of these sections (on the line source 1) at the locations of the various sections on the line source 2 can be written by using fields of a magnetic current dipole in free space [52]. The configuration and
Fig. 9.17
(a) Two arbitrarily spaced magnetic current elements; and ( 6 ) the co-ordinate system used for computation of fields
484
Multiport network approach for modelling
Multiport network approach for modelling
usually larger (typically 12). However, while using MCN for antenna analysis (by segmentation), a small number of ports along radiating edges (typically 4) is sufficient. Thus the original mutual-admittance matrix (48 x 48 for 12 ports
co-ordination system is shown in Fig. 9.17. We have
. koMdl sin8
H, = J
485
4n~or
Here ko is the free-space wave number and r is the distance between the point P and the magnetic current element Mdl. When the two edges (say i and j ) are oriented arbitrarily, as shown in Fig. 9.18a, the magnetic field H at (xi, y j ) produced by a source dliM a t ( x i , y,) may be written as H = fH, + j H y with
(9.54)
.
Hy
=
Hy,cos8, - H,. sin 0,
H,
=
Hy,sin8,
e,=
H, cos 0
+ H,cos
(9.55)
0,
(9.56)
where Hy. = -H,
+ H, sin 8 sine + H,cos0
Co-ordinate systems (x, y) and (x', y') are illustrated in Fig. 9.18b. Mutual admittance between sections j and i may be written in terms of the electric current density 4 induced in the upper surface of the edge segment j. We have
4
= ri
x H = (-H,cosaj
- Hy sinaj)j
(9.59)
The current density induced on the surface of the edge section j underneath the patch is -4. The mutual admittance between sections i and j is given by the negative of the current flow into section j (underneath the patch) divided by the voltage at section i, i.e.
The second minus sign in eqn. 9.60 accounts for the fact that the direction of current for defining the admittance matrix of a multipart network is directed into the network as shown in Fig. 9.19. The two edges shown in Fig. 9 . 1 8 ~may be the edges of the same radiating patch or those of the different patches in a n array environment. When coupling between two adjacent patches in an array environment is being computed, several individual edges of the two patches contribute to the mutual coupling network (MCN). An MCN configuration taking the four radiating edges into account is shown in Fig. 9.20. Here, the MCN is connected to four ports along each radiating edge. In practice, the number of sections considered on each edge for mutual-coupling calculations is
Fig. 9.18 (a) Configuration showing sections i and j of two patch edges; and (b) two different co-ordinate systems used for mutual coupling calculations
Fig. 9.1 9 Representation of the mutual coupling by an admittance matrix
along each edge) is reduced to a smaller size (16 x 16 as shown) by paralleling the ports in subgroups of three each. Contributions of non-radiating edges can also be incorporated in MCN. This is not shown in the Figure. Detailed computations [53] point out that the mutual-coupling contribution by non-
486
Multiport network approach for modelling
Multiport network approach for modelling
radiating edges is usually much smaller and may be ignored as a first-order approximation. Mutual coupling computations based on the above formulation have been verified [53] by comparison with the available experimental results [54]. Some of EAN edge 1
1
patch 1
EAN edge 3
I
I
MCN
I
I
487
mond points) is seen. Also shown in these Figures are results of Van Lil et al. [51], based in transmission-line theory. 1t may be noted that the preceding method of evaluating mutual coupling (based on the equivalent magnetic current model shown in Fig. 9.16) is valid only for electrically thin substrates where the effect of surface waves along the substrate is negligible. This modelling approach has been recently extended to microstrip patches on thin substrates, but covered by a relatively thicker dielectric cover layer [61,62]. The equivalent magnetic current model used in this case
patch 2 a=6.698 cm b=10.56 crn x = 1.84crn f GHz
Fig. 9.20 A mutual coupling network (MCN) representing the coupling between two adjacent patches in an arrav
-15-
m
a =6.698 crn b=10.56cm
-20
-
-25
-
0 -.-30 ;; v, -
network model
Fig. 9.21 Comparison of theoretical and experimental results for E-plane mutual coupling between two rectangular microstrip patches (Reproduced from Reference 5 3 )
these results are shown in Fig. 9.21 for E-plane coupling and in Fig. 9.22 for H-plane coupling between two probe-fed rectangular patches. A very good agreement between the computation (solid line) and experimental results (dia-
Fig. 9.22
Comparison of theoretical and experimental results for H-plane mutual coupling between two rectangular microstrip patches (Reproduced from Reference 53)
is shown in Fig. 9.23. The basic approach is similar to that for the case without a cover layer discussed earlier. Eqns. 9.52 and 9.53 are replaced by H, and H, in the presence of the cover layer. These field components are now dominated by the effect of surface waves in the thicker cover layer. When the substrate thickness is increased, equivalent magnetic current models for Figs. 9.16 and 9.23 become more and more inaccurate. Conceptually, multipart-network modelling of mutual coupling between two patches is still possible if more rigorous analytical/numerical techniques [63, 641 could be extended to arrive at a network representation of mutual coupling.
488
Multiport network approach for modelling
Multiport network approach for modelling
9.5 Analysis of multiport-network model The most outstanding advantage of the multiport-network model is the fact that various analysis and optimisation techniques available for multiport networks can now be used for analysis and optimisation of microstrip antenna elements and arrays. Most widely used techniques for planar networks are segmentation [I-3, 6-81 and desegmentation [4, 5, 81 methods. These two network-analysis techniques are reviewed in this Section. Examples of various microstrip antenna configurations where these techniques have been used are reviewed in Section 9.6.
cover layer
<
489
(shown by rectangular boxes in the figure) can be considered as a 'segment' for application of the segmentation method. Essentially, the segmentation method gives us overall characterisation or performance of the multiport network, when the characterisation of each of the segments is known. Originally the segmentation method was formulated [2] in terms of S-matrices of individual segments; however, it was found subsequently [3] that a 2-matrix formulation is more efficient for microwave planar circuits (also for microstrip antennas). In this Section, we will describe the procedure based on Z-matrices.
\substrate
Fig. 9.24 Segmentation of a ring-shaped structure into four rectangular segments Fig. 9.23
Magnetic-current source model for computation of mutual coupling in case of microstrip patches on a thin substrate but covered with a thick dielectric layer
9.5.1 Segmentation method The name 'segmentation' had been given to this network-analysis method when it was used for planar (two-dimensional) microwave circuits by Okoshi and his colleagues [2, 6, 35, 391. The basic idea is to divide a single large planar circuit into simpler 'segments' which have regular shapes and can therefore be characterised relatively easily. An example of such a segmentation is shown in Fig. 9.24 where a ring-shaped geometry is broken down into four rectangular segments for which Green's functions are available. For the multiport-network model of a two-port microstrip antenna shown in Fig. 9.8, each of the components
Fig. 9.25
Two connected multiport networks A and 8
For illustrating the procedure, we consider a multiport network consisting of only two segments A and B, as shown in Fig. 9.25. Various ports of these two segments are numbered as shown. The external (unconnected) ports of segment A are called p,-ports (which may be more than one). Similarly, the external
490
Multiport network approach for modelling
& = V,
and
iq = -i,
Multiport network approach for modelling
!
unconnected ports of segment B are called p, ports. Connected ports of the segment A are named q-ports and the connected ports of the segment B are designated as r-ports. q- and r-ports are numbered such that q , is connected to r , , q2 to r2, and so on. As a result of these interconnections, we can write: (9.61)
Z-matrices of segments A and B may be written as
+
p,) x (p, p,). The second term It may be noted that the size of ZA, is (p, on the right-hand side is a product of three matrices of the sizes: (pa + p,) x q, q x q, arid q x (p, p,), respectively. From the computational point of view, the most time-consuming step is the evaluation of the inverse of a matrix of size (q x q), where q is the number of interconnected ports. In order to illustrate the above procedure for combining Z-matrices of two segments together, let us consider an example of two lumped resistive networks connected together as shown in Fig. 9.260. Z-matrices of the individual components A and B may be written as
+
where Zpa,Zpaq,Zqpa,z,,, Zpb,Z,,,, Z,pb,Z,, are sub-matrices of appropriate dimensions. As we are dealing with reciprocal components
2-matrices of the segments A and B can be written together as
and
where In terms of the notations of eqn. 9.64, we have and
Superscript t indicates the transpose of a matrix, 0 denotes a null matrix of appropriate dimensions. It may be noted that interconnection conditions 9.61 have not been used for writing eqn. 9.64 which represents a rearrangement of individual matrices ZA and Z, given in eqn. 9.62. Relations 9.61 can now be substituted in the eqns. 9.64 to eliminate V,, 5, i,, and i,. The resulting expression may be written as V, = [Z,,] ip,where
+
491
492
Multiport network approach for modelling
Multiport network approach for modelling
493
Substituting all these sub-matrices in eqn. 9.65 we get
which may be evaluated as
The resultant matrix ZABin eqn. 9.68 may be verified by rewriting the circuit shown in Fig. 9 . 2 6 ~as the one shown in Fig. 9.266.
Fig. 9.27 Segmentation as applied to two sections of a transmission line
Let us consider another example. Two transmission-line sections of electrical lengths 0, and O2 are connected in cascade as shown in Fig. 9.27. Z-matrices of individual sections A and B are given by
and
In terms of notations of eqn. 9.65, we have
Fig. 9.26
(a) Two lumped networks considered for illustrating the segmentation procedure; (b) Circuit simplification for writing Z-matrix of the combination of the networks A and 8
494
Multiport network approach for modelling
Multiport network approach for modelling
495
which Green's functions are known. In cases like this, an alternative method called desegmentation [4] is useful. The concept of desegrnentation can be explained by considering the example of a rectangular patch with a circular hole. Referring to Fig. 9.28, we note that, if a circular disc called segment fl (Fig. 9.28~)is added to the configuration of Fig. 9.28a, the resulting configuration y Substituting all these submatrices in eqn. 9.65 we get
1
(is equivalent t o )
a (desegrnented with) (9.71~)
Substituting for z , and 2, and using trigonometric formulas for sin (8, cos (8, 02), eqn. 9.71a may be expressed
+
+ 8,) and
I
Fig. 9.28
Concept of desegmentation
+
which is a 2-matrix for a uniform transmission line of length (0, 8,) and illustrates the validity of eqn. 9.65. When the segmentation method is applied to the multiport network model of microstrip antennas (such as the one shown in Fig. 9.8), we are interested in 2-matrix with respect to external ports (1 and 2 in Fig. 9.8) and also in the voltages at the ports connecting R-EAN to the patch. This voltage distribution at the radiating edges is expressed in terms of equivalent line source of magnetic current. The radiation field (and associated characteristics like beamwidth, SLL etc.) are obtained from the magnetic current distribution by using far-field (Ilr variation) term of eqn. 9.52 and integrating over the various radiating edges. Referring to Fig. 9.25, voltages at the connected ports (q-ports) may be obtained by (Reference 1, p. 357) where ip is the current vector specifying the input current(s) at the external port(s) of the antenna. 9.5.2 Desegmentation method There are several configurations of planar components which cannot be analysed by the segmentation method discussed above. For example, the configuration shown in Fig. 9.28 cannot be partitioned into regular segments for
F i g . 9.29 Port nomenclature used in desegmentation procedure
is a rectangular segment shown in Fig. 9.286. Green's functions are known for both the circular (Fig. 9.28~)and rectangular (Fig. 9.286) shapes, and therefore 2-matrices for characterising both of these components may be derived. The desegmentation method allows us to derive the Z-matrix of the configuration a shown in Fig. 9 . 2 8 ~when the 2-matrices of the rectangular segment in (6) and the circular segment in (c) are known. For deriving a relationship among the 2-matrices of three shapes we consider a generalised configuration (shown in Fig. 9.29). Here, region fl is not included in the a segment. Ports p,, p, etc. are external ports of a. Characterisation of a is required with respect to these ports. In general p-ports may also be located on the part of the periphery of cc where the segment jis connected. An example of this is portp4 shown in Fig. 9.29.The
496
Multiport network approach for modelling
Z-matrices of /I and y segments are known, and may be written as
As in the case of segmentation, ports q (of a) and ports r (of P ) are numbered such that q, is connected to r , , q, to r,, etc. Ports d a r e unconnected (external) port of the segment /I. Evaluation of Z, is simplified when the number of d-ports is made equal to the number of q (or r ) ports. The number of q (or r ) ports depends upon the nature of field variation along a-/3 interface and, as in the case of segmentation, is decided by iterative computations. On the other hand, the number of d-ports is arbitrary and can be always made equal to that of q- (or r-) ports after that number has been finalised. Under these conditions, the impedance matrix for the a-segment can be expressed (Reference 5 ) in terms of the Z-matrices of /I- and y-segments as
Multiport network approach for modelling
497
Using eqn. 9.74 we get Z, as
which may be verified to the correct value. If the characterisation of the a-network is needed with respect to ports 1 and 3, it becomes necessary to include port 3 in the y-network also. For this purpose the y-network is re-written as in Fig. 9.32. Now 2, becomes
Fig. 9.30 A resistive network considered for itlustrating the desegmentation procedure
It may be noted that the size of Z, is ( p x p) since all the specified ports of a segment have been numbered as p-ports. Let us consider an example for illustrating the implementation of eqn. 9.74. Consider the resistive network shown in Fig. 9.30. Let us say that sub-network a is the one whose Z-matrix is to be determined, the Z-matrix of the fl segment is known, and the combination of these two is the y-segment whose 2-matrix is also known. We have
If the characterisation of cc is to be found with respect to port 1 only, network y can be considered as a 2-port network with one p-port and one d-port. The Z-matrix of y is obtained by re-writing the network as in Fig. 9.31. We have
Fig. 9.31 Reconfiguration of the network in Fig. 9.30 for eva/us?ionof the matrix I, used in desegmentation procedure
Now Z, is obtained by using eqn. 9.74 as follows: =
zm - zpd {z&- zd'}-I zdp
which again may be verified to be the correct result. Let us also consider another example of two transmission-line sections of electrical lengths PI, and PI, connected in cascade as shown in Fig. 9.27. Say we want to find ZAwhen Z , and ZA, are known. When we need characterisation of A only with respect to port 1, the segment y is a two-port network with Z,
498
Multiport network approach for modelling
Multiport network approach for modelling
499
This can be simplified to These two examples illustrate the applications of the desegmentation eqn. 9.74. It may be noted that, for implementing the desegmentation method, d-ports of the j-segment need not be located on the periphery of the j-segment. In fact, in the case of the rectangular patch with a circular hole (Fig. 9.28a), no region is available on the periphery of the circular P-segment for locating d-ports. AS shown in Fig. 9.33, d-ports may be located inside the circular region. In this case three d-ports dl, 4, d, are shown located inside the /?-segment. Since the Green's functions are valid for any point on the segment (or on the periphery), the desegmentation procedure remains unchanged.
and
44 Fig. 9.32 Modification of the y-network for two-port characterisationof the a-segment in desegmentation procedure
The Z-matrix (1 port) of segment A may now be written using eqn. 9.74 as ZPI =
zpP/
- ZpdIZddy - z d d p } - l z *
Fig. 9.33 A configuration where the desegmentation procedure recluires location of d-ports inside the 8-segment
9.6 Examples of microstrip antenna structures analysed by multipart-network approach The multiport-network modelling and analysis approach discussed above has been used for the analysis, design and optimisation of a variety of microstrip radiators [8, 10-181. We will discuss these applications in three groups: (i) ,circularly polarised microstrip patches; (ii) broad-band multiresonator microstrip antennas; and (iii) multiport microstrip antennas and series-fed arrays.
9.6.1 Circularly polarised microstrip patches Single-feed circularly polarised microstrip patches analysed by multiportnetwork approach include: diagonal-fed nearly square patch [lo], truncatedcorners square patch [lo], square patch with a diagonal slot [lo], a pentagonalshaped patch [8], square ring patch [ l q , and cross-shaped patch [17]. The desegmentation method has been used for analysing a truncated-corners square patch and a square patch with a diagonal slot. Implementation of the desegmentation procedure in these two cases is illustrated in Fig. 9.34. For a truncated-corners patch, the a-segment (c.f. Fig. 9.29) is shown in Fig. 9.34~.For
500
Multiport network approach for modelling p-ports
Multiport network approach for modelling
d-ports
feed
501
implementation of the desegmentation procedure in this case, we use two triangular-shaped P-segments P, and P,. Addition of P, and P2 to a-segments results in a perfect square-shaped y-segment shown in Fig. 9.346. Configuration of the u-segment for a square with a diagonal slot is shown in Fig. 9 . 3 4 ~In . this case the P-segment is a rectangle of the size of the slot, and d-ports are located inside the rectangle as shown in Fig. 9.34d (this configuration may be compared with Fig. 9.33). Detailed results for these two configurations are given in
Y-network b
a
feed
d
c
Fig. 9.34 (a) and (b) Desegmentation method applied to a corners-truncated antenna; (c) and (d) desegmentation method applied to a square antenna with a diagonal slot
experiment __----
3170 3180 frequency, MHz Fig. 9.35
3190
Theoreticaland experimentalresults for axial ratio and input VSWR for a truncatedcorner square antenna (Reproduced from Reference 10 @ IEEE 1983)
Fig. 9.36 Radiation pattern for circularly polarized truncated-corners square antenna (Reproduced from Reference 10 @ IEEE 1983) Thickness: 118 in; E, = 2.52; frequency 3.176 GHz
Reference 10. Results based on multiport-network analysis have been compared [lo] with experimental results. The type of agreement observed for the case of a truncated-corner square antenna is illustrated in Figs. 9.35 and 9.36. Theoretical and experimental values of VSWRs and axial ratios are plotted in Fig. 9.35, whereas radiation patterns are compared in Fig. 9.36. A more quantitative comparison of the theoretical and experimental performance is contained in Table 9.2 (from Reference 10). Reasonable agreement between the theoretical and experimental results verifies the validity of the multiport-network approach. Corresponding results for a square antenna with a diagonal slot are depicted in Figs. 9.37 and 9.38 and in Table 9.3 (again from Reference 10). The multiportnetwork approach is seen to perform equally well in this case also. Square-ring patch and cross-shaped patches have been analysed [17] by the segmentation method. Segmentation of a square ring in four rectangular segments is shown in Fig. 9.24. Segmentation of a cross-shaped patch in three rectangular segments is illustrated in Fig. 9.39. Detailed results for these two configurations are given in Reference 17. Comparison for five different shapes (square ring, crossed strip, almost square patch, corner-chopped square patch, and square with a diagonal slot) indicates that the maximum axial-ratio bandwidth (about 5.2% for f = 3.0GHz, E, = 2.5, and h = 0.159cm) is obtained by using a square-ring configuration.
Table 9.2 Performance of corners-chopped square patch antennas (Reproduced from Reference 70 @ IEEE 1983)
f
I
3
Parameters 1 Thickness, E, 2 Dimensions a x a cm2 (see Fig. 9.34) 3 Truncation bla
I1
Performance
1
1 Centre frequency f,(GHz) 2 Resonant frequencies of orthogonal modes (GHz) 3 Axial ratio at centre frequency (dB) 4 Bandwidth (MHz) for axial ratio < 6 dB 5 Input VSWR at centre frequency 6 Beamwidth for 3 dB difference between lE,l and lE41
Antenna I
Antenna I1
1/8", 232 2.73 x 2.73 0.04578
1/16, 2.51 2.86 x 2.86 0.0573
Theoretical
Experimental
Theoretical
Experimental
3.1758 3.1340 3.2 155 0.02 26.4 (0.831 %) 2.26
3.1750 3.1325 3.2125 0.0 29.4 (0.925%) 2.26
3.1756 3.1370 3.2340 0.12 14.0 (044%) 1.6
3.1753 3.1 343 3.2298 0.1 5 14.4 (0.4535%) 1.8
129'
152'
129'
i 3
%
3
3
9 3
Q
3 5
r~
138"
Table 9.3 Performance of square-patch antenna with a diagonal slot (Reproduced from Reference 10 @ IEEE 1983) Theoretical 1 Centre frequency f, (GHz) 2 Resonance frequency of orthogonal modes (GHz) 3 Axial ratio at f, 4 Bandwidth for axial ratio less than 6 dB 5 Input VSWR at chosen feed location 6 Beamwidth for 3 dB difference between lEsl and IEJ
3.130 3.063 3.212 0.198 35.5 MHz (1.134%) 2.9 116"
Substrate thickness = 1/8in, e, = 2.52. Dimensions of square patch = 2 . 6 0 2 ~ ~x 12 , 6 0 2 ~ ~ 1 Dimensions of slot = 2 . 8 9 ~ ~x 10 . 4 7 ~ ~ 1 .
Experimental 3.130 3.060 3.210
2.9 124'
c
5. 2
%
P0 aI 3
9
2
3
P
2
504
Multiport network approach for modelling
Multiport network approach for modelling
505
Another interesting antenna configuration analysed by the multiportnetwork approach is a pentagonal-shaped patch originally proposed in References 55 and 28, and analysed in Reference 8. The antenna configuration is shown ~ two different methods of analysis are depicted in Fig. 9.406 and in Fig. 9 . 4 0 and c. Desegmentation with two triangular segments PI and P, yields a 90'-60'-30'
-
VSWR
0L 3100
Fig. 9.37
I
I
3120
I
I
I
3140 frequency, M H z
I
3160
I
3180
Theoretical and experimental results for a square antenna with a diagonal slot (Reproduced from Reference 10 @ IEEE 1983) Thickness = 118 in: e, = 2.52; frequency = 3.1 30 GHz (Reproduced from Reference 10 @ IEEE 1983)
Fig. 9.39 Segmentation of a cross-shaped patch into three rectangular segments
Fig. 9.40
OdB -10
-20
-30-30
-20
-10
OdB
Fig. 9.38 Radiation pattern for a circularly polarised square antenna with a diagonal slot Thickness = 118in; E, = 2.52; frequency = 3.1 30GHz (Reproduced from Reference 10 @ IEEE 1983)
(a) A pentagonal-shaped microstrip patch (b) Desegmentation procedure applied to the pentagonal shape (c) Combination of segmentation and desegmentation procedure for the pentagonal patch
triangular segment for which Green's function is available. The second approach illustrated in Fig. 9 . 4 0 ~employs desegmentation with one segment PI to yield a kite-shaped geometry. The kite shape is then segmented into two identical 90"-60"-30' triangles as shown. Both of these approaches yield identical results.
506
Fig. 9.41
Fig. 9.42
Multiport network approach for modelling
(a) Configuration of a radiating-edge gap-coupled microstrip antenna (REGCOMA) (6)Configuration of a non-radiating-edge gap-coupled microstrip patch antenna (NEGCOMA) (c) Four-edges gap-coupled microstrip patch antenna (FEGCOMA)
(a) Configuration of a radiating-edge directly coupled microstrip patch antenna (REDCOMA) (b) Configuraton of a non-radiating-edge directly coupled microstrip patch antenna (NEDCOMA) (c) Configuration of a four-edge directly coupled microstrip antenna (FEDCOMA)
Multiport network approach for modelling
507
9.6.2 Broadband muItiresonator microstrip antennas Another group of microstrip antenna configurations which have been analysed using the multipart-network approach are broadband microstrip antennas using coupled resonators [I 1-13]. All these configurations use multiple resonators with slightly different resonant frequencies. These configurations are shown in Figs. 9.41 and 9.42. Different resonators in any of these configurations are coupled to each other, and only one (usually the central one) is connected to the feedline. Two different coupling mechanisms have been used. The three configurations shown in Fig. 9.41 use capacitive coupling across the gaps between the closely spaced edges, whereas the three configurations of Fig. 9.42 employ short sections of microstrip lines for providing the necessary coupling. Analysis procedure for a gap-coupled multiresonator antenna configuration is illustrated in Fig. 9.43. Coupling gaps are modelled by the multiport lumped RC network shown in Fig. 9.436. Values of C,, C, and C, are obtained from coupled microstrip transmission-line analysis. G represents the radiation conductance and is obtained by treating the gap fields as a line source of equivalent magnetic current. Since the feed point is located along the centre line XX (Fig. 9.43a), symmetry of the configuration may be used to simplify the computations and only one-half of the antenna configuration, shown in Fig. 9.43c, need be analysed. The multiport-network model is shown in Fig. 9.43d. RCs represent edge-admittance networks and GCs are two networks modelling the coupling gaps. Mutual coupling networks are not shown in this Figure because the effect of mutual coupling was not incorporated in the results presented in Reference 11. Component REs are planar network models for the three patches. Ports 1, 2, and 3 on the central patch are the three locations investigated for locating the probe feed. Experiments were performed to verify the theoretical results obtained by using the multiport-network approach, and a comparison is shown in Fig. 9.44. In this case, a O.159cm-thick copper-clad substrate (6, = 2.55) was used. The experimental bandwidth of the antenna is 225 MHz (6.9% at centre frequency f, = 3.27GHz), which is slightly more than the theoretical value (207MHz), possibly because of the dielectric, conductor and surface-wave losses ignored in the computations of the results reported in Reference 11. For cornpa&on, the corresponding bandwidth of a single patch is 65 MHz. Thus the microstrip antenna configuration shown in Fig. 9.44 yields a bandwidth nearly 3.5 times that of a single patch. A multiport-network for a directly coupled three-resonator antenna configuration is shown in Fig. 9.45. In this case also, one can make use of geometrical symmetry, and only one-half of the antenna configuration (with a magnetic wall placed along the plane XX) needs to be analysed. The multiport-network model is drawn in 9.45~.Interconnecting microstrip line sections are also modelled by two planar rectangular segments RE,. We have nine edge-admittance networks denoted by RCs. The segmentation formula 9.65 is used for finding the input impedance at the feed port and eqn 9.72 for evaluating the voltage distribution at the edges of the radiating patches.
508
Multiport network approach for modelling
Multiport network approach for modelling
antenna is microstrip microstrip
Fairly wide impedance bandwidth for microstrip antennas can be achieved by using the multiple resonator configurations shown in Figs. 9.41 and 9.42. Typical values for the six configurations fabricated on substrates with E, = 2.55
1.01 3.1
Fig. 9.43 (a) Three-patchgap-coupled antenna configuration (6) Multipart-network modelling of the gap betkeen two patches (c) Half-section of the antenna configuration with a magnetic wall along the plane of symmetry XX (d) Multiport network model of the half-section of the antenna
are summarised in Table 9.4. Various acronyms (REGCOMA etc.) are defined in Figs. 9.41 and 9.42. The factor M gives the bandwidth BW as a multiple of the corresponding value for a single rectangular patch antenna;f, is the centre frequency and d is the thickness of the substrate.
509
Fig. 9.44
I
I
3.2
I
I
3.3
I
J
3.4
frequency, GHz 6 Theoretical I----) and experimental (-) results for a gap-coupled tripleresonator antenna (Reproduced from Reference 11 @ IEEE 1984) (a) Impedance locus on Smith Chart ( 6 ) VSWR variations.
antenna (configuration shown in Fig. 9.46) is being currently developed as a compact broadband microstrip patch [57]. 9.6.3 Multiport microstrip patches and series-fed arrays
Series-fed linear arrays of microstrip patches employ two-port radiators as basic
570
Multiport network approach for modelling
Table 9.4
Multiport network approach for modelling
Typical impedance bandwidth values for microstrip antennas using multiple coupled resonators (Based on Reference 56)
Configuration
d(cm)
f(GHz)
BW(MHz)
BW(%)
M
REGCOMA NEGCOMA FEGCOMA
0.159 0.3 18 0.3 18
3.29 3.1 1 3.16
33 1 480 815
10.0 15.4 25.8
5.3 4.0 6.7
REDCOMA NEDCOMA FEDCOMA
0.3 18 0.3 18 0.3 18
3.20 3.31 3.38
548 605 810
17.1 18.3 24.0
5.0 5.5 7.36
building blocks. For this application, both two-port rectangular patches [14,29] as well as two-port circular patches [15] have been analysed by using the multiport-network modelling approach. Two-port rectangular patch: The multiport-network model of a rectangular patch with two microstrip-line ports along the non-radiating edges is shown in Fig. 9.8. Segments labelled FLN (feed line network) are rectangular planar segments representing small sections (typically 118 long) of microstrip lines connected to the two ports. Widths of FLNs are equal to the effective widths of
radiating edges
RE Fig. 9.45
c
(a) Three-patch antenna configuration with direct (microstrip-line) coupling between the parches (6) Half-section of the antenna configuration in (a) with a magnetic wall along the plane of symmetry XX (c) Multiport-network model of the antenna half-section shown in (b)
51 7
/
Fig. 9.46
Configuration of a broadband coupled microstrip line radiating patch
Fig. 9.47
Variations of the power transmitted to the port 2 (as a percentage of the input power) with the changes in the locations of the two ports (Reproduced from Reference 27)
the two lines, respectively. Multiple interconnections between FLNs and the patch ensure that the parasitic reactances associated with the feed-line-patch junctions are taken into account. Radiating edge admittance networks (R-EAN)
572
Multiport network approach for modelling
Multiport network approach for modelling
and non-radiating edge-admittance networks (NR-EAN) are obtained by modelling fringing fields at the edges as discussed in Section 9.4.1. The mutual coupling network (MCN) represents the external interaction between two radiating edges as discussed in Section 9.4.2. As mentioned earlier, for two-port patches with ports along the non-radiating edges, transmission from port 1 to port 2 can be controlled by su:1.able location of the ports (distance x, and x, in F:g. 9.2b). An example of this feature is presented in Fig. 9.47.This Figure shows the variation of th, power transmitted to port 2 with the relative locations of external ports. Vlr .x of x , are chosen to ensure match at the input port (S,, = 0). When the p i t locations are altered, the associated change in the junction reactances causes the patch resonance frequency to shift slightly. The corresponding change in the resonant dimension a is also plotted in this Figure. The results shown are for a substrate with 6, = 2.48, d = 1/32in, tans = 0.002 and for a resonant "requency of 7.5GHz. A comparison of theoretical and experimental results for S,, of a two-port patch is shown in Fig. 9.48. Design parameters of the two-port patch are also listed in this Figure. Apart from the magnitude of S,, which determines the amplitude
Thus we conclude that the multiport-network model and the analysis approach discussed here are well suited for S-parameter characterisation of the radiating patches.
0
-
II
n -80°-
-looO
7.0
Fig. 9.49
2 -5
A
-
!- / I
7.0
7.2
7.4
l
l
7.6
I
-
A theoretical
I
experimental I 7.2
l
7.8
l
I
I I i 7.4 7.6 frequency, GHz
I
I 7.8
I 8.0
Comparison of the theoretical and experimental values of the transmisson phase angle for a two-port rectangular patch (Reproduced from Reference 29)
circular
theoretical
experimental
513
rectangu/lar circular planer [patch
)
( 8.0
frequency, GHz
Fig. 9.48
Comparison of the theoretical and experimentalresults for transmission coefficient of a two-port rectangular patch (Reproduced from Reference 29)
variation along the linear series-fed array, another parameter of interest in the two-port patches is the phase angle of the transmission coefficient from port 1 to port 2. Theoretical computations of the phase angle of S,, (based on the multipart-network approach) have been compared with experimental values obtained from measurements using an automatic network analyser. Fig. 9.49 shows these results. The excellent agreement obtained demonstrates the usefulness of multiport-network model for computations of the phase angles also.
Fig. 9.50 Analysis of a circular two-port microstrip patch antenna by combining multiport network-modelling approach with the cavity method
Two-port circularpatches: Circular microstrip patches with two ports located along the circumference have been analysed [I51 by using a cavity model for the circular patch ;nd a multiport modelling approach for the input/output microstrip feed-line junction. This approach is illustrated in Fig. 9.50. The physical radius a of the disc and its loss tangent 6 are replaced by effective values a, and 6,. The effective radius a takes into account the fringing capacitance around the
514
Multiport network approach for modelling
Multiport network approach for modelling
circumference [45]. The effective loss tangent 6, includes 'loss' due to the power radiated from the patch. Relation 9.5 or 9.6 may be used for this purpose. Power radiated 8,power dissipated in the dielectric P, and the power lost because of finite conductor conductivity PCmay be evaluated as illustrated in Reference 46, pp. 92-94. Approximate results [15], using the dominant mode only and ignoring the feed-junction reactances, point out that, for a match at the input port (S,, = O), the impedance Zo of the feed line at the input port is related to the Z , , element of the Z-matrix by
515
is not exactly the multipart-network approach discussed in Section 9.2.3 but is a hybrid combination of the conventional cavity method (Section 9.2.2) and the multiport-analysis technique. The multiport-network approach itself can, in principle, be applied to circular patches also, but no such efforts have been reported to date.
C,=2.2 d = 1132 inch f = 7.5GHz a=0.7815cm
d = 1/32 inch f =7.5GHz a-0.7815crn N
V)
5-10
-201 7.0
A
I
7.2
I
7.4
theoretical data measured data I
7.6
I
7.8
L
8.0
frequency, GHz frequency, GHz
Fig. 9.51 Comparison of the theoretical and experimental results for transmission coefficient of a two-port circular patch (Reproduced from Reference 58)
where
4,, is the angular separation
Fig. 9.52
Theoretical and experimental results for transmission phase angle of a two-port circular patch (Reproduced from Reference 58)
between the two ports and
(3
Z , , = 1.674 - 1016, where d is the substrate thickness. The corresponding transmission coefficient S2, is given by Eqn. 9.86 suggests that, for the dominant mode, the transmission coefficient S2, varies from 1 to 0 as the angular separation #+, is changed from 0 to 90". Also we note that, for high values of S,, close to unity, the input-port characteristic impedance becomes very small and makes the design impracticable. Results based on the above method have been verified experimentally and a sample comaprison of theoretical and measured S,, values is presented in Fig. 9.51. Also, a comparison of the transmission phase in this case is shown in Fig. 9.52. Again, a reasonably good agreement is obtained. It may be recalled that, for this example of a two-port circular patch, the method of analysis followed
Series-fed microstrip arrays: The two-port rectangular or circular patches discussed above may be cascaded together to form a series-fed linear array as shown schematically in Fig. 9 . 5 3 ~and b. The rnultiport-network modelling approach has been used [la] for design and sensitivity analysis of series-fed arrays. Each unit cell of the array is characterised in terms of a 2-port Z-matrix. A two-port representation of a typical unit cell of a series-fed array is shown in Fig. 9.54. This is a simplification of the rnultiport-network representation shown in Fig. 9.8. Edge-admittance networks associated with non-radiating edges are not shown. Multiple interconnections between various components are shown symbolically by a single multiconnection symbol defined in the inset of the Figure. Ports 1 and 2 are two external ports of the unit cell. el and e2 are the two radiating edges. Typically, there are four interconnections (at each of these edges) among the R-EAN, the patch, and the mutual coupling network (MCN). Analysis based on the segmentation procedure allows us to determine voltages (or currents) at the input/output ports of each of the cells of the array. This information is used in conjunction with another set of impedance matrices (called Z, matrices) for each cell. The Z, matrices (obtained from eqn. 9.72)
516
Multiport network approach for modelling
relate the voltages at various ports on radiating edges e l and e2 to the input currents at the input/output ports 1 and 2 of each cell. Thus we have a multiportnetwork representation of the series-fed array. This representation may be extended to include MCNs (mutual coupling networks) representing the coupling between adjacent cells. In this case, the two-port representation of each cell
input
Fig. 9.53
Multiport network approach for modelling
517
shown here represents a unit cell of the series-fed array when a non-negligible mutual coupling is present between the adjacent cells. Such a network representation can be used to evaluate the effect of mutual coupling on the array performance and to iteratively modify the array geometry to compensate (as far as possible) for the undesirable effects of the mutual coupling. For analysing multiport-network models of large arrays, a circuit analysis technique called the sub-network growth method [I] is very convenient. In this method, only two adjacent components are combined together (at any stage in the iterative loop) to form a larger sub-network. Consequently, the size of the matrices to be processed is restricted to the number of ports in the two components and does not increase proportionately to the size of the array. At present, research efforts are in progress for using multiport-network modelling techniques for the automated design of one-dimensional and twodimensional arrays of microstrip patches.
I. "
(a) Series-fed linear array of rectangular patches (6) Series-fed linear array of circular patches
in-.
. -1- ports
R-EAN
---@---symbol for multiple Interconnections
Fig. 9.55 Incorporation of mutual coupling between adjacent patches in the network representation of a unit cell shown in Fig. 9.54
---@---symbol
for multiple lnterconnections
Fig. 9.54 Multiport network representation of a typical unit cell of a series-fed linear arrav
needs to be extended to multiple n-port representation, the additional (n - 2) ports being the fictitious ports to account for the mutual coupling. A schematic network representation of such a unit cell of a series-fed array is shown in Fig. 9.55. The network MCN2 denotes a multiport mutual coupling network representing the coupling between the two adjacent patches (i.e. between the patch shown and the next patch on the right-hand side). In the model shown, the coupling to the third patch (on either side) has been ignored. The n-port network
9.7 CAD of microstrip patch antennas and arrays Increasing interest in the use of microstrip antenna technology in phased-array systems, and the potential of fabricating millimeter-wave arrays monolithically on GaAs wafers, have made it necessary to develop CAD techniques for the accurate design of microstrip patches and arrays. The multiport-network approach presented in this Chapter is well suited for CAD (i.e. for modelling, analysis and optimisation) of microstrip patch antennas and arrays [20]. Basic aspects of CAD methodology are well known [l] and are common to the computer-aided-design process in various other disciplines. A generic flow chart for CAD is shown in Fig. 9.56. Starting with a given set of specifications,
578
Mulriport network approach for modelling
synthesis methods and available designs (pre-stored in computer) help us to arrive at the initial design. A model of this initial design is analysed by a computer-aided-analysis (simulation and performance evaluation) package.
specifications design data and synthesis
initiol
I
analysis
I I
Multiport network approach for modelling
519
design for calculating the changes in the designable parameters. Iterations in the optimisation loop are carried out until the specifications are met or the optimum performance of the design (within the given constraints) is achieved. The antenna design so obtained is now fabricated and experimental measurements are carried out. As indicated in the lower part of Fig. 9.56 (portion inside the dashed rectangle), some modifications may still be necessary if the modelling and/or analysis has not been sufficiently accurate. The modifications, hopefully, should be small and the aim of CAD is to minimise these experimental iterations as far as is practicable. The three main aspects of the computer-aided-design process are modelling, analysis and optimisation. Modelling and analysis approaches suitable for CAD of microstrip patches and arrays have been discussed in this Chapter. The most attractive features of the multiple-network approach is the extension of the network-analysis methods to microstrip patches and antennas. Also, the techniques for sensitivity analysis and optimisation, which have been developed extensively for multiport networks [I], can now be extended to network models of microstrip patches and arrays. Use of gradient optimisation techniques involves calculation of gradients of antenna performance with respect to various designable parameters. The adjoint network method of sensitivity analysis has been used extensively for calculating gradients for circuit optimisation. This method can now be used for sensitivity analysis of microstrip patch antenna configurations also. Since the network models involved are passive and reciprocal, the adjoint network is identical to the original network model itself, and thus a single network analysis is sufficient to yield the sensitivity information also. Among other things, this would yield the sensitivity of the voltage distribution along the radiating edges with respect to the various designable parameters of the antenna configuration. Sensitivity of the radiation characteristics with respect to the antenna parameters can be calculated therefrom. It is expected that the techniques reported in this Chapter will lead to implementation of accurate CAD procedures for microstrip patches and arrays.
measurements
I
9.8 Appendix: Green's functions for various planar configurations In this Section Green's functions for some planar shapes, shown in Fig. 9.9, are given. In the expressions that follow, ai is given by rJi
Fig. 9.56
Typical flow chart for computer-aided design methodology for microstrip antennas
The performance characteristics obtained are compared with the given specifications. When the specifications are not met, the designable parameters of the antenna configuration are modified and the analysis is repeated. These analysis, modification and comparison steps constitute a single iteration in the optimisation loop. Several optimisation strategies include sensitivity analysis of the
=
2, otherwise
(a) A rectangle: The Green's function for the rectangle shown in Fig. 9 . 9 ~ is given as [2]
cos (kxxo)cos (kyyo)cos (k,x) cos (kyy)
r ~ ~ r ~ , ,
kt+g-k2
520
Multiport network approach for modelling
ml~ k, = a
and
k,
=
(d) A right-angled isosceles triangle: The Green's function for the rightangled isosceles triangle shown in Fig. 9.9d is given by
n~ b
(b) A 30"-60" right-angled triangle: The Green's functions for the triangle shown in Fig. 9.9b is given as [34]:
where T(x, y)
where Tl(x, y)
= (-
1)'cos
+ (-
=
mnx nny nnx mny cos -cos - + (- I)"+" cos -cos a a a
(A9.9)
(e) A circle: The Green's function for the circle shown in Fig. 9.9e is given by [351
(z)
cos [2n(m3a ")Y]
(-)
I)mcos
2nmx
cos
$a
[
2n(n - I ) y
]
3a
where J,,(.) represents Bessel's function of the nth order, and k,, satisfies
The subscripts m in k,, denotes the m th root of eqn. A9.11. For the zeroth-order Bessel's function, the first root of eqn. A9.11 is taken to be the non-zero root.
with the condition that I = -(m
521
Multiport network approach for modelling
where
+ n)
(n
(c) An equilateral triangle: The Green's function for the equilateral triangle shown in Fig. 9 . 9 ~ is given as [34]
where TI(x, y) is given by eqn. A9.4 and
($)
T,(x, y ) = (- ~)'COS- sin
+-
c o s
+ (-
0
(-1
['"",a
n)~]
[ ( ) [ 2smx
sin
2n(n
-
3a
sin
] ]
1)y
$a
s
A circular sector: The Green's function for circular sectors are available only when the sector angle a is a sub-multiple of R. For the circular sector shown in Fig. 9.9f for which a = all, the Green's function is given as [36]
2n(l - m) y
$a As for Tl(x, y), the integer I in T2(x, y) is given by eqn. A9.5.
(g) An annual ring: The Green's function for the annular ring shown in Fig. 9.9g is given as [36] (A9.6)
522
Multiport network approach for modelling
In the above relations N,(.) denotes Neumann's function of order n and J:(.) and N',(.) denote first derivatives with respect to the arguments. (h) An annular sector: As in the case of circular sectors, the Green's function for annular sectors are available only if the sector angle a is a submultiple of n. For the annular sector shown in Fig. 9.9h for which ir = n/i, the Green's function is given as [36]
where n, = nl, and F,,,(.) is defined in eqn. A9.15. The values of k,,,,,, are obtained from eqn. A9.16. 9.9 Acknowledgments Most of the material discussed irr this Chapter is based on the theses and publications of several of my students and colleagues: Rakesh Chadha, P. C. Sharma, Girish Kumar, Yinggang Tu and Abdelaziz Benalla. Their contributions are gratefully acknowledged.
9.10 References 1 GUPTA, K. C., et al.: 'Computer-aided design of microwave circuits', (Artech House, USA, 1981) chaps 8 and I I 2 OKOSHI, T., and TAKEUCHI, T.: 'Analysis of planar circuits by segmentation method', Electron. Commun. Japan, 1975, 58-B, pp. 71-79 3 CHADHA, R., and GUPTA, K. C.: 'Segmentation method using impedance-matrices for analysis of planar microwave circuits', IEEE Trans., 1981, MlT-29, pp. 71-74 4 SHARMA, P. C., and GUPTA, K. C.: 'Desegmentation method for analysis of two-dimensional microwave circuits', IEEE Trans., 1981, MTT-29, pp. 1094-1098 5 SHARMA, P. C., and GUPTA, K. C.: 'An alternative procedure for implementing desegmentation method', IEEE Trans., 1984, MTT-32, pp. 1-4
Multiport network approach for modelling
523
6 OKOSHI, T.: 'Planar circuits for microwaves and lightwaves' (Springer-Verlag. 1985) chap. 5 7 GUPTA, K. C., et al.: 'Two-dimensional analysis for stripline/microstrip circuits'. 1981 IEEE MTT-S International Microwave Symp. Digest, pp. 504-506 8 GUPTA, K. C., and SHARMA, P. C.: 'Segmentation and desegmentation techniques for analysis of two-dimensional microstrip antennas'. 1981 IEEE AP-S International Antennas and Propagation Symp. Digest, pp. 19-22 9 GUPTA, K. C.: 'Two-dimensional analysis of microstrip circuits and antennas', J. Inst. Electron. Telecommon. Engrs. (India), 1982, 28, pp. 346-364 10 SHARMA, P. C., and GUPTA, K. C.: 'Analysis and optimised design of single feed circularly polarised microstrip antennas', IEEE Trans., 1983, AP-31, pp. 949-955 I I KUMAR, G., and GUFTA, K. C.: 'Broadband microstrip antennas using additional resonators gap-coupled to radiating edges', IEEE Trans., 1984, AP-32, pp. 1375-1379 12 KUMAR, G., and GUPTA, K. C.: 'Non-radiating edges and four-edges gap-coupled multiple resonator, broadband microstrip antennas', IEEE Trans., 1985, AP-33, pp. 173-178 13 KUMAR, G., and GUPTA, K.C.: 'Directly coupled multiple resonator wideband microstrip antennas', IEEE Trans., 1985, AP-33, pp. 588-593 14 GUPTA, K. C.: 'Two-port transmission characteristics of rectangular microstrip patch radiators'. 1985 IEEE AP-S International Antennas Propagat. Symp. Digest, pp. 71-74 15 GUPTA, K. C., and BENALLA, A,: 'Two-port transmission characteristics of circular microstrip patch antennas'. 1986 IEEE AP-S International Symp. Antennas Propagat. Digest, pp. 821-824 16 PALANISAMY, V., and GARG, R.: 'Analysis of arbitrary shaped microstrip patch antennas using segmentation technique and cavity model', IEEE Trans., 1986, AP-34, pp. 1208-1213 17 PALANISAMY, V., and GARG, R.: 'Analysis of circularly polarised square ring and crossedstrip microstrip antennas', IEEE Trans., 1986, AP-34, pp. 1340-1346 18 BENALLA, A., and GUFTA, K. C.: 'A method for sensitivity analysis of series-fed arrays of rectangular microstrip patches'. National Radio Science Meeting (URSI), Boulder (CO), USA, Jan. 1987, Digest, p. 65 19 GUPTA, K. C.: 'Multiport-network modelling approach for computer-aided design of microstrip patches and arrays'. 1987 IEEE AP-S International Symp. Antennas Propagat., Blacksburg (VA), USA, June 1987 20 GUPTA, K. C., and BENALLA, A,: 'Computer-aided design of microstrip patches and arrays'. Int. Microwave Symp./Brazil, July 1987, Symp. Proc. Vol. 1, pp. 591-596 21 LO, Y. T., e t a / . :'Theory and experiment on microstrip antennas', IEEE Trans., 1979, AP-27, pp. 137-145 22 RICHARDS, W. F., et a[.: 'An improved theory for microstrip antennas and applications', IEEE Trans., 1981, AP-29,pp. 38-46 23 MUNSON, R. E.: 'Conformal microstrip antennas and microstrip phased arrays', IEEE Trans., 1974, AP-22, pp. 74-78 24 DERNERYD, A. G.: 'Microstrip array antenna'. Proc. 6th European Microwave Conf., 1976, pp. 339-343 25 CAMPI, M.: 'Design of microstrip linear array antennas by computer'. Proc. Antenna Applications Symp., Robert Alerton Park, Univ. of Illinois, Urbana, USA, Sept. 1981 26 BENALLA, A., and GUPTA, K. C.: 'Transmission line model for 2-port rectangular microstrip patches with ports at the non-radiating edges', Electron. Lett., 1987, 23, pp. 882-884 27 BENALLA, A., and GUPTA, K. C.: 'Two-dimensional analysis of one-port and two-port microstrip antennas'. Electromagnetics Laboratory, Scientific Rept. 85, Univ. of Colorado, May 1986, p. 48 28 COFFEY, E. L., and LEHMAN, T. H.: 'A new analysis technique for calculating the self and mutual impedance of microstrip antennas'. Proc. Workshop Printed Circuit Antenna Technology, New Mexico State Univ., 1979, pp. 31.1-31.21 29 BENALLA, A., and GUPTA, K. C.: 'Multiport-network model and transmission characteristics of two-port rectangular microstrip antennas', IEEE Trans., Oct 1988, AP-36, pp. 1337-42
524
Multiport network approach for modelling
30 GOGOI, A., and GUF'TA, K. C.: 'Wiener-Hopf computation of edge admittances for microstrip patch radiators', AEU, 1982, 36, pp. 247-251 31 VAN DE CAPELLE, A,, et a/.: 'A simple accurate formula for the radiation conductance of a rectangular microstrip antenna'. 1981 IEEE AP-S International Symp. Antennas Propagat., Digest, pp. 23-26 32 KUESTER, E. F., et 01.: 'The thin-substrate approximation for reflection from the end of a slab-loaded parallel plate waveguide with application to microstrip patch antenna', IEEE Trans., 1982, AP-30, pp. 910-917 33 GUPTA, K. C., and BENALLA, A.: 'Effect of mutual coupling on the input impedance and the resonant frequency of a rectangular microstrip patch antenna'. National Radio Science Meeting (URSI), Boulder, Jan. 1986, Digest, p. 226 34 CHADHA, R., and GUPTA, K. C.: 'Green's functions for triangular segments in planar microwave circuits', IEEE Trans., 1980, MTT-28, pp. 1139-1143 35 OKOSHI, T., eta/.: 'Planar 3-dB hybrid circuits', Electron. Commun. Japan, 1975.58-B, pp. 80-90 36 CHADHA, R., and GUPTA, K. C.: 'Green's functions for circular sectors, annular rings and annular sectors in planar microwave circuits', IEEE Trans., 1981, MlT-29, pp. 68-71 37 BENALLA, A., and GUPTA, K. C.: 'Faster computation of Z-matrices for rectangular segments in planar microstrip circuits', IEEE Trans., 1986, MTT-34, pp. 733-736 38 GUPTA, K. C., and ABOUZAHRA, M. D.: 'Analysis and design of four-port and five-port microstrip disc circuits', IEEE Trans., 1985, MTT-33, pp. 1422-1428 39 OKOSHI, T., and MIYOSHI, T.: 'The planar circuit - An approach to microwave integrated circuitry', IEEE Trans ., 1972, MTT-20, pp. 245-252 40 JAMES, J. R., et a/.: 'Microstrip antenna theory and design', (Peter Peregrinus, 1981), p. 23 41 JAMES, J. R., and HENDERSON, A,: 'High-frequency behaviour of microstrip open-end terminations', IEE Microwaves, Optics & Acoustics, 1979, 3, pp. 205-218 42 KATEHI, P. B., and ALEXOPOULOS, N. G.: 'Frequency-dependent characteristics of microstrip discontinuities in millimeter-wave integrated circuits', IEEE Trans., 1985, Mm-33, pp. 1029-1035 43 JACKSON, R. W., and POZAR, D. M.: 'Full-wave analysis of microstrip open-end and gap discontinuities', IEEE Trans., 1985, MTT-33, pp. 1036-1042 44 LEWIN, L.: 'Radiation from discontinuities in stripline', Proc. IEE, 1960, lWC, pp. 163-170 45 WOLFF, I., and KNOPPIK, N.: 'Rectangular and circular microstrip disk capacitors and resonators', IEEE Trans., 1974, MTT-22, pp. 857-864 46 BAHL, I. J., and BHARTIA, P.: 'Microstrip antennas' (Artech House, 1980) chap. 2 47 JANSEN, R. H., and KOSTER, N. H. L.: 'Accurate results on the end effect of single and coupled microstrip lines for use in microwave circuit design', AEV, 1980, 34, pp. 453-459 48 JANSEN, R. H.: 'Hybrid mode analysis of the end effects of planar microwave and millimeterwave transmission lines', Proc. IEE, 1981, 129, pp. 77-86 49 KIRSCHNING, M., e l a/.: 'Accurate model for open end effect of microstrip lines', Electron. Lett., 1981, 17, pp. 123-125 50 HAMMERSTAD, E., and JENSEN, 0.: 'Accurate models for microstrip computer-aided design', 1980 IEEE M l T - S Int. Microwave Symp. Digest, Washington, 1980, pp. 407-409 51 VAN LIL, E. H., and VAN DE CAPELLE, A. R.: 'Transmission line model for mutual coupling between microstrip antennas', IEEE Trans., 1984, AP-32, pp. 816-821 52 BALANIS, C. A,: 'Antenna theory analysis and design', (Harper and Row, 1982). p. 169 53 BENALLA, A,, and GUFTA, K. C.: 'Multiport network approach for modelling mutual coupling effects in microstrip patch antennas and arrays', IEEE Trans., Feb 1989, AP-37, pp. 148-52 54 JEDLICKA, R. P., et a[.: 'Measured mutual coupling between microstrip antennas', IEEE Trans., 1981, AP-29, pp. 147-149 55 WIENCHEL, H. D.: 'A cylindrical array of circularly polarised microstrip antennas'. IEEEAPS Int. Symp. Antennas Propagation Digest, 1975, pp. 177-180
Multiport network approach for modelling
525
56 KUMAR, G., and GUPTA, K. C.: 'Broadband microstrip antennas using coupled resonators'. 1983 IEEE AP-S Int. Antennas Propagat. Symp. Digest, pp. 67-70 57 GUPTA, K. C., and BANDHAUER, B.: 'Coupled line model for multiresonator wide band microstrip antennas'. National Radio Science Meeting (URSI), Boulder, Jan. 1988 58 BENALLA, A,: Unpublished experimental results, 1986 59 CHANG, D. C., and KUESTER, E. F.: 'Total and partial reflection from the end of a parallel-plate waveguide with an extended dielectric slab', Radio Sci., 1981, 16, pp. 1-13 60 CHANG, D. C.: 'Analytical theory of an unloaded microstrip patch', IEEE Trans., 1981, AP-29, pp. 54-62 61 TU, Y.: 'Edge admittance and mutual coupling in rectangular microstrip patch antennas with a dielectric cover layer', Ph.D. Thesis, Univ. of Colorado, 1987, pp. 62-84 62 TU, Y., GUF'TA, K. C., and CHANG, D. C.: 'Mutual coupling computations for rectangular microstrip patch antennas with a dielectric cover layer', URSI National Radio Science Meeting, Boulder, Jan. 1987, Digest p. 66 63 POZAR, D. M.: 'Input impedance and.mutual coupling of rectangular microstrip antennas', IEEE Trans., 1982, AP-30, pp. 1191-1 196 64 JACKSON, D. R., et a/.: 'An exact mutual coupling theory for microstrip patches', 1987 IEEE AP-S Int. Symp. Antennas Propag. Digest, Vol. 2, 1987, pp. 790-793
I
Chapter 10
Transmission-line model for rectangular microstrip antennas A. Van de Capelle
List of sumbols length of patch width of patch thickness of patch or co-planar strip conductor conductivity of patch or co-planar strip conductor RMS surface error of patch or co-planar strip conductor length of substrate width of substrate thickness of substrate relative permittivity of substrate loss tangent of substrate conductivity of ground plane RMS surface error of groun9plane thickness of ground plane width of strip conductor of a microstrip line length of microstrip line Y,, = characteristic admittance of microstrip line y, = propagation constant of microstrip line Y, = characteristic admittance of transmission line representing a rectangular microstrip antenna y, = propagation constant of the above Y, = self-admittance representing the open-end terminations of a microstrip antenna G, = real part of Y,, self-conductance B, = imaginary part of Y,, self-susceptance A, = extra length of microstrip line by open-end effect y, = admittance per unit length of a slot with infinite length g, = real part of y, b, = imaginary part of y, E,, H, = electric, magnetic field in equivalent slot apertures
528
Transmission-line model for rectangular microstrip antennas
excitation voltage of a slot i i,, i,, i, = unit vectors of x, y , z co-ordinates S = width of equivalent slots go,& ! = Fourier transform of E,, H, k,, k,, k, = components of k k = propagation vector p = real part of the complex radiated power per unit length q = imaginary part of the complex radiated power per unit length q = wave impedance in half-space above antenna k = propagation constant in half-space above antenna p = permeability of half-space above antenna E = permittivity of half-space above antenna ym = mutual admittance per unit length g, = real part of y, b, = imaginary part of y, J = Bessel function of the first kind Y = Bessel function of the second kind s = normalised slot width C, = Euler's constant E , ~= effective relative permittivity Kfl = effective width a = attenuation constant /I= phase constant qo = wave impedance of free space k,, = propagation constant in free space 1, = free-space wavelength We = length of equivalent slot w = normalised slot length L, = centre distance between equivalent slots F, = auxiliary coupling function for the mutual conductance E, = relative error on the radiation conductance G, Fb = auxiliary coupling function for the mutual susceptance Y, = mutual admittance Gm = real part of Y, Bm = imaginary part of Y, Kg = correction function for the mutual conductance Kb = correction function for the mutual susceptance D = directivity in broadside direction G = gain in broadside direction q = antenna efficiency Q = antenna quality factor BW = impedance bandwidth =
Transmission-linemodel for rectangular microstrip antennas
529
10.1 Introduction
Microstrip antennas have a physical structure derived from microstrip transmission lines. Therefore a transmission-line model is the first and most obvious choice for the analysis and the design of microstrip antennas. However, the transmission-line model is often regarded as a simplified and somewhat dated theory. This is true for the original, simple transmission-line model; but the accuracy of the improved transmission-line model is comparable to that of other more complicated methods. Even mutual coupling between rectangular microstrip antennas can be calculated in a fairly accurate and very efficient way with the transmission-line approach. The practical design of a microstrip antenna or a microstrip array, including matching and feeding networks, has to be done by means of a CAD software package. Existing programs represent the network components by equivalent transmission lines. If the antenna elements are modelled by the same transmission-line approach, the incorporation in the available CAD software is straightforward. The concept of the transmission-line model can be applied to any microstrip antenna configuration for which separation of variables is possible. In this Chapter we will devote our attention entirely to rectangular (and square) microstrip antennas. The transmission-line model does not include surface waves. Therefore, the application is limited to antenna configurations where the thickness and the substrate permittivity are sufficiently small to avoid considerable excitation of those surface waves. But, in practice, this is not a severe limitation. However, research is going on to also include surface waves in the transmission-line model. 10.2 Simple transmission-line model 10.2.1 Description of the transmission-line model
The transmission-line model will be discussed for rectangular (and square) microstrip antennas. The antenna consists of a conducting patch, a dielectric substrate and a conducting ground plane. The antenna is fed by a microstrip line (as shown in Fig. 10.1) or by a coaxial probe (Fig. 10.2). The patch is characterised by the resonant length L (resonant for the fundamental mode), the width W, the thickness t , the conductivity a, and the RMS surface error Ap . In the analysis, the dielectric substrate is supposed to have infinite dimensions in the plane of the patch. In practice, it has a length L,, a width W, and a thickness h. Electrically, it is characterised by a relative permittivity E, and a loss tangent 6,. It is supposed that the substrate consists of one homogeneous layer. A multilayer substrate can be replaced by an equivalent homogeneous layer with equivalent relative permittivity and loss tangent.
530
Transmission-linemodel for rectangular microstrip antennas
Transmission-line model for rectangular microstrip antennas
The conducting ground plane has the same dimensions as the substrate: L,, K i n practice, infinite of extent for the analysis. It is further characterised by a conductivity u,, a RMS surface error A, and a thickness t,. In the case of an antenna fed by a co-planar microstrip line, the strip conductor has a width W, and a length L,. The other parameters of the microstrip line ( t , h, t,, a,, a,, Ap, A,, E,, 6,) are the same as for the antenna. The cross-sectional geometry of the microstrip line is characterised by the aspect ratio W,/h. Likewise, the microstrip antenna can be considered as a microstrip line with a very large aspect ratio W/h.
Fig. 10.2 Rectangular microstrip antenna fed by a coaxial probe
L = length of patch L,,,=length of feedline W = width of patch WP , width of feedline E,= relative permittivity of substrate t = thickness of conducting patch and feedline = thickness of conducting groundplone thg thickness of substrote
-
Fig. 10.1 Rectangular microstrip antenna fed by a microstrip line
In the case of a microstrip antenna fed by a microstrip line (Fig. 10.1), the introduction of the transmission-line model is straightforward (Fig. 10.3): The microstrip feed line is represented by a transmission line with a characteristic admittance Y , (mainly determined by the aspect ratio W,/h and the relative permittivity E,), a propagation constant y, and a physical length L,. The rectangular microstrip antenna is represented by a transmission line with a characteristic admittance Y , (mainly determined by the aspect ratio W/h and the relative permittivity E,), a propagation constant y, and a physical length L.
I
WL-
b L -38'
Fig. 10.3 Rectangular microstrip antenna with transmission-line model
537
532
Transmission-line model for rectangular microstrip antennas
0 At the cross-sections AA' and BB', in Fig. 10.3a, the microstrip line with aspect ratio Wlh has an open-ended termination, which can be represented by a parallel admittance (Y, = G, jBJ.
+
In the case of excitation with a coaxial probe, the equivalent transmission-line, model has to be modified as shown in Fig. 10.4.
Transmission-line model for rectangular microstrip antennas
533
at port 1 and port 3 has to be left open (Fig. 10.3) in the case of a microstrip line feed. In the case of a coaxial-feed probe the model has to be completed with an inductance at port 3. The main step in the modelling of a microstrip antenna by a transmission-line equivalent, is the representation of the open-ended terminations by a parallel admittance Y,. An open-ended microstrip line does not perform as a perfect open circuit (see Fig. 10.6): 0 The field lines do not stop abruptly at the end of the strip conductor: there is a stray field extending beyond the end of the strip; this can be interpreted as an electrical lengthening A1 of the line, which implies an amount of stored. energy; on the other hand, the stray field is also source of power radiated in the space above the antenna and launched as surface waves along the substrate; The real part G, of the parallel admittance Y, represents the radiation effect (and surface waves), and the imaginary part B, models the stored energy in the extra line length.
Fig. 10.4 Rectangular microstrip antenna with coaxial feed and equivalent transmission-line model
Fig. 10.6 Open-ended microstrip line with aspect ratio Wlh
Fig. 10.5 General three-port equivalent transmission-line model
A general transmission-line model, which can be applied in both cases (microstrip line feed or coaxial feed), consists of a three-port circuit (Fig. 10.5). The general three-port model has to be completed with a piece of transmission line
10.2.2 Expressions for G, and B, The accuracy of the transmission-line model depends strongly on the choice of expressions for G, and B,. In the original transmission-line model, proposed by Munson [I], a simple but very approximate expression for Y, has been proposed:
Y,
= WY,
(10.1)
534
Transmission-line model for rectangular microstrip antennas
with y, = admittance per unit length of a uniformly excited slot with infinite length and width h, in an infinite, perfectly conducting plane. This expression is not accurate enough, but it is important because of the concept behind it:
Transmission-linemodel for rectangular microstrip antennas
535
where i,, i,, i, = unit vectors of the x, y, z co-ordinates; V,, V , = excitation voltage of slot I and slot 2, respectively; S = h = width of the equivalent slots; L, = L + h = centre distance between the equivalent slots.
The radiation of a rectangular microstrip antenna can be explained as originating from the tangential electric field in the plane of the patch. In the fundamental mode, only the contribution from the two open ends is important. The source of radiation can be limited to two narrow zones along the two open ends of the patch. The field in these two narrow zones can be thought of as the field of two rectangular slots in an infinite, perfectly conducting plane. For the fundamental mode of the microstrip antenna the tangential field in these two slots can be considered to be uniformly distributed. A slot with a uniform excitation field can be considered as a cut from an infinitely long, uniformly excited slot. The idea of representing the microstrip antenna by equivalent slots in an infinite, perfectly conducting plane is very powerful. The inaccuracy of eqn. 10.1 is mainly due to the last simplification, where the edge effects of finite-length slots are neglected. We now have two concepts available to explain the radiation of a microstrip antenna: the open end concept the equivalent slot concept.
=
{< V
(0
iy
for elsewhere
L, - S <-y<2
> Le
'II
(10.2)
Two-slot model
The spatial Fourier transform, with respect to y, of this aperture is given by
k,=components of the propagation vector k ; propagation constant. As the field of eqn. 10.2 has only a y-component, the Fourier transform is where
These two concepts can be used to derive expressions for the parameters in the transmission-line model. In the following Sections the equivalent, slot concept will be applied where possible, and the open-end concept where necessary. In this Section we want to derive suitable expressions for the parameters of the simple transmission-line model of Fig. 10.5. We proceed with eqn. 10.1 and derive expressions for the real part g, and the imaginary part b, of y,. A configuration of two equivalent slots, as shown in Fig. 10.7, is considered. The slots are pieces of length W, taken from infinitely long, uniformly excited slots. The tangential electric field in the slot apertures can be written as:
E,
Fig. 10.7
k,,
Ikl = k =
k,,
w@E)'I~ =
=
8,iY
with
The complex radiated power ( p + jq) per unit slot length, in terms of the spatial Fourier transform, is given by [Reference 2 pp. 61-68]:
536
Transmission-line model for rectangular microstrip antennas
From a network point of view, the two-slot configuration of Fig. 10.7 can be considered as a symmetrical two-port with a self-admittance per unit length y,(=g, jb,) and a mutual self-admittance per unit length y,(=g,,, jb,). Expressed in these quantities, the complex radiated power per unit length is given by
+
Transmission-line model for rectangular microstrip antennas
537
From eqns. 10.9-10.17 the following expressions for g, and b, can be derived
+
Taking V, = 0, g, and 6, follow from eqns. 10.5-10.8:
where the terms in s4,s6etc. have been neglected. The maximum truncation error of eqns. 10.18 and 10.19 is not larger than 0.1% for s < 1. Expressions 10.18 and 10.19, combined with expression 10.1, completely determine the parallel admittance Y,. .stria conductor
The single integrals in eqns. 10.9 and 10.10 can be written (see Reference 3 appendix) as double integrals of a Bessel function of the first kind J, and the second kind Y, respectively:
7
\dielectric substrate conducting groundplane
a
Weft *delectric
where s = kS is the normalised slot width =
lIi Jo(v)dvdu
Y/(s) =
&(v) dvdu
J:(s)
By twice integrating the series expansion of Joand Y, [4], the following series are obtained
where X = ln(s/2)
+ C,; C,
=
Euler's constant = 0.577216.
perfect conducting walls
I ' \ + @ ! b
magneticconducting walls
Fig. 10.8 Planar- waveguide model for microstripline a Cross-section of microstripline with aspect ratio Wlh b Cross-section of planar-waveguide model
10.2.3 Expressions for the line parameters To derive expressions for the characteristic admittance Y , and the propagation constant yp(=ap + j&) of the equivalent transmission line representing the antenna, and for the characteristic admittance Y,and the propagation constant y, of the microstrip feed line, the planar-waveguide model is used, see [5]. A microstrip line with aspect ratio W/h (cross-section see Fig. 10.8a) and with a dielectric substrate of relative permittivity E, is modelled by a planar waveguide (cross-section see Fig. 10.86). The top and bottom walls of this planar waveguide are electrically conducting, while the side walls are perfect magnetic conductors. The guide is of height h equal to the microstrip substrate height, but it has an effective width W ,. larger than the physical width W of the strip. The guide is filled with a dielectric that has an effective relative permittivity E , ~ .
538
Transmission-linemodel for rectangular microstrip antennas
The characteristic impedance Z, and the phase constant /3 of the fundamental mode propagating in the microstrip line are given in terms of the planarwaveguide parameters:
a
= k0& (10.21) 6 = propagawhere 4, = && = wave impedance in free space; ko = w tion constant in free space. In the quasi-static approximation, Reference 6 gives convenient expressions for
Kf(0) = tahlln (hF/ W'
W = W
+
{I
+ $ + (2h/ w')'}
+ ln(4/J(t/h)' + ( l / a ) 2 / ( ~ / t+ 1.1)')
(10.22)
539
Transmission-linemodel for rectangular microstrip antennas
(ii) The mutual coupling between the two equivalent slots is neglected; (iii) The radiation from the side walls is not taken into account. Derneryd [ I , 81 has partly eliminated the first two shortcomings: (i) To determine G, = Re(Y,), he considers the two main slots with an identical excitation and a negligible width. He finds an integral expression for G,, for which an approximate analytical solution has been derived by Lier [9]. Derneryd's model corrects the first two shortcomings of [Reference 11 for the real part of Y,,but it still neglects the influence of the side walls on G,. (ii) To determine the susceptance B, = Im(Y,), Derneryd makes this parameter equal to the open-end self-susceptance of the microstrip line formed by the patch. This corrects the first shortcoming of [Reference 11 for the imaginary part of Y,.
(10.24)
and for
Fig. 10.9
The attenuation a and the frequency dependence of Z, and are neglected in the simple transmission-line model. Indeed, as will be explained in the improved transmission-line model, the simple model has important shortcomings, so that it makes no sense to take into account these second-order effects. 10.3 Improved transmission-line model
10.3.1 Description of the improved transmission-he model The simple transmission line model has important shortcomings: (i) The expressions for Y, are inaccurate for the usual patch widths (i.e. for W < lo;& = free-space wavelength);
improved transmission-linemodel represented as a three-port
An improved transmission-line model, proposed by Pues and Van de Capelle [lo], will be discussed here. This model corrects the three shortcomings of [Reference 11for the real as well as for the imaginary part, and has a broad range of validity. The circuit representation of the present model is shown in Fig. 10.9. In this network Y, is the self admittance of the open-end terminations of the patch, and Y, is their mutual (radiation) admittance. The mutual coupling is formally taken into account by voltage-dependent current sources. The admittance matrix of this three-port model is given by [YI
=
I
Y , + Y,coth(y,L,)
-Y,
-
- Y,
Y, + Y, coth (y,L,)
- Y ,csch (y, L,)
- Y, csch (y, L,)
- Y, csch (y, L2)
Y,coth (y,L,)
csch (Y,L,
1
+ Y,coth (y, L2)
(10.29)
where cothz and cschz are the complex hyperbolic cotangent and cosescant
540
Transmission-linemodel for rectangular microstrip antennas
functions of argument z, respectively. The copper and dielectric losses of the antenna are taken into account by the attenuation constant a,, the real part of the complex propagation constant y,. If there is only one feed point, an input admittance can be defined. Assuming I, = I, = 0, it follows from eqn. 10.29 that
Yf
+ Y:
+
Yf Y: - Yi - Yi) coth (ypL)
+ 2Y,Y,coth(yPL) - 2YmY,csch(ypL) + (Yf - Y: + Yi) cash (2ypA)csch (ypL) + 2Y, Y,
541
Transmission-line model for rectangular microstrip antennas
I
(10.30)
been spent in comparing available formulas and deriving new ones where needed. It was a primary goal to combine accuracy with numerical efficiency. We have tried to obtain analytical expressions for all the model parameters. The imaginary part of Y,, the self-susceptance B,, is determined by means of the open-end-effect concept. Indeed, in the equivalent-slot concept, the selfsusceptance depends strongly on the aperture field and there is no information available on an appropriate choice of this field. The real part of Y,, the selfconductance G,, is modelled as the radiation conductance of an equivalent slot. The mutual admittance Y, is also determined from the equivalent-slot concept. For the line parameters, the attenuation and the frequency dependence of Y, and y are included.
where 10.3.2 Expression for the self-susceptance B, For the self-susceptance B,, the correct transmission-line formula is used:
B, = Y, tan (PAI) L, and L, are defined in Fig. 10.9. In the case of a microstrip-line-fed antenna, this corresponds to I, = I3= 0. It follows from eqns. 10.29 and 10.30 that
Y, =
~f
+ Y:
- Y;
+ 2Y, Y,coth (ypL) - 2YmY,csch (y,L) Y,
+ Y ,coth (ypL)
(10.32) To model the parasitic effects of the feed line on the antenna behaviour, the self-admittance of the open-end termination facing the feed line is reduced by a factor
where W, = width of feed line; W& = effective width of patch. This reduction takes into account the partial covering of the open-end termination by the feed line. The reduction of the self-admittance at terminal l can be considered as an addition of a parallel admittance The antenna input admittance is given by
The accuracy of the improved transmission-line model depends strongly on the accuracy of the expressions for the model parameters. Therefore much effort has
(10.36)
where Y,, p, A1 are, respectively, the characteristic admittance, the phase constant and the open-end extension of a microstrip line with aspect ratio W/h, as formed by the patch. The most appropriate expression for A1 is given in Reference 11: where
t,
6';
= 0.434907 60,,,
+ 0.26
(W/h)0'85" + 0.236
,f - 0.189 (W/h)0'85M+ 0.87
(10.38)
0.5274 arctan { 0 ~ 0 8 4 ( ~ / h ) " ~ ~ " " ~ } &0.9236
eff
(10.40)
0.0377 arctan {0.067(W/h)1'456) { 6 - 5 exp [0.036(1
- E,)]}
(10.41)
Expressions for Y,, p and eeffare given in Section 10.3.6. 10.3.3 Expression for the self-conductance G, For the real part of Y,, the self-conductance G,, the equivalent-slot concept explained in Section 10.2.2 is applied. The model is similar to that of Derneryd [7], except for the dimensions of the equivalent slot. The open-end terminations of the patch are replaced by uniformly TE-excited narrow rectangular slots of length W, = Kf (instead of Win Reference 7) and width A1 (instead of h in Reference 7).
542
Transmission-line model for rectangular microstrip antennas
To calculate the self-conductance G,, one such equivalent slot is considered, as shown in Fig. 10.10. The electric field in the slot aperture is assumed to be uniform:
543
Transmission-line model for rectangular microstrip antennas
This complex power can also be written in terms of network parameters:
Equating expressions 10.48 and 10.50, expressions for G, and B, follow where y = excitation voltage of the equivalent slot; S = equivalent slot.
AZ
= width of the
(10.52)
Fig. 10.10 Equivalent slot radiator in an infinite, perfectly conducting plane
Using expression 10.46 for gY,we obtain for G,:
The spatial Fourier transform of the aperture field is defined as
4
+m
j-,
=
I-m +m
En
dkyydx dy
(10.44)
The aperture field has only a y-component, so that the Fourier transform
4
The inner integral can be written as a double integral of the Bessel function of the first kind and order zero 131.Expansion of the Bessel function in a Maclaurin series and double integration term by term give:
= &J,,
where
yW, sin (k, W,12) sin (k,,S/2) x K1 (kyS/2)
&y =
The complex power radiated by this slot may be found by integrating the complex Poynting vector over the aperture surface A:
P +jQ
=
f jl, E. x H $ . i z dxdy
(10.47)
with Ha the magnetic field in the slot aperture A. Expressed in terms of the Fourier-transformed aperture field
The first two terms of this series expression are used in eqn. 10.53 to obtain finally
G,
%
1 -{[wSi(w) ntl
x (1 where =
kz
+ (k2 - kt - k$)'I2
= -j(k2,+g-kl)'12
for k2 2 k:
+g
for k l < e + g
where w = kW, (10.49)
si(x)
=
=
sin w
+ cosw - 21 +w
-;)+q;+-p--&)} cos w
normalised slot length; s = k S
j
0
sin u
-du u
sin w =
normalised slot width;
544
Transmission-line model for rectangular microstrip antennas
545
Transmission-line model for rectangular microstrip antennas
As explained before, expression 10.52 is not used to calculate B,, as it is impossible to define a suitable aperture field. One has to fall back on the open-end-effect concept (see Section 10.3.2).
where the superscript (2n) denotes the 2n th derivative. Truncation of these series, maintaining the first two terms, gives
10.3.4 Expression for the mutual conductance G, The expression for the mutual conductance G,,, of finite-length slots will be derived from the mutual conductance between infinite slots. Therefore, an auxiliary coupling function is defined
Using the identity Ji2'(l)
where g, and g, are the per-unit-length self-conductance and mutual conductance, respectively, of two infinite-length TE-excited slots in a perfectly conducting infinite ground plane, as shown in Fig. 10.7. The aperture field was given in eqn. 10.2. An analytical expression has been derived for x1 in Section 10.2.2:
To obtain an expression for g,, the complex radiated power per unit slot length ( p jq) has to be expressed in terms of the Fourier-transformed aperture field (eqns. 10.6 and 10.7), and in terms of the slot voltages V, and V, (eqn. 10.8). Setting 6 = V,and equating the real partp of the radiated power, the following expression for gmis found:
1
=
2 {J2(l)
- Jo(l))
we finally obtain for g,:
The maximum truncation error of eqn. 10.63 is about 0.1 % of g, for s < 1. Using eqn. 10.18 found for g, and eqn. 10.63 for g, the auxiliary coupling function F, = g,/g, can be expressed as
+
+
where L, = L A1 = centre distance between the two slots; S of the equivalent slots. Notice that 1
cos ( / c , ~ ~ = ) 2 sin2 (ky
=
Al = width
F)
The auxiliary coupling function F, has been introduced to calculate a first approximation of the mutual conductance G, of the finite-length slots by putting (10.65) G,,, = GSF, with G, the self-conductance as given by eqn. 10.55. The results of this approximation are compared to the following reference: the radiation conductance of the four-slot equivalent system shown in Fig. 10.11. This four-slot system consists of two main slots and two side slots. Themain slots have a length W, = and a width 81, as used before, and have a centre distance L, = L + Al. The side slots have a length L,, a width A1 and a centre distance W,. The tangential electric field in the aperture plane z = 0 is:
wfl
Similarly to the derivation of eqn. 10.1 1 from eqn. 10.9, we obtain the following expression for eqn. 10.57 using eqn. 10.58:
v sin E,
with Jf(s) as defined in eqn. 10.13 and 1 = kL,. Expanding J,'(I Taylor series around 1 leads to
=
-
s) in a
($
ix
-3 sin @) i)i Al
for
W L -A1 1x1 < 2; 2 2
Le + A1 < IYI < 2
for
L we- A1 (yl<$;-
W
for
I
L W,- Al -2
+ A1 2
A1 - W , +7
elsewhere (10.66)
546
Transmission-linemodel for rectangular microstrip antennas
This aperture field is an acceptable approximation of the true tangential electric field in the plane z = 0 of the microstrip antenna excited in the fundamental mode. As shown in Reference 12, it allows an accurate computation of the far field and the radiation conductance. The computation is straightforward using
Transmission-line model for rectangular microstrip antennas
Extensive numerical investigation of this quantity for a large number of parameter values in the ranges w > 0.1, 1 < 3.2 and s < 1 shows the surprising result Krf z 1
Fig. 10.11 Four-slot radiation model
the plane-wave spectral method. The resulting integral expression for the radiation conductance is too complicated for analytical integration, but it can be evaluated numerically without any difficulty. We call this numerically evaluated quantity, the reference conductance G/:' and we will use it to verify the accuracy of the radiation conductance G y d as predicted by the transmission-line model (Fig. 10.9). The conductance G y d is given by Gyd
=
2(G,
+ G,)
(10.67)
where G, is calculated from eqn. 10.55 and G, is expressed to a first approximation by eqn. 10.65. Poor correspondence between G r d and Gyf is expected; therefore we add a correction function Kg to compensate for eventual influence of the side slots and of the finite length of the main slots. Instead of eqn. 10.65, we use: G,
= GsFgKg
(10.68)
The correction function Kghas to be determined by comparison of GYdand GYf: GYd
=
2(G,
+ G,,,)
= 2GS(1
+
(10.69)
To obtain a good correspondance between ~ Y " a n dG:'/, thecorrection function Kg has to be a good approximation to the numerical reference quantity
547
(10.71)
Therefore, the simple expression G, = G, F, can be considered as valid within the given parameter ranges. The validity of this expression for both small (> 0.1) and large values of w can be understood as some kind of compensation: the influence of the side slots (which is not taken into account in the calculation of G, and G,) and the influence of the finite length of the main slots (which is neglected in the calculation of the factor F, in G,) appear to cancel each other out almost perfectly. To illustrate this effect, Table 10.1 lists the quantities GI (= 2G,, i.e. 2 x self-conductance of a main slot), G; (= radiation conductance of the two-slot system consisting of the two main slots, see Fig. 10.12), G: ( = G?, i.e. the radiation conductance of the four-slot system consisting of the two main slots and the two side slots, see Fig. 10.11) and G y d(i.e. the radiation conductance found with the transmission-line model of Fig. 10.9 and calculated from expression 10.69), as a function of w for 1 = 2 and s = 0. The influence of the side slots can be deduced from a comparison between G; and G:; the influence of the finite length of the main slots can be seen from a comparison between Gf"""and Gf. In Reference 9 it is argued that the influence of the side slots on the radiation conductance can be neglected, but according to Reference 10 a distinctly better correspondence with experiment is obtained if the side slots are taken into account as described above. Table 10.1 Radiation conductance for 1 = 2 and s w
1 2 3 4 5 6 7 8
G! (mS) 0.55 2.1 1 4.40 7.80 9.87 12.61 15.26 17.86
G; (ms) 0.75 2.84 5.86 9.33 12.84 16.19 19.39 2254
=
0
G,* (mS) 0.69 2.63 5.48 8.79 12.23 15.58 18.82 22.00
GYd (mS) 0.68 2.58 5.38 8.67 12.08 15.43 18.68 21.86
The accuracy of expression 10.65 can also be shown in a systematic way by computing the relative error:
550
Transmission-linemodel for rectangular microstrip antennas
Transmission-line model for rectangular microstrip antennas
we finally obtain for b,
The maximum truncation error of eqn. 10.80 is about 0.1% of b, if s In Section 10.2.2 a closed-form expression for b, was derived:
<
1.
Using eqns. 10.80 and 10.19 in eqn. 10.74 enables to write the auxiliary coupling function Fb as
We consider the product (B,F,) as a first approximation of the mutual susceptance B, and introduce a correction function Kb so that:
Because of problem (b), an aperture field that meets the edge conditions [3] is required: the tangential components of the electric field perpendicular to the edge must decrease with distance d from the edge, and the components parallel to the edge must decrease with d2from the edge. There is no further information availableto select the appropriate field distribution. Different distributions give different values for the aperture susceptance. But a detailed numerical evaluation shows that the dependence of the aperture susceptance on the aperture distribution comes from the dependence of the self-susceptance, not from the mutual susceptance. For the configuration of Fig. 10.12, it can be concluded that the uniform aperture-field distribution predicts the mutual susceptance within 1% of the values obtained using appropriate tapered distributions. Hence our reference correction function K:/ is defined as where BZis the mutuai susceptance of the two-slot system of Fig. 10.12 with a uniform aperture field, and b,,,We is the mutual susceptance of an equivalent system of length W, taken from two infinite-length slots having the same width A1 and the same centre distance L,. Numerical investigation shows that K;Pf is nearly independent of s or I. It can be concluded that an expression having only the variable w can represent the correction function K,:
K, One could expect to apply the same method to determine Kb as is used for K,; i.e. numerical evaluation of the aperture susceptance of the four-slot system of Fig. 10.11 and to consider this quantity as a reference for deriving a suitable expression for Kb. But following problems occur: (a) It is not clear how a reference susceptance evaluated for a four-slot system has to be related to the quantity K, of the transmission-line model. We cannot assume conservation of reactive power passing through two different reference planes: the aperture plane z = 0 in the equivalent slot model and the input port plane (e.g. port 1 or 2) in the transmission-line model. (b) The susceptance of a radiating aperture is much more sensitive to the precise form of the aperture-field distribution than is the conductance. Consequently the approximate field distribution of eqn. 10.66 is not appropriate for computing a reference susceptance. Besides, this field distribution does not even meet the required edge behaviour. (c) It is much more difficult to compute the susceptance of a radiating aperture than its conductance. Using the plane-wave spectral method, the conductance is given by a surface integral over a finite part of the wave-number plane, whereas the susceptance requires a surface integration over an infinite domain. Because of problem (a) we are unable to use a four-slot system to determine the correction function Kb, but must use the two-slot system of Fig. 10.12 consisting of the main slots. Hence we neglect the influence of the side slots on the susceptance.
551
=
1 - exp ( - 0 . 2 1 ~ )
(10.84)
This equation has the correct asymptotic behaviour for w F m, as the influence of the finite length of the main slots disappears and Kb has to approach unity. 10.3.6 Expressions for the line parameters In Section 10.2.3 we discussed the planar waveguide model and the corresponding expressions for the line parameters. Eqns. 10.20-10.28 describe the characteristics of a microstrip line in a quasi-static approach. The frequency dependence of the model parameters can be taken into account through frequency dependence of and Kff. A convenient expression for eCffcan be found in References 13 and 14:
where ~ ~ ( is0given ) in eqns. 10.25-10.28 and
P = P,P2{(0.1844 + P,P4)f,)'5763 PI
=
0.27488
(10.86)
+ (0.6315 + 0.525/(1 + 0.0157S,)20)~
- 0.065683 exp (-
8.7513 u)
(10.87)
P2 = 0.33622{1 - exp(- 0.03442~,))
(10.88)
P, = 0.0363 exp(-4.6 u){l - exp [- (f,/38.7)4'97]}
(10.89)
552
Transmission-line model for rectangular microstrip antennas
Transmission-linemodel for rectangular microstrip antennas
P, f,
=
1
+ 2.751 (1 - exp [-(~,/15.916)~]}
= F [ i n GHzmm] = 47.713 kh
u = {W
+ (W'
-
W)/&,}/h For &(A an expression has been proposed in Reference 15:
(10.90)
553
The dielectric losses are given in Reference 17 as 6, & g ( f ) - 1 tan 8 a, = 0.5P &@(f E r - 1
(10.91) (10.92)
(10.103)
The conducting losses are given in References 17 and 18 as
with W&(O) as given in eqns. 10.22-10.24; according to Reference 15, K can be equal to 1 and
%R,FA,~
a,
=
a~g
= a"R~gF~f
(10.104) (10.105)
with Rm =
,hmz
(10.106)
4
J3&
(10.107)
=
where c, is the free space velocity of light. However, it has been shown by Pues and Van de Capelle [I61 that a better asymptotic behaviour for E, b 1 is obtained if
and a better accuracy, particularly for high frequencies, if
Substitution of eqns. 10.95 and 10.96 in eqn. 10.93 gives a cubic equation from which Kff(f) has to be solved. There is one real solution:
FA, = 1
+ -x2 arctan {~.~(R,A,u,)~}
(10.110)
F,
+ -x2 arctan {1.4(R,Agug)2}
(10.11 1)
= 1
which gives, with eqn. 10.24 for W', where
10.4 Application of the improved transmission-line model
+ Q;)'I2 c,2
(10.100)
+ am + acg
(10.102)
R, = (P;
s,
=
(10.101) 4f2[&es(n - 11 The attenuation constant a can be divided into dielectric losses in the substrate (a,), conducting losses in the strip conductor (a,) and in the ground plane (a,): a = ad
10.4.1 Analysis and design of rectangular microstrip antennas All parameters of the improved transmission-line model have been given in terms of closed-form expressions. This enables one to program the model very easily for analysis as well as for design purposes. The input admittance xn is expressed in eqn. 10.30 and the resonance condition is defined as
Im(&,) = 0
(10.1 14)
554
Transmission-linemodel for rectangular microstrip antennas
For the case of a microstrip-line-fed antenna the input admittance is given in eqn. 10.35. The usefulness of the transmission-line model is illustrated by the simple expressions that can be derived for several important antenna characteristics. For the radiation conductance we find G,
=
G,(r
+ IvI2) - 2G,Re(v)
(10.115) where r is defined in eqn. 10.33; v = voltage-excitation ratio of the main slots
Transmission-line model for rectangular microstrip antennas
555
10.4.2 Comparison with other methods To verify the usefulness of the improved transmission-line model, we compare it with other published results, theoretical as well as experimental. Fig. 10.14 shows the input impedance of a rectangular microstrip antenna excited by a microstrip line. The Figure compares measured results of Lo et al. [20], calculated results published by Deshpande and Bailey [21] and calculated results obtained with the improved transmission-line model. Eqn. 10.35 was evaluated for: W = 144mm, L = 76mm, W, = 4.3 mm, h = 1.59mm, E, = 2.62, tan6 = 0.001, t = 0.035mm, a, = as = 0.556 x loSS/mm, A, = As = 0.00 15 mm.
The antenna efficiency follows from
The directivity in the broadside direction is given by
and the antenna gain by G = qD
(10.1 19)
The resonant input conductance is defined as Gre* = Re ( Kn)l,=,,e,
(10.120)
where f,, is the resonant frequency which follows from eqn. 10.1 14. The antenna input admittance, given by eqn. 10.35, can be modelled fairly accurately by the resonant input conductance G,, connected in parallel with a lossless open-ended half-wavelength transmission line with characteristic admittance Y,:
Consequently, the unloaded antenna quality factor is given by Fig. 10.14 Input impedance of a rectangular microstrip antenna fed by a microstrip line
and the impedance bandwidth by using Reference 19,
where S is the maximum value of the voltage standing-wave ratio that is allowed on the feed line.
The moment-method results of Reference 21 agree somewhat better with the experimental results 1201, than does the transmission-line model. However, detailed comparison with Reference 21 proves that the transmission-line model is more accurate than the calculated results of Lo et al. obtained with a cavity model [20] and of Newman and Tulyathan obtained by a moment method [22]. The discrepancy between the transmission-line model and experiment can be
556
Transmission-linemodel for rectangular microstrip antennas
explained by the tolerances on the structural parameters. For example, almost perfect agreement with experimental results was obtained using E, = 2.64 instead of 2.62, and if the losses were somewhat less. Observe that copper losses are neglected in the calculations of Deshpande and Bailey [21]. 10.4.3 Comparison with experimental results The improved transmission-line model is used to analyse a square microstrip antenna, shown in Fig. 10.15. The antenna is matched to 50 R by a quarter-wave transformer. The structure has been photo-etched on a RT/Duroid 5880 substrate of 0.03 1 in = 0.787 mm thickness and connected to an OSM-215-3 connector. The measured dimensions of the copper pattern are:
L
=
33.147 mm, W = 33.165 mm, W, = 0.473 mm, L,
=
18.713 mm,
Transmission-line model for rectangular microstrip antennas
557
models (see Fig. 10.16): Model for the coaxial-microstripline transition [23], Transmission-line representation of the feed line Model for the step discontinuity in the microstrip lines Transmission-line representation of the quarter-wave transformer Improved transmission-line model for the microstrip antenna
-
---
connector
e--
- antenna line line step -
Fig. 10.16 Schematic representation of complete analysismodelfor the antenna of Fig. 10.15
-40L 2.90
I
2.95
3.00 frequency, GHz
I
3.05
I 3.1 0
Fig. 10.17 Return loss of antenna shown in Fig. 10.15
Fig. 10.15 Square microstrip antenna fed with quarter-wave transformer
The parameters of the substrate are:
The antenna has been analysed completely by a cascade of transmission-line
Fig. 10.17 shows the measured reflection diagram and three calculated curves. To model the antenna element, we have used eqn. 10.35, but with different values of Y, and Y,,. To simulate Derneryd's model [7] we set Y, = 0; and to simulate Munson's model [I] we set Y,, = 0 and Y , = Wey,. One can clearly observe the effect of neglecting the mutual coupling between the equivalent slots (by comparing Derneryd's model with the improved transmission-line model) and of neglecting the influence of the finite length of the slots (by comparing Munson's model with Derneryd's model). 10.4.4 Design application The design of microstrip antennas by the improved transmission-line model is
558
Transmission-line model for rectangular microstrip antennas
Transmission-line model for rectangular microstrip antennas
559
very powerful if the model is combined with CAD packages for microstriplines or striplines. To illustrate this application we discuss the design of a rectangular microstrip antenna, combined with a broadband impedance-matching network. The antenna shown in Fig. 1 0 . 1 8 ~ has the following dimensions: W, = 119.83 mm, L, = 31.68 mm, W, = 4.87mm, L2= 83.32mm. It has been etched on a RT/Duroid 5880 substrate of 200mm x 150mm x 1.5748 mm. The other parameters (E,, tan6, t , a,, a,, A,, As) are the same as in the previous Section. Fig. 10.19 shows the calculated and the measured return loss of this antenna. The best match occurs at 3.025GHz (-21.5dB) and the improved transmission-line model predicts best match at 3.040GHz (- 26.96 dB). Sll
REF O.OdB 2.5dBi
L
I
I
log MAG
I
start stop
I
s
1
1
I
l
l
,
2.600000000 GHz 3.600000000 GHz
Fig. 10.19 Return loss of the antenna of Fig. 10.18a -measured ---- calculated
Fig. 10.18 Rectangular microstrip antenna a Fed by a 5052 microstrip line b Fed by a co-planar impedance-matching network
The impedance bandwidth can be increased with a reactive matching network [24]. A broadband-matching design procedure developed by Pues (US Patent 4445122) can be applied. The design has been carried out combining the improved transmission line model for the antenna element with suitable design models for the microstrip-network components. The design result is shown in Fig. 10.18b. The dimensions are as follows:
560
Transmission-line model for rectangular microstrip antennas
W, = 4.46 mm, L,
=
35.95 mm, W6 = 2.65 mm, L6 = 20.50 mm,
Both prototypes (Figs. 1 0 . 1 8and ~ b) have been realised by the same etch process on pieces of substrate cut from the same sheet. The return loss of the impedancematched antenna is shown in Fig. 10.20. Within the band of operation, the worst match occurs at 3.035 GHz (- 843 dB). The bandwidth at this reflection level (VSWR = 2.14) has been increased by a factor of 3.2 up to a value of 275 MHz sll
REF O.OdB 2.5 dB1
Transmission-line model for rectangular microstrip antennas
567
antenna. It can be observed that the co-planar matching network does not disturb the radiation characteristics. This design procedure can also be applied to combine the antenna element with a stripline matching network in a multi-layer structure [25]. 521
log MAG
REF -28.0 dB 2.OdBl
Log MAG
start stop
start stop
2.600000000 GHz 3.600000000 GHz
Fig. 10.20 Return loss of the antenna of Fig. 70.18b measured ---- calculated
2.600000000 GHz 3.400000000 GHz
Fig. 10.21 Comparison of transmission performance of the antennas of Fig. 10.78 a Antenna of Fig. 10.188 b Antenna of Fig. 10.18b
-
or 9.1%, whereas the theoretical maximum bandwidth-enlargement factor for this degree of matching equals 4.0. For further illustration of this application, Fig. 10.21 compares the transmission performance of the two antennas, which is proportional to the realised gain. The impedance-matched antenna is a more efficient radiator, including dissipation losses in the matching network, over the 2432-2.988 GHz and the 3.055-3.174GHz band, whereas the antenna without impedance matching is more. efficient between both frequency bands. The maximum gain difference equals 0 6 1 d B and occurs at 3.026 GHz. The co- and cross-polar radiation patterns have been recorded in E- and H-plane at three different frequencies: 2.9, 3.0 and 3.1 GHz. The results are shown in Fig. 10.22 for the unmatched antenna and in Fig. 10.23 for the impedance-matched
10.5 Transmission-line model for mutual coupling 10.5.1 Description of the model Although more rigorous methods have been developed to calculate the mutual coupling between microstrip antennas, the transmission-line model provides a numerically efficient alternative. The mutual coupling is caused by the simultaneous effect of: 0
Interaction through free-space radiation Interaction through surface waves.
The influence of surface waves can be neglected if we confine our attention to antennas with substrates of small electrical thickness and low permittivity. In practice, this limitation is not very restrictive. To develop the transmission-line model for mutual coupling, the following procedure is used [26]:
562
Transmission-line model for rectangular microstrip antennas
I
I
-90' H-plane, f = 2 . 9
O0
GHz
a
Fig. 10.22 Radiation patterns of the antenna of Fig. 10.1Ba
I
90°
Transmission-line model for rectangular microstrip antennas
563
564
Transmission-line model for rectangular rnicrostrip antennas
Transmission-line model for rectangular rnicrostrip antennas
% cross
cross
I
-90°
O0
E-plane, f= 3.1 GHz
f
90°
565
566
Transmission-line model for rectangular microstrip antennas
Transmission-line model for rectangular microstrip antennas
I
I
-90° H-plane, f=3.1
I
0"
GHz
90°
e
-3 0 cross
I
-b 90° E-plane, f = 3 0
0"
GHz
d
1
90°
cross
567
568
Transmission-line model for rectangular microstrip antennas
Each microstrip antenna is represented by its improved transmission-line model as described in Section 10.3. To model the mutual coupling between different antennas, each antenna is replaced by a two-slot system, consisting of the two main slots (Fig. 10.246); hence the influence of the side slots on the mutual coupling is neglected. The aperture field in the equivalent slots is assumed to be uniform; the slots have length Ct: = W&, width S = A1 and a centre distance L, = L Al. The transmission line model of each antenna is completed with voltagedependent current sources representing the mutual coupling between equivalent slots of different antennas (Fig. 10.25).
Transmission-linemodel for rectangular microstrip antennas
569
Y: for antenna 2. The mutual admittance between equivalent slots within one antenna is given by Y,!,and Yi, respectively. The mutual admittances between equivalent slots of different antennas are denoted by Y,, Y,, Y,/, Y,,, respectively.
+
Fig. 10.25
Transmission-line model for mutual coupling between rectangular microstrip antennas
Consider the simplest case of feeding directly at the edge of each microstrip antenna (i.e. L,!,= Li = 0 in Fig. 10.25), and assume port 1 of each antenna is the respective input port. The input admittances Y" of antenna 1, Y22of antenna 2 and the mutual admittances yL2= y2' between antennas 1 and 2 are obtained through elimination of the voltages (Vi and v:)at ports 2 of both antennas: y" Fig. 10.24 Two-slot model for the mutual couplingbetween rectangular microstrip antennas
Fig. 10.25 shows the complete transmission-line model, including mutual coupling, for the case of two antennas (1 and 2). The self-admittance in the transmission-line model of each individual antenna is denoted by Y,' for antenna 1,
= (y:l)2y2 - y:t(ymr)2
+ 2yt!ttymrymf - (y:O2y~ N
- (ymf)2y:,
570
Transmission-line model for rectangular microstrip antennas y12
=
y21
= y,
Kl y,:
- ym,( ymr)2 + y,: y,: ym,
N
Transmission-line model for rectangular microstrip antennas
v
571
c
and impressed on the equivalent slots i and j, respectively, and in terms of the self and mutual admittances:
with = Y ,: Y,: - (Ym,)2 YA = Y,' Y,'coth(y;l')
N
+
Y,!,, = YA - Y,' csch (y;ll) Y,: = Y: Y ,:
+ Y: coth ($I2)
= Y; - Y: csch (yi12)
In these expressions a superscript (e.g. i in Y') denotes the number of the antenna (i = 1 or 2); an exponent is denoted as (Yi)2, which means Yi to the power 2.
L . + * $
I
slot
I
10.5.2 Calculation of the model parameters The transmission-line model for mutual coupling (Fig. 10.25) contains: Parameters depending on only one antenna Parameters expressing the mutual admittance between equivalent slots of different antennas For the first kind of parameters, the expressions derived in Section 10.3 are valid: Self conductance Gj = expression 10.55 Self-conductance B: = expression 10.36 Mutual conductance GL = expression 10.65 Mutual susceptance BA = expression 10.82 Line parameters, see Section 10.2.3 and 10.3.6 For the second kind of parameters, the mutual admittance between equivalent slots of different microstrip antennas has to be calculated. The geometrical configuration of two arbitrarily chosen slots i and j is shown in Fig. 10.26. The slots have length Wj, Wi respectively; width Ali and All, respectively; centre distance AxS in the x-direction, and centre distance Ayo in the y-direction. We start from the expression for the complex radiated power:
where A is the aperture surface of the slots i and j, and E and H a r e the electric and magnetic fields, respectively, in the aperture plane. The complex radiated power can be written in terms of the impressed voltages
Fig. 10.26 Geometrical configuration of two arbitrarily chosen slots i and j
where Y,,, Y;, are the self-admittances of slots i and j, respectively. Y;,, Ti is the mutual admittance between slot i and slot j. Owing to the reciprocity theorem the mutual admittances are equal: Eqn. 10.133 can be developed in terms of the fields E, H or in terms of the Fourier-transformed fields 8, Zf. The last one is suitable for deriving analytical series expressions (as used in Section 10.2.2, 10.3.3, 10.3.4 and 10.3.5). The integral expression in terms of the fields E, H is more suitable for direct numerical evaluation. Both methods will be considered. To develop eqn. 10.132 in terms of the E, H fields, the aperture fields have to be expressed in their impressed and induced (by mutual coupling) field components:
where E,, 4, 4 , H; = total tangential fields, slots i, j; E,,,, Ha,, E,, H, = impressed tangential fields, slots i, j; E,,, Hij, El,, Hli = induced tangential fields,
572
Transmission-line model for rectangular microstrip antennas
slots i,j. Eqn. 10.133 is written in terms of impressed voltages; consequently eqn. 10.132 has to be developed in terms of impressed electric fields in order to enable identification of terms. Consequently: Ei.
=
0
E,,
=
0
(10.139) (10.140)
Transmission-linemodel for rectangular microstrip antennas
573
where hji is a dyadic Green's function giving the magnetic field at a position r, on slot j caused by a unit magnetic current source located at position ri on slot i; and K,, is the equivalent magnetic surface current replacing the aperture field Eaiby a current source in free space: The impressed aperture fields Eaiand E, occurring in the two-slot system of Fig. 10.246 have only a -y-component. Consequently, K,, and K,,,, have only an x-component:
and
+ illAJEd x 1
K,, (H:
+ H $ ) i , dxdy
= -2i,
x i,E,,
= 2E,,ix
Km~ = -i, x i,E, = E a1. i* Applying eqns. 10.148-lO.l52 in eqn. 10.147 enables to write
(10.151) (10.152)
e.
(10.141) Equating eqns. 10.133 and 10.141, and identification of terms, gives: Y$ F V) =
JJA,
(i, x E,,) .H*, dx dy
We denote the xx-component of the dyadic Green's function as This depends only on the distance lr, - r,l between observation point and source point. The impressed field distributions were assumed to be uniform in the equivalent two-slot system of Fig. 10.26; consequently:
(10.142) After substitution:
Y$~v:=
JJAJ
(i, x ~ , ) . ~ $ d x d y
(10.145)
x,.
The mutual Eqns. 10.142 and 10.143 determine the self-admittances Y,and admittance F, = can be calculated from eqn. 10.144 or 10.145:
the integration with respect to v can be performed analytically and the fourdimensional integral can be reduced to a two-dimensional one, which improves the numerical efficiency and makes this expression very suited for direct numerical evaluation. In order to avoid numerical evaluation of integral expressions, and to further improve the efficiency, analytical series expressions have been derived [27]. These expressions are obtained starting from the expressions for the mutual admittance in terms of the Fourier-transformed aperture fields.
We proceed with eqn. 10.147. The vector product where K, is an equivalent magnetic surface current. The induced magnetic field q., in slot j is caused by the impressed field E,, in slot i. This induced field can be expressed as
qi
=
A,
hji . K,, dx dy
(10.149)
10.5.3 Comparison with other methods In order to check the validity of the transmission-line model for mutual coupling, comparison with published theoretical and experimental results will be discussed. First we compare with the experimental results published by Jedlicka and Carver [28]. It Gals with the mutual coupling between two identical microstrip antennas in the E-plane (Fig. 10.27) and in the H-plane (Fig. 10.28). The
574
Transmission-line model for rectangular microstrip antennas
coupling is measured as a function of the distance between the patch edges, which is normalised with respect to the free-space wavelength 1,.Neither the dimensions or the location of the feed probe, nor the permittivity of the substrate are mentioned in Reference 28. As the microstrip antenna is matched at 1.405 GHz and the permittivity was estimated in Reference 29 to be 2.50, we obtain a probe diameter of 0.3 mm and a distance between the feed point and the edge of the patch equal to 20.0mm. To account for the probe inductance, Harrington's formula (Reference 30 pp. 378), has been used. The calculated results obtained with the transmission-line model are shown by the solid line in Figs. 10.27 and 10.28. In the E-plane, the correspondence between the transmission-line model and the experimental results is quite good; the largest difference occurs at a small distance of 0.2 & . In the H-plane, the correspondence is less good, as can be expected from neglecting the side slots.
Transmission-line model for rectangular microstrip antennas
575
model, it sometimes gives better agreement with experiment than the transmission-line model, except for very small distances ( < 0.1 &), where Penard's model does not give satisfactory results owing to neglecting the slot width. In Fig. 10.31 the transmission-line model is compared with theoretical and experimental results published by Malkomes [321. In this case the mutual 000 Carver (Exper.)
....
-
Pozar (Theor.) Transrn. (Theor.)
000 Carver (Exper.)
....
-
Pozar (Theor.) Transrn. (Theor.)
ho Fig. 10.28 Mutual coupling between two rectangular microstrip antennas in the H-plane Wx=66mm Wv=105.6mm f=1.405GHz h = 1.5785mm e, = 2.50 W ,, = 20.0 mm 000 Penard (Exper.)
x x x Penard (Theor.)
- Transrn. (Theor.)
Fig. 10.27 Mutual coupling between two rectangular microstrip antennas in the E-plane W, = 66 mm Wv = 105.6 mm f = 1.405 GHz W,, = 20.0 mm h = 1.5785 mm e, = 2.50
In order to compare the transmission-line model with more complicated models, Figs. 10.27 and 10.28 also show by dotted line the results published by Pozar [29]. It is a moment-method solution, which uses the grounded-dielectricslab Green's function to account for the presence of the substrate and surface waves. This method gives, as expected, excellent agreement with experiment, even though the calculations were made with at most three expansion functions. Another theoretical method, due to Penard [31], is based on a cavity model where the mutual coupling is considered as the coupling between two current loops around the patch surface. This method takes into account all the equivalent slots around the patch, but neglects the width of the slots, the surface waves, the variation of the ideal field distribution in the slots versus frequency and the higher-order cavity modes. Figs. 10.29 and 10.30 compare Penard's results with the transmission-line model for a severe test case, i.e. mutual distances smaller than 0.5 1,. Because of the presence of the side slots in Penard's
X$ -20
... 0
.......O
A
2
0
0
.....X. ...... .............Y ........... ............0
2..
-30 -
Fig. 10.29 Comparison of cavity model and transmission-line model for mutual coupling in the E-plane
W,=40rnm
-
W,=6Omrn 2.55
h = 1.52mm e,
f=1.548GHz W,, = 12.5mm
coupling is given as a function of the centre distance between the microstrip antennas. The antennas are fed by microstrip lines and the measurements are done at a frequency of 4.77GHz. Malkomes' theoretical results have been obtained by taking into account all the cavity modes and the four equivalent
578
Transmission-line model for rectangular microstrip antennas
10 PUES, H., and VAN DE CAPELLE, A.: 'Accurate transmission-line model for the rectangular microstrip antenna', IEE Proc., 1984, 131H, pp. 334-340 11 KIRSCHNING, M., JANSEN, R., and KOSTER, N.: 'Accurate model for open end effect of microstrip lines', Electron. Lett., 1981, 17, pp. 123-125 12 HAMMER, P., VAN BOUCHAUTE, D., VERSCHRAEVEN, D., and VAN DE CAPELLE, A.: 'A model for calculating the radiation field of microstrip antennas', IEEE Trans., 1979, AP-27, pp. 267-270 13 KIRSCHNING, M., and JANSEN, R.: 'Accurate model for effective dielectric constant of microstrip with validity up to millimeter-wave frequencies', Electron. Lett., 1982, 18, pp. 272-273 14 WHEELER, H.: 'Transmission-line properties of a strip on a dielectric sheet on a plane', IEEE Trans., 1977, MlT-25, pp. 6 3 1 4 7 15 OWENS, R.: 'Predicted frequency dependence of microstrip characteristic impedance using the planar-waveguide model', Electron. Lett. 1976, 12, pp. 269-270 16 PUES, H., and VAN DE CAPELLE, A.: 'Approximate formulas for frequency dependence of microstrip parameters', Electron. Lett., 1980, 16, pp. 870-872 17 HAMMERSTADT, E., and BEKKADAL, F.: 'Microstrip handbook', ELAB Report STF44 A74169, Trondheim, Norway, Feb. 1975 18 BAHL, I., and GUPTA, K.: 'Average power-handling capability of microstrip lines', IEE J. Microwaves. Optics & Antennas, 1979, 3, pp. 1 4 19 VANDESANDE, J., PUES, H., and VAN DE CAPELLE, A,: 'Calculation of the bandwidth of microstrip resonator antennas'. Proc. 9th European Microwave Conf., Brighton, Sept. 1979, pp. 116-119 20 LO, Y., SOLOMON D., and RICHARDS, W.: 'Theory and experiment on microstrip antennas', IEEE Trans., 1979, AP-27, pp. 137-145 21 DESHPANDE, M., and BAILEY, M.: 'Input impedance of microstrip antennas', IEEE Trans., 1982, AP-30, pp. 645-650 22 NEWMAN, E., and TULYATHAN, P.: 'Analysis of microstrip antennas using moment methods', IEEE Trans., 1981, AP-29, pp. 47-53 23 PUES, H., and VAN DE CAPELLE, A.: 'Computer-aided experimental characterisation of microstrip-to-coaxial transitions'. Proc. 14th European Microw. Conf., Litge, Sept. 1984, pp. 137-141 24 PUES, H., VANDENSANDE, J., and VAN DE CAPELLE, A.: 'Broadband microstrip resonator antennas'. Int. IEEE/AP-S Ant. &Prop. Symp. Digest, Washington, May 1978, pp. 268-27 1 25 PUES, H., VAN LIEBERGEN, H., THISSEN, L., NAUWELAERS, B., and VAN DE CAPELLE, A.: 'Broadband multi-layer microstrip antenna'. Proc. MIOP '87 Conf., Wiesbaden, May 1987 26 VAN LIL, E., and VAN DE CAPELLE, A.: 'Transmission line model for mutual coupling between microstrip antennas', IEEE Trans., 1984, AP-32, pp. 816-821 "' NAUWELAERS, B., VAN DE CAPELLE, A,: 'Formulas for the calculation of mutual coupling between rectangular microstrip antennas'. Proc. Int. Conf. Ant. & Prop., April 1985, Coventry, pp. 99-102 JEDLICKA, R., and CARVER, K.: 'Mutual coupling between microstrip antennas'. Proc. Workshop on Prmted Circuit Antenna Technology, Las Cruces, pp. 4-114-19, Oct. 1979 POZAR, D.: 'Input impedance and mutual coupling of rectangular microstrip antennas', IEEE Trans., 1982, AP-30, pp. 1191-1 196 HARRINGTON, R.: 'Time-harmonic electromagnetic fields', (McGraw-Hill, NY, 1961) PENARD, E., and DANIEL, J.: 'Mutual coupling between microstrip antennas', Electron. Leu., 1982, 18, pp. 605-607 MALKOMES, M.: 'Mutual coupling between microstrip patch antennas', Electron. Lett., 1982, 18, pp. 520-522 DANIEL, J., VAN DE CAPELLE, A,, and FORREST, J.: 'Microstrip patch arrays for satellite communications'. ESAICOST 204 Phased Array Antenna Workshop, ESTEC, Noordwijk, June 1983, pp. 9-14
Chapter 11
Design and technology of low-cost printed antennas J.P. Daniel, E. Penard and C. Terret
11.1 Introduction
In the last decade printed-array antennas have received increasing attention for applications in various communication and navigation systems. Microstrip patches can be very efficient candidates for inexpensive antennas when narrow bandwidth (typically less than 5%) and medium gain are required (15-25 dB). However, divergence in substrate parameters and manufacturing tolerances means that a wider frequency bandwidth and a better control of radiation characteristics are necessary in the mass production of printed antennas. Thus simple but accurate investigations of radiating elements are necessary to obtain the design requirements. Analysis of normal-shaped patches and slots can be developed using both known models (transmission-line or cavity models) or more elaborate theory (spectral-domain-apprbach). On the other hand, the design of planar arrays requires a thorough knowledge of typical properties of printed linear sub-arrays such as directivity versus spacing, mutual-coupling effects, losses etc; for this purpose, simple formulas and analyses have been developed. Two-dimensional arrays, with non-identical sub-arrays, such as cross-fed structures, are well suited for low-cost antennas. Design equations and curves are included. Microstrip patches exhibit different E-plane and H-plane radiation patterns; analytical synthesis methods (Fourier, Chebyshev etc.) are not always suitable for a small number of sources or when the pattern is specified by a given outline. Two new numerical synthesis methods, taking into account the directivity pattern of sources with equal or unequal spacings, are proposed. Numerical programs can be implemented on conventional personal computers. Cost reduction will necessitate common microstrip laminates or new polymer substrates exhibiting good mechanical and electrical properties (typically a low dielectric constant of about 2-2.5 and losses of tan6 z A new low-cost polypropylen! whose fabrication process is quite simple has been developed at
580
Design and technology of low-cost printed antennas
CNET Lannion, France. This substrate can be made as a multi-layer structure or with thick metal backing.
11.2 Analysis of simple patches and slots The microstrip antenna designer needs a method of analysis (not too time consuming) to calculate, as nearly as possible, the parameters of interest: resonant frequency, Q-factor, input impedance, pattern etc. Moreover, he should be able to evaluate the surface-wave effects and to take into account the superstrate applied to the antenna as a protective layer.
581
Design and technology of low-cost printed antennas
OMA with four magnetic walls (as in Fig. 11.1~) HMA with three magnetic walls and one electric wall (as in Fig. Il.lb) The treatment considers perfect magnetic or electric walls and groups all antenna losses together in an effective dielectric loss tangent determined by an iterative process (Fig. 11.2). In this process it is necessary to calculate the electric and magnetic energies We and 4,stored in the cavity.
11.2.1 Rectangular and circular patches Two simple techniques can be used for the analysis of microstrip antennas: transmission-line model [ I , 2, 31 and cavity model. More sophisticated analysis will be presented for multi-layered structures. 11.2.1.1 Cavity-model analysis: Cavity-model analysis [4] allows modal field description and gives good results depending on the effective parameters obtained from previous microstrip line formulas, as long as the substrate thickness is thin compared with the wavelength. This method has often been used with magnetic walls to calculate the electrical properties of open microstrip antennas (OMA) with simple shapes [5, 61 (cf. Chapter 3). Its application to the rectangular hybrid microstrip antenna (HMA) [A permits a comprehensive comparison between OMA (Fig. 1 1 . 1 ~and ) HMA (Fig. I l.lb) antennas [8]. It can also be easily applied to multi-port microstrip antennas [9, 101. In the cavity method, according to the Lo and Richards model, the total interior field with a unit z-directed excitation current at (x,, xo) is given by
(b) Fig. 11.I (a) OMA with four magnetic walls. (b) H M A with three magnetic walls and one electric wall
with
J,(x)
=
sin (x) X
km, is the wave resonant number. The eigen functions $ ,, are solutions of the Helmholtz equation with different boundary conditions:
These quantities are, of course, evaluated by integrating the electric E and magnetic H fields over the cavity volume V. In fact, the exact expression of We and Wh can be obtained in a very simple manner without performing any integration at all, as explained in the following [I I]. The total power P i s injected into the cavity as P
=
VIT = V = -tEl(xo, yo)
(1 1.2)
where V is the voltage at the source point. On the other hand, the same power
582
Design and technology of low-cost printed antennas
Design and technology of low-cost printed antennas
583
can be expressed as a function of W, and W,: Which leads to the following relationships:
Read :
Where Re and Im stand for real and imaginary parts, respectively. Note that is determined without using the H field. Eqns. 11.4-11.5 are obtained independently of the mathematical method employed to derive the expressions for the ELfield or of the geometry of the cavity section, i.e. the patch shape. Thus eqns. 11.4 and 11.5 are general formulas valid for planar microstrip antennas of arbitrary shape. However, the cavity thickness t must be quite small in order to ensure the validity of expression 11.2. compared to ,Ie The analysis yields input impedance, resonant frequency and Q-factor; the radiation pattern is found from the knowledge of the interior field. Two methods are available:
w,
(a) Electric-current method The radiated field is found from the electric currents J, flowing on the patch and on the electric walls. If there is a dielectric, volume polarisation currents J, must be added to the cavity region (Fig. 11.3) [12, 13, 14, 151.
I
0
/
ground plane
5-
b
Y
Fig. 11.3 Electric currents and polarisation currents in an HMA
Far f i e l d Ee,EO calculation
Far f i e l d keep
(+\ Fig. 11.2 Flow chart of the cavity method
(6) Aperture-radiation method One application of the equivalence theorem [16] is to choose a perfect closed electric surface S with null field inside and equivalent magnetic sources outside: M, = E x n; n being the normal outward from S. S defines the limit of an homogeneous exterior medium and must be carefully selected. As the rectangular OMA structure has been extensively described, only the HMA is considered here; e.g., the choice of S for HMA is indicated in Fig. 11.4. The surface S, around the cavity (Fig. 11.4~)is not permitted, except in the case of a vacuum medium ( E , = 1). It seems more convenient to choose S, (Fig. 11.4b) lying on the z = t plane, because it is always available whatever the medium, i.e. E, = 1 or E, # 1. In practice, electric walls are not perfect conductors, but the electric-field distribution in the vicinity of the electric wall (Fig. 11.4~)suggests that antenna radiation occurs mainly from the magnetic walls. This assumption is well confirmed by experiment. It may be assumed that HMA radiation is entirely due
584
Design and technology of low-cost printed antennas
Design and technology of low-cost printed antennas
to the magnetic walls, i.e. three-slots array. Experimental and theoretical results for an HMA are given in Fig. 11.5. The impedance loci in the case of the dominant mode (0, 1) are given in Fig. 11.5~.All the modes have been taken into account in the computation. The antenna was edge-fed by a coaxial-line probe at a position x, = 3.5cm, yo = 0. Two methods were used for the radiated field (equivalence theorem and electric current plus polarisation current) and both agree well with experimental data. The experimental patterns in planes 4 = 0' and 4 = 90" are plotted in Figs. 11.56 and 11.5~.
wall
C
\
electric w a l l
ground plone /
Fig. 11.4 Application of the equivalence theorem to HMA a First choice of surface S, b Second choice of surface S2 c Local geometry of the electric field of an HMA near the shon circuit
The uniform aperture lying along the Ox-axis gives an omnidirectional pattern in the plane 4 = 90' (Fig. 11.5c), the cross-polarisation level being very low ( < 30dB). The discrepancy between the patterns computed from the electric currents alone (broken line) and from the aperture (large broken line) appears clearly in this Figure; it confirms the importance of the dielectric slab. Polarisation currents must be included in the far-field calculation. They are z-directed and therefore contribute only to the E, components. Therefore, the electriccurrent approach gives a useful physical insight into the radiation properties, particularly regarding the major influence of the dielectric constant on the E, component.
b
-60 -30 0 30 0 , degrees
60 c
-60 -30 0 30 60 0 , degrees
Fig. 11.5 Experimental and theoretical results i n the case of an HMA a = 6.00cm. b = 4.00cm, 8, = 2.56 t = 0.146 crn, tan 6 = 0.001, mode(0, 1) (a) Impedance loci Feed point xo = 3,5cm, yo = 0 0-0 experiment 0 magnetic currents X electric currents and polarisation currents (b) Plane 4 = 0" -experiment ---- theory (c) Plane 4 = 90" -experiment ---- theoretical pattern: electric currents only --- theoretical pattern: magnetic-currents method
585
586
Design and technology of low-cost printed antennas
In the plane 4 = 0°, the radiated field of the two slots lying along the y-axis leads to a high level of cross-polarisation radiation with a null in the broadside direction (the magnetic currents are each 180" out of phase). The diffraction [17] at the edge of the ground plane appears particularly in the oscillations of the principal component E, in the planes 4 = O0 (notably for 0 = 30' and 0 = 90"). Nevertheless, the theoretical results are again well confirmed by experiment.
a
-60 -30 0 30 8 . degrees
60 8,degrees
Fig. 11.6 Experimental and theoreticalpatternsin for the HMA with one electrical wall a = 6.00 cm, b = 4.00cm. &, = 2.56, t = 0.148 cm, mode(1 .l) -experiment ---- theory (a) Plane 4 = 0" (b) Plane 4 = 90"
The high-level cross-polarisation can be reduced when the exciting mode is (1, I). The radiation pattern in the 4 = 0" plane (Fig. 11.6~)is therefore due to an array of two slots directed along the y-axis and has a cosine field distribution. The cross-polarisation due to the x-slot is smaller than for mode (0,1) because of the phase inversion along the x-apertures, and is cancelled in the plane 4 = 90" (Fig. 11.6b, theoretical results only). The important reduction of beamwidth is worthy of note here. Feedposition: As in the OMA case, it is possible to match the HMA by properly selecting the feed position along the y-axis. When considering the dominant mode alone and its resonant frequency (given by k2 = k2mn), the input impedance Z(= R, j&), which becomes real at resonance, can be simply expressed as a function of the feed position xo,yo. For the HMA with one electrical wall
+
where R,(O, 0) is the input impedance for xo = 0, yo = 0 (corner feed). For example, in the case of the one-electric-wall antenna and the mode (I, I),
Design and technology of low-cost printed antennas
587
588
Design and technology of low-cost printed antennas
Design and technology of low-cost printed antennas
the impedance loci are given in Figs. 1 1 . 7 ~and 11.76 for two feed positions xo = 3.5 cm, yo = 0 and xo = 4.5 cm, yo = 0 . It can be seen that the impedance decreases as the feed moves along the x-axis toward the centre of the edge. The discrepancy between measurement and the theoretical results is due first to the experimental error in the feed position and secondly to the feed model, which does not take into account the disturbance of the internal field distribution near the probe. ( c ) Comparison between HMA and OMA characteristics The different parameters, Q-factor, input impedance and radiation patterns of the OMA and the HMA, can be compared for the same electrical dimensions. Both act in the dominant mode (0, 1 ) and at the same resonant frequency. The wave number ko in free space is given by
Table 11.1 Comparison of theoretical impedance and Q-factor HMA Experiment
OMA Theory
Experiment
Theory
Table 11.2 Comparison of cavity method with Woo& method [7] OMA Wood
f,,
MHz AJ MHz
1275 26
HMA Cavity method 1257.2 22.4
Wood
Cavity method
12750 22.5
1278 23
'
with b' the OMA dimension along the y-axis and b the HMA dimension along the y-axis; therefore b' = LJ2 and b = 6,/4 (A, is the wavelength in the dielectric). Vacuum medium, E, = 1: The theoretical impedance and Q-factor are compared in Table 11.1 with experimental data for both antennas. In this case the Q-factor of the HMA is smaller but the impedances have approximately the same value. The slight discrepancy between experiment and theory is due to the failure of the magnetic-wall model when E, = 1.
589
590
Design and technology of low-cost printed antennas
Design and technology of low-cost printed antennas
591
Dielectric medium case, E, = 2.5: Theoretical results for the bandwidth and resonant frequency are compared with Wood's measurements [7] in Table 11.2. There is an important difference compared with the previous case: here the bandwidths of the two kinds of antenna are very similar. (d) Theoretical results for different antenna lengths all, Q-factor, input impedance: In Fig. 1 1 . 8 the ~ variation of the input resistance at resonance for the HMA and OMA is given as a function of the parameter all, for E, = 1 and E, = 2.1. The Q-factor variation is given in Fig. 11.8b; for all the different cases considered it can be concluded that, for E, = 1 the Q-factor of the HMA is lower than that of the OMA (the bandwidth is therefore larger). However, the impedances of OMA and HMA are very similar. For E, = 2.1 the HMA and OMA have approximately the same Q-factor (and therefore the same bandwidth), but the input impedance of the HMA is twice that of the OMA. These important differences between the vacuum medium and the dielectric medium can be explained by the contribution of the polarisation currents. Their effect should be more important for the HMA than for the OMA owing to the cosine distribution of the internal field, which has no change of phase along the y-axis (Fig. 11.4~).For a full comparison of the two antennas, the cross-polarisation level must also be considered. Cross-polarisation level as a function of all,: Theoretical results are given in Fig. 11.9 in the plane 4 = O0 for different values of 0 (0 = 20°, 60') and for E, = 2.1. The cross-polarisation Cp is defined here by
It may be seen that, for the HMA, the cross-polarisation remains very high, and therefore this antenna is not suitable for use in an electronically scanned array (except when very small scanning angles are used). In conclusion, the HMA is shorter (lJ4 long) than the OMA (lJ2 long), each having the same resonant frequency for the mode (0, 1). A closer comparison of these two kinds of antenna shows that the dielectric plays a fundamental role in the far-field pattern, the input impedance and the bandwidth. When E, = 1, the impedance of the HMA and OMA have the same values, whereas the HMA bandwidth is twice as broad. On the other hand, with the usual dielectric (E, = 2), the bandwidths have the same value, but the impedance of the HMA is twice that of the OMA. 11.2.1.2 Spectral-domain approach (SDA): As the frequency of operation is
increased, more complex analyses are necessary to rigorously account for the effect of the dielectric substrate, which may couple surface waves. Recently, quite efficient approaches based on integral formulations and numerical resolu-
Fig. 11.9 Comparison of the cross-polarisat~on level of the OMA and HMA for different values of & / a . Results are given for the plane q5 = 0" a OMA 0 HMA ---- E, = 1 -E, = 2.1 ( a ) 8 = 20" ( b ) 0 = 60"
592
Design and technology of low-cost printed antennas
tions were proposed [18-231. These methods use the exact Green's function for the grounded dielectric slab, and hence the results depend on the numerical techniques used to calculate these functions accurately.
Design and technology of low-cost printed antennas E; = E,E,,
593
(i = 0, 1, 2) is the complex permittivity yf = a2 + f12 - k;; k, = E,, ki = W ~ ~ , , & E , ;
(a exp jut time variation is assumed) (a) Resonant frequency and quality factor Among these approaches, the SDA [20] is particularly suitable for determining the resonant frequency and Q-factor of patch antennas embedded in dielectric substrates. The structure and the co-ordinate system employed are shown in Fig. 11.10. In SDA, the Fourier transform of the dielectric field E,(a, P), E,(a, P) at 2 = d, in region 2 is related to the current distributions J,(a, P), J,(a, P) on the
The zeros of dte and dtm define the surface-wave poles in the composite layer, the dominant mode of which, TM,, is always above cut off regardless of slab thicknesses. The matrix M can easily be obtained in terms of an equivalent transmissionline circuit as presented in Fig. 11.11, by generalising the method of Reference 20. Using the moments method and a modal representation of J, a matrix equation is derived:
where the elements of matrix K are given by double integrals on a and P. With the transformation a = kQsin 8, /I= k, cos 0, we have, for example
0 is only satisfied by a complex frequency f = f ' + and the quality factor Q = f ' / 2 f nof this radiating open resonator. In this free regime, ki is complex with Im [k,] > 0, and a proper Riemann surface must be defined for evaluation of yi = ($ k f ) ' I 2 . The sign of y,, y, does not affect the value of the integrals, as the terms involving the radicals are even functions of y,, y,. For this reason, only the branch-cut contribution by the radical yo has to be considered, the branch cuts being shown in Fig. 11.12. It can be shown that this condition involves an integration path in the kQcomplex plane and not only on a real axis as in Reference 20. Furthermore, it is worthy of note that the surface-wave poles lie within the range k, + max [k,, k,]. A possible position of an integration path in the kQ-planeis shown in Fig. 1 1.12, with A % Im [k,], taking into account the presence of the poles. In Table 11.3 and Fig. 11.13, the present method of analysis is compared with available theoretical and experimental results on resonant frequency and quality factor.
The condition det [K]
=
6'that ' leads to the resonant frequency f'
Fig. 11.10 Patch antenna with dielectric layer d, = protective dielectric-layer thickness d, = dielectric-substrate thickness (W, I) = width and length of the patch
conducting patch by
'
ws, dte dtm ~ ( y , . 4 ) [ 8 ] where y, is the propagation constar~tin the z-direction in the i t h region and
594
595
Design and technology of low-cost printed antennas
Design and technology of low-cost printed antennas
Generally, the resonant frequency& of a microstrip antenna is defined as the frequency giving the input reactance X equal to zero. For electrically thin substrates,& is also very close to the frequencyS, where the input resistance R Table 11.3 Measuredandpredicted f, and O of a rectangular patch antenna: TM,, and TM,, modes
&
Method
Q
A
102.7 112 105 97 10
2.2616 2.272 2.3 2.237
TM 10 SDA [24] Cavity [25] Dubost [3] EXP 1251 W = 60 mm; 1
1.5458 1.548 1.52 1.53 = 40 mm;
d,
Q TMo,
*
= 1.46 mm;
E,
= 2.56;
tg A,
=
44.68 47 36.2 44 6
+-
lo-' (d2 = 0)
Table 11.4 Comparison between the present method and results predicted by Bahl[26] "
T.M. woves
T.E.waves
f, GHz
Q
SDA
4.092
33.68
Experience
4'1 04
SDA
3.986
Experience
4.008
SDA
3.9336
Experience
3.934
SDA
3.8767
4 (mm)
Fig. 11.11 Trahsmission-linemodel in the spectral domain
(%) 0
0 0 34.52
2.62
0.8 2.34 33.49
3.9
1.59
4.14 31.82
5.09
3.18
Experience W = 19mm; I = 22.9mm; dl = 1.59mm; e,,
f,
'
\
Fig. 11.12 Branch-cuts position and path integration in the k, plane
=
'
f* -
f#
f,
3.895 =
5.09
2.32 tg A, = lo-'; e,, = 2.32; tg A, = lo-'
= resonant frequency without protection
reaches a maximum, R,,,. In coaxial-feed excitation, as the substrate thickness increases,& lies farther fromf, owing to an inductive shift of the reactance curve. Furthermore, the bandwidth, defined in terms of impedance, is affected by this inductive shift. In order to remove the disturbance of the feed, and to compare measured and predicted results, the resonant frequency and Q-factor were taken
596
Design and technology of low-cost printed antennas
Design and technology of low-cost printed antennas
597
and
It should be noted that the SDA method gives
f
=
f' +JY"
with
The effect of a protective layer on the resonant frequency and Q-factor of a rectangular microstrip antenna is shown in Table 11.4. In this case the Q-factor varies slightly, while the resonant frequency clearly decreases. Additional experiments were carried out on a rectangular patch antenna for several different thicknesses of superstrate and three different values of the superstrate dielectric constant: E,, = 2.17, 2.55 and 3.6. The results are presented in Fig. 11.13. It should be noted that, for d J l , < 0.015, the theoretical Q-factor increases slightly. This corresponds to a better matching of the antenna to free space and a maximum efficiency of radiation. As d, increases, so does the coupling of energy with the superstrate by the surface waves, and radiation efficiency decreases while the bandwidth increases. It is worthy of note that, for a given thickness, Af,/A and bandwidth increase with increasing E,,. ( b ) Input impedance The input impedance can be determined using Richmond's reaction equation in spectral domain. If the real axis is used as the integration path, the residue contribution of the surface-wave poles has to be taken into account [21]. In our approach this is avoided by using the previous integration path in the complex plane (Fig. 11.12). Fig. 11.14 shows our theoretical results compared with those of Bailey et al. for an antenna without (with) dielectric cover. Fig. 11.1 3
(a) Effect of dielectricloading on resonant frequency and Q-factor of a rectangular microstrip antenna I = 22.9 rnrn, W = 19 mm, E,, = 2.1 7, dl = 1.58 rnrn tan A, = 6.0 x 10-4, 6 , = 2.17, tan A, = 6.0 x 10-4 (b) Effect of dielectric loading on f, and Q-factor of a rectangular patch antenna 1 = 22.9 mm, W = 19rnrn. E,, = 2.1 7, dl = 1.58 rnrn tan A, = 6.0 x 10-4, E, = 2.55, tan A, = 10-3 (c) Effect of dielectric loading on f, and Q-factor of a rectangular patch antenna I = 22.9rnrn. W = 19 mrn, E,, = 2.1 7, dl = 1.58rnrn tan A, = 6.0 x lo-', ,&, = 3.6,tan A, = 2 x 10-3
598
Design and technology of low-cost printed antennas
599
Design and technology of low-cost printed antennas
(c) Radiation efficiency [27, 281 The SDA can also be used to calculate the influence of surface waves on the radiation efficiency of a rectangular patch antenna. Once the problem is solved for the resonant frequencyf,, far-field radiation may be obtained by using the inverse Fourier transform. Hence the electric-field components in each point of
region 0 are given by
.
q
=
x
(Z
(x, Y , Z)
- d)) exp (- j(ax
(d2
=
+ by) dadp
0,d, = d )
with yo = ,/a2
+ j2- GRe[yO] > O,Im[yo] > O,ko = 0&(11.13)
and w real. To compute the far field, eqn. 11.13 is first transformed into spherical coordinates and secondly transformed to specify the (a, b) plane in terms of a spherical-polar angle (u, v). Branch points of yo have thus disappeared, and the resulting integral can be evaluated by the saddle-point method, provided that the contribution of the integrand poles is correctly taken into account. The integral along the steepest-descent path corresponds to the space-wave component, while the summation of the residues of these poles is related to the TM- and TE-mode surface waves. Only the dominant lowest-order TM mode which may be excited for the usual values of d/loand E, has been considered here. After integration, the electric far field may be expressed as
I
where Eel,Emland E,, are expressions for the space and surface waves, respectively. Note that the space-wave components are the Fourier-transformed interface (z = d ) fields, and may be expressed as
I
Eel a sin W& ,,
B)
+ cos 4E&,
Em,a cos O[cos 4EN(a, 8)
b)
- sin q5Ed(a,
(11.15) p)]
with a = kosinOcosq5
p
= kosinOsin+
The efficiency of space-wave launching can be calculated as the ratio of radiated power P, to total (radiated plus surface-wave) power: Fig. 11.14 Input impedance of microstrip antenna without (with) dielectric cover compared with Bailey's results (Reference 2 1 ) 9--0 Bailey et a/. X X Our results A-A Bailey eta/. 0 0 Our results
with
600
Design and technology of low-cost printed antennas
zo = Q
=
Jmand
5,
rsin9
pole in the 5 plane
=
d m -=
k,sinup
E, having been deduced from EC Furthermore, the gain may be defined by
Fig. 11.15 Radiation efficiency and gain against dl& for rectangular patch antenna W = l 5 m m ; I = 10mm. d = l.58mm. E, = 2.35, f, = 8.58GHz
601
Design and technology of low-cost printed antennas
11.2.2 Conical antennas In some cases, the narrow bandwidth of microstrip patch antennas continues to be the main constraint. The widest bandwidths are likely to be achieved with thicker substrates 1301, but higher modes and surface waves are limiting factors. Replacing a conventional circular disc by a solid conical patch of the same radius, a new type of 'microstrip antenna' [31] is obtained. This structure
grouhd plane
Fig. 11.16 Microstrip patch antenna with a truncated dielectric layer of radius a
Fig. 11.15 shows numerical results for q and G against dielectric thickness d normalised to 1, for a rectangular patch antenna fed along the x-direction. An optimum value of gain for d x 0.151, with q x 95% is observed. For d > 0.151, the increase of P, causes a slight reduction of the gain, but the first TE-mode surface waves excited for d x 0.2161, are not considered here. Identical results have been obtained for microstrip disc antennas [27] for large values of dielectric constant.
0 (degrees) 0" 7.
(d) Surface-wave effects on radiation patterns [24, 28, 291 Radiation into the horizon: The radiating Eipfield for printed antennas with an infinite dielectric layer tends to zero along the horizon (9 -+ n/2). However, in many cases the dielectric layer should be considered truncated after a certain distance a (Fig. 11.16), and the surface waves radiate some of their energy when they reach this discontinuity. If the radius a is sufficiently large, the far-field E, of the surface wave may be used to calculate the corresponding far-field E,". Fig. 11.17 shows the radiation pattern in the E-plane ( 4 = 0") for the total (Eip E,") electric field of the rectangular patch antenna with a truncated dielectric radius a x 3.51,. Note that, for 9 = 90°, the far field is due only to the components of the surface wave. In the H-plane ( 4 = 90°), ET = 0, and the total field varies as cos 0.
+
Er
Fig. 11.17 Radiation pattern in the E-plane for the total electric field E, = EiP + of a rectangular patch antenna with a truncated dielectric layer W = 1 5 m m . I = 1Omm. d = 1 . 5 8 m m , ~= , 2 , 3 5 , f , = 8 3 8 G H z , a = 3.51, ---- Theory -Experiment
facilitates radiation owing to better matching of the internal field of the microstrip cavity to free space, and it provides a broader bandwidth 1321. 11.2.2.1 Resonant frequency: The cavity model is applied to the volume bounded by the ground plane, the cone surface and the spherical magnetic wall
602
Design and technology of low-cost printed antennas
Design and technology of low-cost printed antennas
603
(Fig. 11.18). By analogy with the circular disc, we can define an effective spherical radius Re given by
where 8, and a are, respectively, the angle and the base radius of the conducting cone, and E, is the relative dielectric constant. The fields within the cavity corresponding to radial TEw-modes may be derived from a scalar electric potential $(r, 0, 4) which must satisfy the wave equation
where k
= wfi.
Table 11.5
Theoretical and experimental resonance frequencies of the
TE,, -mode for several values of 0, and E,
1 74O
&,
80
1 85'
2.1 72'
2.1 75'
J
(GHz) (theoretical)
For 0, near 212, applying boundary conditions on the conducting walls, $ can be written as w , 0, 4 )
$z 2
Jm+
112(kr) cos m 4
is the Bessel function of the first kind and where J,+ll,
Then the resonance frequency can be obtained from the boundary condition on the magnetic wall:
The radiating mode of interest is the TE,,-mode corresponding to a, x 0.618. Solving eqn. 11.21 numerically, we find
604
Design and technology of low-cost printed antennas
Design and technology of low-cost printed antennas
605
where c is the velocity of light in free space. In Table 11.5 the theoretical and experimental resonance frequencies of the TE,,-mode are presented for several values of 0, and E,; the radius of the cone base is fixed at 18.5mm, while the substrate thickness is h = 6 mm. 11.2.2.2 Quality factor: The resonant frequencies, Q-factor and corresponding bandwidth ( B W ) of conical-patch and circular-disc antennas with the same parameters a, and E, are given in Table 11.6. It should be noted that in an air-dielectric (e, = I), the same conical patch leads to: f, = 4-86GHz, Q = 5 and a BW 20%.
Table 11.6 Resonant frequencies and bandwidths of conical-patch and circular- disc antennas
Antenna Disc Conical structure
Fig. 11.19 Input-impedance locus of matched conical patch antenna
Fig. 11.20 Radiation pattern of a conical patch with two excitations
11.2.2.3 Irnpedancernatching: As the substrate is relatively thick (h z O.lR,), the effect of the feed probe introduces an effective reactance and causes a clockwise rotation on the Smith chart of the input impedance seen at the feed port. An open coaxial transmission line situated inside the conducting cone
provides series-reactance compensation of the feed probe. Furthermore, by shifting the probe away to a, = 10mm, we obtain the curve of Fig. 11.19 and a bandwidth (VSWR < 2) of 12%.
606
Design and technology of low-cost printed antennas
11.2.2.4 Radiationpatterns: They are found to be relatively stable for linear polarisation over a wide-frequency range. Dissymetries in the E-plane and cross-polarised components in the H-plane, due to the generation of higher modes, can be suppressed as usual by using two radially opposite feed probes (Fig. 11.20). The necessary 0-180' phase difference can be obtained with a rat-race (3 dB coupler). 11.2.2.5 Circularly polarised conical-patch antennas: It can be observed in Fig. 11.20, contrary to the case of the classical disc antenna, that the patterns are identical in both E- and H-planes. Thus, by feeding the conical patch as shown in Fig. 11.21, a good broadband, circularly polarised antenna can be realised. The axial ratio versus elevation angle 0 is presented. It can be concluded that flat conical-patch antennas are more advantageous in some respects than traditional microstrip antennas. Infact, they present a broader bandwidth, and their structure lends itself to a simple way of impedance matching. 'Moreover, they are well adapted to circular polarisation.
0;
I0
o:
a.
410
9 degrees Fig. 11.21
o:
6b
Design and technology of low-cost printed antennas .electric field lines,
I
groun plane
icrostrip conductor
\ dielectr~csubstrate
a
Fig. 11.22 (a) and (b): Printed slot fed by a microstrip line at first resonance and second resonance
rb
Axial ratio of a microstrip conical patch measured at 3.5GHz versus elevation angle 6
11 J.3 Linear and annular slots Printed slots have received somewhat less attention than patch antennas in array design, since care must be taken to suppress undesired modes such as the parallel-plate mode excited between the ground planes in a typical stripline-fed slot 133-351. However, the feeding and matching techniques remain very simple. 11.2.3.1 Linear slot [36, 371: A microstrip line offers the possibility of
607
radiating slot
Fig. 112 3 VSWR versus OIL of M S A at first resonance L = 13cm F = 1.15GHz
XXXX
L = 15.5cm F = O.94GHz
000
L = 9cm
F = 1.53GHz
+=4.4
w=5.0mm
h=ll.6rnm
608
Design and technology of low-cost printed antennas
feeding the slot antenna at the first or second resonance without excessively disturbing the field distribution in the slot (Fig. 11.22). The strip conductor is connected through the dielectric substrate to the edge of the slot.
Design and technology of low-cost printed antennas
609
Table 11.7 Bandwidth at resonance I st resonance 2nd resonance
BW = 14% for L/2W E 16 B W = 20% for 10 < L/2W < 19
Fig. 11.24 Radiating slot length normalised to A, versus frequency measured at the first and second resonance W = 5mm. E, = 4.4, h = 1.6mm X X X first resonance 000
second resonance
Fig. 11.25 Influence of W on the first and second resonant length of a MSA W = 5 mm, 6, = 4.4, h = 1.6 mm X X X first resonance 000
second resonance
A good match to the 50R microstrip line can be obtained by choosing a centre-fed slot or an offset-fed slot for second-resonance or first-resonance operations, respectively. Fig. 11.23 gives the VSWR of the microstrip slot antenna (MSA) at first-resonance operation as a function of D/L, where L is the
Fig. 11.26 Input impedance of MSA fed by a microstrip line versus L/1,at different frequencies [40] W = 0.6 mrn, E, = 2.1 7, h = 0.8mrn
610
Design and technology of low-cost printed antennas
length normalised to I, of the slot of width W 1,. D is the distance between the centre of the strip conductor of width W, and the small side of the slot, and I, is the free-space wavelength. From the Figure it can be seen that the slot is matched to the feed line for D/L % 0.25. Fig. 11.24 shows the length normalised to 1, of a radiating slot of 0.5cm width, measured at the first and second resonance, versus frequency. The influence of the width W o n the first- and second-resonant length is shown in Fig. 11.25. At the first resonance L = 0.491,, where I, is the free-space wavelength, while at the second resonance L increases with L/2 W. These variations are identical to those obtained for a cylindrical dipole [38, 391. For the previous slot antennas, an optimum value of bandwidth (VSWR < 2) has been obtained (Table 11.71.
Design and technology of low-cost printed antennas
61 1
11.2.3.2 Annular slots (Fig.11.28) ( a ) Model of an annular slot (without reflector plane) [46]: Analysis of radiating slots has been developed using a lossy transmission-line model (Fig. 11.29); it requires the computation of a propagation constant a j p and a characteristic impedance Z,. and Z, are obtained using Cohn's method [47], and a is the solution of the numerical equation P,(a) = P,(a) where P, (a) is the power delivered to the lossy loop and P,(a) is power radiated from the annular slot.
+
annular slot on rnetalllc Dlane
ground plane
reflector plane (distance = d ' )
Fig. 11.28 Printed annular slot above a reflector plane
coplanar waveguide
Fig. 11.27
Printed slot fed by co-planar waveguide
The large bandwidth obtained at the second resonance is due to the weak variation of the input impedance of the MSA, as shown in Fig. 11.26 [40]. Despite various attempts, an exact theoretical study of the input impedance of the MSA with limited ground plane does not really exist [34, 411. An expression for the complex admittance at the first resonance of a radiating slot in the ground plane of a microstripline was found by Das [42] from the complex radiated power and discontinuity in the modal voltage. The concept of a complementary dipole [43] in an uniform medium of effective permittivity 8, = 2&,/(1 + E,) has been used to calculate the radiated power. Experimental studies have been carried out over the frequency range 0.82 GHz using a 5 0 n coplanar waveguide [37] (Fig. 11.27); a bandwidth (VSWR < 2) of about 30% has been obtained. Nesic [44,45] used coplanar-fed slots in primary radiators in a phase-scanned antenna.
Fig. 11 2 9
Transmission-line model of the annular slot
(ai) Guided wavelength and impedance [ 4 8 ] Theory: To date, no result of Cohn's method for calculating the slot parameters on a low-permittivity substrate has appeared in the literature. The use of Cohn's formula, for magnetic walls parallel to the slot and a relative permittivity of 217, gives the ratio of guided wavelength, ,If2,, to wavelength in free space, 1, and
612
Design and technology of low-cost printed antennas
Design and technology of low-cost printed antennas
the characteristic impedance defined in Reference 47. The results of computation are plotted in Fig. 11.30 in the manner they were presented earlier. A simple formula for &/A has been found like that in Reference 51:
613
[52]. Comparison of that method with theoretical results obtained by the spectral-domain technique in a recent paper [49] gives good agreement as shown in Table 11.8.
Fig. 11.31 Resonant-ring transmission-line model
a
b
Fig. 11.30 (a) & / A versus d l l and w l d (b) Characteristic impedance versus d l l and w / A e, = 2.17
Table 11.8
Some theoretical results of A,/A Cohn's method
Frequency
@Hz) 2 2.5
30 3.5
(from Reference 49) and
Cohn's method
Spectral-domain technique [4]
0.8890 0.8840 0.8796 0.8756
0.8885 0.8834 0.879 0.875
Fig. 11.32
The following set of parameters is considered: E,
= 2.17
0.01 0.01
< wld < 2.0 < d/A < 0.1
The previous formula fits the theoretical results with better than 2% accuracy. The upper limit of d / l corresponds to appreciable excitation of surface waves
Theoretical and experimental results for guided wavelength for slots of different width w d e x p e r i m e n t (6, = 2.17, substrate thickness = 0.78mm) ---- theory
Experiment: Experiments were carried out to verify Cohn's method. The meth-
od of the resonant slot ring was chosen, because it has given very good results on substrates of higher permittivity ( E , = 9.6) [SO]. Three rings were etched. The outer radius of the rings was equal to 38 mm. The measured widths were 0.3, 0.99 and 3.3 mm. The thickness of the substrate was 0.78 mm and the relative
614
Design and technology of low-cost printed antennas
dielectric constant was 2.17. Measurements were performed on an automatic network analyser HP 8510. The output and input lines were cut until the signal level weakened at about - 40 dB below the reference set to 10 dBm (Fig. 11.3 I).
Design and technology of low-cost printed antennas 0
615
P,is the power delivered to the lossy loop (analytically known) P, is the radiated power.
then a is the solution to the equation It will be noticed that P,increases with a while P,decreases; thus the solution is unique. An example is given in Fig. 11.33; the loop was designed at X-band from the dimensions given in Fig. 11.33. The variation of a near the resonant frequency is plotted in Fig. 11.34, and it appears that a has a linear variation.
dielectric -thickness
- er=2.17
Fig. 11.33 a solution of P,(a)
=
P , (or) for X-band annular slot
The difference between the theoretical and experimental curves of Fig. 11.32 is due to ohmic, dielectric and radiation losses. In the case of a slot on a dielectric substrate of low permittivity, the radiation loss is important: it increases when the radius of curvature decreases and remains significant for a straight slot. It can be noted that, for quasi-straight slots, the experimental ratio AJA always appears lower than the theoretical one, as in Reference 49. (aii) Attenuation coe8cient and antenna design The method which is used to find cr requires numerical computation.
Fig. 11.34 a variation versus frequency (near the resonant frequency) r = 4,14rnrn, W = 154pm
The design of antennas matched to 50Q has been considered using the following model shown in Fig. 11.35; a quarter-wavelength line (length I,) is used to feed the loop and a second transformer (length I,) is used as a matching section. The equivalent transformer from the microstrip feed line and slot are taken into account. Impedance curves are drawn in Fig. 11.36 for frequencies varying from 9 to 11 GHz. The theoretical results agree well with the experimental values.
676
Design and technology of low-cost printed antennas
Design and technology of low-cost printed antennas
67 7
To facilitate the design of antennas, analytical formulas for a have been derived in the vicinity of the resonant frequency: c!
=
A I.
- + -Bd
c!
=
attenuation, N/m
1 = free-space wavelength
d = thickness of dielectric where A x
Fig. 11.35 Annular slot and its equivalent circuit
z REF 1.0units 4 200.0m units1 V 169.38 n-40.523 n
=11
(Ay+
- 18005.3 -
(
:.)"(:)"
570.8 log,, 200 -
. .
The accuracy of the above formula is better than 2%; it can be used for the following parameters:
a :theory
start 9 . 0 0 0 0 0 0 0 0 0 ~ ~ ~ stop 11.000 b : experiment
Fig. 11.36 Impedance of the printed annular slot r = 4.1 mm, W = 140pm, W, = 0.76mm
(b) Annular slots with rejector planes (Fig.11.28) The analysis is very similar to the previous one; a modification of Cohn's method makes it possible to obtain the two main parameters, guided wavelength and characteristic impedance of the slot line in front of the reflector plane Figs. 11 . 3 7 and ~ b show the variation of and 2, for the two distances d' (d'jd = 3 and d'ld = 11) as a function of dl1. The dielectric constant is 2.17 and the slot is very thin ( Wjd = 0.01). It appears that ,Ig and 2,do not differ from the values for slot lines without a reflector when it is sufficiently displaced. Detailed analysis of the mathematical expressions [46] shows that it is possible to find the limit distance d',im,which leads to identical values of Ag and 2, with or without
678
Design and technology of low-cost printed antennas
1
a reflector plane:
1
Design and technology of low-cost printed antennas
679
(a) Radiation occurs only in the upper half space. (b) No energy couples to the space between the two metallic planes (slot plane and ground plane).
The following assumptions are then necessary to obtain the value of a.
I
Fig. 11.38 u variation versus frequency for slot above reflector plane r = 4.41 mm, w = 154prn
Table 11.9 Dimensions of the two annular slots of Figs. 11.40a and b
Antenna
Fig. 11.37 (a) Variation of &/,I and Z, for slot above reflector plane ( d / d = 3) (b) Variation of 4 1 1 and 2, for slot above reflector plane ( d l d = I I )
r
W
1,
I2
13
w
K
w
Then, for a EMF given generator, the total radiated power is half the value obtained without a reflector plane; a is also reduced by a factor of 2, and the impedance is twice that without a reflector plane. Fig. 1 1.38 shows the frequency variation of a with or without the reflector plane. To avoid guided waves between the two metallic planes, four cylindrical metallic posts are positioned as shown in Fig. 11.39a; the post spacing equals one half-wavelength, and their height is 8.5mm. In Fig. 11.396 impedance curves have been plotted either for theoretical results (assuming radiation in the upper half-space only) or for experimental results with and without posts.
Design and technology of low-cost printed antennas
627
Theory and experiment agrees well when the posts are taken into account. Input impedances have been computed and measured for two different slots and feed lines with the same ground-plane distance d' = 8.5 mm (Fig. 11.40); the reference plane is n, (Fig. 11.35) and the dimensions are given in Table 11.9.
START STOP
.9.000000000GHz 11 00000000 GHz experiment
START ~9.000000000GHz STOP 11.00000000 GHz
T
Fig. 11 3 9 (a) Location of the metallic posts near the annular slot (b) lnput impedance of the annular slot (reference plane n,) ---- theory experience with posts --- experience without posts
-
Fig. 11.40
~
Y
experiment
b
(a) lnput impedance of annular slot no. 1: 6 = 8.5mm ( 6 ) lnput impedance of annular slot no. 2: d = 8.5mm
Conclusion: It has been proved that the transmission-line model of annular slots yields good results in terms of impedance variation versus frequency. However, some problems occur when a ground plane is added to produce a directional
622
Design and technology of low-cost printed antennas
Design and technology of low-cost printed antennas
antenna; further work is necessary to understand the parasitic effects of guided waves between the ground plane and the metallic plane of the antenna.
623
and a,,, is the excitation coefficient (relative to a reference element) of the (m, n) source located at (x,, y,,) (Fig. 11.41). When the radiating elements are regularly spaced along two orthogonal directions (Fig. 11.42), simple ex-
11.3 Design of planar printed arrays
Photo-etching techniques offer great flexibility in designing one- or two-dimensional arrays of microstrip antennas. Many parameters could be considered; e.g. position of elements, spacings, amplitude and phase distribution, feeding lines (on the same side or behind), connection with active devices etc. In fact, each structure is developed in response to a given class of problem. Only the usual design parameters and the realisation of pencil beam antennas are developed here; shaped-beam pattern design will be considered, together with the synthesis methods, in Section 11.4. 1
X
/
Fig. 11.42 A m y of linear sub-arrays
Fig. 11.41
( \ r n , n ) ~element ~ Co-ordinate system and location of the (m, n ) th element
11.3.1 Design parameters With the assumption of identical elements, the array gain is decomposed into the product of array factor, isolated element gain pattern, and a factor displaying the impedance effects of mutual coupling. When mutual coupling is negligible, the overall radiation pattern becomes [53] 40,
$1
=
f (0, $1 g(0, $1
(1 1.25)
where g(0, $) = radiation pattern of one element
Fig. 11.43 Equivalent orthogonal linear arrays of a planar array
f(0, $) = array factor
pressions can be derived for the two main planes, 4 = ' 0 and $ = 4 2 . For any $-direction, the planar array can be analysed using the pattern-multiplication method if the various sub-arrays are identical (same number of elements and
624
Design and technology of low-cost printed antennas
same distribution); then the planar-array factor remains the product of two linear-array factors (Fig. 1 1.43). As planar arrays and linear arrays have much in common, some basic results for linear series microstrip antenna arrays are given first: (i) directivity estimation taking into account the dielectric substrate, (ii) line losses depending on the element impedance value, and (iii) beam width and limitation on gain. =300Cl z0. 5 o n linear serles array
=300fl zO=loon llnear serles array
R,
3.0r
R,
5011 z 0 = loon h e a r s e r ~ e sarray = ?,I
3.0r
T-delta-0001 thickness (MMS):0.78 freq (GHz) = 10
T-delta - 0 6 1 thickness(MMS)=078 freq ( G H z ) :I0
-. - . - - . .- . - -
..
T-delta :O 001 thickness (MMS) = 0.78 freq (GHz) = 10
Fig. 11 .Q4 Line losses of linear series array ( a ) R, = 3000,Z, = 500 ( b ) R, = 3000,Z, = 1000 ( c ) R, = 50R.Zo= 1000
11.3.1.1 Line losses, eflciency of linear series array: Typical linear resonant arrays of microstrip antennas can be considered as a transmission line loaded periodically by shunt resistances whose values depend on the elements themselves (rectangular, circular, triangular with proper feeding points), or on the equivalent sub-array attached to the main line. For the sake of simplicity, let us consider a transmission line with a characteristic impedance Z,, and a complex propagation constant y = a ja. The periodic loads (radiating elements) are located at each guided wavelength in order to get a uniformly excited array. The resonant structure is then represented by a cascade of lossy transmission-line sections. The radiated power P, and input power P), are readily computed, and efficiency can be deduced:
+
Design and technology of low-cost printed antennas
Losses have been plotted (Fig. 11.44a, b, c) on a dB scale (loss (dB) = P,,,, - P,,,) for a number N varying from 2 to 40. Three main parameters have been considered: Zo, the characteristic impedance with typical values of 5 0 0 and 100Q dielectric loss tangent, typically lo--'; and R,equal to 300 or 50R. In each case the usual dielectric-constant value for printed circuits of Teflon fibre substrate is equal to 2.2, and the different curves have been obtained for a frequency of 10 GHz. When N increases, the efficiency is reduced, as might be expected; the highest value of 3dB is obtained only for a large number of elements. However, the slope of the curves depends on the antenna resistance and characteristic impedance; it will be noticed that small R, (typically 50R) and large Zo (here 100R) lead to high losses, even with a moderate number of elements. In order to reduce line losses, the designer should choose a high input impedance R, and a low characteristic impedance 2,. However, the last constraint often conflicts with the necessarily small width of the input feed line compared with the width of the antenna itself. 11.3.1.2 Directivity of unijbrm linear arrays: The simplest type of linear array is the uniform one. Analytical expressions for directivity have been proposed for typical elements such as ideal isotropic sources, co-linear short dipoles and parallel short dipoles [53-561. Rectangular printed antennas radiate from fringing fields around the edges; the fields along the two radiating edges are approximately uniform. Thus each antenna can be considered as an array of two uniformly excited identical slots; its directivity is about 5-8 dB depending on the dielectric substrate. Two linear-array structures are to be considered, namely the H-plane and E-plane (Fig. 11.45); the slots of each patch are defined by their length Wand their spacing do; d equals the distance between each element. The array radiates in the half-space defined by x > 0. Elements are located along Oz to get simple expressions for slot patterns and simple integrals of directivity. ( a ) Directivity expression The element pattern of each patch g(0, 4 ) can be easily expressed in H- and E-plane configuration as:
(Y
) ( -2
H-plane:
g(0, 4 )
=
sin 0 cos k - s ~ 0n sin 4
E-plane
g(0, 4)
=
(1 - sin20 sin24)li2cos k
1
cos 0
and the directivity expression of an N-element array in the broadside direction may be written 2 2 - (1 1.28)
D = .
where Ri,, = input resistance; R, = resistance of each radiating element and = potential at node j.
625
626
Design and technology of low-cost printed antennas
Design and technology of low-cost printed antennas
where
627
where
8
N-l
3 cos a
N-m
and a, = kd, a
=;
a = 0.24774379
mkd
b
a, = mkd
=
0.01294148
+k4
a, = mkd - kd, The a and b constants which occur in the H-plane-configuration expression appear in the 0 integration of !2,
a, H - plane
E -plane
The coefficient 2 arises because the antenna radiates in the half-space, X > 0. With d n = sin 0 d0 d 4 and using the finite-series expression [55, 591 off 2(0): 1 2N-1 ( N - m) cosm$ f2(0) = N2 ,,,=I
1
the results are H-plane configuration:
(9) sin 8 d0 dm
The use of two points x, = 1 and x, = 2.402 leads to the previous values a and b. J,(x), and the approximate polynomial are plotted in Fig. 11.46. There is good agreement within (x, x,).
( b ) Results Figs. 11.47 and 11.48 show the variations of D for linear arrays of printed antennas in H- and E-plane configurations for two kinds of dielectric: PTFE (E, = 2.2 and thickness = 1.6mm) and alumina (E, = 9.8 and thickness = 0.625 mm). The dimensions of the antennas were computed using the following expressions:
E-plane configuration:
D
f2
The kernel of the Bessel function J, remains between 0 and 2.5 for most printed antennas (E, 3 2); then J,(x) can be approximated by a simple polynomial expression:
Fig. 11.45 E-plane and H-plane linear arrays of equivalent slots of microstrip antenna
,+
1; cos2 (Fsin 0 sin 4) 2 (0)
=
d
=
2
(N - m)[2S
O
+ S, + S2- ( ~ S C+ SC, + SCJ
I
-
-2&f
2Ad0 and Ad, = length extension [6]
628
Design and technology of low-cost printed antennas
629
Design and technology of low-cost printed antennas
The curves show that D is an increasing function of dl1 when dl1 is less than 1 and N is large. The optimum distance d for large directivity and no grating lobes lies between 0.71, and 0.91,. For usual substrates ( E , = 2 to 2.5) and with
00 1 0.20.4 ' ,0 6. 0 8. 1.0 , 1.2 . 1.4 . d~rectivity Dllambda linear array H-plane printed antennas die1 const ~ 2 . 2
d.6 0:8 1'0 1' 2 114 00% d~rectivity Dllarnbda linear array E-plane die1 const =2 2 printed antennas
Fig. 11.47 Directivity of an N-element linear array of printed antennas as a function of uniform element spacing Dielectric constant = 2.2.
\ -0.3
approximate polynomial of the 0-order bessel 0
Fig. 11.46 Approximation of the zero-order Bessel function
one-1,-long straight feeding lines between neighbouring elements, the distance d is approximately 0.751,. For small values of N, the E-plane arrays exhibit a larger directivity than H-plane ones. On the other hand, the H-plane arrays present similar directivity variations for E, = 2.2 and 9.8.
directivity linear array prlnted antennas
Ollarnbda H-plane die1 const.9.8
directivity
linear array printed antennas
D l lambda E-plane die1 const.9
8
Fig. 11.48 Directivity of an N-element linear array of printed antennas as a function of uniform element spacing Dielectric constant =
9.8.
630
Design and technology of low-cost printed antennas
Design and technology of low-cost printed antennas
11.3.1.3 Non-uniform linear arrays: The reduction of the sidelobe level requires tapering of the amplitude distribution; some care must be taken in the element spacing; the optimum distance d z 0.75& for printed antennas on a PTFE substrate does not always fulfil the spacing requirement of the Chebyshev design for small number N and low sidelobes. Fig. 11.49 gives (d/l0),, versus sidelobe level for various N; and example of an array factor with N = 6 and
631
power beamwidth (HPBW) increases. Directivity can be computed for isotropic k~ementsusing the following formula [%I:
where A, is the normalised amplitude of the n t h element. However, the excitation efficiency q, = DID, (where Do is the directivity of uniform array of isotropic elements) is available either for Chebyshev, Taylor or Villeneuve distribution [53, 54, 57, 58, 601; assuming that q, of printed antennas remains very similar to q, of isotropic sources, a quick estimate of D can be obtained from Do given previously.
0.5 10
20
30
LO
11.3.2 Cavity-model analysis of mutual coupling Since the experimental work of Jedlicka and Carver [61, 621, many theoretical efforts have been made to calculate the mutual interaction between microstrip antennas [25, 63-68]. Mutual-coupling effects are caused by radiation through free space and by surface waves which propagate along a dielectric substrate. The theoretical method proposed by Penard and Daniel [65, 251 is restricted to the first effect; this is acceptable as long as the dielectric constant is low and the thickness is small compared to the wavelength [67]. The method uses the cavity model of the antenna, and it is assumed that mutual coupling does not disturb the field distribution in the cavity. In the cavity method, by using the equivalence principle, one can relate the internal field in the cavity to the magnetic-current loop radiating in the upper half-space. Then the mutual-coupling coefficients can be derived from the interaction between magnetic current loops. The mutual impedance 2, between two elements is deduced from the reaction theorem
50
-Rde
Fig. 11.49 ( d l l ) ,
Fig. 11.50
versus sidelobe level for Chebvchev taper
where C, = contour of antenna j; M, = magnetic line source; Hi = magnetic field set up by antenna i on antenna j; and 4 = current feeds of the two patches. Only the fundamental mode is usually considered in evaluating integral 11.32 in order to reduce the computation time. The coupling coefficient Sv can easily be calculated by applying the impedance-matrix equations of network theory. Provided the internal electric field is known, printed antennas of any shape can be considered.
Chebpshevpattern of a six-isotropic-source linear array (Spactng = 0.751,)
(dl&) = 0.75, designed for - 40 dB sidelobe level, is shown in Fig. 11 S O . A strong effect appears on the sidelobe level, which reaches - 23 dB at 0 = 90° instead of -40dB. On the other hand, directivity D decreases and the half-
+
11.3.2.1 Rectangular patch antennas: In the H-plane configuration (Fig. 11.51), the mutual impedance between identical OMA (open microstrip anten-
632
Design and technology of low-cost printed antennas
nas) is given by [65]
Design and technology of low-cost printed antennas
633
where C is the width of the excitation and
The expression takes all the equivalent slots around the patch into account. The contribution of the two OX-edge radiating slots appears in the integral R,.
t
.... .... ...:.....::.. :.: .............................. '.X ...... ............. . . . . . . ... .. ... .. ... .. ... .. ..... . . . ............ .. .............. . I.....
ground plane/
Fig. 11.51
Geometry of two rectangular microstrip antennas in H-plane configuration
freq ~ 2 2 9 8GHz Er ~2.55 d. cm increment -0.43cm
I
-3
Fig. 11.52
-2
-1
The effect of the OY slots appears in R, and R, and cannot be ignored, as shown in Fig. 11S2.
I
0.6v1 -,4.08
0
1
yI 24'
Fig. 11.53 Contribution of OX edges and OY edges in mutual-impedance calculation in E-plane configuration; mode(0, I )
ax~s.crn1 real 3
Contribution of OX edges and OY edges in mutual-impedance calculation in H-plane configuration; mode(0, I )
where t is the substrate thickness with It should be noted that R, is cancelled out when the dielectric slab is replaced by a vacuum medium. Similar relations can be found for two patches in the
634
Design and technology of low-cost printed antennas
Design and technology of low-cost printed antennas
635
E-plane configurations [25]
In this case, the effect of the two OX-directed slots (R')) is stronger, but the contribution of the longitudinal slots (R; and R ; ) is not negligible (Fig. 11.53). Fig. 11.54 shows calculated values and experimental data of the coupling between two identical patches for various spacing in E-plane and H-plane. When the distance d becomes smaller than 0.08&, the discrepancy between theoretical and experimental results in the H-plane increases. In this case, the coupling disturbs the internal field distribution, whieh clearly appears on the measured value of the input impedance Zll(Fig. 11.55). Penard [25] has studied the mutual coupling between the hybrid-microstrip antennas (HMA). In this element, the contribution of the apertures situated near the electric walls is very small and can generally be ignored. In Fig. 11.56, the coupling coefficient of HMA and OMA are shown for comparison. In the H-plane, S12is smaller for HMA than for OMA, except when the dielectric is replaced by a vacuum medium (Fig. 11S7). Fig. 11.55 Experimental results of Z,, as a function of the distance dl& between the two patches; H-plane; mode(0, I )
planE . o o o plan H . x x x
\
m
\;--
)
o
=
4
*--- -0--
mode ( 0.1) frequence = 2.273 GHz r L 2.55 5.0001 1.0.52 cm
-4 0
I
0
0.1
I
I
0.2
I
0.3
c
m
-0
Cp.20
-
1
log ISlZ
\
0.4
dlAo
Fig. 115 4 Mutual-coupling coefficient as a function of the distance dl10 of the edges in the E-plane and H-plane; mode(0, I )
Another interesting result, in view of array design, is that the mutual coupling coefficient slowly increases with the substrate thickness (Fig. 11.58). The effect of the dielectric-constant variations on mutual coupling of short-circuited and open microstrip antennas is presented in Fig. 11.59 and 11.60, respectively. 11.3.2.2 Circular patch antennas: In this case, the circular geometry of the elements allows the separation of the co-ordinate variables, disc centre spacing RV,disc angular orientation 4Vand angular feed positions 0 , 0, (Fig. 11.61).
Fig. 11.56 Comparison of coupling coefficient in H-plane, between HMA (a = 6cm. b = 2cm) and OMA (a = 6cm. b = 4cm) structures E, = 2.17, fa = 2.45 GHz, r = 0.157cm. tanb = 10-4
636
Design and technology of low-cost printed antennas
Fig. 11.57 Comparison of coupling coefficient in'H-plane, between H M A and OMA with air-dielectric f, = 1.773 GHz, t = 0.1 50cm
Fig. 11.58
Theoretical coupling coefficient as a function of the dielectric thickness t l k mode(0, I )
Design and technology of low-cost printed antennas
637
Fig. 11.59
Theoretical coupling coefficient between two OMA versus E, for different values of dl10 8, = 1 tl& = 0.017
Fig. 11.60
Theoreticalcoupling coefficient between two HMA versus E for different values of dl& 6,
= 1
tl1, = 0.0093
A
E,
= 2.1
t / l o = 0.0064
0 theory
experiment
638
Design a n d technology of low-cost printed antennas
Mahdjoubi [66] gives a semi-analytical formula for 2, which permits a great reduction in computation charges: m
Z, =
639
pedance Z I 2can be written
m
1 Zy 1 Z;[Yemn(R,,) cos m(4ii - O,)cosn(4,
m=O
Design a n d technology of low-cost printed antennas
n=O
- 0,)
where
+ Y,""(R,)~inm(4~- 0,) sinn(bV - O,)]
(1 1.35) m and n are the angular mode indices for antennas i and j, respectively. The Y, factor corresponds to the E-plane (4 = 0, 8, = 0, = 0) while the Y, factor corresponds to the H-plane ( 4 = 0, Or = 0, = 90') (see Fig. 11.62). The
E plane
H plane Fig. 11.61
Geometry of e/ectromagnetically coupled microstrip disc antennas
= angular width of the feeding probe; Q = radial feed position; a = effective radius of the disc antenna; t = substrate thickness; k = propagation constant in the dielectric, J, and Y, = Bessel functions of first and second kind of
order p. YY(R,,) and Y,""(R,) are the space-wave mutual admittances between mode m of annular slot i and mode n of annular slot j for the E- and H-plane coupling configurations, respectively. For two identical circular discs with only the fundamental modes excited in both antennas (m = n = I), the mutual im-
Fig. 11.62 Magnetic-current distribution along the contour of circularpatch for two principal coupling planes
mutual coupling coefficient S12 calculated at f = 1.4127GHz, for comparison with experimental data (f = 1.44GHz) from Jedlicka et al., are given in Fig. 11.63. Agreement is quite good so long as the frequency shift ( x 2%) due to the cavity model is taken into account. Whatever the mode, the exact dependence of the coupling phenomena on 4 is a simple trigonornetrical function. Eqn. 11.36 and Fig. 11.64 describe the typical form of the coupling coefficient versus 4, normalised to E-plane coupling. The results are compared with those of Bailey and Parks (Reference 5, p. 157). The curves of coupling coefficient against the angular feed position 02(0, = 0) are given in Fig. 1 1.65 for two edge spacings d = 0. I%, and d = Ao.The E-plane
640
Design and technology of low-cost printed antennas
Design and technology of low-cost printed antennas
641
and H-plane of antenna 1 correspond, respectively, to I$ = O0 and I$ = 90". It should be noted that the coupling coefficient varies rapidly near 0, = 90' showing how critical is the precision of the feed angle at this location.
.
E plane
d'
} theory
::]
exper~rnent reference 61
.>,
H plane
O
Fig. 11.63 Coupling coefficient versus distance d between edges 6, = 2.5, t = 1.575 mm, patch radius = 3.85 cm, probe radial distance = 1.1 cm Frequency: Measurement = 1.44 GHz Theory = 1.4127
Q
O measured microstrip disk coupling
------
calculated circular waveguide fed aperture coupling (Bailey and Parks) our theory
Fig. 11.64 Coupling coefficient versus orientation ( f = 5.5GHz)
4,
normalised to the E-plane coupling
(a) Input impedance Z, The input impedance Z, of the elements can be readily calculated by applying the impedance matrix equations of network theory. Fig. 11.66 illustrates Z, variations of the previous two-element array against the edge distance d. It can be observed that, for d > 0.3& ( R > 0.68&), the coupling effect on Z , is negligible. In studying 2, as a function of 4 and frequency, we have chosen a very short distance ( d = 0.1&) in order to observe the coupling influence. Fig. 11.67 shows that in the E-plane ( 4 = 0°), Z, x Z,, = 61.7 /-Y ohms, where Z , , is the proper impedance of the disc antenna. However, in the H-plane ( 4 = 90') where the coupling is stronger, Z, is very different. (b) Circular sub-array of three identical elements (Fig.11.68) [68] In Fig. 11.69 one observes that the coupling effect on the input impedances Z,, , Z,, and Z,, becomes negligible for d > 0.31,. The dependence of the input impedance on feed angular position 0 is presented in Fig. 11.70. Although two of the three impedances can be equal for certain values of 0, nowhere they are identical simultaneously. 82
I
Fig. 11.65 E- and H-plane coupling coefficients for m = I , n = I , versus angle OZ(B, = 0)
642
Design and technology of low-cost printed antennas
Design and technology of low-cost printed antennas
643
( c ) ConcIusion The cavity method and reaction theorem represent very suitable ways to calculate and predict free-space mutual coupling between array elements of simple shape. According to these results, it seems that the H-plane coupling is stronger for the disc than for the patch (see Figs. 11.54 and 11.63) and identical in the E-plane ( d < 0.31,).Mutual coupling effects become important when the edgespacing distance d is lower than 0.31, for an array of few elements.
I I
1 z,, 1
=61.7/
F i g . 11.67 2, of a two-identical-element array against @ ford
Fig. 11.66 Input impedance 2, of each array element as a function of d E Plane ---- H Plane f = 1.391 8 G H z
-
=
O . I I , and f = 1.3918GHz
11.3.3 Linear series array of corner-fed square patches [69] The feed network of microstrip antenna arrays exhibits loses which lead to a limit on the expected gain, and consequently a limited number of elements. The Schelkunoff unit circle, Dolph-Chebyshev and Villeneuve methods are well suited for the design of fairly small arrays; Taylor's method, sampling line source and Fourier's series expansion are better for large arrays. However, the previous synthesis methods consider only the array factor, while the overall diagram obviously needs the element patterns to be taken into account; for e.g. the cos 0 variation in the H-plane of most printed antennas has a strong effect for arrays with few elements; the - 40dB Chebyshev design example previously
644
Design and technology of low-cost printed antennas
mentioned shows a high sidelobe level (- 23 dB) in Fig. 11.50. The sidelobe disappears completely in the H-plane element pattern (Fig. 11.71), and the initial specification is obtained. Two synthesis methods, taking the elementary radiation pattern into account, are developed in Section 11.4.
Fig. 11.68 Geometry of a planar circular array of three microstrip disc antennas
Only one simple structure using square-shaped microstrip antennas is considered here. The corner-fed square patches are easily excited with a single microstrip line (Fig. 11.72); a tapered distribution is readily obtained using quarter-wavelength transformers along the line. In order to get a broadside pattern, one wavelength spacing is necessary; half-wavelength spacing is also possible, with alternate elements to keep the equi-phase condition. The corner-fed square patches have been chosen because they provide a high input impedance well suited for series array. It is also very easy to feed each element on the corner. Two new aspects are considered here: reduction of cross-polarisation using altenate location of the elements on the feeding line, and reduction of sidelobe level using simple tapering for a linear series array.
Design and technology of low-cost printed antennas
645
646
Design and technology of low-cost printed antennas
Design and technology of low-cost printed antennas
647
11.3.3.1 Radiation of corner-fed square patches
(a) Theory: When the patch is excited at one corner (Fig. 11.73a), the cavity model [4, 251 shows that the main part of the internal field is the sum of two degenerate modes with equal amplitudes, i.e. modes (0, 1) and (1, 0). If the higher modes are ignored, the Ex and E, fields along the edges exhibit the
I
input I
A,
1
Fig. 11.72 Corner-fed square-patches array Fig
geometry of the patch
a
Fig. (O.l)and (1.0) modes contributions
Fig.
(1.1) mode contribution
point
-2
In1
fK,(x)
---- z,"2 . . . . . z,
M
T
(
x
)
~
o
Fig. 11.70 Input impedance versus frequency: d = O.7& MO(Y) geometry and magnetic currents of the corner fed patch
Fig. 11.73 Geometry and magnetic currents of the corner-fedpatch
variations shown in Fig. 11.736. The far field is linearly polarised either in the E-plane (I(/ = 0") or in the H-plane ($ = 45"). For instance in the H-plane,
EQ,
=
sin 2C
-jM, -
(2C)' - n2
where M, is proportional to the amplitude of the magnetic current ( x = 0, Y = 0) J 2 sin 8 2C = k,a 2 deg
Fig. 11.71 Chebpshev pattern of a six-microstrip antenna linear array (H-plane, spacing = 0.752,)
a
=
side length
648
Design and technology of low-cost printed antennas
Design and technology of low-cost printed antennas
AS long as the cross-polarised field is needed, higher modes must be considered. The next mode (1, l ) adds a contribution with a magnetic line distribution as shown in Fig. 11.73~.The E,, far-field component is given by E,, = - 2M, cos2C
2C
(1 1.38)
(2C)2 - n'
an anti-phase relationship which cancels the different contributions. The diagram is shown in Fig. 11.77. It shows a large reduction of the cross-polar level, which is close to -28dB instead of - 17dB as previously. Obviously, as the length of this array is half that of the first one, the 3 dB beamwidth is larger. To attain the same directivity, 20 elements spaced 112 would be necessary.
where MI is proportional to the amplitude of the magnetic current ( x = 0, y = 0). It will be noticed that M I is much smaller than M,. The previous formula shows that the cross-polarised component is null for B = 0 and increases with 0.
UNIFORM LlNE ARRAY A1
1-1 I
****it****
FIG.
Uniform linear array A1(FO-
21.3GHz)
fig. H plane pattern of the untform array A1 (FO=Z1.3GHz) copolar cross-polar
-
r10 ELEMENTS *SPACING
-
1 GUIDED WAVELENGTH
*SUBSTRATE PTFE
El-
tgs THICKNESS
-
2.17 0.001
!----
0.38
+FEEDING LlNE lOOn +COAXIAL OUTPUT (AND TWO QUARTER WAVELENGTH TRANSFORMERS) Fig. 11-74 Uniform line array A, (F, = 21.3GHz)
( b ) Examples o f linear arravs When the' spacing along the feeding line equals one guided wavelength, the different elements are uniformly excited (Fig. 11.74). Here the ten-element array is printed on the usual PTFE substrate (dielectric constant 2.17 and thickness 0.38 mm). The quarter-wavelength transformer enables good matching to the 50 i2 coaxial output. As expected, the H-plane diagram exhibits the well-known - 13 dB first sidelobe; the cross-polarisation component is very low at @ = 0 and then quickly increases with 0 to - 17dB (Fig. 11.75). This cross-polarisation component can be reduced in a simple and efficient way. Let us consider each patch located alternatively on each side of the feeding line (Fig. 11.76). Considering half-wavelength spacing, the different co-polar fields (Emfor Hplane) add in phase, while the different cross-polar components ( E B Imaintain )
649
Fig. 11.75 H-plane pattern of the uniform array A , --- co-polar ---- cross-polar
(F, = 21.3GHz)
650
Design and technology of low-cost printed antennas
Design and technology of low-cost printed antennas
657
1I .3.3.2 Tapered linear series array (a) Theory: The previous arrays were uniformly excited; high sidelobes are the consequences of this illumination. The idea was to produce a non-uniform amplitude distribution while keeping the simplicity of the previous series feeding. Let us consider a linear array with wavelength spacing (guided wavelength);
UNIFORM LINEAR ARRAY WITH ALTERNATE ELEMENTS A2 I FIG.
.
I
Uniform array A2 alternate alaments
Fig. 11.76 Uniform linear array with alternate elements A,
as the radiating elements are identical, impedance transformers are necessary to obtain the given amplitude current. To do this, a two-step quarter-wave transformer can be used in each cell (Fig. 11.78). The transformed admittance & in the IT: plane is given by
+
l), and Y,, and Y,, are the characwhere Y,,, is the admittance of node (i teristic admittances of each quarter-wavelength transformer. If necessary, four quarter-wave transformers can be inserted when the spacing equals one wavelength. When the input voltage leads to a unit current in the first element, the current distribution is readily obtained with the following relations:
-
----
Fig. H plane pattern of uniform array A2 (FO=21.3GHz)
copolar cross polar
I
Fig. 11.77 H-plane pattern of the uniform array A, co-polar ---- cross-polar
-
(F, = 21.3GHz)
However, the various ratio nican be deduced step by step from the known values of I,, I,,&, etc. The input impedance at element 1 is z,, =
Z"
1
+ n: + nini + n:n:n: + . . . . .
(1 1.41)
652
Design and technology of low-cost printed antennas
Design and technology of low-cost printed antennas
653
( b ) Results A ten-element array has been constructed (Fig. 11.79). The requirement was to get a sidelobe level lower than - 20 dB. Only eight transformers were used (four
TAPERED LINEAR SERIE'S A R R A Y ***a******
lA~ INPUT
---7aI
- 1, 10 YAV
i,
-
I,
1
n,Y,+V = n l n,n,,
...n,
Fig. 11.78 Tapered linear series array: current distribution
TAPERED LINEAR SERIE'S A R R A Y A3
~~~ **********
fig.
I
FIG.
H plane pattern of tapered array A , (Fo = 21.3 G H z )
I
Tapered array A3
* 10 ELEMENTS *SPACING = ONE GUIDED WAVELENGTH Fig. 11.80 H-plane pattern of tapered amy A, (F, = 21.3GHz)
* 4 TRANSFORMERS (ON EACH SIDE)
* FEEDING LINE lOOn * COAXIAL OUTPUT I
Fig. 11.79 Tapered linear series array A,
I
on each side), because Y,, was chosen equal to the characteristic admittance of the half-wavelength following line. Taking the characteristic impedance of the main line as about loon, the various transformers exhibit impedances between 75 and 95 0 , which are easily realised with microstrip lines. The experimental H-plane diagram is plotted in Fig. 11.80. It shows that the sidelobe level is lower
654
Design and technology of low-cost printed antennas
than - 20 dB while the gain and input-impedance matching remain very similar to those of the uniform array. A combination of alternate elements and tapered distribution yields a pattern with low sidelobe level and low cross-polarisation over the whole space. Fig. 11.81 shows a ten-element array with quarter-wave transformers. The diagrams
deg
Design and technology of low-cost printed antennas
655
are plotted in Fig. 11.8 1, which clearly shows that no degradation occurs to the cross-polarisation level within the frequency band. 11.3.4 Two-dimensional cross-fed arrays [TI, 721 The combination of identical linear sub-arrays leads to a planar array. The feeding network of such structures is developed in Section 11.4. Another simple two-dimensional arrav named the cross-fed structure can be considered as a combination of non-identical linear sub-arrays. Cross-fed printed aerials have already been described by Williams [70]. The basic radiating elements were 45' dipoles inclined along the feeding lines. No analysis was proposed; however, the structure appears very attractive owing to its simple feed geometry which avoids having any transformer. Corner-fed patches were chosen because they are easily fed along a straight microstrip line. Moreover, the discontinuities introduced near the corner of each element are symmetrical and identical for all of them. Thus co-polar and cross-polar :omponents remain symmetrical around the broadside direction. Figure 11.82 shows a typical cross-fed array. Matching networks can be added for a coaxial feed. Inter-element spacing equals one guided wavelength. Design equations for a uniform array are given below.
Fig. 11.81 H-plane pattern of tapered array with alternate elements
11.3.4.1 Uniform illumination and impedance matching: The overall array is constructed from parallel sub-arrays. The number of elements is reduced from N, to N, - 2, considering ith and (i I) th sub-array, respectively. When N is the number along the diagonal, we find:
+
N,
=
(N - 2)N/4 elements for the upper or lower group of subarrays
N, = N2/2 elements for the whole array The input impedances are different for the half main-line section (R,) and the upper or lower group of sub-arrays (R,) (Fig. 1133). The impedance matching needs one or two quarter-wave-section transformers to get suitable characteristic impedances (Z;, Z,, Z',, 2,).The uniform illumination condition yields a second relation (same voltage V for all the elements). Then the transformer impedance ratios are equal on each side as follows:
where R, = resistance of a corner-fed antenna; R, = desired input impedance; N = number of elements on the main line.
Fig. 11.82
11.3.4.2 Radiationpatterns: The total array factor results from the combination of sub-array factors. The expression is P sin(N - 2i)(py/2 (1 1.43) 2 cosicp, sin qy/2
+ 1
Typical cross-fed array of square patches (without matching network)
I
656
Design and technology of low-cost printed antennas
Design and technology of low-cost printed antennas
657
where 4, = kd, cos 4 sin 0; q, = kd, sin 4 sin 0; d, and d, are the inter-element spacing along Ox and Oy; P = number of sub-arrays (above or below the central line); N = number of elements along the central line and S,, = N 2 / 2 .
Fig. 11.83 Input matching transformers of the cross-fed array
It is interesting to consider this expression for d, = dy = d i n the two main planes. In the H-plane, ST is the sum of the usual uniform array factors Si= sin (Micp,/2)/sin(cp,/2). However, the nulls of each Si function have different locations because the sub-arrays have a different number of elements. Then all S, components are added in phase in the broadside direction while a compensation occurs from the oscillating functions outside 9 = 0. The following results are given for usual substrates (6, x 2.2), and the spacing equals one guided wavelength (A8 2, 00.5&). Fig. 11.84 shows the three components So, S , , S, for the case N = 6 and P = 2 (six diagonal elements and four sub-arrays). Summation then leads to a diagram with a large reduction in the previous oscillations of each of the subarrays. In the E-plane, cp, = 0 and ST is the array factor of an equivalent array exhibiting a linear tapered excitation. Fig. 11.85a, b and c show the computed patterns in the three main planes,
Fig. 11.84 Sub-array contributionsSfof the globalarray factor S, (six diagonal elements and four subarrays)
658
Design and technology of low-cost printed antennas
Design and technology of low-cost printed antennas pattern of crass-fed array PHI =go element NB:6 (diagonal) equiampl~tude equ~phase
659
which clearly show that the sidelobe level (SLL) is greatly reduced. However, the = 45' plane yields the - 13 dB sidelobe of the uniformly illuminated square structure. On the other hand, the half-power beamwidth &dB remains very similar in the three planes ( 4 = 0°, 45', 90'). &dB and SLL,, versus the number N of elements on the diagonal feed line is given in Table 11.10.
4
Table 11.10 Half-power beamwidth and sidelobe level of cross-fed array
20
40
60
80
pattern of cross - fed array
elernent NB=6 equiamplitude
-60
-40 -20
0
20
40
60
80
pattern o f cross -fed array PHI - 0 element NB = 6 (diagonal) equ~amplitude equiphase
Fig. 11.85 Computedpatterns of the cross-fed array (six diagonal elements, uniform distribution) ( a ) H-plane 6 = 90" (6)45"-plane 4 = 45" ( c ) E-plane = 0'
N
= number of elements along the
diagonal feed line
It will be noticed that only using the impedance matching condition does not provide a uniform illumination; for instance, if different quarter-wave transformers are used on each arm of the previous structure (N = 6 elements on the diagonal arm), the voltages on each element of the upper and lower sub-arrays differ from the voltages of the central line. The computed patterns are plotted in Fig. 113 6 when the voltage equals 1 on the main line and 0.8 on all the other elements. It appears that the E-plane is quite transformed, sidelobes reaching - I6 dB and 0, dB = 17.8'. 11.3.4.3 Results: Various arrays have been built either with coaxial or waveguide output. Each of them was printed on a PTFE substrate ( E , = 2.17, tg6 = lo-), thickness = 0.38 mm) or on polypropylene, as described in Chapter 5. An 18-element cross-fed array designed for 23.5 GHz is considered first. The same quarter-wave transformer was used on each arm to obtain a SWR better than 1.5 at the coaxial output (Fig. 1137). The measured gain equals 20dB, while a uniform aperture of the same area yields a 21 dB gain. E- and H-plane diagrams are given in Fig. 11.88; the sidelobes reach - 18dB in the E-plane and are lower than -20dB in the H-plane, and beam widths are 15" (H-plane) and 18" (E-plane), as expected. Another 50-element array, printed on polypropylene of the same thickness, has been realised for a frequency near 20 GHz. The number of elements in the upper and lower groups of sub arrays is 40, and the impedance to be matched equals 8 a. The transformer then needs three quarter-wave sections as shown in Fig. 11.89 to get equal voltage on each patch and good impedance matching. The radiation patterns are given in Fig. 11.90. No sidelobes larger than - 25 dB appear in the H-plane while the E-plane exhibits - 18dB sidelobes. In both cases the cross-polarisation level remains acceptable. The measured gain is
660
Design and technology of low-cost printed antennas
Design and technology of low-cost printed antennas
667
Pattern of cross-fed array
0-
PH 1.90 element NB=6 (diagonal) variable ampl equiphase
-10-
-20-
-30-
-"PO
-fi4!-i0 i
i l \ o ~ idoo
a
F(GHz)
Fig. 11.87 VSWR of a 78-element cross-fed array (six diagonal elements, F, = 23.5GHz) pattern of cross-fed array element NB-6
Pattern of cross-fed array
-10
/
\
PH 1.0 element NB=6 (diagonal) variable am01 equiphase '
Fig. 11.86 Computed patterns of the crass-fed array (six-diagonal elements; non-uniform distribution)
b Fig. 11.88 E-plane and H-plane measured pattern of the 78-element cross-fed array
662
Design and technology of low-cost printed antennas
23.2 dB; the uniform aperture of the same area would yield 25.48 dB. Losses reach approximately 2.3dB; the VSWR is lower than 1.8 between 193 and 20.4 GHz. 11.4 Synthesis methods for linear arrays 173, 74, 751
663
Design and technology of low-cost printed antennas
Let F(8) be the directivity pattern of a linear array; then where f (8) = array factor; g(8) = directivity pattern of the source. As usual printed antennas have different diagrams in the two main planes (E-plane and H-plane), so it is better to synthesize F(8).
The usual analytical synthesis methods (Fourier, Chebyshev, Woodward-Lawson) are not always suitable when the directivity pattern is specified by a given outline. Thus, the mean-squared error criterion is a global criterion that does not permit the separation of the main-beam and the sidelobes contribution. Prescribing equi-level sidelobes does not always fit the Chebyshev requirement.
plan
I
E
FzI9.55GHz
CROSS-FED ARRAY A4 **********
+4 4 + ++4 +4+
+ 4 4 + 4 4 4 + + 4 4 4 4 4 + 4 4 + +4++?44++
SO E U M N T S W L L Y EXCITED SILPLE CORPORATE FEED SIMPLE OUTPUT MACHINC (A THIEE SECTION TRANSFORMER ON THE VERTICAL B W H WAS MCESSARY) LOW SIDE LOBES I N E-PLANE H-PLANE s F E W Y BM9 19.5-20.4 CHz VSWR < 1.8 GAIN 23 dB
.
FIG. Cross fed array with coaxial output A4
Fig. 11.89 50-element cross-fed array printed on polypropylene
1
-80
1
~
60
'
~
40
~
20
~
~
0
~
20
~
~
40
~
~
60
~
80
~
'
'
deg b
Lastly, the Woodward-Lawson sampling method needs a great number of sources, and the choice of sample is sometimes critical. Numerical methods can take into account the envelope specification, the directivity pattern of the source and the inter-element spacing. Two numerical methods have been studied:
Fig. 11.90 E-plane and H-plane patterns of a 50-element cross-fed array printed on polypropylene
The relaxation method which enables real excitation coefficients The simplex method which uses the Dantzig algorithm and yields symmetrical or non-symmetrical pattern synthesis (real or complex coefficient).
11.4.1.I Method: Let us consider a symmetrical linear array of 2N elements; FJ8) is the desired directivity pattern and a = (a,):-, is the unknown excitation vector:
11.4.1 Relaxation methods
'
~
664
Design and technology of low-cost printed antennas
Design and technology of low-cost printed antennas
N
Fd(0)
=
1 a, cos j- l
d, = symmetrical-axis relative position of source + j ; A, = free-space wavelength. The following linear system is obtained using discrete values of 0:
C = [c,,],.~, cv
=
)
cos 2a 2 sinei , a T = (a,, a,. . .a,);
(:
The functionals to optimise are those like
We denote a' and a E RNsuch as J(af) = Min J(a) in the sense of the chosen criterion. To realise this, a series of vectors d is built, such as J ( d + 1) < J ( h ) . The search directions are the co-ordinate axes, each of them being taken such as at the periodically. For each component aj, we realise = (k 1) th iteration:
Fig. 11.91
Outline of desired directivity pattern (example of sector of pattern)
4+'
+
For a given quality criterion and choice of convenient functionals to optimise, the relaxation method provides fast convergence. Some portions of the outline pattern can eventually be preferred. Two examples illustrate the method: sector pattern and directive broadside pattern. 11.4.1.2 Sector-pattern case: Let us define the desired directivity pattern from an outline symmetrical on 0 (Fig. 11.91). RIimis the maximum ripple value for 0 E [0, 0, - a] and R = 1 - D(8),. S L L , is the maximum sidelobe level for 0, a < 0 < a/2 and SLL = D(B),,. The pattern in the transition region is related to u values. An initial value can be chosen, such as la:1 = 1 j3(i - l)/(N-1) 0 6 j3 < 1, or it can be equal to the excitation obtained from classical methods. The functional J(a) is replaced by two functionals R(a) and SLL(a), and min J(a) can be expressed by the following improvement criteria
+
Fig. 11.92 (a) Sector pattern of a 10-element array (H-plane). Relaxation synthesis: a C, criterion b C, criterion c
C3criterion
665
666
Design and technology of low-cost printed antennas
c,, c,, c,: let a + be the actual vector of the iteration, c,: [R(a+) < R(a) and SLL(a+) 5 SLL(a)] or [R(af) 6 R(a) and SLL(af) < SLL(a)] c2: [R(a+) < R(a) and
SLL(af) 5 SLL,]
c,: [SLL(a+) < SLL(a) and R(a+) 5 R,;,] The c, criterion application improves the ripple and the sidelobe level. c, gives the best ripple for a given sidelobe level SLL,, and c3the best sidelobe level for a given ripple R,. The c,, c,, c, criteria can be applied successively, depending on the ripple and the sidelobe level requirements.
Fig. 11.93 Directional broadside pattern of a six-element array (H-plane) -Relaxation synthesis ---- Experimental results
11.4.1.3 Directive broadside pattern case: For a broadside array of N equispaced elements with equal excitations, the beamwidth between first nulls is equal to 21,lNd radians. Applying c3 with R , , = 1 and 0, > Ao/Nd provides a main beam with the lowest sidelobe level, taking d/lo and g(0) into account. If d < 0.52, and g(0) = constant, we obtain the Chebyshev excitation. When d > 0.5A0, the Chebyshev method does not always maintain equal sidelobe levels. The relaxation method avoids such limitations, and printed antenna arrays with guided-wavelength spaced sources can be considered. 11.4.1.4 Results: Let us consider a linear printed antenna array on a substrate, having a relative dielectric constant E, = 2.17 (PTFE). For microstrip transmission lines a, = z 0.75&.
(a) Sector pattern We want to design a 10-source array with a 90' sector pattern and a transition width, 2a = 20'. If the sources are equally spaced, the array amplitude factor will be zero with any excitation vector for sin 0 = &/2d. To avoid a null in the sector region, the first distance to the symmetry axis can be taken as 0.252,. With aoT= (1; - 0.75; 0.5; - 0.25; O), g(0) = cos (0) and application of the
667
Design and technology of low-cost printed antennas
c, criterion, we obtain R = - 0.8 dB and SLL = - 29 dB for a solution vector S (Fig. 1 1.92~). With a0 = S, SLL,, = -25dB and application of c,. we obtain R = - 0.3 dB and SLL = - 26 dB (Fig. 11.92b). With a0 = S, R,,,, = - 1.5dB and application of c,, we obtain R = - 1.5 dB and SLL = - 36 dB (Fig. 11.92~). (6) Directive broadside pattern On the same substrate, let us design a linear array of six sources with interelement spacings ,$. For equal excitations, the beamwidth between the first nulls is 25.5" and the first sidelobe is at - 13dB. For 20, z 35", 2u = 10' (outline corresponding to a - 40 dB sidelobe level, Chebyshev excitation), R,, = 1, a: = 1, and a," = 0 V j # I, g(0) = cos(O), the c3 application provides a - 40 dB sidelobe level (Fig. 11.93). The experimental pattern obtained with a linear array of square patches is plotted in Fig. 11.93. The theoretical and experimental outlines agree well if the low-level measurement difficulties are taken into account. 11.4.2 Simplex method Dantzig's algorithm [76] has been developed for linear programming with a real variable. Under symmetrical amplitude and antisymmetrical phase conditions, it is possible to compute real or complex excitations. The desired diagram is also defined with an envelope specification. 11.4.2.1 Symmetrical pattern: If the pattern is considered at M angular values (without correlation with N), the following inequalities are obtained: F ( 0 J 5 F,
F(&) L
F 2
(1 1.45)
F(0M) 5 FM The problem is to find the ensemble V:
c, has been previously defined, and a functional J(a) = ElrJaj has to be optimised (minimum or maximum) in order to promote some part of the diagram for instance. 11.4.2.2 Asymmetrical pattern: Choosing a, = a-j and q5] array factor can be written in the following form: N
f (0) =
1 a, cos (k4 sin 0 + 4,)
j= l
= -q5-j,
the
668
Design and technology of low-cost printed antennas
Design and technology of low-cost printed antennas
669
The expansion of the cosine term leads to: N
F(0)
=
f (0)g(0) =
element
(A, cos (ko4sin0) - B,sin (k04sin0)) g(0)
I
j= l
2 3
1.000 0667 0267
A, and B, are the real unknowns to be determined from the new 2N-dimensions linear problem. The algorithm can be used again, and at the end:
The introduction of M difference variables leads to a new linear system of M equations (instead of inequalities) with N M unknowns associated with the functional J(a) (or 2N M unknowns for an asymmetrical patterns). The Dantzig algorithm shows that only one solution exists (if there is a solution), which is found in a finite number of steps [73, 761.
+
+
element
./-I +I-2 +I-3 4-4 +I-5
m
1.000 -0.236 0.097 -0.073 0.054
D
m 'I)
deg
Fig. 11.94 Sector pattern of a 10-element array (H-plane). Simplex synthesis
deg g(O)=g (0)
11.4.2.3 Examples: The second pattern previously mentioned has been computed using the simplex method (Fig. 11.94). It appears that the amplitudes, sidelobe level and ripple are very similar to the relaxation solution. Directional
Fig. 11.95 Directional patterns of a six-element array for various source patterns. Simplex synthesis a Isotropic source b E-plane pattern c H-plane pattern
670
Design and technology of low-cost printed antennas
patterns are plotted in Fig. 11.95 for an array of six elements spaced 0.75 &; three-element patterns have been considered (isotropic, E-plane and H-plane). The directional patterns of a linear 32-equi-spaced-element array (spacing = 0491,) in the H-plane are plotted in Fig. 11.96. The sidelobe levels were
Design and technology of low-cost printed antennas
671
constrained by the CCIR-TVRO conditions with an extra limitation of - 20dB for the highest one. A cosecant-squared pattern (with a 30' window) was achieved for a 30-element array with half-wavelength spacing. The E-plane-
degrees
Fig. 11 3 7 Computed cosecant squared pattern of 30-element linear array (E-plane and d l l = 0.5). Simplex synthesis
degrees
Fig. 11.98 Fig. 11.96 Computed directional broadside pattern of a 32-linear-element array (H-plane and d l l = 0.87). Simplex synthesis a Equi-amplitude b CCIR-TVRO constraints and -20dB first sidelobe
Computed 30' steered-beam pattern of 20-element linear array (H-plane and d / L = 0.5). Simplex synthesis
element pattern is considered in Fig. 11.97. A 30" steered beam of a 20-element array (with half-wavelength spacing) in the H-plane, with a sidelobe level lower than - 25 dB, is shown in Fig. 11.98.
672
Design and technology of low-cost printed antennas
Design and technology of low-cost printed antennas
673
11.4.3 Experimental results [73]
Both methods have been used to design sector and directional patterns in the X-bands and K-bands, using corner-fed square patches. 11.4.3.1 Sector pattern: The specification is as follows:
ripple SLL
<
=
f l dB
-25dB
To keep the feed line as simple as possible, the linear series array was chosen. The constraint of straight lines between each element leads to a one-guidedwavelength spacing (or a 0.75 free-space wavelength). However, a sector pattern of 90" beamwidth cannot be obtained with this spacing, because a null occurs in the B direction (where 0 = sin-' 1,/(21g)) whatever the amplitudes. T o avoid this effect, one solution is to change the spacing. Fig. 11.99 shows the structure which has been used. The two half arrays have been located closer together, then the synthesis methods can perform the amplitude excitations, taking into account the nonidentical spacing and the H-plane pattern of each patch. Theoretical results are presented in Table 11.I 1. table 11.12 Amplitude distribution along near direction array (in E- and H-plane)
90 Fig.
60
30
I , , . . . , , . ,
0
Measured sector pattern of a F, = 10.8GHz)
30
60
90
10-element linear array
and
Table 11.11 Amplitude and phase distribution along sector pattern array Element
Amplitude
Phase
+I- I
1 0.218 0.117 0.082 0.075
0 180 0 180 0
2 3 4 5
Element nb
H-plane (6 elements)
Element nb
E-plane (8 elements)
+/- 1
1 0.627 0.2 12
+I- 1
1 0.735 0.377 0.110
+/-2 +/-3
+/-2 +/-3 +/-4
The 180" phase shift between two neighbouring elements is easily obtained using alternate positions along the feeding line. Quarter-wave transformers (one or two sections) are used to obtain the amplitude taper. The measured patterns (co- and cross-polarised components) are plotted in Fig. 11.99. 11.4.3.2 Low side-lobe directive array (Fig. 11.100): Two steps were necessary: just to synthesise the H-plane pattern (six elements) and secondly to synthesise the E-plane pattern (eight elements). The amplitude taper was realised in the usual way, using quarter-wave transformers. Table 11.12 presents the taper values. Figs. 1l.lOla and b show the measured patterns in the E and H-planes. The
674
Design and technology of low-cost printed antennas
sidelobe levels are higher than the expected - 10 dB. However, mutual coupling has not been taken into account, and the reflectivity of the anechoid chamber reaches - 40 dB.
I
,point
Fig. 11.100 48-element planar directionelarray (6
d'alimentation
x
8 ) F, = 10.8GHz
11.5 New low-cost low-loss substrates 177,791 11S.1 Substrate choice
A large market demand for low-cost printed antennas has emerged from the development of new types of civil communication such as direct-broadcasting satellite reception, data transmission, communications between satellites and mobiles (trucks, ships, etc.) and intruder detectors. The price of a mass-produced printed antenna is directly related to substrate and connector costs. The choice of the appropriate substrate depends on its
Design and technology of low-cost printed antennas
675
676
Design and technology of low-cost printed antennas temperature (LC)
pressure
thn) Fig. 11 .I02 Pressure and temperature cycles of polypropylene
Raw material
Cu-Polypropy lene-Cu
I
Etching wet process
If necessary goto step 2
Fig. 11 .I03 Steps in manufacture of double-sided printed-circuit board (step 7)
Design and technology of low-cost printed antennas
677
678
Design and technology of low-cost printed antennas
application, nevertheless, many substrate properties may be involved: dielectric constant, loss, and their variations with temperature and frequency ranges, and mechanical and climatic stresses. Conventionally, printed antennas require the use of a low-loss low-dielectricconstant substrate. Unfortunately most printed-circuit boards currently used are quite expensive; some are listed in Table 11.13. CNET (Centre National d'Etudes des Telecommunications France) has developed a polypropylene substrate whose characteristics are very similar to commercial substrates, while remaining inexpensive. Fabrication procedures and evaluation of this new substrate will be discussed in the next Section. 11 S.2 Fabrication procedures The fabrication of polypropylene printed-circuit boards is a very simple procedure. Two types of board are considered:
Double-sided printed circuit: Cu-polypropylene-Cu Thick metal-backing substrate: thick metal base (A1 or Cu) polypropyleneCu 0
Polypropylene of different thicknesses (ranging from 0.25mm to 1.6mm or more) is manufactured by heating polypropylene granules to the melting point (170°C) and pressing them (Fig. 11.103). Pressure and temperature cycles are Raw material
I Double sided ~ r i n t e dcircuit I Copolymere of polypropylene ethylene Copper foil (ZOpm or 35pm)
Design and technology of low-cost printed antennas
679
Thick-backing construction offers significant advantages over conventional designs [78]: 0
It provides high reliability for connector mounting For high-power applications heat generated by devices can be dissipated.
Because the substrate is not loaded with glass fibre, it tends to warp when the internal stress between copper and polypropylene is too high; a thick metal cladding can ensure flatness. The same process can be extended to multilayer structures (Fig. 11.104), but in order not to damage the first layer, a copolymer or polypropylene-ethylene is used. The electrical characteristics are almost similar, but the melting point is 20" lower (150°C instead of 170°C); applications to triplate feeding network and stacked patches are straightforward as there is no need for bonding the film between different layers. Examples of practical applications are discussed below. 11.5.3 Electrical characteristics Dispersion measurements were carried out by the ring-resonator technique in triplate technology (in order to avoid unwanted radiation). Overall losses are plotted against frequency in Fig. 11.105 for different types of printed circuits and are compared with a PTFE substrate (RT Duroid 5880):
A: Cu (20 pm)-polypropylene-Cu (20 pm) B: Aluminium (Al) (4 mm)-polypropylene-Cu (20 pm) C : RT Duroid 5880 The dielectric constant remains constant with frequency. Fig. 11.106 shows that polypropylene and the copolymer of polypropylene-ethylene have the same electrical performance. 11 3 . 4 Environmental tests
V
Multilayer printed cicuit
Fig. 11 .I04 Steps in manufacture of multi-layer printed-circuit board (step 2)
detailed in Fig. 1 1.102. Copper-foil or thick-metal backing is first chemically processed and then laminated to the polypropylene-based dielectric by the same procedure. Laminated copper is usually selected in preference to electrical-grade copper, which is more lossy. Thicknesses are commonly 20pm or 35pm. .
11.5.4.1 Damp heat: 95% relative humidity at 40" and for 22 days: Again, overall losses are plotted as a function of frequency in Fig. 11.107 before and after tests, and are compared with the RT Duroid 5880 substrate. The polypropylene does not seem to be very affected by the test conditions, while the PTFE substrate losses are slightly increased. This is probably due to the fact that this substrate is loaded with glass fibre. 11.5.4.2 Thermal shocks: Tests have been performed on a 0 4 m m printed circuit with 4 mm aluminium (Al) backing. The board survived the following tests:
680
Design and technology of low-cost printed antennas
Design and technology of low-cost printed antennas
681
damp heat (9570hr 40°C 21days)
PTFE af!er test
(4
PTFE before test
2
(-1
polypropylene before test polypropylene after !est
1
0L 35
55
73
90
10.8
12.7
14 5
- frequency GHz
Fig. 11.107 Losses before and after test of damp heat frequency
GHz
Fig. 11 .lo5 Losses (dBlm) versus frequency for various printed circuits ( A ) Cu 20pm-polypropylene-Cu 2 0 p m
(8)A l (4 mm)-polypropylene-Cu 2 0 p m (C) RT-Duroid 58-80 (copper on each side)
01 3.3
6.7
10.1
13.5
16.9
frequency,GHz
Fig. 11.106 Comparison of polypropylene (A) and copolymer of polypropylene ethylene (6)
Fig. 11.108 50-element cross-fed array printed on a 0 . 4 m m polypropylene substrate. Frequency = 2 0 G H z
682
Design and technology of low-cost printed antennas
-40°C
+85OC
- 55OC
+ 10o0c
but was destroyed at
- 65OC
+ 125OC.
Design and technology of low-cost printed antennas
683
a 50-element array is shown in Fig. 11.108. This array operates at 19.6 GHz, and its measured gain is 23 dB. The antenna has already been discussed in a previous Section. The three-element array in Fig. 11.109 was designed for data transmission between mobiles at 23.5 GHz. The required performance was: E-plane: 3 dB beamwidth = 40' H-plane: 3 dB beamwidth = 60' In order to meet the 60" requirement in the H-plane, the distance between patches has to be very small, which is the reason why this three-element geometry was chosen. The measured gain is I1 dB because the patches are very close. It is not possible to match the antenna with 0.25l microstrip line transformer. The problem has been solved by using a coaxial-line transformer machined in the 4 mm aluminium ground plane which provides a VSWR of 1.5. Radiation patterns are given in Fig. 11.110. 11.5.5.2 Multi-layer printed antennas: A printed-slot array was designed in order to test the possibilities of using polypropylene technology for large dimensions. This array was also designed with the aim of replacing a Yagi antenna, whose sidelobes level are very high, by a flat antenna which should have better characteristics and be less expensive. The specifications were:
1.38-1.525 GHz Gain: 16dB to 17dB 3 dB beamwidth = 20' to 25O Linear polarisation Sidelobe level < - 20 dB
Fig. 11.109 Three-element array printed on a 0.4mrn polypropylene substrate. Frequency = 23.5 GHz
113 . 5 Examples of printed antennas on polypropylene substrates The two examples which are described here give a good insight into the possibilities of this new technology. 11.5.5.1 Single-sided printed antennas: A few types of microstrip antenna arrays have been designed for the 20GHz band with gain from I 1 dB to 23 dB [77]. These antennas are printed on a 0.4mm polypropylene substrate with 4mm aluminium backing, which operates as the ground plane of the patches, ensures the flatness of the antenna and eases the connector mounting. A photograph of
The gain specification implies dimensions of 60 x 60cm. The printed-slot element was selected because it can provide wider bandwidth than microstrip patches, and also because it is very easy to feed. The fabrication of the antenna requires few steps. The two copper layers are separated by a 0.8 mm polypropylene layer. The slots are printed on the upper face of the substrate while the feed network is printed on the rear side. The printed-slot plane is covered by a second 0.8 mm polypropylene layer which ensures flatness of the antenna. Photographs of the antenna are given in Fig. 11.111. The printed slots are electromagnetically coupled to the microstrip lines and the array is suspended over a reflector plane in order to get unidirectional radiation patterns. Since the dielectric thickness is very small compared with the wavelength, the dimensions of the slot are such that 2nr = A. Input impedance is measured in the plane of the outer edge of the slot and then matched to 50 0 by a matching network. The slot width is W/1 = 0.017. The VSWR of a single element is plotted against frequency in Figs. 11.112a and b for two spacings h/l = 0.12 and h / l = 0.25 of the reflector plane. In the first case, the matching is provided by a quarter-wavelength transformer, while in the second case a
684
Design and technology of low-cost printed antennas
plan E \
23.5GHz
Design and technology of low-cost printed antennas
685
quarter-wavelength transformer and two stubs are required to fit the bandwidth requirement. It appears that the bandwidth decreases as the spacing increases. The 4 x 4-slots array is designed for a 25 dB Chebyshev taper. The results are
Fig.
11 .I11 Printed slot array. Frequency = 1.5 GHz a Top view of the printed-slot array beside a Yagi antenna under a radome b Rear view of the printed-slot array and its feed network
as follows: Slot width = 0.0171 Reflector height = 0.251 Gain: 17.2 dB Efficiency: 67% Radiation patterns are given in Fig. 11.113. Although the radiation patterns and gain are good, a good match over the whole frequency band could not be obtained. The VSWR remains below 2.5 over the whole-frequency band. This is due to the very high coupling between slots, which is increased by the proximity of the reflector plane.
11.6 Concluding remarks Fig.
11.1 10 Radiation patterns of the three-element array (Fig. 1 1.107) ( a ) E-plane ( b ) H-plane
The design of low-cost printed antenna arrays needs accurate analysis of parameters such as resonant frequency, input impedance, mutual coupling and
686
Design and technology of low-cost printed antennas
Design and technology of low-cost printed antennas
687
688
Design and technology of low-cost printed antennas
sidelobe level with respect to the dimensions, dielectric constant, thickness of protective layer and inter-element spacing. The transmission-line model, the cavity model and the spectral-domain approach are complementary tools which can be used together. In addition, specific synthesis methods have been developed to maintain the flexibility offered by printed structures; namely nonidentical element spacing and non-identical E- and H-plane element patterns. Finally, the polypropylene substrate, whose characteristics are very close to commercial substrates, is very cost competitive in most applications. On the other hand, thick-backing construction using either metal or metallised dielectric, and multi-layer structures without bonding film have been experimented with in order to reduce overall cost.
11.7 References DERNERYD, A. G., and LIND, A. G.: 'Extended analysis of rectangular microstrip resonator antennas', IEEE Trnns., 1979, AP-27, pp. 846-849 VANDESANDE, J., PUES. H., and VAN DE CAPELLE, A.: 'Calculation of the bandwidth of microstrip resonator antennas'. Proc. 9th European Microwave Conference, Brighton, 1979, pp. 116-119 DUBOST. G.: 'Linear transmission-line model analysis of arbitrary shape patch antennas', Electron. Lett., 1986. 22, pp. 798-799 LO, Y. T., SOLOMON, D., and RICHARDS, W. F.: 'Theory and experiment on microstrip antennas', IEEE Trans., 1979, AP-27, pp. 137-145 JAMES, J. C., HALL, P. S., and WOOD, C.: 'Microstrip antenna theory and design' (Peter Peregrinus, 1981) BAHL, I. J., and BHARTHIA, P.: 'Microstrip antennas (Artech House', USA, 1980) WOOD, C.: 'Improved bandwidth of microstrip antennas using parasite elements', IEE Proc., 1980, 127, pp. 231-234 PENARD. E., and DANIEL, J. P.: 'Open and hybrid microstrip antennas'. IEE Proc., 1984, 131H, pp. 3 8 4 4 MAHDJOUBI, K., DANIEL, J. P., and TERRET, C.: 'Etude d'antennes imprimCes a accis multiples', Ann. de Telecom, 1985, 40, pp. 190-203 MAHDJOUBI. K.. DANIEL, J. P., and TERRET, C.: 'Dual frequency disc antenna studied by cavity method', Electron. Lett., 1986, 22, pp. 379-381 MAHDJOUBI, K.. and TERRET, C.: 'Exact expression for stored energies in the cavity volume of microstrip antennas', Electron. Letl., 1985, 21, pp. 1221-1222 PENARD. E., and DANIEL, J. P.: 'Electric and magnetic currents in microstrip antenna theory'. Int. IEEEIURSI, Albulquerque, New Mexico, 1982 PENARD, E.. and DANIEL, J. P.: 'Calcul du rayonnement d'antennes microstrip: deux exemples. Journies Nationales Micro-ondes de Toulouse, 1981 NEWMAN, E. D.. and TULYATHAN, P.: 'Analysis of microstrip antennas using moment method', IEEE Trans., 1981, AP-29, pp. 47-53 LEWIN. L.: 'Radiation from discontinuities in strip-lines', IEE Monograph 358, 1960 HARRINGTON, R. F.: 'Time-harmonic electromagnetic fields' (McGraw-Hill Book, NY, 1961) AAS, J. A., and JAKOBSEN, K.: 'Radiation patterns of rectangular microstrip antennas on finite ground plane'. 12th European Microwave Conference, Helsinki, 1982 POZAR. D. M.: 'Finite phase arrays of rectangular microstr~ppatches', IEEE Trans., 1986, AP-34, pp. 658-665
Design and technology of low-cost printed antennas
689
19 POZAR, D. M.: 'Input impedance and mutual coupling of rectangular microstrip antennas', IEEE Trans., 1982, AP-30, pp. 1191-1 196 20 ITOH. T., and MENZEL, N.: 'A full wave analysis method for open microstrip structures', IEEE Trans., 1981, AP-29, pp. 63-68 21 DESHPANDE, M. D., and BAILEY, M. C.: 'Input impedance of microstrip antennas', IEEE Trans., 1982, AP-30, pp. 645-650 22 MOSIG, J.: 'Les structures microrubans, analyse au moyen des Cquations intigrales', D.Sc Thesis, EPFUL, Lausanne, Switzerland, 1984 23 KATEHI, P. B., and ALEXOPOULOS, N. G.: 'On the modelling of electromagnetically coupled microstrip antennas. The printed strip dipoles', IEEE Trans., 1984, AP-32, pp. 1179-1 I86 24 ROUDOT, B.: 'Analyse d'antennes imprimees par une approache dans le domaine spectral', D.Sc Thesis, University of Rennes, France, 1985 25 PENARD, E.: 'Etude d'antennes imprimies par la mdthode de la caviti applications au couplage'. D.Sc Thesis, University of Rennes, France, 1982 26 BAHL, 1. J., STUCHLY, S. S., and BHARTIA, P.: 'Design of microstrip antennas covered with a dielectric layer', IEEE Trans., 1982, AP-30, pp. 314-318 27 DE ASSIS FONSECA, S. B., and GIAROLA, A. J.: 'Microstrip disk antennas. pt. 2: The problem of surface wave radiated by dielectric truncation', IEEE Trans., 1984, AP-32, pp. 561-573 28 ROUDOT, B., TERRET, C., DANIEL, J. P., PRIBETICH, P., and KENNIS, P.: 'Fundamental surface-wave effects on microstrip antenna radiation'. Electron. Lett., 1985, 21, pp. 1112-1114 29 DE ASSIS FONSECA, S. B., and GIAROLA, A. J.: 'Influence of surface-wave excitation efficiency of space-wave launching in microstrip disc antennas', Electron. Lett., 1982, 18, pp. 406407 30 GRIFFIN, J. M., and FORREST, J. R.: 'Broadband circular disc microstrip antennas', Electron. Lett., 1982, 18, p. 266-269 31 DAS, N., and CHATTERJEE, J. S.: 'Conically depressed microstrip patch antenna', IEE Proc., 1983, 130H. pp. 193-196 32 JEDDARI, L., MAHDJOUBI, K., TERRET, C., and DANIEL, J. P., 'Broadband conical microstrip antenna', Electron. Letl., 1985, 21, pp. 896-898 33 MAILLOUX, R. J.: 'Printed slot arrays with dielectric substrates'. IEEE Symposium on Antenna and Propagation, June 1985 34 OLINER, A. A.: 'The radiation conductance of a series slot in strip transmission line'. IRE Conv. Rec. No. 2, 1954, Pt. 8, pp. 89-90 35 BREITHAUPT, R. W.: 'Conductance data for offset series slot in stripline', IEEE Trans., 1968, MMT-16, pp. 969-970 36 TOBARIAS, 3.: 'Fente rayonnante bidirectionnelle a la rhonance et a I'antiresonance alimentie par une ligne microruban'. Gme Journees Nationales Micro-ondes, Lannion, June 1984, pp. 236-237 37 TOBARIAS, J., and TERRET, C.: 'Fente rayonnante a la resonance et a l'antiresonance alimentie par une ligne coplanaire'. Gme Journees Nationales Micro-ondes, Lannion, June 1984, pp. 242-243 38 DUBOST, G., and ZISLER, S.: 'Antennes a large bande', (Masson Editors, France, 1976) 39 WEEKS, W. L.: 'Antennas engineering' (McGraw-Hill, 1968) 40 MARCANO, D., SAILLARD, J., TERRET, C., and DANIEL, J. P.: 'Reseau de fentes balayage electronique'. 5eme Journees Nationales Micro-ondes, Nice, pp. 265-267 41 YOSHIMURA, Y.: 'A microstrip line slot antenna', IEEE Trans., 1972, MTT-20, pp. 760-762 42 DAS, B. N., and JOSHI, K. K.: 'Impedance of a radiating slot in the ground plane of a mirostripline', IEEE Trans., 1982, AP-30, pp. 922-926 43 BOOKER, G. G.: 'Slot aerials and their relation to complementary wire aerials', J. IEE, 1946, 93, Pt. IIIA, pp. 620-626
690
Design and technology of low-cost printed antennas
44 NESIC, A.: 'Slotted antenna array excited by a coplanar waveguide', Electron. Lett., 1982,13, pp. 404-406 45 NESIC, A,: 'A printed antenna array with slots as primary radiators for phase scanned antenna'. JINA, Nice. Nov. 1986, pp. 281-283 46 DUSSEUX, T.: 'Etude d'antennes fentes annulaires imprimees applications antennas melangeuses, reseaux'. D S c Ing. Thesis, University of Rennes, May 1987 47 COHN, S. B.: 'Slot-line on a dielectric substrate, IEEE Trans., 1969, MTT-17, pp. 768-778 48 DUSSEUX, T., DANIEL, J . P., and TERRET, C.: 'Theoretical and experimental results of guided wavelength of a slot on a low permittivity substrate', Electron. Lett., 1986, 22, pp. 589-590 49 JANASWANY, R., and SCHAUBERT, D. H.: 'Dispersion characteristics for wide slot lines on low permittivity substrates', IEEE Trans., 1985, MTT-33, pp. 723-726 50 KAWANO, K., and TONIMORO, H.: 'Slot ring resonator and dispersion measurement on slot lines'. Electron. Lett., 1981, 17, pp. 916-917 51 GARG, R., and GUPTA, K. C.: 'Expressions for wavelength and impedance of a slot line', IEEE Trans., 1976, M'IT-24, p. 532 52 JAMES, J. R., and HENDERSON, A,: 'High-frequency behaviour of microstrip open-circuit terminations', IEE J. Microwaves. Optics and Acoustics, 1979, 3, pp. 205-218 53 ELLIOTT, R. S.: 'The theory of antenna arrays', in HANSEN, R. C. (Ed.): Microwave scanning antennas: Vol. 11, (Academic Press, 1986), chap. 1 54 HANSEN, R. C.: 'Linear arrays' and 'Planar arrays' in RUDGE, A. W. el al. (Eds): 'The handbook of antenna design: Vol 11' (Peter Peregrinus, 1983). chaps. 9 and 10 55 BACH, H.: 'Directivity of basic linear arrays', IEEE Trans., 1970, AP-18, pp. 107-110 56 BACH, H., and HANSEN, J. E.: 'Uniformly spaced arrays' in COLLIN, R. E., and ZUCKER, F. J. (Eds.): 'Antenna theory. Pt. 1' (McGraw-Hill, NY, 1969) 57 HANSEN, R. C.: 'Aperture efficiency of Villeneuve n arrays', IEEE Trans., 1985, AP-33, pp. 666-669 58 VILLENEUVE, A. T.: 'Taylor patterns for discrete arrays', IEEE Trans., 1984, AP-32, pp. 1089-1093 59 HANSEN, R. C.: 'Comparison of square array directivity formulas', IEEE Trans., 1972, AP-20, pp. 100-102 60 WHITTAKER E. T., and WATSON, G. N.: 'A course of modern analysis', Cambridge, London, 1962, p. 170 61 JEDLICKA, R. P., and CARVER, K. R.: 'Mutual coupling between microstrip patch antennas'. Proc. Workshop on printed circuit antenna technology, Oct. 1979 62 JEDLICKA, R. P., POE, M. T., and CARVER, K. R.: 'Measured mutual coupling between microstrip antennas', IEEE Trans., 1981, AP-29, (1) 63 MALKOMES, M.: 'Mutual coupling between microstrip patch antennas', Electron. Lett., 1982, 18, pp. 520-522 64 VAN LIL, E. H.. and VAN DE CAPELLE, A. R.: 'Transmission line model for mutual coupling between microstrip antennas', IEEE Trans., 1984, AP-32, pp. 816-821 65 PENARD, E., and DANIEL, J. P.: 'Mutual coupling between microstrip antennas', Electron. Lett.. 1982, 18, pp. 605-607 66 MAHDJOUBI, K., PENARD, E., DANIEL, J. P., and TERRET, C.: 'Mutual coupling between circular disc microstrip antennas', Electron. Lett., 1987, 23, pp. 27-28 67 BHAlTACHARYYA, A. K., and SHAFAI, L.: 'Surface wave coupling between circular patch antennas', Electron. Let(., 1986, 22, pp. 1198-1200 68 MAHDJOUBI, K., PENARD, E., TERRET, C., and DANIEL, J. P.: 'Mutual coupling between microstrip disk antennas'. ICAP '87, late papers, University of York, 1987 69 DANIEL, J. P., PENARD, E., NEDELEC, M., and MUTZIG, J. P.: 'Design of low cost printed antenna arrays'. Proceedings of ISAP'85, Kyoto, Aug. 1985, pp. 121-124 70 WILLIAMS, J. C.: 'Cross fed printed aerial'. Proc. 7th European Microwave Conf. Copenhagen, 1977, p. 292
Design and technology of low-cost printed antennas
691
71 DANIEL, J. P., MUTZIG, J. P., NEDELEC, M., and PENARD, E.: 'Reseaux d'antennes imprimees dans la bande 20/30GHz'. 4eme Journees Nationales Microondes, Lannion, France, June 1984, pp. 246-247 72 DANIEL, J. P., MUTZIG, J. P., NEDELEC, M., and PENARD, E.: 'Reseaux d'antennes , 65, pp. 35-41 imprimees dans la bande 20/30GHz', Lbnde ~ I e c t r i ~ u e1985, 73 BOGUAIS, M.: 'Contribution a la synthese de reseaux d'antennes, realisation en technologic imprimbe. D.Sc Thesis, University of Rennes, France 74 BOGUAIS, M., DANIEL, 1. P., and TERRET, C.: 'Antenna pattern synthesis using a relaxation method: application to printed antennas', Electron. Lett., 1986, 22, (7) 75 BOGUAIS, M., DANIEL, I. P., and TERRET, C.: 'Deux methodes de synthese de reseaux d'antennes, application aux antennes imprimees', JINA, Nice, 1986, pp. 3 10-31 1 76 DANTZIG, G. B., and ORCHARD-HAYS, W.: 'The product form for the inverse in the simplex method', Math. Comp., 1959 77 DEMEURE, L.: 'New low cost and low loss substrate: Application to printed antenna', JINA, Nice, France, Nov. 1986 78 BONFIELD, R.: 'Thick metal backing adds value to substrate', Microwaves and RF, Feb. 1987 79 Patent 84 402 7078: 'Support metallis6 a base de polypropylene et procede de fabrication de ce support'
Chapter 12
Analysis and design considerations for printed phased-array antennas D. M. Pozar
12.1 Introduction
Until the last decade or so, phased-array technology generally employed dipole or waveguide radiating elements, with waveguide or coaxial lines for feed networks [l-41. In more recent years, however, printed or microstrip arrays and feedlines have become quite popular [5-71 owing to features including light weight, conformability, ease of manufacture and, probably most important, potentially low cost. Economics is generally the most critical factor affecting the deployment of phased arrays into more systems, as a variety of applications would benefit from the advantages of a phased-array antenna, which include rapid and selective beam steering, adaptive nulling, and other controlled arrayillumination functions. The printed phased array, with its fabrication simplified through the use of photolithographic techniques, offers the promise of lowercost electronically scanned arrays. This is in spite of some inherent disadvantages of printed antennas, such as low bandwidth and power capacity. Printed arrays can take many different forms. Radiating elements may be printed dipoles, printed (microstrip) patches or slot elements. Feed circuitry may be in microstripline, or in stripline form. Several combinations then exist for the interconnection of feed lines to radiating elements. One approach is to etch the radiating elements and feed lines in microstrip form on the same substrate, while other approaches use two or more layers to separate the radiating elements from feed circuitry. Phase shifting and other active circuitry functions can be incorporated in hybrid form. At millimetre-wave frequencies the physical size of the array may be small enough so that circuit integration can be carried one step further, resulting in the 'monolithic phased array'. This concept, discussed in more detail in Section 12.3, involves the integration of all active circuitry required for a sub-array module of a millimetre-wave phased array. This Chapter first considers the rigorous analysis of several canonical printedarray geometries (Section 12.2), and then discusses some design considerations for printed arrays (Section 12.3). During the 1960s, a large analysis effort was
694
Analysis and design considerations for phased-array antennas
Analysis and design considerations for phased-array antennas
695
carried out for waveguide and dipole phased arrays [I-41; a corresponding effort for printed phased arrays is still needed, but the present Chapter consolidates some of the solutions which have been completed to date. Section 12.2.2 treats infinite planar arrays of various printed elements. While most of these cases are idealised in some way, they represent a starting point for the analysis and/or design of more practical arrays. In addition, as discussed in more detail in Section 12.2.2.5, the scan performance of phased arrays is often more dependent on substrate parameters and element spacing than on the particular details of the feeding method. In Section 12.3 dealing with design considerations, the monolithic phased-array concept is emphasised, but much of this material is relevant to non-monolithic printed arrays as well.
cross-polarisation level, and possibly the efficiency of the array. Pattern quantities such as directivity and sidelobe level depend on the size of the array, and so are not very meaningful for infinite arrays (since an infinite array radiates a plane wave, its directivity is infinite, while its sidelobe level is zero). In the following Subsections, we first present some material that is common to most of the solutions which follow, including a brief derivation of a typical Green's function and a discussion of the scan-blindness effect. We then treat several canonical infinite planar printed arrays, and present results for the scan performance of such arrays. Next, solutions are described for finite arrays of dipoles and rectangular microstrip patches. The finite-array problem is considerably more difficult than the corresponding infinite-array problem, but may be of more practical utility since it includes edge effects.
12.2 Analysis of some canonical printed phased-array geometries
12.2.1 Some preliminaries
In this Section we present analyses for several types of printed phased-array geometries. These problems are canonical in that the geometries are idealised in some sense, usually in terms of simplifying assumptions about the feed. The solutions here all have a high degree of commonality, being based on the work of the author and his colleagues at the University of Massachusetts. The relevant work of other researchers, however, is noted and discussed in relation to the analyses presented here. The basic procedure for the analysis of each of the printed-array geometries in this Section is as follows. First, the Green's function for the relevant dielectric-slab geometry is derived in spectral (transform)-domain form, for a single infinitesimal source (electric or magnetic dipole). This result is then extended to an infinite periodic planar array of such sources, with a progressive phase shift for scanning at the desired angle. A moment-method solution is formulated for the unknown current distribution on the antenna element, and an appropriate set of expansion weighting functions is chosen. An impedance matrix results, which can then be used to determine the unknown coefficients of the expansion modes. Because of the periodic nature of the array, the current distributions on all of the elements are the same, except for the imposed progressive phase shift. Thus, formulating the moment-method solution for one 'unit cell' is equivalent to imposing the solution across the entire array. Mutual coupling is implicitly included in the solution. This method has variously been referred to as a 'full-wave solution', or the 'Galerkin method in the spectral domain', and has been applied to a variety of antenna and microwave circuit problems, in both single-element and array form. After the currents have been determined, other quantities of interest can easily be found. The variation of input impedance with scan angle can be calculated; this result is quite important for matching the array over the desired scan range. A related quantity is the active-element pattern, which also gives information about the scan performance of the array. Other quantities of interest include the
12.2.1.1 Derivation of the Green's function of a grounded dielectric slab: Central to the solutions that follow is the exact Green's function of the dielectric-slab geometry in spectral, or transform, domain form. Such Green's functions have appeared in a number of recent papers on printed-antenna analysis [8-121, but generally without derivation. Thus it may be useful to present a short derivation of a Green's function, in case the reader is not familiar with the basic procedure. We will derive the Green's function for a grounded dielectric slab, with an infinitesimal electric-current source on its surface. This is one of the most useful Green's function results, being applicable to all of the array geometries below (some additional Green's functions are needed for the slot elements of Section 12.2.2.4). The same procedure, however, can be used to obtain the Green's functions for a number of more general cases, including the following:
Two (or more) dielectric-layer geometry Dielectric layer with a lossy (surface-impedance) ground plane Substrate with magnetic properties Anisotropic substrates Fig. 12.1 shows the geometry of a grounded isotropic dielectric slab of thickness d and relative permittivity E , . The source is an infinitesimal f-directed electric dipole, of unit strength and located on the surface of the dielectric slab at (x,, yo, d). We desire to find the E,, Ev and E, fields generated by this source. While it is possible, and quite common, to introduce vector potentials, it is actually simpler to work directly with wave equations for El and Hz, and find the transverse fields from these field components. Thus, Maxwell's equations,
V x E = -jopoH
(12.14
V x H
(12.lb)
=
jo~E
can be solved simultaneously for the usual Helmholtz wave equations in a source-free region:
696
Analysis and design considerations for phased-array antennas
where k2 = m2p0c,and E = %er for 0 < z < d, and E = E~ for z > d. Anticipating a plane-wave form of solution, with a propagation factor egk\" e*IkyY etJk:', and substituting this form into eqn. 12.2a,b gives the propagation constants in the z-direction as
Analysis and design considerations for phased-array antennas
These results are for the dielectric region 0 < z < d, but can be used for the air region z < d by setting E, = 1. Similarly, a2/az2= - k: or - k:, depending on whether 0 < z < d, or z z d, respectively. From the wave equations of 1 2 . 2 and ~ 12.26, the general solutions for &and H~are:
fi -
Be-jk~z
Ez =
Ccosk,z
I
+
with B2 = k: g . In the above, the branch of the square-root function should be chosen so that Im(k,) < 0 and Im(k2) < 0.
697
I?,
+ Dsinklz
for z z d
(12.6b)
for 0 < z < d
(12.6~)
= Esink,z+ F C O S ~ for~ Z0 < z < d
(12.6d)
where outgoing waves have been assumed in the region z > d. With these forms the transverse field components of eqns. 12.5~-dcan be rewritten as
Fig. 12.1 Geometry of an infinitesimal f -directed current element on a grounded dielectric slab
We now define a Fourier-transform pair as
Then, in-the transform domain, the transverse fields can be written in terms of
zzand H,as,
(erg +
$) Ex
= jk.
a
which also apply to the region z > dafter E, is set to unity. Applying eqns. 1 2 . 7 ~ and b to eqns. 1 2 . 6 ~and d to enforce the boundary condition that E, = Ey = 0 at z = 0 yields D = F = 0. There then remains four constants (A, B, C, E ) to be evaluated by the continuity of Ex, Ey and H, at z = d (the dielectric-air interface), and a jump condition in H,at z = d (due to the current_source).After some straightforward algebraic manipulation, the results for E, and $ for 0 < z < dare
-
a, E, + oh kyfix
-
-jky sink,
e-jk.r"o e - j k y ~ ~
Hz
=
-
T,
=
~,k,cosk,d jk,sink,d
T,
=
k, cosk,d
Te
(12.8b)
where
+
a.
+ jk,sin k,d
(12.9~) (12.9b)
The zeros of the T,,, and T, functions correspond to the TM and Zo = and TE surface-wave poles of the grounded dielectric slab.
698
Analysis and design considerations for phased-array antennas
Using eqns. 12.7~-dand eqns. 1 2 . 8 ~and b and taking the inverse transform in eqn. 1 2 . 4 ~allows the transverse electric fields at z = d to be evaluated as
Analysis and design considerations for phased-array antennas
699
are the direction cosines. Then by superposition, eqns. 1 2 . 1 0 and ~ b can be used to find the total field from this infinite array (after replacing rn, n, k, and ky with - rn, - n, - k , and - k,, , respectively):
where the following quantities have been defined: G.:; =
, G'"
=
-jZo (E, ki
ko
- kS)k2cos k, d
+ jk, (g - k:)
T, T,
jZo - kxk, sin k, d[k2cos k, d k, T, T ,
sink, d . sin k, d
+ jk, sink, d l (12.11b)
In eqns. 12.10a and b the notation E0 has been used to denote the field due to a single source. The above field expressions are directly applicable to the analysis of isolated antennas printed on the surface of a dielectric slab. Note that the results for Ex and E, of eqns. 12.10~and b satisfy reciprocity, as an interchange of x , x, and y, yo does not change the result. 12.2.1.2 Extension to an infinite array: We now show how the Green's function of the previous Section for a single infinitesimal electric dipole can be generalised to an infinite phased array of such sources. Fig. 12.2 shows the geometry of an infinite periodic array of infinitesimal sources, with spacing a in the E-plane (x) direction, and spacing b in the H-plane (y) direction. Them, nth s a m e is thus located at
where rn, n are integer indices with - co < m, n < co. Now for scanning at the angle 0, q5 the currents on the rn, nth source must be phased as -jko(muu +nbv) (12.13)
Fig. 12.2 Geometry of an infinite periodic array of R-directed infinitesimal current elements on a grounded dielectric slab
Eqns. 12.15a and b give the transverse fields at (x, y, d) due to the infinite array of dipoles and may be thought of as the Green's function of the infinite array. Observe, however, that E, and Ey of eqns. 12.15~ and b do not satisfy reciprocity upon interchange of x , xo and y, yo. This is due to the asymmetry introduced by the phasing of eqn. 12.13. Eqns. 12.15~and b are rigorous expressions, but clearly not in a very usable form from a computational viewpoint. The Poisson-sum formula can be applied to greatly simplify the result. Consider an expression of the form
where u = sinOcos4
v = sin Osin q5
The Poisson sum formula can be written as ejm""' m
F(rnwo)
=
f( t
T m
+ mT)
700
Analysis and design considerations for phased-array antennas
where T
=
2n/w,, and f (t) and F(w) form a Fourier transform pair:
~ ( w )= f(t) =
Jmm
f(t) edw' dl
-In -" 1
2i7
F(w)eJW'dt
(12.18a) (12.186)
Now let f (I) = h(r) el"". Then F(w) = H(w - w, ), and eqn. 12.17 becomes
Now compare eqns. 12.19 and 12.16, and let t = k,u, w, = a, t' = k,, w, = x, T = 2nla and h = q, to get
with
So we see that the Poisson-sum formula can be used to eliminate the infinite integration of eqn. 12.16. This result can be applied twice (fork, and k,,) to eqns. 12.15~and b), to give the following results:
Analysis and design considerations for phased-array antennas
in a number of different types of arrays [2, 4, 8, 131, and is generally related to the resonance of some type of trapped or guided mode of the array structure. For example, waveguide arrays with dielectric plugs or dielectric cover layers have exhibited the scan-blindness phenomenon [4]. Printed phased arrays, because of the presence of a dielectric slab, also show scan-blindness effects. Scan blindness is total only in infinite arrays (or waveguide simulators), but in large arrays the effect can be severe enough to seriously degrade performance. Thus it is important to both understand the scan-blindness effect and to be able to predict the occurrence of this effect in printed phased arrays. Unless otherwise stated, the discussion below refers to an infinite array. One way of observing scan blindness is to look at the reflection-coefficient magnitude at one element of an infinite phased array. Assuming a reasonable impedance match at broadside scan (0 = 0') the reflection-coefficient magnitude will be small there. As the scan angle increases towards endfire (0 = 90°), the reflection-coefficient magnitude must increase to unity, since an infinite phased array does not transmit any real power away from the face of the array at endfire scan. A scan blindness, however, will show its presence by unity (or near unity) reflection-coefficient magnitude at some scan angle before endfire. This means that each element of the transmitting array is reflecting all the power incident on it, and so the array is 'blind' at this scan angle. The active-element pattern of the array provides another way of looking at the scan-blindness effect. The active-element pattern is defined as the radiation pattern of an array obtained when one element is driven and all other elements are terminated in matched loads [3]. If no grating lobes are present, it can be shown [3] that the active-element (power) pattern F(0, 4 ) of an array is related to the active reflection coefficient R(0, 4 ) by w , 4 ) = (1 - I R ( ~4)1*)cose ,
where the variables k, and k, take on the discrete values
k,
=
2nm -+k a
'O
(12.23~)
Note the similarity between eqns. 12.22 and 12.10; eqn. 12.22 can be considered as a discretised version of the continuous integration in eqn. 12.10. 12.2.1.3 The scan-blindness effect: Scan blindness refers to a condition where, for certain scan angles, no real power can be transmitted (or received) by a phased array. This effect has been experimentally and theoretically observed
707
(12.24)
The active-element pattern is significant because it is relatively easy to measure (no power-dividerlphase-shifter network is required), and it provides information about the scan performance of the array. A scan-blindness condition will show up as a null in the active-element pattern, owing to the unity reflection coefficient at the blind spot. Thus, some workers refer to scan blindnesses as nulls in the active-element pattern. One can discuss the scan-blindness effect from several viewpoints. If a specific array geometry is being considered, a rigorous analysis of the scan performance of the array will allow the prediction of the blindness effect. This will be done in the following Sections for several printed arrays of practical interest. In addition, certain canonical problems can be posed which are complete enough to yield data on the scan performance of printed arrays, including blindness angles, in a more general sense. This has been done with the current sheet model discussed in Section 12.2.2.5, and with the infinite array of infinitesimal dipoles discussed below.
702
Analysis and design considerations for phased-array antennas
If no details of the array geometry are available, or if one wishes to look at the blindness effect from a different point of view, an analysis based on mutual coupling (measured or calculated) can be used. Thus, consider an infinite planar array, with the elements indexed as in eqn. 12.12. Let the reference element be the m = n = 0 element, and assume each element is fed with a unit amplitude voltage source having a phase given by eqn. 12.13. If the scattering matrix coefficient between them, n t h element and the 0,0 reference element is S,,, then the reflection coefficient is
This result shows that the reflected wave at any given element is due to the mismatch of the isolated element (So,,),plus contributions from all the neighbouring elements. The effect of the coupling from the neighbouring elements depends on the strength of the coupling, and on the scan angle. For coupling coefficients of a certain magnitude and phase, it is possible for an in-phase accumulation of coupled power to lead to total reflection at certain scan angles. This discussion shows how scan blindness can occur from a mutual-coupling point of view, but drawing more specific conclusions is difficult unless data on the coupling coefficients is available, or can be assumed [14]. We now look at a specific printed-array geometry - an infinite planar array of infinitesimal dipoles - to obtain more information about the scan-blindness effect. This is an idealised case, of course, but is complete enough to show some of the essential blindness mechanisms that occur in this array and in other infinite printed arrays. The preliminary derivations of the Green's function and the extension to an infinite array of infinitesimal %directed currents of Sections 12.2.1.1 and 12.2.1.2 can be applied directly. We assume that the rn = n = 0 element of the array is located at x = y = 0, so that x, = yo = 0 in eqn. 12.22~.We now compute the complex power leaving the unit cell centered around the 0, 0 element from
where Ex is given by eqn. 12.22a, and J, is the electric-surface-current density of the sources at z = d m
m
1 1 m--m
e
-jko(mou+nbv)
6(x - ma)b(y - nb)
(12.27)
n=-m
In eqn. 12.26, the power is evaluated at z = d + , and is the same for each cell in the array. Substituting eqns. 12.27 and 12.22~ into eqn. 12.26 and performing
Analysis and design considerations for phased-array antennas
703
the integration gives
where G C ( k , , k,) is given by eqn. 12.1la. Recall that k , and k, are functions of m, n and the scan angle 9, 4, as given by eqn. 12.23. The result in eqn. 12.28 shows that the complex power leaving the face of the array is a superposition of the powers contained in each of the Floquet modes forming the field solution. Now if we assume that the array spacing is such that a < 112 and b < 112, so that no grating lobes are present for any scan angle, then from eqn. 12.23 it is easy to see that lk,l < ko only for m = n = 0 From eqn. 12.3b, these conditions imply that k, is purely imaginary except for the m = n = 0 Floquet mode, and a study of the G,:! function then leads to the conclusion that only the rn = n = 0 term of eqn. 12.28 contributes a real part to P; all the other terms are purely imaginary. Thus the m = n = 0 Floquet mode is the only mode carrying power away from the array face, and all the other Floquet modes are evanescent, storing energy near the array surface (or carrying power across the surface of the array). Fig. 12.3 shows the complex power P,,, for three Floquet modes (m = - 1, n = 0; m = n = 0; m = 1, n = 0) versus E-plane scan angle for an infinite array of infinitesimal dipoles, with a = b = do/2and a substrate with E, = 12.8 and d = 0.061,. The m = n = 0 mode is the only Floquet mode with a non-zero real part as discussed above. All the modes have imaginary contributions, which are generally well behaved with scan angle. The exception is the rn = - 1, n = 0 Floquet mode, which can be seen from Fig. 12.3 to have a singularity in its imaginary part near a scan angle of about 45'. This results in a sEan blindness at this angle. The singularity in Im (P-,,) can be traced to a zero of the Tmfunction in the denominator of G.2.The zeros of this function correspond to TM surface waves of the unloaded dielectric slab. As the scan angle approaches the blindness angle, the propagation constant of the m = - 1, n = 0 Floquet mode approaches that of the TM surface-wave mode of the dielectric slab, and resonates this mode. The surface wave propagates along the surface of the array, and so does not carry power away from the array. In this situation k, is real, meaning that waves are propagating (up and down) inside the dielectric slab, while k, is imaginary, meaning that the field above the surface of the array is evanescent. Thus, such a wave is sometimes called a 'trapped mode'. This is not unlike the case of total reflection of a plane wave, in a region having a low dielectric constant, incident on a region having a higher dielectric constant. For incidence angles greater than the critical angle, all power is reflected but a surface wave field is excited in the higher dielectric-constant
704
Analysis and design considerations for phased-array antennas
region. This surface wave propagates along the interface, and exponentially decays away from the interface. Since this surface wave field cannot exist in the absence of the incident plane wave, some authors refer to it as a forced surface wave, while other authors feel that it is not a 'true' surface wave field at all, but is only 'surface-wave-like' [13].
Analysis and design considerations for phased-array antennas
pressed as:
where I, is the free-space wavelength. As an example, for the E, = 12.8, d = 0.061, dielectric slab of Fig. 12.3, P,,,,/ko = 1.28582. In the E-plane, u = sin0 and v = 0, so for half-wave spacing eqn. 12.29 reduces to (1.28582)~ = (2m
+
+
Clearly the only solution occurs for m
O,,,,
I
scan angle
/
/-
Fig. 12.3 Complexpowersradiatedby them = - 7 . n = O;m = n = 0;andthem = 7.n = 0 Floquet modes for an infinite array of infinitesimal dipoles, versus E-plane scan angle E, = 12.8, d = 0.06&, a = b = & / 2
Another point to be noted from Fig. 12.3 is that the real part of the power (in the m = n = 0 mode) is well-behaved with scan angle, and is finite and non-zero at the blindness angle. Thus blindness occurs because the imaginary part of the input impedance becomes extremely large, leading to severe impedance mismatch, even though the real part may be non-zero. Some authors [IS] have been led to erroneous conclusions in this regard. Scan blindnesses of this type can be predicted by comparing the propagation constants of the surface wave of the dielectric slab and the various Floquet modes. Let p,, be the propagation constant of the first (TM) surface-wave mode of the unloaded dielectric slab where k,, < P,, < &ko. (In practice, substrates are usually thin enough so that only the lowest-order TM mode propagates.) , a particular FloThen a surface wave resonance will occur when /I,matches quet-mode propagation constant. Mathematically, this condition can be ex-
=
sin-'11.28582 - 21
= - 1 and
=
n
=
0; so
45.6'
A useful graphical technique, referred to as a surface-wave circle diagram [8, 161, can be arrived at by noting that eqn. 12.29 describes a set of circles in the u-v plane. Fig. 12.4 shows such a diagram. The solid-line circles represent the usual grating-lobe circles, with centres at u = - ml,/a, v = - nI,/b, and unit
wave circles
I
\v~sible space
F i g . 12.4 Surface-wave circle diagram for an infinite phased array with a = b = 0.51,. E, = 12.8, d = 0.061.,
radius. For half-wave spacing, the edges of these circles just touch, indicating that no grating lobes are visible. The grating-lobe circle centred at the origin represents visible space, since, within this region, u and v are such that 0 and 4
706
Analysis and design considerations for phased-array antennas
Analysis and design considerations for phased-array antennas
707
correspond to real scan angles. The dotted circles in Fig. 12.4 are solutions to eqn. 12.29, and so are called surface-wave circles. When a surface-wave circle intersects visible space, a scan blindness can occur at those scan angles, unless the scan angle is such that a polarisation mismatch occurs between the fields of the relevant Floquet mode and the surface wave of the slab. This occurs, for example, in the H-plane scan of the infinitesimal dipole array because the polarisation of the xldirected dipoles cannot couple to ;surface wave propagating along the y-axis. Mathematically, an inspection of G.:: in eqn. 12.1l a shows that the T,, function in the denominator is cancelled by an identical term in the numerator when k, = 0 (H-plane scan). Thus, there is no blind spot at 45.6' in the H-plane. The surface-wave circle diagram is a very convenient way to study the effect of grid spacing and substrate parameters ( E , and d ) on the potential blindness angle. For example, the diagram shows that it is possible to completely eliminate a scan blindness by decreasing the element spacing, since this has the effect of moving the grating-lobe and surface-wave circles further apart. The diagram also shows that, for half-wave spacings or greater, there will always be a scan blindness, and that it will occur closest to broadside for E-plane scanning. In practice, however, for electrically thin substrates 3/, will be close to k,, so the scan blindness will occur close to endfire. Decreasing the substrate dielectric constant will also move the blindness angle towards endfire; as E, -+ 1, the blindness angle approaches 90". The surface-wave-type blindnesses discussed above seem to occur in any type of printed array. There are other types of resonances that are also possible, however, depending on the type of array element being used. Patch elements, for example, may in certain circumstances load the dielectric slab enough to support 'leaky wave' modes [15].
Fig. 12.5 Geometry of an infinite array of centre-fedprinted dipoles on a grounded dielectric substrate
12.2.2 Injnite-planar-array solutions
where
12.2.2.1 Printeddipoles: In this Section we consider the analysis of an infinite planar array of printed dipoles. The dipoles are assumed to be thin, and to be fed with idealised delta-gap generators at their mid-points. Isolated printed dipoles and mutual coupling between pairs of such dipoles have been studied by several workers [9,17,18]. Infinite arrays of printed dipoles have been analysed in References 8, 19 and 20. The solution presented here follows that of Reference 8. Fig. 12.5 shows the geometry; the dipoles are of length L and width W. A rectangular grid is shown, but a triangular grid can be treated by replacing k, in the following solution by
where cc is the skew angle of the vertical columns measured from the x-axis (cc = 90" then reduces to the rectangular grid).
Using the results of Section 12.2.1.2, the moment method can be applied to a dipole in a single unit cell; by periodicity, all dipoles in the infinite array and their mutual interactions are then accounted for. The 2-electric-surface-current density on the dipole is expanded in a set of piecewise-sinusoidal (PWS) modes: N
4x(x, YO) =
4<(%, YO)
(12.31)
plane
is the i th expansion mode, and sin k,(h - (x, - xil) for Ix, - xi/ < h (12.33) sin k,h is a piecewise-sinusoidal expansion mode with terminals at xi, and a half-length of h, and fp(xo.x,)
='
is a uniform distribution representing the current variation across the width of the dipole. An edge condition could be incorporated here, but past experience has shown that this is generally not worth the trouble. In eqn. 12.32, the wave number k, can be arbitrarily chosen; here it is set to k, = k , . / m , which has been found to give good results.
708
Analysis and design considerations for phased-array antennas
After the expansion modes have been selected, a Galerkin moment-method procedure can be applied to the electric-field integral equation that enforces E,, = 0 over the surface of a dipole in one unit cell. The other boundary conditions at the ground plane and dielectric-air interface are guaranteed to be satisfied through the use of the Green's function of eqn. 12.22~.A general impedance matrix element, representing the coupling of expansion mode j to weight mode i, is defined as
where E,(x, y, d ) is the field at ( x , y, d) due to a periodic array of infinitesimal dipoles, as given by eqn. 12.22~.The space integratons in eqn. 12.35 can be evaluated as the Fourier transforms of the expansion and weighting modes to give the following:
where F,, and F, are the Fourier transforms of the& and f, functions, as defined by ~ ( k , ) = - m f(x)ed'" dx (12.37) Evaluating eqn. 12.37 for& of eqn. 12.33 a n d f , or eqn. 12.34 gives
Sm
F,.(kx) =
2kJcos k,h - cos k,h] sin keh(G - k:)
-jkx,l
If there are N (odd) PWS expansion modes used on each dipole, the voltagevector elements can be defined as =
1 for i = (N
+ 1)/2
0 otherwise Then in matrix form the expansion coefficients can be found from The input impedance at any dipole in the array is then
+
where k = (N 1)/2 is the index of the mode at the dipole terminals. The active reflection coefficient is calculated as
so that the array is conjugate-matched to its broadside scan impedance.
Analysis and design considerations for phased-array antennas
709
For typical grid spacings a, b of the order of 112, the series in eqn. 12.36 converges for upper limits of about rn, n = _f 60. This makes computational efficiency an issue that requires some attention. One thing that helps is to recognise the Toeplitz-like symmetry in the [Z] matrix. Since the Green's function of eqn. 12.22~is not reciprocal in terms of interchanging xo,yo with x, y the [Z] matrix of eqn. 12.36 is not symmetric. But if the N PWS expansion modes are laid out uniformly on the dipole, other symmetries of the form Z, = Z ,-,,-, , for 1 < i < j, allow the entire matrix to be filled by computing only the first row and the first column of the matrix (2N - 1 elements), rather than all N 2 elements. Additional time savings can be obtained by careful writing of the computer code. In particular, it is relatively easy to write the program so that the G,E;/function of eqn. 12.36is computed only once for a new set of k, and k , values, and not recalculated for each impedance-matrix element. The Fourier-transform functions in eqn. 12.36 can similarly be handled. Such techniques result in an efficient computer program: a given matrix element takes less than 4 s of CPU time, and the input impedance using three PWS modes can be calculated for one scan angle in less than 30 s. (These CPU times are for a Micro VAX/II computer.) The infinite-array solution is considerably faster than a full-wave solution for a single dipole. It is interesting to note that the solution for an isolated dipole can be recovered from the infinite-array solution by an integration over all scan angles defined by a unit square on the grating-lobe diagram (lul < 1, Ivl < I), for a = b = 1,/2. We now present some results for the scan performance of infinite dipole arrays. Fig. 12.6 shows the magnitude of the reflection coefficient of a dipole array with grid spacings a = b = 0.51,, on a substrate with d = 0.191, and E, = 2.55. This substrate is thicker than is usually used in practice, but serves to clearly illustrate some of the important scan effects. The dipole is matched at broadside scan (0 = 0') with an input impedance of 75 jOR, and curves are shown for E-plane scan (4 = 0°), H-plane scan (4 = 90') and a diagonal (D-plane) scan (4 = 45'). Note that all curves tend to unity as 0 -* 90°, and that a scan blindness exists in the E-plane at 0 = 45.8'. The substrate supports a surface wave with fl,,/k, = 1.283. Two solutions to eqn. 12.29 are possible in the principal planes:
+
(b) m = 0, n = - 1; u = 0, v = 0.717 Solution (a) leads to the blindness seen in the E-plane at 0 = 45.8'. Solution (b) would lead to a blindspot in the H-plane at 0 = 454'; but k, = 0, so the TM surface-wave pole is cancelled, as discussed in Section 12.2.1.3. Other solutions to eqn. 12.29, however, are possible off the principal planes. Fig. 12.7 shows a contour plot of the reflection-coefficientmagnitude in the u/v scan plane for this same ariay. Note the two semi-circular loci of the unity reflection-coefficient magnitude, with one starting in the E-plane at 0 = 45.8' and leaving visible space at 4 = 32.7'; and the other entering visible space at $ = 45.8'. The
710
Analysis and design considerations for phased-array antennas
Analysis and design considerations for phased-array antennas
71 1
region of large reflection gets smaller and smaller as the H-plane is approached, however, until the unity-magnitude region vanishes entirely at the H-plane. Another way of viewing this effect is with the surface-wave circle diagram shown in Fig. 12.8. This simply-obtained diagram predicts quite accurately the scan blindnesses seen in Fig. 12.6 and 12.7. The reader is referred to Reference 8 for further examples, including the effects of grid spacing, substrate thickness and dielectric constant, and a triangular grid.
scan angle a=b=0.5A L=0.39h w=o.o02x d =O. 19X c,=2 55
e
..
--- E-plane
---
H-plane D-plane
1
Fig. 1 2 6 Reflection-coefficient magnitude versus scan angle for an infinite printed dipole array
I
visible space
Fig. 12.8 Surface-wave circle diagram for the array of Fig. 72.6
The above theory has been experimentally verified by using a waveguide simulator. Waveguide simulators provide a convenient way to test an element in an infinite-array environment, and have been used extensively for waveguide arrays [4,21]. Here, two printed dipole elements were used in a simulator to test the above theory, and to provide experimental evidence of scan blindness in infinite arrays of printed dipoles. The simulator was made from a piece of C-band waveguide, with inner dimensions of 2.22cm x 4.75 cm. Two printed monopoles of length 1.02cm were laid on a glass-fibre epoxy substrate of thickness d = 0.95cm, with a permittivity 6, = 4.35. The monopoles were fed with SMA coaxial connectors through the broad wall of the waveguide. The element spacings were a = 4.43cm and b = 2.38cm. By varying the frequency from about 4.0 to 6.3 GHz, the simulator scanned in the H-plane to an angle given by u - s i n 8 cos Fig. 12.7
4
Contour plot of the reflection-coefficientmagnitude in the u/v plane for the array of Fig. 12.6
sin 0
=
1/46
Over this frequency range, only the TE,,-mode was propagating in the
.
772
Analysis and design considerations for phased-array antennas
waveguide. A ground plane backed the glass-fibre substrate, and a standard waveguide-matched load was used on the array end. The two printed-antenna elements are fed in phase, with a Wilkinson-type power divider, even though the array is effectively scanning off broadside. This is because the waveguide mode corresponds to two propagating plane waves, one at angle 0 and the other at - 8. For proper simulator operation, the array must generate both of these waves which, by superposition, results in in-phase feed voltages.
0.4
Analysis and design considerations for phased-array antennas
713
the TM, surface wave to the rn = _f 1, n = 0 Floquet mode in the H-plane, as can be seen from the surface-wave circle diagram for the simulator, shown in Fig. 12.10. The diagram shows that, because of the large element spacing in the E-plane and the large diameter of the surface-wave circle, an intersection of the TM, surface-wave circle occurs for H-plane scan, and does not result in cancellation because k, is not zero (since u = 0, but m = I).
+
calculated x x x measured
........ 0
20 c 4
5 frequency, GHz a = 0.0443 rn b = 0.0238m L =O.O204m w=0.0013m d =0.0095rn 6,=4.35 H-plane scan
6
0
8
Fig. 12.9 Measured and calculated active-reflection-coefficient magnitude for a waveguide simulation of an infinite array of printed dipoles
Fig. 12.9 shows the measured reflection-coefficient magnitudes compared with the calculated values. This reflection coefficient is based on the input impedance of a printed monopole and a 50R system. The agreement is generally quite good; the measured results at 4.0 and 4.2 GHz are somewhat higher than calculated owing to some residual mismatch at the power divider. Since the original measurements were made [8],these results have been improved. The blind spot is clearly seen at 4.76 GHz, with a measured reflection-coefficient magnitude of 0.96; it is presumed that a non-unity value resulted because of copper and dielectric loss. The blindness in this case is caused by coupling of
Fig. 12.10 Surface- wave circle diagram for the dipole array simulator of Fig. 12.9
A slightly different solution for the infinite array of printed dipoles has been reported in Reference 20. Results from that work, which include several waveguide simulator measurements, have been favourably compared with those from the present solution. The analysis in Reference 20 uses a singularity subtraction technique in the space domain to improve computational efficiency, and may be limited to substrates that are not too thin. In Reference 19, a solution is described for a planar array of printed dipoles with a superstrate (cover layer). The method of analysis is similar to that presented above. Also treated in Reference 19 is an infinite layer array of dipoles proximity-coupled to microstrip feed lines. 12.2.2.2 Rectangular probe-fed patches: We now consider the analysis of an infinite array of probe-fed rectangular microstrip patches; the geometry is shown in Fig. 12.11. This solution is based on the work reported in Reference
714
Analysis and design considerations for phased-array antennas
22, and assumes an idealised probe feed model. This feed model uses a constantcurrent filament to mode the probe, and does not attempt to model the rapid variation of surface current near the probe-patch junction. Such a model has been found to work quite well for single patches on thin substrates [lo, 18,23, 241, since the patch Q in this case is relatively large, so that the resonant mode current dominates the total current. Reference 25 shows a plot of the currents on a probe-fed patch which graphically illustrates this effect.
Analysis and design considerations for phased-array antennas
775
For the patch problem it is necessary to use both x and y expansion currents; so in the interest of clarity and conciseness it becomes useful to define dyads representing x and y field components as
Thus, consistent with the notation of Section 12.2.1.1, GE represents the$-component of the electric field due to a $directed electric-current source. Gfi and Gf: are given by eqns. 12.1l a and b and G E and G g can be found from eqns. 12.1l a and b by interchanging kx and k,. The results are G$
=
-jZo ( ~ , k i- k;)k2cos k , d
ko
+ jk, (ki - ki) sin k, d sin. k, d
T, Tm
(1 2.46~)
jZo k,k, sin k, d[k, cos k, d + jk, sink, d ] G$' = (12.46b) ko Te Tm Note that G:, = G z . We will also require the E, field due to 2 and 9 currents; from Section 12.2.1.1 these can be derived as GLJ =
Fig. 12.11
Z,,k,rk, sin k, d
kok, T,
Geometry of an infinite array of probe-fed rectangular microstrip patches
The use of this idealised feed model considerably simplifies the analysis, yet provides useful information on the scanning performance of the array and the effects of parameters such as substrate thickness and permittivity, and grid spacings. While the absolute values of active impedance obtained from this solution may only be valid for substrate thicknesses on the order of 0.0212, or less, the active reflection coefficient, being a normalised quantity, has a greater range of validity. In addition, comparisons of patch arrays and printed-dipole arrays with the same substrate parameters and grid spacings show significant similarity in terms of reflection coefficient versus scan angle, suggesting that the element type or feed arrangement is not a dominant factor in the scan performance or active-element patterns. This idea can be pursued further with the current-sheet model discussed in Section 12.2.2.5. The moment-method theory of the analysis of the probe-fed patch array will be developed below, as an extension of the dipole-array solution of Section 12.2.2.1. Then several calculated results will be presented for the scan performance of infinite patch arrays, followed by some measurements from a waveguide simulator.
By reciprocity, G,EJ = - G:, and G$ = - G$. The E, fields represented by eqns. 12.47~and b have been integrated over z for 0 6 z < d, since this is the form in which they will be used later. The electric-fieldintegral equation, representing the boundary condition that the total tangential electric field must vanish on the patch conductor, can be written as
where E;:; is the tangential ( & j ) component of the incident electric field due to the probe source evaluated at z = d, J, is the total vector electric surface-current density on the patch (the sum of the currents on the top and bottom patch surfaces), S is the patch surface, and E:;' is the tangential field scattered by the patch. The surface-current density J i s now expanded in a set of basis functions
716
Analysis and design considerations for phased-array antennas
where J, is an expansion mode representing current flow in either the 2 or $ direction, and I, is the unknown coefficient. Substitution of eqn. 12.49 into eqn. 12.48, multiplication by a weighting function J, and integration overs yields, for i = I, 2, 3 . . . N ,
We can now define an impedance matrix element as
and a voltage-vector element as
where the superscript t indicates that this voltage-vector term is based on a test, or weighting, mode. These matrix elements can be written, using eqn. 12.45, as
Analysis and design considerations for phased-array antennas
777
where a voltage-vector element based on expansion mode j has been defined as
In words, V,' represents a voltage based on the field from the probe integrated over a surface-test mode, while represents a voltage based on the field from # VV ,: in general. a surface-expansion mode integrated over the probe. Thus The above solution may be described as a Galerkin solution in the spectral domain, since the matrix elements are expressed in terms of the Fourier transforms of the fields and currents. The probe self-reactance has been ignored here. The next step is to choose the expansion/weighting functions. Because of their correspondence with the cavity model, entire domain modes of the following form were used:
kx 4(x, y) = f sin - ( x L
Ix + L/2) cos W (y +
W/2)
(12.60~)
for f currents, and x
$+P
(12.54)
&P
where x,, y, are the co-ordinates of the feed probe, and Fi represents the Fourier transform of the Ji expansion mode, defined as
F, (k, , k,)
=
IsJi
(xo, yo) e-jkx* e-jkyyodxOdyO
(12.55)
(Note: Because this definition of the Fourier transform differs from that of Reference 22 in the signs of the exponential terms, some of the above results differ from those of Reference 22 by conjugation.) The unknown expansion coefficients 4 can then be found as solutions to the following set of linear equations:
Z,$
= V:, for all
i
(12.56)
J
Note that [ Z ] is not a symmetric matrix. The input impedance at the probe can be calculated as
where I, is the current on the probe which, if d < &, is assumed to be uniform along the probe, and will be chosen as 1 A. Then from eqn. 12.57, 12.49, 12.48 and 12.45 we can write
kx J(x, y) = j c o s - (x L
In + L/2) sin W ( y + W/2)
(12.606)
for 9 currents, where k and I are integer indices accounting for the number of variations in the x and y directions, respectively. The Fourier transforms of these modes can be easily calculated analytically from eqn. 12.55. Through numerical convergence checks it was found that, for E-plane scanning, the- (k, I) = (I, O), (3, O), (5, O), (7, 0) 2-directed currents and the (k, I) = (0,2) $-directed current gave a fairly stable solution, while for off E-plane scan the (0, 1) $-directed current mode should also be included. The edge condition could be incorporated into the above currents, but it has been found that this is an unnecessary expense in a Galerkin-type solution for patches 110, 231. Fig. 12.12 shows the reflection-coefficient magnitude versus scan angle for an infinite array of probe-fed microstrip patches on a substrate with E, = 2.55 and d = 0.061,, but the E-plane spacing is a = 0.511, which leads to a grating lobe at 0 = 73". The blindspot position in the E-plane then occurs at 68.8". Because of the presence of 9-directed currents, the H-plane also shows a blind angle, at 0 = 76.4"; this blindness has a much higher Q than the E-plane blindness since these J-directed currents are highly reactive and radiate little power. In practice, any loss, probe radiation, or random-error effects would probably 'wash-out' this spurious H-plane blindness. Fig. 12.13 shows the behaviour of an infinite patch array on a thin high-dielectric-constant substrate having d = 0.021, and E, = 12.8. Because of the thinness of the substrate, the blind spots in the E- and H-planes now occur at
778
Analysis and design considerations for phased-array antennas
Analysis and design considerations for phased-array antennas
779
9 = 82.9". This result shows that, even though a scan blindness may be present in the visible range of an array, it may have little effect on the scan range if it is sufficiently close to endfire. The reader is referred to Reference 22 for further examples.
x x x measured 0.6
scan angle 6,=2.55 E-plane H-plane d--0.06ho D-plane a -0.51h0 b = 0.50h0 L=0.28X0 W=0.30ho Xp= L/2 Zb=86n
-
---
---
frequency, GHz L = 1.8cm d=0.159cm W = 1.8cm Xp= 0.48cm a= 2.22cm
4, = 2.33
Fig. 12.12 Reflection-coefficientmagnitude versus scan angle for an infinite array of rectangular microstrip patches. d = 0.06A0, 8, = 2.55
Fig. 12.14
scan angle c,=12.8 E-plane d= 0.02Xo H-plane D-plane a=b= 0.5A0 L= 0.131h0 W= 0.15ho xp= L/2 Zb=403n
-
-----
Fig. 12.13 Reflection-coefficientmagnitude versus scan angle for an infinite array of rectangular microstrip patches. d = 0.02A0,E, = 12.8
Measured and calculated reflection-coefficientmagnitude of a microstrip array in a waveguide simulator. The centre patch is fed
The above theory has been verified with several waveguide simulator measurements, and a typical example is shown in Fig. 12.14. Unlike the dipole simulator described in Section 12.2.2.1, this simulator uses only one fed element centered in the guide, with two half-patches at the sides. These half-patches carry zero feed current. Good agreement with theory is obtained, although it should be pointed out that the data of Fig. 12.14 is dominated by the high-Q resonance of the patch, and differs only slightly from the frequency-dependent behaviour of the isolated patch element. It should also be noted that, although the patches image correctly across the waveguide simulator walls, the feed probes do not. This is felt to be a negligible factor for electrically thin substrates. Another solution for the probe-fed patch array has been reported in Reference 15. This work uses a singularity subtraction technique for the patch current near the feed point, and so overcomes the main drawback of the solution in Reference 22, which is limited to thin substrates because of the idealised feed model. Reference 15 presents some useful design data for patch arrays, and interprets the behaviour of such arrays in terms of surface-wave and leaky-wave
720
Analysis and design considerations for phased-array antennas
effects. It erroneously presumes, however, that the solution of Reference 22 is missing leaky-wave effects, which come about because of the patches loading the dielectric slab. The solution of Reference 22 is full-wave and accounts for the presence of the patches on the dielectric slab through the moment-method procedure, and comparisons with some of the results in Reference 15 show the same effects which are labeled as 'leaky waves' in Reference 15. A recent paper [47] describes experimental confirmation of surface-wave scan blindnesses in large arrays of microstrip patches, in agreement with the theory of Reference 22. 12.2.2.3 Circular probe-fedpatches: Like the rectangular patch, the circular microstrip antenna is often used as an array element, and so we describe here the extension of the previous analysis to an infinite array of circular patches. This case clearly illustrates the versatility of the Green's-function/moment method (or 'Galerkin's method in the spectral domain,' as some authors have referred to it) which has been presented in the preceding Sections. As we will see, the only major change needed to treat circular patches is to use the appropriate expansion modes and Fourier transforms of those modes [26].
Analysis and design considerations for phased-array antennas
721
The analysis for the infinite array of circular patches follows identically the solution for the rectangular-patch case of Section 12.2.2.2, until the expansion modes are chosen. Analogous to the rectangular-patch case, we look to the cavity model and select the TM,, circular waveguide modes as expansion functions. If we assume the feed point of the reference patch lies on the 4 = 0 line, the i th expansion mode can be written in cylindrical co-ordinates as
R= 0.079h0 c=0.077ho a=b=h0/2
- E-plone ....... D-plane H-plane
linear polarized
--
scan ongle
""""""/yg;-/"/nT " plane Fig. 12.15
Geometry of an infinite array of circular probe-fed microstrb patches
The geometry of the infinite circular patch array is shown in Fig. 12.15. A rectangular grid is assumed, but a triangular grid can be easily treated. As in the rectangular-patch case, the probe-feed model here is also idealised in that it does not attempt to mode the singularity in patch current near the probe, thus limiting the solution to thin substrates. The arguments presented in Section 12.2.2.2, concerning the utility and justification for such an approximation, then apply here, as well.
Fig. 12.16 Reflection-coefficientmagnitude versus scan angle for an infinite array of probefed c~rcularmicrostrip patches d = 0.021,. E, = 12.8. Single-probe feed.
where PpqRis the q th zero of Jb(x), where Jp(x) is the Bessel function of order p, and R is the radius of the circular patch elements. In eqn. 12.61, the single index i is used to form a one-dimensional sequence of the TM, modes. To apply eqns. 12.51-12.59, the Fourier transform of the above expansion modes is needed. These expressions can be derived in closed-form [26], but are too lengthy to list here. Fig. 12.16 shows a typical result for the scan performance of an infinite circular-patch array. The grid spacing (a = b = &/2) and substrate parameters (d = 0.02&, 6, = 12.8) are the same as the rectangular-patch case shown in
722
Analysis and design considerations for phased-array antennas
Fig. 12.13, and it is interesting to observe that the results are practically identical. Only in the diagonal plane is there much difference between the rectangular- and circular-patch results. Multiple-probe-fed patches are also of practical interest. Fig. 12.17 shows three common feeding circuits for circular patches, and these techniques are also relevant for rectangular (or square, for circular polarisation) microstrip patches. Fig. 12.17a shows the single probe-fed patch which has already been treated. The two-probe case of Fig. 12.176 is fed with a 180' hybrid, which reduces the amount of cross-polarised radiation. In Fig. 12.17~the two feed probes are in orthogonal planes and are fed with a quadrature hybrid to generate circular polarisation. The theory which has been presented above can easily be extended to handle the two-probe feed cases of Figs. 12.176 and c.
Analysis and design considerations for phased-array antennas
723
where the matrix elements can be determined from
which gives the open-circuit voltage induced on the k th feed probe due to the fields excited by a unit current on the Ith feed probe. After the matrix of eqn. 12.62 is found (which is a generalisation of the single-port input impedance of eqn. 12.57), an equivalent circuit which models the feed network of either Fig. 12.176 or c can be used to find the reflection coefficients R, and R,,seen looking into the antenna element ports. If the hybrids have isolation, then, in general, some of the reflected power from the antenna element will be dissipated in the hybrid and some will pass back through the hybrid. Thus the reflection coefficient R at the input of the hybrid does not account for this lost (non-radiated) power. A better indication is to plot the active-element gain pattern, including the efficiency of the feed network, defined as where q is the feed-network efficiency:
Fig. 12.17
Three common feed circuits for patch antennas a Single probe feed b Balanced 180' hybrid feed for reduced cross-polarisation c Quadrature hybrid feed for circular polarisation
A given element in the infinite-array environment can be treated as a two-port network, with an open-circuit 'port' impedance matrix of the form
and cc is the phase angle between the two feed ports (either 90" or 180"). Since R,and R2in eqn. 12.65 vary with scan angle, q also varies with scan angle. Fig. 12.18 shows such an active-element gain pattern for a circularly polarised circular patch array. The element and substrate geometry is the same as that of Fig. 12.16. The resulting axial ratio is shown in Fig. 12.19. Observe that, while the single-probe-fed array of Fig. 12.16 shows a scan blindness of about 6 = 83" in the E-plane, the corresponding circularly polarised array with the two feed probes per element of Fig. 12.18 does not show a blindness at this angle. This is because the reflection coefficient at the feed probe which drives E-plane currents (probe at 4 = 0) may have a unity reflection-coefficient magnitude at 0 = 83" in the E-plane, but power can still be delivered to the cross-polarised currents fed by the other feed probe (at 4 = 90"). This polarisation, being H-plane directed, is decoupled from the E-plane surface wave. The axial ratio, however, becomes infinite at 6 = 83O, as shown in Fig. 12.18. Because of symmetry, this argument applies to both E- and H-plane scan for the circularly polarised circular-patch array. The above results for circular-patch arrays are preliminary; theoretical work on this problem and experimental verifications are continuing.
12.2.2.4 Aperture-coupled patches: The next type of printed array to be considered is one using aperture-coupled rectangular microstrip patches. The aperture-coupled patch element [27] consists of two substrates, with a ground plane in between. As shown in the geometry for a single aperture-coupled patch in Fig. 12.20, a microstrip feed line is printed on the bottom (feed) substrate,
724
Analysis and design considerations for phased-array antennas
Analysis and design considerations for phased-array antennas
725
while the patch element is printed on the top (antenna) substrate. Coupling between the feed line and the radiating element is through a small slot in the ground plane below the patch. As will be discussed further in Section 12.3.2, this type of element has a number of attractive features when used in a phased-array configuration.
patch antenna
antenna substrate
circularly polarized
,
0.21
OO
I
20
,
I
40 scan angle
60
80
Fig. 12.18 Active elementgain for an infinite array ofprobe-fed circularpatches. d E,
=
0,02L,,
= 72.8
Two-probe feed with a quadrature hybrid for circular polarisation
Fig. 12.20 Geometry of an aperture-coupled microstrip patch antenna element
scan angle (deg)
Fig. 12.19 Axial ratio versus scan angle for the circularly polarised array of Fig. 12.18
The single aperture-coupled patch has been theoretically analysed in References 28 and 29, using Green's-function/moment-methodprocedures. In Reference 28, the currents on the feed line were expanded in terms of travellingwave and piecewise sinusoidal expansion modes, following the method of Reference 30. Since this method requires modelling of the feed line over at least several wavelengths, it cannot be applied directly to an infinite phased array without the feed lines running into neighbouring patches or other feed lines. In contrast, the method of Reference 29 first treats the coupling of the aperture fields to the patch, then relates this to an equivalent series impedance seen by the microstrip feed line. This makes the method of Reference 29 a viable approach for treating the infinite array of aperture-coupled patches, since the feed-line interaction is avoided. The solution thus accounts for mutual coupling between the patches, and between the slots, but assumes the feed lines do not
726
Analysis and design considerations for phased-array antennas
couple to each other. This should be a safe assumption for practical microstrip networks. Aperture coupling is a more complicated way of feeding the patch, as compared to probe feeds or edge feeds (via microstrip line), but it is interesting to note that it is easier to do the analysis of the former case in a more rigorous manner than the latter. This is because the aperture-coupled patch is proximity coupled, without a direct contact, eliminating the difficulty of the patch-current singularity that occurs with probe or edge feeds. The present analysis follows that of Reference 29, as extended to the infinite array. The f and $ surface currents J, are expanded in a set of entire domainbasis functions, as in eqns. 12.49 and 1 2 . 6 0 ~and b. The electric-field integral equation of eqn. 12.48 is then applied to the patch surface, where E"' is the field radiated by the equivalent magnetic current
Analysis and design considerations for phased-array antennas
727
z = 0. The individual components are [29]:
Gg'
=
-jk,k,(~,
-
I) sink, d
T, T m
In eqn. 12.69 s represents the patch surface. Now an aperture admittance Yp can be defined as the reaction of the aperture field and the field scattered by the patch:
where H, is the magnetic field at the aperture due to the currents on the patch, S, represents the aperture surface, and the elements of the voltage vector [VJ] defined as
where e",xo, yo) is the unknown aperture electric field. Since the coupling aperture is electrically small, a good approximation is to model the field distribution with a single PWS mode:
where S, denotes a uniform distribution of field across the width (narrow dimension) of the coupling aperture, as defined in eqn. 12.34, and& denotes a PWS distribution across the length (long dimension) of the aperture, as defined ineqn. 12.33. If thereis some compelling reason to do so, additional PWS modes could be included, as discussed in Reference 29. The electric-field integral equation 12.48 then can be reduced to matrix form as,
where [I] is the column vector of unknown patch expansion mode coefficients, [Z] is the impedance matrix of the patch with elements given by eqn. 12.53, and [ V M ] is the voltage vector due to an excitation of magnetic current in the aperture. The elements of [VM]are
where &, F,, and F, are previously defined Fourier transforms, and G,EM= 2 ~ ; +G&' ~ is a Green's function representing the iand electric field at z = d due to a $-directed infinitesimal magnetic current element at
+
+
where G y = GEB + G r $ is a Green's function representing the Hy field at z = 0 due to an 9 or $-directed infinitesimal electric dipole at z = d. The individual components are [29]:
The coupling aperture also has a self-admittance Y caused by the direct radiation of the aperture on either side of the ground plane. For an assumed aperture field of the form of eqn. 12.67, we have
where ~i~~ refers to the Green's function representing the Hy field radiated on either the top (+) side or the bottom (-) side of the ground plane, due to a $-directed magnetic current in the aperture. These two terms are similar in form, but may have different values if different substrates are used on the two sides of the ground plane. From Reference 29, the contribution from one side of the
728
Analysis and design considerations for phased-array antennas
ground plane is given as G y =
-
(E,%
- $)kt cos k l d
+ jk2e,sink1d) -
kt T m
Analysis and design considerations for phased-array antennas
729
The former has a resonance with an infinite susceptance at 6 = 86", while the latter has a resonance with an infinite susceptance at about B = 62". Thus, surface-wave resonances are possible on both the feed and the antenna substrate, but these blind spots can be moved closer to endfire by making the substrates thinner.
Then, as derived in Reference 29, the slot-coupled patch antenna appears to the microstrip feed line as a series impedance Z, where Z is given by
equivalent series = = impedance
feed line/
=c
where Yp and Ys are given by eqns. 12.71 and 12.74, 2,is the characteristic impedance of the feed line, and Av is a modal voltage due to the discontinuity of the slot. From Reference 29, Av is given by
=c
Fig. 12.21 Equivalent circuit of a stub-tuned aperture-coupled microstrip patch element
where hy(x,y) is the normalised magnetic field of the quasi-TEM microstrip-line mode [29]:
where pm is the propagation constant of the microstrip line. The equivalent circuit is shown in Fig. 12.21. A tuning stub is generally used to terminate the feed line and to adjust the impedance match of the antenna; this is easily treated via the equivalent circuit of Fig. 12.21. Figs. 12.22 and 12.23 show results for an aperture-coupled array geometry with an antenna substrate having E, = 2.55 and d = 0.022,, and a feed substrate having E, = 12.8 and d = 0.0520. The feed substrate was intentionally made thicker than usual to show surface-wave resonances; a thinner substrate would move the feed-substrate resonance closer to endfire. Fig. 12.22 shows the reflection-coefficient magnitude versus scan angle, where surface wave blind spots are seen to occur at B = 62" and at 86" in the E-plane. The former is due to surface-wave excitation on the feed substrate (from the coupling slots), while the latter is due to surface-wave excitation on the antenna substrate (from the slots and the patches). The individual contributions of the patch and slot to this phenomenon are shown in Fig. 12.23, where the real and imaginary components of the patch (YP) and slot (YS)admittances as seen by the microstrip feed line at the coupling slot are plotted against E-plane scan angle. The patch admittance, YP = GP jBP, is seen to have a resonance with a near-zero real part a t about 9 = 85". The slot looks into both the antenna substrate and the feed substrate, and so the slot admittance Y* has been separated into an antenna substrate component, C" + jB", and a feed substrate component, Gsf + jBSf.
+
0
Fig. 12.22
0
30
60 90 scan angle fr,=2.55 frf=12.8 d ,=0.02h0 df =0.05h0 PL =0.279ho SL = 0.115Xo PW=0.279ho SW= 0.01ho a=b=0.5Xo Wf =O.OS L, = 0.075h0
Reflection-coefficient magnitude of an infinite array of aperture-coupledpatches
The results from this solution, which are seen to be qualitatively similar to those of the probe-fed patch solutions of Sections 12.2.2.2 and 12.2.2.3, lend credibility to the feed-model approximations used in those solutions. 12.2.2.5 Other geometries: We have analysed several of the most popular types of printed phased arrays in the preceding Sections, but some other results
730
Analysis and design considerations for phased-array antennas
Analysis and design considerations for phased-array antennas
could not be presented here because of space limitations. We will briefly discuss these results, and refer the interested reader to the literature for more details. After studying a number of different phased-array geometries of dipoles and patches, it becomes evident that many of the dominant characteristics of printed phased arrays are controlled by the element spacing and substrate parameters,
1 1 I
scan angle Fig. 12.23 Active slot admittances of the patch and slot elements for the array of Fig. 12.22
as opposed to the specific type of radiating element or feeding technique. This observation led to a current-sheet model of a printed phased array [31], based on an extension of some early work by Wheeler [32]. The purpose of this model was not to generate a solution or detailed data that was specific for any printed
731
phased array, but to develop a simple analysis that could predict the major trends in the scanning performance of a general printed phased array. Such a model can enhance our understanding of the operation of such antennas. A variety of results, given in Reference 31, show how the relatively simple currentsheet model can be used to predict many of the characteristics, such a reflectioncoefficient variation with scan angle and scan blindnesses, of various types of phased arrays. Another type of phased-array geometry is analysed in Reference 33, where elements are printed on a semi-infinite substrate (half-space). Both dipole and slot elements were considered, and the analysis employed a Green's-function/ moment-method procedure similar to the above work. The motivation for such a study was the possible integration of array elements and circuitry at the surface of an electrically large dielectric lens. Several problems with this configuration, including poor scan performance, have precluded it from further consideration for general applications. 12.2.3 Finite-array solutions Of necessity, all practical phased arrays are finite in size, and so it is important to determine the efficacy of the infinite-array assumption. If it is very large, the central elements of a finite array are generally modelled quite well by the infinite-array approximation. The infinite-array solution, however, does not account for edge effects in a finite array, and it is generally not known a priori how 'big' a finite array has to be before it can be reasonably modelled as infinite. Thus, the analysis of finite arrays may be of more practical utility than either the analysis of isolated elements (no mutual coupling), or infinite arrays (no edge effects). Another reason for considering finite arrays of printed antennas concerns the role of surface waves. It has been shown [6, 9, 12, 181 that a single printed antenna element can convert a significant fraction of its input power into surface waves, as opposed to radiated power. On the other hand, surface waves cannot exist on infinite phased arrays except at blindness angles, where all input power is converted to surface-wave power, and no radiation leaves the surface of the, array. The question then arises as to the effect of array size on the generation of surface-wave power. Does a finite array of printed dipoles, for example, excite more or less surface-wave power than a single printed dipole on the same substrate? And how does this power vary with array size, and scan angle? The analysis of finite printed arrays provides answers to these questions, and clearly shows the relation of surface-wave excitation to the scan-blindness phenomenon. Finite arrays, however, are considerably more difficult to analyse than either single elements or infinite arrays. Using the 'element-by-element' approach [3], the mutual coupling between each pair of elements in the array must be calculated, and matrices of order equal to the number of elements in the array (or larger, if there is more than one expansion mode per element) must be inverted.
732
Analysis and design considerations for phased-array antennas
The size of arrays that can be handled by this method is thus quite limited. It is important to realise that, even though mutual coupling is calculated between pairs of open-circuited elements, the complete solution includes the effect of terminations, and is completely rigorous in the moment-method sense. In the following Section we present the solution for a finite array of printed dipoles [35]. The key step in this analysis is the efficient and accurate calculation of mutual coupling between pairs of dipoles, which is carried out with a moment-method procedure using the Green's function results of Section 12.2.1.1. Quantities such as the active input impedance, reflection coefficient and element patterns can then be calculated. Section 12.2.3.2gives a brief discussion of the analysis of finite probe-fed rectangular patch arrays [36], and presents calculated and measured results for mutual coupling between microstrip patches, and some active element patterns. Besides the element-by-element method used here, a techique called the 'finite periodic structure approach' [34] has recently been develbped, and appears capable of treating large arrays. It is based on a modification of the infinitearray solution, and is similar to a technique that has been applied to finite waveguide arrays [4]. 12.2.3.1 Printed dipoles: Fig. 12.24 shows the geometry of a finite array of printed dipoles. Each dipole is assumed to have a length L, a width W, and to be uniformly spaced from its neighbours by distances a in the x-direction and b in the y-direction. The solution can treat rectangular arrays of arbitrary size, but in the interest of simplicity only square arrays are considered here. The dipoles are assumed to be thin, so only ?-directed currents are used. The appropriate Green's function is then given by eqn. 12.10~.The current on the dipoles is expanded in a set of piecewise sinusoidal (PWS) modes, as defined in eqns. 12.32 and 12.33. The dipoles are assumed to be centre-fed with idealised delta-gap generators with series impedance 2,. The equivalent circuit of the fed is shown in Fig. 12.25. Using a Galerkin procedure the electric-field integral equation reduces to
where [Z] is the impedance matrix representing the mutual coupling between all the PWS modes on the dipoles, [Z,] is the generator terminating impedance matrix (a diagonal matrix), [ I ] is the unknown vector of expansion-mode coefficients, and [V] is the excitation vector of generator voltages. The rnn th element of the impedance matrix is given by
where Fpmis the Fourier transform of the rn th PWS expansion mode given by eqn. 12.38, and F, is the Fourier transform of the uniform y-variation of current
Analysis and design considerations for phased-array antennas
733
given by eqn. 12.39. Note that reciprocity is satisfied, so that Z,, = Z,,,. The efficient numerical evaluation of eqn. 12.80 is discussed in Reference 23. Now consider an N x N planar array of printed dipoles with M PWS expansion modes on each dipole. Then the order of the linear system of equations in eqn. 12.79 is N x N x M. Thus, for example, an I1 x l l square dipole array with three expansion modes per dipole requires an impedance matrix of size 363 x 363, and the order increases as the square of N. It is therefore very important to minimize the number of basis functions used. The PWS mode of eqn. 12.32, with a wave number given by k, = k , , / m , was found to give quite good results for resonant dipoles, even when only one mode was used [8, 18, 341. So, for the majority of calculations in Reference 35, and the results presented here, one PWS mode was used per dipole ( M = 1).
Fig. 12.24 Geometry of an N
x
Nplanar array of dipolesprinted on a grounded dielectric slab
Fig. 12.25 Equivalent circuit of each dipole in the finite array
The issue of a complete modal expansion is an important one. Discussions of current expansions for free-space dipole arrays can be found in Reference 3 and 37. In Reference 37 it was found that for arrays of thin dipoles near resonance, not spaced too closely together, the dipole currents were practically identical. For printed dipoles, the situation should then be even better, because the printed-dipole resonance has a much higher Q than the dipole in free space. A
734
Analysis and design considerations for phased-array antennas
judicious choice of a single basis function can thus give a very good approximation to the true current. The best justification for a single-mode approximation, however, is a comparison with results computed using more than one expansion mode per dipole. Thus, for the example shown in Figs. 12.26-12.28, the input impedance, reflection coefficient and radiation efficiency were computed against scan angle using one and three PWS modes per dipole, for array sizes up to 9 x 9. The input impedance differed by about lo%, and the reflection-coefficient magnitude and radiation efficiency (which are normalised quantities) differed by less than 5%. It should be emphasised that the solution presented above is capable of handling any number of PWS expansion modes per dipole, and that it is desired to use only one mode per dipole in order to analyse larger arrays. The presence of all dipoles in the array and their mutual coupling is accounted for in the solution. In addition, the solution can handle both the 'forced excitation' (Z, = 0) case, as well as the 'free excitation' (Z, # 0) case. If one expansion mode per dipole is used, the voltage-vector elements can be written as
where x,, y,,, are the co-ordinates of the centre of the m th dipole and u, v are direction cosines for scanning, as given by eqn. 12.14. Then after the matrix eqn. 12.79 is solved for the currents, the input impedance at the nth dipole can be computed as Note that the input impedance at a dipole of the finite array is dependent on the location of that dipole, as opposed to the infinite-array case where the input impedance would be the same for all dipoles. The active reflection coefficients at the n t h dipole can then be calculated according to eqn. 12.43. A quantity of interest for the finite-array case is the radiation efficiency e based on the power lost to surface waves:
where e,,is the total input power to the array, and P,,is the surface-wave power excited by the array. These quantities can be calculated as [I81
where Z,, is given by eqn. 12.80, and Z z is the surface-wave contribution (from the residue of the surface-wave pole or poles) to the impedance Z,,. The
Analysis and design considerations for phased-array antennas
735
active-element pattern can also be calculated, as discussed in Reference 35; this Reference also discusses some useful techniques for improving the computational efficiency of the finite-array solution.
E-plane
- Inf. array DO*
19x19
H - plane ---- Inf.array a 0 0 19x19 I
0 w
theto
Fig. 12.26 Reflection-coefficient magnitude versus scan angle (E- and la lane) for a finite (19 x 19 centre element) printed dipole array and an infinite array E, = 2.55,d = 0.19, a = b = 0.51,. L = 0.39&, W = 0.01 A,
Fig. 12.26 shows the reflection coefficient magnitude of a 19 x 19 printed dipole array on an 6, = 2.55 substrate, compared with the result for an infinite array of similar dipoles. The reflection coefficient of the finite array is computed at the centre element of the array, and is matched at broadside scan. Note that the 19 x 19 array is sufficiently large that its reflection-coefficient magnitude versus scan angle follows that of the infinite array relatively closely. This array shows a scan blindness a t 0 = 45.8" in the E-plane. At this scan angle, the reflection-coefficient magnitude of the infinite array is unity, but that of the centre element of the finite array is actually greater than unity. This means that the centre dipole is delivering power back to its generator and load. This power, of course, is being transferred from other ports, and does not violate any conservation laws. The input impedance across the finite array is thus nonuniform. Fig. 12.27 illustrates this variation, showing the reflection-coefficient magnitude as a function of element position across the E-plane (x-direction) of the 19 x 19 array of Fig. 12.26, for various scan angles. The 0 = 0 (broadside) case is symmetrical about the centre of the array, and the data shows that the centre element (no. 10) is perfectly matched, but that other elements are slightly mismatched. For 0 = 30" (scanning to the right of the Figure), the mismatch is greater and is asymmetrical. The 0 = 45" data shows that a number of dipole ports on the right-hand side of the array have reflection-coefficient magnitudes greater than unity; it appears from the data that the left-hand elements are
736
Analysis and design considerations for phased-array antennas
absorbing power from the generators and delivering it to the right-hand elements. Fig. 12.28 shows the efficiency of this array, based on power lost to surface waves as defined in eqn. 12.83, versus E-plane scan angle, for various array sizes. This is a particularly interesting result because it shows the role of surface waves in the transition from a single-element printed antenna, to a finite array, and to an infinite array.
1
5
10 element pos~tion
15
Fig. 12.27 Reflection-coefficient magnitude versus element position across the E-plane of the 19 x 19 finite array of Fig. 12.26
For a single dipole (1 x l), about 22% of the input power is converted to surface-wave power (with the remainder going into space-wave radiation); and this ratio, of course, does not vary with scan angle. For arrays, however, a significant variation of efficiency occurs with scanning. The general trend is that the efficiency improves rapidly for even modest-sized arrays, and increases with array size at all scan angles except those near 4 5 P , at which angle the efficiency decreases (more surface-wave power) with increasing array size. This is precisely the angle at which the infinite array has a scan blindness. If the efficiency of the infinite array were plotted in Fig. 12.28, it would be unity at all scan angles except 45.8', where it would be zero. Since there is no scan blindness in the H-plane of the infinite array, the efficiency of finite arrays for H-plane scan is near unity. This effect can be explained as the destructive or constructive interference of the surface wave of the unloaded dielectric slab with the radiation of the array. As the array becomes larger, the periodicity and phasing of the array tend to cancel the surface wave at all scan angles except at the scan-blindness angle. At
Analysis and design considerations for phased-array antennas
737
this angle, the periodicity and phasing of the array are such as to reinforce, or resonate, the surface wave. As a practical matter, the data of Fig. 12.28 show that the scan-blindness phenomenon can be a problem for even relatively small arrays, and that a prudent array design should probably limit the maximum scan range to about 10" less than the blindness angle. Reference 35 shows the active-element patterns for the array of Fig. 12.26, as well as examples of other arrays.
Fig. 12.28 Radiation efficiency (power loss to surface waves) of the finite dipole array of Fig. 12.26, versus E-plane scan angle for various array sizes
12.2.3.2 Microstrip patches: The above analysis for finite arrays of printed dipoles can be readily extended to finite arrays of rectangular microstrip patches, as reported in Reference 36. This solution uses the idealised probe-feed model discussed in Section 12.2.2.2 and has been verified by mutual coupling and active-element patterns for patches on thin substrates [23, 24, 361. The geometry of the finite patch array is shown in Fig. 12.29. As in Section 12.2.2.2, PWS expansion modes are also used here, and impedance matrix elements can be defined as in eqn. 12.80. It must be realised, however, that the mutual impedance defined by eqn. 12.80 are not the same as those seen at the inputs to the probe feeds of the patches. That is, unlike the dipole case, we must make a distinction between the moment-method impedance matrix [Z] and the 'port' impedance matrix [ZP]defined at the probe terminals. The current flow on the patch is related to the voltage excited at the probe terminals by the modal voltage V, [23]:
where G$ is given by eqn. 12.47~.
738
Analysis and design considerations for phased-array antennas
The computation of Zm,,and V, as given in eqns. 12'30 and 12.85 constitutes the bulk of the computational effort for the finite patch-array solution, and so it is important that these terms be evaluated in an efficient manner. References 23 and 36 discuss this issue. In addition, it is possible and desirable to use only one x-directed expansion mode on each patch. This allows a smaller matrix size to be used for a given array, and the arguments presented in Section 12.2.2.1 for the one-mode approximation can be used here as well. Reference 36 shows a result for the reflection-coefficient magnitude versus scan angle for a 7 x 7 patch array, computed using one and three expansion modes. The results are in good agreement, except for about 10% error in the H-plane scan near endfire. Thus, although the solution can accommodate more than one expansion mode per patch, it appears that in many cases this is not necessary, which then allows the treatment of larger arrays.
Analysis and design considerations for phased-array antennas
739
The active reflection coefficient can then be calculated from eqn. 12.43, and a radiation efficiency calculated as in the dipole-array case. To talk about mutual coupling between the probe feed 'ports' of the array, we must define a port impedance matrix [ZP] as [V"
= [ZP][Ip]
(12.89)
where [ZP] is found from
Scattering matrix elements can then be calculated directly from [ZP]:
where [Z,] is a diagonal matrix with elements Z,, the characteristic impedance of the connecting transmission lines. The active-element pattern can be calculated as follows. From eqns. 12.87, 12.89 and 12.90, the patch currents [I] due to a set of port voltages [VP]can be calculated as -1 [I] = &[Y][YP][VP] = -[VP]
&
(12.92)
Now define [Is] as the driving-current source vector for the active-element pattern of the j t h element. Then all elements of [I"] are zero except for the j t h element, which may be set to unity. The port voltages due to [I"] are found from
0
20
40 theta
60
80
Fig. 12.29 Geometry of a finite array of rectangular microstrip patches
For scanning at the angle 8 , 4 , the probe (port) currents should be driven as
where [Y'] is a square diagonal matrix with elements l/Z,, and where Z, is the termination impedance at each patch port. Then from eqns. 12.92 and 12.93, the patch currents for the active-element pattern are -1 v, {[Yp] [I] = -
+ [YT]}
-I
[I"]
(12.94)
The active-element pattern of the j th element is then computed as El(& 4) = EO(e,
6) 1 1, e-jk~(u-rm +M
(12.95)
m
where x,, ymare the co-ordinates of the probe feed on the rn th patch, and u, v are direction cosines given by eqn. 12.14. The patch-current amplitudes are then given by the column vector [I] and [23]
where [Y] = [Z]-' is the inverse of the moment-method impedance matrix. The active input impedance at the rn th patch is then [23]
where EO(O,$)is the pattern of a single PWS mode [35]. The active-element gain is then
This definition does not include power lost in the terminating impedance of the fed element. An intermediate result that can easily be obtained from this analysis is the mutual coupling between two microstrip patches. Mutual coupling has been
740
Analysis and design considerations for phased-array antennas
calculated or measured by several authors [18,23,24,38-411, with a wide variety of analytical methods. Fig. 12.30 shows data for the E- and H-plane mutual coupling between two rectangular patches using the above formulation. Observe that the magnitude of the H-plane coupling decays much faster than the E-plane coupling. It can be shown that the H-plane coupling decays as I/?, while the
Analysis and design considerations for phased-array antennas
741
active-element patterns can be calculated for finite patch arrays. The patcharray. Scan range is also constrained by the scan-blindness effect, which is losely related to element spacing and substrate parameters, as discussed in Section 12.2.1.3. Table 12.1 Measured and calculated S-parameters
i, J 25, 24 25, 26 25, 23 25, 27 24, 26 25, 18 25, 32 25, 11 25, 39 18, 32
7 x 7 element array; 8, = 2.55; d = 0.16cm; a = b X, = 0.55cm. Y, = 0, f = 4.35GHz
Fig. 12.30 Calculated mutual coupling (magnitude and phase) between two rectangular microstrip patches
E-plane coupling decays much slower owing to surface-wave interaction. It is also interesting to note from the phase data of Fig. 12.30 that there is essentially an e - ~ k ~ phase r dependence with distance for both E- and H-plane coupling. Even though the E-plane coupling is dominated by a surface-wave field, the surface-wave propagation constant of the thin substrate is close to k,. As in the case of printed dipoles, the reflection coefficient, efficiency and
S, (calculated)
S, (measured) - 12.5dB / - 147' - 12'5dB / - 145" - 21.0dB 144' - 21.0dB 1490 - 21.5dB -/ - 24.5 dB 1113" - 25.0 dB 1 1120 -29.5dB /-113" - 30.0dB / - 128' - 30'0dB / - 115"
- 13.4dB / - 140" - 13.4dB / - 140'
-21.5dB 159" - 2 l . 5 d ~1590 - 2 1 4 d ~1570 - 26.0 dB /m2" - 26.0dB - 29.8 dB / - 105" - 29.8 dB / - 105" - 29.8 dB / - 105"
/m
=
3.45cm; L
=
2.0cm, W = 3.0cm;
Measurements were made on a 7 x 7 patch array on a thin substrate to verify the theory. With all ports terminated in 50R, S-parameters were measured and calculated for various element pairs at different locations in the array; typical data are shown in Table 12.1. The elements are numbered across the H-plane, as in Fig. 12.29. Because of the difficulty in obtaining an accurate phase reference, it is estimated that the measured phase data in Table 12.1 may be in error by about 10". Also note that the mutual-coupling data in Table 12.1 are between two patch elements in the presence of all the other (terminated) elements, as opposed to the data of Fig. 12.30, which is for two isolated elements. Element patterns were also measured for the above array, by terminating all but the centre element. Figs. 1 2 . 3 1 ~and b show the measured and calculated patterns. Agreement is generally within 1 dB or so, although it is clear that the evident in the measured patterns. Asymmetry in the E-plane could possibly be due to feed-probe radiation, which was neglected but could easily be included in the solution.
12.3 Design considerations for printed phased arrays
In this Section we will discuss a variety of considerations for the design and development of printed phased arrays. Much of this material has appeared in the literature [42-441, in relation to the monolithic phased-array concept, but is also relevant for a broader class of printed phased-array antennas. Since printed
742
Analysis and design considerations for phased-array antennas
and integrated phased arrays are still very much in the development stages, we unfortunately cannot be completely thorough in this discussion. A phased-array antenna offers a number of desirable features to the systems designer, such as rapid beam scanning, pattern control and compatibility with
- rolrulated
I/
I
I I
o o o measured
Analysis and design considerations for phased-array antennas
743
The integrated phased array is a general concept that refers to an antenna that takes advantage of photolithographic techniqes and microwave integrated circuitry (MIC) for the radiating elements, feed network and active (phase-shifterl amplifierlswitching) circuitry. The logical extension of this concept is the monolithic phased array, where the radiating elements, active circuitry, and feed networks are all integrated on one substrate, (or in sub-array form on one substrate). Such a purely monolithic phased array is far from realisation at the present time and, for reasons discussed below, may not even be desirable from technical viewpoint. Thus it has become more common to speak of an integrated phased array that is as monolithic as possible. The following Section will discuss some general factors affecting the design of integrated arrays. Section 12.3.2 will then describe and discuss the relative merits of a variety of array geometries, or architectures, that may be suitable for various levels of phased-array integration. 12.3.1 Design considerations: Design criteria for integrated phased arrays may be categorised according to electrical or mechanical considerations: ( a ) Electrical considerations Type of substrate: T o achieve a high level of integration, a semiconductor (high E,) substrate (e.g. GaAs) is desirable for active devices and circuitry, but a LOW-E, substrate is preferable for the antenna elements, to enhance bandwidth and scan range.
I
-
H-plane calculated 0 0 o measured
II
I I
! I
I
I
Maximum scan range: The maximum scan range and the desire to avoid grating lobes controls the element spacing, and hence packing density, of the array. Scan range is also constrained by the scan-blindness effect, which is closely related to element spacing and substrate parameters, as discussed in Section 12.2.1.3. Bandwidth: The substrate permittivity and thickness, and the element type, all affect the bandwidth of the array. Thick substrates with low permittivity are generally preferred for improved bandwidth.
Fig. 12.31
(a) E-plane, (b) H-plane measured and calculatedactive element patterns (centre element) of a 7 x 7 rectangular microstrip patch array E, = 2.55. d = 0.159cm. a = b = 3.45cn-1, L = 2 0 c m . W = 34cm. X, 0+5crn. Y, = 0 , f = 4.35GHz
-
adaptive and beam-forming systems. The limiting factor in the deployment of phased-array systems, however, is cost, and the cost of such systems seems to be increasing. There exists, then, a strong interest in the integrated phased array, as such a design would use the technology of integration to (hopefully) lower the cost of phased arrays.
Type ofpolarisation: This basically affects the complexity of the array. Linear polarisation is the easiest to obtain; circular polarisation usually requires a quadrature hybrid, and switched polarisation requires a switching network. Dual polarisation is probably the most complicated, as it requires two separate sets of circuitry for each element. Spurious radiation: Radiation from the feed network and/or active circuitry may degrade the sidelobe level, polarisation or gain of the array.
744
Analysis and design considerations for phased-array antennas
( b ) Mechanical considerations Number of elements: A typical phased array may require from lo3 to loS elements. The array architecture must be able to accommodate this number of elements and the requisite feed and control circuitry. Substrate area: Substrate 'real estate' must exist for radiating elements, feed networks, active circuitry and bias control lines. Heat transfer: The efficiency of most active devices (particularly FETs) is low. Thus heat removal is often a necessity, especially at millimetre-wave frequencies. Modularity: To facilitate the reliable fabrication and repair of an integrated phased array, some type of modularity is needed. A number of the above electrical problems arise from the apparent requirement of using a high-dielectric-constant substrate for both the radiating elements and the active circuitry. For example, microstrip antennas have better bandwidth and less surface-wave excitation for low-dielectric-constant substrates, but the likely semiconductor substrates have a relatively high dielectric constant. In a sense, then, it is a conflicting requirement to have a single substrate for the distinct functions of radiation (loosely bound fields) and circuitry (tightly bound fields). As will be seen in the next Section, a number of new printed-antenna feed methods have been developed to resolve this basic problem by using separate substrates for the radiating elements and the active circuitry. Substrate space is another prime concern, since a scanning array requires R F power-distribution networks, control and bias circuits, phase-shifter circuits, and possibly amplifier circuits, in addition to radiating elements. The amplifiers may be needed to compensate for increased circuit losses at millimetre-wave frequencies. As will be discussed below, a number of array configurations use more than a single substrate to provide more space, as well as some other advantages. In such cases, a method is needed to couple from one substrate to another. Via holes (plated-through holes) can sometimes be used, but in general it is desirable to avoid such direct connections because of very low yields, and because such connections are usually very inductive at high frequencies. As an alternative, some proximity coupling schemes are discussed below. A large integrated phased array will probably consist of a number of subarrays. Such sub-arrays, for example, might be fabricated on a single 'chip', perhaps with one phase-shifterlamplifier circuit feeding all the antenna elements associated with that chip. All the subarray 'chips' could then be mounted on a 'mother board' to supply RF, bias and control lines. Interconnections here also pose a problem. Circular or switchable (dual) polarisation is required for a number of applications, and, of course, such requirements complicate the design. Dual polarisa-
Analysis and design considerations for phased-array antennas
745
tion is probably the most difficult case to accommodate, as this essentially requires two separate orthogonally polarised elements, or at least a single element (such as a square microstrip patch) that can be switched between two polarisation states. Circular polarisation is somewhat easier to obtain, by using a circularly polarised element or a polariser to convert linear polarisation to circular.
I
blindness
'
Fig. 12.32 Scan-blindness angle and bandwidth for a patch array with 1,/2 spacing on a GaAs substrate versus substrate thickness
As discussed in Section 12.2.1.3, the scan-blindness effect can limit the scan range of printed phased arrays. As the substrate is made electrically thicker (as a result of higher frequency, dielectric constant or thickness), the angle at which scan blindness occurs moves closer to broadside. This blindness angle thus effectively limits the scanning range of the array. Fig. 12.32 shows the blindness angle of an infinite microstrip patch array on a GaAs substrate versus substrate thickness. Such a substrate 0.04& thick, for example, would have a blindness angle of about 60°, which would probably limit the useful scan range of the array to less than 50" owing to the rapid increase of the reflection coefficient near the blindness angle. The data of Fig. 12.32 assumes an element spacing of 1,/2 - the blindness angle moves closer to broadside for larger spacings. Also shown in Fig. 12.32 is the approximate bandwidth of the patch element, which shows that a trade-off exists between the bandwidth of the array and its maximum scan range. 12.3.2 Array architectures In this Section we will discuss several types of printed-phased-array geometries, and their relative merits. Several of these configurations correspond to specific canonical arrays analysed in Section 12.2.
746
Analysis and design considerations for phased-array antennas
12.3.2.1 Single-layer substrate: The type of geometry that probably first comes to mind when considering an integrated phased array is the single-layer substrate shown in Fig. 12.33, where radiating patches, active circuitry and the necessary feed networks are all contained on the same substrate. A major problem with this approach is that there may not be enough room on the substrate for all of the components. To avoid grating lobes, antenna elements must be spaced no more than about 1,/2 apart; so if the phase-shifter circuitry, R F feed network and bias lines can be fitted in at all, the spurious coupling between these components may be severe. Another problem with this geometry is the scan-blindnesslbandwidth-trade-offwhich was discussed above. Scan blindness will always occur at some scan angle for a printed array, but, for thin substrates, the blind angle will be closer to endfire. Fig. 12.13, for example, shows a calculated result for the reflection-coefficient magnitude versus scan .angle in the three planes, for an infinite array of microstrip patches on a 0.021,-thick GaAs substrate. The blindness angle is seen to occur at about 82" inthe E-plane (unity reflection-coefficient magnitude), although the reflectioncoefficient magnitude is still about 0.5 at 60° scan in the principal planes. If the substrate thickness is increased, because of higher-frequency operation or a desire for more bandwidth, the blindness angle will move closer to broadside, as indicated in Fig. 12.32. active circu,itry
I
n
d
microstrip pat~h
n
1-5
/I
ground plane
Fig. 12.33 Geometry of an array of microstrip patches on a single-layer substrate
This geometry is also susceptible to spurious radiation from the active circuitry and/or the feed network, which can degrade sidelobe levels or polarisation. 12.3.2.2 Two-sided geometry: Fig. 12.34 shows a two-sided substrate design that eliminated many of the problems encountered with the single-layer case by
Analysis and design considerations for phased-array antennas
747
going to the root cause of those problems, and using two separate substrates for the distinct functions of radiation and circuitry. A substrate with a low dielectric constant holds the radiating microstrip patches, while a parallel semiconductor substrate contains active circuitry and feed networks. The two substrates are separated by a ground plane, and apertures in this ground plane are used to couple R F power from the feeds to the radiating elements. radiating elements coupling aperture\
active circuitry/ and feed network
ground1 plane
Fig. 12.34 Cross-sectional view of a two-sided integrated-array geometry with aperturecoupled patch radiators
This design thus matches the substrate to the electrical function, resulting in improved blindness/bandwidth performance. For example, with an E, = 2.55 antenna substrate, the thickness would have to be about 0.051, for a blindness at 80°, and the situation would be even better for a lower-dielectric-constant substrate. Since we have two substrates, much more space is available than in the single-layer case. In addition, the ground plane effectively isolates the active circuitry and feed network from the radiating elements to reduce spurious coupling and radiation. This array configuration is dependent on the aperture-coupled microstrip antenna, which has been described in detail in Reference 27 and theoretically analysed as a single element in Reference 28 and 29, and as an array in Section 12.2.2.4. Fig. 12.20 shows the geometry of a single aperture-coupled patch antenna, fed by a microstripline on the feed substrate. The feed line is usually terminated in an open-circuited stub for tuning. The aperture is smaller than resonant size, so very little radiation occurs in the back region. Models have been successfully fabricated and tested at frequencies from 2 to 20GHz. A final feature of the two-sided array, and the array configurations to follow, is the fact that it offers better radiation 'hardening' from lightning or EMP effects compared with the single-layer design, owing to the shielding effect of the ground plane. The coupling of the sensitive active circuitry to the outside world must take place through the microstrip antennas and coupling apertures, which present a two-pole (or more) filter response to signals outside their bandwidth. 12.3.2.3 Perpendicular feed substrates: Another design that uses separate substrates for the radiating elements and active circuitry is shown in Fig. 12.35. In this case, a vertical substrate holding the radiating elements is fed by a
748
Analysis and design considerations for phased-array antennas
number of parallel-feed substrates. Coupling is again through apertures in the ground plane of the antenna substrate. This design also allows the use of a low-dielectric-constant substrate for the radiating elements and a separate semiconductor substrate for the active circuitry, similar to the two-sided geometry, and so has the same advantages in relation to scan-blindnessjbandwidth performance and shielding of spurious radiation or coupling. In addition, this architecture has a number of other advantages. First is the fact that the feed substrate can be of virtually unlimited size, since there is no immediate restriction on the 'depth' dimension away from the vertical-antenna substrate. Waveguide phased arrays usually use this depth dimension to a similar advantage. The geometry also permits a modular construction, where feed modules could conceivably be plugged into receptacles on the antenna substrate. A
feed network
Analysis and design considerations for phased-array antennas
749
The array with perpendicular-feed substrates depends on the feasibility of feeding a single patch through an aperture with a microstrip line on a perpendicularly oriented substrate. Such a geometry is shown in Fig. 12.36, and has been discussed in more detail in Reference 45. This design has been verified experimentally, but no theory has been developed beyond the simple arguments presented in Reference 45.
A
microstrip
resonant direction of oatch
radiation
1(
.
..
.,zEz: r o n t n r t s tnn
of aperture
'1
I
,
,
microstrip/ feed line
ground plane Fig. 12.38 Geometry of a rnicrostrip antenna fed through an aperture with a microstrip feed line on a perpendicularly oriented feed substrate
antenna substrates
I
substrates
Fig. 12.35 An integratedphased-arrayconfiguration using a feed substrate perpendicular to the radiating-element substrate
This design also allows efficient heat transfer from the ground plane of the feed substrate. At millimetre-wave frequencies, low device efficiency requires efficient heat transfer from active circuitry. The unobstructed ground plane of the feed substrates allows much heat removal to take place, while the embedded ground plane of the two-sided design makes heat removal more difficult. Finally, such a geometry would lend itself well to space-fed phased-array lens designs, which may be of interest for some applications. This could be implemented by having antenna substrates a t both ends of the feed substrates. It does not appear, however, that this geometry would be useful if dual polarisation were required.
The geometry in Fig. 12.36 shows a direct connection from the feed line to the top of the aperture; the two ground planes are also in electrical contact. Another version of the perpendicularly fed antenna excites the aperture by proximity coupling, eliminating the need for a direct connection of the feed line, as shown in Fig. 12.37. Other variations, including the use of a co-planar waveguide feed, are also possible.
12.3.2.4 Endfie elements: The previously discussed integrated-phased-array designs all used microstrip patches or printed dipoles which radiate normal to the substrate on which they are printed. An alternative to this approach is to use elements which radiate endfire to the substrate, as shown in Fig. 12.38. This example shows the use of tapered-slot antennas, but other elements capable of endfire (to the substrate) radiation, such as dipoles, could be used as well. This type of geometry then uses a single substrate for both active circuitry and radiating elements, but in a rather different manner from the single-layer design discussed earlier. A lot of substrate space is available for feed networks and circuitry, and the design can readily be used for space-fed lens arrays. The individual substrates can be made in modular form, and heat transfer should not be a problem.
750
Analysis and design considerations for phased-array antennas rnicrostrip patch on front side
Analysis and design considerations for phased-array antennas
751
Although surface waves can still be excited on the substrates, an additional problem is the possibility of scan blindness caused by surface waves on the protruding grid of dielectric slabs; such effects have been observed in similar arrays with protruding dielectrics. In addition, this configuration would probably not be useful if circular polarisation is desired. The tapered-slot element has been discussed in Reference 7, and may be constructed with either a linear taper or a curved slot. The slot antenna can be proximity fed with a microstrip-linelslot-linetransition, in Reference 7, or the slot line could be directly fed from the active circuitry. In this regard, it is interesting to note that slot line has a number of distinct advantages over microstrip in such millimetre-wave integrated-circuit applications [46]. 12.4 Conclusion
antenna s u b s t r a t e Fig. 12.37
Geometry of a microstrip antenna fed through an aperture which is proximity coupled to a microstrip feed line on a perpendiculady oriented feed substrate
f e e d network a n d active
This Chapter has discussed the analysis and design of printed phased arrays. Analytical techniques were outlined, and applied to several canonical infinite and finite printed arrays. General considerations for the design of integrated arrays were also discussed. This Chapter has summarised most of the work to date on the anaysis of printed arrays, but there is much yet to be done. Some topics include proximitycoupled elements, the use of wide-angle impedance-matching layers, the development of improved probe-feed models, and the effect of substrate anisotropy. 12.5 Acknowledgment The author would like to thank his graduate students, James Aberle and Fran Harackiewicz, for reviewing the manuscript and making valuable suggestions regarding the consistency of notation.
12.6 References
radiators
Fig. 12.38 An integrated phased-array geometry using tapered-slot elements that radiate in
the endfire direction
1 OLINER, A. A,, and KNITTEL, G. H.: 'Phased array antennas'. in Proc. Phased Array Antenna Symposium', (Artech House, 1972) 2 STARK, L.: 'Microwave theory of phased array antennas - A review', Proc. IEEE, 1974,62, pp. 1661-1701 3 HANSEN, R. C. (Ed.): 'Microwave scanning antennas', (Academic Press, NY, 1966) 4 AMITAY, N., GALINDO, V., and WU, C. P.: 'Theory and analysis of phased array antennas', (Wiley Interscience, NY, 1972) 5 MAILLOUX, R. J., McILVENNA, J. G., and KERNWEIS, N. P.: 'Microstrip array technology', IEEE Trans., 1981, AP-29,pp. 25-37 6 JAMES, J. R., HALL, P. S.,and WOOD,C.: 'Microstrip antenna theory and design', (Peter Peregrinus, 1982)
752
Analysis and design considerations for phased-array antennas
7 BAHL, I. J., and BHARTIA, P.: 'Microstrip antennas (Artect House, 1980) 8 POZAR, D. M., and SCHAUBERT, D. H.: 'Scan blindness in infinite phased arrays of printed dipoles, IEEE Trans., 1984, AP-32, pp. 602-610 9 RANA, I. E., and ALEXOPOULOS, N. G.: 'Current distribution and input impedance of printed dipoles', IEEE Trans., 1981, AP-29, pp. 99-105 10 DESHPANDE, M. D., and BAILEY, M. C.: 'Input impedance of microstrip antennas', IEEE Trans., 1983, AP-31, pp. 740-747 11 MOSIG, R., and GARDIOL, F. E.: 'A dynamical radiation model for microstrip structures in Advances in electronic and electron physics: Vol. 59' (Academic Press, 1982) pp. 139-237 12 PERLMUTTER, P., SHTRIKMAN, S., and TREVES, D.: 'Electric surface current model for the analysis of microstrip antennas with application to rectangular elements', IEEE Trans., 1985, AP-33, pp. 301-31 1 13 KNITTEL, G. H., HESSEL, A,, and OLINER, A. A,: 'Element pattern nulls in phased arrays and their relation to guided waves', Proc. IEEE, 1968, 56, pp. 1822-1836 14 LECHTRECK, L. W.: 'Effects of coupling accumulation in antenna arrays', IEEE Trans., 1968, AP-16 15 LIU, C. C., HESSEL, A,, and SHMOYS, J.: 'Performance of probe-fed microstrip-patch element phased arrays'. Phased Arrays Symposium, Bedford, MA, 1985 16 FRAZITA, R. F.: 'Surface-wave behavior of a phased array analyzed by the grating-lobe series', IEEE Trans., 1967, AP-15, pp. 823-824 17 ALEXOPOULOS, N. G., and RANA, I. E.: 'Mutual impedance computation between printed dipoles', IEEE Trans., 1981, AP-29, pp. 106-111 18 POZAR, D. M.: 'Considerations for millimeter wave printed antennas', IEEE Trans., 1983, AP-31, pp. 740-747 19 CASTANEDA, J., and ALEXOPOULOS, N. G.: 'Infinite arrays of microstrip dipoles with a superstrate (cover) layer'. IEEE AP-S International Symposium Digest, Vancouver, Canada, 1985, pp. 713-717 20 WRIGHT, S. M., and LO, Y. T.: 'Efficient analysis for infinite microstrip dipole arrays', Electron. Lett., 1983, 19, pp. 1043-1045 21 WHEELER, H. A,: 'A survey of the simulator technique for designing a radiating element', in OLINER, A. A,, AND KNITTEL, G. H., (Eds.): 'Phased array antennas' (Artech House, 1972) 22 POZAR, D. M., and SCHAUBERT, D. H.: 'Analysis of an infinite array of rectangular microstrip patches with idealized probe feeds', IEEE Trans., 1984. AP-32, pp. 1101-1107 23 POZAR, D. M.: 'Input impedance and mutual coupling of rectangular microstrip antennas', IEEE Trans., 1982, AP-30, pp. 1191-1 196 24 NEWMAN, E. H., RICHMOND, J. H., and KWAN, B. W.: 'Mutualimpedance computation between microstrip antennas', IEEE Trans., 1983, MlT-31, pp. 941-945 25 MOSIG, J. R., and GARDIOL, F. E.: 'General integral equation formulation for microstrip antennas and scatterers', Proc. IEE, 1985, 132H. pp. 424432 26 ABERLE, J. T., and POZAR, D. M.: 'Analysis of infinite arrays of one- and two-probe-fed circular patches', IEEE Trans., AP. (Accepted for publication) 27 POZAR, D. M.: 'A microstrip antenna aperture coupled to a microstrip line', Electron. Lett, 1985, 21, pp. 49-50 28 SULLIVAN, P. L., and SCHAUBERT, D. H.: 'Analysis of an aperture coupled microstrip antenna', IEEE Trans., 1986, AP-34, pp. 977-984 29 POZAR, D. M.: 'A reciprocity method of analysis for printed slot and slot-coupled microstrip antennas', IEEE Trans., 1986, AP-34, pp. 1439-1446 30 JACKSON, R. W., and POZAR, D. M.: 'Full-wave analysis of microstrip open-end and gap discontinuities', IEEE Trans., 1985, MTT-33, pp. 1036-1042 31 POZAR, D. M.: 'General relations for a phased array of printed antennas derived from infinite current sheets', IEEE Trans., 1985, AP-33, pp. 498-504 32 WHEELER, H. A.: 'Simple relations derived from a phased-array antenna made of an infinite current sheet', IEEE Trans., 1965, AP-13, pp. 506-514
Analysis and design considerations for phased-array antennas
753
33 KOMINAMI, M., POZAR, D. M., and SCHAUBERT, D. H.: 'Dipole and slot elements and arrays on semi-infinite substrates', IEEE Trans., 1985, AP-33, pp. 600-607 34 ISHIMARU, A,, COE, R. J., MILLER, G. E., and GEREN, W. P.: 'Finite periodic structure approach to large scanning array problems', IEEE Trans., 1985, AP-33 35 POZAR, D. M.: 'Analysis of finite phased arrays of printed dipoles', IEEE Trans., 1985, AP-33, pp. 1045-1053 36 POZAR, D. M.: 'Finite phased arrays of rectangular microstrip antennas', IEEE Trans., 1986, AP-34, pp. 658-665 37 KING, R. W. P., MACK, R. B., and SANDLER, S. S.: 'Arrays of cylindrical dipoles' (Cambridge University Press, 1968) 38 JEDLICKA, R. P., POE, M. T., and CARVER, K. R.: 'Measured mutual coupling between microstrip antennas', IEEE Trans., 1981, AP-29, pp. 147-149 39 PENARD, E., and DANIEL, J. P.: 'Mutual coupling between microstrip antennas', Electron. Letr., 1982, 18, pp. 605-607 40 MALKOMES, M.: 'Mutual coupling between microstrip patch antennas', Electron. Lett., 1982, 18, pp. 520-522 41 VAN LIL, E., and VAN DECAPELLE, A,: 'Comparison of models for calculating mutual coupling in microstrip arrays', IEEE AP-S Symposium Digest, Boston, 1984, pp. 745-748 42 POZAR, D. M., and SCHAUBERT, D. H.: 'Comparison of architectures for monolithic phased array antennas', Microwave J., 1986, 29, pp. 93-104 43 POZAR, D. M.: 'Phased arrays of printed antennas', ISAP Symposium, Kyoto, Japan, 1985 44 POZAR, D. M.: 'New architectures for millimeter wave phased array antennas'. JINA International Symposium on Antennas, Nice, France, 1986 45 BUCK, A. C., and POZAR, D. M.: 'An aperture coupled microstrip antenna with a perpendicular feed', Electron. Letr., 1986, 22, pp. 125-126 46 JACKSON, R. W.: 'Coplanar versus microstrip for millimeter wave integrated circuits'. Microwave Theory and Techniques Symposium, Baltimore, 1986 47 SCHUSS, J. J., HANFLING, J. D., and MORROW, R. E.: 'Observation of Scan Blindness Due to Surface Wave Resonance in an Array of Printed Circuit Patch Radiators'. 1987 International IEEE Antennas and Propagation Symposium, Blacksburg, VA, 1987
Chapter 13
Circularly polarised antenna arrays K. Ito, T. Teshirogi and S. Nishimura
Introduction
This chapter is concerned with various techniques for circularly polari3ed microstrip arrays. Circular polarisation is effective for many radio systems, such as communications, remote sensing, navigation and radar systems. In particular, at present, mobile-satellite-communication and direct-broadcastingsatellite systems use circular polarisation, because they do not need polarisation tracking. In these systems, it is desirable for each ground terminal to have a low-profile and lightweight antenna. Also, it is a requirement to achieve a specific gain which cannot be obtained by a single radiating element. In addition to high gain, multiple functions, such as electronic beam scanning, beam shaping and low sidelobe-radiation patterns, are often required. For these reasons, interest in circularly polarised microstrip-array antennas is increasing rapidly. Circularly polarised microstrip arrays are classified into three major categories. The first group includes arrays which are composed of circularly polarised (sometimes linearly or elliptically polarised) microstrip patches. This type of array is the most common and widely used, and it includes many variations. The second type of array is composed of composite elements, which consist of electric- and magnetic-current-source elements. The third type are travellingwave arrays which utilise radiation due to suitable discontinuities in travellingwave transmission lines. These techniques will be discussed in this chapter. 13.1 Various types of circularly polarised arrays 13.1.1 Arrays of patch radiators The conventional method of obtaining a circularly polarised array is to arrange circularly polarised microstrip patches with appropriate feeding.
( a ) Circularly polarised radiating elements: There are various types of circularly polarised patches or resonators, and these are described in Chapter 4. In
756
Circularly polarised antenna arrays
Circularly polarised antenna arrays
Fig. 13.1 typical circularly polarised patches which can be used as array elements are shown. The most direct approach for obtaining circular polarisation is to excite a square or circular patch with two orthogonal modes of equal amplitude and a differential phase shift of 90°, by using a 90' hybrid as shown in Fig. 1 3 . 1 ~ and b. The antenna can be excited from a single feed point by use of a dual-feed device, such as a 90' hybrid or power splitter with the necessary phase shift [I, 21. For wider bandwidth applications, four-probe feeds with 0°, 90°, 180' and 270" phase differentials are used which can suppress higher-order modes formed in the thick substrate [3], as shown in Fig. 13.1~.
757
(b) Feedmethods andarray conjiguration: There are several feed methods for a linear or planar circularly polarised array, and the detail and the corresponding array cbnfiguration will-be described in the next Section.
+
b
0
dual feed
c 4- robe feed
QQQ
b
Fig. 13.2 Example of co-planar amys [671 feeder substrate /I&= 2.55)
single teed
Fig. 13.1
h
Circularly polarised microstrip patch antennas
Several methods have been proposed to provide circular polarisation without the complexities inherent in dual-feed devices. One approach is to attach a single feed point at a location so as to excite two equal-amplitude degenerate orthogonal modes, and then to introduce some asymmetry into the cavity so that the degeneracy of the modes is removed. Examples of this technique are the square microstrip patch with a tilted slot [4], the corner-fed rectangular patch [5, 61, the slightly elliptical patch [7, 81, the pentagon-shaped patch [9], and the circular disc with perturbation element [lo], as shown in Fig. 13.ld-h, respectively. However, these perturbation techniques for generating circular polarisation have very limited axial-ratio bandwidth - generally of the order of 1%.
... antennas substrate Fig. 13.3 Rear-feed microstrip array [471
The most simple is the corporate (or parallel) feed system which splits the power between n output ports with a prescribed distribution while maintaining equal path length from the input to output ports. The bandwidth of this type of array is essentially wide. In practice, it will primarily be limited by the match of the radiating elements. Figs. 13.2 and 13.3 show examples of corporate feeds.
758
Circularly polarised antenna arrays
Fig. 13.2 is a co-planar array in which the array and the corporate feed system are formed on the same plane. Although this array configuration is simpler to manufacture, the radiation from the microstrip feed line deteriorates the overall radiation characteristic of the array. The rear feed system, in which the feed network is located behind the array, is effective for shielding the spurious radiation from the feed lines and devices. One example, as shown in Fig. 13.3, is a circularly polarised array, composed of circular discs with perturbation notches, each of which is driven from the corporate feed circuit in the rear side through a feed probe. Another simple form of feed system is a series feed in which the circularly polarised radiating patches are attached periodically to a transmission line. In this configuration, the phase of the radiating elements is determined by their spacing along the transmission line; therefore, as the frequency is altered, a progressive phase shift results down the array, which causes the main beam direction to change and the beam to squint. Generally, beam squint with frequency is a particular disadvantage of travelling-wave arrays. However, this beam squint can be eliminated by equalising the path lengths between the input and each element. A compact form of such squintless array has been developed by Rodgers [l I]. (c) Circularly polarised array composed of linearly or elliptically polarised elements: A circularly polarised array can also be realised even by using linearly or elliptically polarised elements. In general, since microstrip antennas, and particularly single-feed-type antennas, have a narrow-ellipticity bandwidth, techniques for obtaining an array which is composed of linearly or elliptically polarised elements, but radiates circular polarisation over a wide frequency band, are useful. Details of these wideband techniques will be described in Section 13.4.
Fig. 13.4 Arrangement and excitation of a pair of single-feed-type microstrip antenna [12] (@ 1982 IEEE)
In this Section, these techniques are just introduced as a type included in the category of circularly polarised arrays of patch radiators. There are three kinds of array. The first is when a n array is composed of sets of pairs, in each of which the differential orientation angle and phase shift between two antennas is 90°, as shown in Fig. 13.4 [12]. Although each element has a narrow axial-ratio bandwidth, and radiates a heavily elliptical or almost
Circularly polarised antenna arrays
759
linear polarisation at frequencies off resonance, the cross-polarisations of the paired elements cancel each other out and the array can maintain good polarisation characteristics over a wide bandwidth ( 3 10%). In the second case, circular polarisation is achieved by having a basic 2 x 2 sub-array composed of single-feed linearly polarised elements with unique angular and phase arrangements of the elements, as shown in Fig. 13.50 and b [13]. Both the angular orientation and feed phase of the element are arranged in a 0". 90°, O0, 90°, or 0°, 90°, 180°, 270" fashion.
Fig. 13.5 Circularly polarised 2 x 2 sub-array of linearly polarised elements [13] (@ 1986 IEEE) a 0'. 90', 0'.90' arrangement b 0'. 90'. 180'. 270' arrangement
The third array, which is called a sequential array, is a more generalised configuration [14]. A differential orientation angle and phase shift are provided sequentially for each element of the array. A schematic arrangement of an N-element sequential array is shown in Fig. 13.6. The sequential array provides not only excellent circular polarisation in the boresight, but also low VSWR over the wide frequency band.
13.1.2 Arrays of composite elements In general, a proper combination of electric and magnetic radiating elements will be able to produce circular polarisation when the two radiation fields from the elements are perpendicular to each other and have 90" phase difference. Such a combination of elements is sometimes referred to as a composite element. Several kinds of composite elements for circular polarisation have been reported, including a combination of a slot and two parasitic dipoles [I 51, as shown in Fig. 13.7a, and a combination of a strip and a slot [16], as shown in Fig. 13-76. Fig. 13.7a shows the configuration of an array element composed of an
760
Circularly polarised antenna arrays
Fig. 13.6 Configuration of a sequential array [I41
Circularly polarised antenna arrays
761
excited slot and two parasitic flat dipoles [15]. The slot can be excited by a microstrip line. The dipoles are placed above the slot at a distance d and angle a. The two parameters, d and a, are determined so as to produce circular polarisation. The array element was analysed using the technique of reaction matching. A planar array consisting of four identical elements, as shown in Fig. 13.8, was designed, and its various characteristics were simulated taking into account the inter-element coupling effects. The simulation showed that the planar array could produce a gain of more than 13dB and the 1.5 dB bandwidth of the axial ratio was about 6%. An actual array can be constructed by using a proper substrate and by modifying the design method. Fig. 13.76 shows the fundamental structure of a circularly polarised printed array composed of strips and slots (CP-PASS). It consists of a strip on a thin substrate, a slot in the ground plane and a microstrip feed line. The strip and the slot - basic radiating elements - are almost half a wavelength long and the spacing between them is a quarter of a guide wavelength ,I8 along the line. The strip and the slot are excited by the electric and magnetic fields propagating along the microstrip line, and radiate electric fields E, and Ed, respectively, shown in Fig. 13.7b in the broadside direction.
Fig. 13.8 Configuration of array (four-element sets) [15]
Fig. 13.7 Two types of composite elements for circular polarisation a Slot and two parasitic dipoles [I 53 b Basic elements and working principle of CP-PASS [I61 (@ IEE)
Fig. 13.76 also shows the voltage and current distributions V1and I, along the microstrip line when the line is short-circuited at I = 0. If the strip and the slot are located at the maximum points of V, and I,, respectively, the elements can produce circular polarisation efficiently in the broadside direction. Fig. 13.9 shows a typical configuration of a linear-array-type CP-PASS, which consists of three sets (i.e. six pairs) of elements. Each element pair has a strip element (the term 'strip element' means a combination of a strip dipole and a window) and a slot. The window, a kind of wide and long slot, is located in the ground plane in order to effectively increase the gain and bandwidth of the strip dipole [17].
762
Circularly polarised antenna arrays
Circularly polarised antenna arrays
Tapered window edges are also excited slightly by the magnetic field along the line, and radiate unwanted waves. However, as shown in Fig. 13.9, the strip dipoles are placed at the voltage maxima along the line with a half-wavelength spacing, so that the unwanted radiation from the windows can be effectively suppressed. The details of unwanted radiation will be discussed in Section 13.3.2. Additionally, it is quite easy to control aperture distribution along the feed line by adjusting the coupling gaps between the elements and the feed line. A design procedure for CP-PASS and a design example are given in Section 13.2.2.
763
assumes that electromagnetic waves radiate in the main from the bent parts of the microstrip line. The line electric-current source method [25] assumes that the source of the radiation is the line electric current (of uniform amplitude) along the central line. These two radiation mechanisms, though based on different principles, give the results that are in good agreement. fundamental element
-:&---
(a) r--z-------7
'.04
.kGb,t on 1
, ~ine
b
7 a
,{ ,
I dz LO;:! 3 -
.
1g/$
- ..*
+U
matched load
I
!:
I
II Strip rdipok
B I._,
c t
inout
-- - - - (- -b-)- - - -
matched load
3 Window Fig. 13.9 Configuration of CP-PASS (three-element sets) [38] (@ IEE)
13.1.3 Travelling-wave arrays It is a well known fact that discontinuities in a microstrip line produce radiation [18]. The microstrip-line antenna utilises this phenomenon: the strip conductor of a microstrip line, which is bent periodically like a meander, forms a circularly polarised travelling-wave array. Fig. 13.10 shows some circularly polarised microstrip-line antennas. These are: (a) Rampart-line antenna [19, 201 (b) Chain antenna [21] (c) Square-loop-type microstrip-line antenna [22] (d) Crank-type microstrip-line antenna [23] These antennas will radiate right-handed circularly polarised waves when the power is fed from the left-hand end, and the right-hand end is terminated in a matched load. On the other hand, when the power comes from the right-hand end and the matched load terminates the left-hand end, each antenna radiates left-handed circularly polarised waves. The circularly polarised radiation of the four types of antennas (a)-(d) can be explained by the magnetic-current source method [24] for (a), and the line electric-current source method for (b)-(4. The magnetic-current source method
Fig. 13.10
Circularly polarised microstrip-line antennas a Rampart-line antenna b Chain antenna c Square-loop-type microstrip-line antenna d Crank-type microstrip-line antenna
The rampart-line antenna shown in Fig. 13.10~is built from sets of four right-angled bends. The right-angled bends have to be chamfered in order to reduce the right-angled-discontinuity susceptance [26]. The radiation arises from the bends, and the polarity has the direction shown in Fig. 13.10~.Let us consider the fundamental element surrounded by a dotted line in Fig. 13.10~. When the lengths a, b and c are appropriately chosen, the radiated field from the four bends will produce circular polarisation. For example, when a = 3Ag/8, b = Ag/2 and c = Ag/4 (Ag is the guide wavelength of the microstrip line), the antenna will become a circularl'y polarised travelling-wave-array antenna [20]. The chain antenna and one of its fundamental elements are shown in Fig. 13.106. Each fundamental element is built from a V-shaped circularly polarised radiating element and a U-shaped phase shifter. A U-shaped phase shifter is
764
Circularly polarised antenna arrays
inserted between two V-shaped teeth of the zigzag line. Each arm of the V-shaped radiating element has the length a, and the angle between the two arms is a. For practical purposes, the optimum ranges of the parameters are: a = 0.251g-0.51g, a = 90'-150'. To suppress reflection from the angled parts, a capacitive ear is added to each V-shaped radiating element The square-loop-type microstrip-line antenna, shown in Fig. 13.10c, is formed from a series of fundamental elements. Each fundamental element is made of a square loop, which radiates circular polarisation, and a straight feeder. When the perimeter of the square loop is ,I8, the loop will radiate circular polarisation. In this case, the linear or ti on will oDerate as a feeder, and its effective length will be lgl
Circularly polarised antenna arrays
765
Using the line electric-current source method, we will explain now how these four types of antenna radiate circular polarisation. Suppose that the power is fed from the left-hand end. The instantaneous current distribution is shown by the arrows in Fig. 13.11. The arrows point in the opposite direction every half guide wavelength 4. Fig. 1 3 . 1 1 ~shows the fundamental element of a rampart-line antenna. At time t = 0, the total radiation field from each segment consists only of the radiation from the vertical segments, because the radiated fields of the horizontal segments cancel each other out. When t = 1/(4fi, where f is the frequency, the total radiation field will be of horizontal left-oriented polarity. Similarly, when t = 1/(2fi or t = 3/(4f), the polarity of the total radiation field will be oriented downwards or to the right, respectively. As shown in Fig. 13.1la-d, the polarity of the total field of the radiated electromagnetic waves (normal to the surface of the paper), rotates counterclockwise, and completes one cycle in time I/$ Thus the fundamental element operates as a right-handed circularly polarised antenna. Similarly, the three other types (b), (c) and (d) also operate as right-handed circularly polarised antennas, as can be seen from Figs. 13.11b-d. 13.1.4 Others types of arrays Several other types of circularly polarised microstrip or printed arrays have been developed and reported. In the following, some typical arrays will be introduced.
-
Radiating elements Feed network
Fig. 13.12 Broadband flat radiating element [27] Fig. 13.11 Instantaneous current distribution and polarity
Fig. 13.10d shows a crank-type microstrip-line antenna which gives better frequency characteristics for the axial ratio and radiation pattern, compared with a single rampart-line antenna. The antenna is made of two parallel meander (rampart) lines of the same dimensions. One of the meander lines is shifted for one-half of its period. In order to reduce the susceptance, every bend is chamfered, but in special cases the bends need not be chamfered [23]. When the lengths of each segment of the fundamental element are selected properly, the fundamental element will radiate circular polarisation. The method of selection for the lengths is described in detail in Section 13.2.3.
Dubost [27] has proposed a broadband circularly polarised flat antenna, as shown in Fig. 13.12, which consists of two flat radiating elements that are linearly polarised and placed orthogonally. Each radiating element is a symmetrically fed flat folded dipole, and it is separated from the reflector by a dielectric sheet. Dubost et al. [28] have described a cylindrical array composed of four such flat antennas producing circular polarisation and omnidirectional radiation. Ito et al. [29] have proposed a travelling-wave-type circularly polarised array as shown in Fig. 13.13~.Inclined half-wavelength printed dipoles are arranged along both sides of a microstrip feed line terminated in a matched load. The spacing D, between adjacent dipoles is a quarter of a guide wavelength, and the
766
Circularly polarised antenna arrays
Circularly polarised antenna arrays
I
spacing D, and the angle a are determined from the desired main-beam direction. The frequency bandwidth was as narrow as those of other simple microstrip antennas.
767
13.2 Design of circularly pdarised arrays
,
13.2.1 Arrays of patch radiators The generalised design method for circularly polarised microstrip patch arrays can be divided into two steps: the design of circularly polarised patch radiators themselves and the design of the appropriate feed network. The former is elaborated in Chapter 4.
+
Crossed printed dioote
.....-... ;!j j
__^)
i! 2
. . . i
/j
, j j
A!
.: .i /
j
.
.,0 a
3
Fig. 13.1 3
Travelling-wave printed arrays a Dipole array [29] b Slot array [30]
Nakaoka et al. [30] have proposed another type of circularly polarised travelling-wave array composed of inclined slots, as shown in Fig. 13.136. The slot arrangement can be determined in a similar way to the printed dipole array in Fig. 13.13~.Although the slot array requires a reflector under the substrate in practical use, its frequency bandwidth could be much wider than that of the printed-dipole array. The crossed printed-dipole array [3 I], shown in Fig. 13.14a, or the crossed slot array [32], shown in Fig. 13.146, both fed from microstrip lines, can be used as circularly polarised printed arrays. Compared with microstrip patch arrays, such arrays have relatively wide frequency bandwidths. An alternative method of constructing a circularly polarised array is to place a circular polariser over a linearly polarised microstrip array. As a typical example, Henderson and James [33] have proposed a DBS reception array shown in Fig. 13.15. A parallel-plate polariser is overlaid on a comb-line array antenna [34] with a suitable spacer.
Fig. 13.14
Crossed printed-element arrays a Dipole array [31] b Slot array [32]
As is well known, typical feed systems for microstrip patch arrays are series feeding and parallel or corporate feeding [35]. Such feed systems will be described more fully in Chapter 14.
768
Circularly polarised antenna arrays
Circularly polarised antenna arrays
/
Comb-line array Fig. 13.15
Polariser
Linear polarised array and polariser [33]
(0 IEE)
Circular polarised r a d i a t i n g elements
769
A typical series-fed linear array, as shown in Fig. 13.16a, consists of identical patch radiators producing circular polarisation, a microstrip feed line and its terminal load. Various shapes of patch radiators, as shown in Fig. 13.1, could be candidates for the array. Fig. 13.16~illustrates circular patch radiators with a single feed point. These radiators should be designed to produce circular polarisation and to meet the required conditions mentioned in Chapter 4. For the design of such a series-fed linear array, an equivalent circuit model, as shown in Fig. 13.16b, is employed using transmission-line theory [36]. Normally, the patch radiators are attached to the feed line with equal spacing D. If the load admittance Y L is equal to the line characteristic admittance Y,, a travelling-wave array is formed [35]. On the other hand, if YLis equal to zero or infinity, a resonant array is formed. All the radiating-element admittances Y, (1 < n < N) can be determined from the conditions of input-impedance matching and aperture distribution required. A more generalised design method, using such an equivalent circuit, will be elaborated in the next Section. In the array configuration, the excitation phase of the patch radiators is determined by their element spacing along the feed line. Therefore, the main beam direction will change with frequency variation. A series-fed linear array can minimise the feed-line losses at the sacrifice of frequency bandwidth. Circular polarised radiating elements
Load
i
D
i
i feed line
i
\ I npul
Feed n e lwor
k
Fig. 13.17 Example of corporate- fed linear array
Y r n : R a d i a t i n g element a d m i t t a n c e
Yc
: Characteristic admittance
Y L : Load a d m i t t a n c e Fig. 13.16 Series-fed patch array and its equivalent circuit a Circularly polarised series-fed4inear array b Equivalent circuit
A typical example of the other feed system, parallel or corporate feeding, is shown in Fig. 13.17 feeding a circularly polarised linear array. In general, the patch radiators will be designed independently of the feed system in order to produce circular polarisation and to meet the required conditions mentioned above. The feed system, in this case, splits the input power between the output ports with a prescribed distribution, while maintaining equal electrical path
770
Circularly polarised antenna arrays
lengths from the input to output ports. Therefore, the frequency bandwidth of such an array could be essentially wide. In other words, the frequency bandwidth will be limited by the patch radiators. However, the feed-line losses would be quite large. Detailed design methods for the feed system will be described in Chapter 14. In a practical patch array, the antenna performance with regard to such matters as radiation pattern and axial ratio could be deteriorated by mutual coupling between the tadiating elements or unwanted radiation from, for example, its feed network. These practical design problems will be disussed in Section 13.3. In practice, the frequency bandwidth of a microstrip patch antenna is relatively narrow. Section 13.4 will describe several design techniques for wideband circularly polarised patch arrays. 13.2.2 Arrays of composite elements This Section will concentrate on the design of a circularly polarised printed array composed of strip dipoles and slots (CP-PASS) as a typical design method for series-fed circularly polarised arrays. Fig. 13.9 shows a configuration of CP-PASS consisting of M radiating element sets which are fed in series from a microstrip feed line. For the design of a series-fed linear array, in general, an equivalent-circuit model and transmission-line theory are employed to determine the element spacing and input immittances [36].
Circularly polarised antenna arrays
I
771
scripts f and r indicate forward and reflected waves, respectively, and superscripts + and - indicate the load and generator sides of each element, respectively). For simplicity in the design, we will set and also The relationship between z,, and y,,, may be derived from the design conditions of both circular polarisation and input-impedance matching [37]. As a result, the design conditions for the mth element set will be written as z,,,,, = 2y:", (* is complex conjugate)
(13.3a)
where h and E , are the thickness and the relative dielectric constant of the substrate and 1, is the free-space wavelength a t f , .
Fig. 13.1 9 Equivalent circuit of M-set CP-PASS [38] (@ IEE)
-k
4rnth .section 1 -
Fig. 13.18 Equivalent circuit of mth element set of circularly polarised printed array of strips and slots (CP-PASS) [37] (@ IEE)
In an equivalent-circuit model, a strip dipole and a slot can be approximately represented by a shunt and a series element, respectively, to a transmission line [37]. The effect of the windows placed in the ground plane can be neglected at a design frequency of about f;,. In a practical design, inter-element coupling effects should be included in the determiantion of the element input immittances. Therefore, an equivalent circuit of the mth element set at f;. can be expressed as shown in Fig. 13.18, where z,,, y;,, and d,, are the normalised element input immittances and; etc. are the travelling-wave voltages (sub-
rIn,
Fig. 13.19 shows an equivalent circuit of an M-set CP-PASS atf,, where Y,,, and Z,, are the nth input admittance of a strip element and the mth input impedance of a pair of slots, respectively, and Z , is a terminal load (normally it is a short or open circuit). Y,,, and Z,, can be determined from the design conditions mentioned above and the aperture distribution required. A generalised design procedure for linear-array-type CP-PASS is briefly described as follows [38]: (a) A t f , evaluate the propagation constant y,(= a, + j&) of the microstrip line on a specific substrate. The substrate used throughout this Subsection is mentioned in Table 13.1. (b) Calculate all the input immittances of the elements required for a specific CP-PASS design by applying the design procedure previously described [37]. (c) As a preliminary experiment, make a linear array composed of identical strip elements (no slots) arranged along a feed line. Derive the frequency dependence of the average input admittance from its measured input reflection coefficient I-,, where the superscript st denotes a strip-element array. Then, by testing some arrays which have different coupling gaps, obtain the depen-
772
Circularly polarised antenna arrays
Circularly polarised antenna arrays
ei
dence of resonant conductance and resonant length 4: on the coupling gap S,, atJ;. Fig. 13.20 shows measured values of typical dependences of c::and 4: on S,, at resonance.
773
greater than a specified value AR,,, the element lengths should be adjusted until the axial ratio becomes less than AR,,,. Then obtain the frequency dependences of average input immittances Ef and of the elements, where the superscript cp denotes a circularly polarised array [38].
Table 13.1 Design data for five-set Chebqchev-array CP-PASS
m
1
2
3
4
5
Am G m (mS)
1.OOO 0.420 2.10 1.67 2.80 35.38 38.39
1.609 1.116 5.58 1.32 1.62 34.93 38.02
1,932 1.641 8.21 1.21 1.28 34.73 37.84
1.609 1.148 5.74 1.31 1.59 34.9 1 38.01
1.OOO 0.445 2.23 1.64 2.72 35.35 38.37
(a)
S,rm (mm) (mm) a m (mm) a h (mm)
~~~
Substrate: DICLAD 522 (h = 0.8 mm, E, = 2.6) w = 2.0 mm ( Z , = 50 R), a, = 2 dB/m, 4 = 0.68 j, = 3.0 GHz, D, = D, = D, = 68.0 mm, 2, = 0 R, b,, = 6 , = 2.0, a,, = 55.0, b, = 20.0, e, = 0.3 mm
j
Measured
Measured
f = 3.0GHz
6.0
O
t
L '
l
b 2.0 ' ' ' 3.0' b,, (mm)
41) l T
Fig. 13.21 Measured typical dependences of average resonant resistance and resonant length on the coupling gap for slot arrays [38] (@ IEE)
f =3DGHz
j
Meosured
f =3.OGHz
36.0
Fig. 13.20 Measured typical dependences of average resonant conductance and resonant length of the coupling gap for strip-element arrays [38] (@ IEE)
(4 In a similar way, obtain the dependence of the average resonant resistance RI and resonant length 4;on the coupling gap a,/ for some slot arrays. Typical measured dependences are shown in Fig. 13.21. ( e ) By combining the strip elements with the slots, construct a small array as shown in Fig. 13.9. To facilitate the procedure, the coupling gaps are chosen from Figs. 13.20 and 13.21 as the relationship for circular polarisation R
= 2Zze:
(13.4)
is satisfied, where Z, is the characteristic impedance of the line. Then, measure the axial ratio of the array in the broadside direction. If the axial ratio at f;. is
Fig. 13.22 Measured typical dependences of average resonant conductance and resonant length on the coupling gap for circularly polarised arrays [38] (@ IEE)
(f) By testing some circularly polarised arrays with different coupling gaps, obtain the dependences of resonant conductance @and length aff on S,, and the dependences of resonant resistance @ and length aff on 6 , atf,. Some typical measured dependences are shown in Figs. 13.22 and 13.23, where AR,, was chosen to be 3 dB. It was found that the difference between, for example, Fig. 13.20 and Fig. 13.22arose from mutual coupling between the strip elements and the slots.
774
Circularly polarised antenna arrays
I
Circularly polarised antenna arrays
( g ) Determine all the element lengths and coupling gaps required for the design of CP-PASS from the experimental curves obtained in (f). There will be almost no need to correct the element dimensions because the curves will involve the inter-element coupling effects.
Fig. 13.23 Measured typical dependences of average resonant resistance and resonant length on the coupling gap for circularly polarised arrays (381 (@ IEE) Fig. 13.24 Front view of designed CP-PASS [38](@ IEE) Slots and windows are indicated by broken lines
In addition, when a reflector is placed under the ground plane, the same design procedure will also be available. To demonstrate the validity of this design method, a Chebyshev-array CPPASS consisting of five element sets was designed and measured at S-band [38]. The sidelobe level of -20 dB was specified. Using this design procedure and employing Figs. 13.22 and 13.23, design data for the array were obtained as shown in Table 13.1. A,, is the amplitude ratio of each element set. For simplicity in the experiment, a reflector was not used. Fig. 13.24 shows the front view of the array producing RHCP in the broadside direction. Slots and windows are indicated by broken lines. Fig. 13.25 shows the measured radiation patterns in the yz-plane atf,. The sidelobe levels of the co-polar radiation were less than -20 dB. The maximum cross-polar radiation was about -20 dB because circular polarisation was not achieved at f,, as shown next. Fig. 13.26 shows the measured axial ratio versus frequency. Circular polarisation was obtained at 2.95 GHz, which is 1.7% below A . The 3 dB bandwidth of the axial ratio was 9.3%. Fig. 13.27 shows the measured input impedance of the array versus frequency. Good impedance matching was achieved as predicted, and the bandwidth for VSWR < 2.0 was 8.5%. For stricter designs of CP-PASS, e.g. a requirement for lower sidelobe levels, the cross-polarisation behaviour of the array has to be taken into account. In
Fig. 13.25 Measured radiation patterns in the yz-plane 1381 (@ IEE) f = 3,0GHz (Fig. 13.24)
775
776
Circularly polarised antenna arrays
this case, the strip element will have to be represented instead by a T-type equivalent circuit in the design procedure [40]. For the case of a linear-array-type CP-PASS, the arrangement of the radiating elements shown in Fig. 13.9 seems to be the most suitable and efficient.
Circularly polarised antenna arrays
I
777
13.2.3 Design of travelling-wave arrays Section 13.1.3 gave an outline of the four types of circularly polarised travellingwave-array antennas. In this Section the crank-type microstrip-line antenna is chosen as representative and the method for its design is described. fundamental e l e m e n t m i t e r e d bend
/
Frequency ( GHz)
ground p l a t e
/
d i e l e c t r i c substrate
/
s t r i p conductor
Fig. 13.26 Frequency dependence of axial ratio measured at broadside [38](@ IEE)
<
-:
s t r i p current current
__--. . image
Fig. 13.28 Crank-type microstrip-line antenna a Antenna configuration (four elements) b Fundamental element c ldealised fundamental element
-1.0 Fig. 13.27 Measured input impedance versus frequency [38] (@ IEE)
However, if a planar array is formed using this arrangement, the spacing between elements on adjacent feed lines would be so small that the design would become more complicated because of strong inter-element coupling effects. To avoid this, radiating elements on one side of a microstrip line should be used for a planar array [39].
( a ) Equations for the circularly polarised radiation: Fig. 13.28~shows a crank-type microstrip-line antenna with the fundamental element surrounded by a dotted line. Fig. 13.286 shows the shape of the fundamental element; however, we will study the idealised form shown in Fig. 13.28~.We make the following assumptions:
(i) The neighbourhood of the strip conductor is the medium with the effective relative permittivitiy. (ii) There are two currents: the strip current which is concentrated along the central line of the strip conductor, and the image current formed by the ground plate.
778
Circularly polarised antenna arrays
Circularly polarised antenna arrays
(iii) The amplitude of the strip current is uniform, and the reflection of the electric current on the bent parts can be neglected. Thus, mutual coupling and substrate surface wave effects can also be neglected.
are given, the values for a and c can be obtained from eqns. 13.7 and 13.8. The choices of b is free; however, the optimal value for b is near 442. Fig. 13.286 shows the distance d between the two strip conductors. The value of d should be chosen according to
To obtain the conditions for the radiation of circularly polarised waves in 0 = Om, 4 = 0" direction, the following equation must be satisfied: (13.5)
E4 = +_jER
which is an experimentally derived inequality. The conditions for circularly polarised radiation of the three remaining types of travelling-wave arrays are shown in Table 13.2.
i.e. both components E, and E4 of the electromagnetic wave radiated from the fundamental element must have the same absolute value, and if the phase difference is 90" the resulting wave will be circularly polarised. When a linear-array antenna is constructed from these fundamental elements, the condition for the formation of the main beam in the 0, direction, i.e. the condition that electromagnetic waves radiated in the 6, direction from both end points of the fundamental element are in phase, is given by kLcos 0,
- P(I
779
- 46) = 2nn
+
( b ) Details of the design: We will give the important factors in the construction of the four types of array antennas. However, a full explanation will be given only for the crank-type antenna. The length L of the fundamental element and the electrical length I' of the other three types can be obtained from Table 13.2. (i) Correction of bent parts [41] As shown in Fig. 13.29 the phase constant of the straight-line portion is P, and the phase constant of the bent parts is the effective phase constant P'. In this case, when the width of the straight line is W, the correction length for the crank segments will be
(13.6)
+ +
where k = 2n/lo,/? = 2a/Ag,L = 2a c, 1 = 2a 26 c , 1, is the free space wavelength, ,Ig is the guide wavelength of the microstrip line, L is the length of the fundamental element, 1 is the strip-conductor length of the fundamental element along the central line, a, b, c are the lengths of the crank segments, 6 is the correction length for the crank segments and n is an integer. The physical meaning of 6 is the difference between the physical and electrical lengths of the crank segments. From the components Eo and E, of the electromagnetic wave radiated from the fundamental element, and from eqns. 13.5 and 13.6, we can obtain a condition which ensures that the circularly polarised wave is radiated in the 0, direction when n = - 2. The condition is
W Fig. 13.29 Right-angle bend
where
i
U = (1 - 5 cos em), = l J A o and W is the width of the crank segment. The upper sign represents left-handed circular polarisation and the lower sign represents right-handed circular polarisation. When the values for A,, [, 0, and b
1
The value of 6 must just be determined by the following method: (i) By setting 0, = 90" and 6 = 0 , then a, b and c are obtained from eqns. 13.7 and 13.8. On the basis of these calculated values an experimental antenna is constructed. The value of the frequency, fm is then obtained experimentally by setting the main beam in the broadside direction, 0, = 90'. (ii) From the frequency f, and the design frequency f, the value for 6 is obtained from
where V is the velocity of light. In this manner, a crank-type fundamental
780
Circularly polarised antenna arrays
Circularly polarised antenna arrays
787
element which radiates circular polarisation in the 0, direction can be determined. (ii) Main beam direction 8, and frequency f The crank-type microstrip-line antenna is a series-fed linear-array antenna, and when the frequency changes, the main beam direction will also change. The relationship between these two factors is given by cos 0,
=
1 1-46 --L( c
-
+
y)
where n represents a negative even number. (iiij Length of the fundamental element Normally we make n = -2 in eqn. 13.13 for the construction of a linear-array antenna. However, depending on the choice of the main beam direction 8,, a grating lobe can appear simultaneously. Because of this, there are limitations on the values of 8, when only the main beam, corresponding to n = -2, is present in the visible region. In other words, L Lo
-<
V
cos 0,
+
1
v = 1 for rampart, loop v = 2 for chain, crank
According to this equation, when the lengths of the crank segments a, b and c are calculated from eqns. 13.7 and 13.8 for a given value for Om, the value L = 2a + c must satisfy eqn. 13.14. The direction 8, is usually larger than 60". (iv) Return loss A microstrip-line antenna has its microstrip lines periodically bent. If there are any reflected waves from the bent parts, such an antenna will exhibit a high return loss, no matter how small the reflection. High return loss is a consequence of the total sum of the reflected waves which come from every fundamental element, and are in phase when the electrical length of the fundamental element, I' = I - 46, is equal to a multiple of L,/2. Therefore, the condition I' = mLg/2 (m is an integer) must be avoided. When 0, = 90°, then I' = 21,; therefore, there is always high return loss. In this case the following counter-measures can be applied: (i) The bent parts must be matched very carefully; and (ii) the length of each crank segment must be chosen carefully, so that the sum of the reflected waves from all the four bent parts in the fundamental element equals zero. ( v ) Transmission loss and efficiency In the case of a microstrip-line antenna, the strip current fed through the feeding end decreases exponentially on its way from the feeding end to the matched load, because the strip current is radiated from each fundamental element. Therefore, amplitude distribution, as shown in Fig. 13.30, can be assumed. In this case, the efficiency q of the microstrip-line antenna can be represented by
782
Circularly polarised antenna arrays
Circularly polarised antenna arrays
where q, is the aperture efficiency, q, is the feeding efficiency (1 - R2), qc is the radiating efficiency and R2 represents the power dissipated at the matched load. Here, q, is determined by both the conductor loss and dielectric loss.
voltages. In addition, in the case of circularly polarised arrays, it causes deterioration of the polarisation characteristics. Theoretical studies of mutual coupling in microstrip arrays have been presented by Pozar [42] and Malkomes [43], and experimental work has been done by Jedlicka et al. [44] and Haneishi et al. [45]. All these works, however, dealt with linear polarisation. From a knowledge of mutual coupling in a linearly polarised array, the mutual coupling effects on polarisation characteristics of a circularly polarised array can be derived.
Fig. 13.31 0
5
I0
15
TL(dB) Fig.
Efficiency of travelling-wave antenna (7, = 0.9)
Fig. 13.30 shows the results when r], = 0.9. As can be seen, there is an optimal range for the transmission loss of between 10 and 12 dB, in which case the antenna efficiency is about 72%. An example of the crank-type microstrip-line antenna is given in Chapter 19. 13.3 Practical design problems 13.3.1 Mutual coupling Mutual coupling between radiating elements in microstrip arrays results in both distortion of the element radiation pattern and also errors in the element feed
783
Geometry of circularly polarised linear array
Let us consider a circularly polarised linear array composed of microstrip patches with feed hybrids as shown in Fig. 13.31. The array can be represented in terms of a scattering matrix [46], which expresses the complex coupling coefficients between the incident + and reflected - voltage at each feed part. Each element of the scattering matrix is given by E-plane and H-plane coupling coefficients for the linearly polarised array. Thus, for a circularly polarised array, if we assume the mutual coupling between orthogonal linearly polarised V- and H-components to be neglected, we have
784
Circularly polarised antenna arrays
Circularly polarised antenna arrays
and
785
normal to the array, as shown in Fig. 13.31, the co- and cross-polarised fields radiating from the array are expressed by
and
The excitation voltages Vv,,and VH, at the v- and H-ports of the nth element are given by VV"
=
(vi,
+
v&) = G n ( l
+ rv")
r , , and rHn depend on the scan angle B,, and thus the polarisation characteristics vary with the scan angle due to mutual coupling.
(13.18)
where
where
If each hybrid is ideal, V;, and V;, can be expressed by the input voltage V,f to the hybrid as Fig. 13.32 Measured and calculated mutual coupling IS,212 for circular patches [47]
and
+
The sign corresponds to the sense of polarisation rotation. Thus, the co- and cross-polarised components radiated from the nth element become
and
If the main beam is scanned in the direction B,, where 0, is the angle from the
Next, let us consider the element spacing of circularly polarised arrays. In order to suppress grating lobes and scan the beam widely, the spacing between adjacent element should be small. Small spacing, however, causes large mutual coupling, and deteriorates the radiation characteristics. Thus the spacing for a circularly polarised array should be chosen from practical trade-offs. The calculated and measured mutual coupling of a two-element circular-patch array versus element spacing for both the E-plane and H-plane are shown in Fig. 13.32 [47]. From this Figure, it can be seen that, as the spacing increases, the E-plane coupling becomes larger than the H-plane coupling owing to the stronger surface wave, and the magnitude of coupling for both planes is almost equal at d = 0.681,. Fig. 13.33 shows the effect of orientation on coupling between circular patches for several element spacings. From this Figure, d = 0.681, may be suggested for circularly polarised arrays, because, at this spacing, the mutual couplings for the E- and the H-planes are nearly equal and less than - 22 dB; furthermore, they are almost independent of the orientation angle of the array. This fact almost holds good for rectangular microstrip patches.
786
Fig. 13.33 Mutual coupling between microstrip circular patches as a function of orientation [471
Ey
t
787
Circularly polarised antenna arrays
Circularly polarised antenna arrays
13.3.2 Unwanted radiation For practical design of microstrip-array antennas, and particularly for circularly polarised antennas, so-called 'unwanted radiation' should be taken into account. Unwanted radiation may result from the generation of higher-order modes in microstrip patches (see Chapter 4 for details), co-planar microstrip feed lines and discontinuities [IS], microstrip feed transitions such as connectors [48], surface waves excited on the substrate [49], secondary current sources on the substrate edges [50], and so forth. Unwanted radiation, in general, sometimes causes high cross-polarisation level, degradation of antenna gain, reduction of frequency bandwidth, and alteration to radiation patterns such as sidelobes and nulls. Recently, cross-polarisation effects in linearly polarised microstrip antennas have been studied by, for example, Hall and James [51] and Hansen [52]. For circularly poalrised antennas, the axial ratio.will readily be degraded by crosspolarisation. In the following, the relationship between axial ratio and crosspolarisation level will be discussed. Fig. 13.34 shows a typical circularly polarised array composed of identical radiating elements with a normal microstrip feed network. The array will radiate nearly circular polarised waves in the broadside direction, which can be decomposed into the two orthogonal fields E, and E,. The circularly polarised radiation fields can be written as
Radiation f i e l d s where the subscripts R and L represent right-hand and left-hand circular polarisation, respectively. Then the axial ratio AR is given by
Radiating elements
Suppose that the total radiation fields E,, and Ey, are simply expressed as E,, = E,
(13.32)
where IEr,l expup) represents the unwanted radiation field caused by, say, higher-order modes in the elements or feed network as mentioned above. If right-hand circular polarisation is desired, the relationship E, = jEy must be satisfied for the case of no unwanted radiation. However, we then obtain Next U R is defined as
6 Input Fig. 13.34 Concept of circularly polarised array
Microstrip feed network
in order to examine the influence of unwanted radiation on the axial ratio. Putting E, = IE,I and substituting eqn. 13.34 into eqns. 13.28 and 13.29, we
788
Circularly polarised antenna arrays
Circularly polarised antenna arrays
obtain
789
As the array size increases, the directional gain will increase proportionately. However, as array size increases, the feed-line length become longer, and the feeder loss will eventually increase faster than the directional gain; the power gain will therefore decrease.
Then the axial ratio can be written as
Fig. 13.35 shows the degradation of the axial ratio caused by the unwanted radiation defined in eqn. 13.34. The solid and the broken lines indicate the estimates for the cases p = - n (the worst case) and p = f4 2 , respectively.
mr
I-
\ slot
Calculated
Fig. 13.36 Influence of unwanted radiation on axial ratio -p = -n (worst case) ---- p = n/2
*
The above discussion illustrates that the influence of unwanted radiation on the axial ratio can be quite large. Therefore, it is quite important to suppress such unwanted radiation in the design of circularly polarised antennas. Various methods for suppressing unwanted radiation in circularly polarised microstrip antennas have been proposed. Chapter 4 elaborates on the suppression of higher-order modes in microstrip patches and describes an effective suppression method using 'paired elements'. Another effective method is to form a 'sequential array', which is a generalised method of paried elements. The sequential array is described in detail in Section 13.4.3. - -
13.3.3 Limitations and trade-offs In a large array, the achievable gain is limited owing to the conduction loss and the dielectric loss in the microstrip feed line, and the radiation loss generated from discontinuities in hybrids, impedance transformers and right-angled corners of the microstrip line.
Fig. 13.36
Microstrip ground-plane slot array losses [35] a Array corporate feed arrangement b Power gain of array against number of elements theoretical gain of array with no feeder losses ---- theoretical gain of array with feeder losses feeder attenuation x x x measured values of gain
-
Corporate feed arrays in particular, have longer feed lines and larger feeder loss than series-fed arrays. Reference 53 has quantified the limit for corporate feed arrays. The feed geometry is shown in Fig. 13.36~;each line feeds a ground-plane slot and there are 2L/& and L/& elements in the E-and H-planes, respectively, where L~ is the area of the square array. Although this array is
790
Circularly polarised antenna arrays
Circularly polarised antenna arrays
designed for linear polarisation, circularly polarised array can be treated in a similar manner. For the geometry shown, the length of feeder line from the input point to any element is 3L/2. thus the power gain of the array is given by G = G,,
I
!
2L2 3 + 10 log -T - -LF
n,
where t is the dielectrics thickness, k is the free-space wave number and F(E) depends only on the substrate permittivity, but is different for each microstrip configuration. This equation is for a unit incident current wave, the reflection at the open circuit being assumed complete. The F(E)s for fundamental circuits were derived by Lewin [57]. . Open circuit
5.776 13.3 log e = F F
Fig. 13.36b shows the power gain versus number of elements for a 12 GHz array with a feeder loss F = 0.075 dB/cm. The maximum gain can be seen from the Figure to be about 30dB. An effective method of reducing feed losses in the corporately fed arrays is to replace part of the microstrip feed lines by a low-loss medium such as a coaxial line or waveguide. This approach is used in a synthetic-aperture radar antenna for the SEASAT satellite [54], and in a circularly polarised microstrip array for reception in a 12 GHz direct broadcasting satellite (DBS) [55]. The latter array consists of four 256-disc-element sub-arrays which are connected by a waveguide power combiner mounted on the rear side of the array. A measured gain of more than 33 dB was achieved for this 1024element array. In co-planar arrays, not only conductor loss and dielectric loss of feed lines, but also spurious radiations from power dividers, impedance transformers and corners become significant loss factors. These losses in microstrip lines represent the major limitation of microstrip antennas. Estimates of these losses are summarised as follows:
( a ) Dielectric loss [56]:
+
where E is the dielectric constant of the substrate, E, = 1 q(&- l), q is the dielectric filling factor and a is the conductivity of the substrate. ( b ) Conductor loss [56]:
where W is the width of the strip conductor, 2, is the characteristic impedance, and a, is the conductivity of strip. ( c ) Radiation loss (571: All the expressions for radiated power due to discontinuities take the general form
(13.37) 2 where G,, is the element gain in decibels and F i s the feeder loss in dB/unit-length [351. The optimum value of L which gives the maximum power gain is L =
791
I
Short circuit
Matched termination
Right-angle corner
F4(&) =
& + I In-
&
28
G
n JE-'i - IJm JE
(1 3.46)
The dielectric loss is almost constant for the substrate thickness. Conductor loss and radiation loss, however, depend on the thickness, and furthermore the variations of losses with thickness are quite different. Thus, a study of the optimum thickness of the substrate is necessary. Fig. 13.37 shows a calculated example of conductor losses and the radiation ,losses against thickness of the microstrip substrate [58]. The antenna consists of a 256-element circularly polarised planar array at 12 GHz. It was assumed that each feed line from the input port to each element has a length of 40 cm, eight 2-way dividers, and seven right-angle comers. From the Figure, it can be seen that the conductor losses increase rapidly as the substrate thickness decreases; on the other hand, the radiation losses increase as the substrate becomes thicker. The losses also depend strongly on the characteristic impedance of the microstrip lines. Since an optimum thickness exists at which the sum of conductor loss and radiation loss becomes a minimum, we can determine the substrate with the optimum thickness.
792
!
Circular/y polarised antenna arrays
13.3.4 Non-planar scanning arrays User terminals in aeronautical-satellite and inter-satellite communication links require high-gain beams, capable of being steered to wide angles over a full hemisphere. Scanning losses in planar phased arrays increase rapidly beyond about 60°, necessitating employment of non-planar scanning arrays.
L0ssdZo=50fl
!
I
Circularly polarised antenna arrays
793
Let us consider a general spherical array, whose co-ordinate system is shown in Fig. 13.38. The array is composed of N elements which are located on the limited sphere tilted at an angle a from the vertical axis (z-axis). If M elements are excited and phase-shifted at a time, the radiation pattern is calculated from the following equation:
line
R A D I A T I O N LOSS
Loss [dB]
Fig. 13.38 Co-ordinate system for spherical array [61] (Q IEE)
Fig. 13.37 Conductor loss and radiation loss versus substrate thickness 1581 f = 12GHz,&,=2.17
Electronically switched spherical arrays are simple wide-angle scanning arrays; an example using microstrip antennas has been described in a low-orbiting satellite pointing its beam at at geostationary data-relay satellite [59]. Another example is a dome-shaped switching array which consists of 120 circularly polarised microstrip disc elements, and which provides 14dB of gain with good uniformity over almost 300' of total angle [60]. The array produces a beam by exciting a 12-element sub-array with non-phase compensation, and changes the beam-pointing direction by selecting another sub-array which may or may not contain some of the elements in the first sub-array. A disadvantage of such electronically switched spherical arrays is that they require a large number of elements to cover the hemisphere with high-gain beams; consequently, they are bulky and heavy. A phase-compensated switched-element spherical array for mobile earth stations for satellite communication was proposed by Hori et al. [61]; thus enables one to achieve a high-gain beam with a small number of elements, by providing the same number of variable phase shifters as excited elements.
where, k is the wave number and Y,, is the phase of the nth element. e, and e,, are the vectors of the radiation and element position, respectively, and are given by (13.48) e, = (sin 9 cos 4, sin 9 sin 4, cos 9) e,, = a(sin a cos p,, sin a sin p,,, cos cc)
(13.49)
where a is the radius of the sphere and g ( l , p) is the radiation pattern of the array element. The minimum coverage gain of a simple switched-element spherical array in which the elements are switched one at a time is represented by the crossover level of the radiation patterns of the adjacent array elements within the coverage area (9, - A9 and 9, + A0 from the vertical axis). Since the minimum coverage gain of the antenna is limited, in order to improve it without altering the number of elements, the switched-element array proposed employs the same number of phase shifters as excited elements, as shown in Fig. 13.39. This antenna has both switched-element-array and phased-array functions. It uses the first function to achieve wide scanning and the seond to increase crossover level between adjacent beams. The L-band array developed is shown in Fig. 13.40. It is 40 cm in diameter and 20 cm in height. The antenna is composed of the radiator section, the
794
Circularly polarised antenna arrays
Circularly polarised antenna arrays
switching circuit and the controller. The radiator section consists of six microstrip discs with parasitic elements for broadening the bandwidth, which will be described in the next Section.
6
795
In the design of conformal arrays, the mutual coupling between elements arranged on a curved or folded plane has to be investigated. Hori [62] studied experimentally the mutual coupling between microstrip discs with parasitic elements arranged on a roof-shaped plane as shown in Fig. 13.41. In the same
+Jel+ "ice shifters
Na : number of array elements Ne : number of excited elements Fig. 13.39 Switching spherical array with phase shifters [61] (@ IEE)
7"
.4
.9
1
Fig. 13.41
Measured mutual coupling of the non-planar two-element array with parasitic elements [62]
Fig. 13.42
Measured mutual coupling of the non-planar array versus radius of the arrangement [62]
ARRANGEMENT RAD l US R/ A
Fig. 13.40 Inner construction of the spherical switching array (Courtesy: NTT, Japan)
The two-element-excitation method is applied in this test antenna. T o implement two-element excitation, only one phase shifter consisting of two bits, one of 45" and the other of 90°, is required. Consequently, two elements can generate seven beams, and a six-element array can radiate 42 beams. The minimum coverage gain of a six-element array can be improved by 2.3 dB by using the proposed method, when the coverage area is within 20'-60' from the vertical axis.
.6 .7 .8 ELEMENT SPACING D/h
.5
figure, the mutual coupling versus element spacing D/1 ( 1 is the wavelength) is also shown. Fig. 13.42, however, shows the mutual coupling versus the arrangement radius Rl1. From the Figure, it can be seen that at R > 3L, the mutual coupling becomes almost constant, and at R i21, the mutual coupling in the lOdB less than in planar arrangement. non-planar arrangement is 5
-
796
Circularly polarised antenna arrays
13.4 Wideband circularly polarised arrays
In most communication systems, transmitting and receiving frequencies are separated by several percent (typically 7-10%). In general, a microstrip antenna has a narrow frequency bandwidth; therefore, in the practical design of circularly polarised arrays, techniques for achieving wideband polarisation characteristics, as well as wideband impedance characteristics, are important. There are the following techniques for achieving wideband circularly polarised arrays:
Circularly polarised antenna arrays
797
higher-order modes are excited because of the asymmetrical feed structure, and they generate cross-polarisation. However, it is known that notches in circular patch provide arbitrary elliptical polarisation, and therefore properly designed notches can cancel the cross-polarisatin caused by the asymmetical feed structure.
(i) Employment of wideband circularly polarised radiating elements (ii) Stacked elements for dual-frequency resonance (iii) Special configuration for wideband circularly polarised array. Details of these techniques are described below. 13.4.1 Arrays of wideband elements ( a ) Radiating element with substrate of low dielectric constant: Since the bandwidth of a microstrip antenna is given by [63] BW =
U
Fig. 13.43 Four-probe feed for higher-order mode suppression [3] (@ 7982 IEEE)
VSWR - 1 Q JVSWR
the bandwidth can be increased by reducing the Q-factor. It is well known that the Q-factor is proportional to dielectric constant of the substrate, and inversely proportional to its thickness. Therefore, in order to broaden the bandwidth, the utilisation of a thicker substrate with lower dielectric constant is effective. One such substrate consists of two thin layers of PTFE (polytetrafluoroethylene) bonded on each side of honeycomb material. This method, however, frequently generates higher-order modes in a microstrip antenna. In circularly polarised antennas, the higher-order modes become one of the sources of cross-polarised waves, and therefore they must be suppressed. In a microstrip circular patch, the dominant mode is TM,,, and the first higher-order mode is TM,,,. One method of suppressing the undesired TM,,, is to excite a microstrip radiator by four feeds with 0°, 90°, 180' and 270' phase differentials [3], as shown in Fig. 13.43. The TM,,,, mode is found by measuring the cross-coupling between orthogonal ports. Fig. 13.44 gives a measured example of the coupling between the orthogonal ports; the solid curve shows the case of the four-probe feed in Fig. 13.43, while the broken curve shows the case of a conventional two-probe feed. By using a thicker substrate with four-probe feeds, relativley wide impedance and axial-ratio bandwidths ( 210%) can be achieved. For a large array, a multiple-probe feed system would become complicated, more expensive, and more prone to R F loss. Another technique for suppressing the effect of higher-order modes generated in a thick substrate of low dielectricconstant is to cut two notches on the patches [64]. In a normal microstrip circularly polarised antenna using a thick substrate,
Fig. 13.44 Comparison of coupling between feed ports [3] (@ 1982 IEEE)
Fig. 13.45 shows a seven-element array, in which each element has two notches and is excited from orthogonally located feed points with a phase differential of 90". Fig. 13.46 shows the measured axial ratio of this array, and it can be seen that the effect of the notches on the suppression of higher-order modes is obvious. ( b ) Application of parasitic elements: A two-layer microstrip antenna capable of broadband performance with excellent circular polarisation was proposed [65]. Such antennas are also referred to as electromagnetically coupled
798
Circularly polarised antenna arrays
Circularly polarised antenna arrays
799
patches (EMCP), which have been shown to be broadband radiators for linear polarisation. Fig. 13.47 illustrates the structure of the EMCP. The antenna element consists of two circular patches of diameter Df and D, separated by a
R a d i a t l n q Patch Foam F e e d l n P a t c h Ground
Fig. 13.45
I
Wideband microstrip array composed of notched elements [64]
Fig. 13.47 Electromagnetic coupled patch antenna [65] (@ 1984 IEEE)
3.5
3.7
3.9
4.1 4.3 4.5 frequency (GHz)
4.7
4
Fig. 13.48 Measured return loss [65] (@ 1984 IEEE) 0.01
.
2.0
2.1
2.2
2.3
2.4
Frequency ( G H r )
Fig. 13.46 Improvement of axial ratio of the 7-element array by use of notches [64]
distance S. The top patch is excited by the bottom patch (the feeding patch) which in turn, is fed by a coaxial line from underneath, or by a microstrip line on the same plane as the feeding patch. The return loss of the EMCP, shown in Fig. 13.48, is characterised by two resonant frequencies which vary with
800
Circularly polarised antenna arrays
Circularly polarised antenna arrays
separation. In general, the upper resonant frequency shifts downward and the lower shifts upward when the separation increases. By using EM-coupled patches, a broadband circularly polarised array can be produced. However, when fed at two points (A and B in Fig. 13.47), the EMCP generates highly elliptical polarisation because of its asymmetrical feed structure. One technique of achieving a good axial ratio is shown in Fig. 13.49. This
807
illustrated in Fig. 13.50, where a parasitic element of radius b is mounted over a microstrip antenna of radius a at height h. The parameters a, d and the dielectric constant E, are determined from the substrate and the operating frequency, while b and h are related to the bandwidth. An example of the relative
i
I
I
I
I
0.07
0.08
0.09
0.1
t
Swclng h / Wavelength Fig. 13.51 Relative bandwidth variation against element spacing and radius ratio of circular disc elements [67]
Fig. 13.49 Circularly polarised EMCP array [65] (@ 1984 IEEE)
Fig. 13.52 Frequency dependence of measuredgain of the 4 Fig. 13.50 Microstrip disc antenna with parasitic element [67]
array employs symmetrical deployment of the radiating elements, which are equally excited at two points. The configuration can cancel the radiation difference as a result of the symmetrical arrangement of array elements. The EM-coupled patches are also capable of having only one resonant frequency, and they have broadband characteristics. The antenna was first' described by Taga et al. [66], and more recently it has been applied to a circularly polarised shipborne antenna array for mobile satellite communication [67]. The structure of the broadband microstrip antenna with a parasitic element is
x
4-element array withparasit-
ic elements [67]
bandwidth variation is shown in Fig. 13.51 when hll, (3,is the wavelength) and bla are varied; the relative bandwidth is defined as the ratio of the frequency bandwidth over which the VSWR remains below 1.5 to the centre frequency. A wideband circularly polarised array can be obtained by combining a radiating and a parasitic array. Fig. 13.52 shows the frequency dependence of the gain of an S-band array. Both the radiating array and the parsitic array are composed of 4 x 4 elements. The radiating array has co-planar feeding circuits, and each element is excited by a branch-line coupler. The element spacing is 0.78
802
Circularly polarised antenna arrays
Circularly polarised antenna arrays
wavelength, and the height between the radiating array and the parasitic array is 2 cm. The measured gain shows that the aperture efficiency exceeds 62% over a frequency range of 2.6-2.8 GHz.
803
parts play a role in transmission and reception, respectively. And each layer of the antenna is individually fed at two points with 90' phase shift, in order to obtain circular polarisation. Each upper-layer element is a conventional microstrip antenna, while the lower one is a circular microstrip antenna with an
13.4.2 Arrays of dual-frequency stacked elements For many uses, the increased bandwidth is actually needed at only two distinct frequencies, for transmission and reception, which may be too far apart for a single antenna to operate efficiently at both frequencies. The behaviour of the antenna characteristic at the range of intermediate frequencies may be of no concern. In such cases, an antenna operating in dual-frequency bands is useful.
Fig. 13.54 3
2.83 GHz
x
3 stacked-element array for dual-frequency operation [69] (@ IEE)
A, B : Feed Point (1.545 GHz) C. D : Feed Point (1.6465 GHz)
3.10 GHz
In 0 x
V
40 30 20
10
0
-Io0 2.6
28
3.0
3.2
FREQUENCY (GHz)
Fig. 13.53 Dual-frequency stacked-patch antenna [63] (@ 1981 IEEE) a Cross section of typical stacked circular disc antenna b Measured E, patterns at 2.83and 3.10 GHz c Measured input impedance showing resonance at 2.83 and 3.10 GHz
One technique is to stack one circular patch on top of another in a sandwich construction as shown in Fig. 13.53 [68, 631. This antenna can also be applied as an element of an array, and one can obtain a dual-frequency circularly polarised array. An example is shown in Fig. 13.54. This antenna is nine-element airborne phased array for aeronautical satellite communication, the spacing of which is 94mm (about half a wavelength at 1.611.5 GHz), and the dimensions are about 300 x 300 x lOmm [69]. This phased array can scan its beam by k 45' at least, for gain coverage greater than 12dBi. The element is a newly developed stacked patch antenna as shown in Fig. 13.55. The upper and lower
Dielectric Substrate
I
Receive Port
' ~ r s n m i tPort
Fig. 13.55 Configurat~onof the stacked elements [69] (0 IEE)
I I I I
electrical shielding ring that provides enough space for the upper antenna to be easily fed [70]. Owing to the shielding ring, this antenna has good isolation characteristics between the transmit and receive ports. The measured coupling between two ports is less than -30dB. Consequently, the antenna can be designed optimally for both transmission and reception frequency bands independently.
804
Circularly polarised antenna arrays
13.4.3 Wideband-array techniques For a large array, the use of conventional dual-feed circularly polarised elements has the disadvantage of complicated structure, R F losses due to many feed cables, hybrids and power dividers, and high cost. The application of microstrip elements with single-point feeds is attractive for large circularly polarised arrays, but, in general, these antennas have narrow ellipticity bandwidth. Therefore, the techniques of configuring a circularly polarised arrays with elliptically or linearly polarised elements become important in practice. Three techniques were outlined briefly in Section 13.1.1. In this Section more detailed explanations are provided.
Circularly polarised antenna arrays
805
( b ) A r i a ! of 4-elerlzenr subnrrays: A circularly polarised array can also be formed by using 4-element sub-arrays. each of which is composed of 2 x 2 linearly polarised elements with unique angular and phase arrangements as shown in Fig. 13.5.
( a ) Array of microstrip-patch pairs: This method is to construct a circularly polarised array with pairs of microstrip patches [71]. In each pair, two elements are arranged with an angular orientation of 90' to each other and fed with 90' phase difference, as shown in Fig. 13.4. Using the pairs (or two-element subarrays), a circularly polarised array can be constructed.
Fig. 13.57
Fig. 13.56
Four-element coplanar sub-array unit of CP pairs [77]
Fig. 13.56 shows a four-element co-planar sub-array unit composed of the pairs. In the Figure, T, is a quarter-wavelength impedance transformer which provides both 90' differential phase shift and impedance matching. Fig. 13.57 shows a 64-element circularly polarised array composed of the sub-array units. Typical measured data show that the 3 dB ellipticity bandwidth of the array with paired elements is about 6% and it is greatly improved as compared with the conventional array.
64-element array composed of the sub-array units [77]
It is well known that circular polarisation can be achieved in the broadside direction of an array composed of two linearly polarised elements with angle and phase arranged in a 0°, 90' fashion. This circular polarisation, however, becomes very poor at angles greater than 5" off broadside owing to the spatial phase delay between the two elements, as shown in Fig. 13.58. This spatial phase delay no longer exists in the 2 x 2 subarray shown in Fig. 13.5, since the spatial phase delay in one row or column is opposed to that of the other row or column, and consequently they cancel each other out. The calculated radiation pattern shown in Fig. 13.59 indicates that a 2 x 2 sub-array has excellent quality of circular polarisation over a wide angular region of f 40' from boresight [72]. ( c ) Sequential arrays: A more generalised circularly polarised array which consists of an arbitrary number of identical elements with arbitrary polarisation has been proposed by Teshirogi et a / . [14]. In this array, the incremental angular
806
Circularly polarised antenna arrays
Circularly polarised antenna arrays
orientation and the excitation phase difference are provided sequentially to each element; therefore, the array is called a sequential array. The configuration of an N-element sequential array is illustrated in Fig. 13.6. The nth element is located at an arbitrary position on a plane, but with an orientation angle of
807
A sequential array has another advantage with regard to VSWR. According to the differential path length of each feed line, the reflected wave back to the input terminal from the nth element has a differential phase shift of 24,.
where P is an integer and 1 $ P < N - 1, with respect to the first element, say element 1. The nth element is also fed with a differential phase shift of 4, radians and the same orientation angle.
Fig. 13.59 Calculated radiation pattern in principal plane of 2 [72] (0 1985 IEEE) Element spacing = 0.9 wavelength.
x
2 array shown in Fig. 13.5
THETA ( 8 1
Fig. 13.58 Calculated radiation pattern in principal plane of two-element CP array [72] (@ 1985 IEEE) Element spacing = 0.9 wavelength
We assume that the polarisation of the radiated field from element 1 is elliptical in the boresight direction, and expressed by where U, and V , are orthogonal unit vectors corresponding to the major and the minor axes, respectively, of polarisation ellipse, and a and b are the amplitudes of both components. The total radiated field E from the sequential array in the boresight direction can be derived as
i
( C )
P=3
Fig. 13.60 Possible 4-element sequential linear array
Therefore, if the reflection coefficients of all the elements are the same, the sum of all the reflected waves V, returning to the input terminal of the array becomes This means that the sequential array radiates perfect circularly polarised waves in the boresight direction regardless of the polarisation of the element.
808
Circularly polarised antenna arrays
Circularly polarised antenna arrays
Consequently, it can be seen that the sequential array provides not only perfect circular polarisation in the boresight, but also no reflection at the input terminal. There are several configurations of the sequential array corresponding to P in eqn. 13.51. Fig. 13.60 shows three examples for a four-element linear sequential array. Since each phase difference 4, is usually given by adjusting the feed-line length, these three arrays differ in ellipticity and VSWR bandwidth. Fig. 13.61 shows the improvement factor of cross-polarisation discrimination (XPD) and the ratio of the XPD of the sequential array to that of conventional array. From this Figure, it is clear that XPD is improved as N increases, and the ~ case P = 1 is the best. It should be noticed that the examples in Figs. 1 3 . 5 and b can be interpreted in terms of a sequential array, as a two-pair array of a two-element sequential sub-array, and a four-element sequential array in the case of P = 2. Therefore, from the point of view of ellipticity bandwidth, the configuration in Fig. 13.60~is the widest of these three Celement arrays.
@ ( I
2
I
4
6
I
I
I
8
1
Fig. 13.62 Arrangement of 2-dimensional sequential arrays a Recurrence arrangment for a square array b Generalised arrangement for a rectangular array
0
Number of elements Fig. 13.61 Improvement factor of cross-polarisation discrimination [14]
Two-dimensional arrays can also be composed by combining linear sequential arrays. Fig. 1 3 . 6 2 ~shows an example of a square array. This is a recurrent type of sequential array, in which each row and each column array is a linear sequential array. For rectangular arrays, a more generalised configuration is available, as shown in Fig. 13.626. In this method, the orientation angle and the differential phase shift to be applied to the (m, n)th element 4, is defined by 4nm
=
Ndn
+
M4m
(13.55)
where Verification experiments have demonstrated wideband characteristics of the sequential array. The test array comprises two 2 x 4-element arrays. One is a
Fig. 13.63
Two lest arrays 1141 a Convent~onalarray b Sequential array
809
870
Circularly polarised antenna arrays
Circularly polarised antenna arrays
conventional array and the other is a sequential array, as shown in Fig. 13.63. All the elements are identical microstrip patches which have small notches and are excited by single-point rear-side feeding. The material of the substrate is glass-cloth PTFE, the dielectric constant is 2.6 and the thickness is 4mm.
-
;:'-----
:
conventional sequential
0
8.0
0
2.10
.
0 2.20
1
. 230
FREQUENCY
I 240
,
, 2.50
(GHz)
--.--
?
conventional sequential
FREQUENCY (GHz)
b Fig. 13.64 Measured bandwidth characteristics
2 SANFORD, G.G.: 'Conformal microstrip phased array for aircraft tests with ATS-6', IEEE Trans., 1978, AP-26, pp. 642-646 3 CHIBA, T., SUZUKI, Y., and MIYANO, N.: 'Suppression of higher modes and cross polarised component for microstrip antennas'. IEEE AP-S Int. Symposium Antennas and Propagat. Digest, 1982, pp. 285-288 4 KERR, J. L.: 'Microstrip polarisation techniques'. Proc. Antenna Applications Symposium, 1978 5 CARVER, K. R., and KOFFEY, E. L.: 'Theoretical investigation of the microstrip antenna'. Physic, and Sci. Lab., New Mexico State Univ., Technical Report PT-00929, 1979 6 RICHARDS, W. F., LO, Y. T., SIMON, P., and HARRISON, D. D.: 'Theory and applications for microstrip antennas'. Proc. Workshop on Printed Circuit Antenna Technology, New Mexico State Univ., 1979, pp. 8/1-23 7 SHEN, L. C.: 'The elliptical microstrip antenna with circular polarisation ', lEEE Trans., 1981, AP-29, pp. 90-94 8 LONG.. S. A.. SHEN, L. C., SHAUBERT, D. H., and FARRAR, F. G.: 'An experimental study of the circular-polarised, elliptical, printed circuit antenna', IEEE Trans., 1981, AP-29, pp. 95-99 9 WEINSCHEL, H. D.: 'A cylindrical array of circularly polarised microstrip antennas'. IEEE AP-S Int. Symposium Antennas and Propagat. Digest, 1975, pp. 177-180 10 HANEISHI, M., and YOSHIDA, S.: 'A design method of circularly polarised micrqstrip ~ ; s k antenna by one-point feed', Trans. IECE Japan, 1981, J64-B, pp. 225-231 (in Japanese) I I RODGERS, A,: 'Wideband squintless linear arrays', Marconi Rev., 1972, 35, pp. 221-243 12 HANEISHI, M., YOSHIDA, S., and GOTO, N.: 'A broadband microstrip array composed of single-feed type circularly polarised microstrip antennas'. IEEE AP-S Int. Symposium Antennas and Propagat. Digest, 1982, pp. 160-163 13 HUANG, J.: 'A technique for an array to generate circular polarisation with linearly polarised elements', IEEE Trans., 1986, AP-34, pp. 1113-1 124 14 TESHIROGI, T., TANAKA, M., and CHUJO, W.: 'Wideband circularly polarised array antenna with sequential rotations and phase shifts of elements'. Proc. Int. Symposium on Antennas and Propagat., Japan, 1985, pp. 117-120 15 ITOH, K., ARIGA, T., and SHINADA, H.: 'On some design examples of a circularly polarized wave array antenna using slot antenna combined with parasitically excited dipoles', Trans. IECE Japan, 1982, J65-B, pp. 1385-1392 (in Japanese) 16 ITO, K., AIZAWA, N., and GOTO, N.: 'Circularly polarised printed array antennas composed of strips and slots', Electron. Lett., 1979, 15, pp. 811-812 17 ITO, K.: 'Circularly polarized printed array antenna composed of end-fed strip dipoles and slots', Electro. & Commun. Japan, 1984, 67-B, pp. 56-69 18 LEWIN, L.: 'Radiation from discontinuities in strip-line', IEE Proc., 1960, 107C, pp. 163-170 19 HALL, P. S.: 'Rampart microstrip line antennas'. European Patent Application 79301340.0, 1979 20 WOOD, C., HALL, P. S., and JAMES, J. R.: 'Design of wideband circularly polarised microstrip antennas and arrays'. 1st IEE Int. Conference on Antennas and Propagat., London, 1978, pp. 312-316 21 HENRIKSSON, J., MARKUS. K., and TIURI, M.: 'A circularly polarised travelling-wave chain antenna'. Proc. 9th European Microwave Conference, Brighton, 1979, pp. 174-178 22 MAKIMOTO, T., and NISHIMURA, S.: 'Circularly polarised microstrip line antenna'. US Patent 4 398 199, 1983 23 NISHIMURA, S., SUGIO, Y., and MAKIMOTO, T.: 'Crank-type circularly polarised microstrip line antenna'. IEEE AP-S Int. Symposium Antennas and Propagat. Digest, 1983, pp. 162-165 24 HALL, P. S.: 'Microstrip linear array with polarisation control', IEE Proc., 1983, 130H, pp. 215-224 25 WOLFF, E. A.: 'Antenna analysis' (John Wiley, NY 1966) Chap. 8
.
-
1741
a Axial ratio b VSWR
Fig. 13.64~and b show the axial ratio and VSWR of these arrays. From the Figure, it is clear that the sequential array has much more wideband characteristics of circular polarisation and impedance than the conventional array. For example, 3 dB axial-ratio bandwidth of the sequential array exceeds 14%, which is about 15 times that of the conventional array; while 1.5 VSWR bandwidth is 13.7%, which is about twice that of the conventional array. Several applications of sequential arrays have been for an airborne microstrip phased array in aeronautical satellite communication [73] and for a feed array of a contoured-beam reflector antenna [74].
13.5 References 1 HOWELL, J. Q.: 'Microstrip antennas', IEEE Trans., 1975, AP-23, pp. 90-93
81 7
----
872
Circularly polarised antenna arrays
26 DOUVILLE, R. J. P., and JAMES, D. S.: 'Experimental study of symmetric microstrip bends and their compensation', IEEE Trans., 1978, MTT-26, pp. 175-182 27 DUBOST, G.: 'Broadband circularly polarized flat antenna'. Proc. Int. Symposium on Antennas and Propagat., Japan, 1978, pp. 89-92 28 DUBOST, G., SAMSON, J., and FRIN, R.: 'Large-bandwidth flat cylindrical array with circular polarisation and omnidirectional radiation', Electron. Lett., 1979, 15, pp. 102-103 29 ITO, K., AIZAWA, N., and GOT0,N.: 'Circularly polarized microstrip antennas'. Report of Technical Group, IECE of Japan, AP78-90, 1978, pp. 21-26 (in Japanese) 30 NAKAOKA, K., ARM, K., and ITOH, K.: 'Some problems on circularly polarised microstrip line slot arrays'. National Conv. Records on Optical and Wave Sect., IECE of Japan, 1982, S2-15 (in Japanese) 31 OLTMAN, H. G., and HUEBNER, D. A,,: 'Electromagnetically coupled microstrip dipoles', IEEE Trans., 1981, AP-29, pp. 151-157 32 ITOH, K., BABA, H., OGAWA, Y., WATANABE, F., and YASUNAGA, M.: 'L-band airborne antenna using crossed slots'. Report of Technical Group, IECE of Japan, AP85-101, 1986, pp. 65-72 (in Japanese) 33 HENDERSON, A,, and JAMES, J. R.: 'Low-cost flat-plate array with squinted beam for DBS reception'; IEE Proc., 1987, 134H. pp. 509-514 34 JAMES, J. R., and HALL, P. S.: 'Microstrip antennas and arrays. Pt. 2: New array-design technique', IEE J. MOA, 1977, 1, pp. 175-181 35 JAMES, J. R., HALL, P. S., and WOOD, C.: 'Microstrip antenna theory and design' (Peter Peregrinus, 1981) 36 COLLIN, R. E., and ZUCKER, F. J.: 'Antenna theory: Pt. 1' (McGraw-Hill, 1969) chap. 14 37 ITO, K., and KITAJIMA, H.: 'Design of series-fed circularly polarised printed array antenna'. 4th IEE Int. Conference on Antennas Propagat., Coventry, 1985, pp. 103-107 38 ITO, K., ITOH, K., and KOGO, H.: 'Improved design of series-fed circularly polarised printed linear arrays', IEE Proc., 1986, 133H, pp. 462-466 39 ITO, K., ITOH, K., OHTAKE, T., and KOGO, H.: 'Circularly polarized printed planar array composed of strip dipoles and slots'. IEEE AP-S Int. Symposium Antennas and Propagat. Digest, 1986, pp. 561-564 40 KOBAYASHI, A., ITO, K., and BAN, M.: 'A precise measurement of input immittances of elements coupled to a microstrip line (Continuation)'. Report of Technical Group, IECE of Japan, MW85-106, 1985, pp. 25-30 (in Japanese) 41 NISHIMURA, S., SUGIO, Y., and MAKIMOTO, T.: 'Side-looking circularly polarised microstrip line planar antenna'. Proc. Int. Symposium on Antennas and Propagat., Japan, 1985, pp. 129-132 42 POZER, D. M.: 'Input impedance and mutual coupling of rectangular microstrip antennas', IEEE Trans., 1982, AP-30, pp. 1191-1 196 43 MALKOMES, M.: 'Mutual coupling between microstrip patch antennas', Electron. Lett., 1982, 18, pp. 520-522 44 JEDLICKA, R. P., POE, M. T., and CARVER, K. R.: 'Measured mutual coupling between microstrip antennas', IEEE Trans., 1981, AP-29, pp. 147-149 45 HANEISHI, M., YOSHIDA, S., and TABATA, M.: 'A design of back-feed type circularly polarized microstrip disk antennas having symmetrical perturbation element by one-point feed', Trans. IECE Japan, 1981, 564-8, pp. 612-618 (in Japanese) 46 BAILEY, M. C., and PARKS, F. G.: 'Design of microstrip disk antenna arrays'. NASA Technical Memorandum 7863 1, 1978 47 HANEISHI, M.: 'Studies on circularly polarised microstrip antennas'. Doctoral Thesis, Tokyo Inst. Tech., 1981 (in Japanese) 48 HENDERSON, A., and JAMES, J. R.: 'Design of microstrip antenna feeds. Pt. I: Estimation of radiation loss and design implications', IEE Proc, 1981, 128H. pp. 19-25 49 JAMES, J. R., and WILSON, G. J.: 'Microstrip antennas and arrays. Pt. 1: Fundamental action and limitations', IEE J. MOA, 1977, 1, pp. 165-174
Circularly polarised antenna arrays
813
50 HUANG, J.: 'The finite ground plane effect on the microstrip antenna radiation patterns', IEEE Trans., 1983, AP-31, pp. 649-653 51 HALL, P. S., and JAMES, J. R.: 'Crosspolarisation behaviour of series-fed microstrip linear ar ays', IEE Proc., 1984,13lH, pp. 247-257 52 HANSEN. R. C.: 'Cross polarization of microstrip patch antennas', IEEE Trans., 1987, AP-35, pp. 731-732 53 COLLIER. M.: 'Microstrip antenna array for 12GHz TV', Microwave J., 1977,20, pp. 67-71 54 MURPHY, L. R.: 'SEASAT and SIR-A microstrip antennas'. Proc. Workshop on Printed Antenna Technology, New Mexico State Univ., 1979, pp. 18/1-20 55 HANEISHI, M., HAKURA, Y., SAITO, S., and HASEGAWA, T.: 'A low-profile antenna for DBS reception'. IEEE AP-S Int. Symposium Antennas and Propagat. Digest, 1987, pp. 914-917 56 PUCEL, R. A., MASSE, D. J., and HARTWIG, C. P.: 'Losses in microstrip', IEEE Trans., 1968, MTT-16, pp. 342-350 57 LEWIN, L.: 'Spurious radiation from microstrip', IEE Proc., 1978, 125, pp. 633-642 58 MURATA, T., and OHMARU, K.: 'Characteristics of circularly polarised printed antenna with two layer structure'. Report of Technical Group, IECE of Japan, AP86-101, 1986, pp. 83-87 (in Japanese) 59 STOCKTON, R., and HOCKENSMITH, R.: 'Application of spherical arrays - A simple approach'. IEEE AP-S Int. Symposium Antennas and Propagat. Digest, 1977, pp. 202-205 60 MAILLOUX, R. J., MCILEVENNA, J. F., and KERNWEIS, N. P.: 'Microstrip array technology', IEEE Trans., 1981, AP-29, pp. 25-37 61 HORI, T., TERADA, N., and KAGOSHIMA, K.: 'Electronically steerable spherical array antenna for mobile earth station'. 5th IEE Int. Conference on Antennas and Propagat., York, 1987, pp. 55-58 62 HORI, T.: 'Mutual coupling between broadband microstrip antennas'. National Conv. Records, IECE of Japan, 1984, p. 714 (in Japanese) 63 CARVER, K. R., and MINK, J. W.: 'Microstrip antenna technology', IEEE Trans., 1981, AP-29, pp. 2-24 64 TESHIROGI. T.. and GOTO, N.: 'Recent phased array work in Japan'. ESAICOST 204 Phased-Array Antenna Workshop, 1983, pp.-37-44 CHEN, C. H., TULINTSEFF, A., and SORBELLO, R. M.: 'Broadband two layer microstrip antenna'. IEEE AP-S Int. Symposium Antennas and Propagat. Digest, 1984, pp. 251-254 TAGA, T., MISHIMA, H., and KANEHORI, T.: 'A broadband microstrip antenna at U H F band'. National Conv. Records, IECE of Japan, 1979, pp. 254-255 (in Japanese) HORI, T., and NAKAJIMA, N.: 'Broadband circularly polarised microstrip array antenna with co-planar feed', Trans. IECE Japan, 1985, J68-B, pp. 515-522 (in Japanese) LONG, S. A,, and WALTON, M. D.: A dual-frequency stacked circular-disk antenna', IEEE Trans., 1979, AP-27, pp. 270-273 YASUNAGA, M., WATANABE, F., SHIOKAWA, T. and YAMADA, M.: 'Phased array antennas for aeronautical satellite communications'. 5th IEE Int. Conference on Antennas and Propagat., York, 1987, pp. 47-50 GOTO, N., and KANETA, K.: 'Ring patch antennas for dual frequency use'. IEEE AP-S Int. Symposium Antennas and Propagat. Digest, 1987, pp. 944-947 HANEISHI, M., SAITO, S., YOSHIDA, S., and GOTO, N.: 'A circularly polarized planar arrays composed of the microstrip pairs element'. Report of Technical Group, IECE of Japan, AP 83-64, 1983, pp. 1-4 (in Japanese) HUANG, J.: 'Circularly polarised microstrip array with wide axial ratio bandwidth and single feed L.P. elements'. IEEE AP-S Int. Symposium Antennas and Propagat. Digest, 1985, pp. 705-708 TESHIROGI, T., TANAKA, M., and OHMORI, S.: 'Airborne phased array antenna for mobile satellite communications'. IEEE AP-S Int. Symposium Antennas and Propagat. Digest, 1986, pp. 735-738 BALLING, P,: 'Design and analysis of contoured-beam reflector antenna feed arrays and contoured-beam array antennas'. JINA, 1986, Nice, pp. 315-329
Chapter 14
Microstrip antenna feeds R. P. Owens
14.1 Introduction
When choosing the most appropriate microstrip antenna configuration for a particular application, the means of excitation of the radiating element is an essential and important factor which requires careful consideration. A wide variety of feed mechanisms is available, not just for coupling energy to individual elements, but also for the controlled distribution of energy to a linear or planar array of elements. The feed system may be either co-planar with the radiating elements, or situated in a separate transmission-line layer. Several publications have surveyed many possible types of microstrip antenna feed [l-71. In the present discussion covering the most important types, those aspects which are of particular practical interest to the designer wilI be covered, emphasising available options and including references to the latest advances in feed design. For the sake of descriptive economy and consistency, it will be assumed, unless otherwise stated, that the antenna is radiating rather than receiving energy. The feed network win in general have certain undesirabIe characteristics which must be carefully monitored in order to minimise any adverse effects on the array performance. For example, attenuation due to conductor loss and dielectric loss will occur in a stripline feed, and this win reduce the efficiency, and hence the gain, of the antenna array. The conductor loss cc,depends specificaIly on the type of striplke considered, but it is always proportional to the length of the line and the surface resistivity, R,, of the conductor. R, = 20n& o where f is the operating frequency and a, is the conductivity. In general, a, also increases with increasing line impedance and substrate permittivity, and decreases with increasing substrate thickness. Thedielectric loss a, is proportional to the line length, the frequency, and the dielectric loss tangent, tan 6, and it increases with increasing substrate permittivity.
816
Microstrip antenna feeds
Microstrip antenna feeds
Such features as tapered or stepped impedance transformers, bends, junctions, branches, transitions and terminations will introduce electrical and physical discontinuities into the feed line. In practice it is rarely possible to eliminate the electrical effects completely by normal matching techniques, and as a result reflection losses will occur. In addition, such discontinuities in microstrip feeds will cause surface-wave loss and spurious radiation. The latter will, in general, be uncontrolled, and is likely to increase co-polar sidelobe levels in some directions, and to increase the total energy in the cross-polar radiation pattern, thereby reducing the antenna gain. Theoretical investigations of surface-wave and radiation losses associated with some common discontinuities have been carried out [3, 8-10, 391. Direct radiation losses and surface-wave losses are eliminated in enclosed triplate and suspended stripline feeds, but any discontinuity causing asymmetry in the cross-section, such as a probe feed to a patch, will introduce losses due to the transfer of energy to a parallel-plate mode propagating between the ground planes. This energy is free to couple to adjacent probes, and may thus ultimately result in spurious radiation. The mode can be strongly attenuated by the use of mode-suppressing pins close to the discontinuity, or by means of microwave-absorbent film or sheet material. The following discussion will concentrate mainly on feeds either for conventional resonant microstrip patch radiators, or for the open-end stub radiators which are used in the comb array. However, the series-array design procedure covered in Section 14.3.2.3 could also be applied to microstrip radiating systems such as the serpent, chain, Franklin and rampart arrays which are discussed in Section 14.3.4. In these arrays, radiation takes place from abrupt changes in the direction of the feed line itself. Two distinct types of array feed system can be distinguished. First, there is the parallel or corporate feed, which has a single input port and multiple feed lines in parallel constituting the output ports. Each of these feed lines terminates a t an individual radiating element, and therefore transfers all its energy into the element. The second type of feed system is the series feed, which usually consists of a continuous transmission line, from which small proportions of energy are progressively coupled into the individual radiating elements by various means. This constitutes a travelling-wave array if the feed line is terminated in a matched load, or a resonant array if the termination is an open- or a shortcircuit. The coupling mechanisms available for achievi~geither full or partial transfer of energy to microstrip radiators are discussed in some detail in Section !4.2. Some of the more common parallel and series feed systems are considered in Section 14.3, together with some basic design procedures. It will become clear from Section 14.3 that power dividers and combiners are crucial components in the design of some series feeds and most corporate feed systems. Section 14.4 is concerned with some basic characteristics and limitations of commonly used direct-coupled stripline power dividers/combiners.
817
In Section 14.5, some alternative transmission lines for feed systems are briefly discussed, followed by a survey of some specialised feeds for various types of active and passive multiple-beam-forming networks. 14.2 Coupling to microstrip patches 14.2.1 Co-planar coupling to a single patch 14.2.1.1 Gap-coupledpatch: Coupling to a microstrip patch may be achieved by means of a narrow gap between the feed line and the resonant patch, as shown in Fig. 14.1~.The width of the gap dictates the strength of the coupling at the resonant frequency. When the feed line and the resonant patch are critically coupled, the latter constitutes a matched termination. An approximate equivalent circuit is shown in Fig. 14.lb. For a wide rectangular patch, the radiation conductance G, is given approximately [2, 3, 71 by
where Weis the width of the equivalent waveguide model for a microstrip line of width W [3]. 14.2.1.2 Direct-coupledpatch: If the feed line is directly coupled to the patch, critical coupling a t the resonant frequency may be achieved by one of the two configurations shown in Fig. 14.2. Fig. 1 4 . 2 ~shows a quarter-wave transformer of impedance ZT between the feed line and a rectangular patch [7]. The input impedance to a half-wave resonant patch is equal to R,/2, where R, = 1/G,. Thus
Fig. 14.2b shows an inset feed arrangement which artificially moves the feed point to a lower impedance region inside the patch [7]. For a half-wavelength resonant rectangular patch, the input impedance Z, at a distance I from either radiating edge is given by
where /l= 241,; 3, being the wavelength in the microstrip line. F D a~quarter-wave short-circuited rectangular patch, the input impedance is independent of Z,: Z,
= R,/(l
+ tan2(80)
(14.4)
818
Microstrip antenna feeds
Microstrip antenna feeds
Recently, the case illustrated in Fig. 1 4 . 2 has ~ been investigated, where the feed line enters at a point about one third of the way along a non-radiating edge [I I]. Shorter feed lines with lower loss may be possible using this configuration in a
/[i
feed line
section
microstrip
microstrip
fz;<
cOu$$g
I I
I
I
I
I
L
?!@$., f feed line
gap
20 resonant patch
Fig. 14.1 Gap-coupled patch a Patch b Eauivalent-circuit
corporate feed network. The cross-polarised radiation is relatively high, but it can be minimised by optimising the aspect ratio W/Lof the patch at about 1.5. Two-port coupling at the non-radiating edges has also been tried. When applied to series-fed linear arrays, it has the advantage that the power radiated by the two-port patch can be controlled by adjusting the distance of the input and output ports from a radiating edge 1121. 14.2.2 Series-array co-planar coupling 14.2.2.1 Proximity coupling: This method is used for coupling a single feed line to a linear array of resonant patches. Although gap coupling is involved, in some applications the patches couple over a significant distributed length of line, so proximity coupling is a more appropriate description. In an array configuration, the individual patches do not necessarily need to be matched to the feed line, neither do they have to operate at maximum efficiency. There are two consequences of this: the first is that the coupling gaps
Fig. 14.2 Direct-coupled patch a Quarter-wave matched feed with equivalent circuit b Inset feed with equivalent circuit c Non-radiating edge feed
879
820
Microstrip antenna feeds
Microstrip antenna feeds
821
can be varied to control the proportion of power coupled into the patches, and the second is that the patches themselves can have characteristic impedances rather higher than those normally associated with more conventional lowimpedance patches. Some examples of proximity-coupled patch arrays are shown in Fig. 14.3. Example (a) in this Figure shows discrete gap coupling to patches with a relatively large aspect ratio, and hence fairly high impedance [13]. The gap widths can be theoretically or empirically related to the radiation conductance of the patches, although no design data have been published. The methods of Section 14.3.2 can be applied to produce a tailored aperture distribution across the array. Quite strong coupling can be achieved with narrow gaps, but there is an ultimate limit set by the etching accuracy for the particular substrate, metallisation thickness and line-width combinations. There is effectively no limit to the lowest coupling available from very wide gaps.
Fig. 14.4 Direct-coupled arrays a Comb-line array b Cascaded patch array
(el
Fig. 14.3 Proximity-coupled arrays a End-coupled parasitic patches b 45' inclined parasitic patches c Herringbone array of circularly polarised patch pairs d Edge-coupled parasitic patches e Microstrip patches coupled to dielectric insular guide
Using the nomenclature of waveguide arrays, both transposed arrays (as shown in Fig. 14.3a) and untransposed arrays of this type can be designed. The radiated E-field polarisation is parallel to the length of the patch, i.e. transverse to the axis of the feed line. A variant of this type is shown in fig. 14.36, where the patches are inclined at 45" to the feed-line axis [13, 141. The polarisation is likewise inclined at this angle. An interesting application of this variant is shown in Fig. 14.3~.This is a transposed array of 4.5" inclined patches in which the lower array is displaced by one quarter-wavelength relative to the top array. As a result, the patch pairs shown in the Figure each form a self-matched circularly polarised element [13, 141.
822
Microstrip antenna feeds
Microstrip antenna feeds
In Fig. 14.3d, the resonant patches are capacitively coupled over their whole length [15, 31. Again, the width of the gap dictates the strength of coupling, and hence the radiation conductance of the patch. The polarisation in this case is longitudinal, and the excitation is such that only untransposed arrays are possible. In one interesting variant of this category of feeds, the microstrip line is replaced by a dielectric image guide, or insular guide, as shown in Fig. 14.3e. This arrangement has been employed in millimetre-wave antennas at frequencies where conventional microstrip lines would contribute excessive losses [16]. 14.2.2.2 Direct coupling: Two particular examples of this type of coupling will be considered; the comb-line array [3, 171, and the cascaded patch array [2, 181, both illustrated in Fig. 14.4. The comb-line structure of Fig. 1 4 . 4 ~is seen to bear some resemblance to the gap-coupled array of Fig. 14.3a, but in this case the radiation conductance of the open-circuited stub is determined by its width, as indicated in Section 14.2.1.1 [2, 31. The maximum conductance available for a given feed-line width is dictated by a maximum stub width of about one half-wavelength. The use of a transposed array overcomes this limitation to some extent by spreading the amount of power to be radiated over twice as many elements within a given array length. The minimum conductance available is governed by the practical limitations on etching sufficiently narrow lines. The direct-coupled array, an example of which is shown in Fig. 14.46, consists of a cascaded series of low-impedance resonant patches, linked by sections of a high-impedance feed line. The required aperture distribution is obtained by appropriately varying the widths of the resonant patches [2]. 14.2.3 Probe coupling This method of coupling, illustrated in Fig. 14.5, has been widely analysed in the literature, particularly for circular patches [19-241. It has the advantage that the patch,
,pin
connector Fig. 14.5 Probe-coupled microstrip patch
feed lies behind the radiating surface, and therefore does not itself contribute unwanted radiation. It is a very convenient method of feeding a single patch by means of a surface-mounted coaxial connector attached to the microstrip ground plane, for instance for experimental purposes. The probe is positioned at a point where the input impedance of the patch, Z,", is equal to the characteristic impedance of the coaxial feed line. Eqns. 14.3 and 14.4 may be used to determine Z , for a rectangular patch.
823
The disadvantage for an array system is that the feed network must lie in a separate layer behind the radiating surface, so the complete antenna cannot be etched on a single substrate. There is a consequent increase in complexity, but this may be an acceptable penalty to pay for a resulting increase in design flexibility. An additional disadvantage, particularly at high frequencies, is that the necessity for inserting properly secured probes results in extra mechanical complexity and increased manufacturing costs, particularly for large arrays. The feed network beneath may be constructed in a variety of transmission lines, e.g. microstrip, triplate or suspended stripline, provided that an adequate rightangle transition into the microstrip patch can be designed. The inductive reactance of the probe adversely affects the VSWR bandwidth in this type of coupling, particularly if a thick, low-permittivity substrate is used in order to increase the gain bandwidth. The VSWR bandwidth can be broadened by adding series capacitive-reactance compensation as close as possible to the inductance, to provide a series circuit resonant at the same frequency as the patch [25]. This may be done within the feed network behind the patch [25], within the probe itself [26], or in the form of a small annular gap on the surface of the patch [27]. The latter method results in high cross-polar levels due to the asymmetrical gap, but these can be significantly reduced by introducing a second compensated feed diametrically opposite the first. An additional short-circuiting pin is often placed through the centre of a circular microstrip patch, providing a DC connection between the patch and the ground plane [19]. This has the dual advantage of earthing the patch, and suppressing some higher-order modes which would otherwise exist on the patch. 14.2.4 Aperture coupling Coupling via an aperture in a common ground plane between the radiating microstrip layer and a stripline feed layer is an attractive alternative to probe coupling. No extra components or assembly processes are needed; the only requirement is that the common ground plane should contain etched apertures accurately positioned below the microstrip patch and above the feed line [28301. The microstrip feed system shown in Fig. 14.6 provides stronger coupling than a similar triplate or suspended stripline system because of the higher concentration of fields above the feed line where the aperture is positioned. Furthermore, a relatively high-permittivity substrate can be used if required for the feed system, without compromising the radiating properties of the lowerpermittivity substrate carrying the microstrip patches. Both circular and rectangular apertures have been investigated theoretically and experimentally, to determine the relative influence on coupling factors of the aperture dimensions and the feed line and patch overlap parameters, and good agreement between theory and experiment has been obtained. A dual aperture-fed patch has been reported, with 18 dB isolation between the two ports [31]. If both apertures are excited via a quadrature feed, circular
.
824
Microstrip antenna feeds
Microstrip antenna feeds
polarisation can be obtained from a square or circular patch. Alternatively, if a single-feed circularly polarised patch were used [20], dual circular polarisation would be possible with a dual-aperture feed [32].
825
of the gap-coupled parasitic patch array shown in Fig. 14.3, can be designed in which the coupling is varied along the array by laterally displacing the elements relative to the feed line beneath them. subst rates
substrates
/
ground-plane
feed line
/ crucifor
Fig. 14.6 Aperture-coupledpatch antenna (Reproduced from Pozar [28] with permission of
patch
IEE)
A series-fed aperture-coupled array could be made in which the coupling to each patch is controlled by varying the size of the aperture. A further application relevant to planar arrays with stacked feed substrates involves aperture coupling from a microstrip feed perpendicular to the array plane. The use of a straight feed line [33] and a proximity feed line [34] have been reported.
14.2.5 Electromagnetic coupling This type of coupling, despite the somewhat broad definition implied by its title, is by convention taken to refer to the overlaid resonator configuration illustrated in Fig. 1 4 . 7 ~ [35]. The feed system is a covered microstrip network, and the radiating elements are etched onto the covering substrate immediately above the open-ended feed lines. The elements are thus parasitically coupled to the feed network. They may be regarded as microstrip patches on a double-thickness substrate sharing a common ground plane with the feed network. Successful feed systems have been developed using this type of coupling, but, like the co-planar feed systems, they can suffer from spurious radiation from the feed network itself. As Fig. 14.7b shows, circular polarised radiation can be obtained by suitably exciting a cross-shaped patch [35]. A series-fed system, reminiscent
Fig. 14.7 Electromagnetically coupled patches a Collinear coupled patch (Based on [35] with permission of IEEE @ 1981 IEEE) b Circularly polarised coupled patch
14.3 Parallel and series feed systems
14.3.1 Parallel feeds for one and two dimensions 14.3.1.1 One-dimensionalpara[[e[feed: Fig. 14.8 shows a simple one-dimensional parallel feed system for a linear array, consisting of a branching network of two-way power dividers. The power-divider ratios may be chosen in order to achieve a particular aperture distribution across the array. If the distances from
826
Microstrip antenna feeds
Microstrip antenna feeds
the input port io each of the output ports are identical, and the radiating elements are identically coupled to thse ports, the resulting radiated beam will be in the broadside direction. The beam position will be independent not only
Fig. 14.8 One-dimensionalparallel feed network
aperture plane
ye
main bea direction
827
achieving this. In Fig. 14.9a, an incremental phase difference 6 between the elements is obtained by progressively extending the line lengths to successive elements by the distance A1 = (6/2n)Il, where A, is the wavelength in the transmission line. The same result is obtained by offsetting the power-divider T-junction by multiples of A1/2, as shown in Fig. 14.96. The general equation relating the main-beam angle 8, to phase difference 6, free-space wavelength 1, and element spacing d is as follows:
6 10 sin $ = 2n d It will be observed that, in the general case, the beam angle is no-longer squintless; neither is it independent of d. It is of interest to determine the range of parameters for which the peak of the first possible grating lobe lies outside real space. The relevant formulae are as follows: General phase equation for beam at f? degrees is:
kd sin 0 - 6
=
2Kn
(14.6)
where k = 27r/A0,and K is an integer denoting the order of the mode. This reduces to the main beam equation 14.5 when K = 0. The general equation for grating-lobe angle f? = 0, is thus: sin 8,
=
sin 8,
+ Mold
(14.7)
+
1). If K = - 1 the grating lobe will not exist if d / l , < l/(sin 0, If K = + 1 the grating lobe will not exist if d/A, i 1/(1 - sin 0,) Another variant of the basic parallel feed pattern of Fig. 14.8 is represented by Fig. 14.10. Here, some of the two-way power dividers are removed, but the
Fig. 14.9 Networks for producing inclined beams a Beam squint by line extension b Beam squint by offset power divider
of the frequency, i.e. it will be 'squintless', but also of the spacing between the elements. This spacing can thus be chosen to meet other criteria. For example, it may be desirable to increase the spacing, up to a limit dictated by the onset of grating lobes, in order to minimise the complexity of the feed network by ensuring that a particular number of elements fits within the available aperture. Alternatively, it may be important to maximise the gain from a given aperture by choosing one half-wavelength spacing between the elements; or maybe a favourable spacing with regard to mutual-coupling effects will be preferred. A parallel feed may also be used to produce a radiated beam inclined at an angle to the broadside direction. Fig. 14.9 shows two alternative ways of
Fig. 14.10 Asymmetrical parallel feed network
line lengths to each element are controlled as before to provide the desired phase front. The main advantages of this variant are twofold. First, the network can be readily configured for even numbers of elements which are not powers of two, and for odd numbers of elements. Secondly, it gives greater flexibility in providing tapered aperture distributions which would otherwise necessitate inconveniently large power-divider ratios in the conventional branching network.
828
Microstrip antenna feeds
14.3.1.2 Two-dimensional parallelfeed: Fig. 14.1 1 shows the schematic layout for a two-dimensional corporate feed with four elements per side. This form of layout can be extended to larger arrays with, specifically, 2Nelements per side. Any attempt to modify the feed to deal with other even numbers can result in
Microstrip antenna feeds
829
under these conditions, but the cross-polar components in the radiation pattern are out of phase, and are suppressed over a range of frequencies. The axial-ratio bandwidth is thus significantly increased. Fig. 14.12 shows schematically the feed configuration required for a righthand-polarised group of patches. As may be deduced from the line lengths shown, a by-product of this technique is that, around the design frequency, the mismatches due to the coupled patches tend to cancel out at the input port. Consequently the bandwidth over which the input VSWR is less than some specified value, say 2: 1, should also increase. A relatively minor counteractive effect is that, because the line lengths are unequal, the phase differential between the four patches will be frequency-dependent. 14.3.1.3 Radiation-pattern prediction for arrays fed in paralleI: The details of array theory may be obtained from other sources [40, 411. However, some simple basic principles apply, and these are summarised here. Considering a linear array first, as shown in Fig. 14.13, the far field due to an array of N
Fig. 14.11
Two-dimensional 4
x
4 corporate feed
the need for fairly large power-divider ratios. Nevertheless, there is a basic symmetry which reduces the number of different power dividers needed. If there is an odd number of elements per side, this symmetry is lost. The considerations regarding element spacing, aperture distribution and beam angle are the same as those discussed for the linear array. Recently, the technique termed 'sequential rotation' has been applied specifically to two-dimensional arrays of circularly polarised microstrip patches with single feed points [36-391. As shown in Fig. 14.12, one application of the
element no.
1
2
am Litude of r a J a t e d field
A2
distance dl from reference point
phase on element
n
d2
61
62
dn
6n
Fig. 14.1 3 Parameters for parallel-fed linear array Fig. 14.12
Feedforsequentialrotation: schematic (Copyright @ Controller HMSO, London, 1986. Reproduced with permission)
elements disposed along a straight line is given by
f('M8) where the array factor is =
technique involves rotating each element in a 2 x 2 array of such patches through 90" relative to its immediate neighbours. The line lengths in the feed to the group of elements are adjusted to compensate for the 90" phase change caused by this rotation. The co-polar radiation from this array is unaffected
N
f (8)
=
1I A, exp (jk(d,, - d , ) sin 0 - 6,)
n=
N-l
N
830
Microstrip antenna feeds
g(0) = element factor A, = radiated-field amplitude of element n d,, = distance to element n from some reference point 6, = phase on element n The radiated-field amplitudes are chosen from one of the many distributions available. Apart from the uniform case, commonly used distributions are the Taylor one- and two-parameter, and the Dolph-Chebyshev [40,41]. The choice is dictated by the particular radiation-pattern characteristics required. Array elements are normally uniformly spaced, but random spacing and sparse arrays may be accounted for in this formula. The phase components 6, are primarily dictated by the relative lengths of the feed lines to each element, but may also include a factor due to the relative orientation of the elements. The element factor for rectangular patches is given by the following two approximate formulas, corresponding to the two major axes of the patches [2, 31. Fig. 14.14 shows the co-ordinate system applied to the patch.
Microstrip antenna feeds
831
In many rectangular arrays, it is possible to separate the array factors in the two orthogonal principal planes [40]. In such a case, the far-field radiation pattern of an M x N array with equal element spacings dm and d,, respectively, is given by (14.12) E(0, 4 ) = g(0, 4 ) f ( 4 f Oil where g(0, 4 ) is the element factor. The separate array factors in the principal planes are given by:
z M
f(x) =
A, exp[j(mkd, sin 0 cos
4
-
&,)I
(14.13)
m= I N
f ( y)
=
1A, exp[j(nkd,, sin 0 sin 4
- ti,)]
(14.14)
n= I
The far-field radiation pattern may therefore be derived in any plane, provided that the element factor can be defined in that plane. The directivity of a linear array of isotropic sources is given by the following formula [42]:
The directivity of a two-dimensional array is separable, such that: D(x, y) = nD(x)D(y) cos 0,
(14.16)
where D(x), D(y) are the separate directivities of the orthogonal linear arrays. In a practical microstrip array, the overall gain, measured in decibels, will be made up of several factors:
Fig. 14.14 Patch co-ordinate system
E-plane ( 4 = n/2)
sin =
(x
nW . sm 0)
ILW .in
cos 0 F,
where q = aperture efficiency ( < 1) G, = gain of a single element a = feeder loss in dB per wavelength L = length of the feeder in wavelengths M represents miscellaneous discontinuity losses as discussed in Section 14.1. The dominant first term in eqn. 14.17 increases logarithmically with array size, but the feeder-loss term increases linearly. The gain will therefore reach a maximum for a particular size of array. For example, an N x N array with half-wavelength element spacing will have a directivity D(x, y) of n ~The~ feeder . length L will be close to N/2 wavelengths.
832
Microstrip antenna feeds
Microstrip antenna feeds
G will be a maximum when the differential of eqn. 14.17 with respect to N is equal to zero. The differential is given by 20 log,,(e)/N - a/2, where e is the exponential. So, for maximum gain, N will be the nearest integer to 17.371~.
14.3.2 Series feed for one dimension 14.3.2.1. Travelling-wave feed: The travelling-wave feed is commonly used for arrays in which the beam is required to be inclined away from the broadside direction. In its simplest form, as shown in Fig. 14.15a, the radiating elements are partially coupled to a continuous feed line by one of the methods described in Section 14.2.2. The feed line is terminated in a matched load. This arrangement has the disadvantage that the beam will squint with frequency, but, if necessary, line-length compensation between the couplers and the elements can be introduced to produce the 'squintless' series feed, asshown in Fig. 14.156
Figs. 14.16~and b illustrate the two types in the form of two different comb-array designs. Some microstrip arrays can be of one type only; for example the serpent array [44] in Fig. 14.16~is a transposed array, and the longitudinal parasitic patch array [15] (Fig. 14.16d) is an untransposed array.
I
---. in
WI.
rodiatina elements
power divider network
Fig. 14.15 Lineartravelling-wavearrays a Directly coupled travelling-wave array b Squintless travelling-wave array (Reproduced from [3] with permission of IEE)
The equations relating the element spacing to the required beam angle can be divided into two groups. The first group concerns arrays in which there is no phase change between adjacent elements attributable specifically to the coupling mechanism between the feed line and the elements. Using the nomenclature of waveguide slot arrays, this is termed an untransposed array, or a array. The second group of equations covers the transposed array, or - type, in which a phase change of 180" occurs between adjacent elements due to the effect of the coupling mechanism on the instantaneous phase of the radiated fields.
+
++
833
Fig. 14.16
~ransposedand untransposed arrays a Untransposed comb array b Transposed comb array c Serpent array (transposed) d Parasitic patch array (untransposed)
Considering untransposed arrays first, the general equation is:
where d is the element spacing.
load
-----t
834
Microstrip antenna feeds
Microstrip antenna feeds
K = 0 is not a solution in a stripline medium where /2,/1, > 1. K = - 1 is the solution for the principal beam:
backward-firing option is free from grating lobes for all main beam angles, ~rovided1,/1, > 1. If both options are otherwise equally possible in an array required to occupy a given aperture, the forward-firing option may be convenient if the designer wishes to minimise the number of elements in order to simplify the feed layout. Alternatively, if the array is to be short, it may be advantageous to increase the number of elements in order to minimise the range of radiation conductances required. In that case the backward-firing option may be chosen. It should be borne in mind that the array gain will depend on the spacing of the elements, as will the mutual coupling between elements. The amplitude distribution across an array is determined by the strength of coupling to each element. This may be represented as a coupling factor c, defined as the ratio P,/P,, where PRis the power radiated by the element and P, is the power incident upon it. Alternatively, the normalised radiation conductance g may be used. If matched conditions were to exist beyond each element in the array, g would be defined by the expression g = P,/P,, where P, represents the power transmitted past the element. It is important to note the distinction between c and g, as their definitions are sometimes erroneously interchanged in the literature. Section 14.3.2.3 describes a method for computing the radiation conductances for a travelling-wave array designed to radiate with a specified amplitude distribution. The travelling-wave feed suffers from the disadvantage that the element spacing needed to produce a broadside beam is either one half-wavelength for a transposed array, or one wavelength for an untransposed array. In either case, the mismatches caused by each element conductance loading the transmission line add up in phase, resulting in a large VSWR at the input end of the array and a consequent reduction in efficiency. This situation may be avoided by introducing small matching stubs at each individual element. Alternatively, a lower VSWR has been achieved in a transposed comb array by splitting each stub into two elements spaced by one quarter-wavelength, so that each pair is self-matching [3, 171. The herringbone array of Fig. 1 4 . 3is ~ likewise self-matching.
The element spacing d required to give a beam angle 0, is given by d = l0/(1,/1, - sin 8,)
If beam angles away from broadside are required, there is the choice of backward or forward firing. As the formulas indicate, the element spacing is less for backward-firing beams, so more elements are required to fill a given aperture. It is essential in either case to know whether grating lobes will exist in real space. The general grating-lobe equation is: sin 8,
=
(K
+ I) - - K sin 6, 10
1, K = - 2 is the solution for the first grating lobe, which occurs only if 0, is positive and sin 8, 2 0.5(/2,/1, - I) All of these formulas are concerned only with the effect of phase components in the array factor on the main-beam and grating-lobe positions. If the element factor has some directivity, then this will influence the position and relative amplitude of any grating lobes in the final radiation pattern. The sidelobe levels and positions will be closely dependent on the distribution of radiated amplitudes across the elements of the array, as well as their phases. The corresponding formulas for the transposed array are as follows: The general equation for transposed arrays is:
K = 0 is the solution for the principal beam. Therefore, sin 6, =
10 lo --
1,
2d
I
or element spacing d
=
1,/(2(&/L, - sin 0,))
The general grating-lobe equation is: sin 0,
=
sin 0, (1 - 2K)
+ 2KA0/1,
K = - 1 is the solution for the first grating lobe, which occurs only if 6, is positive and if sin 8, 2 2(1,/1, - 0.5)/3. It will be seen that the transposed array can provide beams over a much wider range of angles without producing grating lobes, and that in both cases the
835
14.3.2.2 Resonant feed: An alternative way of obtaining a broadside beam without the mismatch problem is to use a resonant feed. In this option, the feed line is terminated in an open-circuit one half-wavelength beyond the last element, or a short-circuit one quarter-wavelength beyond. The element spacings are as indicated above. If the array is designed so that the sum of the normalised radiation conductances is equal to unity, the input admittance of the array is given by N
y
=
cgn+jO
=
1
(14.26)
n=l
Within the restriction of this condition, the relative conductance values can be
836
Microstrip antenna feeds
Microstrip antenna feeds
freely chosen to given any desired amplitude distribution, provided the maximum conductance achievable is not exceeded. From a practical point of view, it is an advantage that matched terminations are not needed, particularly if the feed network consists of a microstrip system coplanar with the radiating elements. Open-ended lines generally suffice as open-circuits, although they are, of course, sources of radiation in microstrip feeds. In addition, fringing fields extend the effective electrical length of the line beyond its physical end. Shortcircuited lines are obtained by means of pins or plated-through holes providing a conducting path from the feed line to the ground plane. For all practical purposes, the resonant feed is only useful in the broadside beam case. Its main disadvantage is that, because of its resonant nature, the VSWR bandwidth is very narrow. 14.3.2.3 Series-feed design procedure: The following discussion is intended primarily to apply to travelling-wave array design, but with certain modifications it can be used for the design of resonant arrays. Mutual coupling is not taken into account in the analysis, which utilises conventional lossy transmission-line theory available in standard textbooks [45]. The design of a series-fed array involves the calculation of the normalised radiation conductance required at each element, in order to provide the chosen amplitude distribution across the array. The radiation conductance is then translated into an appropriate physical variable of the array by means of a theoretical or empirical relationship between the two. Ideally, in order to facilitate subsequent analysis of the designed array at frequencies dose to the design frequency, the Q-factor of the resonant element should be known. The radiation conductance calculation should account for the complex propagation characteristics of the transmission-line feed, and for the effects of mismatches introduced by the radiating elements. The termination of the feed line is modelled as a normalised conductance of unity. The following groups of parameters are usually defined by the design requirement:
Fig. 14.17 shows the parameters which are involved in the design procedure. It is convenient to choose an initial value for the fractional efficiency factor q, such that
Fig. 14.17 Power and admittance notation for lossy transmission-line array
where PRnis the power delivered by the nth element normalised to C(Ai); thus (14.28) PL = (1 - d Starting from the load end, the parameters can be calculated iteratively from the following equations, assuming that the elements are resonant at the design frequency:
(a) Design frequency f,, or wavelength &. Beam squint angle, 8,. Available aperture size, or number of elements, N. (b) Propagation constant of chosen transmission line, y = a: j/3, where a is the attenuation constant and /3 is the phase constant, 2x11,. (c) Parameters of particular radiating element; namely maximum achievable radiation conductance and Q-factor.
The radiation conductance of the nth element is
Secondary parameters can be calculated from these; e.g. the spacing between elements (normally the spacing is uniform), and the number of elements N required to fill the aperture, if this has not previously been defined. When N is known, the radiated-field amplitudes A, for the desired radiation pattern can be calculated.
The power-loss ratio [45] is:
+
837
where Re(y,) is the real part of y,, and P,, The power incident on the nth element is: Ph
=
p,
=
PL
+ PT"
(Note that in Reference 45 page 94 there is an error in eqn. 3.93 and in the equation on page 95 because ITle" = =jr,le-"I,nor IrLI).
838
Microstrip antenna feeds
Microstrip antenna feeds
where the reflection coefficient looking into element n is:
and eqn. 14.35 is replaced by Y" = Y h
The admittance y, transformed to the load side of element n
839
+ 1 is:
(14.41)
f Yen
14.3.3 Combined feeds 14.3.3.1 Parallel/series one-dimensionalfeed (centre-fed): Fig. 14.19 illustrates two examples of the type of combined feed which comes under this heading.
The admittance looking into element n is: Yn = Y / n + gn (14.35) where y,, = y,. At the input end, the input reflection coefficient is r,, and the input power is:
The reflected power is: The power otherwise unaccounted for is dissipated in the transmission-line:
input end
element no.
Load end
Fig. 14.18 Radiation-conductance profile for 12-element array
If any of the calculated radiation conductances exceed the maximum achievable value, the computations should be repeated with a lower efficiency factor q. Conversely, if the conductances are relatively small, excessive power is absorbed in the load, and q can be profitably increased. Fig. 14.18 shows a typical radiation-conductance profile. The power entering the feed line diminishes rapidly with distance travelled, so, in order to maintain a symmetrical amplitude distribution, the element conductances in the second half of the array must be consistently higher than the corresponding values in the first half. The maximum-conductance thus occurs about two thirds of the way along the array. Once the radiation conductances have been calculated, then, provided the Q-factor of the elements is known, the array can be analysed at some offresonant frequency, to determine the new distribution of radiated power. The relevant formulas are similar to those used for the design, except that the conductance is replaced by a complex admittance given by
This type is effectively a centre-fed linear array, of either the travelling-wave or resonant-feed type. It will be noted that, in example (a), continuity of the phase front is ensured by offsetting the feed point by one quarter-wavelength from the centre of symmetry of the array. This is not necessary in example (b). If a broadside beam is required, the two halves of the array are in other respects identical; the element spacings are equal on both sides, and the radiation-conductance profile is symmetrical. To obtain a squinted beam, however, the element spacing must be different in each half, so that one half produces a forward inclined phase front, and the other half a backward phase front in the same direction in space. An important property of the centre-fed array with broadside beam is that the beam does not squint with frequency. Any change in frequency causes the phase fronts in the two halves to rotate in opposite directions. The result is that the beam remains fixed in direction, but becomes broader as a consequence of the discontinuity in the overall phase front. Ultimately, for larger frequency excursions, the beam will split into two.
Then, in eqn. 14.30, the new power radiated by the nth element is given by
14.3.3.2 Two-dimensionalfeeds: Two possible forms of two-dimensional network involving feeds are described here. The example shown in Fig. 14.200 is the parallel/series type, involving a one-dimensional parallel feed with the extended output ports forming series feeds. The beam produced by this network will squint in the plane of the series feeds only. This squint may be eliminated
840
Microstrip antenna feeds
Microstrip antenna feeds
841
by placing two such networks back to back, as shown in Fig. 14.206. Since the space between the series feeds will be limited, the parallel feeds may have to be located on a separate transmission-line layer. The example shown in Fig. 1 4 . 2 0 ~is the serieslseries type, which will exhibit beam squint in both major planes. Four such networks, fed in parallel, combine to form a squintless array, centre-fed in both planes as shown in Fig. 14.20d. The primary feed lines couple to the secondary lines via power dividers. The imradiatin elemen2
Fig. 14.20
Two-dimensional feeds: schematic ( a ) end-fed Parallel-series feeds ( 6 ) centre-fed
842
Microstrip antenna feeds
load
f
---t
Microstrip antenna feeds
843
pedance ratios of these may be designed to produce a tapered amplitude distribution in the plane of the primary lines. The cross-fed array shown in Fig. 14.21 [46-481 is a variant of the serieslseries type, in which a square array of elements is series-fed from diagonal branch lines coupled directly to a single centre-fed line on the opposite diagonal. All lines are terminated by radiating elements. The input signal is split four ways at the centre feed point. In order to produce a coherent broadside beam, the elements are spaced by one wavelength along the diagonals, or 0.707 wavelength
Fig. 14.21 Cross-fed array (Reproduced from Williams [46] with permission of IEE)
along the sides of the square. The packing density of elements is thus increased by this configuration. In order to achieve controlled element excitation and good input VSWR, it is necessary to incorporate quarter-wave impedance transformers in each feed line, and on each branch of the central cross [47, 481.
Series-series feeds ('' end-fed (d) centre-fed
14.3.4 Discontinuity arrays In this category, the microstrip feed line itself is the radiator. Radiation occurs at a bend or abrupt change in direction of a microstrip line, as a consequence of imbalance between the fringing-field densities on the outside and inside of the bend. If the radiating discontinuities on the line occur in certain regular geometrical patterns, the phase, amplitude and polarisation of the radiation can be controlled to form a travelling-wave array. These structures may be analysed in terms of an effective magnetic-current source representing the fringing-field imbalance [3]. Alternatively, similar results for the radiation characteristics of a particular structure may be obtained from an analysis of the instantaneous surface currents on the line [9]. The discussions on particular discontinuity arrays that follow reflect the form of analysis used in the original texts. Fig. 14.22 is a schematic representation of part of a serpent array, shown
844
Microstrip antenna feeds
Microstrip antenna feeds
more fully in Fig. 14.16~.The serpent is formed from a series of contiguous half-sinusoids [44, 49, 501. Radiation is concentrated at the peaks of the sinusoids where the curvature is a maximum, and is polarised in a radial direction
Fig. 14.22 Serpent array: schematic
at these peaks. The serpent is therefore a transposed array. The amplitude of the radiation is proportional to the maximum curvature, which is given by where s is the span and a the amplitude of the half-sinusoid. In the simplest case of a constant-amplitude constant-conductance serpent, a plane wavefront at the desired angle 00,relative to broadside, is obtained if the following relationship applies:
where I,, is the meander length of the sinusoid. This is similar to eqn. 14.23, except for the extra factor I,,,/s. For a sinusoid, this ratio is given by lm/s =
+ q) .)E(k)ln
(14.44)
+
where q = ( x a / ~ )k~ ,= ,/(q/(l q)),and E(k) is the complete elliptic integral of the second kind. Any desired amplitude distribution may be obtained by linking half-sinusoids with varying amplitudes and spans. The design equation is then more complicated, and must be solved iteratively. Theoretical and experimental studies have been carried out with a good measure of agreement [49,50], but the design depends on empirical measurement of radiation conductance as a function of sinusoid amplitude and span. Two-dimensional serpent arrays have been built using a one-dimensional corporate feed. The rampart antenna [2, 3, 511, or, more appropriately, the crank antenna, is perhaps the most important example of the discontinuity array. It is an extremely versatile concept which can provide a wide range of radiated polarisations by appropriate choice of array geometry. One factor dictating the geometry is the beam angle, but it will be assumed here that a broadside beam is required. The antenna consists of a cascaded array of unit cells. The general form of the unit
Fig. 14.23 Rampart-line amys (Reproduced from [ 3 ] with permission of IEE) a Unit cell b Circularly polarised array c Longitudinally polarised array d Transversely polarised array
845
846
Microstrip antenna feeds
Microstrip antenna feeds
847
cell is shown in Fig. 14.23~.Radiation, polarised diagonally, occurs at each of the six matched mitre bends as shown. The line lengths, p, r, s, normalised to the microstrip wavelength, are chosen to provide correctly phased polarisation of the required type within a cell. To maintain the correct phasing between cells, the normalised length t must be equal to the fractional part of 201 + r + s). In cases where either t o r s is zero, the unit cell reduces to a four-cornered structure. In the circularly polarised case, s = 0 is a necessary condition, and the parametric relationship between p and r is [51]:
Successive values of n give alternate hands of circular polarisation. Specific choice o f p or r is dictated by considerations of cross-polar levels, line losses and input VSWR, but a good working combination is: This solution is illustrated in Fig. 14.236. Linear polarisation is obtained only if s = p. The parametric relationships are as follows:
+
+
Longitudinal polarisation: either p r = n, or 2p r =n Representative solutions quoted in the literature are: p = s = 0.25, r = 0.5, t = 0; or p = s = r = 113, t = 0 (See Fig. 14.23~) Transverse polarisation: either p + r = n - 0.5, or 2p + r = n - 0.5, Representative solutions are: p = s = 0.125, r = 0.25, t = 0; or P = s = r = 0.25, t = 0.5 (see Fig. 14.234. If the cells are identical, the array is a constant-conductance array. A controlled aperture distribution can be obtained by varying the geometry of successive cells within the constraints of the parametic equations. This is a consequence of an approximately linear relationship between the radiation conductance of a cell and the dimension p [51]. Two-dimensional arrays using a one-dimensional corporate feed have been manufactured [3]. The crank array may also be analysed in terms of electric surface currents over the complete cell, rather than in terms of localised equivalent magneticcurrent sources. The circularly polarised design described above has been analysed in this way, and a two-dimensional version reported [52, 531. In order to improve the overall radiation pattern, the linear arrays were fed in pairs, with a relative displacement of one half-wavelength between them. The meander-line form of the linearly polarised chain antenna [2, 3, 541 may also be regarded as two crank arrays fed in pairs. Fig. 1 4 . 2 4 ~shows this type, and Fig. 14.246 shows the rectangular-loop type [2, 551. In each case the width of the loop 2p, normalised to microstrip wavelength, is about 1, and the lengths r of the sections parallel to the antenna axis are about 0.4. The instantaneous electric-current directions are such that radiation from these parallel sections
Fig. 14.24 Travelling-wave chain antennas (Reproduced from 131 with permission of IEE) a Meander-line b Rectangular loop c Microstrip Franklin antenna d Circularly polarised antenna: schematic
848
Microstrip antenna feeds
Microstrip antenna feeds
combines in phase, whilst radiation from the transverse sections tends to cancel. The polarisation is therefore linear in the longitudinal direction, producing very low cross-polar levels. The beam produced can squint with frequency over a wide range of angles relative to broadside, given by sin 0
=
(r
+ p - I)/r
849
trol is possible by varying the line width, and hence the impedance, of the vertical components in the grid. Good performance has been obtained at lOGHz from a two-plane monopulse array of this type, occupying a fivewavelength-diameter circular aperture.
(14.46)
A two-dimensional array of this type has been reported [54] in which both ends of the linear arrays are connected to corporate feeds, so that there is a single feed port and a single load port. The microstrip Franklin antenna [2, -3, 561, shown in Fig. 14.24c, is also linearly polarised in the longitudinal direction. For broadside radiation, the line lengths AB, BC and CD are each one half-wavelength. The instantaneous currents are in the direction shown. Transverse currents in adjacent parallel sections act in opposition, so that the cross-polar levels are low. Further reduction in the cross-polar levels is obtained in a two-dimensional array by making each linear array the mirror image of its neighbour. Another chain antenna able to generate circular polarisation is shown in Fig. 14.24d [3, 571. The basic radiating elements are v-shaped sections of line, with an included angle a and arms of length s. The sections are linked by Schiffmann phase shifters aranged in alternate directions so that their spurious radiation is cancelled. The practical array consisted of eight 32-element arrays printed on thin plastic sheets suspended above a ground plane. Analysis of the instantaneous current on a single element shows that the quadrature components Eg and E, have equal magnitude, and hence generate circular polarisation, if the following equation holds: tan (42) cos 0 = tan (ksT/2)
(14.47)
where 0 is the beam angle relative to broadside, and T = 1 - sin (a/2) sin 0. The Schiffmann phase shifters [58] have negligible effect on the radiation, but introduce 90" phase shift between elements, thereby maintaining the required phase conditions along the array for a circularly polarised beam in the 8, direction. The phase-shifter length I, and width I, must be adjusted so that sin 0,
=
(2s
+ I, + I,
- I,)/d
(14.48)
where d is the spacing between elements. A further subset of discontinuity arrays worthy of mention is the wire grid o r lattice array, three examples of which are shown in Fig. 14.25 [59, 601. Each example is a resonant structure radiating in the broadside direction. The 'brick wall' configuration of Fig. 14.25~[59] consists of microstrip loops one wavelength wide and one half-wavelength high. The instantaneous currents in the loop are such that the vertically polarised field components combine constructively, and the horizontally polarised components cancel. Amplitude con-
Fig. 14.25 Microstrip wire grid arrays a 'Brick wall' wire grid array (Based on [59]with permission of IEEE @ 1981 IEEE) b Hexagonal lanice array (Reproduced from Hill [60]with permission of IEE) c Square lanice array (Reproduced from Hill [60]with permission of IEE)
The lattice arrays shown in Fig. 14.256 and c utilise three- or four-line junctions having angular symmetry [60]. Such junctions will radiate in the direction normal to the array, only if the line widths at the junction are unequal. A non-radiating lattice of constant-impedance lines each one half-wavelength long can be used, for example, to feed an array of open-circuited stubs placed at the nodes of the lattice. However, in the examples shown, horizontally polarised radiation is caused by the horizontal members of the lattice having a
850
Microstrip antenna feeds
lower impedance than the rest. Of the two alternatives shown, the hexagonal array has advantages in terms of bandwidth.
Microstrip antenna feeds
The performance of this type of power divider is limited by the relatively low isolation between the output ports. If these ports do not have perfectly matched terminations, some power will be reflected back to the input, and some will be
14.4 Direct-coupled stripline power dividers and combiners 14.4.1 Simple three-port power dividers Most corporate feed networks use two-way power splitters for progressively subdividing the power to the array elements. Considering equal power division first, the simplest type is the T-junction [3, 611 shown in Fig. 14.26~.The input port must be matched, and the output ports properly terminated. In the example shown, if the input impedance is, say, 50R, the output impedances are each 100n. A 90" vee, cut as shown, helps to match the junction. Transformation to 50R at the output ports may be achieved by means of step transformers or tapers. An alternative T-junction design, shown in Fig. 14.26b, has 50 line impedances at each port, and a quarter-wave matching transformer with an impedance of 35.36Q. Unequal power splits at the T-junction can be obtained by the use of lines with the required impedance ratio at the two output ports, and appropriate impedance matching at the junction itself, as shown in Fig. 14.26~. S-parameter analysis may be used to determine the effects of mismatched output ports on the power-splitting characteristics of the junction. Apart from the T-junction, the in-line power splitter is also widely used [3,61]. In this configuration, as Fig. 14.27~shows, the input line bifurcates into two lines with the required impedance ratio. To avoid coupling between the two, the output lines bend away from each other a short distance from the junction. It is necessary to choose the input line width such that: (a) its impedance is matched by the parallel combination of the output line impedances; and (b) the output line widths, together with a small gap between them, can be accommodated within the width of the input line. The triplate form of this type of splitter can be analysed by applying modematching techniques to an equivalent waveguide model of the junction, as shown in Fig. 14.276 [3, 611. For chosen reflection coefficients at the output ports, the analysis is able to evaluate the reflection coefficient at the input port, and the transmission coefficients to the two output ports. The S-parameters of the junction are then simple functions of these coefficients and the line impedances. When microstrip, as opposed to triplate, is used for any corporate feed, the dispersive nature of the transmission line should be taken into consideration. The microstrip phase constant is dependent on both frequency and line impedance. Thus, if any significant lengths of unequal impedance are used in parallel, line-length adjustment must be made to ensure equal phase conditions at the element ports. These conditions will strictly only be met at one frequency, although differential dispersion between lines of unequal impedance is normally very small.
851
output port
Fig. 14.26
2
Z:2Zo
z = 2z0
3 output port
T-junction power splitters a Basic T-junction b Quarter-wave matched T-junction c Unequal-split T-junction
coupled to the other output port. As a consequence, the aperture distribution will be distorted, and this could be a serious problem in a low-sidelobe design. Similar internal coupling and reflection effects occur if the device is used as a power combiner.
852
Microstrip antenna feeds
Microstrip antenna feeds
There is also a practical limit to the impedance ratio which may be obtained using the simple three-port power divider. This limit is not much more than 2: 1, and it is mainly dictated by the impedance of the narrowest line which it is possible to etch reliably and accurately.
view through a - a
853
The essential feature of this network is that, for the correctly chosen line impedances and with power entering port 1, the voltages at junctions a and b are equal. A resistor of an appropriate value placed between these junctions will therefore not absorb any power at the design frequency. If power enters port 2
t
view through b-
Fig. 14.27 In-line power splitter a Unequal power split b Triplate junction with equivalent waveguide model (Reproduced from [61] with permission of
IEE)
The following type of power divider is able to provide a larger ratio based on the same limitation on maximum impedance. It also has the important advantage that the output ports are more efficiently isolated. 14.4.2 Isolated power dividers/combiners Parad and Moynihan 1621 first described and analysed the two-way split-tee power divider, or isolated in-line power divider. They based their design on the N-way power divider of Wilkinson [63], after whom these devices are now named. Fig. 1 4 . 2 8 ~shows a basic unequal-split isolated power divider [62, 641.
Fig. 14.28 Isolated in-line power dividers a Uncompensated type b Compensated type
or port 3, some energy will be dissipated in the resistor. The isolation between output ports will be high, and the reflection coefficient looking into any port will be low. The device may be regarded as a T-hybrid, with the resistor acting as a reflectionless load on the internal series port [65]. It will operate well as a
854
Microstrip antenna feeds
power combiner, and if designed in this mode for combining equal in-phase powers it will, in fact, be lossless. Two forms of isolated power divider may be distinguished; the uncompensated type shown in Fig. 14.28a, and the compensated type shown in Fig. 14.286. The latter has an additional quarter-wave transformer at the input port. Over an octave bandwidth, it has better isolation and input VSWR, but worse output VSWR. The network impedances for an output voltage ratio of K are given in the Figure [62, 641. Improvements on the original design have been reported, including multisection-wideband, equal-power-split and unequal-power-split versions [64-671. The original Wilkinson N-way power divider is unsuited to planar networks because the resistors from the N output ports must meet at a common floating star point. Recently, an improvement has been developed using a planar feed network well suited to MIC applications [68]. It consists of a Dolph-Chebyshev single-input tapered transmission line segmented into N strips forming the output lines. The isolating resistors connect between the adjacent coupled transmission lines. Despite the good performance characteristics of the isolated power divider, it has the disadvantage that an additional component in the form of the resistor must be added to the printed feed network. Moreover, the value of the resistor is dependent on the power-divider ratio required. The maximum ratio available in practice is about 4: 1. A larger ratio can be obtained from the four-port power dividers to be described next, which are also able to provide good isolation. 14.4.3 Four-port direct-coupled power dividers Two types of four-port direct-coupled power dividers are useful for planar feed networks. These are the branch-line coupler and the hybrid-ring coupler, shown in Figs. 14.29 and 14.30, respectively. Being four-port devices, they can both be fully matched at the design frequency if their constituent line impedances are correctly chosen. For both, the input power PI entering port 1 is divided between the through port 2, P,, the coupled port 3, P,, and the decoupled port 4, P,. Since the directivity P,/P, is in practice finite over the operating frequency band, a resistive termination is needed on port 4; this is an undesirable feature of these couplers. The through port insertion loss is PJP,, and the coupling factor is P,/P,. The power-divider ratio is PJP,. The branch-line coupler [64,69,70] can provide coupling values up to about 9 dB. The phase difference between the output ports is 90°, independent of coupling and frequency, so correction for this must be made in any corporate feed. As Fig. 14.29 shows, if the normalised admittance of the shunt arm of the coupler is a, the power-divider ratio is given simply by a2, assuming negligible directivity. The maximum ratio available is thus about 7:l. Multi-section branch-line couplers can be designed for greater bandwidth, but owing to the narrow line widths required on the outer shunt arms, only twoand three-arm couplers are used in practice.
Microstrip antenna feeds
855
A six-element corporate feed using microstrip branch-line couplers has been reported for an array with a - 30dB Dolph-Chebyshev aperture distribution 1711. Difficulties in the photo-etching process limited the maximum coupling factor to 9 dB, but - 28 dB sidelobes were achieved with the design.
normalised admittances:
Zo = a . 5 = -
'
Za matched condition:
power ratios: coupling,
b2
b
Zb
- a2 = 1
2 (42 2 =
i n s e r t i i loss,
directivity,
($2
P4 0 -
at resonance
P power divider ratio,
5 , a2 p2
Fig. 14.29 Branch-line coupler
The disadvantage of the branch-line coupler is that its bandwidth is limited. It also takes up a relatively large surface area, leading to additional line losses. The hybrid-ring directional coupler shown in Fig. 14.30, also known as the rat race, consists of a ring of 1.5 wavelengths circumference, with the four ports disposed as shown. The design conditions given in the Figure [64,69] show that the power-divider ratio is the square of the admittance ratio alb. A maximum ratio of about 9 dB, or 8:1, is available with this configuration. A multi-layer, broadband stripline beam-forming network using hybrid rings has recently been reported [72]. It produces both even- and odd-mode beams from an 8 x 8-port Butler matrix (see Section 14.5.2.2). The hybrid rings are
856
Microstrip antenna feeds
Microstrip antenna feeds
of modified design, shown in Fig. 14.3la, to provide broader bandwidth [73]. A similar modification (Fig. 14.31b) is able to give a larger potential power-divider ratio, with a bandwidth of about 20% [74]. The equation governing the operation of the device is indicated in the Figure. An important consideration is that input at port 1 (the sum port) of the hybrid ring produces in-phase outputs at ports 2 and 3. Therefore no adjustments to line lengths in the feed network are necessary, in contrast to the branch-line coupler case. On the other hand, it is sometimes topographically inconvenient to have the loaded port opposite the input port instead of adjacent to it as in the branch-line coupler. Input at port 4 (the difference port) produces 180' phase difference between the output signals at ports 2 and 3. This characteristic is made use of in the monopulse phase comparators to be described in Section 14.5.2.1.
857
14.5 Other feed systems 14.5.1 Alternative transmission lines As indicated in Section 14.2.3, if the radiating patches are coupled via a probe or aperture, there is complete freedom in the choice of transmission line for the
-- 4
difference oor t
matched condition:
b 2 + a 2 :1
power ratios : coupling.
3 ,a2
insertion loss, directivity,
PI P2 = b 2 'pi-
3
I
o
o t resonance
p1
power divider ratio,
2=@
Fig. 14.30 Hybrid-ring coupler (Reproduced from [74] with permission of IEEE @ 1986 IEEE)
For even higher power-divider ratios, parallel-coupled lines would be necessary, but these are not commonly used in microstrip-antenna feed designs. Instead, aperture distributions with high edge-to-centre ratios have been achieved by judicious removal of some power dividers in the corporate feed chain, as illustrated in Fig. 14.10.
Fig. 14.31 Modified hybrid rings
a Broadband type (Reproduced from [73] with permission of IEEE @ 1982 IEEE) b High power-divider ratio type (Reproduced from [74] with permission of IEEE @ 1986 IEEE)
feed system. Hitherto, a microstrip or triplate medium has been assumed, but relatively high loss is associated with both of these, particularly in the millimetre waveband [6,75, 761. Lower loss is obtained from suspended stripline, and from
858
Microstrip antenna feeds
dielectric image guide, which has already been mentioned in the context of co-planar coupling [16]. Air-filled waveguide has exceptionally low losses, so this must not be discounted as a possible medium. However, radiating slots are readily cut in waveguide walls to form complete antennas [77]; so strong justification would be needed for using waveguide to feed microstrip patches instead. Such arrays have not yet been seriously investigated, but the low-loss advantages may become sufficiently
Fig. 14.32 Schematic layout of patch array with interlaced H feeds (Copyright @ Controller HMSO, London, 1986. Reproduced with permission)
attractive in the future. One important feature of waveguide is that its propagating wavelength is greater than that in free space, unless the loss-inducing complication of corrugated walls or dielectric filling is introduced. Consequently, only transposed arrays can be used to produce a broadside beam free from grating lobes. Low-loss feeds based on parallel-plate waveguide may also be considered for two-dimensional-array applications, although to date they also have been used
Microstrip antenna feeds
859
only to feed radiating slots [78]. Cavity feeds and radial waveguide feeds [79] come into this category. In view of the difficulty in obtaining circularly polarised radiation directly from slots in parallel-plate waveguide, one possibility is to use circularly polarised patches requiring a single feed point [20, 321 as radiating elements coupled to a parallel-plate feed system. 14.5.2 Multiple beam-forming networks 14.5.2.1 Special-purpose two- or four-beam networks: Microstrip antennas may be used for applications requiring the formation of two or more independent beams, either simultaneously or sequentially. For example, with the advent of higher-power satellites, printed antennas are becoming acceptable not only as receive-only DBS antennas, but also as transmitlreceive antennas. The two independent modes of operation may be separated by using two orthogonal polarisations with the same frequency, and/or by using two separate frequency bands. A recently developed antenna for this application utilised two interlaced, multi-layer corporate feeds [32]. Fig. 14.32 illustrates schematically how the feeds are coupled via probes to a two-dimensional array of square patches with two opposing bevelled corners. The patches are capable of radiating either hand of circular polarisation, depending on the position of the probes. The required broad axial-ratio bandwidth was achieved by the technique of sequential rotation [36-391. In another example, one type of airborne velocity-measuring radar uses four simultaneous independent beams, each directed into one of the four forward/ backward, leftlright quadrants. This requirement can be met by a two-dimensional microstrip array with the serieslseries feed network shown in Fig. 14.33 [3]. The coupling to the radiating elements in each linear array is such that the radiation conductance is symmetrical about the centre of the array. Each beam is uniquely generated by a signal applied to one of the corners of the array. A further example, applicable to a guidance-radar antenna, is a monopulse comparator, which utilises four hybrid couplers to give sum and difference beams in two orthogonal planes. The principle is illustrated in Fig. 14.34, as applied to a simple 2 x 2 patch array, which could be used as the primary feed in a reflector system [80]. However, a complete microstrip array may be designed, in which each of these single patches is replaced by a two-dimensional array occupying one quadrant of a circular aperture. Each array may be corporately fed, with the monopulse comparator on a separate feed layer [35]. Alternatively, the elements of the array may be fed by a co-planar serieslseries network, with the comparator at the centre of the aperture [76, 811 (Fig. 14.35). 14.5.2.2 Multiple fan beams: Several radar applications require the generation of multiple fan beams from a single linear antenna array. Thisis done by means of a multiple beam-forming network fed by a set of beam ports, with a set of antenna-array output ports. A signal entering any one of the beam ports
860
Microstrip antenna feeds
Microstrip antenna feeds
excites all the array ports to produce a beam in a particular direction. Three alternative feed techniques are commonly used for this purpose, as shown in Fig. 14.36. These are: (a) The parallel-plate lens type originated by Gent, but known in its two more recent forms'as Ruze or Rotman lenses [82, 831. (b) The series-coupled feed type known as the Maxson-Blass matrix [82, 841. (c) The parallel-feed type known as the Butler matrix [82, 851
I
PORT l
861
[82, 841. For an equally spaced, constant-amplitude array, this condition is satisfied when the peak of each beam coincides with the first null of its neighbour. The condition is only met at one frequency, but reasonable bandwidths patch, or subarray /
2
difference port
3
--
-
.,
--
..
7
2
.
-
beam l direction
Fig. 14.33 Four-beam-array feed network: schematic
All are available in printed transmission-line format, and may therefore be used in conjunction with microstrip patch arrays. The parallel-plate Rotman lenses (shown schematically in Fig. 14.36~)are so designed that the beam positions do not change with frequency. However, optimum beam efficiency is only obtained if the beams are spatially orthogonal
Fig. 14.34 Monopulse comparator using branch-line couplers
can be obtained with the lens system. Recently, a Rotman lens system has been used in an experimental flat-plate DBS antenna, to allow selection of the beam most suitable for acquiring the satellite signal when the antenna is fixed to a convenient wall of a house [86]. The Maxson-Blass matrix, shown schematically in Fig. 14.366,is particularly useful when a small number M of narrow beams is required from a relatively large number of array ports N. There is no particular restriction on the values of M or N. A total of M x N directional couplers is necessary in the network, and line lengths between the couplers in the series feeds to the array ports must be designed to ensure spatial orthogonality of the beams at the design frequency. At other frequencies, the beam directions will change, and the orthogonality condition will not be maintained. Because the beam feed lines cross over the array feed lines, the directional couplers must take the form of broadsidecoupled lines on either side of a substrate suspended between parallel ground planes [87, 881. The Butler matrix, shown schematically in Fig. 14.36c, is best suited to a network with N beams and N array ports, where N is an integer power of 2, i.e. N = 2". A total of N x n couplers or hybrids is required in the network, and these can be 90" or 180" hybrids, depending on whether the beams are to be symmetrically distributed about the broadside direction, or whether one of the beams is to be in the broadside direction. In addition, a considerable number of
862
Microstrip antenna feeds
Microstrip antenna feeds
phase shifters must be incorporated in the network. Furthermore. many crossovers are required. and this involves the use of a multi-layer structure. and possibly a combination of different transmission-line types. The overall design for a large number of ports is thus very complicated [85].
transmission
863
-
parallelplate region
beam ports
,antenna elements (a) antenna elements
loads
. directional couplers antenna elements
Fig. 14.35
Two-dimensional microstrip antenna with integrated monopulse comparator (Photograph by courtesy of Ball Communication Systems Division, Broomfield, Colorado, USA)
3dB hybrids phase shifters non - intersecti* crossovers
14.5.2.3 Active phased-array feeds: Many applications are emerging in the areas of radar and satellite communications, for antennas with electronic-beam steering and adaptive beam-forming capabilities. Microstrip-array antennas are well suited to these applications, and it is relevant to consider the feed systems required in such cases. Fig. 14.37 shows the feed network for an S H F receive-only phased array built entirely in microstrip, which has been developed for aircraft-to-satellite communication [89]. The corporate feed network is on a separate layer from the radiating elements, which consist of a n 8 x 8 array of circular patches. The 64 arms of the feed each contain a 3-bit digital phase shifter and a branch-line
(c) Fig. 14.36
Multiple beam-forming networks a Parallel-plate Rotman lens array: schematic (Reproduced from Smith [83]with permission of IERE) b Maxson-Blass matrix: schematic (Reproduced from Shaw [84] with permission of IERE) c Butler matrix: schematic
864
Microstrip antenna feeds
Microstrip antenna feeds
865
hybrid. The latter provides the necessary phase quadrature at two orthogonal feed points to each patch, to satisfy the requirement for left-hand circular polarisation. Each phase shifter contains ten PIN diodes providing a combination of 180' and 90" switched-line and 45" loaded-line phase shifters, including the necessary RF chokes and DC bias tracks. The beam is steered in the required direction by means of a microprocessor-based controller.
and 4-bit PIN diode phase shifters. The T / R capability is thus available for both vertically- and horizontally-polarised signals. The circuit is completed by two 12-way corporate feeds, one for each polarisation. Looking to the future, much effort is currently being devoted to GaAs MMIC realisations of T/R modules incorporating F E T amplifiers, switched-filter and switched-delay-line phase shifters, and both F E T and PIN diode T / R switches [9 1-94]. These are ultimately intended for high-power broad-bandwidth phased-
Fig. 14.37 Microstrip corporate feed for SHF receive-only phased array (Photograph by
Fig. 14.38 Coplanar microstrip antenna and feed for C-band transmitlreceivephased array (Photograph by courtesy of Ball Communication Systems Division, Broomfield. Colorado, USA)
courtesy of Ball Communication Systems Division. Broomfield, Colorado, USA)
A prototype C-band phased array transmit/receive microstrip antenna intended for earth imaging from space has recently been reported [90]. It consists of 12 linear arrays of 18 square patch elements. Each array has two independent co-planar centre-fed series feeds for orthogonal linear polarisation, as shown in Fig. 14.38. Behind the feed layer, in a mixture of microstrip and packaged components, are two sets of 12 T / R modules utilising two-stage high-power and low-noise FET amplifiers with associated PIN switch and PIN limiter diodes,
array radars with full electronic-scanning capabilities. Again, microstrip patches are potentially good candidates for the radiating elements. provided that their limited gain-bandwidth can be accepted. Several potential problems in implementing monolithic phased-array antennas have been identified, and some possible solutions proposed [95]. There is little doubt that many advanced phased-array systems will incorporate microstrip-array antennas, and that ingenious feed networks will continue to be important features in them all.
866
Microstrip antenna feeds
14.6 Acknowledgments
The author is grateful to THORN EM1 Electronics Ltd. for permission to publish this work, and to his colleagues, particularly Mr. J. Thraves and Mr. G. R. Selby, for their help and advice on the manuscript.
14.7 References HALL, P. S., and JAMES, J. R.: 'Survey of design techniques for flat profile microwave antennas and arrays.' Radio & Electron. Engr., Nov. 1978, pp. 549-565 BAHL, I. J., and BHARTIA, P.: 'Microstrip antennas (Artech House, 1980) JAMES, J. R., HALL, P. S., and WOOD, C.: 'Microstrip antenna theory and design (Peter Peregrinus, 1981) MAILLOUX, R. J., MCILVENNA, J. F., and KERNWEIS, N. P.: 'Microstrip array technology' IEEE Trans., Jan. 1981, AP, pp. 25-37 JAMES, J. R., HALL, P. S., WOOD, C., and HENDERSON, A.: 'Some recent developments in microstrlp antenna design.' ibid. pp. 124-128 HENDERSON, A., and JAMES, J. R.: 'A survey of millimetre-wavelength planar antenna arrays for military applications.' Radio & Electron. Engr., Nov/Dec. 1982, pp. 543-550 JOHNSON, R. C., and JASIK, H. (Eds.): 'Antenna engineering handbook.' (McGraw-Hill, 1984) 2nd edn. chap. 7 LEWIN, L.: 'Radiation from discontinuities in stripline, Proc. IEE, Feb. 1960, pp. 163-170 LEWIN, L.: 'Spurious radiation from microstrip' Proc. IEE, July 1978, pp. 633-642 HENDERSON, A., and JAMES, J. R.: 'Design of microstrip antenna feeds. Pt. I: Estimation of radiation loss and design implications' IEE Proc. H, Feb. 1981, pp. 19-25 OBERHART, M. L., LO, Y. T., and LEE, R. Q. H.: 'New simple feed network for an array module of four microstrip elements' Electron. Letts., 23 Apr. 1987, pp. 436-437 BENALLA, A., and GUPTA, K. C.: 'Transmission-line model for two-port rectangular microstrip patches with ports at the nonradiating edges' Eleclron. Letts., 13 Aug. 1987, pp. 882-884 CASHEN, E. R.: British Patent Specification No. 1572273, 1977 OWENS, R. P., and THRAVES, J.: 'Microstrip antenna with dual polarisation capability' Proceedings, Military Microwaves Conf. Oct. 1984, pp. 250-254 CARTER, M. C., and CASHEN, E. R.: 'Linear arrays for centimetric and millimetric wavelengths' Proceedings, Military Microwaves Conf. Oct. 1980, pp. 315-320 JAMES, J. R., JOHN, G., and HALL, C. M.: 'Millimetre-wave hybrid dielectric-microstrip antenna array' IEE Proc. H, Dec. 1984, pp. 341-350 JAMES, J. R., and HALL, P. S.: 'Microstrip antennas and arrays. Pt. 2 New array design technique' IEE J. M O A , Sept. 1977, pp. 175-181 METZLER, T.: 'Microstrip series arrays' IEEE Trans. Jan. 1981, AP, pp. 174-178 CARVER, K. R., and MINK, J. W.: 'Microstrip antenna technology' ibid. pp. 2-24 RICHARDS, W. F., LO, Y. T., and HARRISON, D. D.: 'An improved theory for microstrip antennas and applications' ibid, pp. 38-46 CHEW, W. C., and KONG, J. A.: 'Analysis of a circular microstrip disk antenna with a thick dielectric substrate' ibid. pp. 68-76 YANO, S., and ISHIMARU, A,: 'A theoretical study of the input impedance of a circular microstrip disk antenna, ibid. pp. 77-83 DAS, A., and DAS, S. K.: 'Input impedance of a probe excited circular microstrip ring antenna' IEE Proc. H., Oct. 1985, pp. 384-390 DAVIDOVITZ. M., and LO, Y. T.: 'Input impedance of a probe-fed circular microstrip antenna with thick substrate' IEEE Trans. July 1986, AP, pp. 905-91 1
Microstrip antenna feeds
867
25 GRIFFIN, J. M., and FORREST, J. R.: 'Broadband circular disc microstrip antenna' Electron. Letts., 18 Mar. 1982, pp. 266-269 26 FONG, K. S., PUES, H. F., and WITHERS, M. J.: 'Wideband multilayer coaxial-fed microstrip antenna element' ibid. 23 May 1985, pp. 497499 27 HALL, P. S.: 'Probe compensation in thick microstrip patches' ibid. 21 May 1987, pp. 606-607 28 POZAR, D. M.: 'Microstrip antenna aperture coupled to a microstrip line' ibid. 17 Jan. 1985, pp. 49-50 29 SULLIVAN, P. L., and SCHAUBERT, D. H.: 'Analysis of an aperture coupled microstrip antenna' IEEE Trans. Aug. 1986, AP, pp. 977-984 30 GRONAU, G., and WOLFF, I.: 'Aperture coupling of a rectangular microstrip resonator' Electron. Lett., 8 May 1986, pp. 554-556 31 ADRIAN, A,, and SCHAUBERT, D. H.: 'Dual aperturecoupled microstrip antenna for dual or circular polarisation' Electron Lett. 5 Nov. 1987, pp. 1226-1228 32 OWENS, R. P., and SMITH, A. C.: 'Dual band, dual polarisation microstrip~antennafor X-band satellite communications' Proceedings, Military Microwaves Conf. June 1986, pp. 323-328 33 BUCK, A. C., and POZAR, D. M.: 'Aperture-coupled microstrip antenna with a perpendicular feed' Electron. Lett. 30 Jan. 1986, pp. 125-126 34 POZAR, D. M., and JACKSON, R. W.: 'An aperture coupled microstrip antenna with a proximity feed on a perpendicular substrate' IEEE Trans., June 1987, AP, pp. 728-731 35 OLTMAN, H. G., and HUEBNER, D. A.: 'Electromagnetically coupled microstrip dipoles' IEEE Trans., Jan. 1981, AP, pp. 151-157 36 HANEISHI, M., YOSHIDA, S., and GOTO, N.: 'A broadband microstrip array composed of single-feed type circularly polarised microstrip antennas' IEEE AP-S Digest, 1982, pp. 160-163 37 HANEISHI, M., and TAKAZAWA, H.: 'Broadband circularly polarised planar array composed of a pair of dielectric resonator antennas' Electron. Lett. 9 May 1985, pp. 437-438 38 TESHIROGI, T., TANAKA, M., and CHUJO, W.: 'Wideband circularly polarised array antenna with sequential rotations and phase shift of elements' Proc. ISAP 85, Aug. 1985, pp. 117-120 39 HALL, P. S., and HALL, C.M.: 'Coplanar corporate feed effects in microstrip patch array design' IEE Proc. H., June 1988, pp. 180-186 40 HANSEN, R. C. (Ed.): 'Microwave scanning antennas: Vol. 2' (Academic Press, 1966),chap. 1 41 RUDGE, A. W., MILNE, K., OLVER, A. D., and KNIGHT, P. (Eds.): 'The handbook of antenna design: Vol. 2' (Peter Peregrinus, 1983) chap. 9 42 STUTZMAN, W. A,, and THIELE, G. A,: 'Antenna theory and design' (John Wiley, 1981) chap. 3 43 ROGERS, A,: 'Wideband squintless linear arrays' Marconi Rev. 4th quarter 1972, pp. 221-243 44 SKIDMORE, D. J., and MORRIS, G.: 'The design and performance of covered microstrip serpent antennas' IEE Conf. Publ. 219. Proceedings ICAP 83, Pt. I pp. 456458 45 COLLIN, R. E.: 'Foundations for microwave engineering' (McGraw-Hill, 1966) 46 WILLIAMS, J. C.: 'A 36 GHz printed planar array' Electron. Lett. 2 Mar. 1978, pp. 136-137 47 DANIEL, J-P., MUTZIG, J-P., NEDELEC, M., and PENARD, E.: 'RCseaux d'antennes imprimkes dans la bande des 20 GHz/30 GHz' L'Onde Elecrrique, Jan./Feb. 1985, pp. 35-41 48 DANIEL, J-P., PENARD, E., NEDELEC, M., and MUTZIG, J-P.: 'Design of low cost printed antenna arrays' Proc. ISAP 85, Aug. 1985, pp. 121-124 49 COSSLETT, M. F., FROST, R., and ROSSITER, K. 0.: British Patent Specification No. 1269633, 1968 50 SHAFAI, L., and SEBAK, A. A.: 'Radiation chracteristics and polarisation of undulated microstrip line antennas' IEE Proc. H, Dec. 1985, pp. 433439 51 HALL, P. S.: 'Microstrip linear array with polarisation control' IEE Proc. H., Apr. 1983, pp.215-224
868
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52 NISHIMURA, S., SUGIO, Y., and MAKIMOTO, T.: 'Crank-type circularly polarised microstrip line antenna' IEEE AP-S, Digest, 1983, pp. 162-165 53 NISHIMURA, S., SUGIO, Y., and MAKIMOTO, T.: 'Side-looking circularly polarised microstrip line planar antenna' Proc. ISAP, 1985, pp. 129-132 54 TIURI, M., HENRIKSSON, J., and TALLQVIST, S.: Printed circuit radio link antenna' Proc. 6th EMC, 1976, pp. 280-282 55 TIURI, M., TALLQVIST, S., and URPO, S.: 'The chain antenna' IEEE AP-S Digest, 1974, pp. 274-277 56 NISHIMURA, S., NAKANO, K., and MAKIMOTO, T.: 'Franklin-type microstrip line antenna' IEEE AP-S Digest, 1979, pp. 134-137 57 HENRIKSSON, J., MARKUS, K., and TIURI, M.: 'A circularly polarised travelling-wave chain antenna' Proc. 9th EMC, 1979, pp. 174-178 58 SCHIFFMANN, B. M.: 'A new class of broadband microwave 90 degree phase shifted IRE Trans., Apr. 1958, M'IT, pp. 232-237 59 CONTI, R., TOTH, J., DOWLING, T., and WEISS, J.: 'The wire grid microstrip antenna' IEEE Trans. Jan. 1981, AP, pp. 157-166 60 HILL, R.: 'Printed planar resonant arrays' IEE Conf. Publ. 274. Proceedings ICAP 87, Pt. 1, pp. 473-476 61 HALL, P. S., and JAMES, J. R.: 'Design of microstrip antenna feeds. Pt. 2: Design and performance limitations of triplate corporate feeds' IEE Proc. H, Feb. 1981, pp. 26-34 62 PARAD, L. I., and MOYNIHAN, R. L.: 'Split-tee power divider' lEEE Trans., Jan. 1965, MTT, pp. 91-95 63 WILKINSON, E. J.: 'An N-way hybrid power divider' IRE Tram., Jan. 1960, MTT, pp. 11C118 64 HARLAN HOWE: 'Stripline circuit design (Artech House, 1974) chap. 3 65 COHN, S. B.: 'A class of broadband three-port TEM mode hybrids' IEE Trans, Feb. 1968, MTT, pp. 110-116 66 LI, C. Q., LI, S. H., and BOSISIO, R. G.: 'CADICAE design of an improved, wideband Wilkinson power divider' Microwave J., Nov. 1984, pp. 125-135 67 WAHI, P. K.: 'Wideband, unequal split ratio Wilkinson power divider' Microwave J. Sept, 1985, pp. 205-209 68 YAU, W., and SCHELLENBERG, J. M.: 'An N-way broadband planar power combiner/ divider' Microwave J. Nov. 1986, pp. 147-151 69 REED, J., and WHEELER, G. J.: 'A method of analysis of symmetrical four-port networks' IRE Trans, Oct. 1956, MTT, pp. 246-252 70 MATTHAEI, G. L., YOUNG, L., and JONES, E. M. T.: 'Microwave filters, impedance matching networks, and coupling structures' (McGraw-Hill, 1964) Section 13.09 71 GUPTA, C. D., and DELOGNE, P.: 'Build an integrated Dolph-Chebyshev array' Microwaves, Nov. 1976, pp. 54-58 72 ABOUZAHRA, M. D.: 'Design and performance of a wideband multilayer feed network' IEEE MTT-S Digest, 1986, pp. 143-146 73 KIM, D. I., and YOSHIYUKI, N.: 'Broad-band design of improved hybrid ring 3 dB directional couplers' IEEE Trans., Nov. 1982, MTT, pp. 2040-2046 74 AGRAWAL, A. K., and MIKUCKI, G. F.: 'An improved hybrid-ring directional coupler for higher power split ratios' Microwave J., Nov. 1986, pp. 87-98 (see also, IEEE Trans., Dec. 1986, MlT, pp. 140-1407) 75 POZAR, D. M.: 'Considerations for millimetre wave printed antennas' IEEE Trans., Sept. 1983, AP, pp. 740-747 76 LALEZARI, F., and MASSEY, C. D.: 'MM-wave microstrip antennas' Microwave J. Apr. 1987.. OD. .= 87-96 77 JOHNSON, R. C., and JASIK, H.: 'Antenna engineering handbook' (McGraw-Hill, 1984) 2nd edn. chap. 9 78 RAHMAN, F., SHAFAI, L., BRIDGES, E., and ITITPIBOON, A.: 'A simple coaxial fed planar microstrip slot array' IEEE AP-S Digest, 1981, pp. 207-208
869
79 ANDO, M., SAKURAI, K., GOTO, N., ARIMURA, K., and ITO, Y.: 'A radial line slot antenna for 12 GHz satellite TV reception' IEEE Trans., Dec. 1985, AP, pp. 1347-1352 80 JACKSON, C. M., and NEWMAN, J.: 'Low cost Ka band microstrip patch monopulse antenna' Microwave J. July 1987, pp. 125-131 81 ANDREWS, B. J., MOORE, T. S., and NIAZI, A. Y.: 'Millimetre-wave microstrip antennas for dual polar and monopulse applications' IEE Conf. Publ. 219, Proc. ICAP 83, Pt. 1, pp. 529-533 82 HANSEN, R. C. (Ed.): 'Microwave scanning antennas. Vol. 3' (Academic Press, 1966) chap. 3 83 - SMITH. M. S.: 'Design - considerations for Ruze and Rotman lenses' Radio & Electron. Eng., Apr. 1982, pp. 181-187 84 SHAW. E.: 'The Maxson multi-beam antenna: Theory and design for non-interacting beams' Radio & Electron. Eng., Feb. 1969, pp. 117-129 85 MACNAMARA, T.: 'Simplified design procedures for Butler matrices incorporating 90 degree hybrids or 180 degree hybrids' IEE Proc. H, Feb. 1987, pp. 50-54 86 MADDOCKS, M. C. D.: 'Low-cost approach for steerable flat-plate antenna design with application to reception of broadcasting from satellite' Electron. Lett., 4 Feb. 1988, pp. 173-174 87 SHELTON, J. P.: 'Impedances of offset parallel-coupled strip transmission lines', IEEE Trans., Jan. 1966, MTT, pp. 7-15 88 MOSKO. J. A,: 'Cougling- curves for offset parallel-coupled strip transmission lines' Microwave J. Apr. 1967, pp. 35-37 89 CIPPOLA, F. W.: 'A 7.5 GHz microstrip phased array for aircraft-to-satellite communication' Microwave J., Aug. 1981, pp. 75-78 90 HADDAD, H., FITHIAN, M., and COOMBS, D.: 'Heading for space: C-band phased array' Microwaves & RF, Apr. 1986, pp. 103-108 91 ARNOLD, J., and SMITH, D. C.: 'Commercial availability of GaAs MMICs challenges system designers' MSN & CT, Sept. 1986, pp. 119-131 92 TENEDORIO, J. G.: 'MMICs reshape EW system design' MSN & C T , Nov. 1986, pp. 95-104 93 NASTER, R. J.: 'Affordable MMIC designs for phased arrays' Microwave J.,Mar. 1987, pp. 141-150 94 CHILTON, R. H.: 'MMIC T/R modules and applications' Microwave J., Sept. 1987, pp. 131-146 95 POZAR, D. M., and SCHAUBERT, D. H.: 'Comparison of architectures for monolithic phased array antennas' Microwave J., Mar. 1986, pp. 93-104 -
A
Chapter 15
Advances in substrate technology G.R. Traut
Substrate materials play an essential role in microstrip antenna design, production and finished-product performance. Several aspects of materials must be considered in the design stage when substrates are selected. What may seem ideal from a design viewpoint must be balanced against production and final product requirements. Ability to measure and control critical properties, especially relative permittivity and dissipation factor, cannot be ignored. The possible adverse effects of necessary processing steps or environment in the final application must be taken into account. Successful antenna production will depend on the use of appropriate processing techniques. New substrate types and special substrate features are becoming increasingly available and often ca'n offer significant advantages for designers and producers. This Chapter deals with these issues in five sections: (i) (ii) (iii) (iv) (v)
What to consider when selecting materials Methods for measuring relative permittivity and dissipation factor Processing techniques for antenna fabrication Design considerations related to materials characteristics Opportunities available in special features and new materials
15.1 Considerations for substrate selection This discussion will be limited to five Subsections concerned with properties most important to performance, a list of available choices, discussion of cladding, details about thermal behaviour of PTFE, the polymer base for most microstrip antennas, and some information on anisotropy related to composite structure. 15.1.1 Impact of properties of various substrate systems on microstrip antenna performance Selection of the most suitable substrate for a microstrip antenna needs to be
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Advances in substrate technology
made early in the development of a system. Substrate characteristics must be compatible with design objectives, the processing needed to produce the design and the environmental conditions to which the system will be exposed during its lifetime. Generally this selection process is a compromise to get the best balance of desirable features for a given application. While many properties could be discussed, we can focus on a critical three: complex permittivity, water absorption and adhesion of the metal-foil cladding. 15.1.1.1 Complex permittivity Complex permittivity has two components, which we will call relative permittivity (dielectric constant) and dissipation factor (loss tangent). Both are critical for microstrip antenna performance. Neither can be regarded as a fixed characteristic. Rather, they are functions of several factors in substrate composition, processing and application of an antenna. In most applications low relative permittivity is desirable to the designer for radiation efficiency. Foam materials can have very low relative permittivity, but this must be balanced against processability and resistance to operating stresses. If the radiating elements are to be fed by microstrip transmission lines on the same plane, then increasing its value is usually desirable to get good performance. Close tolerance of relative permittivity, K', from panel to panel, and within a panel, is important for the final antenna system to perform as designed. With production runs of many units, it is possible to accommodate known variations from one panel to another with adjustments in artwork, but then accurate values of K' for each panel are needed. Dissipation factor is a measure of the amount of electrical energy converted to heat in the dielectric, and partially accounts for power losses in a passive device such as a transmission line or microstrip antenna. The dielectric behaves as a distributed capacitor. An idealised lossless capacitor shows reactively a charging rate or current cycle that exactly leads the electric field or voltage cycle by 90". The amount this phase relationship differs from 90' relates to the amount of capacitively stored energy dissipated as heat during charging and discharging. Dissipation factor is also called the loss tangent; i.e., the tangent of the deviation in phase from the 90" ideal. Consideration of the properties of relative permittivity and dissipation factor at an atomic or molecular level may help one to relate these to frequency and temperature. The incidence of an alternating electric field on a dielectric material causes a dipole response that has the effect of increasing the amount of outside charge needed to attain a given potential gradient. This dipole response is usually a combination of two effects: electron shifts creating induced dipoles and movement of groups of one or more atoms comprising pre-existing dipoles. The magnitude of the dipole response is directly related to relative permittivity. The fraction of energy converted to random thermal motion in the material (heat)
I
I I
873
as a fraction of that stored by the dipole and space-related response is the dissipation factor. The electron shift response is common to all dielectric substances. Electrons in a dielectric are bound in orbits with particular atoms or particular molecularbond systems. They shift elastically in response to an external electric field to an extent dependent on molecular structure. Elastic response means the stored potential energy is returned with little or no loss. The other response, movement of atoms, arises from differing electro-negativity among atom types. Such dipoles exist without an external field, but they respond to a field by tending to align with it. Pendent polar groups on polymer chains will rotate, twist or stretch toward alignment. Ionically bonded inorganic structures are usually more rigid with more limited movement of groups, compared with covalently bonded organic polymers. As can be imagined, in molecular structures where such movement is permitted, some of the energy associated with the movement is dissipated in collisions with other groups in the system. The mechanical analogy of this is the visco-elastic response characteristic of most polymers. Bonds in polymeric molecules that give rise to little or no dipole moment include the common carbon-carbon bond and the carbon-hydrogen bond. Bonds that tend toward dipole formation include carbon to oxygen, nitrogen or halogen atoms, including fluorine, chlorine and bromine. Polyethylene, a polymer with molecules consisting of a chain of carbon atoms with two hydrogen atoms bonded to each carbon atom along the chain, has a low dissipation factor and relative permittivity as expected from the low dipole moment of groups within the molecule. Similar chains with chlorine (-CI) or hydroxy (-OH) substitutions on every other carbon atom have higher dissipation factors and relative permittivity, as expected. Electrical properties of polymers relate not only to the presence of polarised structures but also to the degree they can respond to the external electrical field. A polymer in a highly crystalline state, with polar groups closely packed in a rigid structure, will respond less than one in an amorphous state with more mobility of groups. Polytetrafluoroethylene (PTFE), widely used in microwave devices, is of special interest. Highly polar fluorine atoms occupy the available bond positions along the carbon chain. Both dissipation factor and relative permittivity are as low as for polyethylene. This seeming contradiction is explained by the large size of the fluorine groups. The polymer chain is actually stiffened and immobilised by the crowded sheath of fluorine groups forming a helical pattern along the chain. The high dipole moments of the many individual carbon-fluorine bonds have a near-zero vector sum. The following tabulation indicates qualitatively the influence of various factors on relative permittivity and dissipation factor:
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Factor Lamination Mechanical history
Thermal history
Orientation
-
Composition
Board fabrication Contamination Operating temperature Expansion
Group mobility CrystalIinity Frequencv ~hkrmai interrelation
Harmonic of a molecular group vibration
Advances in substrate technology -
Relative permittivity
Dissipation factor
Density change from microvoids causes non-uniformity, lower values
Mechanical degradation can increase value
Crystallinity raises density for higher values. Degradation changes value
Too much heat forms lossy groups by degradation; too little with thermosets leaves unreacted lossy polar groups Small effect
Aligned fibres give anisotropy More fibre or filler raises the value
Fibres or filler usually raise the value
Added dipoles raise value slightly
Solvents or moisture increase the value
Reduced dipole density reduces value
Little effect
Transitions increase dipole response
Increased value, especially in transition region May lower the value
Raises density and thus value Increased frequency raises temperature for transitions
Peak loss temperatures shift upward with frequency
Increase value
Peak loss value
875
In the case of PTFE-based laminates the surfactant for stabilising aqueous colloidal PTFE dispersion must be fully removed from saturated glass fabric before clad panels are laminated to avoid lossiness. Absorbed solvents, moisture or reagents from circuit-board processes can degrade performance. Substrates based on saturated glass-fibre fabrics can exhibit wicking of moisture along the glass-resin interface. Manufacturers apply coupling agents to reduce this effect. The frequency at which a molecular group will respond resonantly to an electric field is a function of its mass, dipole moment, proximity to other groups and the stiffness of its chemical bonds. For smaller groups in polymer systems the fundamental resonance and several harmonics fall in the infra-red and far-infra-red spectrum. Harmonics of these and of larger groups become apparent in the microwave region. In systems where dissipation factor peaks at a given temperature for a given frequency owing to a phase transition, the temperature is shifted upward for higher frequencies. A plot of the logarithm of the peak loss frequency versus the inverse absolute temperature will tend to be linear with a negative slope, proportional to the activation energy of the transition causing the peak. Interestingly, results with mechanical oscillation, such as the torsional pendulum, correlate well with electrical measurements. Mobility of polar groups and internal friction influence dissipation factor. Mobility increases with temperature. At the glass transition temperature T,, the range of transition between glassy and rubbery states of a polymer amorphous phase, the internal friction and mobility are both high, and, if polarised groups are present, dissipation factor shows a peak against temperature. 15.1.1.2 Moisture absorption: As indicated previously, absorbed moisture is of concern because of the adverse effects it has on electrical properties. Environmental conditions where cycling of humidity and temperature is encountered can lead to degradation of resistance to moisture absorption. Moisture penetration can also lead to corrosion of conductor traces and degradation of the bond between conductor and substrate. Absorption can arise through the presence of pores or microvoids in the substrate. Many polymers with polar groups have an affinity for moisture involving chemical bonding. Molecular features such as ester linkages, amide linkages, amine linkages, chloride groups or bromide groups are subject to hydrolysis; absorbed moisture reacts chemically with the polymer to change its characteristics.
15.1.1.3 Foiladhesion: Foil adhesion is usually tested by measuring the force needed to peel an etched strip of clad foil perpendicularly from the substrate. The amount of force required is related to the thickness and stiffness of the foil and to the modulus of the underlying material. For thicker or stiffer foil the radius at the region of peeling will be larger, distributing peeling force over a
Table 15.1 Materials available as clad composites
Material description (see abbr. list below
Test freq., Hz
Non-woven glass-PTFE
1M 10 G 1M 10 G 10 G 10G 10 G 10G 10 G 1M 1G 10G 10G 10G 10G 10G 1M 1M 1M
Woven-glass-PTFE Woven-glass-high-PTFE PTFE Ceramic-PTFE max 6.5 Ceramic-PTFE max 11.0 XPS Glass-XPS PES PSO Glass (10%)-PSO Mineral (10%)-PSO PEI Glass-PEI Woven-glass-epoxy Woven-glass-PI Woven-glass-T Woven-glass-BTE WePTFE-epoxy WePTFE-PI
IM 10G 1M
BTE = bismaleimide-triazine-epoxy PC = polycyanate resin = polyetherimide resin PEI = polyethersulfone resin PES PI = polyimide resin PSO = polysulfone resin PTFE = poly(tetrafluoroethylene) resin T = triazine resin WePTFE = woven expanded PTFE XPS = cross-linked polystyrene resin
Typical K'
2.15-2.35 2.15-2.35 2.5 2.4-2.6 2.15-2.35 2.1 6.0 9.8-1 1.0 2.5 2.6 3.4 3.0 3.3 3.2 3.0 3.4 4.7 4.5 4.3 4.2 2.8 2.8
Tol. of k'% c1
<1 2-5 1-2 <1 <1 2-5 2-5 <1 1-2 -
>5 >5 >5 >5
2-5 2-5
tan d
0.001 0,001 0.002 0.002 0.001 0.0005 0.002 0.002 0.002 0.002 0.008 0.006 0.006 0.006 0.004 0.006 0.025 0,010 0.015 0.015 0.012 0.010
Peel strength N/mm 2.10 2.10 1.40 1.40 1.40 -
Water abs. mg 1 1 1 1 1 0.2
-
-
0.87 0.87 0.87 0.87 1.05 1.05 0.70 0.70 0.87 0.87 1.05 0.70
24 15 22 13 13 13 10 25 15 15 10 25
1.05 1.40
-
%
Temp.
cn
Ti
Tm
"C
"C
-
3 327 $, 327 3
-
327 327 327 327 327 327
115 115
-
-
238 185 185 185 215 215
130 260 200 180 125 260
-
-
-
$
In
Eb
3 0 0
5 o
0'
2
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Advances in substrate technology
greater bond area. Lower modulus of the underlying substrate also has the effect of distributing force over a larger area. Thus peel-test results can vary for reasons other than quality of bond. Some reagents for processing circuit patterns are capable of attacking inadequately bonded foil at the bond line to penetrate the interface, and cause costly damage by adhesion failure of the circuit pattern during board processing. The bond of foil to the substrate must be able to withstand soldering and other lead-attachment processes to minimise the cost of damage during assembly operations. 15.1.2 Comparative list of available substrates A wide range of composites with various polymer systems can be considered for microstrip antenna substrates. Table 15.1 lists materials available as clad laminates. This list was compiled from supplier's information by the raw Materials Subcommittee of the committee on ~ i ~ h - s ~ e e d / ~ i ~ h - ~Materials r e ~ u e of nc~ IPC.* An explanation of the column headings in Table 15.1 follows. Documentation of test methods may be found in IPC TM-650. The test frequency, either 1MHz or lOGHz, is the producer's measurement frequency for relative permittivity and dissipation factor. The typical K' value, or range of values, indicates the nominal relative-permittivity value(s) available. The Tolerance of K' is the lowest commercially available range for percentage tolerance of nominal relative permittivity available. The tand column shows typical dissipation-factor values. The peel-strength values shown are the lowest values in Newtons per mm width (converted from pounds force per inch width) specified for 34pm thick (I oz/ft2) wrought copper-foil cladding for four conditions of test, including as-received, after thermal-stress testing, a t elevated temperature and after exposure to processing solutions. Water absorption is a typical value for mass gain inmilligrammes for a 51 mm (2in) square specimen, etched free of foil, that was conditioned for 1h at 105 2OC, weighed, immersed for 24 h in distilled water at 23 1°C and then reweighed. The temperature data shown in degrees Celsius is characteristic of the polymer portion of the substrate material. Thermoset polymer systems, including epoxy, bismaleimide-triazine-epoxy, polycyanate resin, polyimide resin, triazine resin and cross-linked polystyrene resin, are amorphous, thus having no crystalline melt point. They do show a change in the amorphous phase from a glassy state of low molecular thermal mobility to a rubbery state of high mobility and lower modulus. This change is referred to as the glass transition T,. It is accompanied by an increase in the thermal-expansion coefficient. With polymers having polar groups, relative
+
* Institute for
Interconnecting and Packaging Electronic Circuits, 7380 North Lincoln Avenue, Lincolnwood, Illinois 60646, USA
Advances in substrate technology
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permittivity increases and dissipation factor shows a peak at T,. Applications for thermosets should avoid going above T,. Crystalline thermoplastic materials include polyetherimide resin, poly(tetrafluoroethylene) resin (PTFE), polyethersulfone resin and polysulfone resin. Crystalline melting is accompanied by an expansion. Above the crystalline melt point T,, when the crystalline phase is in an amorphous melt state, there is a loss of mechanical properties. For polymers with polar groups, the dissipation factor is high. The useful temperature limit is usually well below T,. 15.1.3 Selection of metal cladding for performance Copper foils used for clad laminates fall into two broad types: rolled and electrodeposited. They differ widely in the processes used for producing them and also show differences in how they perform in circuit-board applications. Often the user must choose between high bond strength and low insertion loss for a circuit in specifying the foil type.
15.1.3.1 Rolledfoil: One foil type is referred to as rolled foil, or wrought foil. An ingot of copper is subjected to a series of passes through a rolling mill to finally form it into a coil of rolled foil of uniformity of thickness dependent on process factors including the condition of the rolling mill. Annealing steps in the process tend to enlarge the crystal structure and improve ductility. Contamination of the metal with its oxides or other impurities is avoided as much as possible. The crystal or grain structure of rolled copper foil tends toward domains with boundaries running largely in the plane of the foil, as can be seen in a microsection. The rolling process results in a foil that has a polished appearance on both sides. For many laminate substrates this smooth surface does not result in adequate adhesion. Proprietary surface treatments are used by foil producers to improve adhesion. These treatments usually consist of a deposit on one side of the foil of attached nodules or dendrites of metal to give an opportunity for the polymer of the substrate to form an interlocking mechanical bond. The deposited metal can vary, with zinc or nickel used in some cases. For microwave laminates a copper deposit is preferred. At least one rolled-foil producer is using an electro-etch process to remove some of the copper on one side in order to leave a 'tooth' surface for bond improvement. Rolled foil is generally considered to be superior in ductility, conductivity, low conductor loss when transmitting high-frequency energy, and freedom from pinhole defects. It is generally inferior in bond strength attainable, rate of etching and precision of etching for fine detail or close-tolerance conductor features. 15.1.3.2 Electrodeposited foil: Electrodeposited foil is produced by continuous electrodeposition of copper into a non-reactive roll cathode. A highly
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polished inert-metal forming roll is partially immersed in a plating bath. While the forming-roll cathode is rotating, an electric current causes transport of copper ions from the copper anode to the cathode where they are deposited as a thin layer. This layer is continuously peeled off the inert metal surface. The inert metal used for the cathode is most commonly a stainless-steel alloy, although lead has been used. Copper-foil weight per unit area or the related thickness is controlled by roll speed and current. Electrodeposited copper has one side with shiny finish from the forming roll, and the other side is dull in appearance. The dull side has a microscopic nodular appearance, produced by the deposition process. The dull side is used for bonding the foil to substrates. For many substrates the original nodular surface is not sufficient, and a proprietary treatment is applied in a second operation to generate smaller nodules on the original nodules to promote better adhesion. Electrodeposited copper foil typically has a vertical or columnar grain structure with most grain boundaries perpendicular to the plane of the foil. Electrodeposited foil is generally considered to be superior in bond strength, etching rate and precision of fine detail in etched patterns. It is inferior in having occasional pinholes, low conductivity, and conductor loss in transmission of high-frequency energy. 15.1.3.3 Other foil features: Copper-foil cladding is supplied on some laminates with an adherent black copper oxide on the outer surface for promoting adhesion to 'prepreg' interlayers in multilayer board assemblies. This is of special value for internal ground planes. For microwave applications the oxide layer is undesirable owing to high loss of transmitted power. With the elevated temperature used in producing laminates based on PTFE composites, the adhesion of the oxide layer is likely to be destroyed. Very thin copper foils, e.g., 118 oz/ft2 weight at 4 p m thickness, are too thin to be handled practically in the lay up for laminating. Such foils are electroplated onto an aluminum-foil carrier. The laminator uses this foil composite as supplied, and usually provides laminates clad with it still carrying the aluminum foil. The aluminum serves very well as protection until the laminate is to be processed. The aluminum is then removed to leave a bright surface on the underlying copper. This is done by etching the laminate in hydrochloric acid diluted to a concentration of 5N. The laminate, after rinsing and drying, is ready for application of photo-resist. Etching with sodium hydroxide, while possible, is too energetic and does not always leave the copper surface as clean as is desired. 15.1.4 Thermal characteristics of PTFE PTFE-based substrates excel in properties needed for microwave systems, and therefore receive most attention in this Chapter. Unfortunately PTFE is not a perfect material for this application. The thermal characteristics of the polymer
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need to be understood. This Section reviews some of the extensive studies of thermal characteristics of PTFE reported in the literature. While PTFE appears to be a simple chemical structure its thermal characteristics are rather complex, and have proved interesting to many research workers, especially in the 1950s. Commercially available grades of PTFE are prepared in aqueous medium either by suspension or by colloidal free-radical polymerisation processes. As produced, the polymer is very nearly 100% crystalline. After it has been heated above the crystalline melting point of 600 K (327"C), the maximum degree of crystallinity is about 60%. The crystalline phase undergoes an unusual transition in two steps at 292 K (19°C) and 303 K (30°C) which may be detected as steps in the thermal-expansion plot. Most of the transition occurs at the lower temperature. The amorphous phase follows a 213 rule [I] with corresponding transitions at 173K (- 100°C) and 400K (133°C). The mechanical loss and conformance of PTFE specimens at levels of crystallinity from 48 to 92% have been measured against temperature by the torsional-pendulum method [2] to reveal the transitions. Mechanical, electrical and nuclear-magnetic-resonance techniques for detecting transition temperatures have been compared [3]. When the logarithm of frequency for the test method is plotted against the inverse absolute temperature in K units of transition, the plot is linear with a slope that corresponds to the activation energy of the transition. The 19-30°C crystalline transition has been examined by infra-red spectroscopy [4], by linear thermal-expansion measurements [5], and by X-ray diffraction [6]. Studies of the conformational energy levels for PTFE indicate that the molecules tend to be more rigid than polyethylene [7]. The crystalline phase below 19°C has been shown [8] to be triclinic with a. twist in the zigzag -chain formation that is 180' over a distance of 13 carbon atoms distance. Above 19OC the twist decreases to 180" over 15 carbon atoms, accompanied by some crystalline disorder. The crystal structure comes into a hexagonal alignment above 30°C. The thermal transitions of PTFE-based composites are evident in printed circuit boards as changes in the relative permittivity related to density changes of the polymer. Unfortunately the crystalline transition near room temperature appears as a step change in density and relative permittivity. The 133°C amorphous transition is difficult to observe electrically, although mechanical tests do show a peak in lossiness around this temperature. 15.1.5 Anisotropy of relative permittivity Anisotropy of the relative permittivity K' is the degree to which the property varies in value depending on the direction of the electric field with respect to the axes of the material. To simplify microwave circuit-design computations, one usually assumes isotropy of K', i.e., equal values in the X, Y and Z directions, of laminated substrates for microstrip or stripline circuitry. This can lead to
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error, particularly where fringing-capacitance values are critical for performance. The nominal K' value is typically obtained by a test method such as the stripline-resonator test method, in which the electric field is predominantly in the Z(thickness) direction. Normally this method gives no measure of degree of anisotropy.
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ceramic-PTFE composite with nominal K' of 10.5. In both cases a thick block was prepared from thin layers of sheet stock using a laminating press cycle typical of the production process. The card pairs cut from the blocks were machine-finished to suitable thickness and tolerance for use with the striplineresonator method at about lOGHz [9] or the fluid-displacement method at 1 MHz [lo]. The electric field is essentially perpendicular to the plane of the specimen in both methods. Table 15.2 K' data versus electric-field direction for non-woven-glass microfibre-PTFE substrate
Fig. 15.1
Electric
X longitudinal
Y transverse
Z thickness
Thickness mm (in) Relative permittivity l MHz 10 GHz Dissipation factor 1 MHz 10 GHz
1.58 (0.0622)
1.53 (0.0604)
1.60 (0.063)
2.428 2.452
2.430 2.432
2.330 2.347
0.00 14 0.0023
0.0009 0.0024
0.0005 0.0016
Schematic for cutting stripline test cards from a thick panel
A technique for measuring K' of a substrate with the electric field in each of the principal axes should ensure that the same method is applied to each axis for directly comparable results. The stripline-resonator test method at 10 GHz has been used with a series of specimens machined from a specially prepared thick block of the material of interest. As illustrated in Fig. 15.1, pairs of testspecimen cards are cut in planes perpendicular to each of the three principal axes. Each pair is then measured. This technique was applied to RT/duroidm 5870, a non-woven glass microbfibre-PTFE composite with a nominal K' of 2.33, and to RT/duroid 6010, a
Rela t l v e Permittivity, K'
Fig. 15.2 K' anisotropy ratio plotted versus nominal K' for woven andnon- woven glass-PTFE substrates
Glass-fibre-PTFE substrates, either woven or non-woven, have fibres lying in the X Y plane, with K' nearly three times greater than for the polymer matrix. The composite will be anisotropic with K;and K;.nearly equal, but both greater than K''.
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Experimental results for the non-woven glass-PTFE are summarised in Table 15.2. The Z-direction results agree with accumulated quality-assurance test data on production laminates. The degree of anisotropy may be expressed as the ratio of the average of the X and Y values to the Z value. For this material, the degree of anisotropy is 1.040 by the 10GHz method and 1.042 by the fluid-displacement method. Since the only source of this anisotropy is the glass-microfibre content, one would expect the RT/duroid 5880 material at K' = 2.20, with about half the volume fraction of fibre, to have an isotropy ratio of about 1.02. These results are compared graphically in Fig. 15.2 with published values for laminates based on woven glass-fibre-PTFE [I 11. They show that the random glass-microfibre-PTFE structure is less anisotropic than a woven-fabric structure at the equivalent fibre content. This difference may possibly be explained by considering the woven-fabric structure, especially at lower fibre content, to be a series of alternating polymerrich and fibre-rich layers. The Z-direction field in effect 'sees' a series-capacitor network, while the X and Y fields 'see' a parallel-capacitor network. This layer effect augments the fibre-orientation effect in the fibre-rich layers. The results for the ceramic-PTFE substrate material are summarised in Table 15.3.
,-RESONATOR
TEST PATTERN CARD
M3 3 n n DIA. SCREW
L END
LAUNCH 3MM JACK - STRIPLINE CONNECTOR BODY BASE COVER BOARD SPACER BOARD WITH THICKNESS OF PATTERN CARD
Fig. 15.3 Exploded side view of stripline fixture assembly
Dielectric constant Panel A Panel B Panel C Average
X longitudinal 10.64 10.80 10.60 10.68
Y transverse 10.69 10.67 10.74 10.70
Z thickness
RAISED PRESSURE AREA AGAINST CLAMP PLATE THERMOCOUPLE WELL
/
10.61 10.61 10.61 10.61
J
/GROUND
/AND
PLANE FOIL
TEMPERATURE CONTROL PRESSURE BLOCK
-M3
While the ceramic-PTFE substrate is a laminated-sheet product, a significant degree of anisotropy of K' was not found
3 n n DIA. CAP SCREW
\TUBING
FITTING
.EMBEDDED
STEEL BALL
/BASE
POSITION
STRIPLINE BOARD
~ B A S COVER E BOARD
15.2 Measurement of substrate properties The complex permittivity at microwave frequencies is of prime interest. Four methods are described. All of them use resonant measurement techniques that could be implemented at minimal cost with good sensitivity to variations in the substrate. They include the most widely used stripline-resonator method, the microstripresonator method for high R substrates, the non-destructive full-sheet resonance method of increasing use, and the specialised cavity-perturbation method for characterisation of materials.
NUT
M2 2 n n DIA. SCREW & NUT
Table 15.3 Summary of anisotropy of K' data for RTlduroid 6070
Electric field
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BASE PLATE
\\
\--
SLIDE AND BLOCK ASSEMBLY
L ~ 3 n n DIA. SCREW & NUT, BRASS OR SS
M2 2 n n DIA. SCREW & NUT
Fig. 15.4 Face view of stripline fixture assembly
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The following Subsections give details of each method together with some performance data. The relative merits are tabulated in Section 15.2.5. 15.2.1 Stripline-resonator test method Versions of this method exist in a military specification [I21 and in private-sector documents [9, 131. Some information is generally available supporting adaptation of the method to other materials or showing actual experimental determination of end-fringing correction [14]. The most recent updates of the documentation include provision for a range of nominal K' values from 2.2 to 10.5. 15.2.1.1 Brief description of the method: The method uses a fixture with clamp plates, ground-plane foils and a permanent pattern card bearing probe lines and resonator, as illustrated in Figs. 15.3 -15.5. The documentation [13] provides complete drawings for the fixture hardware and electronic-measurement equipment.
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though inexact, is used for consistency with previous practice in the stripline method). L = resonator length as measured. AL = length correction for end fringing. N = number of nodes or half wavelengths in the material. I/ Q, = conductor loss.
Q = Lllh - hl (1 5.3) Conductor loss may be calculated from the known properties of copper, frequency, characteristic impedance of the section of transmission line comprising the resonator, and cross-sectional geometry of the resonator [I 51. This is based on the assumption that the resonator surfaces are smooth and free from lossy films of copper oxides. Since typical resonator pattern cards are based on laminate clad with copper foil having a surface treatment for adhesion, the estimate for l/Q, is generally biased low, giving a high bias to dissipation-factor measurements. For a resonant peak free of unusual features, frequency readings at power levels differing somewhat from the 3 dB level below the peak can be used to calculate Q by a more exact formula: l/Q
=
RESONATOR LENGTH CHAMFER
Ih
- f,ll[L{ex~(Piln(10)) -
+ IL - f,I/[L{ex~(P2W o ) )
- 1)0'51
(15.4)
where f: is the power level in dB corresponding tof;. 1 RESONATOR IWIDTH
Nilnerlc dimensions
In millimeters
Fig. 15.5 Generalisedresonatorpattern cardshowing dimensions of Table 75.5,andmade of laminate matching nominal dielectric constant of material to be tested
The specimen, consisting of two unclad cards or stacks of cards to the correct thickness, is interleaved on either side of the pattern card. A 4.448 kN (1000 Ib) clamping force is applied before measurement. The resonant frequency f, and bandwidthf, andf, at 3 dB down from resonance is determined experimentally by observing power transmitted against frequency. From these data the relative permittivity K' and dissipation factor tan d are determined by simple formulas:
K'
=
{Nc/[2f,(L
tand = l/Q
-
+ AL)]}'
l/Q,
where c = speed of light in a vacuum
=
300mm/ns (this rounded value for c,
15.2.1.2 Some factors to consider in the stripline method: The resonator is a short length of stripline open at both ends. A signal induced by the probe at one end will propagate in the transverse electric field mode, TEM, at a velocity inversely proportional to the square root of the relative permittivity of the dielectric. When it is excited at a resonant frequency by the probe, there will be a self-reinforcing standing-wave pattern along the line with node number equal to the number of half wavelengths and voltage maxima at the ends. End-fringing capacitance causes the resonator to appear electrically longer than its measured length L, by an amount AL discussed in Section 15.2.1.3. Inverse Q is the ratio of dissipated power per cycle to stored power in the resonator. For the TEM-mode of stripline, dissipation by radiation can essentially be ignored. The other causes of dissipation are resistance losses in the conductor, dissipation losses in the dielectric and coupling to the probe lines. The Q with coupling losses is referred to as loaded Q, Q,, while an ideal resonator with no coupling would have an unloaded Q, Q,. The degree of coupling to probe lines is observed by comparing the transmission insertion loss of the probe-resonator system at resonance with the same fixture having a straight-through transmission line on the pattern card. A wide gap between probe and resonator reduces coupling to bring insertion loss above 30 dB. When both probe gaps are equal, the following relationship between Q, and Q, can be derived from given formulas [16]:
QLIQu
=
1 - (PLIPO)~~
(15.5)
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where PL = transmitted power with the resonator at resonance. Po = transmitted power with the straight-through line. dB insertion loss = - 10logl0(PL/ Po). The loaded Q differs from the unloaded Q as follows: dB insertion loss QL, as % less than Q,
1 89
5 56
10 32
15 18
20 10
25 5.6
30 3.2
35 1.8
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frequency of resonance. From eqn. 15.1 these 12 data values have a linear relationship of the form FLIN = Bo + B, FIN
(15.7)
40 1.0
Losses due to radiation are assumed negligible in stripline. Losses due to coupling to probe lines are made low enough to ignore. The total loss is then assumed to consist of conductor resistive losses and dielectric losses as in eqn. 15.2. The end-fringing-capacitance correction AL, used in the relative-permittivity calculation, has been estimated from a published formula [17]: where K = Bln(2)/n, B = ground-plane spacing, W = resonator width. With W = 6.35 mm and B = 3.39 mm, AL is predicted to be 1.28 mm. Experimentally AL was found to be about 1.42mm for substrates of non-woven glass/ PTFE at K' values of 2.20 and 2.33. This difference arises from several causes. The test fixture with specimen is offset from centre by half the dielectric thickness of the resonator pattern card. The resonator conductor has a finite thickness ignored in Reference 17. Capacitance is increased by the proximity of the probe lines. The substrate under test has anisotropic K' from the loading with oriented glass fibre; i.e., K'' or K;, with the electric field parallel to the X or Y axes of the substrate, is higher than K', and end-fringing capacitance is larger than predicted. 15.2.1.3 Experimental determination of end-fringing correction: A series of test pattern cards with resonator lengths for I-, 2-, 3- and 4-node resonances near the 10GHz test frequency are prepared so that they are identical in gap size, probe width etc. Fig. 15.6 shows typical photomask artwork for this purpose. The resonator length L is measured by optical comparator or X, Y co-ordinograph for each of the resonator pattern cards. Specimens will show variations of thickness from the fixture design value with associated variation in the AL fringing correction. An experimental procedure to determine AL as it varies with specimen thickness i s based on a series of specimens representing the range of thickness to be encountered. The average thickness T of each specimen pair is determined. With each resonator pattern card in turn mounted in the test fixture, resonant-frequency readings F a r e obtained on each of the selected series of test specimens. It is good practice to replicate this series of readings with each pattern card and use the average F value. For each test specimen there will be four sets of F, L and N data, where N is the number of nodes of the resonance, L the resonator length and F the
F o r K' = 2.20,
node 4
I F o r K' = 2.20,
Fig. 15.6
node 3
Examples o f pattern-card artwork for probe-line impedance and AL determination
where Bo
=
C/(2K'0'5) and B,
=
-AL
The slope B, and Y-axis intercept Bocan be obtained by plotting, as in Fig. 15.7, or by numerical linear regression analysis to yield AL values for each specimen.
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When this is done, the average thickness T and AL data for all the selected specimens may be plotted to correlate AL with average thickness T, as in Fig. 15.8, with good results. Experimental data for two substrate types are summarised in Table 15.4. Table 15.4 Summary of experimental AL values as a function of specimen thickness
Material Nominal K' Co, null Std. dev. about fit, mm
c,
Std. err. of est. AL for 1.524mm thickness AL for 1.626 mm thickness
(Res, f r e q . ) / (Nodes), I / n s Fig. 15.7 Example of plot of FLIN versus F I N for a specimen of RTJduroid 5880 with the series of pattern cards for nodes I to 4
1.52
1.54 1.56 1.58 1.60 Specimen thickness, mm
1.62
Fig. 15.8 Plot of experimentally determined AL versus specimen thickness for a series of specimens of differing thickness
AL
=
RT/Duroid 5880
RT/Duroid 5870
2.20 0.032 0.005563 0.864486 0.09462 1 1.349 1.438
2.33 0.150 0.006 121 0.800966 0.09575 1 1.371 1.453
.
C,,+ C, (thickness)
15.2.1.4 Adaptation of the method: The latest documentation [13] provides for a wide range of R values at convenient specimen thicknesses, as summarised in Table 15.5. The following comments apply to the Table. Chamfer values are based on published design curves [la]. Calculation of probe-line widths, for 50Q characteristic impedance Z,, assumes that the ground-plane spacing is twice the nominal specimen thickness plus the thickness of the pattern card and its 34pm thick (1 oz/ft2) copper-foil pattern. The simplified case of the stripline centred between ground planes is used [19, 201. To use the stripline-resonator test for a new substrate type, test pattern cards are prepared from a clad laminate of the substrate at 0.216mm (0.0085in) dielectric thickness. A 0 node pattern is included which consists of a straightthrough line (no resonator) to be used to verify the 50Q value of Z, for the probe-line width. The fixture is assembled with the new substrate type used for the base cards. Specimens of the 0.216mm-thick dielectric laminate used for the test pattern cards are stacked in the fixture and tested with the 1-, 2-, 3- and 4-node pattern cards to verify that its K' matches that of the thicker substrate to be routinely tested. The I-, 2-, 3- and 4-node pattern cards are used with a series of substrate specimens covering the expected range of thicknesses to determine AL as a function of specimen thickness, as outlined previously.
15.2.1.5 Considerationsfor precision and accuracy: Two sources of possible error were studied in the laboratory. The test fixture with resonator pattern card
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could develop a bias with use over a period of time; and the resonator pattern card does wear with use and requires replacement. A series of 12 test specimens were used for each of two non-woven glassPTFE substrates at R values of 2.20 (RTIduroid 5880) and 2.33 (RTIduroid 5870). For each of these materials a test fixture was prepared with a 4-node test pattern card in place. The specimens were tested in rotation in ten test sessions Table 15.5 Dimensions for stripline test-pattern cards in mm referring to Fig. 15.5
Nom. Nom. Patter- Probe Chamfer Probe Resonator Conductor K' thk. card thk. width X, Y gap width length loss as 4 node l/Q, MIL-P13949F [I 21 2.55 1.588 0.216 2.18 2.56 2 3 4 6.35 38.1 0.0006
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electric field parallel to the plane of the substrate. Thus a value for K' obtained by the stripiine method must be understood to include both Z and X-Y-plane components. There are some other sources of error in the test method. A fixed-frequency resonant cavity traceable to an acceptable standard should be used to verify performance of the frequency counter. Resonator distortion can be detected by looking for drift in reference-standard specimens and verifying it by actual re-measurement. Erratic performance or multiple resonant peaks may be evidence of fatigue fracture of the probe lines where they leave the base-card region.
Table 15.6 Summary of K' readings for specimens and patterns 2.20 2.33 Nominal K' 12 12 Number of specimens Number of readings per specimen 10 10 Mean of standard deviations of K' readings 0.00131 0.00 164 on specimens with a single pattern card Std. deviation of the specimen std. deviations 0.00032 0.00022 Number of 4-node pattern cards 18 10 Mean of standard deviations of R readings 0.00313 0.002 12 on specimens when changing pattern cards 0.000 19 0.000 13 Std. deviation of pattern card std. deviations
$---I
RESONATOR
Earlier adaptation [I41 10.5 1.27 0.254
.
0.42
radius
2.03
2.54
17.3
.
.
0-0009
Note: See comments in 15.2.1.4.
over a period of more than five working days. For each specimen the standard deviation for K' readings with a single pattern card was determined. For each type, a series of 18 or 10 test pattern cards were used for a measurement session with specimens in rotation. The standard deviation of K' was determined for each specimen as pattern cards were changed. Table 15.6 summarises the results of the study. The stripline test applied to laminates in the K' = 2.0-2.5 range should have a precision of better than 0.5%, considering the drift of the fixture and pattern-card changes. Accuracy is related to certain features of the test method. The K' value obtained is based largely on the case of electric field perpendicular to the plane of the substrate, i.e., Z direction. However, part of the electric field in the fringing region along the lengthwise edges of the resonator has a component of
.
-
TRIMMED SIZE
1.27 mm THICKNESS
0.635 mm THICKNESS
Fig. 15.9 Plan views of the microstrip test specimens for 1.27 and 0.635mm dielectric thickness
15.2.2 Microstrip-resonator test method The microstrip-resonator test method has been used for several years with ceramic-PTFE soft substrates for K in the 9.5-1 1.0 range, where the application is for microstrip devices not necessarily limited to antennas. Variations of the method have been specified by at least one user, and it has been in routine use by at least two suppliers. It is most readily used for substrates clad on one side with thick metal.
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15.2.2.1 Brief description of the microstrip-resonator method: Rectangular specimen cards 30.5 x 19.0mm (1.20 x 0.75in) with thick metal backing are prepared by photomasking and etching a pattern consisting of two probe lines and a resonator element, as shown in Fig. 15.9. The probe-line width is designed to match the 50R characteristic impedance of the test system. BRASS COVER BLOCK
r.----7/
p-
895
fittings and contact the probe lines to the pins. The movable end plate is applied with force to ensure ground contact of the coaxial fittings to the thick metal backing on the specimen. A metal cover is placed over the mounted specimen. The resonant frequency f, and bandwidth, f, and f , , at 3 dB down from the resonance are determined experimentally by observing power transmitted through the fixture against frequency. From these data the relative permittivity K' and dissipation factor tan d are determined from the simplified formula (eqn. 15.8) with constants A-F specified as in Table 15.7.
MDVABLE END PLATE FIXED END PLATE
7
-
I
BASE BLOCK
SIDE VIEW
RIGHT ANGLE COAX BULKHEAD FEEDTHROUGH FITTING WITH PIN I N CONTACT WITH PRUBE LINE ON SPECIMEN
I
\ \
SPECIMEN, 0.635 nn DIELECTRIC WITH RESONATOR PATTERN ON TOP AND THICK METAL CLADDING ON BOTTOM
\
SPRING LOADED L I F T PLATE
END 'VIEW Fig. 15.10 Side and end views of the microstrip test fixture with specimen in place
To perform a measurement, the specimen is mounted in the test fixture shown in Fig. 15.10 to provide connection of the specimen ground plane and probe lines into 3mm coaxial connectors. The spring-loaded floor of the fixture is pushed down so that the specimen can fit under the centre pins of the coaxial
where L = length of the resonator, in. The l / Q value may be determined from eqn. 15.3 or 15.4 for the stripline method. For the microstrip method, the observed dissipation of the resonator element is the sum of losses from radiation, conductor resistive loss, coupling loss and loss in the dielectric. Normally no attempt is made to separate these effects, and the material under test is rated by the Q value of the resonator. The Q measurement is made after the specimen has been exposed to conditions representative of a circuit-board processing environment, as a way of predicting the sensitivity of the substrate to impairment of electrical performance. 15.2.2.2 Some factors to consider in the microstrip method: This method may be adapted to other values of substrate thickness and nominal relative permittivity. The resonator pattern would require redesign. More exact formulas relating effective K' to substrate K' [21, 221 would need to be used to derive a simplified formula for computing K' from the resonant frequency. The length of the resonator on each specimen should be read accurately by an optical comparator or X, Y co-ordinograph to avoid test-result bias by pattern variation from the photomask dimension. The metal cover specified for the test is subject to variation in the quality of contact it makes to ground. The presence of the cover affects the resonant frequency. For comparability of measurements from one specimen to another, they should always be made with the cover in place. The intention of the metal cover is to remove the effect of radiation losses from the Q measurement. Based on experience, there is some question as to whether this cover is effective for the purpose. The method is primarily intended for use with laminates clad on one side with thick metal, typically 3.2mm (0.125in) thick or more. When specimens made from laminates clad on both sides with thin copper foil are to be used a thick metal back-up plate is also used.
15.2.2.3 Considerationsforprecision andaccuracy: This test method does not use a test-pattern card that is part of the fixture, as is used for the striplineresonator method. The possible source of bias imposed by the pattern card is
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thus eliminated. This method seems rather more relevant to microstrip applications, although the section of line used for the resonator is wider than a microstrip transmission line at the typical 50R characteristic impedance. The metal cover has been observed to change the resonant frequency, and hence the computed K' value. Constant F for eqn. 15.18, listed in Table 15.7, includes a correction for this test bias. The quality of fit of metal cover over the specimen and end plates is expected to influence accuracy.
is based on the assumed values of dielectric thickness and resonator width. Ignoring these will bias the calculated results. More exact formulas [21, 221 were used to calculate the bias associated with errors in the assumed resonator width and dielectric thickness, as shown in Table 15.8. Table 15.8 Predicted bias in calculated bulk K' from ignoring specimen dimension variations in the microstrip resonator test method
Table 15.7 Microstrip resonator test: pattern design data and constants for calculation of results
Nominal K' Dielectric thickness Card length Card width Probe-line width Probe-resonator gap Resonator length Resonator width Number of nodes Constants for calculation of K by eqn. 15.8 using length in inches: AL A
B C D E F
Bulk 10.2 0.635 30.5 19.0 0.53 0.46 17.2 0.318 2
0.0205 69.73 0.0 0,175 0.0089 1.533 0.14
10.2 .. -
(0.025) (1.20) (0.75) (0.021) (0.018) (0.676) (0.125)
1.27 30.5 19.0 1.14 1.78 17.8 0.318 2
(0.050) (1.20) (0.75) (0.045) (0.070) (0.700) (0.125)
0.0375 34.869 0.3403 - 0.2992 0.0098 0.7008 0.33
D~mensionsare in mm (in)
The end-fringing effect AL in the calculation of K' is based on consideration of the ratio resonator-widthlheight, but does not include the effect of resonatorconductor thickness, proximity of the probe line and its width, or the anisotropy of the dielectric. Accuracy of the method would be improved by an empirical derivation of this constant for the conditions of the test method. The approach used for stripline in Section 15.2.1.3 would be applicable. The etched pattern can also vary in the gap between the probe lines and resonator. This variation will have an, as yet undetermined, effect on the value to be used for the AL end-fringing correction. If the gap is larger due to over-etching, the AL should be smaller. The simplified formula provides for a fixed resonator width and substrate thickness with no provision for actual variations between specimens. The relationship of effective K', obtained by the test, to the bulk K' of the substrate
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R
Dielectric thickness, mm
Resonator width, mm
10.2 10.2 2.2 2.2
0.635 1.27 0.79 1.58
3.18 3.18 5.08 5.08
Bias in calculated bulk K' ignoring a 25 pm variation in: Diele. thk. Resonator width
+
-0.39 -0.14 -0.18 - 0.084
% % % %
+0.10 +0.10 +0.031 f0.031
% % % %
15.2.3 Full-sheet-resonance test method The full-sheet-resonance (FSR) test method, also called the parallel-platewaveguide resonator method, is a valuable non-destructive method for measuring the dielectric constant at microwave frequencies of clad laminate panels. While the FSR method is beginning to find use in individual cases with users and producers of clad laminates for microwave applications, a standard procedure or apparatus has not yet been established in the industry. 15.2.3.1 Brief description of the full-sheet-resonator method: In the full-sheetresonator (FSR) test method a metal-clad laminate panel, trimmed to the rectangular size to be supplied or used, is treated as a parallel-plate-waveguide resonator in which the electric field is in the Z direction and the open edges form an electrical boundary. Probe connections are made at two edge or corner positions, as shown in example of Fig. 15.11. The frequencies of selected unambiguous resonant modes are measured experimentally by observing power transmission between probes against frequency. Two probe and specimen fixtures, shown in side and face views in Fig. 15.12, provide a convenient and non-destructive way to couple probes to the specimen. They can accommodate a wide range of panel sizes and thicknesses, with o r without thick metal backing. They allow precise air-gap adjustment to reduce the coupling of probes. A simple formula is used to calculate K' for an observed resonant frequency of known mode number [M:N], ignoring the fringing-capacitance effect of the open edges forming the electrical boundary.
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he ref,,^,.^ = resonant frequency, GHz, c = speed of light, 299.792 mm/ns, M = integer number of nodes along length, L = length, mm, N = integer number of nodes along width, W = width, mm, K' = dielectric constant of the substrate. MARKER FOR NODE SHOWING VOLTAGE POLARITY AT A G I V E N INSTANT FOR MODE C3t21
COAXIAL PROBE CONNECTION TO CENTER OF EDGE WITH GROUND TO TOP PLATE AND CENTER P I N TO BOTTOM
Fig. 15.1 1 Schematic of coaxial-probe connection to parallel-plate resonator with voltage nodes for a typical resonant mode indicated by arrows
15.2.3.2 Some factors to consider in the FSR method: The FSR method applied to microwave integrated-circuit substrates used the plane of an APC-7 coaxial connector for coupling to the metallised substrate [23, 241. The fixture of Fig. 15.12 combines specimen support with better adjustability. Firm electrical contact of the coaxial ground of the probe is made to the top metal edge, while either contact or air capacitive coupling is made between the centre pin and the lower metal edge. The ground contact assembly is lifted against spring tension to permit placing the specimen. Measurements at controlled temperatures may be carried out by clamping a specimen between two aluminum blocks, as in Fig. 15.13, through which fluid is circulated from a constant-temperature bath. Specimen size exceeds block dimensions by about 1 mm. For a given K' the limited useful frequency range for testing increases as the panel size decreases. The calculation is based on two assumptions: the cladding on the top and
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bottom of the specimen is parallel, i.e., thickness of the substrate is uniform; K' of the substrate is uniform over the area of the specimen. If these assumptions are false, inconsistent measurements can arise.
----------DRILL HELE AND TAP BOTH ENDS FUR 3 nn PIPE FITTINGS
is at less magnitude than, earlier work on metallised integrated-circuit substrates 1241. The influence on apparent K' of extra fringing capacitance of open edges is not well explained. Intuitively it seems that some modes have fringing field in air along the edge, acting as a heterogeneous medium for lower KiPp.Other modes 'see' the fringing as increasing electrical length - in effect, increasing K:pp. Some modes will predominate in one effect or the other, while others may tend to cancel the two effects. For lack of an accepted model the effect is ignored, which appears adequate for specimens of small thickness versus length and width.
I . 0.0
CHz
.
. 1.0
2.0
Fig. 15.14 Diagram of expectedresonancesfor a 254 nominal K' of 70.2. --- Selected modes above 0.5GHz
Fig. 15.13 Aluminum block for temperature control of
FSR specimens: two required
The three fundamental resonant modes are of two kinds. First, the [I :0] and [O: 11 modes have voltage maxima oppositely polarised along two opposite
edges. Secondly, the [1:1] mode has voltage maxima of alternating polarity around the four corners. Higher-order resonant modes simply involve multiple patterns of a fundamental mode. The node number M or N is the pattern count lengthwise or widthwise. A specimen at resonance [M:N ] has ( N 1)(M 1) voltage maxima with 2(M N ) on the edges. Resonant modes with odd-node numbers along an edge are suppressed when a probe is centered on the edge. The f; for a given mode is associated with an average K' for the panel's area weighted for regions of voltage maxima. Observed values off, differ somewhat from the prediction of eqn. 15.9 (lower apparent K') than [O:N] or [M:O]modes. This deviation agrees in sign with, but
+
+
+
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3.0 x
4.0
102mm (10
x
5.0 4in) cladpanel with
15.2.3.3 Ambiguous mode limitation of the FSR method: The spectrum of resonant modes for FSR rapidly becomes too dense for practical use as frequency increases for a given specimen size. For the example in Fig. 15.14 suppose that the substrate K' is known to be always within 5% tolerance of nominal K', but measurement has to be done to detect boards that fall outside a 2% tolerance. The 5% possible tolerance of K' will be observed as a possible 2.5% tolerance of the expected resonant frequency for a given mode. A mode is ambiguous if the expected nominal frequency is in a region of the spectrum where adjacent frequencies on either side are within the 2.5% tolerance; i.e., there is no assurance as to whether a frequency observed in the expected region is actually the expected mode or not. In the crowded part of the spectrum one can surely find a resonance close enough to indicate whatever value of K' is desired, whether it is correctly assigned a mode or not. Thus selection of unambiguous modes for a particular specimen length/ width ratio is an essential part of the method. It is desirable to select unambiguous modes of higher order, if possible, in order to obtain a larger number of voltage maxima better representing the area of the laminate specimen. In the example of Fig. 15.14 all the modes except four have nominal frequencies with neighbours closer than the 2.5% test, and thus are ambiguous. The five
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frequencies most widely spaced from their nearest neighbours are: Mode
Nominal f, GHz
[3:01 [4:0] [4:2] [2:2) [7:21
0554 0.739 1.183 0.995 1.589
Closeness of nearest other f,, % 16.66 accent 12.50 accept 3.15 accept 2.66 accept 2.31 reject
The FSR method will usually be applied to large numbers of panels of the same nominal length, width and K'. Practical application of FSR requires not only consideration of possible variations of K' from the nominal but also of the length and width. Variation of the aspect ratio of length to width alters the relative position of resonances in the spectrum, and could make previously selected modes ambiguous. Thus the possible range of aspect ratio one could encounter must also be considered in the selection of modes for test. The following stepwise procedure, best implemented by a computer program, may be used for selection of unambiguous resonances: (a) Determine the nominal and largest expected deviation from nominal for the parameters of length L, width Wand relative permittivity K'; Set L = nominal length; set W = nominal width. (b) Decide whether probes will be on corners or centred on opposite edges. If centred on edges, use the distance between those edges as the length, and exclude all modes with odd-width node values N from this selection procedure. For probes at corners the increment for N = 1; otherwise it is 2. (c) Decide on an upper frequency limit for consideration, f,. ( d ) Set N = Oand M = 1. (e) Use eqn. 15.9 to predict a value off,. Record the values for M, N and S,. ( f ) Increment M by 1, and repeat step (e) until f, exceeds f;,. (g) Set M = 0 and increment N by the value I or 2 determined by probe position. Perform steps (e) and Cf). (h) Repeat (g) until the firstf, for a given value of N is found to exceedf;,,. ( i ) Rearrange the sets of M, N andf, values in order of increasing value off,. ( j ) For each set, determine which adjacent set has the nearestf, value to be used asf,,,,. Determine percentage proximity value P. ( k ) Rearrange the sets of M, N andf, values in order of decreasing P value, and note as unambiguous those modes with P greater than half the percentage value for the largest expected deviation of K' from nominal.
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(I) Set L = nominal L minus largest deviation expected. Set W = nominal W plus largest deviation expected. Repeat steps (d)-(k). Retain as unambiguous and usable only those modes that were found before and also this time. (m) Set L = nominal L plus largest deviation expected. Set W = nominal W minus largest deviation expected. Repeat steps (d)-(k). Retain as unambiguous and usable only those modes that were found before and also this time. 15.2.3.4 Test procedure for clad laminates: Test specimens are clad laminate panels trimmed accurately to a rectangular shape. All four edges should be straight and smooth without edge contamination such as metallic chips that might occur with cutting. All four corners should be right angles. Failure to achieve smooth, straight, clean, perpendicular edges will impair the accuracy of the test. Experimental data are not yet available on the effect of these parameters on accuracy. Measure specimens for length and width as the distance between centres of opposite edges. Use either a vernier caliper or an X , Y co-ordinograph. Record dimensions to the degree of resolution of the measuring equipment. The accuracy of dimensional readings influence the accuracy of the test. An error of 1% in a dimensional reading can cause a calculated relative-permittivity error of up to 2%, depending on the resonant mode used. 15.2.3.5 Precision and accuracy, supporting data: Almost all data on precision and accuracy of the FSR method obtained so far have been with high-K' ceramic-PTFE substrates, such as RT/duroid 6010 laminate. The method is expected to be as useful with low-K' substrates such as glass-fibre-PTFE substrates. 15.2.3.5.1 Effect of temperature: Aluminum blocks, 254 x 96mm, as mentioned in Section 15.2.3.2, were used to control the temperature of two specimens of nominal 254 x 108 mm size, 0.64mm dielectric thickness, 34pm copper-foil clad both sides. Mean K' values from modes [3:0], [4:0] and [32] were obtained in replicate for several temperatures, as summarised in Table 15.9. Where corresponding data were available, no difference in K' was observed with or without the aluminum blocks at 23OC ambient temperature. Temperature effect is similar to that observed with stripline-resonator measurements, and indicates that varying the laboratory temperature over a 20-26OC range will account for less than 0.2% error in K'. 15.2.3.5.2 Effect of decoupling Opening capacitive gaps of probes to increase the insertion loss at resonance did increase Q as expected, but has not shiftedf,, as predicted in earlier work with integrated-circuit substrates [24]. It does, however, yield 'cleaner' resonant peaks; i.e., the plot of dB versus frequency became smoother and showed less low-level noise above and below resonance.
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Work on metallised integrated-circuit substrates used coupling at a corner with the face of an APC7 coaxial connector [25]. Perturbation errors were introduced by the method of coupling into either closed or open cavities. The conclusion was that, in the [O:N] mode, the electric- and magnetic-field effects of the probe cancel. The recommendation was to ignore all but the zero-mode resonances. Experience with the method applied to laminates of larger area with the fixture of Fig. 15.12 seems to indicate less error for any mode.
tions of replicate readings for specimens averaged 0.008 for K' z 10.0 in the laboratory with better temperature control. 15.2.3.5.4 Consistency among specimen sizes and mode selections A study to evalute the FSR method for consistency of test results with respect to specimen size was performed with RT/duroid 6010.5 high-K' ceramic-PTFE composite substrate. The study started with six panels of nominal 508 x 254 mm size, 0.64 mm dielectric thickness with 34 pm copper clad both sides. These were measured at full size and successively cut into smaller portions which were again measured and averaged. Table 15.11 summarises the sizes, number of portions and average change in K' reading from that of the original size.
Table 15.9 K' values by FSR norrnalised as percentage difference from 23°C value
Length, mm Width, mm
Specimen A 254.7 108.7
Temperature setting, OC
Mean K'
13 14
10.828 10.817
23 23
Specimen B 254.4 108.4
% diff.
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Table 15.10 Average K' value summary of FSR repeatability study on seven
Mean K'
% diff.
0.637 0.534
10.674 10.678
0.386 0.423
10.754 10.765
- 0,051 0.05 1
10.630 10.636
- 0.028
32 32
10.702 10.727
- 0.534 - 0.302
10.587 10.593
- 0.433
40 40
10.660 10.669
- 0.925 - 0.841
10.562 10.564
- 0.668 - 0.649
45 45
10.641 10.642
- 1.101 - 1.092
10343 10.540
- 0.846
specimens at nominal 2 5 4 x 108rnm size with modes [3:0], [4:0] and [3:2]
-
-
0.028
- 0.376
- 0.875
The average K' value from resonances of modes [3:0],[4:0]and [3:2]are shown for each temperature
15.2.3.5.3 Repeatability With three selected unambiguous modes, the FSR method has proved to be reproducible in replicate test runs, comparing laboratories and test fixtures for a series of specimens. Seven specimens from two suppliers of high-K ceramic-PTFE substrate with nominal 254 x 104mm size were measured repeatedly in rotation at selected modes [3:0], [4:0] and [3:2]. The dielectric thickness was 0.64mm with thick metal cladding one side and 34pm-thick copper on the other. For each run an average of the three modes was used as the K'-value. Summarised data are given in Table 15.10. Replicate runs comparing two fixtures and two laboratories showed insignificant fixture difference. The difference between laboratories is attributed to poorer temperature control in one, which was later improved. Standard devia-
I
H R
Specimen Supplier Thick metal thk.. mm
A R alum. 3.18
B R alum. 3.18
C M alum. 3.18
D M alum. 3.18
G R brass 6.35
brass 6.35
I R brass 6.35
Group X Mean value Std. dev. Number
10.201 0.005 4
10.069 0.008 4
9.733 0.008 4
9.968 0.010 4
10.165 0.001 3
10.376 0.013 4
10.077 0.012 4
Group Y Meanvalue Std. dev. Number
10.189 0.010 4
10.072 0.010 4
9.739 0.010 4
9.962 0.002 4
10.172 0.013 4
10.388 0.001 4
10.080 0.003 4
Group Y Mean value Std. dev. Number
10.166 0.019 5
10.035 9.722 0.014 0.014 3 4
9.939 0.020 4
10.134 0.004 2
10.371 0.004 2
10,082 0.018 3
Group X Rotated replicate runs with fixture I , laboratory E Group Y:Rotated replicate runs with fixture 2, laboratory E Group Z: Rotated replicate Nns with fixture 2, laboratory W Laboratory W had higher and less controlled ambient temperature
The results are consistent until the final 76 x 76mm sizes, which showed lower K' values. 15.2.3.5.5 CorreLation with the stripline-resonator test Among the 72 specimens of 76 x 76 mm size resulting from the study discussed in Section 15.2.3.5.4, seven pairs were selected to have nearly identical average
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K' values by the FSR method and to cover a range of K' values. Specimens were prepared by cutting the two 76 x 76 mm cards into four 38 x 76 mm cards to be stacked to the nominal 1.27 mm thickness on both sides of the striplineresonator pattern card for testing. K' was measured by the stripline-resonator method.
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3 dB down from resonance is determined experimentally by observing the power transmitted versus frequency. Electronic equipment for this may be the same as is required for the stripline-resonator method [13], except that a higher degree of frequency resolution is needed. The Q value is determined from eqn. 15.3 or 15.4 in Section 15.2.1.1.
Table 15.11 Summary of average K' values by FSR for panels successively divided andlor trimmed
Nominal size, mm 508 x 254 254 x 254 254 x 108 254 x 96
76 x 76
FSR modes selected
[5 :21 [4:21 [6:01
No. of specimens 1 averaged per panel
[3:21 [2:21 [3:01
[3 :21 [3:01 [4:0]
[3:01 [4 :01 [4:21
[I :0] [3 :21 [I :2]
2
4
4
12
Mean change of average K' for panel from initial size As change in K' 0.000 0.003 - 0.020 - 0.015 0.000 0.028 -0.19 -0.014 AS % of R
- 0.200 -1.90
The FSR K' values for each mode and their means are plotted versus stripline
R values in Fig. 15.15. Correlation coefficients of the [I :0], [3:2], [1:2] and mean FSR values versus the stripline values were 0.97,049,0.95 and 0.95, respectively. As can be seen from the plots, the population of specimens seems to fall in a similar K' region from either method, but the slope shows the FSR method to be about twice as sensitive to variations in specimen K' as the stripline method. This is consistent with the use of an unchanging pattern card adjacent to the resonator in the stripline method. We conclude that the FSR method is more sensitive to K' variations than the stripline method, but correlates strongly with it. Specifications calling for the method should be wider in tolerance than they would be for the stripline-resonator method. 15.2.4 Perturbation cavity method
The resonant-cavity perturbation method of test for complex permittivity is discussed here because it has some unique features useful for characterising substrate materials. A standard method for measuring the dielectric constant and dissipation factor (complex permittivity) is published [26]. It is primarily intended for testing ceramic materials at about 10 GHz. 15.2.4.1 Brief description of the method: A section of rectangular waveguide is provided with flanges at the ends. At each end an iris plate is clamped between the waveguide flange and the transition into coaxial cable for connection to the electronic equipment. The resonant frequency, f, and bandwidth, f,and f2, at
10.5
10.6
10.7
10.8
K' by strlpline method F i g . 15.15 Plot of K' values by modes and mean FSR versus stripline K' values
To be useful for microstrip-antenna substrate materials, the means for loading the specimen into the cavity must have minimal effect on the emptyf, and Q values. Fig. 15.16 shows a sketch of an effective perturbation cavity. The flanged joint at the centre of the cavity length is fitted with dowel pins and alignment holes. Clamping is done in the same way each time with lever-type clamps applied to two specific locations on the flanges. Specimen types described in the standard [26] include vertical bar, vertical
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rod, horizontal rod, thin strip and sphere, all with dimensions qualitatively described as much smaller than the cavity. This discussion will focus on the vertical-bar and sphere types most useful for microstrip antenna needs. A cavity size for transverse electrical resonance mode TE,,, at the desired frequency is selected with inside dimensions such that the length is seven times the width and the height is half the width. The TE-mode numbers designate number of nodes in the width, height and length directions, respectively. The electric field is in the height direction. ENDPLATE FOR CAVITY WITH I R I S HOLE
CENTER FLANGE FOR OPENING CAVITY
SPECIMEN POSITION
WAVEGUIDE-COAXIAL
Fig. 15.16
L I N E TRANSITION
Sketch of perturbation cavity
Frequencyf, and Q of an odd-node (N-) resonance of the waveguide cavity is measured with and without a dielectric specimen in the cavity. The method specifies symmetrical positioning of the specimen. The odd-node number is required to ensure a voltage maximum at the centre where the specimen is located. Bothf, and Q decrease when a specimen is present to a degree related to the specimen shape, size, orientation, R and dissipation factor D. Collected data on the empty and loaded cavity is reduced to K' and D values by simple formulas as follows: For the vertical bar
D
=
For the sphere
LIP
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where
= volume of specimen, f , = f, of empty = volume of waveguide cavity, cavity, f, = f, of cavity with specimen, Q, = unloaded Q of empty cavity, Q, = unloaded Q of cavity with specimen.
15.2.4.2 Perturbation test fixture for microstrip substrates: For the TE,,, mode at about 10 GHz the cavity should be 109 x 22.9 x 10.2 mm. A recommended rod-specimen diameter is 1.0mm. For a 2.0mm-diameter rod with K' of about 8-10 an error of approximately - 2% in K' is reported [26]. Ceramic materials that lend themselves to precision grinding can be used for small rod or sphere specimens. Soft microstrip-antenna substrate materials, such as non-woven glass-PTFE or ceramic-PTFE, are difficult to fabricate with quality. woven-glass fabric-based substrates pose greater difficulties. These problems are reduced by a larger cavity for lower frequency such as 3 GHz with recommended rod diameter of 3.2mm. Vertical bars from most substrate materials can be shear cut or sawn to a width of 6-12mm at the original thickness. For spheres, bars cut from a specially made thick laminate are lathe-turned with special fixtures. A cavity with TE,,,-mode resonance at 3.0GHz is made from extruded copper waveguide with inside dimensions of 486 x 72 x 34mm and is provided with a 15.5 mm diameter iris opening centred at the ends. Insertion loss of the empty cavity is about 40dB. With proper polishing of flange surfaces the Q is about 10000. The flanged joint for loading is within 0.13 mm of the centre of the length. Spherical specimens are of particular interest, since they can be variously oriented with respect to the cavity field in order to observe the degree of anisotropy of substrate materials. The vertical bar is convenient to prepare but has the electric field along the length of the bar, which is not typical of microstrip-antenna applications. 15.2.4.3 Considerations for precision and accuracy: Sources of error in the perturbation method can involve measurement errors of frequency or specimen size, with predictable consequences. Less obvious are errors related to incorrectly positioning the specimen. The discussion of error is confined to the 3 GHz cavity. It is important to have a frequency source that is stable and resolvable to less than one part in lo6 since the perturbation method is concerned with small differences in frequencies. 15.2.4.3.1 Errors in dimension or frequency data: Previously discussed methods use a resonator based on the material under test. In the perturbation method
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small changes in frequency readings are much more significant. Small errors in specimen dimension o r f , values affect the K:,, of the material significantly. A small error in one of the four frequency readings for bandwidth of the empty and loaded cavity affects D,,. The sensitivity to frequency errors is related to Table 15.12 Predicted bias of the perturbation method from dimensional
91 1
Table 15.12 shows the computed bias of K' and D measurements resulting from singular errors in specimen dimension or frequency. Specimen features, such as non-uniform width or thickness of bars or diameter of rods or spheres, give rise to measurement errors than can be reduced by averaging multiple readings of each dimension. Surface roughness of a specimen can also bias dimension readings away from the effective dimension.
and frequency errors Vertical bar: Area = thickness
x
Parameter with error Amount of error
Area 1%
100 kHz
l kHz
1 kHz
3.2 x 12.7mm K' = 3.0 and D = 0.002 Resulting % bias of K' Resulting % bias of D
- 0.66 -
- 0.49 -
- 0.005 -
- 1.2
3.2 x 12.7mm K' = 10 and D = 0.002 Resulting % bias of K' Resulting % bias of D
width f,
- 0.59
- 0.89 -
-
fi
- 0.005 -
- 1.5
Sphere: Diameter
Parameter with error Amount of error
Dia f, fi 0.22% 0.022% lOOkHz l kHz 1 kHz 0.1 kHz
11.4 mm diameter K' = 3.0 and D = 0.002 Resulting % bias of K' - 0.73 Resulting % bias of D -
-
-
6.35 mm diameter K' = 3.0 and D = 0.002 Resulting % bias of K' - 1.31 Resulting % bias of D -
-
-
-
6.35 mm diameter K' = 10 and D = 0.002 Resulting % bias of K' - 4.14 ~ e s u l t i n e% bias of D
- 0.43 -
-
- 19.8 -
15.2.4.3.2 Changes in cavity performance: Cavity characteristics drift with use. This is not a problem if it is gradual and the practice of alternating empty and loaded cavity readings is followed. Use the average of the empty cavity readings before and after a loaded reading for calculations of K' and D. Abrupt changes in cavity performance can arise from irregular laboratory techniques, varying flange-clamp force, changing position of clamps and inclusion of contamination in the cavity or on the flange face. Data showing variable empty-cavity performance is suspect. 15.2.4.3.3 Position of specimen in the cavity: Little comment is made on how critical this is [26]. Work was done with both the vertical bar and the sphere. The orientation of the width dimension of vertical-bar specimens and mislocation from the centre widthwise, and to lesser extent lengthwise, were investigated. The data-collection programme served the dual purpose of showing reproducibility on repeatedly loading a specimen at the same position, and the effect of deliberate changes in placement. A single vertical-bar specimen machined from a dimensionally stable and uniform thermoset moulding composition, with good microwave properties but somewhat high dissipation factor, was used. The 3 GHz waveguide cavity with flange joint at the centre was used. Readings alternated between cavity empty and cavity loaded. The vertical bar size was 34 x 12.7 x 3.2mm and fit snugly between top and bottom walls of the cavity. A series of 20 specimen positions were used involving all combinations of five degrees of widthwise offset with four orientations and lengthwise offset. The five widthwise-offset values from the centre of the cavity were:
0.00,
1.52,
3.05,
4.57
and
6.10mm
0.0,
2.1,
4.2,
6.3
and
8.4% of the cavity width
The four orientation variations were: the stability of the signal, not to the accuracy with which the frequency is known. If there is a bias in frequency readings that applies proportionally to all the readings, the error cancels out in the calculation. However, if frequency is unsteady and bias is variable, measurement accuracy will suffer.
(a) Specimen width crosswise and centred over the joint (b) Crosswise and flush with the joint (1.6 mm lengthwise offset) (c) Crosswise but rotated 180" and flush with the joint (d) Specimen width lengthwise in the cavity, centred over the joint
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A vernier caliper was used to verify each location. Each of the 20 positions was used for a measurement. This test sequence was repeated six times to provide six replicated data values for each position taken over a period of time. With each loading, data were collected for the designed 7-node resonance at 3.0 GHz and also for 9-node resonance at 3.47 GHz. Table 15.13
Condensed statistics on reproducibility and sensitivity to position and orientation of a vertical bar specimen in the perturbation-cavity method for K' and D
Attribute for which mean and std. dev. are shown
Std. devs. of six replicate readings of K' at each position
Node number of 7 resonance
9
Means of six replicate readings of D at each position 7
9
The data for K' values showed a pattern of decreasing value as the widthwise offset increased. However, for the four orientations there did not appear to be any pattern. At each offset the standard deviation among the four sets of means for the orientations were remarkably small, more so for 7-node than for 9-node. This is summarised in Table 15.14. The effect of widthwise offset is shown graphically in Fig. 15.17.
-
Std. devs. of six replicate readings of D at each position 7
973
Values wtth 9 node resonance
--
9
A
Mean Std. dev. as % of mean Number of data
-
0.0028 0.0028 0.0066 0.0067 0.00010 0.00005 0.0013 0.0012 0.0002 0.0002 0.00004 0~00002 46 43 3 45 39 20 20 20 20 20 20
Table 15.14 Effect of widthwise offset of vertical-bar specimen in perturbation-cavity: averaging mean K:, values for four variations in
3.10 0.00
With 9-node resonance at 3.47 GHz Mean Std. dev. as % of mean Number of data
0.00
1.52
3.05
4.57
6.10
3.2503 0.0033 0.10 4
3.2424 0.0038 0.12 4
3.2189 0.0036 0.1 l 4
3.1779 0.0050 0.16 4
3.1213 0.0065 0.2 1 4
3.2690 0.0170 052 4
3.2623 0.0180 0.55 4
3.2420 0.0175 0.54 4
3.2068 0.0191 0.59 4
3.1573 0.0191 0.60 4
For all 20 positions there was no significant difference in D values. The standard deviations for the six K' or D values at each position did not show any trends. Overall averaging of these, shown in Table 15.13, indicates generally very satisfactory reproducibility for the perturbation method.
I
I
I
1.52
3.05
4.57
6.10
OFFSET I N nn UF VERTICAL BAR SPECIMEN FROM CENTER OF 72 m n VIDTH
orientation
Widthwise offset, mm With 7-node resonance at 3.0 GHz Mean Std. dev. as % of mean Number of data
Values wtth 7 node resonance
Fig. 15.17
Plot showing effect of widthwise offset from centre of waveguide perturbation cavity for vertical-bar specimen
Table 15.15
Comparison off, and I / Q for an empty waveguide cavity with and without a foam polystyrene specimen support
Nodes Resonant freq., GHz Empty freq., GHz With spacer
5 2386485 2.586387
7
9
11
2.995648 2.995539
3.466802 3.46680
3.977994 3.977860
1061Q Empty cavity
Similar widthwise behaviour is seen with spherical specimens. Another series of measurements was carried out with spheres of four diameters centred lengthwise and widthwise. Vertical offset was varied. Fig. 15.18 illustrates how K',, increases with increasing vertical offset from the centre of the cavity height. A block of very low-density polystyrene foam may be mounted in the cavity
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Advances in substrate technology
Advances in substrate technology
to support the specimen. When this is done the foam should be left in the cavity for the empty readings as well. Empty-cavity resonant frequency a n d Q readings were found to change very slightly when a foam support is in place, as shown by data in Table 15.15.
SPECIMEN DIAMETER, nn 6.31 8 8 6 ................. 11 39 - . - - . - . 1385 - - - - - - - - - - -
Adapted for detailed material tvves
915
Full details
Full details
Not needed
Not
Convenience Skills for preparation
Minimal
Photomasking, etching, cutting
Minimal
Machining
Equip. for preparation
To cut cards etch off foil
Photomasking, etching, sawing size
Trim panels
Special fixtures for spheres
Potential for specimen loss
Very little
High - bad mask or etch
None
Moderate
Skills for
Minimal
Loading fixture
High-mod., automate
High- moderate automate loadine --
Cost Destruction of product W E CLW
I
aC z a w
ao
Fig. 15.1 8
10 OFFSET I N nn FROM CENTER UF VERTICAL 3 4 nn DIMENSION I N 486 x 72 x 3 4 nm WAVEGUIDE CAVITY
15
Plots of KLppversus vertical offsetposition in perturbation cavity for four spherical specimens of differingdiameter
15.2.5 Tabulated evaluation of methods for measuring relative permittivity and dissipation factor Feature evaluated
Stripline resonator
Standardisation Routine use. Standard for K' = 2.15-2.55 Higher K' starting
Less than 645 mm2, locate conveniently
None
Labour for preparation, measurement
Under half hour
Up to 1h
Under quarter- Over 1h hour or less automation
Time from selection to results
About one day
Over one day
About 1h. In-process control
Over one day. Machine-shop help needed
Unlikely
Likely and critical
Unlikely. Rectangular
Moderate
I
5
0
Enough cards 51 x 76 mm for 1.27 or 1.5 mm thick
Small, special type
Microstrip resonator
Full-sheet resonator
Perturbation cavity
Error Likelihood specimen preparation
Spec. 1 user K' near 10
Few cases of user-supplier
Not routine
Detectability of error
Monitor of fixture deterioration
Monitor with reference specimens
Monitor with reference specimens
Dimensionally verifiable
Apparatus deterioration
Fatigue fracture of pattern card Stretching of resonator
Less than stripline
Littlelnone
Self-checking versus cavity
Fairly good
Good vs. microstrip; vs. process, cladding
K' sensitivity Limited exceeds stripline good scale-up
Reproducibility High degree
Fair
Excellent
Correlation among labs.
Good
Acceptable
Very good
Citations in specs.
MIL-P-13949 (12) and users
Two user specs.
1 or more user specs.
Good for sphere No data None
Usefuhess Correlation with application
91 6
Advances in substrate technology
Advances in substrate technology
Orientation of field VS.antenna
Similar
Similar
Similar no X, Y fringing
Vertical bar is poor; Sphere allows control
Sensitivitydissipation factor
Good but includes conductor loss
Variable experience Includes cladding
Radiation at Separates edges obscures dielectric losses
Limitations
Range of thicknesses and types
Limited thickness Limited thickness Wide-range and K' range 0.63 & 1.27mm; thickness, K' K' near 10 for a fixture
Wide-range machinable
Field orientations measurable
Limited to Z
Limited to Z
X, Y, Z for sphere spec.
Frequency range
10 GHz/4-node, 3 GHz could use 2.5, 5.0, 7.5
Limited by specimen dimensions
Practical waveguide sizes, 3-10 GHz
Questionable results
Clear result, monitor fixture
Positioning cover, ground contacts
Critical that Clear result. K' separated modes be unambiguous from magnetic permeability
Substrate thickness range
Single or stacked to 1,2711.57mm
0.6311.27 mrn
Wide range Machined under 2.5 mm sphere is to over 3 mm small versus cavity
Problems of thickness extremes
Fringing correction varies
No account for fringing error
Best when thin versus length, width
LImted to Z
Not applicable
15.3 Processing laminates into antennas The volume of information on processing of printed wiring boards from copperfoil-clad laminates is expanding rapidly. Contributors include technical societies, individual workers and producers of equipment and supplies used in this growing industry. While producers of microstrip antenna boards can use much of this information, they also have special concerns. These include the high cost of substrate materials, safety with PTFE, etch-strain relief, machining, bending boards, bonding assemblies, plating holes and edges. This section is not intended to be a complete guide to processing printed wiring boards, but will address selected topics of value to producers of microstrip antennas.
977
15.3.1 Handling incoming copper-clad laminates Attention to incoming packaging, storage and pre-process handling of clad laminates for microstrip antennas will pay off in improved manufacturing yield. 15.3.1.1 Packaging: Suppliers of clad laminates for microwave applications generally take special precautions to ensure minimal damage from shipping or storage. In addition to a rigid container and compressible spacers in the container, the individual panels are usually specially protected by either thick plastic film with lightly adherent pressure-sensitive adhesive or polyethylene bag enclosure. Tarnish inhibiting paper is often used against the copper-foil surface. Such care is especially needed for PTFE-based substrates which are relatively soft. While shipping containers must be opened on receipt to verify the contents and detect any damage, it is usually most efficient to take advantage of the existing protection for storage until processing is started. Most producers of microwave substrates provide individual panel identification, and should include a serial number for traceability. The user should provide practical means for maintaining panel identity through the process to the final microstrip antenna unit. 15.3.1.2 Storage: Metal cladding of laminated substrates is the feature having greatest susceptibility to chemical damage in storage. Individual packaging of panels provides some degree of protection, but the storage area should have a room-temperature atmosphere free of high humidity, sulphur oxides and other corrosive materials. Small amounts of corrosion can be removed through the cleaning steps to be discussed. Physical-storage hazards to the quality of laminates can be avoided by attention to a few rules. These are particularly applicable to soft substrates such as those based on PTFE. Material in original containers should be stored flat but not stacked high enough to crush the containers. Material removed from containers should be kept in the original bags or protective film to prevent scratches, pits or dents from handling during storage. Panels can be stored on edge to provide easy access to a variety of panels in the inventory. If they are to be stacked horizontally, the shelf should be flat and larger than the panels. Panels of different sizes should not be combined in a single stack. The area should be free of chips and particles that can get between panels causing pits and dents. For PTFE-based laminates, the timeltemperatwe cycle of the manufacturer's laminating process leaves aluminum plate or copper-foil cladding in a fully annealed state that is particularly susceptible to scratches and dents. These materials require greater care in storage and subsequent handling than other substrate types.
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Advances in substrate technology
15.3.2 Handling prior to processing Quality problems in processing can be reduced by attention to some details in handling before the processing begins. 15.3.2.1 Avoid scratches, dents andfinger prints: The initial process steps of shearing, sawing or blanking to size and of forming tooling holes should be done with surface protection present. This can be the plastic film or protective paper used in packaging. Avoid sliding or stacking unprotected surfaces against each other. Use gloves of knit nylon or other non-absorbent material for handling unprotected panels to avoid finger prints, which contain acidic skin oils that corrode copper surfaces. If a dilute-acid bright dip is used to remove visible corrosion, the corrosive oil remaining on the copper surface causes the finger print to reappear hours or days later. Finger prints can be removed by a bright dip in dilute hydrochloric acid with rinse and drying, followed by degreasing in ketone solvent or chlorinated solvent vapours. A second bright dip, water rinse and drying is then used. 15.3.2.2 Remove any adhesive residue: If panels are protected by the lightly adherent thick plastic film, it will need to be peeled off and the surface cleaned just before etch masking is applied. Residual adhesive on the copper surface may be removed by wiping the surface with a soft, lint-free cloth soaked in an alcohol solvent. Isopropanol at 70-100% concentration is preferred for its low toxicity and flammability. Panels that have had long-term or high-temperature storage may require a soak in isopropanol and scrubbing with a soft bristled brush to remove all the adhesive residue. 15.3.2.3 Ensure adhesion of the photomask: Poor adhesion of the photomask through the etching process can occur with no apparent cause. The following procedure has been found effective for avoiding this costly problem: (a) Immerse the board for 5 min in Neutraclean 68 solution* (b) Hold for at least 1 min in each of two successive water-rinse tanks (c) Immerse for 1 min in a 10% by volume solution of sulphuric acid ( d ) Hold for at least 1 min in each of two successive water-rinse tanks (e) Drain the board and allow it to dry in air (f) If dry film is to be applied, preheat the board for at least one hour in an oven set for 125°C. Allow enough time for the rolls on the laminator to stabilise at the required laminating temperature before using it to bond the film to the board. (g) If wet film is to be applied, use a constant speed for withdrawal of the board from the dip tank
* Neutraclean 68 is an aqueous formulation of sodium bisulphite at neutral pH with proprietary additives for removing oxides and contaminants from the copper surface. The supplier, Shipley Company, 2300 Washington Street, Newton, MA 02162, USA, phone 6171969-5500, provides instructins for preparation of the solution.
Advances in substrate technology
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15.3.3 Safety considerations for PTFE-based substrates PTFE is exceptional among plastics materials for its chemical inertness, insolubility, non-flammability, non-toxicity and long-term resistance to thermal degradation. It is such a stable polymer that the tendency may be to assume that no safety precautions at all are needed. At temperatures of 380°C and above, thermal decomposition of PTFE becomes measurable. The decomposition and toxicity of the decomposition products have been studied and reported in detail [27-471. Good summary bulletins are available from the polymer producers [48, 491. There are no reported incidents of which we are aware of permanent human injury from fumes in normal processing. Particulate decomposition products, if inhaled, are believed to be the cause of a syndrome of influenza-like features described as 'polymer fume fever'. Symptoms arise after a latent period of a few hours. The symptoms subside within 24-48 h with no apparent known after effects. PTFE has a limiting oxygen index for flammability of 95% and resists auto-ignition to very high temperatures: 575OC in air, 512°C in oxygen. The toxicity of products from very high-temperature decomposition are more dangerous. The fumes and smoke from a fire containing PTFE can be hig~.,, toxic and corrosive. Hazards peculiar to PTFE-based substrate materials can be encountered in machining processes and in bonding operations at elevated temperature. They are avoided entirely by simple precautions. While PTFE is probably the most inert of all available polymeric materials, it is capable of producing toxic fumes at very high temperatures. 15.3.3.1 Machining hazard: Chips and particles from machining can take an electrostatic charge and be transferred by hands or clothing onto cigarettes and tobacco. Particles in tobacco can encounter temperatures in excess of 1600°C, where they decompose to impart 'fume fever' symptoms to the smoker. Smoking should be prohibited in machining areas and washing of hands and changing of clothing are advised for smokers. Non-smokers do not have this hazard. Dispose of scrap by landfill, putting scrap into bags or boxes clearly marked Do not incinerate. If high temperatures are generated by machining conditions, forced ventilation is advisable. Enough heating to generate fumes or smoke indicates poor machining practice, leading to sub-standard workpiece quality. 15.3.3.2 Fumes from bonding boards: While temperatures normally used for bonding multilayer boards are below 300°C, there is the possibility of a control malfunction or set temperature error. It is good practice to ventilate the press area as a precaution in anticipation of such an event. 15.3.4 Reducing the effects of etch strain relief The lamination of copper-foil-clad panels involves clamping substrate material
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Advances in substrate technology
and metal foil between steel plates, followed by heating the assembly to effect either a thermoset reaction, in the case of thermosetting-resin systems such as polyimides, or a fusing together of components, in the case of thermoplastic polymer systems such as those based on PTFE. In either case the clamped assembly is cooled to room temperature before the clamping force is removed and the clad panels are removed from the press package. During cooling the difference in coefficient of thermal expansion between the substrate and the metal-foil cladding gives rise to internal strain. In addition, there is internal strain associated with the change of state of the substrate material. Thermoset materials tend to shrink when converted from their fusible initial stage to the final fully reacted state. Thermoplastics may undergo a change in degree of crystallinity with associated specific volume change. Thus metal and substrate are strained to dimensions different from what they would be if they were not attached. When some or all of the metal cladding is removed by etching for production of a circuit board, some or all of the strain on the substrate is relieved by a change in dimensions. This characteristic strain-relief behaviour is common to some degree in all clad laminates. PTFE substrates preferred for microstrip antenna boards are laminated at temperatures above the 327OC crystalline melt point of the polymer. This relatively large temperature excursion makes etch strain relief of important concern to designs with tight tolerances on dimensions between features. The process sequence described here is specifically intended for overcoming strain-relief characteristics of glass-PTFE substrates, though the principles may apply to other materials. 15.3.4.1 Metal-foil removal without fiwing feature position: Photomask and etch to a preliminary pattern with oversize features designed to remove at least 90% of the metal foil to be finally removed without precisely defining the location of features. Provide narrow X- and Y-axis centre lines in this preliminary pattern for later alignment. When the copper has been removed, stresses related to the internal strains become unbalanced. If the substrate material were perfectly elastic, the substrate would instantly change dimension to relieve the internal-strain imbalance. However, the visco-elastic nature of the PTFE makes this response time-dependent. The time required for strain relief is reduced at elevated temperature. The mask material is stripped from the board so that subsequent heating does not make it difficult to remove later. 15.3.4.2 Complete strain relief before,fixingfeature positions: Rate of strain relief varies approximately in proportion to the remaining unbalanced internal stress, and is a logarithmic function. Suppose, for lack of precise data, it takes 48 h at room temperature for one half of the strain to be relieved. Allow 96 h for three-quarters relief, 144 h for seven-eighths relief, etc. This hypothetical 48 h
Advances in substrate technology
921
time constant can be regarded as the half life for residual strain. At some later time, further strain relief is no longer practically detectable. About half of the PTFE in the substrate exists as the amorphous phase with visco-elastic control of strain relief. The transition temperature from glassy to rubbery state, T,, of the amorphous phase takes place at about 130°C. Time for strain relief decreases gradually with increasing temperature up to T,, where a greater decrease occurs. Increased temperature does little to change the amount of strain to be relieved, but it does much to reduce the time needed for most of it to occur. Thus oven-heating boards well above T,, e.g., 150 or 170°C, will reduce the time required to 16h or less. Higher temperatures will cause excessive oxidation of the copper foil. The time needed at a particular temperature for strain relief of a given laminate construction and antenna-pattern may be verified by measuring the change between marked locations on a test board versus time. 15.3.4.3 Process to fix feature positions: The X, Y centre lines from the preliminary pattern are used for optical alignment for drilling or punching the registration holes used for the rest of the process. Very little dimensional change is to be expected from here on. Various sequences of steps can be devised to etch the conductor pattern to its final dimensions and to provide other required features such as holes or routed edges. A feasible outline of steps is given as an example. This starts with a board pre-etched as in Section 15.3.4.1 and strain relieved as in Section 15.3.4.2. (a) Drill holes to be plated through. (b) Treat PTFE surfaces with a sodium etch solution for adhesion of electroless plating. (c) Electroless plate all surfaces. This thin deposit is a base for plating in holes, and it electrically connects isolated elements. ( d ) Apply a second photomask and develop to expose holes and other regions to be plated. Then electroplate these areas to a desired thickness. Strip the mask. (e) Apply a third photomask over the final conductor pattern shape to be retained. If a dry film mask is used it will need to bridge over plated-through holes. If wet film is applied by dipping, the viscosity must be low enough to ensure that holes are coated and free of bubbles. Etch away exposed metal, which will include electroless deposit over previously conductor-free areas, as well as extra conductor area left from the first etching operation.
An alternative to steps ( d ) and (e) that avoids a third photomask and the concern for protecting plated-through holes is as follows: ( d ) Apply a second photomask exposing the final conductor pattern including holes to be plated through. Electroplate the exposed areas with copper to the desired thickness. Electroplate a thin layer of tin. Strip the mask. (e) Use an etchant specific to copper to remove all copper from areas not
.
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Advances in substrate technology
protected by the tin plate. Then strip the tin-plate mask using a commercially available tin-stripping solution. 15.3.5 Machining of PTFE-based boards While typical microstrip antennas require little machining, some discussion of the topic with respect to substrates based on PTFE seems worthwhile. Holes are often employed for feeds to microstrip radiation elements. Often microstrip antenna boards are trimmed to size by routing. 15.3.5.1 Generalprinciples: Substrates based on PTFE for microstrip antennas usually contain one of the following in a soft PTFE matrix: For non-woven glass-PTFE: Discontinuous glass fibres of wide diameter distribution, averaging about 1 pm, uniformly distributed in the matrix and individually oriented in all directions in the X, Y plane of the substrate. For woven glass-PTFE: A fabric of glass-fibre strands, where each strand consists of 30 or more continuous glass fibres of narrow fibre-diameter distribution, typically about IOpm. For ceramic-PTFE: Particulate ceramic filler with hardness similar to chrome, uniformly distributed in the matrix and occupying a significant fraction of the volume.
These composites are all capable of rapidly destroying the cutting edge of a steel tool even though the matrix is relatively soft. Carbide cutting tools are recommended, and in the case of ceramic filler are mandatory. Woven glass tends to produce rough edges when routed or drilled. Smalldiameter drills tend to be deflected, reducing hole-location accuracy. Cutting edges of tools must be sharp as viewed under a 30-60 power stereomicroscope. Incidents of rejection as high as 25% in new tool lots have been mentioned. As a radius forms from wear, the cutting mechanism of fracture propagation ahead of the edge degrades to a sliding-tearing action. This rapidly increases edge wear and generates frictional heat which softens the matrix and further reduces the cutting quality. Solid-carbide drills and routers are regularly used in large quantities by the printed-wiring-board industry, and are available from various suppliers. 15.3.5.2 Drilling burr-free holes: PTFE tends to form tough burrs at machined edges that are hard to remove once they are formed. A few precautions assure smooth, burr-free holes: (a) Use entry and back-up boards. Hard phenolic-paper laminates have been found effective. (b) If holes are to be located in areas free of copper-foil cladding, do the drilling prior to etching away the copper.
Advances in substrate technology
923
(c) Maintain adequate clamping force on the stack during drilling to prevent burr formation. ( d ) The exact drill-bit diameter needed for a specified hole size is based on trials. The low modulus of the substrate matrix can result in the hole diameter differing from the bit, depending on drilling parameters such as diameter, board type, drill speed and feed rate. (e) Limit the number of hits per drill bit to a number found by trial to produce good-quality holes.
15.3.5.3 Avoiding 'smear' on hole walls: Smear on drilled hole walls is well known with epoxy-glass laminates, where over-heated tool bits can partially decompose the epoxy resin and redeposit it on the hole wall. Smear interferes with adhesion of the copper deposit to the edge of the substrate and the clad foil in plated-through holes. With PTFE-based laminates smear arises somewhat differently. Excessive heat from a worn tool edge, high drill speed or a plugged flute softens polymer particles so that they can be shear-deformed to a poorly adherent very thin transfer film. The following principles minimise concern about smear. (a) Do not exceed a tool surface speed of 0.76m/s (150ft/min), significantly slower than that recommended for most substrates. (b) Use drill bits with a relatively shallow included lip angle and with a relief along the flutes. An included angle of 130" and a 127 pm (0.005 in) reduction in flute diameter after the first 0.64 mm (0.025 in) length have been found to work well with carbide drills for 0.64mm holes. (c) Use a feed rate for a 50 pm (0.002 in) chip load.
15.3.5.4 Routing edges of PTFE-based substrates: Non-woven glass-PTFE and ceramic-PTFE substrates can be shear cut as in punch and die tooling for remarkably smooth edge finish. For woven-glass-PTFE or for quantities too small to justify special tooling, edges are cut with a routing bit. The following suggestions should be considered in setting up the operation: (a) Select a carbide router bit with single cutting edge that is either straight and parallel to the axis, or a reverse helix so that it tends to push the work against the back-up board. (b) Rout with clad foil forming the edge if possible. (c) Use a rough cut followed by a fine cut to dimension. Tool-axis movement relative to the work follows the cutting edge direction. i.e., for clockwise tool rotation inside edges are cut moving clockwise, while outside edges are cut moving counter-clockwise. ( d ) Keep tool surface speed down to 0.76 m/s (150 ft/min) as for drilling.
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Advances in substrate technology
Advances in substrate technology
15.3.6 Bending etched antenna boards A significant number of microstrip antennas based on non-woven glass-PTFE are formed to a cylindrical shape for missile telemetry applications. The nonwoven glass-PTFE substrate is particularly suited for this application. It can be bent without measurable damage to the microstructure or the mechanical and electrical properties. Three methods are being used to bend antenna boards to the desired radius: use of forming rolls, heating a board clamped on a mandrel and bonding thinner boards together around a mandrel. 15.3.6.1 Forming rolls: Forming rolls are commonly used in sheet-metal work for forming bends with a radius much larger than the metal thickness. The three-roll former has two metal rollers working against a third base roller. The system forms two nips along the circumference of the base roller. When material is fed into one nip so that it is next caught in the second, it is forced to conform to the radius of the base roller. The nips can be opened to increase the radius of curvature producing less conformance. A second type of forming-roll apparatus consists of a metal base roll working against a rubber roll. The rolls are brought together so that the rubber roll deforms along the circumference of the base roll. Material fed into this nip is conformed to the radius of the base roll to an extent which is controlled by how tightly the rolls are pressed together. In either type of apparatus the principle is the same: the material is forced to conform to a radius. If this radius causes the material near its surfaces to exceed the elastic limit of the sheet material, permanent deformation results in a smooth curved shape. When the conforming force is removed, a certain amount of elastic spring back occurs. Thus, to bend a given radius, the material is overbent to a smaller radius, held there for perhaps 0.25 s and then released. The smaller radius could be as small as one-third or one-quarter of the desired final radius. With metals the permanent deformation and spring back are rapid. When the method is applied to a copper-foil-clad PTFE substrate with one side etched to form an antenna pattern, care is needed to prevent deformation damage in the roll-forming operation. The copper on the inner and outer surfaces is forced to accommodate to the opposed changes in length of these surfaces. It is either elastically and permanently deformed by the imposed change or it fractures and buckles. When typical sheet metal is deformed, the deformation almost instantly resolves into permanent and elastic portions. The elastic portion accounts for spring back. For a visco-elastic material as discussed in Section 15.3.4.2, the small instantaneous ratio of permanent to elastic portions of the deformation will increase with time. The instantaneous ratio and the rate of increase are both greater at higher temperatures. Thus the amount of overbending needed in a roll-forming operation may be reduced by pre-heating the board and by lowering the speed of the forming rolls. Heating above the 130°C amorphous-phase glass transition temperature of the PTFE is advised.
I
925
15.3.6.2 Heat forming on a mandrel: A board clamped around a mandrel somewhat smaller than the desired diameter of curvature is held at elevated temperature to allow strain relief to occur. This process is slower than roll forming, but, as should be obvious from the discussion in Section 15.3.6.1, it does not require as great a degree of over-bending. For a given substrate thickness, smaller-diameter bends can be more practically obtained by heat forming than by roll forming. The two processes differ in time and temperature of conformation imposed on the material. A laboratory experiment on heat forming was performed with a 114mm ( 4 5 in)-diameter mandrel and 1.57 mm (0.062 in)-thick non-woven glass-PTFE substrate, RT/duroid 5870 microwave-circuit-board material from Rogers Corporation. The substrate was clad on both sides with copper foil of 34pm thickness (1 oz/ft2 weight). The thickness/radius ratio selected was just less than sufficient to cause immediate board damage when a specimen was clamped to a mandrel. Specimens were etched to leave a narrow conductor trace runing circumferentially on one side, leaving the other side fully clad. Experiments were run with specimens having the trace on the concave and on the convex side. The specimen clamped on the mandrel was held at elevated temperature, cooled, then released from the mandrel and allowed to stand in standard laboratory conditions for 16 or more hours before its curvature was measured.
Table 15.16 Summary of mandrel heat- forming investigation 260 23 177 Temperature, OC ~ i m dh, 24 1 9 1 9 % Retention of curvature Ground-plane concave side 43 77 76 86 85 Ground-vlane convex side 38 73 76 86 87 3 2 1 1 0 Defects in copper*
302 1
9
88 94 5
96 99 4
* 0 to 5 represent subjective ratings of none, slight, few, much and severe Curvature retention was calculated as the ratio of the mandrel radius to the final specimen radius of curvature. Copper-foil damage was also noted. Table 15.16 is an abbreviated summary of the work. For less severe bends, no defects in the copper cladding are expected at forming temperatures up to 170°C for periods of nine hours or more. With protection from oxygen, higher temperatures could probably be used to improve curvature retention without copper-foil damage, but this is not likely to be worth the effort since mandrel size can be adjusted to get a desired curvature at lower temperatures. 15.3.6.3 Bonding layers on a mandrel: The process includes heat forming on a mandrel since heat is used to activate the bond.
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Advances in substrate technology
A microstrip antenna is assembled from two or more boards that are interleaved with bonding film and clamped around a mandrel for a thermal cycle to activate the bonding film. A direct bond procedure omitting bonding film has also been demonstrated and will be discussed in a later Section. Bonding processes follow the principles outlined for flat antennas in Section 15.3.7. A higher thickness/radius ratio can be achieved for the assembly than would be practical with a single board. Curvature retention is very good since the degree of strain applied to the individual layers is low. Any spring back arising from individual layers is offset by the fact that the difference in length between the inner and outer layers is retained by the bond line. This process is often used for microstrip antennas requiring a protective radome. One board carries the ground plane and antenna pattern. A second board is etched free of copper foil and bonded to the first in the curved shape. Where very high thicknesslradius ratios of curved antennas are needed, several boards can be combined in an assembly so that the innermost board includes the ground plane and the outermost board, not counting an optional radome cover, carries the anntena pattern. 15.3.7 Bonded-board assemblies
The use of bonded assemblies for stripline applications has almost completely displaced clamped assemblies for the obvious advantages of size, weight, imperviousness and long-term performance stability. The topic is discussed here because it affords the only practical means for environmental protection in many microstrip antenna applications. Bonded assemblies are also finding use as the means of integrating the antenna into a compact system, including devices such as feed networks built in stripline. Properly built bonded-circuit-board assemblies resist moisture or other contaminants that degrade long-term performance. 15.3.7.1 Selection of a bonding system: A variety of possibilities exist for
producing a bonded assembly. With PTFE-based substrates, boards can be clamped together and direct bonded by heating the assembly above the crystalline melt point of the PTFE, so that the substrate material itself acts as the adhesive. For most substrates, the boards to be bonded can be interleaved with bonding film or 'prepreg' and heated while clamped to activate the bonding action. The options for clamping and heating include the use of a platen press or the use of vacuum-bag moulding techniques in a pressure vessel. In selecting the bonding system many factors need consideration. If the boards to be bonded already have mounted components or soldered joints, low bonding temperatures must be used. If substrates to be bonded are based on PTFE then provision is usually made for the surface treatment to enhance the bond. The bonding options may be limited by the availability of a suitable platen press or heated pressure vessel for vacuum-bag moulding, and its tem-
927
Advances in substrate technology
perature capability. The bonding system must be serviceable at least to the maximum application or storage temperature expected. Bonding material should match the substrate's relative permittivity. Low dissipation factor is usually important as well. Compatibility of the temperature needed to activate the bond with the application environment must be considered. A comparison of advantages and disadvantages of several types of bonding systems may help to put them in perspective. The bonding systems discussed here fall into three categories: thermoplastic films, thermoset systems and direct bonding. Thermoplastic films of practical value for bonding include, among others, low-density polyethylene (LDPE), irradiated polyolefin (IPO), chloro-fluorocopolymer (CFP), and fluoropolymers such as poly(tetrafluoroethene-co-hexafluoropropene) (FEP). These bonding films will fail in service if the melt point is exceeded. Low dissipation factor and permittivity values nearly matching the glassPTFE substrates make them useful materials for bonding. If ultrasonic scan testing of an assembly indicates bond defects, thermoplastic film offers the advantage of repairability; i.e., a second bonding cycle can be effectively run to pass inspection before processing the board further. Generally, for thermoplastic films a dwell time at bonding temperature of 15-20 min is sufficient. The clamp stress needed for a suitable bond depends on the board and copper pattern thickness, the fraction of area occupied by conductor pattern and the rigidity of the boards being bonded. Adequate clamp stress levels can range from 170 to 1380 MPa, and need to be determined by trial for a given part. Characteristics of the films mentioned are summarised in Table 15.17. Table 15.17
Thermoplastic bonding films
LDPE IPO* CFP Film type 200 110 Melt point, "C 2.35 2.3 2.3 Relative permittivity 0.0028 1 04)02 0.0005 Dissipation factor Bond temperature, OC 120 121-149 220 * Irradiated polyolefin co-polymer from MPC, Inc., Lowell, MA 01854, USA
't
FEP' 260 2.1 0.0003 280
Teflon FEP fluoropolymer film from the Du Pont Co., Wilmington, DE 19898, USA
Thermoset resin systems may be used where higher dissipation factors can be tolerated. Microstrip antenna assemblies have been bonded with two-part liquid-epoxy adhesive systems at modest clamp stress and with unsupported films of thermosettable resin. In some cases, a prepreg of woven glass fabric saturated with an epoxy resin or a polyimide precursor resin system could be used, especially for attaching the antenna to underlying circuit boards. Thermosets have the advantage of developing heat resistance to above the
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Advances in substrate technology
bond temperature used. In contrast, thermoplastics are bonded at a temperature well above the melt-point limitation to heat resistance in service. In general, the parts to be bonded are interleaved with the thermoset system, clamped, then heated to a set point and held long enough to accomplish the cross-linking reaction in the resin system. The clamped assembly is then cooled. Oven baking after assembly may be desirable to further advance the degree of cross-linking. A few systems are summarised in Table 15.18. Table 15.18 Thermoset bonding materials Form Film Film Prepreg Prepreg Resin system Epoxy* Not givent ~ ~ o x y : Polyimides Relative permittivity 3.76 1 MHz 4.0 1 MHz 4.35 4.25 Dissipation factor 0.064 0,027 0.027 0.014 Temperature, OC 171 171-191 171-177 215-221 Pressure, MPa 0.7-1.4 1.4-2.8 1.7-2.8 2.8-4.2 Time. min 45-60 30-45 45 240 * Poly-Cast EP from Fortin Laminating Corp., San Fernando, CA 91340, USA
' Pyralux WA/A from the Du Pont Co., Wilmington, DE 19898, USA
:Information and prepregs from Norplex Div. of Allied-Signal Inc., La Crosse, WI 54602-1448, USA
Direct bonding, also referred to as fusion bonding, is feasible with substrates based on PTFE. It takes advantage of the very high melt viscosity characteristic of PTFE; i.e., when PTFE is heated above its 327OC crystalline melt point, it continues to behave as a solid and will resist flow at low stress values. Contacting surfaces of PTFE in this melt state will intermingle at a molecular scale to form a fused joint. A melted PTFE surface contacting a clean copper surface will wet the surface to form a bond. Direct bonding affords several advantages. The low dissipation factor or the dielectric constant of the substrate are not compromised by a layer of bonding material in the assembly. The PTFE surfaces to be joined do not need any special treatment to ensure adhesion. The heat and environmental resistance of the assembly is fully equivalent to the substrate material. Direct-bonded assemblies of PTFE can be functional above 3 15°C. Direct bonding has the disadvantage of requiring equipment operable at much higher temperature, up to 388OC. The assembly must be clamped at a well controlled low-level stress in a way that will not increase stress from thermal expansion. Air must be excluded from the assembly during the temperature cycle to avoid oxygen-accelerated thermal degradation of PTFE. 15.3.7.2 Preparation for bonding: Board surfaces to be bonded should be free of contamination, including complete removal of the etching mask. For PTFE-based substrates the area exposed by etching away the copper foil has a textured surface formed by the nodular finish of the copper foil's adhesion
Advances in substrate technology
929
promoting treatment. It is important to preserve this finish for good bond results. Avoid any mechanical scrubbing or rubbing. If possible, boards should be stored in racks and used in the bonding operation as soon as possible. The precautions are not needed when direct bonding is used. For PTFE boards, surface treatment is performed to enhance the bondability. Some users are treating the boards with commerically available sodium etch solutions. The alternative is the use of plasma etching with oxygen and fluorocarbon gas. Plasma etching is becoming a popular process for de-smearing drilled holes in mutlilayer circuit boards of woven glass-epoxy resin laminates. Several companies are supplying plasma de-smearing equipment for the printedwiring-board industry. Either process should leave the surface to be bonded water wettable; i.e., water poured on the surface and drained off will form a film rather than draw up into droplets. Neither treatment is needed for PTFE substrates if direct bonding is to be used. A word of caution concerning plasma etching for bonding is in order. While plasma etching has been successful in plated-through holes where wettability and not bond strength is the major issue, it may be less successful for bonding. There is a suspicion that some plasma-processing conditions not only produce wettable polar groups on the I T F E surface but also attack carbon-carbon bonds. This chain-scission effect forms a weak surface layer of reduced-molecular-weight polymer, yielding a poor bond. Surfaces of PTFE boards etched free of copper and awaiting bonding should be protected from ultra-violet-light exposure during storage. Even fluorescent overhead lighting is sufficient to render the treatment non-wettable by water after a few days. Bonding should be carried out soon after treatment-8 h for plasma-etched surfaces and within 48 h for sodium-etched ones. 15.3.7.3 Bonding in a heatedplaten press: Platen-press equipment is usually more commonly available and a less costly investment than equipment for vacuum-bag processing in a pressure vessel. The boards to be bonded are positioned in a tooling-plate fixture with alignment pins and then subjected to clamping force during the heating-cooling cycle in the press. Aluminum tooling plates are usually preferred for the fixture because the high thermal conductivity greatly improves temperature uniformity across the bonding area, and makes up for some degree of non-uniformity in heating of the plates as well as unevenness of heat transfer from platens to fixture. The work is constrained between the planar surfaces of the fixture, so that the adhesive layer is required to flow in the plane of the boards away from areas with conductor pattern to areas without conductor pattern where there is more space between boards to be filled. If an inadequate quantity of bonding material is used there will be void areas. When the thin layer of bonding material melts it becomes a lubricating layer capable of allowing slippage between boards if the clamp pressure is uneven. In the case of direct bonding where no bonding layer is used, the board
930
Advances in substrate technology
material itself will be required to move. Since the board thickness relative to the total thickness difference from the presence of conductor patterns is large, this movement is very slight compared to that required of a bonding film. The method avoids any slippage between the layers to be bonded. Use a press with flat parallel platen surfaces that has adequate heating and cooling capability. For higher temperatures the edges of the press platens should be provided with high-temperature thermal insulation to prevent uneven platen heating due to excessive radiation losses from the edges. When boards for bonding are laid up with bonding material in the toolingplate fixture, it is good practice to provide a layer of thin aluminum foil as'a disposable separator sheet between the fixture surfaces and the boards. In the case of direct bonding, air must be excluded from the work. This is done by enveloping the work in 50-100pm-thick aluminum foil. The edges of the foil envelope are closed by folding them over twice and rolling the folds into tight creases. A nitrogen purge in the envelope is desirable. A whitened appearance of the PTFE substrate or corrosion of the copper surface are evidence of failure to protect from air. A series of board assemblies may be bonded in the same lay up by providing interleaving plates between assemblies. Too many assemblies in a stack may impair temperature uniformity, so that a compromise is needed for the optimum productivity. It is critical to provide for frictionless relief of expansion of the work in the press during heating to avoid damage from build up of clamp stress. 15.3.7.4 Bonding with vacuum-bag moulding equipment: The boards and bonding material are assembled for a single assembly on a single-plate tooling fixture placed on a flat metal plate of larger area. The plate is fitted with a vacuum line. Usually grooves are provided on the plate in the fixture area to aid evacuation. A barrier film is draped over the work and attached to the plate with a high-temperature pressure-sensitive adhesive strip. Barrier films and adhesive strip are commercially available as hightemperature bag-moulding supplies. The major application is in construction of composite airframe parts. When a vacuum is drawn, the barrier film will draw down to the plate. This assembly, including vacuum connection, is enclosed in a pressure vessel provided with a heater and circulation system. Inert gas such as nitrogen or carbon dioxide is used to provide both clamping stress and heat transfer to, and later from, the plate and bonded boards. With suitable fixtures, bonded boards of non-woven glass-PTFE can be prepared with a curved shape. 15.3.7.5 Bonding of curved shapes clamped on a mandrel: The reader is referred to the discussion of bending in Section 15.3.6.3. Microstrip antenna boards based on non-woven glass-PTFE substrate are combined with a cover board or
I I I
1 1 I I
I
I
i
I I
~ I
I
Advances in substrate technology
931
radome of the same substrate material to form antennas conforming to the fuselage of a missile or piloted craft. Many of these units serve for telemetry on missiles. A preferred method uses a cylindrical mandrel that is hollow in order to keep the heat capacity down to reduce the time and energy needed for the heating and cooling cycle. Aluminum is a desirable mandrel material. Its low density facilitates handling and the high thermal conductivity tends to ensure uniform heating. The higher thermal coefficient of expansion of aluminum compared with the clamping hardware ensures a clamping force during the heating of a bonding unit. The microstrip antenna pattern is masked and etched on the board while it is still flat. In some cases the board layers to be bonded are cold-formed to the curved shape as discussed in Section 15.3.6.1 in order to ease layup on the mandrel. The layers and interleaving bonding material are positioned around the mandrel. Usually a disposable thin sheet of aluminum foil is placed between the mandrel and the first layer to ensure release after the bonding cycle. Any of the bonding materials mentioned in Section 15.3.7.1 may be used. In at least one instance, a two-part heat-resistant epoxy-resin system was mixed and applied to the first board with a hand-held spreading tool. The excess epoxy resin was allowed to flow out of the edges when the assembly was clamped and heated. Over the outer board an outside release foil is applied. Over this is placed a curved sheet of stiff sheet metal, such as a 0.5 mm (0.020 in) thick stainless-steel strap, with a screw mechanism for applying tension circumferentially. The stiff sheet metal distributes the clamping force evenly to the work. In another arrangement a series of screw and nut connections between ends of the wide strap provide circumferential tension on the strap. This tension, provided either by a series of narrow stainless-steel straps or by take up on the wide strap itself, resolves itself into a stress normal to the mandrel circumferential surface. If the screw and nut connections are replaced by an extended threaded rod and a steel compression spring mounted on the rod, tension applied by tightening the nut will also compress the spring and provide a mechanism for adjusting to thermal-expansion differences. The assembly of curved boards and clamp straps around the mandrel is placed in a forced-circulation air oven. The oven is programmed through a heating, dwell and cooling cycle to activate the bonding layer. A technique has been demonstrated for directly bonding non-woven glassPTFE substrate boards into a curved microstrip antenna-radome assembly capable of remaining functional as a telemetry antenna for a short time at or above the PTFE crystalline melt point of 327°C under frictional heating of hyper-velocity flight. The apparatus and procedure are described here as an example of a feasible process. The material used was RTtduroid 5870 non-woven glass-PTFE microwave laminate from Rogers Corporation. A microstrip patch array with a distribu-
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Advances in substrate technology
Advances in substrate technology
The last assembly was retained and sectioned for analysis of thickness uniformity, substrate-specific-gravity uniformity and quality of bond of the cover board to the top surface of the copper-foil patch areas. Seven locations evenly spaced around the curved assembly were examined at seven positions across the width for a 49-point analysis. No failures of the bond were found between the cover board and base or between the cover board and copper-foil surfaces. Thickness uniformity over the points measured had a standard deviation of 1.3% of the mean. Specificgravity standard deviation was 1.0% of the mean. The oven used lacked adequate radiation shielding between the electric-heater elements and the mandrel assembly, which probably created considerable temperature non-uniformities. The rolled-steel mandrel was not finished to a true cylinder. A thicker and somewhat narrower steel strap would have better resisted stretching to provide more even stress across the width of the boards. It is believed that improvements of these features would greatly improve uniformity of thickness and specific gravity, although the initial efforts yielded quite good results.
edge. Such a defect can arise when abrasive scrubbing or other metal-removal methods are used on a drilled board, presumably to remove metal burrs. Substrates based on woven-glass fabric with concentrated fibre bundles produce edges and hole walls that characteristically have fibre bundles extending out of the matrix. The remedy for this has been to etch the extended fibres back with hydrofluoric acid. Such a treatment corrects the rough surface, but tends to penetrate into the exposed fibre-bundle ends, making them vulnerable to absorption of corrosive reagents from later board processing. 15.3.8.2 Wettability of surfaces to be plated: If copper deposition is to be made on hole walls and edges of a board by the usual wet-processing techniques, it is essential that the surfaces be wettable. For most substrates other than PTFE this wettability is attained with the process steps and reagents conventionally used in the printed wiring industry. PTFE substrates require special surface preparation to promote wettability either by sodium etching or by plasma etching. These were discussed briefly in Section 15.3.7.2. When edges or holes are plated on boards that have been bonded with a thermoplastic fluoropolymer film, it is particularly important to ensure that the exposed edges of the bonding film are also wettable.
15.3.8 Plating through holes in microstrip antenna boards Very often microstrip antenna designs require an array of microstrip radiating elements to be connected electrically to feed lines at a lower level, e.g., a stripline distribution network on a level below the ground plane. A plated-through hole (PTH) is usually the preferred way to accomplish this in a production run. Plated edges may also be used in some cases. If done properly, this provides consistent performance with minimal labour. I
15.3.8.1 Quality of edges and hole walls for plating: Attention is needed for several types of hole-wall and edge defects that contribute to faulty PTHs and edges. Some of these can be avoided by precautions in drilling and other machining steps discussed in Section 15.3.5. Smear, a non-adherent layer deposited during drilling, can interfere with the attachment of plated copper to the edges of clad copper, a defect that acts as a stress riser to induce metal failure with thermal shock or exposure to stress. Protrusions from the edge, such as burrs, can have a similar effect. A less obvious defect causing failure in thermal stress and shock tests is a stepped hole or stepped edge. The machined edge of the clad copper does not align with the machined substrate edge. Heating and excess sideways force from a cutting tool deflects the substrate, which recovers after the tool is removed. When plating is deposited over a stepped edge it tends to form a smooth radius. The thickness of metal drops to a minimum at the protruding corner of substrate. This thinned region is a stress riser during thermal shock or stress, which leads to a fracture. A similar effect results from a hole or edge where the thickness of the clad copper is reduced at the edge. In a microsection it appears to taper to a knife
935
15.3.8.3 Electroless copper deposition: Through-hole and edge plating of adherent copper requires a layer of electroless copper, either to the required thickness or thick enough to provide the conductive base for electroplating more copper to the final thickness. The deposition of electroless copper from a copper-formaldehyde solution of carefully controlled stability is usually initiated on a surface by a layer of colloidal palladium particles previously deposited from a commercially available aqueous 'catalyst' solution. One common problem encountered in through-hole plating is the occurrence of voids or open spots in the hole wall. They can arise from several causes. If the process is not started with suitable reagents for cleaning and conditioning the surface, subsequent depositions will fail to attach. Air bubbles can be trapped in the hole during some process steps, particularly the catalyst treatment. An excessively heavy deposit of the catalyst, by overheating, long immersion time or high concentration, results in a non-cohesive deposit that can later break away after the initial electroless copper is deposited. Inadequate use of the accelerator can result in tin contamination that will inhibit electroless copper deposition. Several electroless systems are available from various manufacturers that should provide adequate plating if the instructions are followed. The rinses between reagent baths cannot be over-emphasized. They are needed to prevent carrying the reagent from one bath to subsequernt baths. If such contamination does not destroy the performance of the process it certainly impairs its quality. De-ionised water for rinses is recommended as a way of maximising the life of reagent baths.
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Advances in substrate technology
937
15.3.8.4 Electroplating: A large body of information is available in the literature and from plating-system suppliers on the electroplating process for applying copper to edges or hole walls in printed-circuit boards. Ductility is of special concern with glass-PTFE substrates. All microwave printed-circuit-board materials based on PTFE with woven or non-woven reinforcement share the characteristic of a high Z-direction (thickness) thermalexpansion coefficient compared with copper. The high thermal expansion of PTFE is enhanced in the Z-direction when constrained in the X- and Y-axes by reinforcing fibre. This puts strain on the plated copper during soldering or other assembly operations. Further cyclic strain can occur on the finished printedcircuit board in service. If copper ductility is low, the strain of thermal mismatch leads to fracture failure of plated-through holes. Special care is needed in electroplating to maintain ductility. Excessive brightener additives and contamination, carried in with the boards being plated or from degradation of the organic additives in the plating bath, induce low ductility. Frequent testing of the bath for composition, and of ductility of test deposits on polished stainless-steel plates, is required. Copper-plating baths fall into four general classifications: copper cyanide, acid copper, copper pyrophosphate and copper fluoborate. While the cyanide bath offers the best ductility, it is deficient in throwing power and in its tendency to attack most resist films, which discourages its use in printed-circuit manufacturing. Copper pyrophosphate has been used primarily for circuits, but requires careful control. Acid copper seems to be gaining popularity for circuit boards.. Copper-fluoborate systems are seldom specified because of poor throwing power and the tendency towards non-uniform plating thickness.
Cold peel tests at 90" angle were run at standard laboratory conditions after specimens were floated on solder for 30 s at a series of temperatures. Hot peel tests at 90" angle were done with the specimen immersed in the solder. In both cases the test was run at a speed or 045ms-' (2inImin). For the shear test the peel strip was separated from the substrate at its narrow end by exposure to a flame to destroy bond. It was then peeled back to the 6.35 mm-square pad which remained bonded. The pad end of the specimen was immersed for at least one minute in the solder at temperature. The force on the peeled strip required in a direction parallel to the specimen surface for shear failure of the bond of the pad was measured. This test was intended to simulate the effect of sideways force applied to circuit elements on a board during component attachment. The data are summarised in Table 15.19. In all cases the solder provided shielding from ambient oxygen during heat exposure. Exposure to temperatures approaching the 327°C PTFE melt point does not damage the peel strength if the specimen is allowed to cool without applied stress. Peel strength at ttmperature, while decreasing with temperature, is measurable up to at least 260cC. Shear strength at temperature decreases with heating, but persists to near the PTFE melting point. This indicates that, with protection from ambient oxygen in air and care to avoid shear or pulling forces, one can use high temperatures to attach components.
15.3.9 Device attachment to microstrip antenna substrates Integration of active devices onto the same board as the microstrip antenna offers advantages in space, weight and performance for many applications. Many of the methods for making the electrical connections from the device to the substrate were developed for use with ceramic substrates. Substrates based on other materials either become soft at the temperatures used and/or can be damaged by deformation, loss of adhesion of conductive circuit elements, or thermal degradation.
Peel, N/mm width cold/30 s float
2.59
2.59
2.59
2.59
2.22
2.08
1.10
1.12
Immersed in solder
0.94
0.56
0.28
0.14
0.02
0.00
0.00
0.00
Table 15.19 Heat effects on conductor adhesion to PTFE substrate
'
15.3.9.1 Effect of heating on conductor bond with PTFE: A study has been carried out on the effect of heating on conductor adhesion for PTFE-based substrates. The work was performed with RT/duroid 5870 non-woven glassPTFE substrate clad with 34pm-thick (1 oz/ft2 weight) electrodeposited-type copper foil. Similar results should be expected for other PTFE substrates. A series of 76 x 76 mm (3 x 3 in) specimens were taken from a single sample of 1.57 mm (0.062 in) thick laminate. Each was masked and etched to provide several 3.18 mm (0.125 in) wide peel-test conductor lines having a 6.35 x 6.35 mm (0.25 x 0.25 in)-square pad at one end.
Solder temp.
Shear N16.35 mm square immersed in solder
OC182 OF360
71+
204 400
71+
232 450
71+
260 500
57
288 550
36
316 600
28
343 650
28
371 700
7
(1) Cold-peel failure up to 288°C was into the substrate. All other peel failures were between foil and substrate. (2) The cold-peel value for material not floated on solder averaged 240N/mm width with failure into the substrate. (3) The 71 + N hot shear values represent breakage of the 118 in copper-foil strip used to apply force to the pad.
15.3.9.2 Various lead bonding methods: Several lead bonding methods are briefly described here to provide some definition of terms. The methods employed to achieve low-resistance electrical connections and good mechanical integrity fall into one of the two categories of welding or diffusion bonding.
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Advances in substrate technology
Fusion-welded bonds are formed when metals of the lead and circuit board are melted to resolidify upon cooling. A variety of techniques are available. Resistance welding is done by pressing the lead and circuit conductor together, and passing a high electric-current pulse between them to momentarily melt metal at the contact points. Parallel gap welding is a variation of resistance welding where parallel electrodes with a gap press the lead to the conductor so that heat from a high-current pulse is conducted to the contact. Percussive arc welding uses R F energy to initiate a pulsed DC arc between lead and pad, which are then forced together to weld. Electron-beam welding focuses high-energy electrons in a vacuum at the clamped lead and conductor to heat and weld them together. Laser welding uses the energy of a laser beam to do the heating without the need for vacuum. Solder reflow uses either localised or general heating by infra-red or air oven to melt layers of low-melting alloy which were previously plated onto both the lead and the circuit conductor. Diffusion bonding depends on solid-state metal-diffusion phenomena to join the lead and circuit conductor without the temperature ever reaching the melt point. Ultrasonic welding uses ultrasonic energy to rub the surfaces together. Friction from this cleans and heats the surfaces so that diffusion below the melt point is induced. Thermal-compression bonding uses heat and pressure to force cleaned surface of the lead and circuit-board conductor together for diffusion to occur. Thermosonic bonding combines ultrasonic and thermal-compression bonding by pre-heating the parts before use of ultrasonic energy. 15.3.9.3 Lead bonding to PTFE-based substrates: Ultrasonic wire bonding, thermosonic bonding, parallel-gap welding, thermal-compression bonding and solder re-flow are effective with PTFE-based microstrip-antenna substrates. Ultrasonic wire bonding using a 25 pm (0.001 in)-diameter wire of aluminum alloyed with 1 % silica can produce bonds of no less than 39 mN (4 gf) and typically 54 mN against copper conductors with or without pumice scrubbing beforehand. The abrasive oxide on the wire seems to aid in the rubbing action to clean the surfaces. This can be done without distortion of conductors or the dielectric substrate. Thermosonic ball bonding uses a gold wire in a capillary stylus. The protruding tip of wire is formed into a ball by flame heating. The ball forms a nail-head shape when pressed and ultrasonically rubbed against the preheated gold-plated conductor surface to form the diffusion bond. Preheating is to 200°C with 25pm-diameter gold wire. The stylus moves to the next connect point to make a joint, after which the wire is cut. Gold plating is needed because gold is not able to break through the thin oxide layer on copper that exists at the preheat temperature. If the gold is plated directly onto the copper the copper can bloom to the surface and interfere with bond. A nickel strike coat before 2-5 pm of gold is plated prevents this. Some deformation of conductor and substrate may occur. Parallel-gap welding of 13 x 51 1 pm (0.0005 x 0.002 in) gold ribbon leads
Advances in substrate technology
939
with typically IOOA current for 04-1.3 s produced bonds averaging 343 mN (35 gf) when the copper conductor is cleaned first. Machine settings are possible to avoid distortion of the substrate or conductor. Plating on the circuit-board conductor would improve the bond. Thermal-compression bonding uses a resistance-heated stylus and just enough pressure to get good contact without distortion. Very clean surfaces with gold ribbon and gold-plated circuit conductors are necessary for suitable results. Solder reflow is effective with the tin-lead plated alloys widely used in the printed-wiring-board industry. Low-melting-point solders based on indium are effective where severe process-temperature limitations exist. The device lead and circuit-board conductor are both plated. A resistance-heater head can be used in a parallel-gap welding machine to form bonds and hold them until they cool to get good-quality bonds.
15.4 Design considerations with selected materials This Section offers a few selected topics for consideration in microstrip antenna design which particularly pertain to substrate materials. There is potential for degradation of performance from substrate changes in the application environment. Conductor losses become increasingly important at higher frequencies. The use of multilayer circuit-board technology offers potential benefits in space, weight and cost. 15.4.1 Environmental effects on antenna substrates Environmental effects of space, temperature change and weather exposure can impair performance by changing critical substrate properties. 15.4.1.1 Effects of space environment: Two environmental factors peculiar to space and affecting design are vacuum outgassing and radiation exposure. 15.4.1.1.1 Outgassing: Many materials lose mass in the form of gases or volatile condensable matter when subjected to a vacuum, especially when they are heated, as is likely for an antenna exposed to sunlight in space. Excessive mass loss degrades the ability to control the space vehicle. If the material is condensable on a cooler surface, then, in a space environment, critical areas of a vehicle can become contaminated as well as experiencing a change in the mass of various parts. Non-woven glass-PTFE and ceramic-PTFE substrates have outstanding resistance to outgassing in space applications according to compiled test data [50] (see Table 15.20). This would be expected of PTFE-based substrates generally, since the PTFE polymer is highly stable thermally and any volatiles would be driven off during the high temperatures encountered during manufacture.
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Advances in substrate technology
Advances in substrate technology
Test data shown in Table 15.20 were obtained on specimens etched free of copper foil. The test procedure [51] consists of vacuum heating 100-300mg specimens in a copper enclosure, with the exit port at 125OC, for 24 h while a chrome-plated collector, located 12.7mm from the exit port, is maintained at 25OC. The total mass loss (TML) and the collected volatile condensable materials (CVCM) are expressed as a percentage of the original specimen mass. In general, materials with TML over 1.0 or CVCM over 0.10 should be avoided in spacecraft applications.
Table 15.20 Outgassing data Substrate type Product name Nominal K' ASTM E 595 test % TML % CVCM
Non-woven glass-PTFE RT/Duroid 5870 2.33
Non-woven glass-PTFE RT/Duroid 5880 2.20
0.05 0.00
0.03 0.00
Ceramic-PTFE RT/Duroid 6010 10.5 0.03 0.00
15.4.1.1.2 Radiation: Exposure to high-energy radiation is an important factor in space applications. Cosmic radiation is similar to nuclear radiation in many respects. It can damage materials after the prolonged exposure typical of a space-vehicle mission. For PTFE-based substrates the component most susceptible to nuclear-radiation damage is the PTFE itself. Several investigations of the resistance of PTFE to nuclear radiation have been reported [52-581. Primarily, radiation of PTFE reduces molecular weight by chain scission. Low cohesive forces between PTFE molecular chains require that the polymer have very high molecular weight to exhibit polymer-like mechanical properties. Thus PTFE ranks poorly in ability to withstand nuclear radiation. While this sounds very unfavourable at first glance, the other feature of space environment, vaccum, tends to reduce the problem. Oxygen is essential to many of the radiation-induced scission reactions. Its absence in vacuum reduces the damage or delays the effect of the damage. Molecular-weight reduction of PTFE principally affects mechanical properties, increasing brittleness and reducing tensile strength, modulus and extensibility. Mechanical changes in PTFE appear to depend on the total radiation dose and to be independent of dose rate (see Table 15.21). Radiation affects dielectric properties by embedding an electrical charge in the PTFE, which decays with time. Thus dose rate, not total dose, is important to electrical performance. During irradiation the permittivity and loss factor at lower frequencies will be temporarily increased. This effect is lower at the elevated frequencies of interest in microstrip antenna applications.
941
The degree to which PTFE is affected by radiation is essentially a function of the amount of energy absorbed, regardless of the identity of the radiation; i.e., p, y, X-rays, etc. have about an equivalent effect. The radiation dose unit usually employed in radiation studies is the rad. I rad equals IOOergs/gm. A dose rate of 10rads/h is often given for the Van Allen radiation belt. At this rate PTFE could operate for 5-50 years before a threshold-level damage would be detectable mechanically.
Table 15.21 Summary of radiation dosage versus damage to PTFE Rads in vacuum Rads in air (2 to 7) x 10' or more (2 to 7) x lo4 Threshold damage level lo7 or more 50% tensile strength 1O6 lo7 or more 8 x 10' or more 40% tensile strength (2 to 5) x lo6 (2 to 5) x lo5 Retain 100% elongation Since the primary function of microstrip antenna substrates is electrical, with mechanical support usually provided by metallic components, the exposures cited above can be expected to be well below the point where electrical performance is impaired. The resistance of PTFE to radiation damage is generally better than that of solid-state electronic devices such as transistors and diodes. 15.4.1.1.3 Weathering: The features of low profile and conformability that distinguish microstrip antennas also make them candidates for outdoor applications. Thus they are exposed to varying degrees of moisture, temperature and ultra-violet radiation that constitutes weathering. Many polymer systems are badly affected by weathering. Polymer-chain scission occurs from ultra-violet-activated free radical mechanisms, from hydrolysis in hot and wet conditions, or from a synergistic interaction of both. Thermoplastic materials generally become brittle, develop porosity, and exhibit surface crazing that serves to increase vulnerability. Thermoset materials usually show an increased tendency to absorb moisture as the quality of the interface between resin and filler particle breaks down. Woven-glass-fabric reinforced substrates show wicking effects as moisture follows polymer-glass interfaces along continuous fibre multi-filament strands. The wet/dry cycling tends to promote dissolving of components from glass or mineral fillers. Compared with the rather mediocre rating PTFE has earned for resistance to nuclear types of radiation, PTFE-based substrates show very good resistance to weathering. The extremely hydrophobic nature of PTFE, combined with the absence of low-energy bonds or hydrolysable groups in the polymer itself, account for this. PTFE-impregnated glass fabric is well known for its long-term weathering resistance as the roof material in inflatable buildings, and as a protective radome for steerable microwave antenna systems. Non-woven glass-
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Advances in substrate technology
PTFE is especially resistant to long-term moisture penetration owing to the discontinuous nature of the glass-fibre reinforcement. As manufactured, PTFE-based substrates have colour ranging from light tan to dark grey. This is attributed to trace quantities of organic materials which have been partially decomposed at the high processing temperatures used in PTFE-substrate manufacture. Weathering tends to bleach the substrate. This visible effect of weathering is not accompanied by any measurable degradation of properties, however. 15.4.1.2 Temperature exposure: The effect of temperature on electrical properties of the substrate must be taken into account. Some microstrip designs are more sensitive than others to a change in K' of the substrate. With PTFE, the effect unfortunately includes a change in the R value at the 19OC secondorder crystalline phase transition discussed earlier. Various schemes have been devised to handle this effect. The stripline-resonator method of Section 2.1 and a modified version of this method have been used to collect data on the variation of K' with temperature for PTFE-based substrate materials. The stripline-resonator test is a precise observation of propagation velocity along a stripline, which is then converted to a K' value. Since propagation of signals in stripline is TEM, the thickness change in the substrate under test does not directly affect the test result. For PTFE-based substrates the thermal change in the observed value of K' appears to be explained primarily by the thermal change in density. The situation is somewhat different for microstrip. The effective K' of microstrip is related not only to the K' of the substrate but also to the frequency and cross-sectional geometry of the transmission line. Thus thermal variation with temperature of microstrip characteristic impedance and propagation velocity is not only related to thermal variation of K' but also to thermal variation of thickness. Table 15.22 for non-woven glass-PTFE and Table 15.23 for ceramic-PTFE were generated as an example of the expected response of microstrip transmission line to temperature change. The microstrip data are derived from known test data on the Z-direction (thickness) expansion and stripline dielectric-constant/temperature relationship. The known thickness and stripline dielectric-constant data at various temperatures were interpolated for the temperature increments in the Table and then used for the microstrip-transmissionline designs shown. The analytical formulas of Hammerstad and Jensen [59] were used for the microstrip calculations. 15.4.2 Conductor losses at millimetre-wave frequencies Even with low-loss PTFE-based substrates, the dissipation factor of the dielectric becomes an important contributor to attenuation of signals on transmission lines in either stripline or microstrip from about 0.5 GHz upwards. Somewhere
Advances in substrate technology
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between 10 GHz in X-band and the 35 GHz start of the millimetre-wave frequency spectrum, the losses associated with the conductor become the major contributor to transmission-line attentuation. Table 15.22 Predicted thermal change in thickness, Ki,, and Z, of stripline (SIL) and microstrip on non- woven glass-PTFE with nominal dielectric thickness of 7.57mm clad with 341tm foil
Z, nom. f, GHz Width
25 1 12.29
50 1 4.80
75 1 2.44
Temp. % Change from 20°C value: OC of thk. of K' of K& in microstrip SIL 1.31 1.23 1.16 1.37 - 100 - 1.31 0.96 0.91 0.89 1.04 -60 -0.89 0.65 0.64 0.61 0.71 -20 -0.48 0.00 0.00 0.00 20 0.00 0.00 30 0.26 -0.27 - 0.30 - 0.27 -0.28 1.32 -0.55 -0.60 - 0.53 -0.50 70 -0.91 110 2.37 -0.91 -0.96 -0.89 150 3.42 - 1.53 - 1.61 - 1.49 - 1.44
I I
25 18 13.94
50 18 5.79
75 18 3.07
1.40 1.07 0.74 0.00 -0.28 -0.56 -0.88 - 1.53
1.36 1.02 0.68 0.00 -0.29 -0.53 -0.87 - 1.50
1.32 1.01 0.71 0.00 -0.20 -0.51 -0.81 - 1.42
% Change of Z,,er from 20°C value
- 1.60
- 1.40
- 1.20
- 1.00
-0.80 0.00 0.40 1.20 2.40 3.60
- 0.60
0.00 0.20 1.20 2.00 3.00
- 1.33 -0.93 -0.53 0.00 0.27 0.93 1.60 2.53
- 1.60 - 1.20
-0.80 0.00 0.40 1.60 2.40 4.00
There are two causes for this. First the skin effect increases with frequency, reducing the effective available cross-sectional area of conductor at a given line width. Secondly, the maximum allowable dielectric thickness to avoid mode problems decreases with increasing frequency. This requires a narrower line width for a given impedance, further reducing the available conductor crosssection. The problem can be offset somewhat by selecting a substrate with the lowest possible K', maximising line width for a given impedance and substrate thickness.
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Advances in substrate technology
Advances in substrate technology
The problem of conductor loss sets an upper frequency limit to practical microstrip antenna designs. As clad laminates combining adequate copper-foil adhesion with a smoother dielectric material-copper interface become available, the limit will be extended. Table 15.23 Predicted thermal change in thickness and KA,, of stripline (SIL) and microstrip on ceramic-PTFE with nominal dielectric thickness of 1.57mm clad with 34um foil -
Zo nom. f, GHz Width
25 1 4.67
50 1 1.40
7
75 1 0.48
--
50 12 1.88
25
12 5.61
75 12 0.74
Temp % Change from 20°C value: "C of thk. of K' of K:, in microstrip S/L
I I
T
-
-
% Change of Zo,e,from 20°C value
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accomplished by a divider network on the same conductor level. In other cases there are constraints that require more elaborate circuitry. The available area may be limited. Beam-width requirements may call for limited interaction between radiator elements and distribution lines. Broad-band ability to control phase relationships among radiators may be required. The power budget may be tight. Space constraints may call for combining the antenna and RF processor in the same unit. The interconnecting circuitry for the microstrip array to serve multiple antenna functions may be complicated. These are some of the reasons for multilayer circuit-board technology in microstrip antenna boards. In'many cases protection of the microstrip radiator pattern by a radome is needed. This is provided for by bonding a superstrate layer similar to the substrate over the exposed microstrip pattern. Successful systems are being built as multilayer units. Some features offered by the technology include: (a) Bonding boards into a unitised assembly (b) Combining stripline and microstrip layers in a single board (c) Combining boards of dissimilar relative permittivity, as needed (d) Copper-plated holes to provide vias between layers ( e ) Assembling multilayer boards with buried and blind vias designed to minimise reflection coefficients at the transition from one signal layer to another (f) Alternating ground plane and signal lines (g) Complicated interconnections with crossovers (h) New materials with good microwave properties, combined with low Zdirection thermal-expansion coefficient for minimal thermal stress on platedthrough holes (i) Practical tight registration tolerances among layers ( j ) Combining stripline, where its features of low radiative losses and low dispersion are needed, with the features of microstrip
The limits of what can be done with multilayer techniques for microstrip antennas is being extended by ingenious designers and by the emergence of new materials. 15.5 Special features and new materials developments Alternative ways to interface with microstrip radiator elements, such as conductor-free dielectric waveguides, have been proposed. Suitable substrate materials, and the technology to form such structures cost-effectively, will also push the limit upward. 15.43 Multilayer circuit-board technology in microstrip antennas For many applications an adequate microstrip antenna can be a single microstrip board. Distribution of the signal to or from the radiating elements is
The number of options in substrate materials for microstrip antennas is expanding. Some of these are special features that offer value exceeding added cost; others are new substrate materials that may meet a specific need in certain microstrip antenna applications. Selected topics are discussed in this Section. Thick metal-clad substrates offer built-in mechanical support for microstrip antennas. Co-polymers of PTFE improve antenna performance in changing temperature. Resistors can be incorporated by printed-circuit processing for better designs. Microwave-quality
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Advances in substrate technology
Advances in substrate technology
thermoset composites introduce a new approach to antenna needs. Developing technology for very low-K' substrates shows promise of improved antenna performance.
Table 15.24 Characteristics of thick metals for clad substrates Metal Alloy Composition, % Al Cr CU Mg Si Zn Machinability indext Hardness, ~ i i n e l l Tensile strength, MPa Specific gravity Specific heat, mJ/g/K Thermal conductivity, W/m/K Thermal expansivity, 10-6/K Resistivity, R/m Relative-cost/unit-volume t On a scale where clock brass is 100.
Aluminum 606 1
Copper 110
Brass cartridge
97.5 0.25 0.28 1.o 0.6 0 20 30 124 2.7 960 180 24 47 1.O
0 0 99.8 0 0 0 20 25 226 8.9 385 390 17 30 1.5
0 0 70 0 0 30 30 --
45 314 8.5 375 120 20 110 1.4
15.5.1 Substrates clad on one side with thick metal Producers of glass-PTFE and ceramic-PTFE substrates are supplying clad laminates having one side clad with heavy-thickness metal plate. The thickness can be in the range from 0.5-13 mm (0.020-0.500 in). Table 15.24 outlines the characteristics of three frequently used metal-cladding materials. Other possibilities include stainless-steel alloys and copper-Invar-copper laminates for matching thermal-expansion coefficients with other components. After the high-temperature exposure required for laminating PTFE substrates, both aluminum and copper are fully annealed and too soft for easy machining. Where machining is critical, brass is preferred. Usually aluminum is preferred for its combination of thermal conductivity, low cost and low specific gravity. For microstrip antennas the thick metal-backing offers several useful features: Connectors can be mounted directly onto the board. The higher modulus of the thick metal cladding controls dimensional change of the softer substrate material, so that precise location of antenna-pattern features is attainable. Fracturing of features in the thin conductor layer from cyclic strain induced by
947
thermal cycling in the application is avoided. The antenna can be self-supporting without added hardware. If the metal cladding is not sufficiently thick, the unbalanced construction of the laminate with stresses induced from the laminating cycle will tend to produce a bowed shape. Special care is needed when etching antenna patterns and when plating to ensure that the thick metal ground plane is masked to prevent either damage to the cladding or contamination of the etching or plating baths. 15.5.2 Low thermal coeficient of K' inJuoropolymer laminates PTFE is the preferred polymer matrix for microwave-circuit composites in spite of the undesirable characteristic of a step change in thickness and K' during the 19°C crystalline transition. This undesirable feature is particularly troublesome for microstrip antennas, where changing ambient temperatures can result in some areas being below the transition while others are above. Co-polymers of tetrafluoroethylene with other perfluorinated olefin monomers are available that either do not exhibit this crystalline transition behaviour, or show it to a much lesser degree at a much lower temperature. However, this improvement is a trade off. Co-polymers melt at lower temperatures, have a lower melt viscosity and have a slightly increased dissipation factor. As an example of a special-feature material, RT/duroid 5500 non-woven glass-fluoropolymer composite from Rogers Corporation is based on such a co-polymer and has proved an effective solution to the microstrip-antenna of changing ambient temperature in various microstrip-antenna applications. Typical properties include R = 2 5 0 f 0.04, dissipation factor = 0.0025, and a linear thermal coefficient of permittivity of - 110 parts in lo6 perdegK at 0-80°C. Other properties are similar to those of PTFE-based substrates, but the temperatures in processing and service must be kept below 260°C to avoid the lower crystalline melt point. 15.5.3 Microwave laminates with a resistive layer Divider networks for feeding arrays of microstrip radiator elements usually require resistors for suppressing unwanted signal propagations, especially in Wilkinson power-divider designs. The high cost of mounting resistors onto circuit boards often discourages wider use of this design approach. Ceramic-PTFE and glass-fibre-PTFE substrates are now becoming available clad with Ohmega-Ply* foil. Ohmega-Ply foil consists of either 17pm (0.5 oz ft2)or 35 pm (1 oz ft2) electrodeposited copper foil with an added 0.4pm layer of resistive metal alloy on the side against the substrate. 15.5.3.1 Characteristics: When microstrip or stripline transmission lines at a characteristic impedance of 50 p are formed with the Ohmega-Ply resistive layer
* Ohmega-Ply
is a trademark of Ohmega
Technolgies, Inc., Culver City, CA, USA
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Advances in substrate technology
Advances in substrate technology
between the line and the substrate, comparisons with conventional electrodeposited foil cladding in various laboratories have shown no detectable increase in insertion loss over the frequency range, at least up to 18 GHz. Selective etching techniques provide areas where the copper has been removed to leave a trace of the thin resistive alloy on the substrate surface to serve as an integral resistor element. When properly processed and provided with a protective coating, tight tolerances of resistance can be produced and maintained through exposure to high humidity, solder dip, thermal cycling and immersion in boiling water, as detailed in Table 15.25. Table 15.25 Characteristics of Ohmega-Ply resistive layer Surface resistivity, 0 Resistivity tolerance, % DC power-dissipation capability, kW/m2 Substrate Percent change in resistance maximum after: I00 h/95% RH/35'C 20 s dip in 280°C solder 100 cycles between - 55°C and 125°C 15 min in boiling water
25 6.0 UD to 620 non-woven glass-PTFE
ceramicPTFE
1.O 1.O 3.0 I .O
0.5 1.O 1.O 0.5
the resistive layer is characterised for simplicity in terms of surface resisitivity, ignoring its constant and small thickness. This is essentially the same as the term 'sheet resisitivity'. Some refer to the units as Q/square to distinguish the resistivity from the resistance. The presently available cladding with 2552 surface resisitivity value is adequate for designing most of the DC resistors needed in microwave boards. For resistors handling R F it is desirable to keep the resistor length as short as possible, and higher resisitivities are desirable so that the width of resistive elements may be as wide as possible for better control of value. At present, for Ohmega-Ply, resistivity values higher than 2 5 0 have not been adequately reliable for consideration in antenna applications on PTFE-based substrates. Development effort is in progress to produce a reliable material of higher resistivity. in -;>,
gular-shaped resistor element between edges attached to conductors, W = width of the rectangular-shaped resistor element between unconnected edges. For a square resistive element connected on two adjacent edges the formula for resistance becomes and its effective length is A meander line with resistive layer can be designed for high values. If the line is of uniform width and simple right-angle corners without radius or chamfer are used, the line can be considered as a collection of rectangular elements in series, where the length of each element is the orthogonal distance between inside corners and the corners are considered to be square elements connected at adjacent edges. Thus a meander line of uniform width W, having five straight sections of lengths L,, L2, L,, L, and L, with four square corners would have a resistance of [15.21] R = 4(0.441)W (L, L2 L, L4 L5)/W
+
+
+
+
+
The short segments of a meander line and the corners may be eliminated by retaining conductive-copper-foil rectangles as jumper connections. The copperfoil areas are made slightly oversize to ease registration requirements in processing.
,I:-.-,,,sion,
15.5.3.2 Designprinciples: If the resistor element is of rectangular shape with copper conductors connected to opposite edges of the rectangle, the resistance is simply the product of the surface resistivity and the ratio of length to width.
15.5.3.3 Processing boards with a resistive layer: A circuit pattern with integral resistors is generated in a process sequence that uses two photomasks and three etching steps. The first mask for the composite pattern protects areas that will finally be either copper or resistive conductor. The second mask protects copper areas while copper is being removed over areas that will become resistors. With the composite-pattern mask in place, copper is removed with one of the conventional copper etchants - ferric chloride, acid cupric chloride, alkaline cupric chloride, or persulfate. Etch rates for the resistive layer in copper etchant are slower. Attempting to remove the grey-coloured exposed resistive layer with the same etchant will result in undercutting of the copper foil and loss of pattern resolution. Etching is stopped as soon as all the exposed copper is removed. A second etchant specific for the exposed resistive layer is used next to remove exposed resistive layer without undercutting the copper. The etchant is made up as follows:
Water to which sulfuric acid is added: where R
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=
resistance,
1, P
=
surface resistivity, 250, L
=
length of rectan-
Concentrated sulphuric acid (100% H2S0,):
800 ml 2 ml
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Advances in substrate technology
Advances in substrate technology
Copper-sulphate pentahydrate (CuS0,-5H20):
250g
Water for a final volume of:
I000 ml Note: Never add water to concentrated sulphuric acid as it may boil and spatter with possible personal injury. Etching conditions of 3-5min at 80-100°C with agitation are sufficient to remove the resistive layer. Since this etchant does not attack copper, it can be used on boards from which the photomask has been stripped. A second photomask is applied to the board, which is designed to leave copper exposed only in areas where resistors are to be formed. This mask should be designed so that its coverage extends beyond the copper to be protected. This will minimise the potential for damage to the copper conductors by undercutting or slight misalignment of the photo-tool. Exposed copper is etched away with a chromic-acid solution, which also serves to passivate the newly exposed resistive layer. It is prepared as follows: Water to which sulphuric acid is added: Concentrated sulphuric acid (100% H,SO,): Chromium trioxide, anhydrous (CrO,):
800 ml 30 ml 300 g
Water for a final volume of:
1000 ml Notes (i) Never add water to concentrated sulphuric acid as it may boil and spatter with possible personal injury. (ii) Be sure to keep the chromic-acid etchant free of surfactants and other additives which can inhibit passivation. Etching conditions are 5-7 min at 45-55OC with agitation. Rinse in deionised water followed by a spray rinse with acidic sodium-bisulphite solution. Water rinse again and dry in an air oven at 100°C. The acid sodium-bisulphite solution is made up by first dissolving 50g of sodium bisulphite in 1 litre of water. Add dilute sulphuric acid to pH 3. Use care to avoid abrading resistor elements. Strip the photomask. If possible use an aqueous resist stripper. Solvent-based resist strippers may attack and degrade the exposed resistors. 15.5.3.4 Resistor protection: In addition to passivation of resistors to enhance thermal stability, protection against thermal shock, moisture and mechanical damage is required. This can be accomplished by a conformal coating on the resistor area. The considerations in selection of a conformal coating for Ohmega-Ply resistors include ease of application, electrical properties, heat resistance and moisture resistance. The coating may be hand-brushed or silk-screened only
951
onto resistor areas. Types of coatings can include cross-linkable epoxy-resin systems, solvent or aqueous dispersion forms of polyester-resin systems, acrylicresin systems, and various silicone-resin systems. Hysol PC-17, a two-component epoxy coating from the Hysol Division of the Dexter Corporation, 15051 East Don Julian Road, Industry, California 91749, USA, has been effective. HumiSeal lB3 1, a one-component acrylic resin from the HumiSeal Division of Columbia Chase Corporation, 26-60 BrooklynQueens Expressway, West Woodside, New York 11377 USA, has proven to be a reliable protective coating. 15.5.4 Thermoset microwave materials A completely new class of microwave substrate materials is being introduced with strong prospects for major benefits to the microwave industry. Some types of microstrip antennas should benefit. The substrate materials are referred to here as thermoset microwave materials, or TMM. Thermoset resin systems, in general, seem to be characterised by K' values well above 3, and with dissipation factor values too high for many microwave applications. This is evident in the materials listed in Table 15.1, where crosslinked systems include polyimides, triazine systems, bismaleimide resin and epoxy systems. These materials are characterised by highly polar organic groups for the cross-linking or curing reaction, which contribute to high dissipation factors. The nature of the cross-linking reactions used is such that highly polar and lossy groups are required. Typically the cross-linking is a condensation-type reaction with volatile by-products that also contribute to dissipation. With extended heating to complete the cure, low-molecular-weight fractions or byproducts volatilise and the voids left are susceptible to moisture penetration, making the thermoset sensitive to humidity and moisture with respect to electronic properties. The thermoset resins are an unexpected quarter from which to find good microwave materials. Polar groups and volatile by-products in TMMs are at low levels, if present at all. The polymer portion of the composition is almost entirely hydrocarbon polymer chains with a very high cross-link density. TMMs are highly crosslinked hydrocarbons. Before the cross-linking reaction TMM resin systems have low melt viscosity, so that much higher levels of filler content can be accommodated with intimate blending compared with the higher-molecular-weight and higher-melt-viscosity thermoplastic polymers, with PTFE as the extreme. This ability to accept fillers at high levels allows TMM composites to be designed for low thermal-expansion coefficient as well as other desirable attributes. Copper-clad panels of TMM are being evaluated for several microwave applications including microstrip antennas. These are based on a series of designed TMM substrate composites, as summarked in Table 15.26. Dielectric thicknesses presently practical for manufacture start at 0.38 mm (0.015 in). Clad laminates of TMM exhibit linear thermal change of K'. There are no
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Advances i n substrate technology
thermal transitions detectable up to 400°C. Some composites have extremely low thermal coefficients of K' values. Weight loss with thermal aging is low, namely 1.5% after lOOh at 270°C. Weight loss exceeding 1% in air or nitrogen does not occur until well above 400°C with a heating rate of 10K/min for 20-40 mg specimens. Table 15.26 Summary of characteristics of various TMM composites
TMM tvue K' at 3 GHZ (1) D at 3 GHz (2) Therm. coeff./K', 10-6K-1(3) CTE, 10-6K-1 from 0 to 140°C X, Y dir. Z dir. from 20 to 280°C X, Y dir. Z dir. Ins. res., TR/23OC after 96 h/95 RH Water absorption, % 48 h/50°C 0.125 in thick 0,050in thick Flexural strength, MPa Flexural modulus, GPa Tensile strength, MPa Rockwell hardness (E scale) Specific gravity Dielectric strength, kV/mm (4) Water permeability, mg/m/h (5) ( I ) K' values by perturbation cavity at 3 GHz for types 3,3E and 20, by FSR method for types IOT and I ?
(2) D values were by perturbation cavity at 3GHz on a vertical-bar specimen: (3) The FSR method at 4.3, 2.4, and 2.3GHz, respectively, was used for determining thermal coefficient of K'. (4) The short-timemethod [60]in air with type 1 electrodes was used with 0.3-0.4mm-thick x 102mm-d~ametermoulded disc specimens. (5) The equilibrium rate was measured for 0.012-0,021 in thick specimens from 95RH/21.5°C. Compare with published [61]values: 51-75 for polyvinyl chloride, 13 for high-density polyethylene, 6.4 for PTFE film, 15 for Mylar film control.
TMM composites are typically inert with respect to solvents and most strong reagents, and are also resistant to penetration by moisture. Dissipation factor D is similar to PTFE-based composites at microwave frequencies. The high degree of rigidity, bordering on brittleness, of TMM composites rules out any bending of substrates, but it allows fast automated lead bonding
Advances i n substrate technology
953
comparable to that done on metallised ceramic substrates, with the important difference that large flat areas with precise thickness control can be processed. This capability should make more complex microstrip antennas an economic option. Complex moulded shapes of TMM composites are feasible and could serve as subsirates for special types of microstrip antennas. TMM composites are readily drilled and routed with numerically controlled machine tools as commonly used in the printed-wiring-board industry. The carbide-tool bits required are typical of those used for other types of laminates. TMM composites differ in not having any tendency to form smears in drilled holes. The chip produced in machining is in the form of granular particles easily cleared by a vacuum system. Machined surfaces can be very smooth, with precise control and no distortion during machining. Hard entry and backer boards are needed to prevent chipping away edges. Plated-through holes have been produced with standard procedures for electroless and electroplating deposition of copper. Boards with plated-through holes have not shown any hole wall damage after several minutes immersion in solder at 288OC. 15.5.5 Low-permittivity ceramic-PTFE laminates A special ceramic-PTFE composite combines low K' with low Z-direction
thermal expansivity close to that of copper. This material* has demonstrated its value for multilayer printed wiring boards with high interconnection density for high-speed digital-electronics applications. The thermal-expansion match to copper gives reliability to the plated-through hole vias widely used in such boards. In addition to the reliability of vias, the low modulus of the composite has proved to be of value for ceramic-surface-mount chip-carrier devices. X, Y shear strains are induced either from thermal mismatch of the ceramic with the substrate, or from actual differences in temperature during start up of equipment. The low modulus of the low-K' ceramic-PTFE results in strain being absorbed by the substrate rather than by the solder used to attach the surfacemount chip package to the board. The substrate does not harden, fatigue and fracture, as does solder. A third special feature has become apparent - the combination of PTFE and ceramic filler shows essentially a zero thermal coefficient of K' over the 0-100°C temperature range. This makes it of special interest to microstrip antenna users and producers, who have had performance problems with less thermal stability. K' at 2.94 f 0.04 is somewhat higher than glass-PTFE substrates. 15.5.6 Very-low-dielectric-constant substrates
Techniques have been found for producing a uniform fine-structured foam
* Low-K' ceramic-PTFE substrate is designated RO 2800TMPTFE composite by the Microwave Materials Division of Rogers Corportion, Chandler, AZ 85226, USA.
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Advances in substrate technology
Advances in substrate technology
based on the TMM polymer system, and referred to as thermoset microwave foam (TMF). The foam is unusual in its combination of attributes, including high degree of heat resistance, resilience under compressive loading, low affinity for moisture and low dissipation factor. Clad panels in 0.76-6.35 mm (0.030-0.25 in) thickness with precise thickness tolerance of less than 51 pm (0.002in) make the foam of particular interest to designers of microstrip antennas where a K' value of 1.4-1.6 in a clad laminate can offer efficient radiation performance over a wide bandwidth. Although TMF is in the early stages of investigation and availability is limited, the characteristics summarised in Table 15.27 indicate its value for future microstrip-antenna applications.
Table 15.27 Summary of characteristics of TMF
IS by waveguide perturbation at 3 GHz Tolerance of K' D at 3GHz Specific gravity Cell size, pm CTE, 10-6K-' Flexural modulus, MPa Failure strain, % Retention of modulus at 100°C. %
1.4 or more
+ 0.02
< = 0.0006 0.4 or more 100 50-60 9.7 5 > 90
15.6 References I. KOO, G. P.: 'Structural and mechanical properties of fluoropolymers' in L. A. WALL, (Ed.): 'Fluoropolymers' (Wiley Interscience, 1972) pp. 516-521 2. MCCRUM, N. G.: 'An internal friction study of PTFE,' J. Polymer Sci. 1959, 34, p. 355 3. BUR, A. J.: 'Dielectric properties of fluorine containing polymers' in WALL, L. A. (Ed.): 'Fluoropolymers' (Wiley Interscience, 1972) pp. 475-503 4. BROWN, R. G.: 'Vibrational spectra of PTFE: Effects of temperature and pressure,' J . Chem. Phys., 1969,40, p. 2900 5. KIRBY, R. K.: 'Thermal expansion of PTFE Teflon from - 190" to 300°C.' J. Research NBS, 1965, 57, pp. 91-94 6. BUNN, C. W., and HOWELLS, E. R.: 'Structure of molecules and crystals of fluorocarbons,' Nature, 1954, 174, p. 549 7. DESANTIS, P., GIGLIO, E., LIGUORI, A. M., and RIPIMONTI, A,: 'Stability of helical conformations of simple linear polymers,' J. Polymer Sci., 1963, A-I, p. 1383 8. MCCRUM, READ, and WILLIAMS: 'Anelastic and Dielectric Effects in Polymeric Solids' (Wiley) 9. 'Standard test method for permittivity (dielectric constant) and dissipation factor of plasticbased microwave circuit substrates* Annual Book of ASTM Standards, 10.02, 1985, D 3380-82 10. 'Standard test method for dielectric constant and dissipation factor of polyethylene by liquid displacement procedure' Annual Book of ASTM Standards, 10.02, 1985, D 1531-81 11. NOWICKI, T. E.: 'Microwave substrates present and future,' New Electronics, 1980, 13, pp. 85-86. 88
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-12. 'X-band effective stripline dielectric constant and dissipation factor for copper clad glass woven fabric GR and GX laminates,' US Military Specification, MIL-P-13949F 13. Institute for Interconnections and Packaging Electronic Circuits, 'Stripline test for permittivity and loss tangent (dielectric constant and dissipation factor) at X-band', ibid., 1988, IPC-TM650, Method 2.5.5.5 14. 'Modified ASTM D 3380 stripline test method for X-band measurements of dielectric constant and dissipation factor of RT/duroid 6010 ceramic-PTFE laminates.' Rogers Corporation, RT6.1.2, I983 15. COHN, S. B.: IRE Trans., 1955, M T T J , pp. 119-126 16. SUCHER, M.: 'Measurement of Q' in' Handbook of microwave measurements' (Polytechnic Press, 1963). p. 456 17. ALTSCHULER, H. M., and OLINER, A. A.: 'Discontinuities in the center conductor strip transmission line,' IRE Trans., 1960, MT-8, p. 328 18. MATI'HAEI, G. L., YOUNG, L., and JONES, E. M. T.: 'Microwave filters, impedancematching networks and coupling structures' (McGraw Hill, 1964) p. 206 19. COHN, S. B.: 'Characteristic impedance of the shielded-strip transmission line,' IRE Trans., July 1954, M l T , pp. 52-57 20. COHN, S. B.: 'Problems in strip transmission lines,' IRE Trans., March 1955, MTT 21. EDWARDS, T. C.: 'Foundations for microstrip circuitry' (Wiley, 1981) pp. 45, 58, 73, 74, 104 22. HAMMERSTAD, E. O., and JENSEN, 0.: 'Accurate models for microstrip computer aided design.' IEEE MBTT-S International Microwave Symposium Digest, May 1980, pp. 407409 23. NAPOLI, L. S., and HUGHES, J. J.: 'A simple technique for the accurate determination of the microwave dielectric constant for microwave integrated circuit substrates,' IEEE Trans., 1971, MlT-19, pp. 664-665 24. HOWELL, J. Q.: 'A quick accurate method to measure the dielectric constant of microwave integrated circuit substrates,' IEEE Trans., 1973, MlT-21, pp. 142-143 25. LADBROOKE, P. H., POTOK, M. H. N., and ENGLAND, E. H.: 'Coupling errors in cavity-resonance measurements on MIC dielectrics,' IEEE Trans., 1973, MTT-21, pp. 560-562 26. 'Test methods for complex permittivity (dielectric constant) of solid electrical insulating materials at microwave frequencies and temperatures to 1650°C.' Annual Book of ASTM Standards 10.02, 1985, D 2520-81 27. HARRIS, D. K.: Lancet, 1951, 2, p. 1008 28. American Industrial Hygiene Associate Quarterly, 1956, 17, p. 98 29. HARRIS, D. K.: British J . Industrial Medicine, 1959, 16, p. 221 30. WAGNER, W. D.: Letter Report to Research & Technical Service Br., August, 1961 31. CLAYTON, I. W.: J . Occupational Medicine, 1962, 4, p. 262 32. Federal Register Title 21, 12125555, 13 October, 1962 33. LEHMAN, A. J.: Association of Food and Drug Oficials US Quarterly Bull., 1962, 26, p. 109 34. ZAPP, J. A,: 'Toxicity of plastics and resins,' Arch. Environmental Health, 1962, 4, p. 335 35. Hygienic Guide Series (American Industrial Hygienic Association, 1963), p. 198 36. CLAYTON, J. W.: Fluorine Chemistry Rev., 1967, 1, pp. 197-252 37. LEWIS, E. E., and NAYLOR, M. A. J.: American Chem. Soc. J., 1967, 69, p. 1968 38. WARITZ, R. S., and KWON, B. K.: 'The inhalation toxicity of pyrolysis products of polytetrafluoroethylene heated below 500 degrees centigrade.' American Industrial Hygiene Assoc. J., 1968, 29, pp. 19-26 39. COLEMAN, W. E., SCHEEL, L. D., KUPEL, R. E., and LARKIN, R. L.: 'The identification of toxic compounds in the pyrolysis products of polytetrafluoroethylene (PTFE),' American Industrial Hygiene Assoc. J., 1968, 29, pp. 33-40 40. COLEMAN, W. E., SCHEEL, L. D., and GORSKI, C. H.: 'The particles resulting from polytetrafluoroethylene (PTFE) pyrolysis in air,' American Industrial Hygiene Assoc. J., 1968, 29, pp. 54-60 41. KUPEL, R. E. and SCHEEL, L. D.: American Industrial Hygiene Assoc. J., 1968, 29, p. 27
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Advances in substrate technology
42. SCHEEL, L. D., LANE, W. C., and COLEMAN, W. E.: American Industrial Hygiene Assoc. J., 1968, 29, p. 41 43. SCHEEL, L. D., MCMILLAND, L., and PHIPPS, F. C.: American Industrial Hygiene Assoc. J., 1968, 29, p. 49 44. 'Listing of Plastic Materials'. National Sanitation Foundation, March 1968, p. LO 45. DUPONT DE NEMOURS & CO.: J. Teflon, 1976, 1 1 , p. 8 46. GASKILL, J. R.: 'Smoke development in polymers during pyrolysis or combustion,' Smoke and Products of Combustion, 1973, 2, pp. 1-34 47. PACIOREK, K. L., KRATZER, R. H., and KAUFMAN, J.: 'Oxidative thermal degradation of polytetrafluoroethylene,' J. Polymer Sci.: Polymer Chemistry Edition, 1973, 2, 1465-1473 48. 'Teflon fluorocarbon resins-Safety in handling and use' (DuPont de Nemours & Co., 1970) p. 19898 49. 'Health and safety aspects of fluoro-polytetrafluoroethylene' (ICI Technical Service, 1978) 2nd edn 50. CAMPBELL, W. A., JR., and MARRIOTT, R. S.: 'Outgassing data for selecting spacecraft materials.' NASA Reference Publication 1124 (revised), August 1987 51. 'ANSIIASTM E 595-77 standard test method for total mass loss (TML) and collected volatile condensable materials (CVCM) from outgassing in a vacuum environment' Annual Book of ASTM Standards, 1980, pp. 595-77 52. MORRIS, P. 0.. JR.: 'The effects of combined environments on PTFE.' AIEE CP62-1284, 1962 53. FLORIN, R. E., and WALL, L. A.: J. Appl. Polymer Sci., 1959, 2, p. 251 54. BOPP, C. D., and SISMAN, 0.: 'Physical properties of irradiated plastics.' ORNL-928, 1951 55. 'Radiation resistance of Teflon in a simulated space environment.' Components & Materials Laboratory, Hughes Aircraft Co., TM-687, August 1961 56. LINNENBOM, V. J.: 'The radiation challenge,' Instrlation, Feb. 1962, p. 80 57. FRISCO, L. J.: 'Dielectrics for satellites and space vehicles.' John Hopkins University, Dieletric Lab., ASTIA No. AD276-867, 1962 58. DUPONT Co.: 'Radiation tolerance of Teflon resins.' J. Teflon, Jan.-Feb. 1969, 10 59. HAMMERSTAD, and JENSEN: IEEE MTT-S Int. Microwave Symposium Digest, May 1980, pp. 28-30 60. 'Standard test method for dielectric breakdown voltage and dielectric strength of solid electrical insulating materials at commercial power frequencies.' Annual Book of ASTM Standards, 10.02, 1985, D 149-81 61. 'Encyclopedia of Polymer Science & Technology. Supplement Vol. 1.' 1976, p. 65
Chapter I 6
Special measurement techniques for printed antennas E. Levine
16.1 Introduction The measurements of printed antennas are essentially the same as the measurements of other antennas. The majority of these measurements lie within two basic categories: impedance measurements and radiation pattern measurements. The first category deals with the complex reflection coefficient or equivalently the input impedance at the antenna terminals. The second category is broad in scope and includes various radiation properties such as beamwidth, sidelobe levels, gain, polarisation etc. Measurements of the noise figure and the efficiency, both of which are a combination of the two categories, are sometimes also required. In this Chapter we will not describe standard experimental methods in antennas. Readers interested in such methods should refer to textbooks such as [I-41. Furthermore, experimental techniques for microstrip circuits in general can also be found in the textbooks [5-61. The purpose here is to reveiw some specific experimental techniques which can be useful in the design and manufacturing processes of microstrip and other printed antennas. These techniques are suggested, of course, only to supplement measurements of the far fields and the input impedance. These techniques are motivated by several reasons: first, the use of dielectric materials whose physical . properties are not always known accurately or the use of multilayer substrates made of different materials. Secondly, the transition from a coaxial transmission line or a waveguide into the printed network is a difficult analytical problem. The electrical properties of such transitions cannot be neglected in many cases, and moreover the electrical properties can be used in the antenna design. Thirdly, the use of complicated feed networks in large arrays suggests that their properties should be checked experimentally, by resonant techniques, by timedomain reflectometry (TDR) or by probing the near field. Direct efficiency measurement of such arrays may also be of great help. The characterisation of printed antennas can therefore be divided into three levels, each of which will be described in subsequent Sections of this Chapter:
958
Special measurement techniques for printed antennas
(a) Physical constants of the substrate (Section 16.2) and properties of the connector (Section 16.3). (b) Measurements of the electrical properties of printed lines and networks (Section 16.4). (c) The characterisation of the entire antenna by probing the near field (Section 16.5) and efficiency measurement (Section 16.6).
Special measurement techniques for printed antennas
959
where m, n are the mode numbers of the resonance. Certain improvements can be achieved by preparing an almost totally enclosed resonator whose narrow edges are metallised as well [9]. The resonator is excited by input/output printed strips via small apertures, as shown in Fig. 16.2. input coaxial connector
parallel plate resonator
output coaxial connector
A
16.2 Substrate properties
Commercial substrates are supplied with measured data on the two main physical properties: the dielectric constant (or permittivity) E, and the loss tangent (or dissipation factor) tan 6. The measured values are usually given at a low frequency, e.g. 1 MHz, and at some operating microwave frequency like 10 GHz. Another physical property of interest is the surface resistivity of the metallic cladding R,,which is related to the conductivity a, by Fig. 16.1 A parallel plate resonator with a coaxial coupling (Source: Reference 10)
(in SI units) is the permeability where f is the frequency and p, = 4n x of the vacuum. Conductivities of bulk metals are well known in the literature. For example, copper has a conductivity u, = 5.88 x lo7 mho/m [7]. Although E, and tan 6 are usually known, there are instances in which their precise characterisation is required. One typical case is when the substrate is used at higher frequencies than those tested by the manufacturer. Another case is when high accuracy and reproducibility are needed in mass production and one wishes to cross-check the variations among different production series. In other cases, multilayer substrates made of several materials, such as combinations of spacer foam plates with dielectric layers, have to be characterised. Since the tested materials used for antenna applications are shaped as flat plates, with one o r more metallised walls, it is natural to choose techniques based on parallel-plate resonators. This simple geometry is preferred over various techniques in which a small dielectric sample is inserted into a waveguide or other cavity, although the achieved accuracy is limited. A measurement procedure which utilises a flat dielectric plate, metallised on both top and bottom sides [8], is described in Fig. 16.1. The rectangular cavity whose dimensions are a x b x h (h is much smaller than one wavelength) is excited in its corner by a coaxial connector. The resonant frequency f,, is measured either by the reflection from the connector or by the transmission into another connector. The dielectric constant of the substrate is given by
circular
wholly
Fig. 16.2 A parallelplate resonator with aperture coupling. The resonator is wholly metallised (Source: Reference 10)
The main source of measurement error in these resonators is the shift in the resonant frequency due to losses. If the quality factor Q is also measured, the following correction to the frequency can be made
wheref, is the measured frequency and& is the corrected frequency that should be used in eqn. 16.2. Another source of error, caused by the coupling of the probe into the resonator, is discussed in Reference 10. It is shown there that the coupling errors in the two cases of totally and partly metallised substrates are of opposite sense. Thus the two methods may be averaged to improve the overall
960
Special measurement techniques for printed antennas
measurement precision, which may be of the order of 0.5%. A re-examination of the results obtained and a comparison with other methods is given in Reference 11. The conclusion drawn there is that it is difficult to account for the fringing errors; hence the overall precision in the measured dielectric constant is of the order of 1 %. An interesting procedure for measurement of tan 6 and u,,of substrates is outlined in Reference 12. The procedure consists of cutting the double-clad substrate to some arbitrary-shaped closed resonator and measuring its Q. A second cavity is constructed of twice the thickness of the first cavity. Since the ohmic losses are not changed much in the two cases, one can separate the dielectric and the conductive loss parameters. resonator strip \
967
Special measurement techniques for printed antennas
by a coaxial connector. The fixture is closed by air pressure in order to prevent air gaps. By comparison with a known reference, checked in the same fixture, the dielectric constant of the unknown substrate is obtained from the relationship
tested sample /(non-metallised)
connects input strip
strip
(
T
V
standard substrate
Fig. 16.3 A microstrip resonator coupled by a gap. The resonator is loaded by the tested dielectric sample (Source: Reference 73)
A different method suggested in Reference 13 is shown in Fig. 16.3. Here, a non-metallised flat sample is placed above a microstrip section, creating a cavity. The microstrip section, which is built on a standard and known substrate (with EL, tan 6') is coupled to input and output terminals through small gaps. In addition to the measurements of the resonant frequencyf, and the quality factor Q, of this cavity, a second measurement (giving f , and Q,) is done while replacing the tested sample by a reference material with known properties. The four measured valuesf, ,f,, Q, , Q, and the knowledge of the reference properties E,, , tan 6, enables one to compute the unknown properties E,,, tan d2, using the equations given in the appendix of Reference 13. Although the calculations involved in this technique are quite complicated, and the reported accuracy of the dielectric constant is only 3% (but often as good as 0.5%) it has the significant advantage that the loss tangent is also obtained. Another test configuration, described in Reference 14, is suitable especially for high E, materials like ceramics and semiconductors. The dielectric layer to be measured is placed between two films of polymide (such as Dupont Kapton) as shown in Fig. 16.4. The bottom side of the lower film is metallised while the upper film contains a half-wavelength circular resonator and a coupling strip fed
connects t o outer cond ucror of coax. n.*-F-
measured
'0' ring
air pressure
Fig. 16.4 A test fixture for precise measurement of thin dielectric substrate (Source: Reference 14)
where AE,/E,is the relative change in the dielectric constant and Afm/fmis tlie relative change in the measured resonant frequency. K is a constant determined by the shape of the resonant circuit and the material used. The value for the specific structure in Reference 14 was K = 2.15. This relatively complicated test configuration gave repeatable results of the dielectric constant within 0.1% relative to the known standard, and the deviations from the described techniques can provide the measurement of the dielectric constant with accuracies of the order of 1%. The measurement of the loss tangent is more complicated and less accurate. A possible way to measure the loss tangent is to build a nonradiating transmission line (like stripline) and measure the attenuation along the line.
+
962
Special measurement techniques for printed antennas
The limited accuracies mentioned so far are inherently affected by the use of medium-Q cavities in the described geometries. In cases where higher accuracies are needed, one should use either small samples inserted into closed cavities, or employ open interferometry techniques. Various such methods are summarised in Reference 15 and reviewed in Reference 16 with a comprehensive list of references. More recent contributions on dielectric-rod measurements and quasi-optical spectroscopy in millimetre waves can be found in References 17 and 18, respectively.
Special measurement techniques for printed antennas
experimental techniques for the characterisation and improvement of transitions from the printed antenna to the 'outer world' of the microwave circuitry. Furthermore, it is strongly recommended that any design process of printed antenna will include independent characterisation of the connector in use, by one of the techniques described in this Section.
input connector
16.3 Connector characterisation In most cases there is a transition from the printed antenna to transmitlreceive modules or to some measurement equipment having coaxial or waveguide terminals. The inherent discontinuity of the currents in the vicinity of the transition is a source of radiation and surface-wave losses. Also, its reactive nature may cause unwanted reflections and sometimes even changes the resonant frequency of the antenna. These effects influence the antenna performance, since all the radiated power of the antenna passes through this transition. The typical and most frequently used transition, from a coaxial line to the microstrip line, is accomplished by extending the inner conductor of the coaxial line and soldering it to the printed board. This connection is especially useful for thin substrates, where the discontinuity is small in size and many commercial connectors can do the job properly. Other transitions of interest are between microstrip lines and waveguides, striplines and slotlines. There are many cases in which the transition effects should be studied or taken into account: (a) In applications where very high level of impedance matching is necessary. (b) In thick substrates, which are chosen in order to achieve increased bandwidth, the connector effects are severe and cannot be neglected. In such cases, several simple geometrical changes can often improve the transition. (c) In the design of printed antennas, especially when large bandwidth for matching is needed [19-211, the parasitic impedance of the transition may be used. (4 In research and development of new printed radiators, especially those combined with modern integrated and monolithic circuits, unconventional feedings are often used. The analytical modelling of the coaxial/microstrip and the other transitions is a complicated field-theory problem. Remarkable progress in this subject has been achieved in recent years [22-261, but still the works published seem to be impracticable for design use. On the other hand, simple approximations which model the transition as short transmission lines or as lumped element networks [27-311 are not accurate enough in many cases. It is therefore important to use
963
Fig. 16.5
output connector
Testing a coaxial connector by a mated pair of connectors flange
I
\
Fig. 16.6 A coaxial/microstrip transition test fixture (Source: Reference 30) Typical dimensions are: dielectric-substrate thickness ranges between 0.25 mm and 3.2mm and the central pin extension should be less than 1 mm
Commercial connectors are usually tested by the manufacturer in a coaxial structure consisting of two identical connectors in contact [32] as shown in Fig. 16.5, or through a high-precision air line. This configuration is tested in reflection or in transmission by a network analyser or by a TDR technique [33]. A basic test fixture of a coaxial/microstrip transition, mounted on a jig, is presented in Fig. 16.6 [34, 351. The microstrip line here is open ended, but a shorted end may be used as well. The reflection coefficient (or VSWR) of the transition is found from the overall measured reflection at the connector input. An interesting suggestion [36] is to repeat the measurement for several lengths of the
964
Special measurement techniques for printed antennas
printed line. Averaging the measured data reduces the error caused by the radiation loss of the open end. Naturally one would like also to measure the reflection while the end of the printed line is matched by a termination. However, the realisation of high-quality microstrip terminations is not easy. Several types of terminations are described in the literature [6, 37, 381 and in technical catalogues such as References 32, 39 and 40. Three examples are shown in Fig. 16.7. The first example is a 50 iZ thick-film resistor inserted into the substrate and shorted at one end to the ground plane [32]. The quality of such resistors in terms of VSWR is not high, but they are easy to build. A second termination is made of a precision attenuator pad made in thin-film technology [39]. The significant advantage here is its small and compact size. The third example is a tapered resistive layer mounted on the top of the printed line [40]. This configuration gives good matching over a broad band of frequencies, but it requires a long length of at least half a wavelength. A comparison of various printed terminations and experimental testing of connectors by such terminations are given in Reference 37. thin film pod
Special measurement techniques for printed antennas
965
connector is terminated by a high-quality coaxial matched load PI(/). The total reflection coefficient is a superposition of the two reflections coming from the two connectors. This coefficient is given by
microstrip \ line
ground plone
resistive box
w a
.!'? I
L--
b
metallic short to ground plane
Fig. 16.8 Svmmetrical pair of coaxial/microstrip transitions makes a sensitive test set
Since the summing- of the two waves is coherent, ~ ~ r o l ~= 2
tapered absorbing film
V
I Er 401 a shorted thick-film resistor [32], b Precision attenuator pad [39] c Tapered resistance film [40]
A simple, sensitive and accurate test set can be made from a pair of identical transitions [3O, 31, 411 where no shorts, open ends or terminations in printed form are needed. The schematic structure, shown in Fig. 16.8, enables not only characterisation of the connectors, but also gives valuable information about the printed line itself. The test procedure is as follows: two measurements are made over as wide a frequency range as possible. The first measurement is the reflected power from a coaxial short (without any transitions) PI0).The second measurement is the reflected power from the test fixture while the second
+
(16.6) r 2 I 2
where l-, is the reflection from connector 1, and l-, is the reflection from connector 2, the individual reflection can be written as I-, = jr, le'+ (16.7)
ground plane
Fig. 16.7 Typicalmatched terminations for use in microstrip lines (Source: References 32.39.
ll-I
.
-.
where I r,1 and 1 Fzlare the respective amplitudes, 4 is an arbitrary phase and 4nlKf/1,is the phase added by the round-trip propagation in the microstrip frame. The phase 4 can be selected to be zero and the reflected amplitudes of the two connectors are assumed to be identical. Hence, the total reflection is
. . . which is the well known expression for interference effects. The measured reflection coefficient will be a periodic function of the frequency, with maxima and minima Il-torliax
= 41I-l2
966
Special measurement techniques for printed antennas
Special measurement techniques for printed antennas
and with a period of
i l
where c is the speed of light in vacuum. This measurement is very sensitive because the coherent summing multiplies the reflection from the single connector by a factor of 4, as shown in eqn. 16.9. This technique may also be used to measure the effective dielectric constant of the printed line using eqn. 16.10, and additional information about the losses can be gained by measuring the transmission to the second connector.
1
967
centre-conductor diameter [42,43], insertion of the connector into the dielectric [42,44], addition of a metallic ring around the central conductor 121,421,drilling a hole in the ground plane [34], an off-centre shift of the central pin [41] and the commercial x connector [45] Measured graphs of the last two improved conneclOOn microstrip
iOOn microstrip
b
0
lOOn microstrip
I
L
50, rnicrostrip
d
\ hole in
base plate
Fig. 16.9 The microstrip test frame consists of a closed microstrip line printed on a dielectric substrate and two identical connectors (Source: Reference 42)
A modification of this method, introduced in Reference 42, is useful for vertical connectors where the outer conductor is soldered to the ground plane of the antenna. Since usual coaxial connectors have an impedance of 50 Q, it is convenient to attach the connector to the middle of a 100 R microstrip line. In this way, two lines of 100 R are seen in parallel, providing an impedance of 50 R. Such 100 R lines are used, of course, later on in the feed network of the antenna. The measurement structure in this case is made up by a closed microstrip line and two identical connectors which are soldered to the line so that the line is divided into two equal lengths (Fig. 16.9). Smooth corners are preferable for the frame, but chamfered corners are also acceptable. The measured reflection coefficient of the coaxial transition is the result of the discontinuity between different types of transmission lines. The transition area is modelled sometimes by some parasitic reactance in an equivalent electrical network [27-311. In cases where information about the reactive nature of the connector is needed, the complex reflection coefficient should be studied; e.g. both amplitude and the phase are to be measured. Several geometrical changes in the transition can help compensate for the reflections, either by a 'cut and try' procedure or by numerical modelling of an equivalent circuit. A few examples of improved connectors are shown in Fig. 16.10, both for horizontally and vertically mounted connectors. These improvements include: reduction of the
e
alternate attachment techniques f
Fig. 16.10 improved coaxial/microstrip transitions (Sources: References 21. 34. 47-45) a Narrow pin 142. 431 b Inserted connector [42. 441 c Metallic ring [21, 421 d Compensating hole 1341 e Off-centered pin [41 I f K connector [451
tors, which were performed using the two-identical-connectors approach (via a straight microstrip line) are shown in Fig. 16.11. A close look at these graphs reveals the periodic behaviour of the reflection and the remarkable VSWR values of the single connector. In Fig. 16.11a [41] the period is Av = 0.9 GHz, the length of the microstrip section is 2.0 in and thus = 3.28. The maximal
Ld
968
Special measurement techniques for printed antennas
Special measurement techniques for printed antennas
measured VSWR is 1.1 and hence the VSWR of the single connector is 1.05. In Fig. 16.11b [45] the period is Av = 3.9 GHz, the microstrip length is 0.5 in, and thus = 3.03. The maximal return loss is - 15 dB, which is equivalent to a VSWR of 1.43, and thus the VSWR of each connector is 1.2, most impressive for this band of frequencies.
Kf
I, 1
wafer under test
1
969
vlew contacts
coplanar max VSWR=1.1 VSWR of each connector 1.05
wafer under test
bottom view
frequency, GHz contact wafer under test
m'0
$
rnax RL=-15dB 20 VSWR of each " connector 1:l.Z 30
Fig. 16.12 Details of the 'on wafer'probe in top, bottom andside views (Source: Reference 49)
$
40
0
view
10
20 30 frequency, GHz
40
Fig. 16.11 Measured results of VSWR and return loss of two improved connectors. The measurements were done by a connector pair (Sources: References 41, 45) a Two off-centered pin connectors of Fig. 16.10e [41], b Two K connectors of Fig. 16.1Of [45]
The idea of two identical connectors can be applied to all kinds of transitions. For example, the integrated waveguide/microstrip transition described in Reference 46 or the microslot/microstrip transition shown in Reference 47 were tested in this way. In another recent work [48], a versatile mounting fixture has been proposed for Gallium-Arsenide substrates. This fixture has an adjustable ground plane which is capable of acommodating substrates of arbitrary thicknesses. Good electrical contacts are achieved by a conductive rubber layer. A novel tool for integrated and monolithic circuits, known as 'wafer probing' [49, 501, is applied to the bonding pads of a semiconductor chip. Two probes described in Fig. 16.12 are made of coplanar lines and small metallic contacts. They are connected to a network analyser through wideband baluns, as shown in Fig. 16.13. This microwave-wafer probing has been shown to be an accurate and convenient tool for the detailed network analysis of monolithic elements, and any new feeding configurations of printed antennas can be tested as well.
balanced probe heads
ANALYZER NETWORK
Fig. 16.13 'On wafer' measurement by two balanced probes and a corrected network analyzer (Source: Reference 49)
970
Special measurement techniques for printed antennas
16.4 Measurements of printed lines and networks
1i I
After presenting the characterisation of substrate properties and measurement of connector effects, we come to the printed line itself and the building blocks of feed networks, to be discussed. First, one is interested in the three fundamental parameters of the basic printed line:
Special measurement techniques for printed antennas 971 the characterisation of printed-line parameters and networks. Most of the examples deal with microstrip lines, but they are general enough to be applied to all kinds of printed or dielectric transmission lines.
16.4.1 Measurements of printed-line parameters
(a) The effective dielectric constant ce8, related to the propagation constant P by
where k,,is the free-space wave number. (6) The attenuation factor a, consisting of an ohmic part a, and a dielectric part ad.
(c) The characteristic impedance of the line Z,. It should be noted that these are not physical properties of the substrate, but rather the electrical properties of a specific given line. Secondly, one should investigate the properties of certain printed structures used in feed networks: bends, width changes, T junctions, cross-junctions etc. Each one of these structures is actually some kind of a discontinuity that causes reflections and losses. One is interested either in quantitative measurements of these effects or in modelling them by equivalent electrical circuits. In antenna applications, the power splitters and the delay lines are the most important building- blocks to be considered. General methods for measurement of microwave transmission lines are well known in the literature and in practice. The great majority of the measurements are performed in the frequency domain using network analysers, with or without automatic error correction. The main problem with the network analysis of printed circuits is the fact that the test ports and the standard calibration units (short, open and matched terminations) are available in coaxial or waveguide forms. Any measurements of printed lines have to be made, therefore, through transitions. The inherent ,reflections from the transition and the difficult determination of the reference planes limit the obtainable precision. One simple solution is, of course, to use excellent connectors (VSWR of about 1.01) for the network analysis. Another solution is to use a pair of the tested devices, separated sufficiently from the connectors, and to get different resonances for the connectors and for the devices under test. A third solution, which is often the most practical one, is to use resonators which contain the devices under test. These resonators, which are coupled by air gaps or by other means of weak coupling, have high sensitivity and high accuracy, as will be described later on in this Section. A different approach is to use time-domain reflectometry in which discontinuities, including the transitions, are separated on the time axis. Direct probing along printed lines and printed structures may also be considered as a quantitative tool, and this technique will be discussed in the next Section. The purpose of this section is therefore to review several practical methods for
4
I I
16.4.1.1 E ~ The ~ . three fundamental parameters to be measured are the effective dielectric constant, the attenuation factor and the characteristic impedance. An example of the measurement of cef has been shown in eqn. 16.10. This method, based on a straight printed line between two connectors, is not very accurate, mainly because the distance between the two connectors is subjected to different definitions. High-sensitivity and well-defined lengths are achieved in printed resonators. The idea is to create an exact printed structure and bring it into resonance by weak coupling via small air gaps. The ring resonator is an attractive candidate for this purpose [S, 6, 51-53]. The ring shown in Fig. 16.14 is excited and measured by an 'input' strip and an 'output' strip. The effective dielectric constant of the tested line is related to the resonant frequency of the ringf, by
where n is the order of resonance and 1 is the mean circumference of the ring.
input
resonator
Fig. 16.14 A ring resonator for measuring the effective dielectric constant of a microstrip line (Source: Reference 51)
The main advantage of a ring resonator is that it is free of end effects. However, the curvature effect reduces the accuracy and a corrected procedure for determining the value of E~ is described in Reference 53 as follows: The ring is characterised now by three geometrical parameters: ri, r, (inner and outer radii of the ring) and w (width of the line). Now define two effective radii Ri and R, by
972
Special measurement techniques for printed antennas
The effective width at frequency f is defined by
where Wcff(0)is the effective width at zero frequency, and
Special measurement techniques for printed antennas
For successful operation of this technique it is recommended to make I, = 21, + 1,; thus an approximate a priori knowledge of I, is required. The obvious advantages of this 'two-resonators' technique over the ring resonator are that the accuracy does not depend on the size of the resonator and that the production tolerances for straight section are better than those for curved lines.
Here h is the thickness of the substrate, q, is the free-space impedance (377 R) and Z, is the characteristic impedance of the line. ~ ~ ~is( the 0 )electrostatic approximation for E@ and f , is defined by
The k number of the resonance is found by solving the equation
The value of I, should be taken from theoretical calculations or from known data. A most practical arrangement, made of two straight resonators with lengths of I, and 1, [6, 54-56] is shown in Fig. 16.15. The two resonators are measured independently and two resonant frequencies f , and f, are found. These two measured values are then used to find both E,, and 1, [54] nc(2fi - f,) f
f
= 2f,t;h(12 - I,)
)7
input
11
1
t 2 = 211
Two open resonators for measuring the effective dielectric constant (Sources: References 6 and 54)
Fig. 16.15
J"(~R,)Y"(~R.)- J"(~R,)Y"(~R,)= o (16.17) where Ji, are derivatives of the Bessel function of the first and second kinds of order n. Finally one gets
This procedure is shown to provide improved accuracy over eqn. 16.12, and it is estimated to be better than 1%. The accuracy is better for large radii and for thin substrates. Another configuration for measuring the effective dielectric constant is a straight resonator of length I, coupled at its edges or through its sides [6]. This resonator has two abruptly open ends which are best accounted for by considering the line to be longer by I, on each edge. The effective dielectric constant is therefore
973
input
( 7 11
Fig. 16.16
Two open resonators for measuring the effective dielectric constant and the end-effect of a microstrip line (Sources: References 6 and 57)
Another version of the straight-line resonator is described in Fig. 16.16 [6,57]. Here, the first resonator consists of two sections 1, and 1, while I, equals 1,/4.The second resonator is made of the section I, alone, or practically it is the first resonator after the I, section has been removed. This configuration distinguishes between the effective length of the gap and the effective length of the open end. The procedure is as follows: first, the effective dielectric constant of the tested line is measured by one of the techniques described earlier. Then the two resonant frequenciesf, andf, are found and the two equations
nc -J-
2f
8.8
= li+lq+L0
(16.23)
are used, to find the effective length of the gap, I,, and the effective length of the open end, .I,,. Now the final value of the effective dielectric constant is obtained iteratively.
974
Special measurement techniques for printed antennas
16.4.1.2 a: The attenuation factor a is another parameter of interest, and detailed theoretical and experimental data on microstrip lines are available in References 58-60. Direct measurement of the power loss of a straight line is not practicable unless the losses are high as occurs with millimetre waves [61]. Usual values of a for commercial substrates are between 0.05 and 0.1 dB/&. In the presence of radiation and surface-wave losses, such values are difficult to measure without careful calibration. It may be useful to use a stripline made of the substrate under test and measure the attenuation. An alternative way is to measure the quality factor Q of a resonator and then solve for the attenuation factor using the basic expression [62]
General reviews of Q-factor measurements can be found in References 63-65. To determine a from the Q measurement one has to separate the radiation and the surface-wave losses. The situation is summarised by the equation
where Q is the measured quality factor defined by f/AA where f is the resonant frequency and Af is the width between half-powc- points. Q, is the unloaded quality factor and Q, is the unknown, to be found. A suggested procedure for reduction of the error [6] is the following: (a) Measure the quality factor of a ring resonator where radiation losses are smaller and find an approximate value of Q = Q,. (b) Measure the quality factor in a straight-line resonator having the same parameters, and find the value of Q. (c) Use eqn. 16.25 to calculate Q,. (4 Use eqn. 16.24 to find a. More information on the printed-line attenuation can be achieved by measuring another line with very low dielectric constant, where the dielectric and the surface-wave losses are close to zero. Also, the procedure described in Section 16.2 of measuring two resonators of two thicknesses may be used for the same purpose. Another technique requires only a straight-line resonator. A relationship between Q, and the reflection coefficient p at the resonator input is proved in Reference 6 to be
n is the order of resbnance. Thus the measured end-reflection magnitude p enables the estimate of Q,, and hence of a. 16.4.1.3 2,: 'Characteristic impedance' is a fundamental concept in microwave circuits; however, its exact meaning in quasi-TEM (transverse electric
Special measurement techniques for printed antennas
975
magnetic) lines is not always very clear. Getsinger [66] uses the term 'apparent characteristic impedance' to denote the parameter which describes how printed line (microstrip in this case) exchanges power with a TEM line. The term 'characteristic impedance' defines how one TEM line exchanges power with another TEM line. Experimentally, there are at least three accurate and reliable methods for impedance measurements [66, 671, denoted as: the slotted line, the real-axis intercept and the group-delay method. A brief description of each technique is given here for the microstrip case. The slotted line procedure for finding Z, is as follows: (a) Prepare a microstrip line short-circuited at both ends and find the effective dielectric constant by a resonant technique. (b) Replace one short-circuit with a high-quality transition to the coaxial line and predict the frequencies for which the line presents short-circuits, opencircuits or +jZ, at the junction of the connectors (c) Use a slotted line to measure the reactance at each of these frequencies. Use a shorted coaxial reference to define the terminal plane at the connector end of the microstrip. This technique eliminates equipment calibrations because only distances and frequencies are measured, and the overall accuracy is of the order of 0.1%.
The real-axis intercept procedure for determining Z, is done as follows: (a) A long uniform microstrip line is placed between two connectors with very low reflections. One of the connectors is matched by a coaxial load with an impedance Z , = 50 a. (b) The input impedance at the other connector is measured by a network analyser as a function of frequency, and a Smith chart is recorded. (c) The input impedance makes nearly circular spirals on the Smith chart and XI and X, are the extreme values of the reactance. The algebraic average Xis the residual reactance of the transition, i.e. (16.27) x = (XI X2)/2
+
The intercept of the input impedance with the real axis of the Smith chart is found experimentally at some value R and the characteristic impedance of the tested line is (16.28) Z, = (RZ, - y ) l i 2 The real-axis intercept is both a simple and a fast procedure, but it has a significant disadvantage: If R is close to Z , , the impedance locus is nearly parallel to the real axis and a small reflection from the transition causes a large error in the real-axis crossing. Thus poor accuracy would be expected for printed lines with Z, close to 50 8. The group-delay method is important because it is almost independent of the coaxial-connector parasitics and it is fairly simple to perform. First, prepare a
976
Special measurement techniques for printed antennas
microstrip line terminated with a flat-plate short. Second, measure the reflection delayT about frequencies for which the shorted microstrip presents zero reactance at the transition. The equation for T is
which represents the total phase shift of the reflected wave (i.e. the angle of the reflection coefficient). Z, is then given by
Special measurement techniques for printed antennas
977
analysers. Typical examples of such resonant techniques will be shown in this Subsection, followed by a short description of time-domain reflectometry. A classical example of the characterisation of a bend in microstrip line [68] is shown in Fig. 16.17, In this method, two bends are joined by curved lines of lengths I, to form a continuous 'ring' resonator. This resonator keeps two resonances related to 1, and to 21,, and thus the properties of the bends can be found. Additional comparison is made with a circular ring built on the same substrate.
where n, an integer, is the length of the microstrip in half wavelengths atf, and D is given by
E, is the relative dielectric constant of the substrate and ~ ~ ~is (the 0 effective ) dielectric constant at zero frequency (see eqn. 16.15 and 16.16). The last method needs specific theoretical adaptation for each type of printed line in use. In summary it can be seen that the slotted-line method is accurate but difficult to perform. The real-axis-intercept method is the easiest to make but requires excellent connectors and loads. The group-delay method is simple and accurate, and does not require good transitions. But the interpretation of the result is specific to microstrip lines.
Fig. 16.18 An arrangementfor measuring the equivalent electricalparametersof a T-junction (Source: Reference 69) The components L,, L,, C and n are measured in ( a ) - ( d ) , respectively. The output
equivalent circuit is given in ( e )
Fig. 16.17 A closed 'ring' resonator with bends for characterisation of the bend properties (Source: Reference 68)
16.4.2 Measurements of printed networks 16.4.2.1 Resonant techniques Networks and line discontinuities can be characterised by the techniques described heretofore, namely, the investigation of resonant structures by network
Another common discontinuity is the T-junction, often found in power splitters. A detailed arrangement for measuring the equivalent electrical parameters of the T-junction is suggested in Reference 69. Four different test junctions are shown in Figs. 16.18a-d. Each of these junctions gives the best modelling for a different component in the equivalent electrical circuit, shown in Fig. 16.18e. More theoretical and experimental information about discontinuities can be found in References 69-73.
978
Special measurement techniques for printed antennas
Further demonstrations of practical measurements of T-junctions are shown in Figs. 16.19 and 16.20. Fig. 16.19 shows a straightforward arrangement in which a 50 Q line is connected to two 50 Q lines, using a quarter-wave transformer. The overall losses and phase shifts of this splitter can be easily found, but the connectors have a significant effect on the results. A modified version, shown in Fig. 16.20, is intended to check the T-junction between 50 R line and two oppositely directed 100 R lines. Here, two symmetrical junctions are built with a distance I2 between them, while the distance between the connector and the T-junction is I,. Recalling the interferometric relation in eqn. 16.10, one can easily find that the periodic ripple due to the connectors is
Special measurement techniques for printed antennas
979
known as the 'six-port reflectometer' [74-781. The main feature of this technique is that a six-port network with square-law detectors on four of the 'output' ports, can be calibrated by a computer, to determine the amplitude and the phase of signals at the other two 'input' ports. The simplicity of the detection reduces the cost of precise hardware, although the accuracies are of the same order as in error-corrected vector network analysers. One important attraction of the six-port technique is the relative ease with which it can be employed in the millimetre-wave range. So far as the characterisation of printed lines is concerned, the six-port technique, being based on coaxial components, has the same drawbacks as the vector network analysers. 16.4.2.2 Time-domain rejectometry: Time-domain measurements are performed by transmitting a known waveform out into the test network o r into a discontinuity and measuring the waveform returned as a function of time. The delay of the returned waveform aids in finding the distance to the network, and the shape of the returned waveform gives information about the impedance of the network. Since commercial pulse generators have a typical rise time of about t, = 30 ps, the resolution of the distance is of the order of
Fig. 16.19 Practical testing of a T-junction
,
Fig. 16.20 Improved test of a T-junction by two junctions Different resonances are measured due to the connectors and due to the Tjunctions
while the periodic ripple due to the T-junctions is
+
1,) is required in order to A sufficiently large difference between I2 and (21, achieve high accuracy. An additional test of two connectors alone will give a good reference for this measurement. A few words should be injected here about an alternative network analysis
for air lines, and up to A[,& z 1.5 mm for printed lines on alumina. The time-domain technique eliminates the problems involved with coaxial connectors and coaxial standard references. It gives an immediate recognition of the impedance of various networks, while the accuracies are limited by the rise time of the source. Improved accuracies and sensitivities are reported in References 79-81 by the use of combined reflection and transmission measurements, or by statistical signal processing. An example of TDR results is shown in Fig. 16.21. A 16-element microstrip antenna, designed to operate at 10 GHz is shown in Fig. 1 6 . 2 1in ~ top view. The central 100 R line is fed at its centre by a coaxial SMA connector. The other feed lines have impedance of 200 R,which is also the calculated radiation impedance of each radiating element at resonance. The TDR oscillogram of this antenna was made with Tektronix equipment (7603 mainframe, S-52 pulse-generator head and S-6 sampling head) having a typical rise time of 30 ps. Three points of interest are noted as A, B and c, both on the antenna layout and on the TDR oscillogram. Point A is the connector area which is found to have a small inductance. Point B is the first T-junction which has a small capacitance, and point c is the second junction which is almost free of any parasitic reactance. The time delays between A-B and B-c are equal and measured from the oscillogram to be
AT = (1.1 f 0.1)200 picoseconds This time delay is equivalent to a distance of
A& !
= c(A~/2) = 3.3 $. 0.3 centimetres
980
Special measurement techniques for printed antennas
The physical distances between the noted points, A1 = 2.4 cm, and the electrical distances z 3.4 cm, are in good agreement with the TDR results. The dominant slope, which comes after c, is the result of the capacitive nature of the radiating elements.
AIJE~~
Special measurement techniques for printed antennas
981
An indirect TDR can also be made by measuring the frequency response and using a fast fourier transform (FFT) to convert the data into the time domain. Such measurements made by wideband network analysers have gained much interest in recent years [82, 831, and several commercial products like the HEWLETT PACKARD 8510 network analyzer 1841or the WILTRON 360 [82] are adequate for these applications. 16.5 Near-field probing
Fig. 16.21 A TDR oscillogram of a 16-element rnicroslrip array (Courtesy: Dr. P. Pertmutter, Bellcore NJ, USA) Points A. B and C are shown both on the antenna layout and on the TDR trace.
Near-field measurements are usually considered as a special case of pattern measurements, which are done in the vicinity of the radiating aperture. They are performed in cases where the far-field pattern measurement is very difficult, expensive or even impossible, e.g. high-gain or low-frequency antennas, antennas mounted on large bodies, or if there is a need in secure and controlled test environments or with all-weather capability. The near field is detected by a scanning probe over a chosen surface (planar, cylindrical or spherical), and the measured results are processed by analytical or numerical methods to give the required far field. General reviews on near-field techniques, including scanning procedures, data analysis and error corrections - especially errors caused by the probes - can be found in References, 2 and 85-89. Near-field scanning is also required in cases where the knowledge of the exact current or field distribution on the aperture is important; e.g. in arrays with tapered aperture distribution, in phased arrays where the relative phases of excitation should be characterised, or in R F applicators which operate on biological tissues at close distances. In most of these cases, precise quantitative information is needed, which means that the measurement of the near field must be very accurate and the effects of the probe on the measured fields must be taken into account. There are, however, a variety of applications in which a qualitative mapping of radiating aperture is very useful. One such application is the near-field probing of microstrip antennas. This near-field probing, which is done at distances of millimetres from the printed board, can serve as a diagnostic tool in the design and the production stages of the antenna. It can be used to find local defects, to reveal asymmetries in the feed networks, to improve excitation details of the radiating elements, and even to provide quantitative profiles of the aperture field distribution. The discussion in this Section is restricted to practical and immediate techniques which can be used by any microstrip antenna designer. The most important consideration for these applications is the choice of a miniature probe. The probe should be sensitive enough to the tested fields on one hand, while having minimal effect on the tested aperture. Furthermore, the probe should have high spatial resolution. A second consideration is the use of efficient yet inexpensive scanners. Both of these considerations are discussed here, several schemes are presented and some experimental mappings are demonstrated.
982
Special measurement techniques for printed antennas
The majority of the miniature probes can be divided into three types: (a)Jield probes which are small antennas that are sensitive to electric or magnetic fields, (b) intensity probes which are basically square-law detectors connected to miniature dipoles, and (c) thermal probes which are flat layers of liquid crystals or thermo-electric junctions that are sensitive to the R F power in their vicinity. The specific choice between the three types depends mainly on the required information. A comprehensive review of electric-field probes of the first and the second types is given in Reference 90. A detailed analysis of miniature electricfield probes with resistive tranmission lines is given in Reference 91. Examples of a sub-millimetre probe and a three-dimensional probe are given in References 92 and 93, respectively.
Special measurement techniques for printed antennas
983
sensitive. Their major disadvantage is the undesired change in the phase of the transmission line which connects them to the receiver, while the probes are moving. These probes are usually sensitive with respect to the frequency. In addition, special baluns (balanced to unbalanced transitions) are needed to reduce their influence on the tested apertures. Four practical field probes are shown in Fig. 16.22. The first one (a) is a very simple monopole which is created microwave
A
Schotky diode
a
/
Af3soREEFi
\
SEMI- RIGID CABLE
b
( M A 402149)
n
whiskers
I
b
'*guided or free-air beam electro-optical modulator
@ I
photo-detector electronic detector
Fig. 16.22
Practical field probes for near-field mapping (Sources: References 2, 85,95,96) a A shon monopole with vertical polarisation [95] b A split-coaxial balun with horizontal polarisation [85, 961 c A small loop for magnetic-field probing (perpendicular to the plane of the paper) d A small loop with balun [2]
The field probes are generally used when both the amplitude and the phase of the tested aperture are needed. They are small in size and their sensitivity depends on the quality of the receiver in use. Field probes are polarisation
Fig. 16.23 Electric-field probes with square-law detectors (Sources: References 90,98) a A diode mounted in a plastic holder [98]. The dipole length is 3 mm. b A printed version [SO] where the dipole length is 1.5 mm c An electric probe coupled to optical modulator [go]
by extending the inner conductor of a coaxial line. This sensitive and reliable probe has been used for precise measurements of printed-line parameters [94, 951. A second field probe (b) is a combined balun, made of a split coaxial section and an absorber [85,96], both intended to reduce its effect on the tested aperture to a minimum. A simple loop for magnetic-field detection is shown in Fig. 16.22c, and another balun arrangement for the magnetic field [2] is shown in 16.22 (4.
984
Special measurement techniques for printed antennas
The second type - miniature square-law detectors - are very attractive for automatic scanning over large surfaces and for diagnostic purposes. Like the field probes they are polarisation sensitive, but, unlike the field probes, miniature square-law detectors cannot measure phase. These detectors have a weak effect on the field at the antenna aperture and perform best when they are connected to the recording system by highly resistive transmission lines. Three inlensiry probes used to measure the electric field with square-law detectors are shown in Fig. 16.23. A first example (a) is a sensitive diode mounted in a plastic holder and connected to a coaxial amplifier through highly resistive coatings [97, 981. The mean size of such a probe can be between 1 and 4 mm and its low sensitivity requires high-quality amplifiers for the DC output. Fig. 16.236 presents a printed version of the intensity probe [90] and Fig. 1 6 . 2 3 illustrates ~ a novel concept of an electric probe that modulates a laser beam [90]. Any R F voltage developed by the dipole causes a direct, instantaneous change in the amplitude of the beam of light passing through the modulator. This probe ensures high isolation of the probe's antenna and a very quick response which can be used for phase measurements. antenna under test\
transparent cover \
liquid crystal
Special measurement techniques for printed antennas
985
resolution, and the possibility of extracting quantitative information, make the scanning probes more attractive for near-field measurements. What specific applications can be done with scanning probes? The first is checking the parameters of a printed transmission line, especially the effective dielectric constant. Several examples can be found in References 94, 95 and 103-105. Of special interest is the description given by Ladbrooke [I041 of how a microstrip standing-wave indicator can be used to study the line parameters and the effects of discontinuities. Such probing can be most useful for unconventional printed lines like the suspended air line shown in Fig. 16.25 or dielectric lines [94], where analytical expressions or design curves are not available.
to recorder arm
paint
ground
Fig. 16.25 Near-fieldprobing along a printedline can be used for the measurement of the line parameters
plane
Fig. 16.24 Liquid-crystal diagnostics of a microstrip radiator (Source: Reference 100)
The third group - thermal detectors - are the least sensitive and least accurate, but they can be used in the most direct and simple way. A thin layer of liquid crystal, placed on the antenna as shown in Fig. 16.24, can give immediately a good visual impression of the standing waves existing in the feed network, the relative magnitudes of the element excitations and the field profile on each radiator. Further details and examples can be found in References 99-102. The second consideration in preparing a near-field system is the scanning instrumentation. Although the liquid-crystal diagnostic is extremely simple since no scanning is needed, it seems that the requirements of high spatial
A second application for scanning probing is to locate defects and asymmetries in printed feed networks. Any mechanical scanning system can be used to move the probe in a planar, cylindrical or on any desired surface. An example of a low-cost mechanical system, based on two general-purpose XY recorders is shown in Fig. 16.26 [98]. Here, one of the recorders serves as a scanner ('master'). Another recorder, referred to as the 'slave', receives the X and Y signals from the 'master', and, in addition, its Y input also receives the detected output from the probe. In this Figure a lock-in amplifier in used in order to improve the sensitivity. Another example of standard laboratory equipment used for this purpose appears in Reference 106. A modified version uses a moving-field probe connected through a semi-rigid line to a high-quality detector. Such an arrangement can give accurate mapping of the near field, since the detector is far away from the aperture, as well as high sensitivity. For example, antennas with area of 0.1 m2, fed by a source of 20 mW, can easily be detected with a conventional detector (like the HP 8473) and XY recorders without any external amplifiers. The phase distribution on the aperture is also often needed. For instance, in beam-shifted arrays one is interested in the relative phase changes between the elements. Also in circular-polarisation designs one is interested in checking if an
986
Special measurement techniques for printed antennas
appropriate 90" phase shift is achieved. The scanning with a phase-sensitive probe is quite complicated. The main difficulty is that it is necessary to convey the signal back to a phase-sensitive receiver from the mobile probe without
-
signal generator
Pin switch
antenna mech. ------1master
A recorder
switch driver (25 Hz) lock-in amplifier ref
Special measurement techniques for printed antennas
987
with an aperture size of 47 mm. The deviations from the theoretical profile were about 0.5 dB in amplitude and 5" in phase. Special phase mapping, which is done by a low-frequency modulation of the .robe., is described in Reference 107. Small dipoles which are coupled to optical modulators are expected to play an important role in future developments. As mentioned earlier, they are both sensitive and 'transparent' to the tested fields. Another novel idea is the use of an active radiating probe [I081 to test printed and even integrated circuits. This is done by very thin radiators which are placed on the printed circuit, and the change in their radiation pattern is detected by another receiving antenna.
in slave recorder
Fig. 16.26 Block diagram of a scanning system for near- fieldprobing (Source: Reference 98) The probe is a square law detector connected to a small dipole
n
recorder 2 (plotter)
recorder 1 (scanner)
amplitudelphase output Fig. 16.28 Near-field mapping of a four-element array at 10.1 GHz a in original state b After two cuts were made near the left elements
probe
a RF cable
Fig. 16.27 Block diagram of amplitude andphase mapping by a network analyser. The probe is a small antenna
changing the electrical path length of the transmission line. A possible solution is to keep the probe in one place and move the tested antenna instead. The block diagram of Fig. 16.27 shows how both amplitude and phase information can be achieved using a network analyser (HP 8410) and two recorders. The detector in use here is the split coaxial line and the R F cables are Gore flexible cables. This scheme has been checked on the aperture of a standard horn at 10 GHz,
We conclude this Section with several demonstrations of near-field mappings of microstrip antennas [98]. All these mappings were done by miniature electric probes (Fig. 16.226 or 16.23 a) and two XY recorders, as described in Fig. 16.26. Fig. 16.28 demonstrates the influence of a defect on the near field of a fourelement array. Fig. 1 6 . 2 8 is ~ the layout of the antenna, Fig. 16.286 is an original field pattern, which was taken at 10.1 GHz at a distance of 3 mm from the antenna, and Fig. 16.28~shows the near-field pattern after two cuts were made near the two left elements. Such a diagnostic test can reveal local defects even in cases where ohmic contacts do exist. A second example, shown in Fig. 16.29, shows the layout of a 16-element array, built at 10.6 GHz (Fig. 16.29a), a near-field pattern which was produced at distance of 1 mm from the antenna (Fig. 16.29b), and another pattern which was made at distance of 30 mm. It can be seen here that the asymmetry between the left and the right sides of the
988
Special measurement techniques for printed antennas
Special measurement techniques for printed antennas
989
antenna almost disappears at a distance of one wavelength, which is much closer than the far-field region. The local asymmetries in this specific antenna are caused by different excitation angles of the elements. In corporate-feed designs, all the elements are fed from the same angle and the local asymmetries are expected to be reduced. The third example, shown in Fig. 16.30, presents the near-field pattern of a four-element array at 6.3 GHz, with corporate-feed network. In this case there are standing waves in the central feed line that have some influence on the elements. Such near-field mapping can be used in this case to check how relative translations of the central line change the antenna excitation.
------'Fig. 16.29 Near-field mapping of a 76-element array at 10.6 GHz a At distance of 1 mm b At distance of 30 mm from the aperture
Fig. 16.31 Near-field mapping of a 16-element array of double-sided printed dipoles at 4.7 GHz The dark area in the antenna layout is an upper print and the dashed area is a lower print. The two-sided board is placed above a metallic ground plane. Two orthogonal mappings are presented
Fig. 16.30 Near-field mapping of a four-element array with a corporate feed network, at 6.3 GHz The scanning was performed at a distance of 3 mm from the antenna.
Fig. 16.31 shows scanning results on the aperture of a 16-element array of printed dipoles at 4.7 GHz. The array is printed on both sides of a thin dielectric substrte. The black area is the upper print and the dashed area is the lower print. The printed substrate is placed above a metallic ground plane with a foam spacer of 0.15 A, thickness in between. The two scans in Fig. 16.31 were carried out in the same polarisation of the probe. The standing waves in the feed network and some local asymmetries are shown in the two orthogonal views.
990
Special measurement techniques for printed antennas
These standing waves, recorded at a distance of 2 mm from the printed board (0.03 Lo), are related to the overall feed radiation, although a quantitative interpretation is difficult. The last example, shown in Fig. 16.32, is the near-field mapping of a single disc, fed at its centre by a coaxial connector, at 7.1 GHz.
/'
I\-ground \+plane
/ / " - - ' , \
\ center-fed
/
/
I /
I disk in
top view
Fig. 16.32 Near-field mapping at 7.1 GHz of a centre-fed disc, with foam spacer as a dielectric substrate. The disc is placed 3 mm above the ground plane and the scanning was done 6 mrn above the ground plane. The mode number is n = 0
fJbfk,rJ
=
0)
The size of the probe (length of the dipole) is 4 mm. The disc is mounted 3 mm above a ground plane with a foam spacer in between, and the scanning was done 6 mm above the ground. This map of the element excitation shows the existence of the first symmetrical mode on the patch. Important information can be gained from this map as to the decay of the field along the ground plane. In this case the fields are bounded within a circle with a diametre of 70mm. Near-field probing can be thus used for combined theoretical and empirical modelling of printed radiators, testing the influence of a finite ground plane or testing the contribution of the vertical currents in the feed.
Special measurement techniques for printed antennas
997
16.6 Efficiency measurement
Printed array antennas show low efficiency owing to inherent dielectric and ohmic losses in their feeding network and owing to the excitation of surface waves in the substrate. The efficiency limitation is most severe in large arrays where the feed network is long and complicated, and in arrays operated at high frequencies. In addition to the dissipation losses, there are usually also 'radiation losses' caused by unwanted radiation from the feed lines or from the connectors. All these mechanisms reduce the available gain of the printed antenna, but it is quite difficult to identify the contribution of each loss. Experimental characterisation of the different losses is frequently desired. One major motivation is the fact that in low-noise receivers there is a difference between dissipation losses and radiation losses. Dissipation losses act as an attenuator placed in front of an ideal antenna; thus they reduce directly the overall noise figure of the system. On the other hand, radiation losses change the radiation pattern, but they do not affect the noise figure unless the sidelobes are directed towards a noisy environment. A similar separation between losses is also required when a plastic cover (radome) is put in front of the antenna. The ohmic and dielectric losses of microstrip lines are well known in the literature both from theoretical and experimental aspects. The losses of any specific materials or feed lines can be measured independently by standard methods mentioned in Sections 16.2 and 16.4. We would like to concentrate here on the overall power efficiency of the printed antenna, and, in particular, to describe a simple technique for its measurement. The power efficiency of an antenna is the ratio of the total power radiated by the antenna to the input power accepted by the antenna at its terminals. The efficiency can also be expressed in terms of the gain and the directivity
gain directivity Here, the radiated power PRis given by integrating the radiation intensity P(0, 4) over the far-field surface s completely enclosing the antenna. Thus an accurate evaluation of requires the measurement of P(B, 4) for a sufficiently large number of angles, and a numerical integration of the results. This is often slow and complciated and requires a well-designed antenna range [109-1101. A simpler, but less accurate method, requires the measurement of the two principal E- and H-plane patterns of the tested antenna, and the use of the following approximation for the directivity D (for a uniform illuminated aperture) [Reference 3, p. 331
992
Special measurement techniques for printed antennas
where 8, and 8, are, respectively, the half-power beamwidths in degrees. Combining this directivity with the measurement of gain gives the efficiency (eqn. 16.35). A quick method for measuring the efficiency of an antenna, which directly integrates the antenna pattern, is described in Reference I I 1. In this method, the antenna to be tested is at the input of a radiometer that is directed towards extended 'warm' and 'cold' targets. A convenient cold target is a clear sky, and a warm one is an extended absorber, usually at room temperature. The use of extended sources automatically integrates over the whole radiation pattern. The relationship between the desired efficiency q and the measured voltages at the radiometer output is given by
where E is the ratio of the voltage when the antenna is directed towards a warm target to the voltage when the antenna is directed towards a cold target. 6 is the same measured ratio for a high-efficiency antenna such as a horn, for which we assume q = 1. A block diagram of the system is shown in Fig. 16.33. The R F amplifier is the most important component because it has the dominant effect on the overall noise figure of the radiometer. In many radiometers an integrated mixer/amplifier is used as an input stage, and in these cases its noise figure is dominant. The validity and the accuracy of this measurement technique were tested by connecting a waveguide calibrated attenuator after the horn antenna, and measuring the radiometer output. For example, a test set in the Ku-band was built with a low-noise amplifier Miteq AMF-3D-1218 with 20 dB gain and a 5.7 dB noise figure. The I F bandwidth of 200 MHz was determined by a low-pass filter that was introduced between the I F amplifier and the detector. The difference between the attenuator readings and the losses computed from the measured radiometric results was less than 0.3 dB. reference horn mixer
I
1
detector
RF amplifier
tested antenna Fig. 16.33 Block diagram of a radiometer for antenna-efficiency measurement (Source: Reference 1 7 7)
A set of 16-, 64-, 256- and 1024-element microstrip antennas [I 121 in frequencies of 10, 20 and 35 GHz were tested by this technique, and their measured efficiencies were found to be in a good agreement with theoretical estimates. A
993
Special measurement techniques for printed antennas
Table 16.1 List of components used in radiometric systems
10 GHz
20 GHz
35 GHz
RF Amplifier
Miteq AFD4040 130 NF = 4dB
none
none
Mixer
Anaren 7G0118
Alpha ATD9606K09 NF = 5dB
Honeywell F35UP NF = 5dB
Local oscillator
Varian VSX900 1M G
Varian VSK9004FS
Varian VSA90 10JC
IF amplifier
Avantek SD30632M
Avantek SD30632M
Avantek SD30632M
LP filter
200 MHz
200 MHz
200 MHz
Reference horn
FXR X638A
self-made
TRG A861
Table 16.2 Measured and calculated results (in dB) of the losses in microstrip arrays
Number of elements 16
64
256
1024
10 GHz D(ca1culated) - Gtmeasured) Calculated loss Measured loss
0.7 0.8 0.5
1.O 1.1 1.2
1.5 1.6 1.7
-
-
20 GHz D-G Calculated loss Measured loss
0.3 0.9 0.7
1.5 0.2 1.3
2.0 2.1 2.2
3.2 3.0 2.7
35 GHz D-G Calculated loss Measured loss
1.1 1.1 1.4
1 .5 1.5 1.8
2.7 2.5 2.8
4.8 4.1 4.0
2.3
994
Special measurement techniques for printed antennas
list of the components used in these measurements is given in Table 16.1 and measured results are given in Table 16.2. A few remarks should be noted concerning the accuracy and the repeatability achieved by this method: (a) The expression used for the efficiency is valid under the assumption that the antenna is perfectly matched. However, standing waves in the measurement system may cause significant errors in the interpretation of the measured data. It is therefore recommended the measurements be repeated at several frequencies near the operating frequency of the antenna. (b) The transition from the printed antenna into a waveguide input of a mixer or an amplifier is also a source of systematic errors. These errors can be reduced by performing an additional measurement of 6 for the reference horn, while connecting it through two waveguide/coaxial-line adapters, and averaging the results with the original value of 6. (c) Special care should be taken to ensure that the extended cold target will cover the upper half-sphere around the tested antennas. Any surface-wave launching in near-endfire angles can change the entire effective temperature of the antenna; thus the area in the vicinity of the ground plane should be clear of obstacles. (4 The radiometric measurement is not sensitive to the antenna polarisation; and hence it can handle both linear and circular polarisations with the same accuracy.
16.7 Concluding remarks
The experimental techniques described in this Chapter can be most helpful in the design and the manufacturing processes of microstrip and other printed antennas. They are suggested as supplements to the conventional far-field measurements and network analysis. The frequency range discussed here covers microwaves up to 40 GHz, and in some cases perhaps a little higher. It should be pointed out that all these measurements are limited by calibration errors and by wrong interpretation, and not by signal/noise or dynamic range considerations. This is, of course, due to the passive nature of the antennas and their feed network. The topics covered in this Chapter include: the substrate properties, the connector, the printed network and two specific techniques of near-field probing and radiometric measurement. The properties of the substrate are usually given by the manufacturer. However, in some cases one wishes to characterise the substrate by oneself. Examples are: combination of different substrates, the use of substrates at higher frequencies than reported, or when an exact characterisation is needed as a function of a parameter such as the temperature. The accuracy achieved for the dielectric constant in the described techniques is of the order of 1%. The measurement of the loss tangent is difficult for common
Special measurement techniques for printed antennas
995
low-loss materials. This information can be achieved by a stripline made of the materials under test. The characterisation of connectors is very important since the manufacturers do not give specific data about transitions into printed lines. Two typical examples in which the connector measurement is recommended are: thin (i 0.4 mm) and thick ( > 3.2 mm) substrates, and at higher frequencies than recommended by the manufacturer. The characterisation of connectors is sensitive and accurate while using the interferometric methods. The reactance of the connector may even by used for broadband matching of antennas. Printed lines and structures can be tested accurately by the resonant method given in this Chapter. Of special interest is the TDR technique, which can identify local defects with accuracy of several millimetres. Near-field probing is a qualitative tool which can help in understanding the behaviour of printed antennas and finding local defects. The main limitation is the interpretation of these mappings. The radiometric technique is useful, especially for large printed arrays with high losses. One can expect to find the dissipation losses of medium- and high-gain arrays with accuracies better than 1 dB. Future developments in the instrumentation for printed antennas will probably include the following: better substrates with accurate data sheets; novel calibration sets for accurate measurement of connectors and printed structures; new feed lines and new feed techniques for the radiators. Another promising area is the combination of radiators with active devices and MMIC chips. Such combinations will also lead to better measurement techniques and instrumentation. In the future there will be also combinations of printed antennas with electro-optical devices and optical fibres. Such combinations will, of course, require special measurement techniques. Finally, one may expect in the future to find some miniature probes, fed by optical means, for near-field probing. 16.8 References 1 HOLLIS, J. S., LYON, T. J., and CLAYTON, L. (Eds.): 'Microwave antenna measurements' (Scientific Atlanta, 1970) 2 APPEL-HANSEN, J., DYSON, J. D., GILLESPIE, E. S. and HICKMAN, T. G.: 'Antenna measurements' (in RUDGE, A. W., MILNE, K., OLVER, A. D., and KNIGHT, P. (Eds): 'The Handbook of antenna design' (Peter Peregrinus, 1982) Chap 8 3 BALANIS, C. A,: 'Antenna theory - analysis and design' (Harper and Row, NY, 1982) Chap. 15. 4 BLAKE, L. V.: 'Antennas' (Artech House, Mass., 1984) chap 8. chap 9-9 5 GUPTA, K. C., GARG, R., and BAHL, I. J.: 'Microstrip lines and slotlines' (Artech House, Mass., 1979) pp. 28-38, 184-193, 331-336 6 EDWARDS, T. C.: 'Foundations for microstrip circuit design' (John Wiley, 1981) pp. 172-207 7 LAVERGHETTA, T. S.: 'Microwave materials and fabrication techniques' (Artech House, Mass., 1984) p. 56 8 NAPOLI, L. S. and HUGHES J. J.: 'A simple technique for the accurate determination of the microwave dielectric constant for microwave integrated circuit substrates', IEEE Trans., 1971, MTT-19,pp. 664-665
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9 HOWELL, J. Q.: 'Quick accurate method to measure the dielectric constant of microwave integrated circuit substrates', IEEE Trans., 1973, MTT-21, pp. 142-143 10 LADBROOKE, P. H., POTOK, M. H. N., and ENGLAND, E. H.: 'Coupling errors in cavity resonance measurements on MIC dielectrics', IEEE Trans., 1973, MTT-21, pp. 560-562 11 OWENS, R. P., AITKEN, J. E. and EDWARDS, T. C.: 'Quasi static characteristics of microstrip on an anisotropic sapphire substrate', IEEE Trans., 1976, MTT-24, pp. 499-505 I2 RICHARDS, W. F., LO, Y. T. and BREWER, J.: 'A simple experimental method for separatmg loss parameters of a microstrip antenna', IEEE Trans., 1981, AP-29, pp. 150-151 13 ITOH, T.: 'A new method for measuring properties of dielectric materials using a microstrip cavity', IEEE Trans., 1974, MTT-22 pp. 572-576 14 GERHARD, A. R.: 'Measuring dielectric constant of substrates for microstrip applications', lEEE Trans., 1976, MTT-24, pp. .. 485437 IS BUSSEY, H. E.: 'Measurement of RF properties of materials - survey', proc. IEEE, 1967, 55, pp. 1046-1053 16 LYNCH, A. C.: 'Precise measurements on dielectric and magnetic materials', IEEE Trans., 1974, IM-23, pp. 425-431 17 KOBAYASHI, Y. and KATOH, M.: 'Microwave measurement of dielectric properties of low loss materials by the dielectric rod resonator method', IEEE Trans., 1985, MTT-33, pp. 586-592 18 AFSAR, M. N.: 'Dielectric measurements of millimeter wave materials', IEEE Trans., 1984, MTT-32, pp. 1598-1 609 19 PUES, H. F. and VAN D E CAPELLE, A. R.: 'Wideband impedance matched microstrip resonator antenna'. Proc. 2nd ICAP, 1981, pp. 402-405 20 GRIFFIN, J. M. and FORREST, J. R.: 'Broadband circular disc microstrip antenna', Electron. Lett., 1982, 18, pp. 266-269 21 FONG, K. S., PUES, H. F., and WITHERS, M. J.: 'Wideband multilayer coaxial fed microstrip antenna element', Electron. Lett., 1985, 21, pp. 497-499 22 CHEW, W. C. and KONG, J. A.: 'Analysis of a circular disk antenna with a thick substrate', IEEE Trans., 1981, AP-29, pp. 68-76 23 YANO, S. and ISHIMARU, A,: 'A theoretical study of the input impedance of a circular microstrip disk', IEEE Trans., 1981, AP-29, pp. 77-83 24 HENDERSON, A. and JAMES, J. R.: 'Design of microstrip antenna feeds. Part I: Estimation of radiation loss and design implications', IEE Proc., 1981, 128H. pp. 19-25 25 HENDERSON, A. and JAMES, 1. R.: 'Estimation of radiation from microstrip antenna feed transition', Radio Sci., 1981, 16, pp. 1119-1 123 26 PINHAS, S., and SHTRIKMAN, s.: 'Vertical currents in microstrip antennas', IEEE Trans., 1987, AP-35, pp. 1285-1289 27 WIGHT, 1. S., JAIN, 0. P., CHUDABIAK. W. J., and MAKIAS, V.: 'Equivalent circuits of microstrip impedance discontinuities and launchers*, IEEE Trans., 1974, MTT-22, pp. 48-52 28 AJOSE, S. 0 . and MATHEWS, N. A,: 'Equivalent circuit of coaxial to microstrip connector over the 8-12 GHz range, Electron. Lett., 1977, 13, pp. 465-466 29. HALL, P. S. and JAMES, J. R. 'Design of microstrip antenna feeds. Part 2: Design and performance limitations of triplate feeds' IEE Proc., 1981, 128H, pp. 26-34 30 MAJEWSKI, M. L., ROSE, R. W. and S C O T , J. S.: 'Modeling and characterization of microstrip to coaxial transitions', IEEE Trans., 1981, MTT-29, pp. 799-805 31 PUES, H. F. and VAN DE CAPELLE, A. R.: 'Computer aided experimental charaterization of microstrip to coaxial transitions'. Proc. 14th European Microwave Conference, 1984, pp. 137-141 32 EMC Technology: Microwave components catalog 882-15, 1982, p. 38 33 MIA-COM Omni Spectra Inc: Microwave coaxial connectors catalog, 1983, p. I I 34 ENGLAND, E. H.: 'A coaxial to microstrip transition', lEEE Trans., 1976, MTT-24, pp. 4748 35 AJOSE, S. O., MATHEWS, N. A. and AITCHISON, C. S.:'Characterisation of coaxial to
Special measurement techniques for printed antennas
1
i
i
I
1 i
I
997
microstrip connector suitable for evaluation of microstrip Zports', Electron. Lett., 1976, 12, pp. 430-43 1 36 GOURLEY, S. E. and CHAPMAN, A. G.: 'Broadband characterization ofcoaxial to microstrip transitions'. Proc. 12th European Microwave Conference, 1982, pp. 622-627 37 RICKARD, D. C.: 'Thick film mic components in the range 10-20 GHz. Proc. 6th European Microwave Conference, 1976, pp. 687-691 38 FINLAY, H. J., HOPKINS, L. G. T. and OZAMIZ, J. M.: 'Design and applications of precision microstrip multioctave attenuators and loads'. Proc. 6th European Microwave Conference, 1976, pp. 692696 39 KDI-Pyrofilm: RF resistive components catalog, PSA 1/80, 1980 40 EMI-Varian: Microstrip circuits data sheets, mc2m/10/70 41 EISENHART, R. L.: 'A better microstrip connector'. IEEE Int. Symp. Digest MTT-S, 1978, pp. 318-320 42 LEVINE, E., and TREVES, D.: 'Test technique improves coax to microstrip transitions', Microwaves and RF, July 1986, pp. 99-102 43 GUPTA, C. D., and TOMAR, R. S.: 'Resonance method of measurement of input impedance of any broadwall launched discontinuity in microstrip transmission lines', IEEE Trans., 1986, IM-35, pp. 126-129 44 SEALECTRO Co.: SMA catalog, SMA-9, 1980, pp. 25-26 45 WILTRON Co.: K Connector and semirigid cable, data sheet, 35K, Oct. 1984; K l I0 Series sliding contacts data sheet, DS 110-1, April 1985 46 HEUVEN, VAN 1. H. C.: 'A new integrated waveguide microstrip transition', IEEE Trans., 1976, MlT-24, pp. 144-147 47 SCHIEK, B. and KOHLER, J.: 'An improved microstrip to microslot transition', IEEE Trans., 1976, MTT-24, pp. 231-233 48 SHEPHERD, P. R. and POLLARD, R. D.: 'Direct calibration and measurement of microstrip structures on Gallium Arsenide'. IEEE Int. Symp. Digest MTT-S, 1986, pp. 629-632 49 CARLTON, D. E., GLEASON, K. R. and STRID, E. W.: 'Microwave wafer probing', Microwave J . Jan. 1985, pp. 121-129 50 HEWLETT PACKARD COMPANY: 'On wafer measurements using the HP 8510 network analyzer and Cascade Microtech wafer probes'. Product note 8510-6, May 1986 51 TROUGHTON. P.: 'Measurement techniques in microstrip', Electron. Lett., 1969, 5, pp. 25-26 52 WOLFF, I. and KNOPPIK, N.: 'Microstrip ring resonator and dispersion measurement on microstrip lines', Electron. Lett., 1971, 7 , pp.779-781 53 OWENS, R. P.: 'Curvature effect in microstrip ring resonators', Electron. Lett., 1976, 12, pp. 356-357 54 DEUTCH, J. and JUNG, H. J.: 'Measurement of the effective dielectricconstant of microstrip lines in the frequency range from 2 GHz to 12 GHz', Nachrichtenlech Z., 1970,12, pp. 620-624 55 EDWARDS, T. C. and OWENS, R. P.: '2-18 GHz dispersion measurements on 10-100 ohm microstrip lines on sapphire', IEEE Trans., 1976, MTT-a, pp. 506-513 56 ROMANOFSKY, R. R., BHASIN, K. B., PONCHAK, G. E., DOWNEY, A. N. and CONNOLLY, D. J.: 'An experimental investigation of microstrip properties on soft substrates from 2 to 40 GHz' IEEE Int. Symp. digest MTT-S, 1985, pp. 675-678 57 RICHINGS, J. G.: 'An accurate experimental method for determ~ningthe important parameters of microstrip transmission lines', Marconi Rev. 1974, pp. 209-216 58 BELOHOUBEK, E. and DENLINGER, E.: 'Loss considerations for microstrip resonators', IEEE Trans., 1975, MTT-23, pp. 522-526 59 PUCEL, R. A,, MASSE, D. J. and HARTWIG, C. P.: 'Losses in microstrip', IEEE Trans., 1968, MTT-16, pp. 342-350, 1064 60 DENLINGER, E. J.: 'Losses in microstrip lines', IEEE Trans., 1980, MTT-28, pp. 513-522 61 JAMES. J. R. and HENDERSON, A,: 'Planar millimeter wave antenna arrays in Infrared and millimeter waves'; Vol. 14 (Academic Press, 1985) pp. 189-247
,
998
Special measurement techniques for printed antennas
62 TROUGHTON, P.: 'High Q factor resonators in microstrip', Electron. Lett., 1968, 4, pp. 520-522 63 AITKEN, J. E.: 'Swept frequency microwave Q factor measurement', Proc. IEE, 1976, 123, pp.855-862 64 KAJFEZ, D. and HWAN, E.: 'Q factor measurement with network analyzer', IEEE Trans., 1984, MTT-32, pp. 666-669 65 LADBROOKE, P. H.: 'Some effects of field perturbation upon cavity resonance and dispersion measurements on MIC dielectrics', IEEE Trans., 1977, MTT-25, pp. 892-903 66 GETSINGER, W. J., 'Measurement and modeling of the apparent characteristic impedance of microstrip', IEEE Trans., 1983, M'IT-31, pp. 624-632 67 SHEPHERD, P. R., and DALY, P.: 'Modeling and measurement of microstrip transmissionline structures', IEEE Trans., 1985, MTT-33, pp. 1501-1506 68 STEPHENSON, I. M. and EASTER, B.: 'Resonant techniques for establishing the equivalent circuits of small discontinuities in microstrip', Electron. Lett., 1971, 7, pp. 582-584 69 EASTER, B.: 'The equivalent circuit of some microstrip discontinuities'. IEEE Trans., 1975, MTT-23, pp. 655-660 70 MENZEL, W. and WOLFF, I.: 'A method for calculating the frequency dependent properties of microstrip discontinuities', IEEE Trans., 1977, MIT-25, pp. 107-1 12 71 EASTER, B., GOPINATH, A. and STEPHENSON, I. M.: 'Theoretical and experimental methods for evaluating discontinuities in microstrip', Radio & Electron. Eng., 1978, 48, pp. 73-84 72 RIZZOLI, V.: 'A general approach to the resonance measurement of asymmetric microstrip discontinuities'. IEEE Int. Symp. Digest MTT-S, 1980, pp.422424 73 GARG, R. and BAHL, I. J.: 'Microstrip discontinuities', Int. J. Electron., 1978,45, pp. 81-87 74 ENGEN, G. F.: 'The six-port reflectometer: an alternative network analyzer', IEEE Trans., 1977. M'IT-25. DD. 1075-1080 75 CRONSON, H. M. and SUSMAN, L. A.: 'Six-port automatic netowrk analyzer' IEEE Trans., 1977, MTT-25, -DD. - 1086-1091 76 CULLEN, A. L.: 'The six-port and the microprocessor in microwave measurements'. Proc. 9th European Microwave Conference, 1979, pp. 74-82 77 SOMLO, P. I. and HUNTER, J. D.: 'A six-port reflectometer and its complete characterization by convenient calibration procedure' IEEE Trans., 1982, MTT-30, pp. 186-192 78 EL-DEEB, N. A,: 'The calibration and performance of a microstrip six-port reflectometer', ZEEE Trans., 1983, MlT-31, pp. 509-514 79 ELLIOT, B. J.: 'High sensitivity picosecond time domain reflectometry', IEEE Trans., 1976, IM-25, pp. 376-379 80 PILLER, U.: 'Time domain immittance measurements'. Proc. 4th European Microwave Conference, 1974, pp. 61-65 81 CASPERS, F.: 'Precision time domain measurement system', Electron. Lett., 1980, 16, pp. 29-30 82 'Microprocessor based fault finder pinpoints transmission line faults within inches', Microwave J., Nov. 1981. *DD. - 49-57 83 'Real time measurements in a wideband network analyzer', Microwave J., Jan. 1984, pp. 138-145 84 HEWLETT PACKARD COMPANY: H P 8510 network analyzer, operating and service manual, 1984, pp. 127-149 85 DYSON, J. D.: '~easurement of near fields of antennas and scatterers', IEEE Trans., 1973, AP-21, pp. 445-460 86 JOHNSON, R. C., ECKER, H. A. and HOLLIS, J. S.: 'Determination of far-field antenna patterns from near-field measurements', Proc. IEEE, 1973, 61, pp. 1668-1694 87 PARIS, D. T., LEACH, W. M. and JOY, E. B.: 'Basic theory ofprobe-compensated near field measurements', IEEE Trans., 1978, AP-26, pp. 373-379 88 JORY, V. V., JOY, E. B. and LEACH, W. M.: 'Current antenna near field measurement
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research at the Georgia Institute of Technology'. Proc. 13th European Microwave Conference, 1983, pp. 823-828 89 YAGHJIAN, A. D.: 'An overview of near field antenna measurements', IEEE Trans., 1986, AP-34, pp. 30-45 90 BASSEN, H. I. and SMITH, G. S.: 'Electric field probes - a review', IEEE Trans., 1983, AP-31, pp. 710-718 91 SMITH, G. S.: 'Analysis of miniature electric field probes with resistive transmission lines', IEEE Trans., 1981, MTT-29, pp. 1213-1224 92 BATCHMAN, T. E. and GIMPELSON, G.: 'An implantable electric field probe of submillimeter dimensions', IEEE Trans., 1983, MTT-31, pp. 745-751 93 KANDA, M. and RIES, F. X.: 'Dipole based EM probe grabs complex fields', Microwaves & RF, Jan. 1981, pp. 63-66 94 SOLBACH, K.: 'Electric probe measurements on dielectric image lines in the frequency range of 26-90 GHz', IEEE Trans., 1978, MTT-26, pp. 755-758 95 DAHELE, J. S. and CULLEN, A. L.: 'Electric probe measurements on microstrip', IEEE Trans., 1980, MTT-28, pp. 752-755 96 WEEKS, W. L.: 'Antenna engineering' (McGraw Hill, 1968) pp. 179-180 97 CHUNG, I., ANDREWS, C. L. and LIBELO, L. F.: 'Near field diffraction on the axes of disks'. J. Opt. Soc. Am., 1977, 67, pp. 1561-1566 98 LEVINE, E., SHTRIKMAN, S. and TREVES, D.: 'Near field mapping of microstrip antennas'. Proc. 12th European Microwave Conference, 1982, pp. 337-342 99 -KERNWEIS. N. P. and McILVENNA, J. F.: 'Liquid crystal diagnostic techniques -An --- .. antenna design aid', Microwave J., Oct. 1977, pp. 41-44 100 GIANNINI, F., MALTESE, P. and SORRENTINO, R.: 'Liquid crystal technique for field detection - - .- ..... in microwave integrated circuitry' AIta Frequenza, 1977, XLVI pp. 170-178 101 GIANNINI, F., MALTESE; P. and SORRENTINO, R.: 'Liquid crystals improved technique for thermal field measurements', Applied Optics, 1979, 17, pp. 3048-3052 102 NEWHAM, P.: 'Monolithic patch array antenna for small missile applications'. Military Microwaves Conf. MM-86, 1986, pp. 335-340 103 HASEGAWA, H., FURUKAWA, M. and YANAI, H.: 'Measurements on high frequency transmission characteristics of metallization patterns in monolithic ICs', Electron & Commun. in Japan, 1971.54-B, pp. 52-60 104 LADBROOKE, P. H.: 'A novel standing-wave indicator in microstrip', Radio & Electron. Eng., 1974,44, pp. 273-280 105 HUBBELL. S. and ANGELAKOS, D. J.: 'A technique for measuring the effective dielectric constant of microstrip line', IEEE Trans., 1983, MlT-31, pp. 687-688 106 GAJDA, G., STUCHLY, M. A. and STUCHLY, S. S.: 'Mapping of the near field pattern in simulated biological tissues', Electron. Lett., 1979, 15, pp. 120-121 107 DAVIES, D. E. N. and VAKIL, S. M.: 'Field probe for measuring both amplitude and phase of antenna radiation patterns', Electron. Lett., 1980, 16, pp. 873-875 108 HELIER, M. and BOLOMEY, J. C.: 'Test of monolithic microwave integrated circuits with radiating probes', Proc. 13th European Microwave Conference, 1983, pp. 621-645 109 NEWMAN, E. H., BOHLEY, P. and WALTER, C. H.: 'Two methods for the measurement of antenna efficiency', IEEE Trans., 1975, AP-23, pp. 457461 110 KUMMER, W. H. and GILLESPIE, E. S.: 'Antenna measurements-l978', Proc. IEEE, 1978, 66, pp. 483-507 111 ASHKENAZY, J., LEVINE, E. and TREVES, D.: 'Radiometric measurement of antenna efficiency', Electron. Lett., 1985, 21, pp. 111-112 112 LEVINE, E., MALAMUD, G. and TREVES, D.: 'High gain modular microstrip antennas', Proc. 16th European Microwave Conference, 1986, pp. 655-660 >
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Chapter 17
Computer-aided design of microstrip and triplate circuits J-F. Zurcher and F.E. Gardiol
17.1 Introduction, definition of the structure 17.1.1 Outline The basic purpose of this Chapter is to provide general background information about circuits in microstrip and balanced stripline (triplate) technologies, that are currently used to interconnect elements and realise antenna feed networks. It will describe the general appearance of the circuits, the techniques utilised to fabricate them and interconnect them, the materials most currently used and, finally, the very powerful computer programs presently available to analyse, design and actually draw the pattern and cut the masks required for the manufacturing process. The Chapter will be completed with worked examples and an extended Bibliography. 17.1.2 Microwaves The field of microwaves extends over the frequency range 300 MHz -300 GHz or, in terms of wavelengths, from 1 mm up to 1 m. The sizes of instruments required to generate them and to measure them are thus of the same order of magnitude as a wavelength. One cannot assume that circuits are much smaller than a wavelength, as one generally does in circuit theory. One cannot either assume that they are much larger, as is the case in optics. This means, in fact, that the finite velocity of light must be taken into account. The traditional applications of microwave antennas, in radar and communications, cover the frequency bands below 12-15 GHz, while heating and medical applications are restricted to a narrow band around 2450 MHz and, in certain countries, 915 MHz [14]. Recently, frequency bands in the millimetrewave range (up to 100 GHz) are also being considered. 17.1.3 Transmission lines for microwaves Metallic waveguides, i.e. hollow metallic tubes of rectangular, circular or ellipti-
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Computer-aided design of microstrip and triplate circuits
'cal cross-sections, have generally been used in the past to carry microwave signals, in particular in antenna feed systems. They are most often rigid and bulky, difficult to interconnect with discrete components (diodes, transistors), for which special fixtures must be designed and machined. They are presently used only when specifically required, for high power levels or at very high frequencies. In all other situations, they are replaced by a variety of planar lines (Fig. 17.1).
Strlpllne
Mlcrostrlp
Slotllne
Suspended
Coplanar
stripline
lnuerted
llne
Computer-aided design of microstrip and triplate circuits
7003
critical). A mask of the circuit is made, and the conductor outline $then imprinted on a suitable photoresistive layer deposited on the printed-circuit material. Metal is then either etched away from the exposed region, or deposited onto it (Section 17.4). The main difference between low-frequency printed circuits and microwave planar structures is that, at microwaves, all dimensions are significant. Microstrip antennas are also planar structures, similarly realised by the photolithographic process, but adapted for their larger size (in particular for arrays). When the antenna patches are fed by microstrip lines or striplines, one obtains a fully integrated system, in which both the radiators and the circuit elements are realised using the same technology. Solid-state components like transistors can be inserted to realise active antennas, while whole monolithic antenna structures are deposited on a semiconductor substrate. In contrast, waveguide or fin-line feeds (at millimetre wavelengths) are better suited for use with horn radiators. 17.1.4 Balanced stripline or triplate A thin centre conductor, of width w, is located between two flat metal plates, or ground planes (Fig. 17.2). The material between the two plates is a low-loss
stripllne
Dielectric Flnllne
Metal
Fig. 17.1 Planar transmission lines
Planar lines make use of the photolithographic technique developed to realise electronic circuits, permitting miniaturisation and series production. A sheet of insulating material (ceramic or plastic), the substrate, provides mechanical rigidity and permits the accurate positioning of components, while metal strips desposited on the substrate provide the necessary connections (at low frequencies, only a low-resistance path is required; i.e. strip dimensions are not
Fig. 17.2 Ideal homogeneous balanced stripline
dielectric, which may be air (in which case some provision is needed for mechanical support). The structure is homogeneous; i.e. the electromagnetic fields extend over one single propagation medium of uniform dielectric properties - at least in theory. In practice, however, the centre conductor is deposited on a dielectric substrate, and a dielectric plate of the same thickness is then placed on top. Since the metal layer cannot be infinitely thin, an air-filled gap remains between the two dielectric layers (Fig. 17.3). When very high performance is required, this gap may in turn be filled with a special dielectric glue, of the same permittivity as that of the two plates.
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Computer-aided design of microstrip and triplate circuits
Basically, the balanced stripline is a homogeneous transmission line, whose dominant mode is purely transverse electromagnetic (both the electric and the magnetic field are perpendicular to the longitudinal direction of the transmission line). While it is an open structure, since the ground planes do not
Fig. 17.3 Balanced stripline with air gap between the two dielectric layers
extend to infinity, the fields decay quite rapidly in the transverse direction and there is practically no radiation. 17.1.5 Microstrip A microstrip line may be considered to be one-half of a balanced stripline (Fig. 17.4), in which one of the ground planes and half of the dielectric have been
Fig. 17.4 Microstrip line
removed. This means that the line is inherently open and inhomogeneous, with fields extending all the way to infinity over both the dielectric substrate and the air. Radiation and surface waves (see Chapter 8) can to somt: extent be avoided, by using thin substrates of high-permittivity material. The fields are then mostly concentrated within the dielectric, up to a certain frequency limit. The velocity
Computer-aided design of microstrip and triplate circuits
7005
of propagation for a plane wave is different in the two media, so that the dominant mode of the structure cannot be tranverse electromagnetic: longitudinal field components are required to satisfy the boundary conditions on the air-dielectric interface. The longitudinal components, however, remain much smaller than the transverse ones and can be safely neglected in most pratical situations. The dominant mode of the transmission line is then called quasiTEM. 17.1.6 Adjustments 'Classical' microwave designs, based on waveguide technology, always permit final adjustments: one may always reduce a mismatch by placing an inductive post or a dielectric plate in a waveguide. Frequency-sensitive waveguide components such as filters generally require a 'final tuning' step to meet their specifications. Printed structures, on the other hand, have little or no capability for adjustments, because they result from a lengthy fabrication procedure. One must first prepare a layout, analyse its theoretical response, optimise it to meet the desired performance, draw the circuit's outline, cut the mask, reduce it photographically, expose it, etch it, dry it, and then mount the finished circuit and measure its actual performance (Section 17.8). If the circuit does not meet expectations, the entire procedure must be carried out again. The design of printed circuits should therefore be right the first time. Accurate descriptions of the components must be available, resulting from a thorough theoretical analysis. The performance predicted should coincide with the measured data (since Maxwell, electromagnetics is an exact science). The realisation of feeds for microstrip antennas, however, is not as critical as that of filters: microstrip or striplines provide fairly broadband operation, whereas the frequency band of microstrip patches is notoriously narrow. As a result, feeds may be easier to realise than the antenna itself. A waveguide design is assembled by bolting components together. In microwave printed-circuit technology, on the other hand, connectors introduce mismatches that can badly damage the performance of the system. These are difficult to avoid or to compensate for. Wherever feasible, one should realise and assemble all the components on the same substrate. In the case of microstrip antennas, the feed system can be deposited on the same substrate, or a multiplelayer system can be used. 17.1.7 Multiple inhomogeneity In terms of the electromagnetic field distribution, printed structures (circuits or antennas) are quite complex, since most of them possess three different types of inhomogeneity: (a) With the exception of the balanced stripline (Fig. 17.2), the fields on printed microwave structures extend over an inhomogeneous region, formed partly of dielectric (one or several layers) and partly of air. Waves propagating along the structure cannot be transverse electromagnetic, and therefore exhibit dispersion (fortunately, this effect is small for microstrip) [14].
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Computer-aided design of microstrip and triplate circuits
(b) A metal layer extends only partially across the structure (center or upper conductor): the boundary conditions for the fields are not the same at all points on a plane, e.g. the air-dielectric interface of inhomogeneous structures. (c) The whole structure has finite transverse dimensions. Circuits are enclosed in a box, while antennas are open. Radiated waves and surface waves on the air-dielectric substrate bounce back and forth, scattered by the edges, producing spurious coupling between elements.
Computer-aided design of microstrip and triplate circuits
1007
The longitudinal dependence of the fields on the line is expressed in terms of the line voltage U ( z )and of the line current I(z). Complex phasors simplify the notation when the time dependence is sinusoidal. The actual voltage and current
An accurate analysis of the electromagnetic fields on printed structures becomes almost prohibitively difficult, owing to the presence of inhomogeneities. Circuits in stripline and microstrip can, however, be designed quite satisfactorily using electrostatic and quasi-static approximations, which are quite adequate for most practical applications (radiation and surface waves can be neglected at sufficiently low frequencies). 17.1.8 Measurement problems In all technical developments, measurements are used to check the validity of theoretical derivations and the accuracy of numerical calculations. When analysing stripline or microstrip structures, the measurements are never made on the structure itself. Instruments are always connected to the coaxial line or waveguide, so that the structure is 'seeen' across transitions and connectors (like through a glass, darkly?). It is then difficult to analyse its behaviour, since transitions and connectors add reflections, attenuation and phase shifts that combine in a complex manner with the characteristics of the structure itself (Fig. 17.5). Several ways of 'de-embedding' the circuit were proposed. One may compare it with straight sections of line (assuming connections to be identical). Also, one may insert the circuit within a resonant structure, and deduct its properties from the measured changes of the resonance parameters (Fig. 17.6). The 'time gating' function of modem vector network analysers permits one to separate connector and circuit parameters. No reliable data can, however, be obtained across a transition that is very lossy or mismatched. The difficulties encountered in the measurement process mean that it may be difficult to check the validity of a model and to determine the accuracy of the computation process. This, in turn, affects the capability of CAD procedures.
17.2 Basic relationships for uniform lines 17.2.1 Uniform lines We first consider straight transmission lines, aligned with the longitudinal co-ordinate z. Sliding the whole structure along this axis does not modify it, the cross-section and the material parameters being independent of z (Fig. 17.7). The transmission line is then called uniform or translation-invariant. It is then possible to separate the transverse and longitudinal dependences of the fields along the line [16].
Fig. 17.5 Connections from microstrip to coaxial line a Soldered strip b Pressed beam c Direct soldering d Sliding sleeve
are given by the real part of the corresponding complex quantities multiplied by J2 e x p m t ) (17.1) U(z, t) = Re [$ U ( z ) exp (jot)] IV] I(z, t) = Re [$ I(z) exp (jot)] [A]
(17.2)
In complex phasor notation, all time derivatives are replaced by the factor jw.
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Computer-aided design of microstrip and triplate circuits
Computer-aided design of microstrip and triplate circuits
The time dependence is thus altogether suppressed. Solving the line equations (derived from Maxwell's equations) yields the longitudinal dependences of the voltage and the current along the line: U(z) I(z)
= =
U+ exp ( - yz)
+ U - exp (+ yz)
Y, [U+ exp ( - yz)
-
[vl =
of them (inhomogeneous conditions). In a homogeneous transmission line, the transverse-wave equation becomes Laplace's equation in the two-dimensional transverse plane [16]. Since the boundary conditions are inhomogeneous, La-
(17.3)
U- exp (+ yz)] [A]
where y is the propagation constant (metre-') and Y,
1009
(17.4)
I/Z, is the character-
Fig. 17.7 Uniform infinite straight transmission lines
Fig. 17.6 Resonant ring with slot [used to determine the equivalent circuit of the slot (Section 17.3.8)]
istic admittance of the line [Siemens]. Both quantities depend on the transverse distribution of the fields across the line. The quantities U+ and U- are, respectively, the amplitudes of the forward wave (travelling towards increasing values of z) and the reverse wave (travelling towards decreasing values of z) (Fig. 17.8). These two terms are determined from boundary conditions at the ends of the line (generator and load).
17.2.2 Conformal mapping In stripline and microstrip lines, the conductor boundaries within the transverse plane are located along rectangular co-ordinate lines, but cover only over part
place's equations cannot be solved directly in the rectangular system of coordinates. Particular cylindrical co-ordinate systems can, however, be defined by conformal mapping, a technique based on transformation properties within the complex plane [45]. One may then obtain exact solutions within the transformed system. A complex number z is assigned to every point in the transverse plane of the transmission line, referenced by its rectangular co-ordinates .u and y (the complex number z should not be confused with the direction of propagation z)
In another complex plane, there exists another complex number w: that is connected to z by a complex function, which defines the conformal mapping (Fig. 17.9)
701 1
Computer-aided design of microstrip and triplate circuits
Computer-aided design of microstrip and triplate circuits
The function f(z) must be analytical, meaning that its derivative is continuous and single-valued. The basic idea is to map the transverse plane of the transmission line (z-plane) onto the complex plane of the transformed function w in
17.2.3 Schwartz-Christoflel transforms When boundaries are located along straight lines, the Schwartz-Christoffel transform provides the conformal mapping for the problem. It allows one to 'straighten up' the angles. A polygon is thus transformed into a straight line, which is most often taken as the real axis. This provides an integral equation, and the function w = f(z) is then obtained by integration. A similar transform is applied to a section of parallel-plate capacitor. The desired conformal mapping is the combination of the two transforms. The integration is the most crucial part of the whole process. When this integral cannot be evaluated analytically, z cannot be expressed as an explicit function of w. In the case of striplines and microstrip, the integration can be performed analytically, but yields rather exotic functions.
1010
* forward
17.2.4 Zero-thickness balanced stripline Outside the centre conductor strip, the two transverse co-ordinate axes (Fig. 17.2) form electric-field lines, or perfect magnetic conductors. Assuming that the two ground planes extend sideways to infinity, and that the centre conductor is infinitely thin (b = O), the Schwartz-Christoffel transform maps one quarter of the stripline's cross-section to a section of parallel-plate capacitor [ I 31. Carrying out the calculations eventually yields the characteristic impedance of the balanced stripline [9, 211
wave
z, =
-
k = [cosh (rrwl4h)l-' [l]
Fig. 17.8 Forward and reverse travelling waves
2
[a]
(17.8)
where K(k) is the complete elliptic integral of first kind [l] and reverse wave
Y
( w & ) R(k)/K(k)
plane
(17.9)
The symbol [I] indicates that a quantity is dimensionless. v
qy plane
17.2.5 Finite-thickness balanced stripline 0, An exact analysis by means of conformal mapping is also feasible when b i.e. when the thickness of the centre strip is taken into account [59]. However, the resulting developments become quite involved, yielding an implicit expression for the characteristic impedance. Calculated values have been published in Tables [21]. A simplified approximate formula for the impedance, derived from the exact values, is
+
where Fig. 17.9 Principle o f conformal mapping
F(x)
x such a way that the transforms of the conductor boundaries become straight lines. The mapping process replaces the complex geometry of the transmission line by a simple two-plane geometry.
=
=
(x
+ I)'"
+
"/(x - 1)'" - ') [I]
l/(l - b/2h) [l]
(17.11) (17.12)
The characteristic impedance of a balanced stripline is displayed in Fig. 17.10 as a function of geometrical dimensions.
7072
Computer-aided design of microstrip and triplate circuits
Computer-aided design of microstrip and triplate circuits
7073
17.2.6 Equivalent homogeneous microstrip line The inhomogeneous microstrip line is replaced by an 'equivalent' homogeneous line (Fig. 17.1 I) with conductors having exactly the same geometry (w, h, b), but
The relative error included in these approximations is smaller than 0.2% for 0.01 ,< w/h < 100 and 1 < E, < 128. The phase velocity v4 and the line wavelength ig are related to the effective permittivity by v4
= GI/&
[m/d
(17.16)
Ag = &I& [ml (17.17) Both the velocity and the wavelength are functions of the transverse geometry of the transmission line.
h Oo
1
3
2
4
5
wlh
17.2.7 Characteristic impedance of microstrip T h e homogeneous microstrip (Fig. 17.1 1) structure was analysed by means of the Schwartz-Christoffel transform by Schneider [55]. The mapping is carried out by means of the logarithmic derivative of the theta function 0, (t, k):
Fig. 17.10 Characteristic impedance of balanced stripline
z ( t ) = - (2hK/7c) 8,In [8,(t, K)] [I]
(17.18)
where K
=
K'(m)/K(m) [I]
(17.19)
with K(m) the complete elliptic integral of the first kind with modulus m. The characteristic impedance 2, of the microstrip having width w, substrate height h and thickness b = 0 is obtained by solving the set of simultaneous equations
all the other parameters remain unchanged
Fig. 17.11 Definition of the equivalent homogeneous microstrip
surrounded by a single homogeneous dielectric of effective permittivity E,. This permittivity is determined by calculating the DC capacitance of the inhomogeneous structure [23] E,
E (E,
+ 1)/2 + [(E, - 1)/2][1 + IO~/W]-'~[I]
(17.13)
where E(m) is the complete elliptic integral of the second kind, and dn is the Jacobian elliptic function. The characteristic impedance cannot be expressed explicitly from these equations, so that approximate design formulas have been derived by Hammerstad and Jensen [23], which provide an accuracy better than 0.01% for w/h < 1 and 0.03% for w/h ,< 1000 with respect to the SchwartzChristoffel transform
with where F,
=
6
+ (2a - 6) exp [ -
(30.666 h / ~ ) ~ "[l]~ ~ ~ ]
(17.24)
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Computer-aided design of microstrip and triplate circuits
and where Zo 2. 12077 = 376.6 ohms The characteristic impedance of microstrip is displayed in Fig. 17.12. 17.2.8 Finite-thickness homogeneous microstrip The thickness b of the upper conductor can be approximately taken into account
Computer-aided design of microstrip and triplate circuits
1075
17.2.9 Microstrip line synthesis for b = 0 The equations given in the previous Sections yield the line's electrical characteristics E,, Z, and IZ, in terms of the geometrical and material parameters (analysis of a specified structure). Most often, in practice, one wishes to determine the wlh ratio that yields a specified impedance 2,. This reverse operation of synthesis is carried out by means of approximate expressions (within 1% accuracy) derived by Wheeler [60]. For wlh < 2:
wlh r 4[(1/2) exp (A) - exp (- A)]-' [I]
(1 7.26)
with
while for wlh 2 2:
with Fig. 17.12
Characteristic impedance of microstrip
17.2.10 Dispersion in microstrip For high frequencies, the fields tend to concentrate within the dielectric substrate, so that the effective permittivity E, increases. This may be taken into account by means of the following approximation [17]:
all the other parameters remain unchanged
Fig. 17.13 Microstrip with conductor of finite thickness
where E, is the low-frequency permittivity defined in eqn. 17.13,f is the frequency of the signal and the remaining parameters are given by
by defining an effective width we to be used instead of the actual width in the calculations [2 11 (Fig. 17.13):
with x = h if w > h/2n and x = ~ X W if h/2n > w > 26.
17.2.11 Effect of an enclosure The relations presented above were all obtained for structures assumed to be 'uncovered', in which the air-filled half space above the microstrip extends to
10 7 6
Computer-aided design of microstrip and triplate circuits
infinity, the structure also being infinite in the tranverse directions. In practice, a circuit is always placed within a box, the walls and covers of which are relatively close to the circuit. The characteristic impedance and the effective permittivity may then be affected, in ways difficult to determine accurately [27]. Rules of thumb determine roughly when the uncovered line expressions are valid. For aluminia (E, = 9.8), this is the case when the height to cover is more than eight times the substrate thickness and the distance to the walls is more than five times the conductor thickness.
Computer-aided design of microstrip and triplate circuits
1017
The characteristics of lossy microstrip can be evaluated using a program developed by Kajfez and Tew [37]. 17.2.13 Higher-order modes and radiation Just like any other transmission line, striplines and microstrips cannot be utilised above a certain frequency limit, since other modes of propagation,
17.2.12 Attenuation Three kinds of losses are encountered: Ohmic losses within the conductors, owing to the finite conductivity of the metal. The losses may be increased by the presence of an adhesion layer between the substrate (in the case of ceramics) and the conductor. Also, the surface roughness increases the attenuation. For striplines, the ohmic-loss contribution to the attenuation is given by 1301
x
wz
{
x
+
+ "'(I
b'h'
In
*}
x - 1
for w/2h 2 0.35 (17.33)
where x is defined in eqn. 17.12. In microstrip lines, an approximate value is given by Janssen [36] Fig. 17.14 Circuit with bends and junctions
with the metal-wall resistance
Dielectric losses are produced by the energy dissipated in the substrate, proportional to its dielectric loss factor tan 6. In stripline, the resulting attenuation is given by [30]
-
called higher-order modes, would then start to propagate. In the homogeneous stripline, these modes are either transverse electric (TE) or transverse magnetic (TM) modes, similar to the ones encountered in hollow metallic waveguides. In the inhomogeneous microstrip, higher-order modes are hybrid modes (like modes on optical fibres). Since both structures are open, i.e. not completely enclosed within a metal envelope, they may also start radiating when the frequency increases, then behaving like antennas. For a microstrip line, radiation becomes significant for frequencies larger than [22]:
while for microstrip lines, they become [22]: ci,
27.3
E, -E,
1 E, tan 6
- 1 E,
- [dB/ml A8
Radiation losses: An infinite straight transmission line propagating in the dominant mode does not radiate. However, at every discontinuity, higher-order modes are excited, some of which radiate part of the signal (Section 17.2.13).
17.3 Discontinuities: bends, junctions 17.3.1 Dejnition In actual circuits, transmission lines are neither straight nor infinite; they start, and then stop, at some definite points, bend, change width, branch out, etc (Fig.
1018
Computer-aided design of microstrip and triplate circuits
17.14). The discontinuities most often encountered in microstrip are sketched in Fig. 17.15, while the main mathematical techniques used for their study are listed in Table 17.1. Discontinuities produce reflections of the propagating mode Open line
Computer-aided design of microstrip and triplate circuits
1019
nuity; these modes store electric and magnetic energy locally. An increase in charge density on a conductor can be represented by an additional capacitance, while changes in current distribution produce inductances. Discontinuities can therefore be represented by LC equivalent circuits, in which the components are frequency-independent at low frequencies (static/ quasi-static models), becoming generally frequency-dependent as frequency increases (dispersive models). Reactive elements can further be combined to form sections of transmission lines with particular characteristics. An alternative description provides the scattering parameters of the discontinuity (more generally used for high-frequency studies). The relationships between different representations of a discontinuity were considered by Mehran 1471.
Double step Discontinuity infinite
Fig. 17.15
with
impedance
- I 7-
Common discontinuities Discontinuity
(TEM or quasi-TEM), with accumulation of reactive energy in evanescent higher-order modes, and also radiation. The latter effect only becomes significant for very large signal frequencies; i.e. when the structure cannot be used for signal transmission anyway (Section 17.2.13). Microstrip discontinuities are difficult to analyse, due to their inhomogeneous nature (Section 17.1.7) and the presence of radiation together with propagation phenomena. 17.3.2 Models The boundary conditions for the fields in the presence of discontinuities can only be matched by the complete set of modes in the structure. Higher-order modes are excited, but if the dimensions of the lines are selected properly, they cannot propagate along the transmission line and remain evanescent (Section 17.2.12: the same situation is encountered in metallic waveguides [14]). The fields of the higher-order modes decay as one moves away from the disconti-
with
zero impedance
Fig. 17.16
-r 7-
Zero- and infinite-impedance discontinuities
While one might expect results from dispersive models to be more accurate, this is not always true. The DC extrapolation of results provided by a dispersive model was found to yield incorrect values in many situations [lo]. Discontinuities can generally be separated into two main families (Fig. 17.16): With zero DC resistance, with a continuous upper conductor extending completely across the discontinuity. The equivalent circuit then contains both capacitances and inductances. With injnite DC resistance, when the upper conductor is interrupted between
1020
Computer-aided design of microstrip and triplate circuits
the ends of the discontinuity. No direct current can flow across the structure, which is represented by a purely capacitive equivalent circuit. 17.3.3 TEM-line models The shunt capacitance of an open microstrip line is given by a perturbation of the uniform line (Section 17.2), that takes into account the fringing fields at the open edge [33, 321. Fairly approximate results were obtained, and the approach could not really be extended to consider other discontinuities. 17.3.4 Variational techniques A variational (stationary) mathematical expression for the shunt capacitance of an open circuit was established by Maeda [42]. The unknown potentials within a closed structure are expanded over the infinite set of solutions for Laplace's equation. The approach is rather involved and would be difficult to generalise in order to analyse more complex discontinuities. 17.3.5 Fourier transform The approach used for an uniform transmission line [62] was extended to cover also three-dimensional structures [31]. The Green's function is solved in the spectral domain by a Galerkin technique [34]. The calculated capacitance of an open microstrip line agrees quite well with measured data. This approach was used by Koster and Jansen [39] to analyse step discontinuities. 17.3.6 Dielectric Green'sfunction This flexible approach to determine capacitance remains accurate even in the DC limit. It was applied to most geometries (Table 17.1) by Farrar and Adams [ l l , 121, and by Silvester and Benedek [6, 56, 5 7 . A three-dimensional Green's function is defined by generalising the one introduced for the uniform microstrip line. The integral equation is solved with the moment's method, either with functions defined over the whole discontinuity [56], or with step functions that are constant over a rectangular sub-domain and vanish everywhere else [I I]. A similar approach was developed to solve the much more complex problem of radiation from microstrip antennas (Chapter 8). 17.3.7 Integral equations for induttances The inductance of a bend was determined from the magnetic energy, replacing the surface current by a wire net [18]. Since inductance becomes infinite for infinitely thin wires, some approximations were introduced, but they proved to be rather inaccurate. These drawbacks were avoided by the use of an integral equation based on the skin effect. Results were obtained for the microstrip bend [58] and for the impedance jump in Xand Yjunctions [19]. Since this technique considers actual surface currents, the magnetic energy can be determined without mathematical difficulties. However, the computation process becomes quite involved, and one
Computer-aided design of microstrip and triplate circuits
1021
7022
Computer-aided design of rnicrostrip and triplate circuits
Computer-aided design of rnicrostrip and triplate circuits
1023
must first compute a scalar-potential solution of Laplace's equation at the discontinuity, which becomes the kernel of the integral equation. 17.3.8 Green's function and integral equation The two techniques presented in previous Sections were improved upon, simplified and combined to determine the complete equivalent circuit of a slot [52], of a double step and a mitred bend [5]. 17.3.9 Green's function and electrostatic-inductance computation Another combined technique determines the capacitance by means of a dielectric Green's function. Inductances are then assumed to be proportional to the square of the difference of the electrostatic potentials with and without the discontinuity, producing a virtual lengthening of the microstrip line. The impedance step [28] and the bend [29] were analyzed by this approach. Calculated results did not compare well with measured data. 17.3.10 TLM (transmission-line-matrix) method A technique developed for uniform transmission lines was extended to study discontinuities like impedance steps [3] in completely enclosed structures. The technique provides resonant frequencies for discontinuities of variable length, but the equivalent circuit is not uniquely defined by these resonances. 17.3.11 Waveguide model The first development of the waveguide model for stripline discontinuities is due to Altschuler and Oliner [4]. Babinet's principle allows one to replace the original problem by an equivalent rectangular waveguide, for which solutions are known [44]. This approach was applied directly to microstrip T-junctions 1411. The width and the internal permittivity of the waveguide are 'effective' values obtained from the static analysis of the uniform line (Section 17.2). The frequency-dependent scattering parameters were determined for the impedance step [61, 381, the simple bend [46], the mitred bend [48], the T-junction [61,46], the Y-junction [49] and the X-junction [50]. The LC equivalent circuit of a slot was determined using a simplified version of this model [24, 251. 17.4 Technological realization: materials and manufacturing process
17.4.1 Introduction Physically, any microstrip structure - circuit or antenna - is made of two parts: the substrate, a dielectric material with losses as small as possible, and a metallisation (partial or total) on the substrate's faces. Various processes can provide the desired metallisation pattern.
7024
Computer-aided design of microstrip and triplate circuits
17.4.2 Dielec?ric substrate The substrate fulfils two different functions: it is the mechanical support for the structure, and it is also an integral part of the transmission lines, determining the electrical characteristics of the circuit or antenna (Section 17.2, Chap. 8). Mechanically, the following properties of the substrate must be considered: 0 Mechanical strength (e.g. breaking point), which determines the impact and vibration resistance Shape stability, in particular for encasing 0 Dilatation factor, which should be small, as close as possible to that of the metal used for the conductors and the enclosure Long-term behaviour in the presence of difficult environmental conditions (moisture, temperature cycling).
The electrical parameters that must be considered are: 0 Relative permittivity E , , which determines the miniaturisation factor. When all other parameters are kept equal, the size of a circuit is proportional to ~ / J E , . By choosing a large permittivity one may reduce the circuit dimensions 0 Uniformity of the permittivity 8, over the whole circuit 0 Low dispersion of the permittivity E, and the thickness among different batches of a given material (circuit reproducibility) 0 Small dielectric losses (one should have tan 6 < 0.001) in order to have high-performance circuits and acceptable quality factors for resonant circuits, filters and radiating elements 0 No absorption of water (water exhibits a high permittivity and high losses). The following physico-chemical parameters are significant: 0 Mechanical stability up to high temperatures (soldering, deposition of components in the thick-film technique) Resistance to chemicals, in particular during the different stages of the photolithography process 0 Surface flatness (bending tends to render the encasing procedure difficult) Smooth surface, to reduce losses and ensure good adhesion of conductors, 0 Easy machining, for the cutting and drilling of holes. Production requirements are: 0 Low cost 0 Guaranteed availability of the material Availability of adequate sizes 0 Non-hazardous machining. 17.4.3 Comment Considering all the above requirements, some being conflicting, it is fairly obvious that no actual substrate would simultaneously meet them all. For every application, one must carefully consider the different requirements and select the material providing the best compromise. There are, in fact, many kinds of
Computer-aided design of microstrip and triplate circuits
1025
substrates, and they can be grouped in four main categories: inorganic, plastic, semiconductor and ferrite. Table 17.2 provides the relevant data on some common substrate materials. 17.4.4 Inorganic substrates This category contains mainly ceramics. Alumina (AI,03) is one of the most commonly used substrate materials. It is characterised by good surface quality, very low losses and very little dispersion between batches. However, it is slightly anisotropic. Common thicknesses are 0.254, 0.635 and 1.27 mm, while dimensions are generally stated in inches (1 x 1 in to 4 x 4 in). Alumina is a very hard and brittle material; hence it is quite difficult to machine and its permittivity depends on its porosity. Since adhesion of copper and gold to alumina is poor, an intermediate layer of chromium (or of some other lossy conductor) is required. Sapphire is the monocrystalline form of alumina. It is used in particular applications at very high frequencies, when a very smooth surface is required. Sapphire exhibits crystalline anisotropy. Beryllia (BeO), with a lower permittivity than alumina, presents a very large thermal conductivity, which makes its use particularly appropriate for highpower applications (removal of heat produced by semiconductors). However, Be0 powder is highly toxic, so that particular precautions must be taken while machining. Rutile (TiO,) has a very high permittivity, and is unfortunately temperaturesensitive. 17.4.5 Plastic substrates Pure synthetic materials may be used, such as PTFE (Teflon) or polyolefin. Their permittivity is generally low (E, = 2-3) and the mechanical properties are rather poor (mechanical distortion, poor temperature behaviour). By adding ceramic powders or glass fibre, the mechanical stability can be improved and the permittivity increased, but losses also become larger. PTFE has a low permittivity and very low losses. It is quite poor mechanically. (e.g. dilatation). Glass-Jibre reinforced plastics (such as RT-Duroid 5870) are much better substrates mechanically, but their permittivity is slightly higher, as well as their losses, and they present some anisotropy (in particular, for woven fibres). Ceramic-loaded plastics (such as RT-Duroid 6006 and 6010.5) can have a permittivity approaching that of alumina, with very good mechanical properties. Machining and drilling is easy, and they can adequately replace alumina during prototype development, even though their losses are somewhat higher. Synthetic substrates are available in large sizes, which is very convenient in practice. A slight anisotropy can be tolerated in most usual applications.
1028
Computer-aided design of microstrip and triplate circuits
17.4.9 Circuit realisation A particular metallisation pattern has to be realised on the substrate: centre conductor in stripline, upper conductor in microstrip. In all cases, this is done by means of a mask, first designed and cut to a larger scale (on a co-ordinatograph or plotter, Section 17.6), then photographically reduced to the proper size. A photosensitive lacquer is deposited on the structure; several processes may be used to do this: Dipping: The entire structure is dipped into the lacquer, and then pulled out at constant speed. The thickness of the layer depends on the withdrawal speed and the viscosity of the photoresist. This process generally yields rather thick layers, with a bulge on the lower edge. Spraying: The photoresist is sprayed on the structure through a nozzle. It is difficult to obtain a constant thickness in this manner. Centrifuge: The structure rotates rapidly, and the photoresist is deposited at the centre of rotation, being swept towards the outside by the centrifugal force. Thin and uniform layers are obtained in this manner, but the technique can only be used for small substrate sizes.
Computer-aided design of microstrip and triplate circuits
17.4.12 Removal of photoresist Once the previous steps have been completely carried out, the remaining photoresist is removed with a solvant or a concentrated alkaline solution. The metallic layer is sometimes thickened by electrolytic deposition of metal, or a protective layer (e.g. gold) is deposited to prevent oxidation. metal dielectric
17.4.11 Metal deposition This is the opposite process, in which one deposits metal on the substrate throught the holes in the photoresist (Fig. 17.18).~everalprocesses may be used: vacuum evaporation, sputtering, electroless plating. The layers obtained are generally thin (2-1 5 pm).
printed circuit material
-metal
After deposition, the photoresist must be cured at a high temperature, becoming tougher and more adhesive. The photographic mask is then vacuum-pressed on the structure, with the emulsion side next to the photoresist layer. The photoresist is exposed to ultraviolet rays through the mask. The UV radiation must be parallel and the photoresist layer thin, to ensure accurate reproduction of the pattern. By developing in a suitable chemical, either the UV-exposed part of the photoresist layer (positive photoresist) or the non-exposed one (negative photoresist) is removed. The circuit is then ready for the next step, which is either the deposition or the removal of metal. 17.4.10 Etching When starting with an entirely metallised substrate, part of the metal must be removed by etching (Fig. 17.17). The structure is exposed to an acid that dissolves the metal but does not affect the remaining photoresist. The process can become complex when several metallic layers are involved, since specific etching solutions are required to remove each metal layer. Careful rinsing is necessary between the different baths.
1029
development
etching
proter tiue lacquer
photo1 esirt remoudl
Fig. 17.17 Realisation af a circuit by the etching process
All the steps in the procedure must be carefully separated by rinsing and cleaning operations, sometimes followed by drying in an oven. Drying is particularly critical for some plastic substrates, which tend to absorb water.
7030
Computer-aided design of microstrip and triplate circuits
1
I
Computer-aided design of microsfrip and triplate circuits
1031
I
17.4.13 Under-etching
Of course, one wishes to realise a circuit having a pattern as similar as possible to the one of the photographic mask. However, in both the etching and the metal-deposition processes, the most annoying phenomenon of under-etching takes place. Considering the cross-section of a transmission line (Fig. 17.19), one
,
so long as the electrical conduction requirements are satisfied. Under-etching is a predictable process, which can be taken into account when designing the circuit and cutting the mask (Section 17.6).
cerarnlc substrate
chromium gold
mask
enporure t o
/
uu
electrolytic gold
deuelopment
Fig. 17.19 Effect of under-etching m e t a l deposition
17.4.14 Thin and thick film The techniques described so far realise 'thin-film' circuits, used, in practice, for most microwave circuits. The 'thick-film' approach deposits a paste through a silk screen. It is not usually accurate enough for microwave circuits, but is used to realise components like resistors or capacitors (Section 17.7.5).
pholorerisl removal
17.5 Analysis and synthesis programs Fig. 17.18 Realisation of a circuit by metal deposition
17.5.1 Introduction
notices that the conductors do not have rectangular, but trapezoidal crosssections. The acid does not remove the metal uniformly, while metal-deposition processes do not yield constant growth. Under-etching is more important when the metal layer is thick: for this reason, thin conductor strips are preferred,
While CAD packages for the design of low-frequency electronics systems have been available for some time, the choice of microwave programs used to be limited and expensive. As a result, traditional 'cut and try' methods still remain a commonly used way to realise circuits, despite their many drawbacks and inadequacies.
.
7032
Computer-aided design o f microstrip and triplate circuits
The situation has changed radically since the arrival of personal computers: considerable computing power has suddenly become available, while increasingly sophisticated microwave CAD packages have appeared on the market. The designer, faced with a wide variety of choice, must now determine which software is best suited to his particular requirement. Software comes in many kinds, and it is therefore difficult to make comparisons. Most packages are based on models and equivalent circuits, while some make use of electromagnetic-field analysis. Programs can be classified into two main categories: those devoted to analysis, in which the user describes a structure and wishes to know its electrical response; and those devoted to synthesis, where the program defines a physical structure meeting a specified electrical behaviour. The latter can be done either by circuit-synthesis techniques, or by an analysis software inserted into an optimisation loop (many packages then require an approximate solution as starting point). The models used must be rigorous enough to provide an accurate analysis, but not too complex, as computations would become too lengthy [26]. Some software packages were developed specifically to design particular devices (couplers, filters, amplifiers), while others have more general scope. The next Sections describe some of the present programs for microstrip design (the list is not exhaustive), on the basis of available literature and opinions received from users. Surveys of available CAD software appear occasionally in the technical literature [51, 151. 17.5.2 EEsof: Touchstone (IBM-PC, HP 9000, Apollo) Touchstone is a very fast general-purpose RF and microwave circuit-design, analysis and optimisation program, specifically developed for personal computers. More than 80 elements, including microstrip, stripline, waveguide and co-planar lines and discontinuities, lumped elements and electronic-device models are contained in its catalogue. In addition, the user can define his own elements, specifying their scattering matrix. It offers possibilities of adjustment, and two optimisation algorithms (random perturbation and gradient method) for up to 15 variables. The companion program Monte Carlo determines the sensitivity of the circuit. Touchstone is the CAD software most often used nowadays in microstrip circuit design. EEsof also provides several device-synthesis programs compatible with Touchstone: waveguide, microstrip and stripline bandpass, low-pass and bandstop filters, and coaxial low-pass and band-stop filters. The program E-Syn synthesises matching circuits. Microwave SPICE provides nonlinear circuit analysis and synthesis. The program Anacat is geared towards measurements, particularly with vector network analysers, and provides embedding and deembedding functions (Section 17.1.8). A graphics program MICAD, running on the same software, draws the artwork and can generate masks on co-ordinatographs and photo-plotters [43] and on some regular plotters as well, using a diamond stylus (Section 17.6.3).
Computer-aided design o f microstrip and triplate circuits
703.3
17.5.3 CCC: The Supercompact Family (VAX, IBM, IBM-PC, Apollo, PC, HP 9000) Supercompact is a general analysis and optimisation design tool for microwaves and RF. Four-port circuit analysis and optimisation can be achieved, as well as transistor impedance modelling (its library includes specifications of commercially available transistors) and matching network synthesis. Single, coupled and inter-digitated microstrip designs can be created. Microstrip and other planar lines can be specified, both in terms of their electrical and physical dimensions; approximate expressions are included, with accuracies of I % or better. The effects of dispersion, radiation, discontinuities, multi-layers, metallisation, surface roughness, and dielectric and conductor losses are taken into account. An FFT time-domain option is available. Circuits are optimised by the random perturbation and gradient techniques, their parameter sensitivity is determined with a Monte Carlo algorithm. The companion program Autoart, that uses the same hardware, was the first microwave CAD layout package offered commercially (Section 17.6.2). Super-compact and Autoart were f rst developed on main-frame computers; they are also available now for perso1.al computers. Microcompact is a simpler program, that runs on HP computers of the 200 series. 17.5.4 CCC: CADECf (Computer-Aided Design of Electronic Circuits, on HP 200/500, Tektronix and IBM-PC XTIAT) CADEC, a circuit analysis and optimisation package, is one of the oldest programs (1973), and became commercially available in 1980. Covering the range VLF-40 GHz, it performs frequency- and time-domain analysis, utilising matrix representation and nodal analysis for two-ports, including lumped elements, stripline, coplanar lines and discontinuities, and couplers [53]. Dispersion is taken into account, and the domain of validity determined. Amplifier analysis also evaluates the noise parameters. The optimisation is based on a search technique followed by a gradient approach, and the sensitivity is determined. Design kits run on the same hardware: Microwave Design Kit, (amplifiers), Filter Design Kit, (filters) and Sonata (oscillators). 17.5.5 Acline (VAX, Apollo and HP 9000) A c h e is a high-level program, somewhat similar to Supercompact, developed by Professor C. Vidallon of the Universite Paul Sabatier in Toulouse, France. It provides impressive optimisation facilities to its users, and a number of microstrip elements are available in an interactive way. A new version, called AC-LINE, offers considerably increased performances. Unfortunately, little information about Acline has appeared so far in the technical literature. 17.5.6 Thom'6: Esope (Vax, IBM, Apollo) Esope is an interactive software for the analysis and optimisation of linear microwave circuits. Most components (lumped RLC, transmission lines,
1034
Computer-aided design of microstrip and triplate circuits
waveguides, coupled lines, microstrip) are implemented. Active circuits are described by their scattering parameters. Optimisation can be carried out with one or several objectives: three algorithms are available (min-max, least squares, fixed tolerance), the sensitivity and worst case are determined, and results are represented graphically. The program is in Fortran 77. Drafting of the circuit's outline is carried out by software Hyper'6-D.
Computer-aided design of microstrip and triplate circuits
1035
direction algorithm, in terms of reflections, gain, insertion losses, ripple, noise and stability, as defined by 60 or more parameters. The sensitivity with respecr to those parameters is analyzed. Very high accuracy, wide validity range and a high computation speed drastically expand the range of applications. It is highly portable, since 98% of its code is written in Fortran 77.
/
metal strip
17.5.7 RCA: Midas (UNIX and SUN on most 32 bit processors) This program analyses and optimises circuits with up to 20 nodes and five ports, utilising algebraic expressions to define the parameters required to analyse the circuit. It is compatible with the PIana software for two-port measurements on the HP 8409 network analyser. All the usual components (lumped RLC, transmission lines, coupled lines, discontinuities, gyrators, ideal transformers and controlled sources) are implemented. Particular emphasis is placed on striplines an? nicrostrip. Inter-element coupling is determined for an arbitrary net of h e s , in order to analyse comb and inter-digitated structures. The companion program N-Fet is specifically devoted to the design of FET amplifiers. 17.5.8 LINMIC (HP 9000 series 500 and 300, Microvax 11) The CAD package LINMIC introduces a significant new approach to the layout-oriented design of single or multi-layered planar and monolithic structures: it combines, apparently for the first time, a rigorous field analysis - based on an enhanced spectral-domain technique [34] - with the more usual models and equivalent circuits (for simple and coupled lines, discontinuities, T-junctions, capacitances, resistors, transistors and other lumped elements) [35]. The LINMIC package can actually describe complex structures for which no analytical models are available: interdigitated capacitors (Fig. 17.20), multi-turn
j i e l e c t r i c bridge
substrate
dielectric br
1
Fig. 17.21 Multi-turn square inductor
MCAD comes from the same source as LINMIC, for considering various simple and coupled planar lines (up to 20 coupled lines) on multi-layer substrates (up to 4 substrates). It is used to analyse discontinuities, junctions, couplers and filters, as well as lumped elements. Three optimisation algorithms are provided.
Fig. 17.20 Interdigitaced capacitor
17.5.9 High Tech. Tournesol: Micpatch ( V A X , PC) The package Micpatch was developed by Dr. Mosig at LEMA. Lausanne, Switzerland, primarily to analyse microstrip patch antennas. It can just as well be applied to the study of microstrip circuits of arbitrary shape. The scattering matrix of multiple-port components is determined, taking into account radiation and surface waves, metal and dielectric losses. It is written in Fortran 77, and a more detailed description of the procedure used is given in Chapter 8.
square inductors (Fig. 17.21) and coupled meander lines. Up to four dielectric layers can be considered, including passivation and metallisation layers, ohmic and dielectric losses, coupling and higher-order-mode effects. Up to 40 connecting points to the outside can be considered, and the structure can be divided into 20 sub-lattices. An interactive optimisation procedure is provided, based on a conjugate
17.5.10 Spefco Software: CiAO (IBM PC-XT or AT) CiAO is a general analysis and optimisation program for circuits composed of RLC lumped elements, controlled sources, gyrators, lossy or lossless transmission lines, and one- and two-ports described by their scattering matrix. The companion program Design synthesizes wideband matching circuits for linear-gain amplifiers.
7036
Computer-aided design of microstrip and triplate circuits
17.5.11 Made-it-associates: Mama (Measurement And Microwave Analysis, HP 9836 or HP 9000 series 300) This program analyses and designs: quarter-wave transformers, Lange couplers, directional couplers, microstrip lines and discontinuities, hybrid circles, power dividers [in fact, most of these elements can be realised by Micros (Section 17.6.4), which additionally draws them and cuts the masks]. It synthesizes filters and rectangular printed antennas. It can be used for de-embedding components (Section 17.1.8) and interfaces with Microcompact (Section 17.5.3). 17.5.12 Ampsa: Multimatch ( I B M PC) Multimatch is a matching package for microwave loads and amplifiers developed by Abrie [2]. The potential performance of a transistor is determined from its scattering matrix, and matching circuits are directly synthesized for stable operation, either with lumped components or with transmission-line sections. Discontinuities are taken into account and corrected for. The approach provides the user with several possible designs to choose from, together with their electrical performances. If needed, the circuits developed can be used as starting points for an optimisation program. In many practical applications, the solutions proposed by Multimatch were found to be close enough to optimal not to require further refinements. 17.5.13 Radar systems technology: Analop (IB-PC and CP/M-80) The program analyses and optimises, on 15 variables at 15 frequencies, twoports having up to 200 elements: lumped RLC components, series and parallel resonators, transmission lines, transformers, impedance inverters, microstriplines and discontinuities, rectangular waveguides (dominant mode), controlled sources, filters and couplers. 17.5.14 MicrokoplSuspend (IBM PCJXT) An iteration algorithm allows both analysis and synthesis of coupled lines for microstrip and suspended substrates [8]. 17.5.15 Microwave software applications (MS-DOS or PC-DOS) A series of small programs specifically dealing with couplers is proposed: single-section, symmetrical or asymmetrical multiple-section, Lange in various technologies: balanced stripline, microstrip, rectangular and ridged waveguides. 17.5.16 Planim The planar circuit approach to the characterisation of microstrip circuits is combined with the image-parameter method to give a new powerful technique for integrated-circuit design of microstrip filters [54]. The inclusion of twodimensional effects in the synthesis procedure makes the Planim approach particularly suited for monolithic microwave circuits.
Computer-aided design of microstrip and triplate circuits
1037
17.5.1 7 DGS Associates: SIFilsyn (PC, HP 9000, V A X ) A broad series of programs for the synthesis of filters, active and passive, analog and digital, lumped component design or microstrip, that were developed in 1967 by Dr. Georges Szentirmai. 17.5.18 Webb Laboratories: Transcad (IBM PC-XTIAT) This specialized program is devoted to the study of transitions between transmission lines (coaxial, bifilar, planar structures) and waveguides.
17.6 Layout of circuits and cutting of masks 17.6.1 Description When a design has been analysed with the most accurate decription available, and then optimised by sophisticated CAD techniques (Section 17.5), a most critical part of the procedure still remains to be carried out: its physical realisation. Before moving on to the photolithographic process (Section 17.4.9), the pattern of the upper conductor must be drawn, and then the scaled mask must be cut. Co-ordinatographs or photoplotters can generate very accurate masks, but these machines are quite expensive, and well beyond the reach of many small research laboratories or academic institutions. The layout and cutting of masks can now be done accurately enough, but at a much lower cost, directly on a standard plotter connected to a desktop computer. 17.6.2 CCC: Autoart The Autoart program converts to artwork microwave circuit models described by their physical dimensions (single and coupled transmission lines, circular radial stubs, tapered lines, Lange couplers, circuit discontinuities). It is presently restricted to planar geometries with a single path from input to output (this restriction may, however, be overcome by declaring other ports to be open or short-circuited). Circuit data provided by the Supercompact package (Section 17.5.3) can thus be used to prepare the conductor pattern, and the geometrical data is then transferred to a co-ordinatograph or a photoplotter. Autoart interfaces directly with Wild Heerbrugg precision flat-bed plotting tables, with Aristo Graphics automatic co-ordinatographs, with Gerber Scientific photoplotters and, through an Initial Graphics Exchange Specification, with pattern generators and mechanical drafting equipment (these instruments can all be used to generate masks) [40]. 17.6.3 EESOF: Micad In a similar manner, the data provided by the general-purpose program Touchstone can be transferred through the Micad software to generate a mask on a co-ordinatograph or a photoplotter [43]. Using a specially configured diamond stylus (MICknife), masks can also be cut on standard plotters.
1038
Computer-aided design o f microstrip and triplate circuits
17.6.4 High Tech. Tournesol: Micros (HP 9000 series 200 and 300) In contrast with the two previous packages, which are additions to general analysis/synthesis software packages, Micros is a complete design tool, that generates the drawings of selected components, interconnects them and cuts the mask on a standard plotter [63]. The program is 'user-friendly' and completely
Computer-aided design o f microstrip and triplate circuits
1039
nect them at will, with compensated bends and sections of line, right on his computer screen, in order to prepare his layout. He may also define his own elements, e.g. patch antennas. The mask is then cut on a Rubylith sheet with a specifically designed sharp cutting tool, all in a matter of minutes to computer accuracy. Circuits realised with Micros were measured on a vector network analyser, and showed very good agreement between specifications and measured data, even for highly frequency-sensitive elements. The design of frequency-sensitive components such as filters requires a precise knowledge of the substrate characteristics (permittivity and thickness). Some manufacturer's specifications were found to be much too loose for design purposes, particularly for composite high-permittivity substrates. A companion program, Epsilon, was developed to measure the substrate's permittivity under actual operating conditions. A circular resonant ring is designed to resonate close to the operating frequency, and a mask is generated. When the resonant frequency has been measured, the program determines the permittivity [64]. 17.6.5 British Telecom: Temcad ( H P 9000 series 200 and 300) A general program for the layout of planar circuits was recently developed by British Telecom, combining theoretical models with experimental data, and including a wide range of flexible facilities to improve designer productivity [20].
17.7 Insertion of components 17.7.1 Definitions Lumped elements, such as capacitors, resistors and inductors, can either be manufactured by metal or dielectric deposition, right on the microstrip or in the balanced stripline, or alternatively discrete manufactured miniature components can be connected on the microstrip, or within the stripline (the last procedure is somewhat more complex, since a cavity must be carved within the dielectric materials). A number of semiconductor devices, diodes and transistors, as well as nonreciprocal ferrite devices (isolators and circulators), can also be inserted into planar circuits to realise active antenna feeds and interconnecting networks. These two categories are distinguished in the forthcoming Sections, and labelled, respectively, 'deposited' and 'discrete'. Fig. 17.22 Microstrip components realised by the program Micros
self-contained (it does not require extensive reading of manuals before use). The operator specifies circuit dimensions, operating frequency, substrate permittivity and width, and characteristic line impedance. A number of elements then become available to design the circuit: couplers, hybrids, dividers, step transformers, bandpass and low-pass filters (Fig. 17.22). He can position and intercon-
17.7.2 Discrete components Discrete components are in general commercially available, and ready to be inserted into a circuit. Most of the common electronic components - active and passive - are presently available at microwave frequencies in a package suitable for insertion within a microstrip circuit. Their main characteristic is their small size: a lumped element is small with respect to the wavelength. In addition, parasitic effects must be kept as small as possible, so that wire connections are extremely short or altogether absent, being replaced by metallised
1040
Computer-aided design of microstrip and triplate circuits
connecting surfaces. Special device cases were developed, to reduce the discontinuities as much as possible. Resistors: are small 'blocks' with sides from a few tenths of a millimetre up to a few millimetres (Fig. 17.23). They are generally made of a ceramic block, on which a resistive layer is deposited, between two metallised regions for connection purposes. The geometry of the resistive layer is adjusted with a laser during the fabrication process. It is possible in this way to meet tight tolerances. resistive
laser trimming
Computer-aided design of microstrip and triplate circuits
104 1
can be either series or shunt connected (in which case a hole must be drilled through the substrate). These capacitors are a few millimetres in size, so that their use is limited up to a few gigahertz, while resonances appear at higher frequencies. These adjustable components are most useful for fine tuning, or to compensate for component non-uniformity. Miniature inductors for microstrip are fairly recent additions. They consist of helically deposited metal strips on very thin multi-layer ceramic substrates, connecting from a layer to the next at each turn. A multi-turn 'coil' of very small dimensions is obtained in this manner. Large inductance values with small loss can be realised in a small volume. In practice, however, inductances are directly deposited on the microstrip (Section 17.7.5). Junction isolators and circulators can be mounted on microstrip. They are small ferrite discs, a few tens of millimetres in diameter, with small ribbons for connection within the circuit (Fig. 17.25). Holes must be drilled into the substrate to permit insertion. These components are relatively heavy and large, owing to the presence of permanent magnets.
for connections Fig. 17.23 Miniature resisto~
Sometimes, two connecting ribbons are attached, to facilitate the insertion procedure. Resistive loads and attenuators (Fig. 17.24) are manufactured by the same technique. connecting strips Fig. 17.25 Circulator for insertion in microstrip circuit
connecting strips Fig. 17.24 Miniature attenuator
Seen from the outside, capacitors look very much like resistors, they consist of a sandwich of ceramic and metal layers. Available capacitance values range from fractions of a picofarad up to several nanofarads. Adjustable capacitors are available for insertion into microstrip circuits, and
Most kinds of diodes suitable for mounting on microstrip are presently available: Schottky, PIN, varactors, Gunn, Impatt, Trapatt, etc. The diodes can be either inserted in chip form, or encased in various packages: LID ( Leadless inverted device, Fig. 17.26a), beam lead (connection with thin strips, Fig. 17.266) or cylindrical cases, with or without a mounting screw (Fig. 17.26~).The last package is mounted through the substrate, with the lower part in close contact with the ground plane to ensure heat removal. The increasing significance of microstrip circuits is closely related to the availability of transistors, both bipolar and MESFET, that have steadily improving characteristics. Cases that degrade as little as possible the performances of the chip have been designed. The usual cases (Fig. 17.27) permit easy insertion, with minimal discontinuities. A hole must be drilled through the substrate for power devices. However, the best performances are achieved when using chip-mounted transistors.
,
7042
Computer-aided design of rnicrostrip and triplate circuits ceramic support
I
/
Computer-aided design of microstrip and triplate circuits
1043
Precautions are required to avoid overheating of delicate components during the mounting procedure Connections may deteriorate owing to aging (oxidation, etc). Since components are generally quite small, their mechanical stability is most often ensured by the electrical connections themselves.
\
metallization
metal bond ceramic case(Be0)
a. Leadless I n v e r t e d Oeuice ILIOI
connecting strips b. "beam-lead"
Fig. 17.27 Transistor for microstrip circuit
c. t h r e e cyllndrlcal ceramic cares Fig. 17.26
Various diode packages a Leadless inverted device (LID)
b Beam lead c Three cylindrical cases
17.7.3 Mounting procedure Particular care must be taken when mounting lumped elements on microstrip substrates:
The electrical connections must be made very carefully Discontinuities between component and circuit must be as small as possible The mounting must be mechanically rigid
The classical soldering, currently used in electronics, can be used for mounting components on a microstrip substrate, but particular care and equipment are required. The soldering iron must have a very narrow tip, and a number of solders based on indium, tin and lead can be used, with melting points in the range 143OC to 280°C [40]. Thermocompression bonding, applying heat and pressure at the same time, produces an inter-atomic diffusion, and thus a high-quality weld. This process usually utilises gold as the welding material. Several bonding methods are shown in Fig. 17.28~-c.The duration of the bonding operation (typically in the 1-3 s range) is a critical parameter in the bonding process. Ultrasonic welding uses the same physical principle as bonding: heat and pressure. In this case, the heat is produced by mechanical rubbing by a point vibrating at ultrasonic frequencies (Fig. 17.29). This technique is particularly well suited to very sensitive components. Welding can also be realised by Joule heating, by circulating a current between two electrodes (Fig. 17.30). The interest of this process lies in the fact that heat can be applied very locally. On the other hand, semiconductor devices may become damaged.
1044
Computer-aided design of microstrip and triplate circuits
Computer-aided design of microstrip and triplate circuits
7045
Finally, devices can also be glued using conductive epoxy, loaded with fine metal particles, generally gold or silver. This process is extremely useful for mounting very delicate components, and also for encasing microstrip circuits
ultrasonic transducer
I
heating plate
Fig. 17.29 Ultrasonic welding gold thread
\
Tungsten Jube
lifting
pressure
!I!!
current source
electrode
drop
I
torch
electrode pressure \
solQer
conductor
b heat and pressure
gold thread
sudstrate
Fig. 17.30 Electric-current welding
17.7.4 Drilling holes in the dielectric substrate Several components require a hole to be drilled through the substrarte. either to provide a ground connection or a good thermal contact to remove the heat ,dissipated in the device. With plastic substrates, the process is straightforward, and perfect holes can be drilled, so long as the drill and the speed are selected correctly. The matter is far more complex with ceramic substrates, which are hard and brittle. Two techniques can be used: cutting of thread C
Fig. 17.28
Themocornpression bonding a Edge bonding b Drop bonding c Lateral-point bonding
Drilling with an abrasive powder (carborundum) and a rotating tube (Fig. 17.3 1) or an ultrasonically driven point. This approach is rather time-consuming A laser can realise perfect holes, even non-round ones, in a fraction of a second. However, a special drilling set-up is required. In all situations one tries to drill as few holes as possible in ceramic substrates.
7046
Computer-aided design of microstrip and triplate circuits
17.7.5 Deposited components These components are not introduced from the outside, but are built right on the substrate, and thus are an integral part of the circuit. Resistors, capacitors and inductors can be realised by this process. They are, in general, better suited to very high-frequency operation, since they do not present the discontinuities that always appear when a component is inserted. They are also generally smaller. Resistors are realised with either of two techniques (Fig. 17.32). A resistive rotation
Computer-aided design of microstrip and triplate circuits
7047
can be used to realise resistors in an easy way: one just has to remove the superior high-conductivity layers. Capacitors can be realised by the successive deposition of dielectric and metal layers, either by silk screening (thick-film process) or by evaporation (thin-film process). Additionally, a single-layer capacitor can also be made by the photolithographic process, using an interdigitated geometry (Fig. 17.20). Inductances are also realised by the photolithographic process, in the form of a loop or a spiral. In the latter case, the inner connection must be 'pulled out', either by bonding a thin gold wire, or by building a dielectric bridge with a metal strip deposited on top (Fig. 17.21).
17.8 Examples nickel tube
pressure
abrasiue Substrate
-
Fig. 17.31 Drifting of microstrip substrate with a rotating tube resistive paste lPd/PdOt
flu Cr ri substrate a. r e s l s t l v e p a s t e deposlted by silk screening
b.
use o f t h e adheslue Cr or TI l a y e r
Fig. 17.32 Resistors deposited on circuit
paste (palladium-oxide mixture) may be deposited by silk screening (thick-film technique), and then cured. This process can only be applied to substrates that can withstand high temperatures. Alternately, the low-conductivity nickel or chromium layers required for adhesion on ceramic substrates (Section 17.4.8)
17.8.I Design of a broadband amplifier One of the most current applications of microstrip CAD is the design of amplifiers to have a constant gain over a specified frequency band. As an example, an amplifier with a gain as flat as possible over the range 3-5 GHz was designed around a GaAs MESFET of the type DXL-2501 (Dexcel). The first step in the procedure is the actual measurement of the transistor parameters, carried out on a specialised transistor test fixture connected to an automatic vector network analyser. The complete test set-up is first calibrated to compensate for recurrent errors. The transistor is then mounted on the test fixture, and measurements are carried out at 101 frequency points over the range 2-8 GHz. The scattering parameters of the transistor are then obtained by computerised 'de-embedding' of the measured data, making use of the equivalent circuit of the transistor test fixture. The values obtained agreed quite well with the manufacturer's indications. The transistor was found to be practically unilateral (very small values of s,,). It was noted that the values of r provided by a commercially available program were erroneous, apparently due to inconsistent definitions. The CAD program used, Touchstone, is an analysis and optimisation program, but not a synthesis program. This means that a first approximation must be provided as starting point. This step is carried out by using the Smith chart, and conjugate match is provided at 5 GHz at the input and output. The first design proved unacceptable, as a transmission-line section was too short. A suitable matching structure was obtained on the second try and it is sketched in Fig. 17.33. The corresponding structure and values are then introduced into the CAD program Touchstone (Section 17.5.2), and optimisation was carried out, requiring a flat gain within the range 9.5 dB < G < 10.5 dB over the range 3-5 GHz. The microstrip losses are taken into account, as well as the effects of discontinuities at T-junctions and at steps. The predicted gain of the amplifier, prior to
1048
Computer-aided design of microstrip and triplate circuits
optimisation, is given in the curve a of Fig. 17.34, whereas the optimised value appears in curve b. The two circuits then realised, the layout was drawn with the help of the program Micros (Section 17.6.4), and the mask was cut on a plotter. The
Computer-aided design of microstrip and triplate circuits
7049
mask is cut on a Rubylith sheet. The mask is reduced and the circuit realised by means of the photolithographic process (Section 17.4.9). After mounting and connecting, the filter is measured on a vector network analyser; the transmission factor is shown in Fig. 17.36. The passband falls right in the specified range, and the 25 dB off-band requirement is also met.
Transistor
-
Fig. 1 7 . 3 3 Transistor amplifier with matching circuit
complete photolithographic process was carried out (Fig. 17.17), and the transistor was soldered on the microstrip circuit, under a microscope. Measurements were then carried out on an automatic network analyser, that had been previously calibrated, and the measured results are presented in Fig. 17.34, curve c, showing the unoptimised amplifier, and curve d the optimised one. It will be noted that the measured amphfication curve (d),while showing the same general behaviour as the predicted one, lies a few dB lower and is shifted somewhat towards lower frequencies. 17.8.2 Bandpass filter design We wish to realise a bandpass filter for the range 3.8-4.2 GHz, that has to meet the following requirements:
Passband ripple: Stopband attenuation: Substrate permittivity: Substrate thickness:
0.3 dB 25.0 dB at 4.6 GHz 2.33 (relative) 0.51 mm
These requirements are introduced into the CAD program Micros [63], which determines the response for a Chebjrshev design, formed of anti-resonant series cells and resonant shunt cells. The program determines the order of the filter that is required to meet the specification, and the operator can check the theoretical response before proceeding further with the filter design. The microstrip structure is then realised with broadside-coupled resonant strips. The program carries out the complete synthesis process, taking into account the effect of open ends (Section 17.3). The dimensions of the strips and the spacings are determined, and the layout is drawn (Fig. 17.35). The filter structure is in turn connected to the sides of the circuit, and a scale
I
\\\
\c
' "'
IC
------ measurements mpned
values
frequency (GHz)
Fig. 17.34 Amplifier gain a Predicted unoptimised gain b Predicted optimised gain c Measured unoptimised gain d Measured optimised gain
17.8.3 Design of a miniature Doppler radar It is possible to combine circuit and antenna functions on the same microstrip substrate, and this was used to develop a small proximity detector, sensitive to
1050
Computer-aided design of microstrip and triplate circuits
the presence of moving objects. A rectangular patch antenna resonates at 2.45 GHz and is also used as the frequency-sensitive element (filter) in the feedback loop. A MESFET amplifier is connected across the resonatorantenna. The low-frequency Doppler signal is detected directly at the MESFET connections, taking advantage of its nonlinearity to provide signal mixing. The mask of the circuit is shown in Fig. 17.37. While this circuit is quite simple, its
Computer-aided design of microstrip and triplate circuits
1051
performance is limited: the dielectric permittivity and thickness that are adequate for the design of a circuit are far from optimal as far as antenna radiation is involved, and vice versa. A better approach would be to separate the two functions by making use of a multi-layer structure (Section 8.12).
3.6-6.2 GHZ Fig. 17.35 Bandpass-filter design 52 1 l o g MAG REF 0 . 0 dB
A
s.ade/
Fig. 17.37 Mask for miniatwised Doppler radar
17.9 Conclusion
START STCP
3.000000000 M x 5.000000000 GHz
Fig. 17.36 Measured bandpass filter response
Computer-aided design requires suitable mathematical descriptions of the elements, which should be accurate enough, but not too complex mathematically [26]. The particularities of microwave printed circuits, outlined in Sections i7.1.6-1-711.8, make the design particularly demanding in terms of accuracy. It is seldom possible to define equivalent circuits that are at the same time general, simple and easy to use, and whenever electromagnetic-field calculations are required within an optimisation loop, the resulting computation time may well prove prohibitive. Highly accurate approximate expressions are now available for straight transmission lines and for many discontinuities, sometimes with errors smaller than fractions of a percent (Sections 17.2 and 17.3). However, these approximations are only valid over specified ranges of parameters, because they neglect radiated and surface waves: this is quite acceptable for microstrip lines, but obviously not
I
!
7052
Computer-aided design of microstrip and triplate circuits
for radiating patches. Furthermore, the number of structures analysed until now is limited, and proximity effects cannot be evaluated as accurately. The interactions of a line with a nearby wall, with the edge of a microstrip substrate, with a discontinuity or with a patch have not as yet been determined to a similar degree of accuracy, and much remains to be done in this respect. In fact, the possible combinations of components are almost infinite in number. The problem becomes particularly stringent for microwave- and millimetre-wave monolithic integrated circuits, where different lines, circuits and components are located very close to one another. It must also be kept in mind that the physical dimensions are generally not accurately known: substrate thickness is specified within 5% or even 10% by some manufacturers. This means that one should measure it before actually drawing the circuit pattern and cutting the mask. A given design is valid only with the substrate material for which it was prepared - or an almost identical one. Dimensional effects like under-etching also introduce errors that are much larger than the ones encountered in the theory. Fortunately, systematic errors can be compensated for. Section 17.5 shows that there is no shortage of CAD software packages for microstrip design. Some are rather broadband general-purpose analysis/ synthesis packages, while others have been specifically elaborated to design a single kind of component. The task of the designer, who is supposed to select one particular software is clearly not obvious, since many of the programs apparently fulfil similar tasks. To compare different software packages, one should actually use several of them to develop the same circuit, and compare them in terms of the results actually measured, their ease of operation, the computer time and memory requirements, compatibility and portability, service, bugs etc. Many different computer systems are presently available and in constant evolution, so that the task is by no means simple. Cost, availability and service are non-technical parameters that become most significant in actual operation. The accuracy provided by a program is a most significant parameter for selection; in particular, when optimisation processes are involved. Besser [7] noted that the use of low-accuracy models in the initial microwave CAD packages considerably slowed down their actual implementation within the industrial market, but this problem has been corrected to a large extent in more recent designs. It was also noted that many optimisation algorithms did not perform as well as was claimed, and they did not always converge towards the best possible solution. In conclusion, one must remember that the CAD is a most valuable tool, useful to a designer who understands its operation and is aware of its limitations, but useless and wasteful when put in the wrong hands. It can significantly increase the capabilities of a skilled operator, both in terms of time and quality. On the other hand, the GA+A principle applies (garbage in, garbage out): for instance, if the substrate properties are not accurately introduced, the
Computer-aided design of microstrip and triplate circuits
I
7053
results cannot be expected to be accurate (even though miracles sometimes happen - but generally at random!). An expert microwave designer will immediately detect possible trouble areas, where lines are too close to one another, or too close to an edge etc., but it would be practically impossible to program a computer to detect and take care of all such possible combinations. In microstrip and stripline circuit design, like in many other technological areas, the computer does not replace the skilled designer.
1
17.10 Acknowledgments
The authors wish to thank Miss Anja Skrivervik, Mr. Lionel Barlatey and Dr. Juan Mosig, who contributed to the realisation of circuits and to the elaboration of parts of the text. The continuous support of the Swiss National Research Foundation is gratefully acknowledged. Thanks are also extended to the firm High Tech Tournesol, that granted permission to reproduce Figures originally prepared for the intensive short course 'Initiation to Microstrip'. I
17.11 References I
2 3 4 5
6 7 R-
9 10 II
12 13 14
ABRAMOWITZ, M., and STEGUN, I. A. (1972): 'Handbook of mathematical functions' (New York, Dover) ABRIE, P. L. (1986): 'The design of impedance-matching networks for radio-frequency and microwave amplifiers' (Norwood, MA, Artech House) AKHTARZAD, S., and JOHNS, P. B. (1975): 'Dispersion characteristics of a microstrip line with a step discontinuity', Electron. Letts., 11, pp. 31&311 ALTSCHULER, H. M., and OLINER, A. A. (1960): 'Discontinuities in the center conductor of symetric strip transmission line' IEEE Trans. MTT-8, pp. 328-338 ANDERS, P., and ARNDT, F. (1980): 'Microstrip discontinuity capacitances and inductances for double steps, mitered bends with arbitrary angle, and asymetric right-angle bends' IEEE Trans. MTT-28, pp. 1213-1217 BENEDEK, P., and SILVESTER, P. (1972): 'Equivalent capacitances for microstrip gaps and steps' IEEE Trans. MTT-20, pp. 729-733 BESSER, L. (1985): 'What is the direction of commercial microwave technology?, Microwave Syst. News, 15, pp. 65-67 ROCHTLER. U.. and ENDRESS, F. (1986): 'CAD program designs stripline couplers', -. Microwaves and RF, 25, pp. 91-95 COHN, S. B. (1955): 'Problems in strip transmission lines', IEEE Trans. MTT-3, pp. 119-126 EASTER, B. (1975): 'The equivalent circuit of some microstrip discontinuities', IEEE Trans., MTT-23, pp. 655-660 FARRAR, A,, and ADAMS, A. T. (1971): 'Computation of lumped microstrip capacities by matrix-methods: rectangular sections and end effect', IEEE Trans, MTT-19, pp. 495-497 FARRAR, A,, and ADAMS, A. T. (1972): 'Matrix method for microstrip three-dimensional problems', IEEE Trans.. MTT-20. pp. 497-504 FRANKEL, S. (1977): 'Multiconductor transmission line analysis' (Artech House, Dedham, MA) GARDIOL, F. E. (1984): 'Introduction to microwaves' (Artech House, Dedham, MA) - - - - -
7054
Computer-aided design of microstrip and triplate circuits
15 GARDIOL, F. E. (1986): 'Microstrip computer-aided design in Europe', IEEE Trans. M m 34, pp. 1271-1275 16 GARDIOL, F. E. (1987): 'Lossy transmission lines' (Artech House, Norwood, MA) 17 GETSINGER, W. J. (1973): 'Microstrip dispersion model', IEEE Trans., MTT-21, pp. 34-39 18 GOPINATH, A., and EASTER, B. (1974): 'Moment method of calculating discontinuity inductance of microstrip right-angle bends', IEEE Trans. MTT-22, pp. 880-883 19 GOPINATH, A., THOMSON, A. F., and STEPHENSON, I. M. (1976): 'Equivalent circuit parameter of microstrip step change in width and cross junctions', IEEE Trans, MlT-24, pp. 142- 144 20 GOSLING, I. G. (1985): 'A new microwave CAD layout program'. IEE/EI2 Colloquium on Computer Aided Design of Microwave Circuits, London, Nov. 1985 21 GUNSTON, M. A. R. (1972): 'Microwave transmission line impedance data' (Van Nostrand Reinhold, NY) 22 HAMMERSTAD, E. O., and BEKKADAL, F. (1975): 'Microstrip handbook'. Norwegian Institute of Technology, Trondheim, report ELAB STF44 A74169. 23 HAMMERSTAD, E. O., and JENSEN, 0. (1980): 'Accuratemodels for microstrip computeraided design', IEEE MTT-S International Microwave Symposium Digest, pp. 407-409 24 HOEFER, W. J. R. (1977): 'Theoretical and experimental characterization of narrow transverse slits in microstrip', Nachrichrentechni. Zfr, 30, pp. 582-585 25 HOEFER, W. J. R. (1977): 'Equivalent series inductivity of a narrow transverse slit in microstrip', IEEE Trans., MlT-25, pp. 822-824 26 HOFFMAN, G. R. (1984): 'Introduction to computer aided design of microwave circuits'. Proceedings of the 14th European Microwave Conference, Likge, Belgium, pp. 731-737 27 HOFFMANN, R. K. (1983): 'Integrierte Mikrowellenschaltungen' (Springer, Berlin) 28 HORTON, R. (1973): 'The electrical characterization of a right-angle bend in microstrip line' IEEE Trans., MTT-21, pp. 427-429 29 HORTON, R. (1973): 'Equivalent representation of an abrupt impedance step in microstrip line', IEEE Trans., MlT-21, pp. 562-564 30 HOWE, H. (1974): 'Stripline circuit design' (Artech House Dedham, MA) ITOH, T., MITTRA, R., and WARD, R. D. (1972): 'A new method for solving discontinuity problems in microstrip lines'. IEEE-GMTT International Symposium Digest, pp. 68-70 JAIN, 0. P., MAKIOS, V., and CHUDOBIAK, W. J. (1971): 'Coupled-mode model of 405-406 dispersion in microstrio'. - . Electron Letts. 7. DO. rr -JAMES, D. S. and TSE, H. S. (1972): 'Microstrip end effects', Electron. Letts., 8, pp. 46-47 JANSEN, R. H. (1985): 'The spectral domain approach for microwave integrated circuits', IEEE Trans., Mm-33, pp. 1043-1056 JANSEN, R. H. (1986): 'LINMIC, a CAD package for the layout-oriented design of singleand multi-layer MICs/MMICs up to mm. wave frequencies', Microwave J., 29, (2) JANSSEN, W. (1977): 'Hohlleiter und Streifenleiter' (Hiithig, Heidelberg) KAJFEZ, D., and TEW, M. D. (1980): 'Pocket calculator program for analysis of lossy microstrip:, Microwave J., 23, pp. 39-48 KOMPA, G. (1976): 'S-matrix computations of microstrip discontinuities with a planar waveguide model', Archiv Elekr. Uber~ragun~stech., 30, pp. 58-64 KOSTER, N. H. L., and JANSEN, R. H. (1986): 'The microstrip step discontinuity, a revised description', IEEE Trans., MTT-34, pp. 213-223 LAVERGHETTA, T. S. (1984): 'Microwave materials and fabrication techniques', (Artech House, Dedham, MA) LEIGHTON, W. H., and MILNES, A. G. (1971): 'Junction reactance and dimensional tolerance effects on X-band 3-dB directional couplers', IEEE Trans., MlT-19, pp. 814-824 MAEDA, M. (1972): 'An analysis of gap in microstrip transmission line', IEEE Trans., MTT-20, pp. 390-396 MARCH, S. L. (1984): 'Microwave circuit layout: a dynamic plot emerges', Microwaves and RF, 23, pp. 59-161
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Computer-aided design of microstrip and triplate circuits
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44 MARCUVITZ, N. (1951): 'Waveguide handbook'. MIT Rad. Lab. Series, 10, (McGraw-Hill, New York) 45 MARSDEN, J. E. (1973): 'Basic complex analysis' (W. H. Freeman, San Francisco) 46 MEHRAN, R. (1975): 'The frequency-dependent scattering matrix of microstrip right-angle bends, T-junctions and crossings', Arch. Elek. Uberrragungstech., 29, pp. 454-460 47 MEHRAN, R. (1976): 'Frequency dependent equivalent circuits for microstrip right-angle bends, T-junctions and crossings', Arch. Elek. Ubcrrragungstech., 30, pp. 80-82 48 MENZEL, W. (1976): 'Frequency-dependent transmission properties of truncated microstrip right-angle bends', Elecrron. Lett, 12, pp. 641 49 MENZEL, W. (1978): 'Frequency-dependent transmission properties of microstrip Yjunctions and 120' bends', IEE J . Microwaves. Optics and Acoustics, 2, pp. 55-59 50 MENZEL, W., and WOLFF, 1. (1977): 'A method for calculating the frequency dependent properties of microstrip discontinuities', IEEE Trans., MTT-25, pp. 107-1 12 51 Microwaves and RF (1984): 'The software selector', 23, pp. 70-95 52 MOSIG, J. R., and GARDIOL, F. E. (1977): 'Equivalent inductance and capacitance of a microstrip slot'. Proceedings 7th European Microwave Conference, Copenhagen, pp. 455-459 53 ROHDE. U. L. (1985): 'Models and nonlinearities: major factors in microwave CAD software', Microwave Syst. News, 15, pp. 123-143 54 SALERNO, M., and SORRENTINO, R. (1986): 'Planim: a new concept in the design of MIC filters'. Electron. Letts, 22, pp. 1054-1056 55 SCHNEIDER, M. V. (1969): 'Microstrip lines for microwave integrated circuits', BeN Syst. Techn J.. 48. pp. 1421-1444 56 SILVESTER, P., and BENEDEK, P. (1972): 'Equivalent capacitances of microstrip opencircuits' IEEE Trans., MTl-20, pp. 51 1-516 57 SILVESTER, P., and BENEDEK, P. (1973): 'Microstrip discontinuity capacitances for rightangle bends, T-junctions and crossings', IEEE Trans., MlT-21, pp. 341-346 58 THOMSON, A. F., and GOPINATH, A. (1975): 'Calculation of microstrip discontinuity inductances', IEEE Trans., MTT-23, pp. 648-655 59 WALDRON, R. A. (1970): 'Theory of guided electromagnetic waves' (Van Nostrand Reinhold, London) 60 WHEELER, H. A. (1965): 'Transmission line properties of parallel strips separated by a . dielectric sheet', IEEE Trans., MTT-13, pp. 172-185 61 WOLFF, I., KOMPA, G., and MEHRAN, R. (1972): 'Calculation method for microstrip discontinuities and T-junctions', Electron. Letts., 8, pp. 177-179 62 YAMASHITA, E., and MITTRA, R. (1968): 'Variational method for the analysis of microstrip lines', IEEE Trans., MTT-16, pp. 251-256 63 ZURCHER, J. F. (1985): 'MICROS3 - A CAD/CAM program for fast realisation of microstrip masks'. Proceedings IEEE MTT-S International Microwave Symposium, Saint Louis, Missouri 64 ZtiRCHER, J. F., BARLATEY, L., and GARDIOL, F. E. (1986): 'Computer-aided method to measure the permittivity of microstrip substrates'. Proceedings MIOP Symposium, Wiesbaden, Germany
Resonant microstrip antenna elements and arrays for aerospace applications A.G. Derneryd
18.1 Introduction Several advantages associated with microstrip antennas, namely light weight, low profile and structural conformity, make them ideally suited to aerospace applications. A number of single microstrip-patch antenna elements and microstrip arrays for communication and radar systems are described in this Chapter. The objective is to demonstrate practical designs and results, together with the engineering tools used. Antennas for dual frequency bands, dual beams and dual polarisations are considered. The frequency range covered is from L-band to c-band. Patches that are resonant in the dominant mode are usually employed. However, in Section 18.2 different mode structures actually excited on a circular disc are displayed using a liquid-crystal detector. This is an effective tool for visualising the RF field excited on a microstrip antenna. In Section 18.3 a dual-band circularly polarised patch antenna element is presented. The antenna is a low-gain antenna used for data communication. It was successfully flown on the Giotto space probe that encountered the comet Halley at its recent appearance. A monopulse array antenna for secondary surveillance radar applications is discussed in Section 18.4. The array aperture consists of two rows of microstrip antenna elements. A corporate feed network in stripline is mounted as an integrated part behind the antenna aperture. A low-density foam is used as a dielectric to achieve a lightweight design. An array-antenna concept suitable for a space-borne imaging radar system is described in Section 18.5. It is an integral feed-array structure with two separate feeding networks to enable horizontal and vertical polarisations to be obtained using a single antenna aperture. This antenna was designed and tested by Dr Lars Pettersson of the National Defence Research Institute, Sweden.
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18.2 Circular antenna element
Various design techniques for resonant microstrip antenna elements of simple geometries are available. The simplest method, useful for predicting radiation characteristics, is the cavity model. This model has been used to predict the resonant frequencies of a circular disc. An antenna element was manufactured and the different mode structures were visualised using a liquid-crystal detector. The basic circular antenna element comprises a conducting circular patch on a thin dielectric substrate backed by a ground plane, as shown in Fig. 18.1. The antenna can be viewed as a cylindrical cavity bounded at its top by the patch and at its bottom by the ground plane.
Resonant microstrip antenna elements
Thus, for each mode configuration, a resonant frequency is evaluated from [I]:
where Xis a zero of the derivative of the Bessel function of order n, and c is the velocity of light in free space. In practice, only the first few zeros are of interest. These are listed in Table 18.1 in ascending magnitude of X for convenience, since no closed-form expression exists for the roots X of J;(X). For any given radius, the mode corresponding to n = 1 has the lowest resonant frequency, and is known as the dominant mode. Table 18.1 Roots of J i ( X )
Fig. 18.1
Circular microstrip antenna element and liquid-crystal detector in wooden mount (Courtesy: N. P. Kernweis and J. F. Mcllvenna. RADC)
The resonant frequencies are functions of the radius a of the patch, the thickness h of the dielectric and the dielectric constant E,. However, an effective radius a,, slightly larger than the physical one, is introduced to account for the fringe field along the edge of the resonator cavity. The relation between the effective and physical radii is given by [I]:
This expression is derived assuming a quasi-static field distribution. However, it can be used to estimate the higher-order resonant frequencies as well.
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=
0
An antenna element was manufactured from a 1/16 in (1.58 mm) doubly-clad Teflon glass-fibre board with a dielectric constant of 2.55. The actual radius of the disc is 18.3mm but the effective radius is 5% larger, as calculated using eqn. 18.1. The 5 0 n feeding point is located at a radius 0.3 times the total radius of the patch. There is a shorting pin at the centre of the patch in order to reject the static mode (n = 0). The calculated resonant frequency for the dominant mode is 2.8 GHz using eqns. 18.1 and 18.2. The next two higher-order resonant frequencies are 4.7 GHz and 6.5 GHz, similarly calculated. The theoretical E-field structures for these three modes are shown in Fig. 18.2 [2]. It is possible to monitor mode changes as antenna patch dimensions or frequency are varied, by using a liquid-crystal detector. This consists of an encapsulated liquid-crystal solution that changes colour with applied heat. When a resistive coating is sprayed onto the back of the crystal, RF field components produce localised heating. Thus, a colour display results that varies with the intensity of the field. The liquid-crystal detector shown in Fig. 18.1 was placed on top of the circular patch [3].Visual colour displays of the E-field, corresponding to the first three modes, were observed using a liquid crystal with a resistive backing of 1100 Rlsquare. Black-and-white reproductions of the different mode structures actually excited on the circular patch are shown in Fig. 18.3. To effectively excite the second higher-order mode, the feed had to be repositioned closer to the
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centre of the patch. The new feed position produces changes both in the dominant mode and in the first higher-order mode behaviour, which can be observed with the liquid-crystal detector.
Fig. 18.2 Calculated E-field structures on a circular microstrip antenna element at resonance a Dominant mode, TM, b First higher order mode, TM, c Second higher order mode, TM,
The photographs were taken with about 1 W of power applied to the antenna input. The liquid-crystal detector was directly on top of the patch. The loading effect on the antenna is thus at its maximum, but the displays are always bright and well defined. There is about 1% decrease in resonant frequency with the detector at this maximum loading position. However, the liquid-crystal detector is an effective aid in experimentally determining the relation between the feed position and the mode structure actually excited on a patch antenna. 18.3 Dual-band circularly polarised antenna element On 13 March 1986 the European Space Agency (ESA) spacecraft named Giotto encountered the comet Halley at a distance less than 500 km from the nucleus.
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Among the antennas on board was an S-band microstrip antenna for data communication between Earth and the Giofto space probe [4]. The antenna is a low-gain antenna providing an omnidirectional radiation-pattern coverage, together with a second low-gain antenna of the helix type.
The principal requirement of these two antennas was to provide real-time receiveltransmit of telemetry and telecommand signals during the geostationary transfer orbit. The antennas operate on a right-hand circular-polarisation mode in both frequency bands. The microstrip antenna is located on the outer surface of the dust-protection shield of the spacecraft. The gain requirement, including a 1 dB allowance for cable loss, is given in Table 18.2. This provides the necessary radiation-pattern overlap in the overall coverage pattern. Table 18.2
Gain requirement including cable loss
Angular interval, deg
Fig. 18.3 Observed mode structures on a circular microstrip antenna element (Courtesy: N. P. Kernweis and J. F Mcllvenna, RADC) a Dominant mode (2.8 GHz) b First higher-order mode (4.7 GHz) c Second higher-order mode (6.5 GHz)
Minimum gain, dBi
The microstrip antenna is a square radiating element resonant in its dominant mode. The element is etched on one side of a doubly clad PTFE board. The thickness of the laminate is 1/16in (1.58 mm) and the dielectric constant is 2.32.
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Resonant microstrip antenna elements
The element is fed at two adjacent sides via a 90" hybrid to generate right-hand circular polarisation. Each feeding line between the patch and the hybrid contains a two-section impedance transformer for double tuning [5]. The geometry of the transformer and the radiating patch is shown in Fig. 18.4. The input impedance, as seen from the 50R line, can be expressed in terms of the transformer parameters and the input impedance ZAof the radiator alone as
1065
The impedance matching transformers and the hybrid are etched on a thin doubly clad board which is contained in a stripline network bonded to the rear side of the radiating element board. A layout of the different boards is shown in Fig. 18.5. The transmission lines on the top board and in the stripline board are connected via copper strips surrounded by mode-suppressing pins. The fourth arm of the hybrid is terminated in a matched load placed inside the stripline board.
The explicit expression is Zin
=
Z* 2, Z2
+ jZz tan (k21z) + jZL tan (k21z)
where
z, Z, + jZ,
tan (k, I,) Z , jZA tan (k, I, ) and k, and k, are the propagation constants of the two transformer sections, respectively.
z,
=
+
Fig. 18.5 Layout of the complete microstrip antenna boards
rodlalor
2-section transformer
5011
Fig. 18.4 Dual-frequency microstrip antenna using an impedance-matching transformer
The characteristic impedances Z, and Z, of the transformer and the corresponding lengths I, and I2 are the parameters to be chosen to fulfil the matching conditions
The single and double prime signs refer to the two frequencies to be matched. In this case the input impedance is set to 50R, i.e. the characteristic impedance of the feed line. The input impedance of the patch alone is found from measurements at the two frequencies to be matched.
The overall dimensions of the complete antenna, including a mounting frame, are 139mm x 139 mm and the weight is 0.2 kg. The front surface is covered with a thin layer of black thermal paint with low electrical conductivity to prevent electrostatic charging in space. A picture of a prototype antenna is shown in Fig. 18.6. The measured return loss of the antenna including the cable, is presented in Fig. 18.7. The voltage standing-wave ratio is better than 1.2:1 at both the telecommand frequency (2116.7MHz) and at the telemetry frequency (2298.7 MHz). Recorded antenna patterns at three different cuts through the broadside direction are plotted in Fig. 18.8. The antenna is mounted on a ground plane to simulate the dust-protection shield. The specified gain as a function of the angle is shown as a broken line. The dual-band circularly polarised microstrip antenna was successfully flown on the Giotto spacecraft, and it was proved to fulfil all the specified data.
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Fig. 18.6 A prototype microstrip antenna for the Giotto space probe
-50
-25 0 25 angle from broadside, degrees
50
75
Fig. 18.8 Recorded antenna patterns at 2298.7 MHz for three different cuts (0". 4 5 , 90")
frequency, MHz
Fig. 18.7
Measured return loss of the antenna including the cable
Fig. 18.9 Monopulse microstrip-array antenna
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18.4 Monopulse-array antenna In this Section an L-band planar-array antenna of the monopulse type intended for a secondary surveillance radar is described. Besides the usual sum radiation pattern, the antenna also generates a difference radiation pattern in one plane. In the current application the latter is used to separate signals received in the main beam from those received in the sum sidelobe region. This requires that the difference sidelobe level exceeds the sum sidelobe level at all angles. The antenna array consists of an aperture with 2 x 6 rectangular patches, as shown in Fig. 18.9. A stripline feed network is placed on the rear side of the aperture. The size of the antenna is 650 mm x 1300mm and the weight is 10 kg. Mechanically, the antenna is of sandwich design with foam as a spacer to achieve low weight and low losses. A cross-section of the aperture and the stripline feed network is shown in Fig. 18.10. The radiating patches, the transmission lines and the ground planes are supported by glass-fibre-reinforced plastic (GFRP) skins. Standard techniques are used to etch the radiating elements and the feed lines. The final assembly is done by bonding the different layers together in a step-by-step procedure.
radiating elements
-.
GFRP skin foam
feed network
-
ground plane ---,
A stripline corporate feed network is connected to the microstrip elements from underneath. Unequal power dividers of the Wilkinson type are used to get a 25 dB Chebyschev amplitude taper in the H-plane. A layout of the corporate feed network is given in Fig. 18.11. The first power divider, however, is a rat-race hybrid with equal power split to feed the two antenna halves. The sum signal of the two identical antenna halves is formed at one port of the hybrid, while the difference signal is formed at an opposite port. The far fields are calculated assuming a two-slot model for each patch [6]. However, this model does not take into account the effect of the finite ground plane. The edge eiYects are included by adding the field components diffracted from the edges to those radiated directly from the slots [7]. This effect is particularly noticeable at angles close to endfire and in the backward direction.
GFRP skin foam
ground Plane
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GFRP skin foam GFRP sktn
Fig. 18.1 0 Cross-section of the monopulse-array antenna
The basic radiating element used in the array is the rectangular patch with dimensions 90mm x 121 mm, resonant in the dominant mode. Two such elements, spaced 258 mm and fed in series from a single feed point, are employed to form the E-plane radiation pattern. The element pair is fed at the lOOQ input-impedance point of one of the patches. The second patch is connected to the first one by a half-wavelength microstrip line. The resulting input impedance of the pair is thus 50Q since the elements act in parallel when transformed to the common input port. The H-plane pattern is generated using six such pair of elements. The centre-to-centre spacing is 175mm.
Fig. 18.11 Layout of the corporate feednetwork (Courtesy:J. P.Starski, Chalmers University of Technology)
The radiation mechanism in the E-plane of a single slot in a finite ground plane is illustrated graphically in Fig. 18.12. The pattern is calculated by summing three rays; i.e. the direct geometrical-optics field, the singly edgediffracted field and the doubly edge-diffracted field. The direct field is obtained by assuming the ground plane to be infinite in extent. Using the co-ordinate system of Fig. 18.12, the normalised direct field in the E-plane from each slot can be written as sin (nh& sin 8) e-jk" Eoo = e ~ h &sin 8 s where k is the propagation constant in free space, h is the slot width normalised to the free-space wavelength, E, is the relative dielectric constant of the substrate and s is the distance from the slot centre to the observation point. The slot width is usually assumed to be equal to the substrate thickness. The singly diffracted field from each edge, generated from the same slot, is given as the incident field at the edge times a hard-boundary diffraction coefficient neglecting the dielectric effect [a]:
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The far field diffracted from the edges is thus expressed as ( + sign refers to edge 1 and - sign to edge 2) E: =
(xh&) e-jkdt + e sinah& -Dr(e Jz
= d,,
Pi,
n = 2)
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where n + P C + ( p , n) = cot 2n a - P C - ( p , n) = cot 2n
+ cos (/I - 2 n n N + ) + cos ( p - 2 n n N - )
g+ (P) = 1 g-(P) = 1
Fig. 18.12 Co-ordinate system and geometry in the E-plane of a slot in a finite groundplane
with
.
-90
.
.
.
.
.
-60
-30
b
.
o
0
.
l
l
l
l
l
30
.
60
a
I
90
angle from broads~de~degrees
and D' is the reflected diffraction coefficient given in eqn. 11.716 of Reference 8 and reproduced here:
Fig. 18.13 Recorded and calculated E-plane radiation patterns of an element pair at 1060 MHz
in which N + and N - are the integers that most closely satisfy the equations 2nnNf 2nnN-
-P -P
=
n
=
- n.
(18.15)
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Resonant microstrip antenna elements
Since the edge is relatively close to the slot, cylindrical-wave propagation is assumed. The doubly diffracted field is expressed as in eqn. 18.9. However, the incident field in this case is the singly diffracted field from the other edge assuming cylindrical-wave propagation. A calculated radiation pattern along the E-plane of an element pair is plotted in Fig. 18.13. The far field is computed using eqns. 18.8 and 18.10 referred to the same phase centre and assuming four radiating slots. The double edgediffracted fields are also included; e.g. fields diffracted from a first edge and incident on a seond edge. Diffracted rays on both sides of the aperture are considered. The corresponding measured pattern at 1060 MHz is included in Fig. 18.13 as well. The half-power beamwidth is 27'.
18.5 Dual-polarised-array antenna
Part of the active microwave instrumentation on board the European Remote Sensing Satellite 1 (ERS-I) developed for the European Space Agency is a scatterometer. It is an incoherent radar system at 5.3 GHz which measures the back scattering of the ocean. The values are used to calculate wind speed and wind direction.
Fig. 18.1 5
-90
-60
-30
0
30
60
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Series-parallel fed array of square microstrip patches
90
angle from broads~de.degrees
Fig. 18.14 Recorded and calculated sum-and-difference radiation patterns along the Hplane at 7060MHz
Recorded H-plane sum and difference patterns of the antenna are presented in Fig. 18.14. Calculated patterns using the method outlined in Reference 7 are also included as broken lines. The sum sidelobe level is below - 22 dB and the half-power beamwidth is 16'. The gain measured at the sum input port is 17 dBi and the losses are estimated to 1.3 dB. The difference sidelobe level exceeds the sum sidelobe level as required.
The scatterometer antenna is a narrow-band (2 MHz) planar array generating a fan beam. As an alternative to the current slotted-waveguide antenna solution a microstrip array is presented. The advantage of such a design is that the same aperture can be utilised for two orthogonal polarisations simultaneously [9]. A section of the microstrip array is shown in Fig. 18.15. It consists of 6 x 6 square microstrip patches arranged in 12 identical linear sub-arrays with three elements each. Every element is excited in two orthogonal modes from two separate feed networks. The feed point of the network for vertical polarisation is marked with an A on the central feeding line in Fig. 18.15. The feed network for horizontal polarisation is split into two symmetrical parts. These are fed 180° out of phase
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at points B and C on the outer feeding lines in order to generate a broadside beam. Each square element is fed at the mid-point of the edge of the element. This is the low-impedance point of the orthogonal mode in each case, thus maximising the isolation between the two polarisations. This cross-coupling is further surpressed by the symmetric feeding of the array. The three elements in each sub-array are fed by resonant feed networks. In the vertical-polarisation case the elements are fed from a common microstrip line of constant-impedance level at positions spaced one wavelength apart. The total input admittance of a sub-array is thus the sum of all patch admittances first transformed through a quarter-wave section. This is matched to the rest of the feeding structure by two quarter-wave transformers. In the horizontal-polarisation case the elements are fed in series separated by half-wave transmission lines. The input admittance of the three series patches is the sum of the patch admittances transformed through a quarter-wave section. The networks to feed the 12 identical sub-arrays are non-resonant to make them less sensitive to internal reflections and to enable future beam shaping by feeding the sub-arrays with different amplitudes and phases. The feed networks for the two polarisations are basically identical since the input impedance of a three-element sub-array for vertical polarisation is chosen to be twice the input impedance of the sub-array for horizontal polarisation.
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(TEM) method [lo]. The radiation resistance at each end of the patches is assumed to be 360R, a value found from measurements on test circuits. A microstrip substrate of the type shown in Fig. 18.16 is used. The base plate is a carbon-fibre-reinforced plastic (CFRP) skin to provide high mechanical stiffness and low thermal expansion. The metallic coating forming the ground plane is realised by an aluminium foil of 0.1 mm thickness. The top dielectric skin, carrying the patches and the feed network, is made from three layers of Kevlar-epoxy prepreg. A prefabricated 0.005 mm copper foil on an aluminium carrier is cured to the skin in a vacuum press. The aluminium carrier is then removed by means of an alkaline etching solution and the etching of the pattern is carried out by the standard photo-etching technique. Spacers in CFRP are used to support the dielectric skin, and they are positionedat locations with low electric field. c~rcutt
spacer dielectrtc layer
l g r o u n d plane
Fig. 18.16
Cross-section of the microstrip substrate
Table 18.3 Impedance levels and dimensions of the microstrip lines in the feed network
Line
Impedance,
Length, mm
Width, mm
The characteristic impedances of the feed lines are given in Table 18.3, together with the corresponding lengths and widths. The effective dielectric constants and the line widths have been determined using a low-frequency
The dimensions of the radiating patches and of the microstrip transmission lines are functions of the substrate thickness and the dielectric constant. The thickness has been determined from a minimum-loss point of view. The variation of the different types of losses as a function of the substrate thickness at a fixed impedance level can be derived, for example, from References 11-13. The proportional factors are determined by calculating the various losses for different thicknesses. The total losses in this particular design and for the substrate used, given a fixed impedance level, depend on the height h (in mm) approximately as Conductor loss
0.2/h dB
Dielectric loss
0.3 dB
Radiation and surface wave losses
0.05h2dB
The minimum-loss substrate thickness calculated from the above is 1.3 mm. The calculations were made on the assumption of a uniform dielectric. However, a suspended Kevlar skin is used, and instead the dielectric loss decreases slightly with increasing thickness. The actual optimum is therefore slightly larger than found above. A thickness of 1.6 mm is used, i.e. 0.4 mm for the Kevlar skin and 1.2 mm for air with sparsely scattered spacers. A photograph of a section of the antenna is shown in Fig. 18.17. The size of
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the radiating patches is 23.5 mm x 23.5 mm and the element separation is 23.7mm. Two recorded radiation patterns of the array are presented. A cut along the H-plane for the vertical-polarisation case is plotted in Fig. 18.18. The sidelobe level is about -13dB, as expected from a uniform amplitude distribution. The corresponding pattern cut for the horizontal-polarisation case along the E-plane is shown in Fig. 18.19. The measured sidelobe levels are somewhat unsymmetrical, mainly owing to an amplitude unbalance at the input ports. The half-power beamwidth is 10" for the measured patterns. The isolation between the two polarisation ports is 31 dB, and this will improve with a better amplitude balance.
Fig. 18.17 Dual polarised rnicrostrip array antenna
a n g l e from b r o a d s ~ d e ,degrees '
Fig. 18.19 Recorded radiation pattern along the E-plane at 5.3GHz. Horizontal polarisation
18.6 Concluding remarks
- 401
-180
I, 620
\
-60 0 60 a n g l e from broadside, degrees
8
120
I
180
Fig. 18.18 Recorded radiation pattern along the H-plane at 5.3G M Vertical polarisation
The procedures employed for designing the microstrip antenna elements and arrays make use of transmission-line and cavity models coupled with experimental iterations of the initial designs. This is adequate for antennas with moderate requirements in terms of bandwidth and sidelobe levels. The effect of a finite ground plane on the radiation-pattern predictions is included by adding fields diffracted off the edges to the direct radiated fields. By doing this, the
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Resonant microstrip antenna elements
radiation patterns are more accurately estimated in the backlobe and wide-angle regions. Chapter 19
18.7 References 1 SHEN, L. C., LONG, S. A,, ALLERDING, M. R., and WALTON, M. D.: 'Resonant frequency of a circular disc, printed-circuit antenna', IEEE Trans., 1977, AP-25, pp. 595-596 2 WATKINS, J.: 'Circular resonant structures in microstrip', Electron. Lett., 1969, 5, pp. 524-525 3 KERNWEIS, N. P., and McILVENNA, J. F.: 'Liquid crystal diagnostic techniques, an antenna design aid', Microwave J., Oct 1977, 20, pp. 47-51, 58 4 BENGTSSON, P., HALM, R., and CRONE, G. A,: 'The Giotto spacecraft antenna subsystem design', IEEE Int. AP-S Symp. digest, 1986, pp. 711-714 5 DERNERYD, A. G.: 'Microstrip disc antenna covers multiple frequencies', Microwave J., May 1978, 21, pp. 77-79 6 DERNERYD, A. G.: 'Linearly polarized microstrip antennas', IEEE Trans., 1976, AP-24, pp. 846-851 7 HUANG, J.: 'The finite ground plane effect on the microstrip antenna radiation patterns', lEEE Trans., 1983, AP-31, pp. 649-653 8 BALANIS, C. A,: 'Antenna theory: Analysis and design', (Harper & Row, 1982), pp. 502-514 9 DERNERYD, A. G.: 'Microstrip array antenna', Proc. 6th European Microwave Conf., 1976, pp. 339-343 10 SMITH, J. I.: 'The even- and odd-mode capacitance parameters for coupled lines in suspended substrate', IEEE Trans., 1971, MTT-19, pp. 424-431 11 DENLINGER, E. J.: 'Losses of microstrip lines', IEEE Trans., 1980, MlT-28, pp. 513-522 12 JAMES, J. R., HALL, P. S., WOOD C., and HENDERSON, A.: 'Some recent developments in microstrip antenna design', IEEE Trans., 1981, AP-29, pp. 124-128 13 LEWIN, L.: 'Spurious radiation from microstrip', Proc. IEE, 1978, 125, pp. 633-642
Applications in mobile and satellite systems K. Fujimoto, T. Hori, S. Nishimura and K. Hirasawa
19.1 Introduction
Mobile communications often require antennas having small size, light weight, low profile and low cost. Microstrip antennas (MSA) are a type of antenna which can meet these requirements, and various MSAs have so far been developed and used for mobile communication systems. The practical applications for mobile systems are in portable or pocket-size equipment and in vehicles. UHF pagers, manpack radars, and car telephones are typical of those. Base stations for mobile communications need antennas with sector radiation patterns. Small, simple antennas are also favoured, since the antenna tower built for the base station can then be smaller and need less support for the weight. Ships and aircraft also demand small, lightweight antennas, and sometimes conformal structures are desirable to allow antennas to be mounted flush on the body of the moving vehicle. MSAs are considered to be suitable for such conditions and many antennas have been developed and installed on ships and aircraft. Examples are a marine radar antenna and a surveillance radar antenna. In satellite communications, circularly polarised radiation pattefns are required and MSAs of either square or circular patches with one or two feeding points can be used for generating the circular polarisation. Beam shapes such as a sector beam and a multi-beam can be produced by an array of MSA elements, which can be easily fabricated to form a flat structure, even though thousands of elements are used, by means of a photo-etch technique applied to the copper-clad dielectric substrate. A flat structure can be a feature of an MSA array used for receiving satellite broadcasting. Parabolic antennas are very popular for receiving broadcasts from satellites, but replacing them by small, flat antennas is preferable, especially for the home use. A large parabolic antenna, with the primary feed placed in front of the reflector, needs a wide area for installation, while a small, flat antenna can possibly be mounted flush on the wall of the house or even placed inside the window at home, depending on the field strength at the receiving environment. Several types of flat antennas have
1080
Applications in mobile and satellite systems
Applications in mobile and satellite systems
been developed: antenna elements used are the crank type, four-element square patch of either single- or two-point feed, etc.. In this Chapter, various types of MSAs which have been developed and applied in mobile and satellite systems are described. 19.2 Mobile systems
19.2.1 Design considerations MSAs used for land, maritime and aeronautical mobile systems are described in this Section. Antennas for land-mobile base-stations are also included. In these applications, the features of MSAs, such as flat structure, lightweight and compactness, which are generally required for mobile systems, are fully taken into account in the design. Antennas used for cellular mobile base-stations are described in the first part of this Section. In the cellular mobile phone system a service zone covered by a base-station antenna is divided into small sectors to increase the use of radio-frequency channels. The antennas are then designed to have a sector or a multi-beam pattern to form three to six zones in a 360' coverage. These patterns can be synthesised by an antenna array and MSAs are employed as being the most suitable array elements. Using antennas such as a dipole and a paraboloidal or corner reflector, beam shaping cannot easily be realised. In addition, the utilisation of MSA elements for the base-station antenna is advantageous, because the array can be made in flat structures and of light weight; and the antenna tower construction is easier and less costly from installing the MSA array on the tower than by using conventional heavy metallic antennas. A base station of small power, applied, for example, to home security, may represent an interesting problem. To overcome severe multipath fading in signal reception during indoor operation, the system is designed to receive both electric (E) and magnetic (H) field components at the same time, thereby obtaining smooth signal output. For this purpose, a system with a combined slot and rectangular patch antenna has been developed to receive both E- and H-field components simultaneously. Those antenna elements are placed flush on the panel of the equipment box, which can be hung on the wall of a room when used operationally. The second part of this Section describes the applications of MSAs to the automobile. Two types of antennas have been introduced: one is an antenna which can be used in the interior of an automobile and the other is an antenna which is installed on the roof of a vehicle. Both should be a thin and compact antennas, and MSAs can satisfy such requirements. Two antennas are located in the interior: one on the dashboard and the other on the back of the rear seat, for the purpose of the diversity performance. Successful operation of the diversity system has been reported after an experiment was undertaken in the Tokyo metropolitan area.
1087
When an antenna is placed on the roof of a car, the radiation pattern usually tends to be directed upwards; however low-angle radiation is preferred for urban mobile operations. An annular slot is used to obtain a relatively low-angle pattern when installed on the roof of a car. Also its flat structure is preferable, because a thick or bulky antenna cannot be mounted on the roof. The next Subsection introduces antennas for pedestrians. This application requires special consideration, especially when the equipment is used in an operator's pocket or near a human body. The effect of adjacent materials on antenna performance can scarcely be avoided; however, by using an antenna excited by a magnetic current, instead of electric current, the degradation of antenna performance due to adjacent materials can be reduced. The ground plane of an MSA acts as a type of shield against adjacent materials such as circuit components and other metallic materials, and yet the image of the magnetic current, with respect to the ground plane, will provide enhanced radiation in front of the MSA element, which results in reducing the degradation of the radiation. Four types of modified quarter-wavelength MSAs used for the pocket-size equipment are introduced. The remainder of the Section deals with radar antennas. The first is a marine radar antenna. Antennas used on ships are mainly either reflector antennas or slot arrays. An MSA array, formed as a flat structure and placed on a rotating pedestal similar to the usual radar antennas, is introduced. The MSA application reduces the weight, and makes the antenna rotation simple, smooth and tolerable over a long period of time. This is very important for use in small boats, because a heavy and large antenna with bulky counterweight cannot be mounted on the top of a mast. 19.2.2 Base stations
(a) Sector-beam array: The microstrip-antenna concept is applied to basestation antennas for land-mobile communications to create small, simple and low-cost antennas. The configuration of base-station antennas which have sector beams is shown in Fig. 19.1 [I]. Fig. 19.l a shows a 60"-120" sector-beam array [2], and Fig. 19.lb shows a 180' one [3]. The former is composed of two or four sub-arrays, and the sub-array is composed of 2 x 4 microstrip patch elements. The patch element is a broadband microstrip antenna with a parasitic element. This antenna radiates vertical and horizontal polarisation in the 900 MHz band. It has 60"-120" sector-beam patterns in the horizontal plane. For realising these patterns in the horizontal plane, a two-element excitation method is used, in which two elements are excited with different amplitudes and out of phase. The feeder section is composed of two hybrids and a phase shifter. The amplitude ratio of the two elements can be changed by controlling a phase shifter. The measured radiation patterns are shown in Fig. 19.2. The gain deviation is less than 4 dB within the
7082
Applications in mobile and satellite systems
60"-120" beam. The measured VSWR is less than 1.5 over a frequency bandwidth of 9%. The other array (shown in Fig. 19.lb) is composed of 8 or 16 printed dipole elements with a corner reflector. This antenna radiates vertical polarisation in the 900 MHz band. It has 180" sector-beam patterns in the horizontal plane.
Applications in mobile and satellite systems
7083
(b) Multi-beam array: The configuration of the multi-beam base-station antenna for land-mobile communications is shown in Fig. 19.4 [4]. This antenna is composed of 8 x 8 microstrip patch elements. The patch element is a broadband microstrip antenna with a parasitic element. The antenna operates in
Parasitic, Element
-30 1 -180
-90
0 Angle
90
180
(')
Fig. 19.3 Measured azimuthal radiation patterns of the 180' sector-beam array (@ 1988 IEICE)
--- 860 MHz -900 MHz
- - - 940 MHz
. . . . Cal (900 MHz)
Fig. 19.1
Configuration of the sector-beam base-station antenna (Courtesy: NTT, Japan) ( a ) 60-120' sector-beam array (V/H polariation) ( b ) 180' sector-beam array (V polarisation)
Input/Output
Butler matrix
Fig. 19.4 Configuration of the multi-beam base-station antenna (@ 1988 IEICE)
Fig. 19.2 Measured azimuthal radiation patterns of the 60- 12LT sector-beam array (@ 1988 IEICE) ( a ) amplitude ratio, 1 :0.27 (6)amplitude ratio, 1 : -0.33. V polarisation, - - - H polarisation.
-
The corner angle of the reflector is optimised to realise these patterns in the H-plane. The measured radiation patterns are shown in Fig. 19.3. Here, the corner angle is 26O0, and the reflector size is 0.62 wavelength width. The measured VSWR is less than 1.2 over a frequency bandwidth of 9%.
vertical/horizontal polarisation, and has eight beams within 120" area. The eight beams are switched by a Butler matrix circuit. For simplicity and low cost, the microstrip antenna elements and the feed circuits are arranged and etched on the same surface. The measured radiation patterns are shown in Fig. 19.5. The measured gain is more than 22 dBi at 900 MHz, and the circuit loss is less than 2 dB. (c) E-H antenna: Conventional or shortened dipole antennas have been used as base-station antennas for small indoor communication systems. One of the biggest problems is that indoor communication is sometimes interrupted
7084
Applications in mobile and satellite systems
when a receiving antenna happens to be located near the minimum points of a standing-wave distribution of electric fields, as shown in Fig. 19.6. Several techniques, such as space diversity or frequency diversity, have been introduced to the communication system to solve the problem. However, the system may be rather bulky and expensive for most small base stations.
Applications in mobile and satellite systems
7085
by a standard dipole antenna, but the solid line shows little fluctuation in the combined signals received by the E-H antenna. In addition, the present antenna can receive both vertically and horizontally polarised waves using a proper signal combiner. This will be quite useful for Indoor communication. wide strip microstrip
Angle
(')
out
Fig. 19.5 Measured azimuthal radiation patterns of the multi-beam base-station antenna (@ 1 9 8 8 IEICE) measured --- calculated
-
Fig. 19.7 Configuration of the E-H antenna (@ 1988 IEEE)
antenna standing waves
I
....................
present ................................................. antenna
.....-.... ...
,,.........*.
metal 1 ic -1
...
1
i standard dipole
I
... ,,,,' .\! .
! , :
'*
.. t i
y
floor
measured
Fig. 19.6 Idealised standing- wave distribution (@ 1 9 8 8 IEEE)
Ito et al. [5] have proposed a simple printed antenna, as shown in Fig. 19.7, composed of a half-wavelength slot, a wide strip and a signal combiner. The antenna can receive transmitted signals through both magnetic and electric fields, so that there will be almost no interruption from standing waves. The antenna is referred to as an E-H antenna. The slot and the strip are constructed on both sides of a printed circuit board. Received signals from the slot and the strip are combined directly and sent to a receiver. A reflector is placed under the ground plane of the substrate to form a unidirectional pattern. Fig. 19.8 shows an example of received-signal fluctuations for varying antenna location. Each maximum value was normalised to unity. D denotes the distance of the antenna from a metallic wall in wavelengths (the frequency was 320 MHz). The dotted line shows the standing wave of the electric field received
Fig. 19.8 Example of received-signalfluctuations (@ 1 988 IEEE) Each maximum value was norrnalised to unity -E-H antenna - - - standard dipole antenna
19.2.3 Wheeled vehicles ( a ) Cabin antenna: The circular microstrip antenna is used for cabin-antenna applications [6].It is necessary for a cabin antenna to have 1 dB more gain than a haif-wavelength dipole, based on the assumption that the degradation in the average received power caused by installing an antenna inside the vehicle is 3 dB, and the improvement caused by receiving both dominant and cross-
7086
Applications in mobile and satellite systems
polarisation is 2 dB. The cabin antenna is a broadband microstrip antenna with a parasitic element, as shown in Fig. 19.9. The measured radiation patterns are shown in Fig. 19.10. The relative gain compared with a half-wavelength dipole is about 1.5 -- 2 dBd for a microstrip antenna with a parasitic element.
Applications in mobile and satellite systems
7087
switching the capacitance loaded on the slot by the bias supply. This type of pattern can be considered for a vehicular antenna system to reduce the multipath fading in urban mobile communications. 1
Fig. 19.9 Outer view of cabin antenna (Courtesy: NTT, Japan)
( b ) Rooftop (annular slot): The annular slot [7, 81 is a candidate for use in vehicular antennas for mobile communications, since it can radiate power at low elevation angles. In urban mobile communications, incident waves to mobile stations come mostly from directions having low elevation angles, - about 30" up from the horizontal plane. The antenna structure is shown in Fig. 19.1 I . The radiation pattern depends on the radius of the slot, and its variation is shown in Figs.19.12 - 19.14, where the antenna radius is taken as a parameter. Fig. 19.15 illustrates a way of mounting an annular-slot antenna on the roof of a vehicle. An example of an annular-slot antenna with k, = 0.5 (k = 2n/l, where I is the wavelength) is shown in Fig. 19.16. The radiation pattern can be controlled by loading a capacitor on a slot as shown in Fig. 19.17 and by varying its capacitance electronically. One method is to make the radiation pattern asymmetric. An almost one-sided radiation pattern is obtainable, and a typical example is shown in Fig. 19.18, where the antenna parameter k, = 1.5, the loaded reactance is - 80 ohms, and the operating frequency is 1.5 GHz. The radiation pattern can be rotated electronically by
Fig. 19.10 Measuredradiation patterns of cabin antenna (Courtesy: NTT. Japan) (a) Vertical plane (E- lane) (b) Vertical plane ( ~ i p l a n e ) (c) Horizontal plane
19.2.4 Railways A train antenna is required to have wide beamwidth, with a low profile and small structure. TOsatisfy these requirements, a short-circuit rectangular micro-
1088
Applications in mobile and satellite systems
Applications in mobile and satellite systems
1089
z
X
/
' f e e d point "
10 ABAIV.
C
10 WOIV.
ielectrlc material 0 0' 10 dB/DIV.
Fig. 19.13 Radiationpatterns
Fig. 19.11 Annular-slot antenna structure and the co-ordinate system ( a ) Antenna structure and co-ordinate system ( b ) Feed point
b Fig. 19.12 Radiation patterns
10 dWOIV.
d
10 WON.
Fig. 19.14
Radiation patterns
d
10 W l V .
7090
Applications in mobile and satellite systems
Applications in mobile and satellite systems
1091
strip antenna is used [9]. A train antenna is shown in Fig. 19.19; it is 2300 mm in width, 350 mm in height and 90 mm in depth. The antenna is composed of the transmitting antenna and the receiving antenna. Each antenna is a fourpatch array, and it operates at 413 MHz and 452 MHz. The measured radiation
Fig. 19.15 Concept of mounting an annular-slot antenna on the roof of a vehicle
Fig. 19.18 Measured radiation patterns Fig. 19.16
Example of annular-slot antenna element
rodlotor feeder
&N#M~B&Y~
i $5 t'i $5 j J1 ! mn i,
,
!
Dower d i v i d e r
Fig. 19.19 Configuration of train antenna (@ 1988 IEICE) reactance component
Fig. 19.17 Dimensions of antenna
'feed
point
patterns are shown in Fig. 19.20. The half-power beamwidth is more than 34' in the horizontal plane, and more than 153" in the vertical plane. The measured gain is 5.8 dBd at 452 MHz, and the VSWR is less than 1.4.
7092
Applications in mobile a n d satellite systems
Applications in mobile a n d satellite systems
I 1
7093
units in the VHF/UHF bands. A practical example of one of these antennas mounted in a pocket-size pager at the 900 MHz band is shown in Fig. 19.21 [IO]. The gain required for this type of pager antenna is about -4 dB compared to a
Fig. 19.20 Measured radiation patterns of train antenna (@ 1988 IEICE) -measured - - - calculated
19.2.5 Pedestrian Antennas for VHF/UHF hand-held portable equipment, such as pagers, portable telephones and transceivers, must naturally be small in size, light in weight, and compact in structure. Some of this equipment, especially that used most of the time in an operator's pocket, demands either flush-mounted or built-in antennas. It is well known that the smaller the antenna size, the lower the antenna efficiency. There is a growing tendency for portable equipment to be made smaller and smaller as the demand for personal communication rapidly increases, and the development of hand-held or hand-portable units has become urgent. Requirements on antenna performance for such small equipment are becoming increasingly severe, since the antenna performance should not be significantly degraded as the size becomes smaller. The microstip antenna is one of the most preferable for small equipment, especially when a flush-mounted or built-in antenna is required. Since the microstrip antenna can be made with a very thin and compact structure, it can easily match various types of portable units. One possible problem to be considered when using a microstrip antenna is its narrow bandwidth, which is usually only a few percent, depending on the thickness of the antenna and the manner of feeding. Efforts have been made to increase the bandwidth, but a wide bandwidth of, say, 10% would be hard to obtain in the present state of the art. Fortunately, some systems such as pagers do not need a wide bandwidth in their operation, and so the microstrip antenna can be applied to small VHF/UHF equipment used in such systems. Four types of microstrip antennas (MSA) are introduced in this Section QMSA, PMSA, WMSA and FVMSA: Q stands for quarter-wavelength, P for post-loading, W for window-attached, and FV for frequency-variable. Antennas other than QMSA are modified from QMSA. They have basically similar radiation patterns. The difference is that PMSA has two radiation apertures in order to increase the gain, WMSA has a reactance slit on the patch to make the QMSA length shorter, and FVMSA is a QMSA with its resonance frequency electronically variable. Any of these antennas can be applied to small portable
Dimensions Weight Display Sensitivity Battery life Spurious -
Freauencv . -
1 (
1
1
I /
8 5 x85 x 1 9 mm 140g 12 digits numerals 5pVh
3 months -40dB 9OOMHz band with frequency stobility 2.5 part in 1 0 ~ ( - 1 0 + 5 0 ~ )
Fig. 19.21 Example of pocket-sized pager having an MSA element (Courtesy: Matsushita Communication Ind. Co. Ltd., Japan)
half-wave dipole. The four types of MSA variations for 900 MHz pagers are as follows: ( a ) Quarter-~avelengtlmicrostrip antenna ( Q M S A ) : QMSA is a quarterwavelength rectangular patch antenna with one end of the patch shorted electrically. (Fig. 19.22) There are slight differences from an ordinary quarter-
7094
Applications in mobile and satellite systems
wavelength patch antenna; the sides of the patch are cut so that the ground plane has the same width as the radiation patch, and a part of the ground plane is extended from the radiation aperture by a length of G, as shown in Fig. 19.22.
Applications in mobile and satellite systems
1095
(6, = 2.4), Teflon ( E , = 2.5), and glass-fibre-reinforced epoxy resin ( E , = 3.7); E, is the relative permittivity of the substrate. 0 dB in the Figure is the gain of
the standard half-wave-dipole antenna. This is also used in later Figures in this Section. 0-
; i
-cB -0
d
[?$,/
. 5
-
.
patch radiator\ -10
.feed
; 1
0
Fig. 19.22 Quarter wavelength microstrip antenna (OMSA) structure
v
polyethylene teflon
X
epoxy-fibreglass
50
L
Fig. 19.24 Gain versus patch length L (QMSA)
f
teflon x
epoxy-f lbreglasr
Fig. 19.23 Gain versus length G,
Fig. 19.25 Gain versus patch width W (QMSA)
The length G, plays an important role in increasing radiation. The variation of gain of a QMSA with respect to the length G, is shown in Fig. 19.23: Three types of substrate material are treated as typical: polyethylene
The gain versus the total length L is illustrated in Fig. 19.24. The patch width W also affects the gain, as shown in Fig. 19.25. An example of measured radiation patterns of the QMSA is shown in Fig. 19.26, where patterns in the
7096
Applications in mobile and satellite systems
three planes XY, Y Z and ZX are illustrated. Consideration of the radiation patterns in these three planes is important, since their evaluation becomes meaningful when the antenna is used in an urban environment for mobile communications, where multipath fading problems exist. The antenna performance should be evaluated three-dimensionally: not only in the horizontal plane, but also in the two other planes. For example, the antenna-pattern maximum may exist in a plane other than the horizontal, and incoming waves may often come from directions not in the horizontal plane. For these reasons, gain defined only in the XY plane is not sufficient for evaluation of the actual antenna performance. The antenna parameters used are as follows: L = 76.7 mm, G, = 27.9 mm, W = 30 mm, t = 1.2 mm and 8, = 2.5 (Teflon).
Applications in mobile and satellite systems
i I
7097
form another radiation aperture at its end. The ground plane is further extended from the end of the radiation aperture by a length G, as shown in Fig. 19.27. The dimensions of the antenna and the co-ordinate system are also shown in the Figure. radiator /patch
post
L Fig. 19.27 PMSA antenna structure
m
-
.c
-5-
9
%
-
- 10 o
polyethylene
0
teflon
a epoxy-fibreglass
I
Fig. 19.26 Radiation pattern (G, = 27.9 mm) (QMSA)
0
'0
,
, , ,
.
, 20
, , (mr
Gz
(b) Post-loaded microstrip antenna (PMSA): PMSA [I 1 , 121 is an antenna modified from an ordinary QMSA and designed to have two radiation apertures driven by a single feed, as shown in Fig. 19.27. Several reactance posts are used to replace the shorted termination of the QMSA, and the patch is extended to
Fig. 19.28 Gain versus length G, (PMSA)
The gain of the PMSA with three posts versus the length G, ( = G, = G,) is shown in Fig. 19.28. The operating frequency is 930 MHz. Three kinds of substrate materials (8, = 2.4,2.5 and 3.7) are again taken into account, and the
1098
Applications in mobile and satellite systems
Applications in mobile and satellite systems
Table 19.1 Dimensions of PMSA used in the experiments (see Fig. G m = G, = Gz) Substrate er t W a G, b (mm) (mm) (mm) (mm) (mm) (mm) Poly1.2 30 48.9 4.5 24.5 ethylene 47.9 7.0 24.2
Teflon
1.2
30
apoxyglassfibre
1.2
30
- -
O
-
19.27,
L
(mm) 82.1 85.1
47.4 46.1
20.0 3.8
24.0 23.9
111.4 77.9
39.6 38.8
4.0 7.5
20.2 22.0
66.9 75.3
7099
antenna parameters t = 1.2 mm, W = 30 mm, and lengths a and b in Table 19.1 are used. The gain versus total length L is shown in Fig. 19.29. The length b is about a quarter wavelength, while the length a is about 24 mm, which is slightly altered by the change in G,. Fig. 19.30 shows the variation of gain with length a, where the parameters used are the number of posts. Two examples of measured radiaton patterns are shown in Figs.19.31 and 19.32. They resemble those of QMSA, although there is a difference in two apertures driven in this instance.
e polyethylene 0
teflon epoxy-fibreglass
Fig. 19.30 Gain versus length a (PMSA)
m
9
-10
0
50 L
Fig. 19.29 Gain versus patch length L (PMSA)
100
(mn)
( c ) Window-reactance-loaded microstrip antenna (WMSA): WMSA [I31 is designed to have a shorter length than QMSA by putting a reactance window (slit) with a length W, on the patch, as shown in Fig. 19.33. The window acts as a reactance component and its value is altered by the length W, of the window. The resonance frequency versus the length W, of the window is given in Fig. 19.34, which also gives the dimensions of the antenna. The gain is affected by the length W,, and is shown in Fig. 19.35.The gain differs depending upon the location of the window, and the distance S-W of the window from the end of the patch (see Fig. 19.35). For larger S-W, the gain is higher. Two slits placed on the patch, as shown in Fig. 19.36a, can also form a reactance component in the antenna structure, and the length of the radiation patch can be shortened. If the length Wsis altered, the resonant frequency alters as shown in Fig. 19.36b. It increases with W,.
7 700
Applications in mobile and satellite systems
Applications in mobile and satellite systems
7 707
( d ) Frequency-variable microstrip antenna (FVMSA): The resonance frequency of a QMSA can be altered electronically by varying the value of a reactance loaded on the antenna structure. For this pirpose, the shorted termination of the QMSA is replaced by a reactance component and the reactance is varied by its bias supply. This type of antenna is called FVMSA (Frequencyvariable MSA) [14]. A diode can be used as a reactance element, and its
substrate
-
Fig. 19.31 Radiation pattern
(G, = 7.0 mm)
(PMSA)
Fig. 19.33 Window reactance loaded microstrip (WMSA no. 1 )
(unit rnm)
Fig. 19.34 WMSA no. 1 ( a ) Dimensions ( b ) Resonant frequency versus slot width W,.,
Fig. 19.32 Radiation pattern
(G, = 20.2 mm)
(PMSA)
resonance frequency, depending on the bias voltage to the diode, is shown in Fig. 19.37, which also shows the gaintfrequency as the bias voltage is altered from 6 to 10 V. The diode used is an MA325 (Fig. 19.38) and its characteristics,
7 702
Applications in mobile and satellite systems
Applications in mobile and satellite systems
0
1103
- 8
0 0
o
bias voltage
- 7
0
0
5
10
0
20 (mm)
15
0
Ww
I
~
8 50
Fig. 19.35 Gain versus slot width W, (WMSA no. I )
~
~
~
900 950 FREQ (MHz)
Fig. 19.37 Gain versus frequency and bias voltage (FVMSA)
Unit :mm
"
Jl.
I"
Ws (mm) a
b
__H___
Fig. 19.38 WMSA no.2 ( a ) Dimensions ( b ) Resonant frequency versus slot width W,
1' Cathode 2 Anode Fig. 19.38 Dimensions of M A 325
~
~
1704
Applications in mobile and satellite systems
Applications in mobile and satellite systems
7 105
and capacitance variation with bias voltage, are shown in Fig. 19.39. The antenna structure and its dimensions are given in Fig. 19.40 and Table 19.2, respectively.
40
30
-a 20
LL
0 U
10
0 0.1
0.3050.71
v,
35710 (v)
3050X)lOO
Fig. 19.39 Bias voltage V, versus capacitance C, ( M A 325)
Fig. 19.41 Microstripline planar antenna for manpack radar
19.2.6 Radar
Fig. 19.40 FVMSA antenna structure
Table 19.2 Dimensions of FVMSA (see Figs. 19.22 and 19.40) er
t
(mm)
W (mm)
F~ (mm)
b (mm)
Gz
(mm)
Diode type
( a ) Manpack radar: Portable manpack radars operating by the pulse Doppler method can serve as detectors of moving targets such as people, vehicles etc. They are small, light devices which utilise microstripline antennas, as shown in Fig. 19.41. such-an antenna is constructed of 16 centre-fed Franklin-type microstripline antennas [15]. It is centrally fed through the front side hybrid networks. Each network is fed through the parallel-feeding network on the rear side. Each microstripline . . antenna works as a standing-wave antenna terminated by an open clrcult. The characteristics of this antenna are as follows: frequency, X-band; antenna
1106
Applications in mobile and satellite systems
aperture, 34cm x 45cm; half-power beamwidth, about 4.5"; gain, 30dBi; weight, about 2 kg. ( 6 ) Marine radar: Microstrip arrays have been used in marine radars [16]. Fig. 19.42 shows an inside view of a radar system installed on ocean vessels. This type of radar system has been in service since 1981. The antenna array consists of 48 (3 x 16) circular patch microstrip elements and is mounted on a rotating pedestal. The specification of the system is given in Table 19.3. Fig. 19.43 shows
Applications in mobile and satellite systems
1107
( c ) Radar rejector: A bidirectional communication system is shown in Fig. 19.45 [17, 181. The radar reflector can transmit information from the reflector site to a radar station as well as receiving signals from a radar station. The reflector consists of a Luneburg lens with a reflector plate on it. Fig. 19.46 shows
I
I
0.97
I
I
I
I
I
I
0.98
0.99
1.00
1.01
1.02
1.03
flfo
Fig. 19.43 Sidelobe level and gain versus frequency
Fig. 19.42 Marrne radar antenna (Courtesy: Japan Rad~oCo. Ltd.)
Table 19.3 S~ecificationsof marine radar Frequency Gain Beamwidth Dimension
X band over 22 dB 6.0" in azimuth 25" in elevation 367 x 88.0mm
the gain and first-sidelobe characteristics against frequency in the azimuth direction. Typical radiation patterns are shown in Fig. 19.44. By replacing the metallic waveguide-fed antennas with microstrip elements, the antenna system can be made smaller and lighter, so that smoother rotation of the antenna and increased reliability is achieved. In addition, the production cost can be reduced and mass production becomes easier.
Fig. 19.44 Radiation pattern
details of the reflector plate. The two quarter-wavelength sections A and B are an impedance transformer and RF blocks, respectively. When the diode is off, signals are received. When the diode is switched on/off by coded pulses to be
1708
Applications in mobile and satellite systems Reflecting
Demodulator Encoder
Transmitter
Recorder Fig. 19.45 Block diagram of bidirectional communication systems (@ 1988 IEICE) Switching circuit
( MSA
n
To Recewer
Applications in mobile and satellite systems
7 109
transmitted from the reflector to a radar station, the radar cross-section is modulated by them and is detected at the radar station. Thus no transmitter is needed to transmit information from a reflector site to a radar station. A Luneberg lens focuses on incoming R F waves at any angle incident on the antipodes of the lens sphere. Then a reflecting plate placed on the antipodes reflects the waves back exactly in the incident direction. The same lens sphere can be used to establish communication channels with other radar stations in different directions by placing reflecting plates at the corresponding antipodes. The gain is 26.5 dB and the beamwidth is 7" at 9.375 GHz when the relecting plate is used as a receiving antenna. At the same frequency the radar crosssection is 33 m2 and the beamwidth is 3" when the reflecting plate is used as a reflector. Fig. 19.47 shows the VSWR when the diode is off, and the return loss when the diode is on, as a function of frequency. At the centre frequency, a VSWR of less than 1.1 and a return loss of 0.5 dB are obtained. Fig. 19.48 shows the radar cross-section of the reflector normalised to that of a metal plate of the same area. A modulation ratio of 13 dB is obtained when the diode is switched on and off. Field experiments using a marine radar and the reflector have been carried out successfully.
Rodidor top view
-2 1 Bias ON
Bias side view C
Fig. 19.48 Configuration of reflector plate (@ 1988 IEICE) a Equivalent circuit b Top view c Side view
Fig. 19.47 VSWR and return loss of reflector without lens (@ 1988 IEICE)
Fig. 19.48 Radar cross-section of reflector with lens (@ 1988 IEICE)
( d ) Secondary surveillance radar: In order to cope with the rapidly increasing air traffic, replacement of the existing secondary surveillance radar (SSR) with the next generation of SSR (mode S) is being studied at an international level. For the purposes of improving data rate, the cylindrical electronic scanning antenna, which can be turned instantaneously in any direction and aimed at any target, is believed to be more promising than the existing SSR with a constant rotation. Fig. 19.49 shows an experimental antenna. This is a cylindrical array of one-third arc, and it has a 90" active sector. Its radiating elements are vertically polarised circular patch antennas, and it operates in the frequency range 10301090 MHz. A paper honeycomb substrate is used. Ten radiating elements are arranged in elevation, forming a cosecant-squared pattern. The azimuth is
111 0
Applications in mobile and satellite systems
Applications in mobile and satellite systems
1 1 11
composed of 32 active sector lines and a pencil beam is formed on the azimuth plane, which can be scanned horizontally by gradually changing the transfer switch.
( e ) Three-faced array: The vertically polarised antenna, which has an omnidirectional pattern in the horizontal plane and a desired pattern in the vertical plane, is mainly utilised for broadcasting, telecommunications and as a transponder. In addition, this antenna can be used in an aircraft system. When used together with the MLS (Microwave Landing System) it works as a DME (Distance Measurement Equipment) antenna.
Fig. 19.49 Cylindrical-array antenna for SSR mode S
reflector
microstrip line slot feed point 3 way power
Fig. 19.51 Three-faced microstrip slot array antenna (Courtesy: Japan Radio Co., Japan) Fig. 19.50 Three-faced array antenna a antenna configuration b Feeding network (After Hara, and Goto [I91,@ 1988 IEEE)
The shape of the antenna is shown in Fig. 19.50. The antenna gives an omnidirectional pattern when a suitable flared reflection board is set on each of the three faces. Each face produces a cosecant-squared pattern through pattern synthesis.
1 1 12
Applications in mobile and satellite systems
Applications in mobile and satellite systems
1 1 13
Fig. 19.51 shows a trial antenna. The characteristics of this antenna are: frequency, 3 GHz; height, about 80 cm; peak gain, 9.5 dBi; antenna efficiency, 85% [19].
antenna is not considered wise, owing to its large size and the complexity of manufacture. Again, an array structure is preferred to a large-aperture antenna, and MSA elements in the S- and L-bands have been employed in such array systems.
19.3 Satellite system
19.3.2 Direct-broadcasting reception Several planar antennas for satellite TV reception using circularly polarised printed arrays have been proposed. In Japan, with the start of satellite broadcasting in December 1986 utilising the satellite Yuri 26 (BS-2b), efforts have been made with the R & D of the planar antenna. When the characteristics of a planar antenna are set at 11.7-12.0 GHz and the gain is 33-34 dBi, the antenna will receive signals in the high-field-strength area (except during heavy rains), as shown in Fig. 19.52.
19.3.1 Design considerations This Section describes MSA applied to three areas of satellite systems: direct broadcasting systems (DBS), the earth stations and the satellite-borne systems. ( i ) DBS antennas: In the design of the DBS antennas, there are the problems of reducing the size and weight, and yet it must~havea gain high enough to be competitive with the popular parabolic reflector antennas. A number of flat antennas using MSA elements have been developed so far with the features of light weight and ease of installation on the walls of a house or a building, or location inside a room. Another advantage of using a flat structure is that its performance is less affected by the snow or wind than by using parabolic reflector antennas. (ii) Earth stations: The general requirements for an earth-station antenna are: simple structure, low cost, tracking capability and fading-suppression performance. Two types of satellite tracking are considered: the first is to use the radiation patterns of either a wide beam or a conical beam, thereby ensuring that the antenna beam always tracks a satellite, and the second is to use either a spherical array or a phased array. Antenna-beam shaping in the vertical plane is designed to achieve fading suppression. By making best use of the MSA feature, wide-beam or the conical-beam antennas of simple structure and low cost have been developed and are presently in practical use. MSA elements are also considered to be suitable as L-, S- and C-band antennas, and applicable to spherical (switching) arrays, phased arrays and sector-beam arrays. A unique transportable equipment for satellite communications has been developed and tested by using a link with the Japanese communication satellite ETS-V. The equipment hardware is put in an small attachk case which the operator carries. Two antennas, one for the transmitter and the other for the receiver, are used instead of only one antenna operating as both a transmitter and a receiver. By this means the heavy diplexer can be eliminated. As the antennas must be located on the back of the attachk-case lid, the MSA element is chosen as the best fit antenna. (iii) Satellite-borne antennas: Light weight, compactness, vibration-tolerable characteristics etc. are the major requirements for satellite-borne antennas. Although high gain in the L-, S- and C-band is desirable, the use of an aperture
Fig. 19.52 Operational area (Japan)
We shall describe a few types of planar antennas for satellite-TV reception, and a parabolic-cylinder reflector. These antennas have the following characteristics; Frequency range Polarisation Gain Axial ratio VSWR
: 11.7 - 12.0 GHz : right-hand circular polarisation : more than 33 dBi : less than 1 dB : less than 1.5
( a ) Circular-patch array: Fig. 19.53 shows a sub-array of singly fed circularly polarised patch elements [20]. In order to provide wide-bandwidth axial ratio and impedance characteristics, the paired elements, described in Chapter 4, form the fundamental element of the antenna.
1 1 74
Applications in mobile and satellite systems
Fig. 19.54 shows a circular-patch array. The antenna exhibits a 30' inclination of the beam direction (towards the front side of the board), it has 1024 elements (size of the antenna is 48 cm x 64 cm) and has about 33 dBi gain. In order to decrease the feeder loss, the main feeding line for four 256-element panels tY
I
I
Applications in mobile and satellite systems
1 1 15
( 6 ) Square-parch array: Fig. 1 9 . 5 6 ~shows the structure of the elements. In order to increase the bandwidth and to decrease the feeder loss of the patch element, the thickness of the substrate, which supports the patch and the feeder, was altered. In this case the substrate has a complex two-layered structure which results in increased bandwidth and efficiency of the antenna [21].
I
di=0.6h0, dzr0.8ho Fig. 19.53 Sub-array of singly fed patch elements
Fig. 19.55 Flat antenna (Courtesy: Yagi Antenna. Japan)
Fig. 19.54 Planar array of circular patch elements (Courtesy: Yagi Antenna, Japan)
utilises the rear-mounted rectangular waveguide. As shown in Fig. 19.55 the beam-tilt type can be set almost vertically. Thus, it has advantages such as being easily installed on a wall, and snow does not affect it.
Fig. 19.57 shows a square-patch planar array which has 512 patch elements (see Fig. 19.566). The main feeding line for the eight 64-element panels has a rear-mounted rectangular waveguide. The size of the antenna is 32 cm x 64 cm and its gain is 34 dBi. ( c ) Crank-rype tnicrostrip-line array: Fig. 19.58 shows the configuration of a crank-type microstrip-line antenna. This antenna, described in Chapter 13, is formed by crank-type undulation of two strip conductors of a microstrip line.
11 1 6
Applications in mobile and satellite systems
Applications in mobile and satellite systems fundamental element
11 77
dielectric substrate
feed
*x g r o u n d plate
s t r i p conductor
Fig. 19.58 Configuration of crank-type microstripline antenna
gap (height 1 m m )
Er
Fig. 19.56
= 2.17
-
A1 -4 circularly polarised microstrip patches
Circularly polarised patch element and sub-array a Patch element with two-layered structure b Sub-array (After Murata and Ohrnaru [Zl],@ 198 IEICE)
Fig. 19.57 Planar array of square patch elements (Courtesy: NHK, Japan)
Fig. 19.59 Planar array of microstripline antennas terminated in patch element (Courtesy: DX Antenna, Japan)
7 118
Applications in mobile and satellite systems
The two strip conductors are shifted by half their periods with respect to one another. In the Figure, the section surrounded by a dotted line shows the fundamental element of a travelling-wave array [22]. Fig. 19.59 shows a crank-type microstrip-line planar array, and Fig. 19.60 shows the same antenna array set in its actual position. This antenna, with 332 elements, has a gain of 33-34.2 dBi at a frequency of 11.7 - 12.0 GHz. The size of the antenna is 40cm x 60 cm, its thickness is 2.1 cm and its weight is 4.7 kg [23]. As shown in Fig. 19.59, an open end of each microstrip-line antenna terminates in a square-patch element. The power at the patch element is totally radiated in order to improve the efficiency of the antenna [24].
I
,
I
Applications in mobile a n d satellite systems
7 719
( e ) Circular-patch-slot array: Fig. 19.64 shows the structure of a circularpatch-slot array. This antenna consists of a ground plate, a patch and feedingline plate, a slot plate and a radome. The circularly polarised patch elements, with a single feeding point 1201and the feeding line, are printed on a plastic-film radome -radiation plate (slot and patch) feeding line plate ground plate
/ Fig. 19.61 Structure of rectangular-slot array
feeder
slot
patch
Fig. 19.60 Actual position of planar antenna (Courtesy: DX Antenna, Japan)
(d) Rectangular-slot array: Fig. 19.61 shows the structure of a rectangularslot array. This antenna consists of a ground plate, a feeding-line plate, a radiation plate and a radome. Each plate is supported by a honeycomb-foam spacer in order to reduce the feeder loss. The radiating element consists of a rectangular slot with a patch, and it operates by electromagnetical coupling to the feeding line. The feeding line and radiating elements are printed on a film substrate as shown in Fig. 19.62. The fundamental element of this antenna seems to be complementary to the square-patch element with the slot open on its surface. Fig. 19.63 shows a rectangular-slot planar array. This antenna with 512 elements has a gain of 35 dBi. The size of the antenna is 36 cm x 72 cm, its thickness 1.7 cm and its weight is 6 kg.
Fig. 19.62 Mask of sub-array a Feeding-line plate b Rad~ationplate
substrate. The substrate is covered with two sheets of shield board. Both the upper and lower board are at a distance of 1 mm from the substrate, with air between. The feeding line has the form of a suspended line system having low loss. The circular-patch element radiates through a circular slot open on the upper board.
1720
.
Applications in mobile and satellite systems
Applications in mobile and satellite systems
Fig. 19.65 shows a scaled-down mask of the patch elements and the slots. Fig. 19.66 shows a circular-patch-slot planar array. The main beam direction of this antenna is inclined at 10' to the front board. With 476 elements it has a gain of 34.1 dBi. The size of the antenna is 42 cm x 50.4 cm, its thickness 2.2 cm and its weight is 4.2 kg.
~atch
feeder
slot
(b) Fig. 19.65
Mask of sub-array a Feeding line with patches plate b Slot plate
Fig. 19.63 Planar array of rectangular-slot elements (Courtesy: Matsushita Electric Works, Japan)
n
radome slot plate
p a t c h and f e e d i n g line plate ground p l a t e
/ Fig. 19.64 Structure of circular-patch-slot array
(f) Parabolic-cylinder rejector: Fig. 19.67 shows a parabolic-cylinder reflector antenna. It is an example of the microstrip-line antenna application. The antenna utilises a side-looking circularly polarised microstrip-line antenna [25] on the line-source feed of the parabolic-cylinder reflector. The reflector can be
&,'
7 -
Fig. 19.66 Planar array of orcular-patch-slot elements (Courtesy Sony, Japan)
1121
1122
Applications in mobile and satellite systems parabolic-cylinder reflector
Applications in mobile and satellite systems
1123
installed in the vertical position because the direction of line-source feed is inclined. Consequently, it has advantages such as ease of installation on a wall and ;now does not affect it.
line-source feed (side-looking microstrip line antenna) Fig. 19.67
Configuration of parabolic-cylinder reflector-antenna
Fig. 9.69
Fig. 19.68 Parabolic-cylinder reflector with side-looking line-source feed (Courtesy: DX Antenna, Japan)
GPS microstrip antenna (Courtesy: Toyo Communication Equipment Co. Ltd., Japan)
Fig. 19.68 shows an experimental antenna. It has a reflector of :size 60 cm x 70 cm, the size of line-source feed is 4 x 42 cm, and the gain at 12 GHz is 34 dBi. The axial ratio is 0.8 dB and the VSWR is less than 1.5.
1124
Applications in mobile and satellite systems
iI
Applications in mobile and satellite systems
I
19.3.3. E a r t h stations I
( a ) Wide-heam antennas
1125
Fig. 19.72 shows the vertical radiation pattern. Although the gain near the horizontal direct~onis less than -5 dBi, the low-noise amplifier provides enough gain to receive signals in this direction.
(i) G l o b a l positioning system: Microstrip antennas are being developed for automobile navigation using the NAVSTAR satellite global positioning system (GPS). They are designed to be installed on the roof of an automobile. The antenna of a GPS receiver presents characteristics little different from those of most satellite systems. Hemispherical beamwidth and right-hand circular polarisation are required to receive signals from NAVSTAR satellites anywhere in the sky. Fig. 19.69 shows a microstrip antenna fed by two feeds from the bottom, where the two feed voltages are of equal magnitude and 90" out of phase. In the frequency range 1574-1577 MHz, the axial ratio is less than 2 dB in the boresight direction and the gain is greater than -3 dBi in the direction between 6.5' and 90" above the horizontal plane. The vertical radiation pattern is shown in Fig. 19.70.
Fig. 19.70 Vertical radiation pattern (Courtesy: Toyo Communication Equipment Co. Ltd., Japan)
Fig. 19.71 shows another GPS microstrip antenna viewed from the top and the bottom. The antenna is fed at the two points from the bottom, with feeds of equal amplitude and 90' out of phase. The thickness of the antenna is 1.6 mm. In the frequency range 1573 - 1577 MHz, the axial ratio is less than 1 dB and the gain is 5.5 dBi, both in the boresight direction.
Fig. 19.71
GPS microstr~pantenna (Courtesy: Toyota Central Research Laboratory, Japan)
( i i ) Transportable earth station: A hand-held message-communication terminal (HMCT), shown in Fig. 19.73 for a very small earth station, can transmit and receive messages of 20 - 30 characters via geostationary Engineering Test
1726
Applications in mobile and satellite systems
Applications in mobile and satellite systems
7 127
Satellite - Five (ETS-V) at 150' east 1261. The HMCT is contained in an attach6 case. On the lid are stuck very thin and light circular-patch antennas as shown in Fig. 19.74, and they are left-hand circularly polarised. The lid is opened and placed to face the satellite at a suitable angle to communicate with a fixed earth station. Each antenna is used, respectively, for transmitting (1645 MHz) and receiving (1543 MHz). The advantages of this configuration are that each antenna can be designed independently to maximise its efficiency, and a diplexer, which is usually heavy, is unnecessary. The gain and axial ratio of each antenna in the boresight direction are about 7 dBi and 2.5 dBi, respectively.
Fig. 19.72 Vertical radiation pattern (Courtesy: Toyota Central Research Laboratory, Japan)
Fig. 19.74 Circular microstrip antennas for the HMCT (@ 1988 IEEE)
( b ) Conical-beam antennas: T o create a low G/T and low-cost antenna for land-mobile and maritime satellite communications services, conical-beam antennas are required because there is no need for tracking. For this requirement, three types of circularly polarised microstrip antennas with a conical baam have been developed: (i) six-element circular array, (ii) higher-mode microstrip antenna and (iii) circular array of strips and slots.
a '' Fig. 19.73 Schematic view of the HMCT (@ 1988 IEEE)
( i ) Six-element circular array: A conical-beam microstrip array which is fabricated in the S-band and radiates circularly polarised waves is shown in Fig. 19.75 [27]. The antenna is a six-element circular array, and each pair, located symmetrically with respect to the array centre, is fed out of phase. Therefore the antenna has radiation null at the boresight, and hence a conical beam. The radiation pattern is calculated using the following equation:
7 728
Applications in mobile and satellite systems
I
I
Applications in mobile and satellite systems
I
1129
where g(%,4-$,) is the element pattern, k , is the propagation constant in free space, and e, and e, are the vectors of the radiation and element position, respectively, and are given as: e,
=
(sin Q cos 4 , sin % sin 4 , cos 8)
(19.2)
e,
=
(d cos $, d sin $, 0)
(19.3)
Here, the variable d represents the radius of the circular array, and angular position of nth element, given as:
I//,, is the
For simplicity of feeding, elliptical patches with a single feed which can radiate circularly polarised waves are used. 0.9 dBi at 30" from the The measured gain of the fabricated antenna is 6.6 vertical axis. The measured axial ratio is less than 2.5 dB in the same direction. The measured radiation patterns are shown in Fig. 19.76. (ii) Higher-mode microstrip antenna: A higher-mode microstrip antenna can be designed to have a conical beam. In the case of the TM,,,-mode microstrip antenna, circular polarisation can be obtained by exciting the patch with two feeds which are 90" out of phase and displaced 45" and 135" apart. For the purposes of mobile communication services, the earth-station antennas must have broadband characteristics.
Fig. 19.75 Outer view of conical-beam microstrip array (@ 19 8 8 IEICE)
tic element Excitation element Fig. 19.77 Configuration of conical-beam broadband microstrip antenna
Fig. 19.76
Measured radiation patterns of conical-beam microstrip array (circular polarisation) (@ 1 9 8 8 IEICE)
(01 9 8 8 IEICE)
A circularly polarised broadband microstrip antenna with a conical beam is shown in Fig. 19.77 [28]. This antenna is a TM,,,-mode microstrip antenna with a parasitic element which is placed in front of the excitation element. The parasitic element is used to broaden the usable frequency band. The frequency dependence of VSWR with and without a parasitic element is shown in Fig. 19.78. The parasitic element increases the bandwidth more than
7 730
Applications in mobile and satellite systems
.
,
2 5 1 p 1 a l f l l ~1 ,,
,96
I
,
1 1.04 Normal lzed frequency
Applications in mobile and satellite systems
1131
1
Fig. 19.78 Frequency dependence of measured VSWR with and without parasitic element (@ 1988 IEICE)
radiation pattern
0
Fig. 19.79 Measured radiation patterns of conical-beam broadband microstrip antenna (circular polarisation) (@ 1988 IEICE)
8=3 5-
___---- ---------------- --------------_-8=45' -2 -
-1
strip dipole
/ ref lector
\
p I ane
subst r a t e
Fig. 19.80 Configuration of the circular array (Courtesy: J.P. Daniel, University of Rennes; and Koichi lto, Chiba University) (Windows and feed network are not shown)
Fig. 19.81 Calculated co-polar radiation patterns and axial ratios (Courtesy: J.P. Daniel, University of Rennes; and Koichi Ito, Chiba University) a Vertical plane -4 = 0' plane - - - 4 = Wplane b Conical-cut plane -0 = 3 5 plane - - - 0 = 4 5 plane
1732
Applications in mobile and satellite systems
six times. The measured directive gain of the fabricated antenna is 6.5 dBi in the frequency band of 8%. The measured radiation patterns are shown in Fig. 19.79. (iii) Circular arra.v of strips and slofs: The third type of conical-beam antenna with circular polarisation can be realised by modifying a circularly polarised printed array composed of strip dipoles and slots [29]. Fig. 19.80 shows an example of a circular array consisting of four-pair strip dipoles and slots. Windows, not shown in the Figure, are placed in the ground plane to increase the gain and bandwidth of the strip dipoles [29]. The radiating elements are arranged radially and fed by an appropriate microstrip feed network. A substrate with high dielectric constant should be used to reduce the antenna diameter. Fig. 19.81 shows calculated results of co-polar radiation patterns and axial ratios for a four-pair array with a larger reflector. The frequency was 2.5 GHz and the diameter and height of the antenna were about 10 cm and 3 cm, respectively. The axial ratio was less than 2 dB over most of the hemisphere. The ripples of both the radiation pattern and the axial ratio in the conical-cut planes were less than I dB.
Applications in mobile and satellite systems
1133
as shown in Fig. 19.83~.The switching circuit is composed of two SP-3T switches and one DP-DT switch. Each radiator is electronically switched one by one through a control which compares its received power level with that of the
Array Element
A
(a) C o o r d i n a t e S y s t e m
Fig. 19.82 Outer view of six-element switched-element spherical array (@ 1988 IEE)
( c ) Spherical arrays ( i ) six-element switched-element spherical array: An outer view of six-element switched-element spherical array, which is fabricated in the L-band and radiates circularly polarised waves, is shown in Fig. 19.82 [30]. It is 40 cm in diameter and 20 cm in height. This antenna comprises the radiator section, the switching circuit and the controller. The radiator section is composed of six circularly polarised elements. Each element is a circular microstrip antenna with a parasitic element for broadening the bandwidth, and is located on the limited sphere tilted at an angle a from the vertical axis (Z-axis)
( c ) 2-dimensional
radiation patterns
Fig. 19.83 Calculated two-dimensional radiation patterns of optimised six-element spherical array (@ 1988 IEE)
adjacent radiators. It is postulated that the coverage area of the antenna is between B,, - AB, and Oo+ AO, from the vertical axis and omni-directional in the horizontal plane, as shown in Fig. 19.83~.
Applications in mobile and satellite systems
Applications in mobile and satellite systems
1134
The radiation pattern is calculated from the following equation:
1 135
4
where, ko is the propagation constant in free space, and JI, is the phase of the nth element. e, and e, are the vectors of the radiation and element position, respectively, and are given as
4, sin 0 sin 4, cos 0) a (sin ct cos p,, sin a sin fin, cos a)
e, = (sin 0 cos
(19.6)
ep =
(19.7)
Here, the variable a represents the radius of the spherical array. g(l, p) is the radiation pattern of the array elements. Assuming the use of a broadband microstrip antenna, g(l, p) can be approximated by the following equation: The relation between 0, cos l =
4 and 1 is therefore given as follows:
(er .ep) -
lerllepl The calculated 2-dimensional radiation patterns of an optimised six-element array antenna are shown in Fig. 19.83. The angle 0 from the antenna vertical axis is indicated by the distance from the origin, and the angle 4 rotated about the vertical axis is indicated by the angle from the horizontal axis. The six radiators are located at a position a = 44" as shown in Fig. 19.83. The solid and dotted curves in Fig. 19.83 indicate the contour lines in which the directive gain for each beam is 7 and 8 dBi, respectively. It can be seen in Fig. 19.83 that the minimum coverage gain is 7 dBi when the coverage area is between 40' - 20' 20". and 40" The measured directive gain of the fabricated array is more than 7 dBi for a coverage area of within 20"-60" from the vertical axis and a frequency band of 8%. The peak gain is 8.5 0.3 dBi given the same frequency band. The measured axial ratio is less than 3 dB and the measured VSWR is less than 1.4. The total insertion loss for the switching circuit is less than 1.6 dB. Therefore, actual coverage gain can be more than 5.4 dBi.
Fig. 19.84 Configuration of 86-element spherical array (Courtesy: KDD, Japan)
Antenna
-
+
+
(ii) 86-element spherical array: The configuration of an 86-element spherical array is shown in Fig. 19.84 [31]. This array is composed of 86 microstrip radiators, and the sub-array, which is composed of six or seven radiators, is switched one by one. The coverage gain of this antenna is more than 12 dBi within 115' from the vertical axis. The configuration of feeder section is shown in Fig. 19.85. The active elements are used in order to provide higher G/T. The calculated radiation patterns of an 86-element spherical array are shown in Fig. 19.86.
8x6 Switch Matrix
611
Combiner
/
Group #8
Fig. 19.85 Configuration of feeder section of 86-element spherical array (Courtesy: KDD, Japan)
1136
Applications in mobile and satellite systems
Applications in mobile and satellite systems
( d ) Sector-beam array: The sector-beam array is used for shipborne antennas [32]. The outer view of the sector-beam array, which is fabricated in the L-band and radiates circularly polarised waves, is shown in Fig. 19.87. The size of the array is 1000 mm x 1200 mm. The array is composed of 48 circular microstrip discs. This antenna has a 40" sector beam in the elevation plane. The measured radiation pattern of the fabricated antenna is shown in Fig. 19.88. The half-power beamwidth is less than 39" in the vertical-plane and less than 20" in the horizontal-plane. The sidelobe level is lower than -25 dB, the axial ratio is less than 1.5 dB and the measured gain of the antenna is more than 16 dBi.
Fig. 19.87 Outer view of sector-beam array (@ 1988 I EICE)
Fig. 19.86 Calculated radiation patterns of 86-element spherical array (Courtesy: KDD, Japan)
( e ) Phased arrays (i) Slot antenna: The airborne antenna shown in Fig.19.89 is a 16-element cross-slot antenna (XSA) developed for satellite communications at L-band [33, 341. The element spacing is 97 mm and its volume is about 560 x 560 x 20 mm. Fig.19.90 shows the configuration of the XSA element. It is called a cavitybacked cross-slot antenna and is fed with equal amplitude and phase at the two points shown in Fig.19.90 in order to get wider-band impedance matching characteristics compared with a centre-fed slot. The two perpendicular slots are fed with a 90' phase difference through hybrid circuits to obtain right-hand circular polarisation. The length and width of the slots are about 112 mm and 5 mm, respectively, and the volume of the cavity is about 80 x 20 x 20 mm.
Azimuth Angle
(')
Elevation Angle
Fig. 19.88 Radiation patterns of sector-beam array (@ 1988 IEICE) I
(')
7 137
1738
Applications in mobile and satellite systems
Applications in mobile and satellite systems
1139
Beam scanning is performed by controlling 4-bit variable phase shifters attached to each antenna element. Fig.19.91 shows the patterns at 1.6465 and 1.545 GHt. In this Figure, there is a slight difference between the beam direction to scan and the actual beam direction. The boresight gain is 15.7 dBi.
I I
I
I
slot
feed Lircuit
I
dielectric
I
I
I
metal
Fig. 19.90 Element configuration (@ 1988 IEE)
Fig. 19.89 Cross-slot antenna (@ 1988
IEE)
(ii) Patch antenna: The airborne antennas shown in Fig.19.92 is a 3 x 3element microstrip antenna (MSA) developed for satellite communications at L-band [33, 341. The element spacing is 94 mm (about half a wavelength at 1.6113 GHz) and its antenna volume is about 300 x 300 x 10 mm. Fig.19.93 illustrates the configuration of an MSA element. This is a newly developed two-layer patch antenna. Glass-microfibre-reinforced PTFE with a dielectric constant of 2.3 (thickness = 3.2 mm) is used as a dielectric substrate because of its good temperature characteristics. The two-layer MSA is adopted in which the upper and lower parts are used for transmissin (16465 GHz) and reception (1.545 GHz), respectively. Each layer is independently fed at two points with a 90' phase difference to obtain right-hand circular polarisation. The upper antenna is a conventional circular MSA and is used for transmission, while the lower one is a circular MSA with an electric shielding ring to separate
1140
Applications in mobile and satellite systems
Applications in mobile and satellite systems
e ('1 b
Fig. 19.91 Antenna patterns (@ 1988 IEE) a Radiation b Reception
1$) X
Fig. 19.92 3
x 3-element microstrip antenna
(@ 1988 IEE)
1141
1 142
Applications in mobile and satellite systems
the lower from the upper MSA and to feed the upper MSA easily. The diameters of the upper and lower MSA and the shielding ring are about 66 mm, 84 and 27 mm, respectively. The distance from the centre to the feed points are about 10 mm and 20 mm for the upper and the lower MSA, respectively. Beam scanning is performed by controlling the 4-bit variable phase shifters attached to each antenna element. Fig.19.94 shows the antenna patterns of radiation (1.6465 GHz) and reception (1.545 GHz). In this Figure, there is a slight difference between the beam direction to scan and the actual beam direction. The boresight gain is 15.2 dBi.
Feed Point
(1.545 GHz) Feed Point
(1.6465 GHz)
Dielectric Substrate
I
Receive Port
\ Transmit Port
Fig. 19.93 Element configuration (@ 1988 I E E )
(iii) Sequential-array antenna: Japanese experimental domestic mobilesatellite communications, using Engineering Test Satellite-V (ETS-V) launched in 1987 [35], will provide high-quality links for ships and aircraft at L-band. For this purpose the antenna shown in Fig.19.95 has been developed [36]. It is mounted in the fairing of a Boeing 747 Jumbo Jet. Each of the two array panels consists of 2 x 8 microstrip circular patches, and only one of the array panels facing the satellite is used for communication. The beam can be scanned only in the horizontal plane. Thus each of eight 4-bit digital phase shifters is connected to two vertical elements, as shown in Fig.19.96. Each circular patch fed by two points is sequentially rotated and differentially phase-shifted [35]. In such a sequential array, perfect circular
Applications in mobile and satellite systems
1143
1144
Applications in mobile and satellite systems
polarisation is obtained at a boresight direction independently of the polarisation of elements, and the reflected waves returned to the input port cancel1 each other. For the rectangular sequential array shown in Fig.19.95 high cross-
995mm-4 sequential phased array (2x8)
substrate (6 = 2.8)
A
Applications in mobile and satellite systems
Table 19.4 Sequential phased-array characteristics
Frequency
1545-1548 MHz (transmitting) 1647-1 650 MHz (receiving)
Polarisation
left circular
Gain
12-14.5 dBi (beam scanning)
Bandwidth
8% (VSWR < 2)
Antenna element
circular patch antenna
Array type
2 x 8 element sequential phased array
Phase shifter
4 bits (digital)
Substrate
Teflon ( E , thickness
Volume
15 x 40 x 90cm3 18 kg
Weight
= =
2.6) 4mm
Fig. 19.95 Airborne phased array (@ 1988 IEEE)
sequential arravs
1
feed circuit
in fairing -1-
in fuselage I
~ w rDIV.: . Power divider
Fig. 19.96 Configuration of antenna systems (@ 1988 IEEE)
polarisation discrimination is obtained over a wide angle in the two principal planes, which is useful for reducing fading due to reflections from the sea surface. The characteristics of the array in Fig.19.95 are given in Table 19.4.
1 745
Fig. 19.97 Outer view of synthetic aperture radar (Courtesy: MELCO, Japan)
7 746
Applications in mobile and satellite systems
Applications in mobile and satellite systems
19.3.4 Satellite-borne antenna
( a ) Synthetic-aperture radar (SAR): A rectangular microstrip array is applied to a synthetic-aperture radar (SAR) [37]. The outer view and the configuration of this radar are shown in Figs.19.97 and 19.98, respectively. This antenna is composed of eight panels, the size of leach being 1390 mm x 2060 mm. Each panel has eight sub-arrays and each sub-array has 16 rectangular microstrip antennas, which radiate linearly polarised waves. The substrate is made of honeycomb foam, the dielectric constant being 1.14. The amplitude distribution of the array is uniform in the E-plane, and it is tapered in the H-plane so as to obtain -18 dB sidelobe level. The measured gain is more than 26 dBi in the 1.3 GHz band. The calculated two-dimensional radiation patterns are shown in Fig.19.99. The half-power beamwidth is less than 8.7' in the E-plane and less than 6.3' in the H-plane; the sidelobe level is lower than -12.7 dB in the E-plane and lower than - 17.9 dB in the H-plane.
U b . 1.3 9m
-$*k
1m
flexible
!microstrip
array coax. cab
cable
4
Iflcxlble coax. wave
joint
gu l do
Fig. 19.98 Configuration of synthetic-aperture radar (@ 1988 IEICE)
( b ) 19-element muliibeam array: The outer view of a 19-element multibeamarray antenna for a data-relay satellite is shown in Fig. 19.100 [38]. The antenna operates at 2.1 and 2.3 GHz. The receiving system employs a fixed multibeam antenna of 19 contiguous beams, while the transmitting system uses a singlebeam phased array; 12 radiating elements are shared by both transmission and reception, and the remaining seven elements are dedicated to reception. The sub-array of the 19-element array is composed of seven circular microstrip patches, as shown in Fig.19.101. To broaden the bandwidth, these patches are printed on a Nomex honeycomb substrate of 10 mm thickness. Each patch is excited at two points with 90' phase shift by the rear feeding circuit. The
1747
1148
Applications in mobile and satellite systems
Applications in mobile and satellite systems
7 749
microstrip antenna is arranged so that each patch has small notches to cancel the elliptically polarised components generated owing to the asymmetrical feed structure. The measured gain of this sub-array is more than 15.1 dBi at 2.1 GHz. The measured radiation patterns are shown in Fig.19.102.
Fig. 19.100 Outer view of 19-element multi-beam array (@ 1 988 IEICE)
Fig. 19.102 Radiation patterns of sub-array of 19-element multi-beam array (@ 1 988 1 EICE)
honey-comb-core substrate
19.4 References
2.2 h h:2.3GHz
I feeding circuit 1
Fig. 19.101 Structure of sub-array of 19-element multi-beam array (@ 1 9 8 8
IEICE)
I KURAMOTO, M., and SHINJI, M. (1986): 'Second generation mobile radio telephone system in Japan', IEEE Commun. Mag. 24, pp. 16-21 2 HORI, T., and NAKAJIMA, N. (1983): 'Sector-beam base station antenna for land mobile communication' Natl. Conv. Rec. IECE Japan 754 (in Japanese) 3 NAKAJIMA, N., NARA, T., KAMEO, S., ABE, H., and TAKAMATSU, Y. (1985):A major angle comer reflector antenna with 180" beam width'. Natl. Conv. Rec. IECE Japan 752 (in Japanese) 4 NAKAJIMA, N., and HORI, T. (1984): '900 MHz-band multibeam antenna using butler matrix', IECE Japan Technical Report, AP84-50 (in Japanese) 5 ITO, K., and SASAKI, S. (1988) 'A small printed antenna composed of slot and wide strip for indoor communication systems', IEEE Int. Antennas and Propagation Symp. pp. 716-719
1150
Applications in mobile and satellite systems
Applications in mobile and satellite systems
6 MISHIMA, H., and TAGA, T . (1982): 'Antenna and duplexer for new mobile radio unit', Rev. Elect. Commun. Labs NTT, 30, pp. 359-370 7 JASlK H, (1961): 'Antenna Engineering Handbook' (McGraw Hill, NY) 8 OHISHI, Y. (1983): 'Analysis of reactance-loaded annular slot antenna directivity performance'. Graduation Thesis, University of Tsukuba, Japan (in Japanese) 9 KONDO, M., SASAKI, S., MATSUMOTO, K., ABE, H., CHATANI, Y., FURUNO, T., and MANO, S. (1986): 'A train antenna for a leaky coaxial cable'. Natl. Conv. Rec. IECE Japan 618 (in Japanese) 10 YAMAMOTO, J. (1985): '900 MHz numeric pager' Nat. Conv. Rec. IECE Japan 2411 (in Japanese) 11 KUBOYAMA, H., el al. (1985): Post loaded microstrip antenna for pocket size equipment at UHF'. Int. Symp. on Antennas and Propagation, Japan, pp. 434-436 12 FUJIMOTO, K., er al. (1986): 'Small Antennas' (Research Studies Press, London). pp. 243-249 13 BABA, T. (1987): 'Analysis of reactance-loaded square microstrip antenna performance'. M.S.C. Thesis, University of Tsukuba, Japan, pp. 78-84 (in Japanese) 14 BABA, T. (1987): 'Analysis of reactance-loaded square microstrip antenna performance'. M.S.C. Thesis, University of Tsukuba, pp. 85-89 (in Japanese) 15 NISHIMURA, S., NAKANO, K., and MAKIMOTO, T. (1979): 'Franklin-type microstrip line antenna'. IEEE Int. Antennas and Propagation Symp. pp. 134-137 16 FUJII, K., and ISHIKAWA, H. (1984): 'Low sidelobe microstrip array antenna', Nat. Conv. Rec. 49, Optical and Electronics, IECE Japan (in Japanese) 17 HASEBE, N., and ONOE, M. (1984): 'Radar reflector with bidirectional communication capability'. IEEE Int. Antennas and Propagation Symp., pp. 788-791 18 HASEBE, N., er 01. (1985): 'Radar reflector with bidirectional communication capabaility', Trans IECE Japan, J66-B, pp. 1177-1 184 (in Japanese) 19 HARA, Y., and GOTO, N. (1984): 'An omnidirectional vertical shaped-beam three faced microstrip slot array antenna', IEEE Int. Antennas and Propagation Symp., pp. 527-530 20 HANEISHI, M. (1985): 'A circularly polarized SHF planar array composed of microstrip pairs-element', Int. Symp. on Antennas and Propagation, Japan, pp. 125-128 21 MURATA, T., and OHMARU, K. (1986): 'Characteristics of circularly polarized printed antenna with two layer structure'. IECE Japan Technical Report, AP86-101 (in Japanese) 22 NISHIMURA, S., SUGIO, Y., and MAKIMOTO, T. (1983): 'Crank-type circularly polarized microstrip line antenna'. IEEE Int. Antennas and Propagation Symp., pp. 162-165 23 WATANABE, T., FUJITA, T., and DEGUCHI, F. (1987): 'Microwave planar array antenna design'. ITE Japan Technical Report R E 8 7 4 (in Japanese) 24 NISHIMURA, S., NISHIGAKI, A., WATANABE, T., SUGIO, Y., and MAKIMOTO, T. (1987): 'Circularly polarized microstrip line antenna terminated by patch antenna'. IECE Japan Technical Report, AP86-124 (in Japanese) 25 NISHIMURA, S., SUGIO, Y., and MAKIMOTO, T. (1985): 'Side-looking circularly polarized microstrip line planar antenna', Int. Symp. on Antennas and Propagation, Japan, pp. 129-132 26 HASE, Y ., et al. (1987): 'Very low speed message communication system using hand-held earth station'. IEEE Int. Conf. on Communicatins, pp. 520-524 27 HORI, T., ITAMI, Y., and NAKAJIMA, N. (1982): 'Circularly polarized microstrip array antenna with conical beam'. Natl. Conv. Rec. IECE Japan 655 (in Japanese) 28 HORI, T., TERADA, N., and KAGOSHIMA, K. (1986): 'Circularly polarized broadband microstrip antenna radiating conical beam'. Natl. Conv. Rec. IECE Japan 637 (in Japanese) 29 ITO, K. (1987): 'Circularly polarized printed arrays composed of strip dipoles and slots', Microwave Jol, 30, pp. 143-153 30 HORI, T., TERADA, N., and KAGOSHIMA, K. (1987): 'Electronically steerable spherical array antenna for mobile earth station'. IEE Int. Antennas and Propagation Conf., pp. 55-58 31 SHIOKAWA, T., WATANABE, F., and NOMOTO, S. (1984): 'Spherical array antenna for
32
33
34 35 36 37
38
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general mobi!e satellite communications', IECE Japan Technical Report, AP84-30 (in Japanese) OHMORI, S., MORIKAWA, H., MIYANO, N., SUZUKI, Y., and CHIBA, T., (1980): 'Circularly polarized sector-beam shipborne antenna', Nat. Conv. Rec. IECE Japan S1-4 (in Japanese) SHIOKAWA, T., er 01. (1986): 'Cross slot array antenna for aeronautical satellite communications', IECE Japan Technical Report, AP86-59, pp. 17-21 (in Japanese) YASUNAGA, M., el al. (1987): 'Phased array antennas for aeronautical satellite communications'. IEE lnt. Antennas and Propagation Conf., pp. 47-50 OHMORI, S. el al. (1986): 'Aircraft earth station for experimental mobile satellite system'. IEEE Int. Conf. on Communications, pp. 1392-1395 TESHIROGI, T., er al. (1986): 'Airborne phased array antenna for mobile satellite communications:. IEEE Int. Antennas and Propagation Symp., pp. 735-738 HISADA, Y., ITO, Y., AKAISHI, A,, IMURA, N., and ONO, M. (1983): 'The results of partial experimental manufacturing of syntheticaperture radar antenna', IECE Japan Technical Report, AP83-39 (in Japanese) TESHIROSI, T., CHUJO, W., AKAISHI, A,, and HIROSE, M. (1986): 'Multibeam array antenna for data relay satellite'. Trans. IECE Japan, J69-B, pp. 1441-1452 (in Japanese)
Chapter 20
Conical conformal microstrip tracking antenna P. Newham and G. Morris
20.1 Introduction This Chapter describes the design, construction and testing of a prototype monopulse tracking antenna that is realised as a thin microstrip/triplate structure conformal to the surface of a cone. The main application of such an antenna configuration is to provide gul'ded-weapon seeker antennas for high speed ( > Mach 2.5) missiles and shells where the pointed (high fineness) front ends make conventional antenna (reflector or flat plate) plus radome designs impracticable owing to severe radome aberration effects. The latter is due to the high angles of incidence with which the antenna must necessarily illuminate the radome, as well as radome-tip scattering and blockage. Other applications exist where conical, or near conical, geometries are found - there are obviously many possible aircraft sites, and the antenna configuration described should find applications here. In the context of guided weapons, tracking antennas are required for both narrow and broadband applications: narrow band for active and semi-active seekers and broadband for passive anti-radiation seekers. The design as discussed is narrow band, having a bandwidth of 10% centered at 10 GHz; techniques to extend the bandwidth to over 50% are discussed at the end of the Chapter. The antenna as described consists of microstrip radiators on the conical surface with an adjacent (underneath) triplate feed network. Emphasis is given in the chapter to the practical engineering problems that have been encountered and solved during the design and development programme.
-
20.2 Single patch element 20.2.1 Choice of array element The choice of a sutable printed array element is governed mainly by its performance in the endfire direction. The directivity of an antenna array in a particular
1 154
Conical conformal microstrip tracking antenna
direction is only as good as that of its constituent elements in that direction. Thus, for the conical array, a radiator with almost omnidirectional coverage in the plane containing the cone axis is required. The choice is essentially limited to either a half-wavelength rectangular patch element or its quarter-wavelength short-circuited version. Other alternatives, such as the slot or dipole, possess a natural null in their radiation patterns at endfire. Others, such as the V-antenna, with good directivity at endfire, are seriously degraded by the necessary presence of a ground-plane associated with the inner, but adjacent, conformal feeding circuitry. The effect here is to squint the pattern considerably from endfire. For several reasons the quarter-wavelength patch is seen to offer the best solution. In particular: (a) Its theoretical pattern is more omnidirectional than that of the halfwavelength patch. For example, in the E-plane at endfire (with a substrate of relative dielectric onstant E, = 2.45), the pattern drops to - 6 dB below peak, as against - 11 dB for the half-wavelength patch [I]. For the case of the 20' cone under consideration, the main interest is in the performance at 10' from endfire, i.e. along the cone axis. Here the values are -2 dB and -8 dB, respectively; and since the theoretical gains are 5 dBi and 7 dBi, respectively [2], the gain of the quarter-wavelength patch along the cone axis exceeds that of the halfwavelength patch by 4 dB. (b) The quarter-wavelength patch occupies approximately half the area of the half-wavelength patch. One particular drawback of the quarter-wavelength patch, however, is the difficulty in feeding it from microstripline, owing to the high input impedance present at its radiating edge - this is typically 240R. It becomes necessary to break into the patch via a notch in order to find a suitable impedance level. The design of the single patch element is now considered in detail. , 20.2.2 Choice of substrate Several factors govern the choice of substrate for the microstrip layer onto which the antenna arrays are printed. First and foremost is the requirement that the substrate must be capable of being formed into a truncated cone without physical damage, and preferably without changing its electrical properties. Secondly, the material should be low loss with a low relative dielectric constant. This is in order to maximise the available bandwidth of the patch element to allow for small performance differences between array elements owing to manufacturing tolerances. For this purpose the substrate should also be as thick as possible, but not so thick as to generate excessive surface-wave energy. The criterion adopted for the maximum thickness h is such that h < 0.071, for E, = 2.32 [3]; at 10 GHz this gives h < 2.1 mm. RTIDuroid 5880, manufactured by Rogers Corporation with E, = 2.2 and loss tangent tan 6 = 0.001, has been found to be a suitable material, using a standard thickness of 1.57 mm. Rogers provide valuable information on bending their Duroid products [4], and
1
I
i
Conical conformal microstrip tracking antenna
1 155
it is the randomness of the glass microfibres embedded in the PTFE base material that suppresses any tendency for the material to fracture under bending stresses. 20.2.3 Feeding the patch A patch antenna may be fed either from a microstrip line on the same substrate or via a probe extending through the ground plane. Probe feeding was rejected for the conical array application for two important reasons. First it would have entailed a combination of both the power division and hybrid tracking circuitry on the same triplate feed network. Owing to the limited space available on the triplate substrate, as will be evident from Section 20.4, this was not possible to achieve in practice. Secondly the additional probe inductance, associated with the thick antenna substrate, would also need to be matched within the limited space on the triplate. As mentioned in Section 20.2.1, the quarter-wavelength patch is difficult to feed via a microstrip line owing to the high input impedance at its radiating edge. In order to feed the patch at a suitable impedance level, it is necessary to break into the patch via a notch in the radiating edge. At frequencies below about 5-6 GHz, the size of a patch becomes large relative to the width of a typical microstrip feed line, which remains almost constant with frequency for a given impedance. In this case, the patch may be fed through its short-circuit plane with negligible effect on its performance [5]. However, at 10 GHz this is no longer possible unless a very narrow high-impedance feed line is used. Even at 100 R, the width of the line is comparable to that of the patch. For reasons which will become apparent later, the 100 R feed line was the most suitable means of feeding the patch, and for this reason the patch was fed through its radiating edge. Weinschel [6] has measured the impedance variation with the notch width ( s in Fig. 20.1) for a half-wavelength patch. From his graphs it is apparent that the measured impedance corresponds to that of a probe-fed patch when the notch width is nearly equal to the substrate thickness. The notch width for the patch design was thus fixed at 1.5 mm. 20.2.4 Theoretical design method The design of the quarter-wavelength patch is based on the procedure outlined in Reference 7, and considers the patch as a short-circuited length of resonant transmission line. Fig. 20.1 shows the geometry of the patch together with its equivalent circuit. Yo is the characteristic admittance of the microstrip (patch) transmission line. The feed point is located a distance x from the short-circuit plane and d from the radiating edge. The patch resonant length x + d is somewhat less than a quarter wavelength in the transmission line owing to the fringing field extension beyond the physical edge of the patch. This field extension is incorporated into the susceptive part of the aperture admittance Yo of the radiating edge, which is made up of a radiation conductance G, and the susceptance B,.
1156
Conical conformal rnicrostrip tracking antenna
Conical conformal microstrip tracking antenna
Looking into the right-hand side of the transmission line from the feed point, the admittance, assuming a lossless line, is given by Gh -
= G, (Yo - B, tan pd)
+
+
G, (B, Yo tan pd) tanpd (Yo - B, tan pd)' + Gi tan2 pd
yo
(20.1)
i
1157
The f sign in eqn. 20.3 is chosen according to whether the denominator is negative or positive. On evaluation, Podis then inserted into eqn. 20.2 to obtain B,,. Resonance occurs, of course, when the shunt susceptance to the left of the feed point cancels that to the right; i.e. when: - j Yocotp0X = - j B , , ,
Bi,, - B, Yo + (Y: - Gi - &) tan pd- B, Yo tan2 Dd (20.2) (Yo - B, tan fld)2 Gt tan2 j d YO where is the propagation constant at the frequency in question. Note that eqns.20.1 and 20.2 are in error in Reference 7.
+
short circuit plane
The patch resonant length x + d is thus obtained, together with the feed-point position relative to the short circuit plane. An expression for 2, = l/Y,, the characteristic impedance of the microstrip (patch) transmission line, has been taken to be [8]:
radiating edge
quarter wavelength patch
where murostrtp feed lfne
and
short circuit
transmission line model
I /
driving polnt
d
,$
/
where W = patch width h = substrate thickness t = conductor thickness E, = substrate relative dielectric constant The aperture conductance Gois taken to be [8]:
Fig. 20.1 Microstrip quarter-wavelengthpatch and its equivalent transmission-line model
The short circuit to the left of the feed point simply presents a shunt susceptance of value - j Yo cot px. To proceed, Gin is set equal to the desired driving-point admittance G,, at the centre frequency (P = Po), and eqn. 20.1 is then solved for d. This takes the form of a quadratic equation with solution:
where ko =
2n and Lo is the free space wavelength. 20
It should be noted that the expression for the aperture susceptance B, differs considerably between References 7 and 8. In Reference 7 the aperture fringing capacitance is given by:
1758
Conical conformal microstrip tracking antenna
where L is the patch resonant length. Then B, = jw,C', where w, is the resonant angular frequency. In Reference 8 B, is expressed in terms of the fringing field extension, AI:
Conical conformal microstrip tracking antenna
7 159
choice of 100 R input impedance is that a superior performance dual patch element - described in Section 20.3 - can be fed directly and symmetrically from a 50 Cl coaxial probe without the need for impedance transformers. Table 20.1 Single patch design at 70 GHz
where
Susceptance term
Width (mm)
Post and Stephenson [7] Bahl and Bhartia [8]
11.9 11.9
-
Length (mm)
Short-circuit to feed (mm) 50R l OOR
4.17 4.59
1.35 1.40
1.94 2.02
Both expressions have been examined experimentally and the results are discussed in Section 20.2.5. The width W of the patch is given by the following well-proven formula [8]:
Finally, it should be noted that it is, in practice, convenient to realise the short circuit at one end of the patch by using a grid of conducting pins, as shown in Fig. 20.4. However, this produces a residual inductance at the patch edge rather than the desired perfect short circuit, so that the patch will need to be shortened slightly. James et al. [9] provide an expression for the shift Alin the short-circuit plane, based on the equivalent circuit of an array of posts across a parallel-plate transmission line backed by an open circuit: Fig. 20.2 Measured return loss for alternative parch designs Aperture susceptance (from Reference 7) - - Aperture susceptance (from Reference 8)
-
where r = radius of each post, a = distance between posts, 1, = free-space wavelength; A1 is positive when the short circuit plane lies away from the patch and behind the grid. Eqns. 20.1 - 20.14 were incorporated into a patch design software package, requiring inputs of patch width, substrate thickness and dielectric constant, input impedance and resonant frequency, and producing the patch resonant length and feed position as output data.
20.2.5 Patch design Table 20.1 lists the computed patch dimensions for an input impedance of 100 R at a resonant frequency of 10 GHz. The choice of 100 R rather than the usual 50 R is twofold. First, the width of a 50 12 microstrip feed line on 1.57 mm thick RT/Duroid is 5.13 mm, which is close to 50% of the patch width, and hence an unacceptable choice of feed. On the other hand, the width of a 100 R line is 1.52 mm, and is thus suited to the patch dimensions. The second reason for the
The patch dimensions of Table 20.1 are given using both expressions for the aperture susceptance B, (eqns. 20.10 and 20.1 1) taken from References 7 and 8. Fig. 20.2 shows the measured return loss for two patches built to the two alternative designs. It is evident that the measured resonant frequency of 9.88 GHz for the patch designed using B, taken from Reference 7 is in better agreement with theory than that designed using Reference 8, which resonates at 9.08 GHz. The former patch was therefore taken as the design. However, the resonant frequency of the patch is still 120 MHz below the theoretical value. This problem was investigated further with the aid of liquid crystal diagnostic techniques. Liquid crystals of the cholesteric variety possess a molecular structure which enables them to exhibit colour changes over a narrow temperature band. As the temperature increases, the crystals reflect the spectral range of colours from red to blue over a temperature range dependent on the concentration of a dopant additive. This technique has been used to observe the electric field in the vicinity of the patch. The approach taken was to
1 760
Conical conformal microstrip tracking antenna
Conical conformal microstrip tracking antenna
mount a commercially available sheet of liquid crystal material, sensitive to a temperature range around 35"C, onto a resistive card, and to place this card over the patch, which was radiating several watts of R F power at the resonant frequency. The resistive card is sensitive to the electric field component tangential to its surface and dissipates power as heat, which results in bands of colour in the liquid-crystal sheet dependent on the electric field strength. Fig. 20.3 shows the results of this test applied to the patch, and indicates a concentration
7 161
20.3 Dual patch element 20.3.1 Choice of design Endfire radiation may be further enhanced by constructing the basic array radiating element out of two quarter-wavelength patches phased for constructive interference in the endfire direction. Fig. 20.5 shows such an arrangement, in which the two patches are set 'face-to-face' and joined by a straight length of microstrip line. The feed point position has to be chosen to produce the required excitation phase of each patch. Using the 100 R input impedance patch design of the previous Section implies that the microstrip connecting line is of 100 R impedance, thus making for a 50 R termination at the element feed point. This dual patch element, with its 50 R feed point on a microstrip line, is eminently suitable for a through-substrate probe connection to an underside feeding network. The design of this element is now considered in detail.
Fig. 20.3 Liquid-crystal display showing coupling between patch and feed line, for patch resonant at 9.88 GHz
U loon
of the fringing field around the centre of the radiating aperture. Under normal conditions the dominant mode within the patch should yield a uniform electric field strength across the aperture. This concentration is therefore indicative of a coupling between the patch aperture and the microstrip feed line. This results in an extension of the fringing field, equivalent to an apparent lengthening of the patch resonant length and hence lowering the resonant frequency. By shortening the patch in the ratio of the measured to the desired resonant frequency, the patch was made to resonate at 10 GHz. Fig. 20.4 shows the final dimensions of the single patch element design.
microstrip Fig. 20.4
Final single patch design
Dimensions in rnm
20.3.2 Location of patch phase centre In order to produce the required beam at an angle of 10" to endfire, corresponding to the axis of the cone, it is necessary to know the location of the apparent phase centre of each patch of the dual patch element. This position is some
7 7 62
Conical conformal microstrip tracking antenna
Conical conformal microstrip tracking antenna
distance beyond the physical boundary of each patch, owing to the extent of the fringing field. It was assumed that this extension dl (eqn. 20.12) defined the postion of the phase centre, being exactly one quarter-wavelength in the dielectric from the patch short-circuit plane. This position is indicated in Fig. 20.5. Knowing the wavelength in the dielectric and the physical size of the patch from Table 20.1 it may be shown that A1 x 1.2 mm at 10 GHz.
m-
fi $-
forward d~rection
-- phasb
7163
relate to RTIDuroid 5880 substrate with E , = 2.2 and thickness 1.57 mm. VSWR measurements made on a prototype element, fed from below by a coaxial surface launcher, showed a shift in the resonance frequency to 9.6 GHz from the case of a single isolated patch. This was attributed to mutual coupling, and the original 10 GHz resonance could only be restored by empirically adjusting the notch depth of the patch closest to the feed probe. A reduction of approximately I mm was found to be optimum.
centre
0.9A element size
19. 5
elemenl feed point
-
mod~fied feed posilion
Fig. 20.5
Dual-patch element design Dimensions in mm; other patch dimensions as for Fig.20.4
20.3.3 Design and optimisation The distance between the patch phase centres was taken to be 0.9 wavelengths at 10 GHz. This value was chosen for several reasons. First it enables a more directive four-patch array to be constructed, if desired, by interleaving two dual patch elements with correct phasing, as shown in Fig. 20.6. The inter-patch spacing of 0.451 would thus be suitable for minimising the grating lobe structure in the endfire radiation pattern. If the size of a dual patch element were halved (to 0.451) then interleaving would not be possible in a four-patch array, and' more space would be required for the array. Fig. 20.6 contrasts these two alternative constructions. The four-patch array was not used in the final construction since the intention was only to investigate the performance of dual patch elements mounted on the conical surface. Secondly, mutual coupling between the two patches of the dual patch element at 0.9 wavelength spacing is less than at 0.45 wavelength, thus requiring only small changes to the original single patch design. Finally, the two nulls in the far field pattern for the dual patch element (clearly defined by the 0.9 wavelength spacing) enable an independent check to be made of the true phase centre positions. The feed-point position was chosen to phase the element at 10" to endfire with due regard being taken of the 180" phase difference inherent in the face-to-face array configuration. The dimensions are given in Fig. 20.5. These dimensions
3ci I
O.45h element size
Fig. 20.6 Comparison in overall width of four-patch array for different element size
w, < w2 Fig. 20.7 shows the measured far-field E-plane radiation pattern for the dual patch element. From the angular positions of the two nulls, an estimate was made of the actual phase centre position of each patch. This was found to be 1.4 mm from the physical boundary of each patch and is in close agreement with the 1.2 mm prediction of Section 20.3.2. The radiation pattern displays a slope beyond 60" from broadside and is attributable to the single patch element factor which tends to fall off as endfire is approached. Nevertheless, at 10" from endfire the fall off is only 3 dB below the peak level.
20.4 Hybrid feeding network 20.4.1 Overview The most efficient means of generating a tracking signal using four circum-
7 764
Conical conformal microstrip tracking antenna
Conical conformal microstrip tracking antenna
ferentially mounted antenna elements is shown in Fig. 20.8 [lo]. Both sum and difference channels are generated by a combination of three 180" hybrid couplers, one 90" hybrid and phase-matched lines. It can be shown that each port of the 90" hybrid will provide a progressive 360" phase shift around the cone circumerence, with opposite sign for each port. This corresponds to a circularly polarised sum channel along the cone axis, with opposite hand of polarisation
antennas positioned at 90' mtervals around c~rcumference
-element
1 A channel
polor~~tion perpendicularto cone surface
I channel
0. I phase (0). A phase Fig. 20.8 Schematic of monopulse tracking feed network hybrid element
elevalion angle.deg
Fig. 20.7 Measured E-plane radiation pattern of dual-patch element
for each of the two ports, provided the other port is well matched. One port of the first 180° hybrid will generate equi-phased signals at each antenna element. In this case a difference channel is formed which is sensitive only to horizontal polarisation in the horizontal plane, and vertical polarisation in the vertical plane. The second port generates alternate 0°, 180°, 0°, 180" phasing around the cone circumference. This is a difference channel sensitive to vertical polarisation in the horizontal plane and horizontal polarisation in the vertical plane. With the addition of one further 90" hybrid in front of the first 180" hybrid, these two
1 165
antenna feed port
substrate 'periphery
A channels
Fig. 20.9 Schematic of triplate feeding network
9
channels
1 7 66
Conical conformal microstrip tracking antenna
Conical conformal microstrip tracking antenna
modes can be generated in phase quadrature, resulting in a circularly polarised difference channel. This last refinement has not been adopted in the current design. A monolithic version of the hybrid feeding network requires that the antenna elements be situated within the confines of the circuit itself in order to avoid the crossing of lines. This can be most easily achieved by placing the complete feeding network on a triplate layer beneath the antenna substrate and joining the two electrically by coaxial probes. A schematic arrangement of this circuit is shown in Fig. 20.9, where each hybrid is represented in block form. The physical implementation of this arrangement is complicated by the need to mount the assembly on the surface of a cone. The procedure undertaken was to design the circuit on an opened-out section of the cone, using tracks of variable curvature dependent on their distance from the cone apex. The triplate substrate components have been chosen again to be RT/Duroid 5880 with thickness 0.79 mm. The resulting triplate is therefore of the same thickness as the antenna substrate, and hence uses the same bending procedure. The main track impedance was chosen to be 50 0,since the corresponding track width of 1.21 mm is well suited to the limited available space, as well as being able to be fed directly from standard SMA edge connectors. A further advantage is in the fact that the antenna elements can be fed directly from 50 Q, as mentioned in Section 20.3.1. The following Sections deal with the design of each circuit component. 20.4.2 Hybrid designs The conventional narrow-band 90" hybrid coupler is essentially a four-port device comprising four arms, each of length one quarter-wavelength at midband. Two configurations are shown schematically in Fig. 20.10 for the case of 50 R output lines. The two configurations are, in effect, identical. However, the second configuration is more suited to our purposes since it comprises, essentially, two continuous 50 R tracks joined by two parallel arms of impedance 5 0 1 4 = 35.35 Q. The operation of the coupler is to split a signal entering at port 1 into two equal output signals at ports 2 and 4, but with a 90" difference in phase. Port 3 is loaded with its characteristic impedance. The device is totally symmetric in that port 3 could be used as the input port with port 1 loaded. Implementation of the 90" hybrid in triplate is complicated by the effect of the junctions on reference plane positions. Ifjunction effects were absent, each arm of the hybrid would be exactly one quarter-wavelength in length and the complete device would be square. However, each corner of the hybrid is actually a T-junction, and may be represented as shown in Fig. 20.1 1 for the general case of series arm impedance Z,, and shunt arm impedance Z,,, with corresponding track widths W, and W2.The reference plane for each track is displaced from the geometric centre by an amount dl and 4 , respectively. Consequently, the series arms of the hybrid are extended by an amount 2d, and the shunt arms by 2d2. Reference 11 provides design curves for these displacement factors in
4
-
in both cases
0
@ 1s
Fig. 20.10 Atternative 9V hybrid configurations
Fig. 20.11
T-junction in triplate
@ i @ "=soe
loaded
7 767
1 168
Conical conformal microstrip tracking antenna
Conical conformal microstrip tracking antenna
air-filled stripline, together with suggestions for the case when 8, > 1. For the triplate configuration defined, these values are calculated to be d, = 0.23 mm and d, = 0.87 mm. Fig. 20.12 shows the layout of the final theoretical 90" hybrid design operating at a mid-band frequency of 10 GHz. The 90" hybrid design may be simply converted into a 180' design by extending one of the output arms by one quarter wavelength. In this case the two output signals are either equi-phased or displaced by 180°, depending on which input port is energised.
1 769
The even and odd-mode characteristic impedances for coupled triplate lines are given by 94.15
( W/b
+ [ln2 + In (1 + tanh m/2b)]/n)
JE,{W/b
+ [In2 + In (1 + coth ns/2b)]/n)
ZOe
= Je.
2 ,
=
94.15
and 2;; = Z , Z ,
(20.16) (20.17)
Voltage coupling Cois given by
and CJb = - 20 logl0CO where s = distance between coupled lines W = width of each line b = triplate thickness
Fig. 20.12 Final SO' hybrid design Dimensions in mm
20.4.3 90" benak Several 90" bends are required in the triplate circuitry, and consequently a suitable design is required to minimise the bend VSWR. At the same time it is necessary to know the effect of each bend on the reference plane in order that the correct phasing can be applied to each antenna element. Fig. 20.13 shows a mitred bend in which the optimum mitre dimension a for minimum VSWR has been given in Reference 11 as a = 1.1 W for the triplate parameters under consideration. For a 50 R track, W = 1.21 mm; hence a = 1.33 mm. The electrical line extension associated with the bend is also given as I = 0.58 W = 0.7 mm.
Fig. 20.13 Mitredbend I= electrical length of bend between two reference planes
20.4.4 Minimum track distance The narrow confines of the triplate substrate required that tracks be brought close to each other. It is therefore necessary to know the minimum acceptable distance between neighbouring tracks in order to avoid excessive cross coupling. Howe [I21 provides formulae for the evaluation of cross-coupling, and these are surnmarised in eqns. 20.15 - 20.19.
For 50 R coupled lines in 1.57 mm triplate with E, = 2.2, it can be shown that, for s/b = 1, the coupling factor is -40 dB, and for s/b = 2 it is -66 dB. A minimum distance between tracks corresponding to s/b = 2 was chosen, corresponding to 5 mm between track centres.
Conical conformal microstrip tracking antenna
Conical conformal microstrip tracking antenna
rn~crostrlp
probe tab
50a tnplate track
feed track
7.62 rnm
cross-section
plan (in tr~plate)
Fig. 20.14 Feed-point termination
cone apex
1171
20.4.5 Feed-point terminations The triplate hybrid network is connected electrically to the antenna elements on the upper microstrip layer via four probes soldered to the track terminations. These probes possess a flat tab to enable a clean soldered joint to be made at each triplate junction. A typical track termination is shown in both plan and cross-section in Fig. 20.14. A discontinuity of this type in triplate, however, tends to generate parallel-plate waveguide modes which emanate from the probe and couple to adjacent tracks, degrading circuit performances. These modes may be suppressed by a grid of conducting pins surrounding the discontinuity. The grid design has been taken from the positions of the mode suppression screws in standard SMA surface-launch connectors. The grid is also shown in Fig. 20.14. 20.4.6 Track lengths The individual track lengths of the feeding network must be accurately calculated and realised in order to avoid any phase error at the antenna ports. The situation is complicated by the need to design these tracks on an opened-out section of a cone. For convenience and to facilitate the drawing of the circuit mask, the tracks were divided into two classes: radial and circumferential. These are shown in Fig. 20.15 together with the shape of the substrate. The angular width of the substate is given by the expression
Om,,
=
360 sin 0, degrees
(20.20)
where 0, is the semi-angle of the cone of which the substrate is a part. For the required 0, = lo0, Om, = 62.5'. The circumferential track is just an arc of a circle of radius r centered on the cone apex. Its length a, can be expressed in terms of its angular width AO: 7cr a = AO180
radial track
/ clrcurnferent~al track
Fig. 20.15 Types of triplate track on opened out conical surface
where A0 is in degrees The length of a radial track is simply its physical length along a radial line from the cone apex. This track classification is particularly useful in that all circumferential tracks are parallel and are always perpendicular to radial tracks, thus simplifying the design of 90" bends. The main design problem, however, is related to the hybrid couplers. The use of radial rather than parallel tracks results in unequal circumferential track lengths, as illustrated in Fig. 20.16, and thus introduces phase errors. The typical phase error, however, is only 1.3' at each hybrid, resulting in a maximum of 2.6' for each antenna port. These errors are negligible in comparison to that expected at the electrical connections between triplate and antenna elements, and can thus be safely ignored.
1 1 72
Conical conformal rnicrostrip tracking antenni,
Conical conformal microstrip tracking antenna
20.4.7 Overall design The hybrid network was designed for the cone (semi-angle 10' and length 300 mm) with the substrate extending to the base perimeter. The substrate width was taken to be 55 mm, which is the minimum possible to enable all circumferential tracks to be spaced apart by a minimum of 5 mm according to the criterion given in Section 20.4.4. These dimensions are indicated in Fig. 20.15. The circuit layout is shown in Fig. 20.17, where each track is represented by a line. Extra quarter-wavelength sections of track have been added to create 180' hybrids from 90" hybrids as required. All other tracks have been designed, with due regard to their radial distance from the cone apex, to ensure correct phase matching at each antenna port.
mode suppression grid circle
\
output pwt
cone apex
\substrate periphery
Fig. 20.17 Final hybrid-circuit layout
Fig. 20.16 Phase error at each hybrid
It is of interest to note the position of the first 90° hybrid in the difference channel. This position, although resulting in exceptionally long input tracks, gives the network an elegant symmetry and minimises the total number of bends in the tracks. On bending the triplate around the cone, it also results in all input ports being situated within the same region of the cone base.
antenna element
radius 47.32mm
20.5 Conical antenna array
The dual patch antenna elements are printed on a microstrip layer lying immediately above the triplate hybrid network to form the conical antenna array. As such, there is an inherent problem associated with the different radii of curvature of the two layers. It is necessary to ensure that, on assembly, each antenna-
trtplate track termmatson
Fig. 20.18
Geometry of triplatelmicrostri~interface
1 7 73
1 1 74
Conical conformal microstrip tracking antenna
Conical conformal microstrip tracking antenna
element feed point lies immediately above its associated triplate output port to enable the two to be joined electrically. Consider the situation as depicted in Fig. 20.18. It is assumed for the moment that both the microstrip and triplate layers terminate at the base of the cone and that the connecting probe is in position. From Fig. 20.17 it is known that the triplate track terminations are situated midway along the substrate, and thus 272.5 mm from the apex of the 20' cone of which the circuit is a part. The radius of the cone at this point is then 272.5 sin 10' = 47.32 mm. From the geometry it can then be shown that the antenna element feed point, which is at a height of 2.38 mm above the circuit, is situated cone aoex
7 175
20.6 Substrate fabrication 20.6.1 Overview There are several stages involved in the fabrication of the three substratelayers comprising the antenna array and feeding network. The procedure commences with the drawing of all the masks, corresponding to the two sides of each substrate layer, on a CAD computer-graphics terminal. The output, in the form of photoplots, are then reduced to the required scale via precision photographic reproduction. The resulting masks are used in the substrate etching process. The three substrates are then cut to the correct shapes. All necessary holes are then drilled and various sections are milled out. Finally the two triplate components are bonded together. At his point the substrates are ready for bending into the required shape, prior to final assembly and attachment of electrical connectors. 20.6.2 Mask drawing and preparation A standard CAD system was used to produce the masks. The main difficulty in drawing the feeding network was due to the fact that the majority of tracks are arcs of circles of large radius of curvature. This necessitated defining each curved track by a set of three points which could then be used by the CAD software to generate the curve passing through the points. By necessity, a rectangular co-ordinate system was required, and the origin was defined at the lowest point of the substrate periphery, denoted as '0' in Fig. 20.17. The rectangular co-ordinates of each point are easily calculated from its radial distance r from the cone apex and angle 0 from the central axis passing through the origin: y = 300 - r cos 0
x antenna element
Fig. 20.19
micrdstrip substrate outline
Layout of antenna array elements
on another coaxial 20" cone at a radius of 49.66 mm, corresponding to a distance of 286.0 mm from the apex. Thus the feed points of all four antenna elements on the opened-out microstrip substrate surface will lie on an arc of radius 286.0 rnm centered on the cone apex. This is depicted in Fig. 20.19, where the microstrip track of each element is oriented along the radius at that point to ensure that, in the final assembly, all elements lie along the generatrices of the cone. The base of the substrate was chosen to allow an 8 mm overlap by the triplate on final assembly to facilitate the attachment of edge connectors. The overall width of the microstrip substrate was taken to be 70 mm. This ensured a one wavelength ground plane extension beyond the forward patches in order to minimise edge diffraction effects. The antenna elements are situated at equal angular intervals on the substrate as shown in the Figure.
=
r sin 0
(20.22)
where 300 is the radial distance in millimeters from the substrate lower periphery to the cone apex. The substrate periphery was included in the mask to facilitate cutting to the correct shape. A second mask was drawn for the upper triplate ground plane comprising the outer substrate periphery and four small circular non-metallised regions opposite the antenna output ports. These regions prevent the probes from shortcircuiting to the ground plane and form a quasi-coaxial region with the probes, of approximately 50 C2 impedance. Outside the substrate periphery, each of the two masks was provided with four fiducial crosses at the corners to enable the two to be lined up accurately with each other during the etching process. A further mask was drawn, comprising only the outer substrate periphery, to define the shape of the lower triplate half. In a similar manner the two masks for the microstrip antenna substrate were drawn, one comprising the four antenna elements and the other containing the four circular non-metallised regions at the feed input positions. The antenna
1 176
Conical conformal microstrip tracking antenna
mask was drawn using four identical dual patch elements oriented at the angks shown in Fig. 20.19. All masks were drawn to a scale of 2: 1, and the resulting photoplots were then photographically reduced and printed in reverse on clear plastic film to form the final masks. 20.6.3 Etching
Etching involves the removal of copper cladding in a controlled manner in order to print the mask pattern onto the surface of a substrate. The process is standard in a well equippedlaboratory and will not be described here. It should, however, be emphasised that the alignment of the two masks defining both the triplate circuit pattern and its upper ground plane (as well as those of the antenna substrate) is crucial in order that the circular non-metallised regions in the ground plane are accurately positioned at the antenna feed ports. For this purpose holes were punched, centered on each of the four fiducial crosses on each mask. Four additional holes were drilled through the substrate, and the three layers were aligned by the use of dowel pins prior to etching. This process gives an alignment accuracy of 0.1 mm.
Conical conformal microstrip tracking antenna
1 177
of Duroid were prepared for filling the cut-outs at the track input points. The complete assembly is shown in Fig. 20.20. 20.6.5 Triplate bonding
Bonding of two substrates under high pressure and temperature, using an intermediate layer of thermoplastic dielectric film, is a well established procedure in microstrip circuit technology, and details are given in the Rogers' literature [4]. For the case of RT/Duroid. the surfaces are pre-etched to provide a key for the thermoplastic (Dupont FEP) film by immersion in a sodiumnaphthalene solution. Alignment of the two components was maintained during bonding by dowel pins passing through both the bolt holes and edge connector holes. A heated hydraulic press was used to provide the necessary pressure and temperature.
20.6.4 Substrate preparation
After etching, the substrates were cut to shape and drilled while still in their flat state. For the case of the upper microstrip layer, holes were drilled at marked positions on each patch to take the short-circuit grid of conducting pins. Additional holes, defined by the mask, were drilled through the substrate to take the bolts through which the antenna would eventually be attached to the cone. The position of the feed probe for each antenna element had been defined by a small circle of etched copper on the microstrip track, and this was accurately drilled to a diameter of 0.92 mm to take a standard OSSM probe. In a similar manner, the various holes in the upper triplate layer were drilled. These comprised: the antenna feed ports, the circular grid of mode-suppression screw holes (defined by the mask), bolt holes (aligned with those of the microstrip substrate) and two holes on either side of the track input points to take the triplate edge connectors. The two triplate halves were then brought together and the various hole positions were marked through to the lower substrate, including the positions of the track input points. The bolt and edge connector holes were then drilled as before. It is impossible to solder the antenna feed probes into position prior to bonding the triplate halves and subsequent bending. Consequently, in order to gain access to the track terminations, a circular hole centered on the output probe position and of 10 mm diameter was milled out at each of the four antenna feed points on the lower triplate half. In addition, a semicircular cut-out was milled at each track input point to enable the edge connectors to be attached. Four Duroid discs were punched out to fill the feed-probe holes, and were drilled to take mode-suppression screws. Finally small semicircular discs
Fig. 20.20 Substrate components
20.7 Forming the antenna 20.7.1 Bending the substrates
It is possible to bend RT/Duroid at room temperature. However, the large degree of springback imposes an excessive strain on the substrate when it is
1 1 78
Conical conformal microstrip tracking antenna
clamped in postion and may result in a fracture. It is necessary to first stressrelieve the substrate by passing it through a temperature cycle which exceeds the PTFE glass/rubber transition temperature of 130°C; beyond this temperature, stresses are minimised [4]. For this purpose, two conical aluminium mandrels were fabricated for bending both the triplate and microstrip layers. Each mandrel contained an inner depression for seating the substrate, and an outer depression to take a stainless-steel clamping band. In each case the substrate and band were bent slowly around the mandrel at room temperature and held in postion with studs. The assembly is shown in Fig.20.21~.The mandrel was then placed in an oven at 100°C in an inert atmosphere. The temperature cycle consisted of a warming-up period of one hour to 180°C, one hour at that temperature, and a one hour cooling-off period. Upon disassembly, no major faults were seen in either the dielectric or the copper ground plane, except for some very minor wrinkling in the copper. The smooth walls of both the mandrel and clamping band provided excellent surfaces against which the substrate could rest and thus avoid distortion. Any springback tendency for both substrates was found to be minimal.
a
Conical conformal rnicrostrip tracking antenna
into place on both the patch surfaces and the ground plane. These can be seen in Fig.20.216, which shows the microstrip layer in its final shape, prior to assembly.
b
the antenna substrate
c
the triplate (fully assembled)
the mandrel
Fig. 20.21 Bending the substrates
20.7.2 Attachment of components Once the substrates have been bent into shape, the various probes, pins and mode-suppression screws can be attached. For the upper microstrip layer, the short-circuit grids of pins were inserted into the patch elements and soldered
7 7 79
1180
Conical conformal microstrip tracking antenna
For the case of the triplate layer, the antenna feed probes were inserted through the access holes in the lower substrate and their tabs soldered into place on each track. Small relief channels were cut into the circular Duroid discs into which the soldered tabs could sit without creating an air gap, and the discs were pushed in place into the four access holes, ensuring that the mode-suppression screw holes lined up with those of the upper triplate half. The discs were held in position by the mode-suppression screws themselves. The countersunk screw heads were embedded into the upper ground plane to produce a uniformly smooth surface. Both the upper and lower ground planes around the screws were coated with a conducting silver paint to ensure good electrical continuity. In order that the probes simulate a coaxial line, it is essential that good electrical continuity exists between the upper triplate ground plane and that of the microstrip in the vicinity of the probes. It is very unlikely that this can be guaranteed when the two substrates are finally brought together because of the large surface areas in contact with each other. For this reason thin metallic shims, milled from the flanges of standard OSSM surface launchers, were inserted past the probes and bonded to the ground plane with conducting epoxy. The shims were bent slightly to conform to the shape of the triplate surface. The final triplate assembly is shown in Fig. 20.21~.
Conical conformal microstrip tracking antenna
7 18 7
feed holes in the microstriplines and the two units bolted together with nylon screws. Finally the probes were soldered into place and DC electrical continuity was checked between the exposed triplate track terminations and the patch surfaces. 20.7.3 Final assembly The cone itself was machined from aluminium. A de~ressionat the rear end allowed the triplate to seat properly while the upper microstrip layer could rest on the main body of the cone. The remaining bolt holes were used to attach the assembly to the cone using nylon screws. The free ends of the substrates were brought together and held in position with Duroid fishplates against the pressure of the residual springback. The final procedure involved the attachment of the triplate coaxial connectors. These were standard OSM in edge launchers. Curved shims were fabricated to interface between the flat connector flanges and the curved substrate surface. After soldering each centre tab to the exposed triplate track, the access cut-out was filled with the semicircular Duroid disc and the complete connector unit with shims was screwed into position. The final antenna assembly is shown in Fig. 20.22. 20.8 Antenna performance
Fig. 20.22
Final antenna assembly
On mating the triplate and microstrip substrates together, the shim surfaces were coated with a thin layer of conducting epoxy to ensure good electrical continuity between the substrates. The probes were then inserted through the
Electrical measurements have been carried out on the conical conformal antenna over a 1 GHz bandwidth centered at 10 GHz. Both sum and difference radiation patterns have been obtained from all four ports of the antenna using a linearly polarised source antenna. With reference to Fig. 20.8, the scan axis is taken to be the x-axis with the individual antenna elements oriented at 45' to this axis. In this way, both the difference-channel ports could be tested individu-' ally without needing to rotate the cone. From Section 20.4.1 it will be recalled that the two difference channels are sensitive to orthogonal linear polarisations; thus the equi-phased channel will receive horizontally (x-directed) polarised signals, whereas the alternate 0°, 180" channel will receive vertically @-directed) polarised signals. Measured radiation patterns at 9.5, 10.0 and 10.5 GHz are shown in Fig. 20.23 for the two sum channel ports and in Fig. 20.24 for the two difference ports. Fig. 20.25 shows the measured response in one sum channel to rotating linear polarisation at 10 GHz. Finally, Fig. 20.26 shows the measured antenna boresight gain matched to the linearly polarised source antenna for vertical @-directed) polarisation. The antenna-performance results of Fig. 20.23-20.26 require some detailed explanation, because, on careful consideration, many characteristics cannot, of course, be explained by recourse to conventional (planar) array behaviour. The subjects of grating lobe supression, axial ratio, gain and tracking slope are now
1 182
7 183
Conical conformal microstrip tracking antenna
Conical conformal microstrip tracking antenna
considered in more detail. This treatment is largely qualitative owing to the electromagnetic complexity of the problem and the bounds of this book. A detailed mathematical treatment of conformal array antennas may be found in References 13 and 14.
demand explanation. The most prominent feature is the lack of grating lobes in the sum channel for horizontal polarisation, whereas those for vertical polarisation are well developed. This phenomenon may be explained, most easily in the porl 1
- horizonlal polarisation
port 2 -vertical oolarisotion
port 2
port 1
m P
-301
-30
I
ri
-40
-20
9.5 GHz -20
0
-301 20
9.5 GHz
9.5 GHz
9.5 GHz
u
40 -40 -20 Azimuth anale (dea
0
20
-40
-20
0
20
40
40 -40 -20 Azimuth angle (deg. )
Or
m u
I 0
20
40 -40 -20 Azimuth angle (deg.) 0
0
20
0
20
40
0
20
40
-2 0
I -40
I -20
40
Or
-30
-40
20
0
10.0 GHz I
-20
0
20
40 0r
L
,
40 -40 -20 Azimuth angle (deg.) 0r
-10
-20
-30
B -2 0 I \ I \ I \ l
\ \ 10 5 GHz
\I -40
-20
0
20
40 -40 -20 Azimuth angle (deg.)
0
- vertical
-- horizontal
20
1
40
polarrsatlon
Fig. 20.23 Sum channel radiation patterns (measured)
20.8.1 Grating lobe suppression Although the sum and difference patterns are well defined over the frequency band in the angular region close to boresight, there are several features which
-30 -40
10.5 GHz -20
0
-3 0 20
40 -40 -20 Az~muthangle (deg.)
Fig. 20.24 Difference channel radiation patterns (measured)
transmit mode, by the difference in the fields radiated towards an observation point between a visible antenna element and one hidden by the presence of the cone. Use of GTD surface-field methods in the analysis of radiation from conical arrays is well documented [15] and only a summary need be given here. With reference to Fig. 20.27, each diametrically opposed pair of array ele-
1184
Conical conformal microstrip tracking antenna
Conical conformal microstrip tracking antenna
1 185
ments are equi-phased with respect to the observation point in the sum channel. The opposite pair, in phase quadrature, may be ignored in this explanation. Grating lobes will appear when the path difference between diametric elements at the observation point is an integral number of wavelengths. The cone diameter at the centre of the array elements is 110 mm, and therefore the horizontal distance between diametric pairs is 1 1 0 ~ = 4 78 mm. At 10 GHz the condition for grating lobes is that sin 0 = &Id = 30178 = 0.384; this corresponds to 0 = ) 22.5', and indeed corresponds exactly to the measured positions at 10 GHz for vertical polarisation. At 22.5' from boresight, one array element is in the lit region and is therefore sensitive to both vertical and horizontal polarisations. The diametrically opposed element, however, is in shadow. In this
iurface ray
- 40
-20
0
20
LO
I
A z ~ m u t hangle (degrees)
Fig. 20.25 Rotating linear sum pattern at 10 GHz (measured)
I
i1 1 I
Fig. 20.27 Rad~atlonfrom a h~ddenarray element on a conical surface
case a surface ray creeps around the cone on a geodesic with respect to the observation point, radiating tangentially as it proceeds. The ray that is eventually directed towards the observation point will radiate from the cone horizon as perceived by the observer. Now the magnetic field vector associated with the surface ray remains parallel to the cone surface over which it travels, and therefore the observer will perceive this vector as parallel to the cone horizon, which itself subtends a small angle to the horizontal at the 22.5" scan angle. This implies that the diffracted field is predominantly vertically polarised as seen at the observation point, and will thus contribute to the observed grating lobes seen in vertical polarisation, but not to horizontal polarisation. This further implies that the grating lobes in the vertical polarisation pattern are about 6 dB higher than the mean signal level at the same scan angle in the horizontal polarisation pattern. On normalising the co-polar peaks to each other in Fig. 20.23 this is seen to be indeed the case. 20.8.2 Axial ratio The second important feature requiring explanation is the difference in boresight amplitude in each sum channel between vertical and horizontal pol-
Fig. 20.26 Measured antenna boresight gain in sum channel for vertical polarisation
1 186
Conical conformal microstrip tracking antenna
Conical conformal microstrip tracking antenna
1187
arisations. The effect is reversed between the two ports, so that for one port the vertical component exceeds the horizontal by an average of 3.5 dB across the frequency band, whereas for the other port the reverse is the case. The effect is clearly visible in the response to rotating linear polarisation, as seen in Fig. 20.25. ~ , = c o s ( w t + 2~ * ~ )
E, ' C O S W ~
\
Thus the maximum amplitudes in the vertical and horizontal directions are given by:
and the ratio in decibels is
X
Fig. 20.28 Effect of phase error in the sum channel
For the opposite hand of circular polarisation the 2 factor changes sign and:
This feature may be explained if it is assumed that a constant phase error exists at the input to each antenna array element. This may be due to differing path lengths at the interface between the triplate and microstrip layers. Consider the situation depicted in Fig. 20.28 for the case of two adjacent elements in phase quadrature, each element polarised at 45' to the vertical. Let one antenna element possess a constant phase error 4 with respect to the other, both radiating at equal amplitude. The time-dependent electric field amplitudes for one hand of circular polarisation are then: Element 1 : El = coswt Element 2 : E2 = cos(wt
+ 4 + Z) X
The resultant component in the + y direction is then (ignoring constants):
Ey
= coswt
+ cos(wt + 4
X
and in the + x direction: E, = coswt - cos(wt
+ - 4 + -)2 X
(20.24)
=
- I0 log,,
r3
cot2
-
= -Rm,
This is equivalent to saying that the difference between vertical and horizontal polarisation is reversed between the two sum channels, as seen in the measured results. The average measured difference of 3.5 dB is then equivalent to an inherent phase error of 22.5'. It must be remembered, however, that this phase error is distributed around the four antenna elements in a random manner. It is therefore clear that the inherent phase error in each element is typically 5.5'.
20.8.3 Antenna gain The measured antenna boresight gain, shown in Fig. 20.26, depends to a great extent on the tilt angle of the polarisation ellipse, which in turn depends on the inherent element phase error as discussed above. As such, the measured am-
7 188
Conical conformal microstrip tracking antenna
plitude is somewhat irrelevant, and it is the shape of the response as a function of frequency which is of interest. The gain around 10 GHz exhibits a sinusoidal frequency dependence which drops off rapidly above 10.3 GHz. Two mechanisms are attributable to this shape. In the former case the element phase error is changing as a function of frequency, thus changing the tilt angle of the polarisation ellipse, resulting in a fluctuating vertical polarisation component. The latter effect is attributable to the bandwidth of the elements. With reference to Fig. 20.2, the single patch return loss increases to - 3 dB at 10.5 GHz. This implies that half the power is no longer radiated. The gain is therefore expected to drop by 3 dB from that at resonance. It can be seen in Fig. 20.26 that this is indeed the case.
Conical conformal microstrip tracking antenna
1 189
radius of the antenna substrate, resulting in a spacing of several wavelengths between adjacent elements. However, it is noted that the measured 12' coverage could be acceptable for many purposes.
20.8.4 Tracking slope Fig. 20.29 shows the tracking characteristics at band edges and centre extracted from the sum and difference patterns. The tracking parameter is defined as the ratio, in amplitude, of the difference signal to the sum signal, and is plotted as a function of scan angle for both vertical and horizontal sum channel patterns. It is important that the tracking slope remain constant over the angular region of interest in order that a single parameter at each frequency may be used to locate the angular position of a target. It is evident from the Figure that, for the conical conformal antenna, this is true over an angular width of about 12' across the frequency band; although some degradation is seen at 10.5 GHz. This angular width is totally dependent on the positions of the two main lobes in the difference channel, which are in turn dependent on the cone circumference at the antenna elements. The only means of increasing this coverage is to mount the elements closer to the cone apex. With the mechanical construction described in this Chapter this is not possible. The 12" angular coverage is thus a limitation of the present design, but may be acceptable for many purposes. 20.9 Conclusions and future developments This Chapter has described in detail the application of microstrip technology to a particularly demanding requirement - the fabrication of a conical microstrip tracking antenna. The antenna element design has centered on the need for acceptable endfire performance and a suitable solution has been described. The problem associated with the siting of the tracking circuitry has been solved by the use of an independent triplate feed network located beneath and adjacent to the printed antenna substrate. This, however, raises additional problems in the electrical interfacing of the two units when mounted in position on the surface of the cone. One possible technique has been described in detail. The antenna electrical performance has been measured and analysed, and suggestions have been given to explain some of the peculiarities and trends in the data. Angular tracking coverage is found to be somewhat limited owing to the minimum bend
X ----
(vertical)
X (horizontal)
Fig. 20.29
Tracking characteristics of conical conformal antenna (measured)
The development and fabrication of the antenna has shed light on the various engineering problems associated with the design of a cone-mounted system. In particular, the need for designing the antenna and feed circuitry on an opened-
1190
Conical conformal microstrip tracking antenna
out conical surface has emphasised the procedures necessary for non-linear track layouts. It is evident, however, that several enhancements to the design are possible in order to improve further the electrical performance and to facilitate easier manufacture; these are now briefly described. The antenna bandwidth, being a function of both the thickness and dielectric constant of the substrate, may be increased by increasing the former and decreasing the latter. However, the improvement is limited by the onset of higher order modes, which result in additional circuit inductance and degraded VSWR. The effect has been used to advantage in a novel procedure outlined by Griffin [16]. He uses the unwanted inductance, together with that of the probe feed, of a microstrip disc antenna to design an impedence-matching network in the triplate feed track. He reports impressive performance, using a thick, low dielectric constant (8, = 1.2) substrate, with a VSWR bandwidth of 20%. The technique is applicable to any probe-fed patch antenna. Increased antenna directivity at endfire is desirable to reduce the high sum channel grating lobes seen in Fig. 20.23. It can readily be shown that an eight element linear patch phased array will suppress all sidelobes in the forward hemisphere to below - 10 dB over the 20% bandwidth, provided the interelement spacing is less than 0.45 wavelengths. antenna elements printed on this layer antenna substrate (expanded foam) upper triplate (power divlsion and broad bonding) -lower tr~plate (tracking) Fig. 20.30 Cross-section through a broadband conformal antenna
A single triplate circuit containing the hybrid tracking network together with power-division and impedance-matching components is not feasible within the limited space available over the cone circumference. A more attractive solution is to share the circuitry between two triplate layers linked together electrically. By careful choice of track impedances, the two layers could be made extremely thin and bonded together as one unit before being bent into shape. The use of a thick low-permittivity foam as the antenna substrate for broadband performance means that the antenna elements cannot be printed onto such a surface. A possible solution would be to print the arrays onto a thin sheet of copper-clad Kapton or similar material, and then to bond this to the foam, which will have been pre-formed into conical segments and bonded to the triplate. The final antenna assembly would therefore comprise six substrate layers as shown in Fig. 20.30.
Conical conformal microstrip tracking antenna
1191
Acknowledgment
The authors wish to thank the directors of the Marconi Company Ltd. for permission to publish this chapter, which is an expanded version of a paper presented at the Military Microwaves 1986 Conference held at the Metropole Hotel, Brighton, England, 24th-26th June 1986.
20.10 References JOHNSON, R.C., and JASIK, H. (1961): Antenna engineering handbook, (McGraw Hill, NY, pp. 7-10) RUDGE, A.W., et al. (1986): Handbook of antenna design, (Peter Peregrinus) Section 7.4 JAMES, J.R., HALL, P.S., and WOOD C, (1981): Microstrip antenna, theory and design, (Peter Peregrinus) Deduced from Fig.3.16~ Mektron Circuit Systems Ltd. (1983): Product information-RTIDuroids; and private communication HALL, P.S., WOOD, C., and JAMES, J.R. (1981): Recent examples of conformal microstrip antenna arrays for aerospace applications. 'Antennas and Propagation'. IEE Conf. Publ. 195, Pt. 1, pp. 397-401 WEINSCHEL, H.D. (1979): Measurement of various microstrip parameters, Proc. Workshop on Printed Circuit Antenna Technology, New Mexico State University, pp. 2-1 POST, R.E., and STEPHENSON, D.T., (1981): The design of a microstrip antenna array for a UHF space telemetry link, IEEE Trans. AP-29, pp. 129-133 BAHL, LJ., and BHARTIA, P. (1980): Microstrip antennas (Artech House, London) Reference 3, Section 4.6 Reference 2, Section 12.6 MATTHAEI, G.L., YOUNG L., and JONES, E.M.T. (1964): Microwave filters, impedance matching networks and coupling structures (McGraw Hill, NY Section 5.07) HOWE, H. (1974): Stripline circuit design (Artech House, London) RIZK, M.S.A.S., MORRIS, G., and CLIPTON, P. (1985): Projected aperture synthesis method for the design of conformal array antennas. 'Antennas and Propagation' IEE Conf. Publ. 248, pp. 48-52 SHAPIRA, J., FELSEN, L.B., and HESSEL, A. (1974): Ray analysis of conformal antenna arrays, IEEE Trans, AP-22, pp. 49-63 Reference 2, Section 11.6 GRIFFIN, J.M. (1985): Broadband microstrip disc antenna for satellite communications, M.Phil./PhD Transfer Thesis, GEC Hirst Research Centre, Wembley, Middx.
Chapter 21
Microstrip field diagnostics P. G. Frayne
21.1 Introduction
In this Chapter we are concerned with the relatively undeveloped subjec of surface-field metrology for 'open' microstrip and other related 'open' plaiiar transmission structures. Early measurements on microstrip lines were aimed at determining the dispersive properties of the medium using a number of different techniques, some of which are listed below: (a) Measurements on open-circuited and short-circuited resonant microstrip
lines (6) Ring-resonator techniques
(c) Variation of phase shift of a line with frequency ( d ) Nodal-shift techniques None of these methods, however, provide much insight into the detailed field distributions that actually reside on the conductors. Liquid crystals have been employed to render mode patterns and regions of high electric field 'visible' to the unaided eye, but the spatial resolution and general applicability of the technique is very limited. The growing need for reduction in the size, weight and cost of millimetric guidance and radar equipments has stimulated the design of circuits with a much higher degree of component integration than is possible with the modular approach to circuit construction. With the growing complexity of circuit-integration techniques, both fault location and test procedures become increasingly difficult. The accessible R F input and output ports provide little information about the detailed internal operation of the system, and the conventional network analyser, much valued for the assessment of isolated modular components, is of limited use as a diagnostic for large-scale circuits. The use of a greater degree of component integration not only makes circuit evaluation difficult, but can also create severe problems owing to unwanted electrical coupling between components.
1194
Microstrip field diagnostics
Microstrip field diagnostics
21.2 Surface analytical techniques To the author's knowledge there have been at least two prior experimental investigations of possible surface diagnostic techniques for microstrip, namely the work of Dahele and Cullen [I] and also that of Ladbrooke [2]. The detailed plots of the near-field radiation pattern of a polyrod antenna obtained by Neumann [3, 41 are also of interest in the context of field-plotting techniques. In the work of Ladbrooke, a special jig was constructed which enabled the top microstrip conductor, defining the circuit pattern, to be moved independently of the ground plane and the 50R microstrip feed line. The ground plane contained a small disc probe 0.1 mm in diameter, separated from the surrounding region by an annular gap. The thin dielectric sheet which supported the microstrip circuit was pressed into contact with the ground plane and feed line. The probe disc was connected to the inner conductor of a miniature coaxial cable whilst the outer conductor was grounded. Connection of the microstrip feed and probe output signal to a vector network analyser enabled the circuit transmission (amplitude and phase) to be measured over a wide frequency range. The measurements presented in Ladbrooke's paper appear to be restricted to longitudinal distributions on open-circuited microstriplines. Evidence for the excitation of surface waves beyond the edge of the open microstrip termination was discussed in a later paper. It is interesting to note that a distortion of the standing-wave pattern similar to that discussed in the books by Ginzton [5] and MOI'-ornery [61. due to probe reactance, was actually observed, but accredited by Ladbruoke to a mismatch of the feed line. The investigation by Dahele and Cullen was more concerned with evaluating, the response of a small coaxial probe with an extended inner conductor to a calculable RF electric-field distribution produced by a boxed cylindrical conductor. A wire, 1.6 mm in diameter was supported along the axis of wide rebate (of rectangular section) cut in a metal plate. The rebate was closed off by a movable plate which also supported the coaxial probe. The inner probe conductor protruded about 2mm into the waveguide region and the probe tip was 6.4 mm from the surface of the wire. The experimentally determined VSWR pattern agreed well with theoretical predictions, and the experiment was subsequently repeated after replacing the cylindrical wire by a flat microstrip line. In a more recent paper accredited to Schwarz and Turner [7], a co-planar waveguide probe is discussed which uses a miniature bismuth bolometer for the direct detection of the microwave signal at the probe tip. Although the bolometer can be made very small, it suffers from the disadvantages of being restricted to scalar measurements and also the need to be specially constructed for each width of co-planar waveguide under investigation. Co-planar waveguide probes have been investigated in our own laboratory where a beam-lead Schottky barrier diode was employed for detection purposes. In order to avoid over-coupling the probe to the co-planar waveguide circuit, it was necessary to employ a very thin low-permittivity substrate for supporting
1195
the probe circuitry. A highly resistive probe circuit was also considered desirable in order to reduce the possibility of internal probe resonances and reflection of the microwave signal from the probe metallisation.
Fig. 21.1
Scanning-nework probe-plotting table
21.3 Scanning-network probe The scanning network probe was originally intended for use as a circuit diagnostic of high frequencies above the normal working range of commercially available network analysers. With this application in mind, a mechanically stable, high-precision two-axis transport mechanism shown in Fig. 21.1 was constructed. A conventional leadscrew drive was employed which had a minimum incremental step size of 0.5pm. Owing to the extreme fragility of the probe sensors necessary at frequencies above 100GHz the majority of the data presented in this Chapter was obtained over the frequency range 26-40 GHz with the coaxial probe shown in Fig. 21.2. The probe is very simply constructed from a rigid single-bore alumina tube of 0.5 mm external diameter. The alumina is metallised on its outer surface and the inner conductor extends approximately 0.2mm beyond the end of the tube. The other end of the probe is terminated in an adjustable cylindrical post, which, in conjunction with a tunable backshort, effectively launches a TE,, waveguide mode. The coupled signal from the probe is fed to a dual-channel homodyne (phase and amplitude) detection system. In order to eliminate the need for soldering the ground plane to a flat rigid backing plate, a vacuum clutch was employed, which had the additional facility for mounting coaxial microstrip launchers anywhere around its periphery. Since the
7 796
Microstrip field diagnostics
probe shown in Fig. 21.2 is axisymmetric, it may be used for recording the distribution of electric field over any irregularly shaped planar circuit configured in open microstrip, slotline, co-planar waveguide or co-planar stripline. The completely automatic data storage and processing facility is extremely versatile in so far as it provides a range of options such as monochrome and colourcontouring routines or a three-dimensional representation of the measured data. The contours may also be sectioned so as to generate a plot of the voltage-standing-wave ratio. An axis of symmetry would normally be selected for this purpose so as to ensure (a) the probe-strip capacitance remains sensibly conat stant along the line of measurement and (b) the magnetic coupling c a n c e ~ ~the VSWR maxima and minima.
Microstrip field diagnostics
7 197
on the two surfaces of the top microstrip conductor are different. It is significant, however, that the edge conditions for the two surfaces are identical, which leads to a common axial periodicity of the charge and current densities on a microstrip line. for, example. z
Fig. 21.3 Probe geometry for deriving near-field pattern of a monopole from an equivalent azimuthal magnetic current M+
Fig. 21.2 26-40 GHz monopole probe
21.4 Theory of the monopole probe
When the tip of the probe approaches an edge discontinuity, the capacitive coupling to the top conductor rapidly decreases. The recorded field intensity, however, does not fall off as rapidly as might be expected, owing to a local enhancement of the surface charge and current densities due to the skin effect. Close to an edge, the recorded distribution can only be regarded as a qualitative indication of the true excitation. However, this apparent failure of the technique does not seriously detract from the physical insight into high-frequency circuit behaviour that is revealed by the tutorial nature of the contour maps. For many purposes it is irrelevant that the magnitude of the charge and current densities
An exact theory for the near field coupling between a short monopole and a narrow conducting strip does not exist at the present time. A realistic theory for the charge and current-density distributions on the top microstrip conductor would need to take into account the lateral skin effect and the proximity effect due to the ground plane. Reference 8 and Fig. 21.3 show that if the probe were considered to be a transmitter located in free space, it would generate both radial and axial electric-field components in the near field. Expressions for these components may be calculated in terms of an equivalent azimuthal magnetic current density k , / ~flowing within the annular aperture of the monopole.
7 198
Microstrip field diagnostics
Microstrip field diagnostics
Expressions for the field components are given in eqns. 21.1 and 2 1.2. Conversely, in reception, the monopole will respond to the net radial and axial field components generated by the microstrip line.
1799
In the majority of practical applications of the probe technique, the surface fields arise from a standing-wave distribution rather than a simple travelling wave, so it is more appropriate to calculate the contributions to A: from each half-period zone along the axis of a narrow strip as given in eqn. 21.6 and shown in Fig. 21.4, where 0 is confined to the Y Z plane:
When the monopole is located above the symmetry axis of the microstrip line it will respond not only to the vertical component of the electric field but also to the surface-field gradient taken in the direction of the symmetry axis. The latter form of coupling alternatively may be considered magnetic in origin, as shown in Fig. 21.5. The total coupling to the probe arises from both the conservative and non-conservative sources of electric field, which may be expressed in terms of the vector magnetic potential A , given by
The derivation of an expression for the magnetic vector potential at a height h above a flat conducting strip of finite width and length is straightforward for the case of a steady axial current I;. The appropriate expression is given by
Strictly, the derivation of this expression assumes the presence of a coaxial return circuit of infinite radius. In the case of a high-frequency current in the form of a travelling wave, a number of additional phenomena need to be taken into account. The most improtant of these is the rapid variation of phase over the dimensions of the strip and also the lateral non-uniformity of the surface current due to the skin effect. Owing to the close proximity of the probe tip to the surface of the flat conductor, the effect of electrical-image charges should also be considered in any realistic calculation of the probe response. When the lateral skin effect is neglected and only the axial phase variation associated with a uniform travelling wave is taken into account, the resulting integral equation 21.5 for the axial component of the magnetic vector potential cannot be solved analytically in the near field: cos (kh tan 8) sec 8 exp (- jkh sec 0) dB
(2 1.5)
Fig. 21.4 Geometry for computing the magnetic vector potential at a height h above an isolated conducting strip
In the case of a large VSWR on the strip, the computation of A, is modified to some extent by the fact that the phase varies discontinuously along the length of the line, increasing rapidly by n at the current maxima and remaining almost constant at the voltage maxima. Since the amplitude of the probe signal falls off rapidly with increasing height h, the slow variation of phase at the voltage maxima could be neglected. However, the rapid phase variation at the voltage minima rather implies that the spatial resolution or radius of the probe 'footprint' will be a function of the standing-wave ratio and frequency, and not purely a constant geometrical factor dependent on the probe diameter. By developing the idea of a combined response to the vertical component of the electric field and transverse component of the magnetic field, a simple phenomenological theory for the probe coupling has been derived. Reference to Fig. 21.5 shows that a quasi-static contribution to the probe signal is visualised in terms of more electric lines of force terminating on the central conductor than the sheath owing to its proximity to the charged microstrip. Increasing the length of protrusion h will cause more lines of force to terminate on the central conductor and a reduction in the number of lines terminating on the sheath, which results in a larger potential difference V being induced on the open-circuited coaxial line. The voltage V can be expressed in terms of line integrals around the contours a-b-a and a'-&-a' in a vertical
1200
Microstrip field diagnostics
Microstrip field diagnostics
section through the probe taken along the symmetry axis of the microstrip. Thus
v
=
r ~ . d i +J : , ' ~ . d i
(21.7)
For any other probe location, the line integrals should be replaced by surface integrals over the probe aperture and tip. The circuital EMFs (5,) from the non-conservative sources-may be found from a similar contour integration. Under the assumption that the probe capture area is determined by the sheath radius b and the probe height h, the circuital E M F may be expressed in terms of the mean phase error 4, ( 4 = b&) as given by
120 1
not on the symmetry axis, there will be a net magnetic contribution to the total measured electric field. The analysis of lines in terms of the voltage standing wave ratio implicitly requires that the probe sensor responds either to the conservative electric field or the magnetic field, but not a combination of both. Under these circumstances the vertical component of electric field close to the surface is proportional to the local surface charge density, whereas the-local transverse component of the magnetic field is proportional to the axial current density. Figs. 21.6 and 21.7 give some indication of the probe size necessary for a particular frequency range. In high-permittivity lines the magnetic coupling is relatively large and is proportional to the effective permittivity.
outer conductor radius b dielectric Inner conductor, rad~us a
X
I
Fig. 21.5 Schematic of coaxial monopole probe (2 figs.)
re
If the electric coupling is taken to be predominantly due to the vertical component of the potential gradient E,h, the magnitude of the total coupled electric field k;, and associated phase angle A are given by eqns. 21.9 and 21.10:
I ~ =, I~ , h { l- ( b ~ , ) ~ ) A z tan-'
I
10
I'
frequency IGHz
Fig. 21.6
Travelling-wave amplitude error against frequency (e,,
= 7.7)
(21.9)
2Bej
{1
The second term in eqn. 21.9 represents the magnetic contribution to the total measured electric field associated with a travelling wave, and may be regarded as an error arising from unwanted coupling. The variation of the amplitude and phase errors as defined above are plotted in Figs. 21.6 and 21.7 as a function of increasing frequency for three different probe diameters. If the probe is used to measure the voltage standing wave ratio of a mismatched microstrip line, the magnetic contribution cancels at both the current and voltage maxima owing to the symmetry of the tangential magnetic field along the axis of the microstrip. At some intermediate axial position or a some point
The extension 6 of the central probe conductor beyond the dielectric tube and co-axial screen has a significant effect on the voltage sensitivity and spatial resolution of the probe. Whereas the sensitivity is easily seen to be proportional to 6, the resolution cannot be readily quantified. As shown in Fig. 21.4, the electric coupling must be determined by summing contributions from an area of line equivalent to the probe 'footprint'. Although this area is difficult to calculate, it may be investigated experimentally by comparing data obtained with progressively smaller-diameter probes. A more tractable approach to the problem of obtaining a quantitative validation of probe technique is by detailed comparison of experimentally measured and theoretically computed surface distributions. For example, resonator geometries possessing high symmetry generally have a calculable field distribu-
7202
Microstrip field diagnostics
Microstrip field diagnostics
tion and mode structure. The book by Bahl and Bhartia [9] contains many references to resonant discs, rings and triangular patches, all of which possess high symmetry and are suitable for comparative studies.
Fig. 21.7
Travelling-wave phase error against frequency
(E,
=
1203
The boundary condition at the magnetic wall, [aEpe]',, requires that the azimuthal component of the magnetic field should vanish at the boundary. The roots of the equation J:,(ka) = 0 determine the TM,,,,, resonant modes of the
1.7)
21.5 Resonant microstrip discs
The four disc resonators shown in Fig. 21.8 were constructed on a proprietary substrate of relative permittivity 2.2. Each disc was excited from a 140Q microstrip line which was tapered up so as to match a 50Q ridged waveguide transformer. Provided that the substrate thickness is much less than the guide wavelength, the system can be treated as a T M cavity bounded by perfect magnetic walls. The solution to the wave equation in cylindrical co-ordinates results in the following equation for the vertical component of electric field E2 inside the cavity: where J,(ke) is the Bessel function of order n and k = wJpo~,. The components of the magnetic field are given by
Fig. 21.8 Microstrip disc resonators
cavity. The integer n represents the order of the Bessel function describing the electric field, and physically corresponds to the number of half wavelength changes around the edge of the disc. The integer rn represents the m th zero of
1204
Microstrip field diagnostics
J,(ka) and corresponds to the number of minima in the range 0 resonant frequency of the nm th mode is given by:
Microstrip field diagnostics
< Q < a. The
where c is the velocity of light, K,,, = m th zero of the first derivative of the Bessel function of order n. An expression for the effective radius a, of the disc is given in Reference 9. Eqn. 21.14 was plotted as a function of Q in order to determine the physical radius necessary to tune each mode to a centre frequency of 35 GHz. The comparative theoretical and experimental plots for the T M , ,, TM,, and TM,, modes given in Figs. 21.9-21.11 generally show a striking resemblance to each other except for obvious differences at the feed point. It is evident from eqn. 21.11 that the cavity modes have the same intensity and are spaced in azimuth by (360/2n) degrees. Table 21.1 lists the experimentally determined excitations and angular location of the maxima for each of the three modes investigated. The 'corrugated' edges seen in the theoretical plots are due to the finite size of the sampling grid used for the computations. Since the theoretical model assumes 'perfect' magnetic walls, there are no fringe fields leaking out of the sides of the cavity, which explains why the surrounding ground plane is completely free of detail. The model is incapable of giving the surface field just above the top conductor, but since the two surfaces share the same boundary, it is assumed that the two distributions are identical to within a constant scale factor. In reality, the side walls are imperfect and the field lines leaving the upper surface of the disc must eventually return to the ground plane. Phase plots have shown that a local ground-plane feature is n out of phase with the corresponding feature on the upper surface of the disc as expected. The lack of nodal symmetry seen in Fig. 21.1 1, arises where a particular voltage node in the upper surfack is locally diminished and the corresponding feature on the ground plane is enhanced. This effect is commonly observed, and will be referred to again in the context of microstrip lines. An enhanced ground-plane feature implies either an enhanced leakage of electric-flux lines out of the cavity, or for some reason the distribution within the cavity is not exactly 'mirrored' on the upper surface of the disc. It is encouraging to note from the data given in Table 21.2 that there is very good agreement between the return-loss figures deduced from slotted-line measurements made in the waveguide feed and those deduced from the VSWR in the microstrip line. The VSWR on the line was deduced from a computergenerated axial section taken through a region of the map corresponding to the parallel-sided section of the line which exists between the stepped ridge transformer and the microstrip taper leading to the disc feed point. The good agreement between the two sets of data suggests that the transformer was well matched at the frequency of operation and that the scanning-network probe yields quantitatively accurate data.
1205
7206
Microstrip field diagnostics
Microstrip field diagnostics
1207
7208
Microstrip field diagnostics
Microstrip field diagnostics
7209
21.6 Resonant microstrip triangles
Equilateral triangular patch antennas also possess high symmetry and support a readily calculable TM-mode structure which is discussed in a paper by Helszajn and James [lo]. The electric-field distribution within the microstrip cavity is given by eqns. 21.15 and 21.16 for a triangle centered at the origin with one of its sides normal to the x-axis: where
+ cos
+ cos
[(g+ q) [26;~ r n ] cos
[(z q) +
'1 y ]
rz] cos [ 2 x ( 1 ~m, y
]
(2 1.16)
Table 21.2 Comparison of scalar network analyser and scanning-network probe return-loss measurements for the microstrip disk resonatnrs
Mode
Waveeuide return loss (dB)
SNP return loss (dB)
A,,, is the amplitude of the mode described by the integers m, n, I which must n 1 = 0. Clearly, the integers cannot all be simulsatisfy the conditions rn taneously zero. The patch geometry and resonant frequencies are determined by
+ +
Patches were constructed on low-permittivity substrates (e, = 2.2) with the edge dimension scaled so that each mode was nominally resonant at a frequency of 35 GHz. The E: distribution within the microstrip cavity and the experimental distribution for the upper surface were determined for the TM,,, TM,,, TM,,, TM,, and TM,, modes. The input impedance of the corner feed point generally increased with increasing complexity of the mode structure. The TM,, mode achieved the best match to the tapered 140R feed line and exhibited a VSWR of approximately 1.4. In order to investigate the mode intensity distribution, the signal levels were determined from the area scan data at six equi-spaced test
Table 21.3
Test-point (TP) data for triangular patches
Mode
TP I
TP2
TP3
TP4
TP5
TP6
2:
TM,, Theory Expt.
1.O
+ 0.2
0.0 0.0 0.02
0.25 0.27 0.03
0.0 0.0 f 0.02
0-25 0.34 +_ 0.05
0.0 0.0 $_ 0.02
$ 2
TM,, Theory Expt.
1.O 1.0 $ 1
0.25 0.25 0.03
1 .O
+ 0.1
0.25 0.25 $_ 0.03
2
0.7
TM,, Theory Expt.
1.O 1.0*0.1
0.25 0.14&0.02
0.25 0.14+0.02
0.25 0.05
0.25 0.31 0.04
TM,, Theory Expt.
1.0
+ 0.1
0.0
0.0 0.02
0.25 0.69 0.07
+
0.19
TM,, Theory Expt.
1.O 1.0 f 0.1
0.37
1.O 1.1 f 0.01
0.48
1.0
+
+
1.O
+
1.O
+ 0.04
+
1.O
+ 0.14
0.1
0.25 0.05
+
1.O 1.1 f 0.1
0.0
+ 0.03
1.O
+ 0.05
1.0 0.4
+
+
0.25 1.1 0.1
+
0.0
1.O 0.79 & 0.07
0.48
0.0 $_ 0.02 1.O
+ 0.05
scale X,Y =2.Ommldivision Z~ZdBlievel
Fig. 21.128
Theoretical (E,I2 for TM,, triangular patch mode
Fig. 21.1 2b Experimental IEJ2 for TM,, triangular patch mode
m, Q
5
72 72
Microstrip field diagnostics
Microstrip field diagnostics
points. The measured intensities were normalised with respect to the feed-point intensity and then compared with the theoretical values calculated from eqn. 21.15. The results of this investigation are summarised in Table 21.3 for the five different modes. The theoretical and experimental distributions for the TM,, mode are given in Fig. 21.12. The TM,, mode has particularly high symmetry owing to the equality of the indices n, rn and also the equality of the intensities at the six test points. However, in practice there is considerable variation between the testpoint intensities, and some asymmetry is observed between features on opposite sides of the feed-point axis. It is of interest to note that, among the five modes investigated, the asymmetry maxima, for example, d o not always occur on the same side of the feed-point axis. Furthermore, there are neither observable blemishes in the etch-back process nor irregularities in the flatness of the substrates. Owing to the rather long recording time necessary for some of the plots, frequency drift could possibly account for some of the asymmetries that have been observed. As a result of the foregoing studies, the potential use of the network probe for mode analysis and in situ circuit diagnostics has been demonstrated. The various test pieces have also shown beyond any reasonable doubt that the distributions observed on the upper surface of the metallisation closely resemble those inside the microstrip cavity.
72 7 3
the outer edges of the line is less pronounced in narrow lines and is not observed experimentally because of the overriding influence of the reduction of the probe-coupling capacitance near an edge discontinuity. However, the depression of the axial current density by the skin effect is more pronounced in the wider lines and is clearly resolved by the probe, as shown in Fig. 21.14. Furthermore,
21.7 Open-circuited microstrip lines In order to investigate the mode structure supported by wide microstrip lines and the frequency dependence of the open-circuit terminations, a series of lines were constructed on 0.254mm-thick PTFE glass-fibre-reinforced substrates with a relative permittivity E, = 2.2. The lines were linearly tapered over a distance of 10 mm to a feedpoint impedance of 50 R. Stepped ridge transformers were used to couple the lines to waveguide WG22, and the overall line length of 60 mm was accommodated on a substrate of dimensions 40mm x 80 mm. The area scans for line impedances of 50 and 22 R given in Figs. 21.13 and 21.14 have been optimised to show the overall field distribution, which inevitably results in an apparent loss of detail on the conducting strip. In order to obtain the VSWR pattern, the contours can be sectioned along the symmetry axis of the microstrip line. If the area scan is not required, it is only necessary to record a single axial scan in order to obtain the VSWR. Although the practising engineer will be pleased to learn that high-impedance lines possess relatively simple field distributions, the wider lines exhibit features which are difficult to explain mathematically. In spite of the overall complexity of the mode structure, the distributions have a number of features in common. For example, both the sectioned axial plots (not shown) and the area scans exhibit a long-wavelength periodicity of the VSWR along the length of the line. The tendency for the lateral skin effect to concentrate the current density along
normal to str~p-lmelrnm
Fig. 21.13
50n open-circuited microstripline at 36GHz
there are complicated periodic longitudinal shifts between the VSWR maxima on the strip and those on the ground plane. These shifts are particularly large close to the open-circuit termination. Another striking observation is the lack of radial symmetry of the features over the ground plane owing to a pronounced curvature of the contours, which periodically alternates from concave to convex along the line. This effect is associated with the waxing and waning of the intensity maxima along the microstrip conductor. It will also be observed that a strong feature over the microstrip is generally correlated with a weak feature over the ground plane. It should be noted that the VSWR maxima and minima
72 7 4
Microstrip field diagnostics
observed along a section through the symmetry axis are equi-spaced for sufficiently narrow lines with characteristic impedances greater than about 4 0 0 . This observation demonstrates that the probe susceptance causes a negligible distortion of the measured data in these lines.
normal to str~p-llnelmm
Microstrip field diagnostics
at the input port. However, when the network probe area scan data is correlated with measurements of the return loss, the E-plane, H-plane and cross-polar radiation patterns, a very detailed understanding of the performance of the system is obtained. Area scan analysis is particularly useful for studying the mutual coupling between parasitically coupled array elements, the voltage standing wave ratio on the feed lines, and the relative excitation of directly coupled elements in an array.
scale
X,Y =l.Ornmldivision
Fig. 21.14 22R open-circuitid microstripline at 35GHz
72 75
Z=l.OdB/level
Fig. 21.1 5 Rectangular patch antenna excited at resonance, F = 3 0 5 G H z
21.8 Antenna diagnostics
One of the most important applications of the scanning-network probe technique is to the analysis of the mode structure supported by planar microstrip antennas. Antennas are necessarily open structures and are therefore generally accessible to probing. Knowledge of the surface charge-density distribution, both in amplitude and in phase, reveals a considerable amount of information about the mode of operation of the antenna, which cannot in the case of multi-element arrays be deduced simply from S-parameter measurements taken
21.8.1 Rectangular patch A return-loss sweep for the isolated patch antenna depicted in Figs. 21.15 and 21.16 showed that the principal resonance at 30.6GHz was associated with a return loss of 18dB. The bandwidth for a lOdB return loss was k415MHz. The fringing effects associated with microstrip open circuits are usually considered to be limited to a few substrate thicknesses distant from the edge; yet here there is evidence for an effect extending over more than 10 substrate thicknesses beyond the edge discontinuity. Another consistent feature of these
12 16
Microstrip field diagnostics
plots is the appearance of a weak 'mushroom shaped' maximum which is located over the ground plane almost a quarter wavelength away from the discontinuity. This feature is particularly large at resonance. As the frequency is raised, the VSWR maxima move along the microstrip line towards the antenna feed point owing to overall shrinkage of the mode pattern supported by the patch. The shift in the positions of the VSWR maxima and minima along the feed line is particularly rapid close to the resonant frequency of the patch. The variation of guide wavelength with increasing frequency can be accurately measured by the probe technique, and generally is in excellent agreement with the theoretically predicted values. Movement of the first feed-point maximum with respect of the edge of the patch may also be used to investigate the change of input impedance of the patch with increasing frequency.
Microstrip field diagnostics
7217
lateral splitting of the patch mode. At somewhat higher frequencies than shown here, all four corners of the patch become relatively strongly excited. The network probe has also been of immense value in clarifying the mode structure supported by simple self-oscillating microstrip patch antenna systems which incorporate a Gunn or Impatt diode. Space does not permit inclusion of this material here, but further information can be found in References 1 1 and 12.
scale Z. Zd Bllevel X,Y=Z.Ommld~v~s~on
Fig. 21.17 I E , I ~distribution for linear four-element array, F = 3 3 . 8 ~ ~ 1 '
21.9 Linear four-element patch array
scale X,Y =l.Ornm/divislon
Z = l OdB/level
Fig. 21.16 Rectangular patch antenna just above resonance F = 31.2GHz
As the frequency of excitation is raised above resonance there is evidence for the excitation of the cross-polar TM,, mode, as shown in Fig. 21.16. Further 'mushrooms' appear on the ground plane and are clearly associated with the
A striking example of the application of the technique to arrays is given in Fig. 21.17. The four-element array was constructed on a low-permittivity substrate (E, = 2.2) and has return-loss dips at 33.8 and 37.8 GHz. The main advantage of the T-junction splitter is its wide bandwidth and simple design, but it does suffer from the disadvantage of being non-isolating. Since the patch feed-point discontinuity produces a substantial reflection, each element in the array directly interacts with every other element owing to the back-reflected waves. However, owing to the high overall symmetry of the array and also a measure of good fortune, each element receives approximately the same excitation in this design. In order to avoid the problem of etching very narrow 200R lines, the output arms of the primary splitter were tapered to 50R and then split again into two
12 18
Microstrip field diagnostics
Microstrip field diagnostics
IOOR outputs. Contrary to the normal practice of avoiding the use of sharp microstrip bends, the corporate feed was laid out using parallel or perpendicular sections of line in order that the position of the VSWR maxima and minima could be determined more precisely for analytical purposes. The array elements exhibit a mode structure similar to that found with the isolated element discussed in the previous Section. One striking observation is that the locus of the current maxima along the width of the array is curved in such a way that the two outer elements appear to be excited below resonance, whereas the two inner elements appear to be excited above resonance. The observed curvature of the phase front suggests that there might be significant mutual-coupling effects between the elements.
I
scale X.Y = Z.Ornrn/divlsion Z=66.66pV/level
Fig. 21.1 8
IEzIZdistribution for four-element circularly polarised array, F
=
34.9GHz
21.10 Circularly polarised patch antennas Two possible methods for generating circularly polarised radiation are shown in Figs. 21.18 and 21.19. It was not immediately apparent, at the outset, what problems might arise with these designs, and they were originally constructed with a view to using them as antenna test pieces purely for demonstrating the two-dimensional field-plotting capability. However, it was clear from Reference 13 that the circularly polarised pentagonal patch mode had been successfully employed by Weinschel in a practical antenna array operating in the UHF frequency band.
12 19
7220
Microstrip field diagnostics
In the case of the four-element array shown in Fig. 21.18 the corporate feed network generates a progressive phase lag of n/2 between adjacent elements, starting with the top right-hand patch, in a clockwise direction~aroundthe array. The primary power splitter contains an additional 112 section in the left-hand output arm so that each of the secondary power splitters is excited with a relative phase of n. The secondary power splitters are of identical design and incorporate an additional 114 section in one output arm in order to generate the required progressive lag. This arrangement by no means represents an optimum solution for the generation of circularly polarised radiation owing to the impedancetransformation properties of the 114 sections of line. Nevertheless, it does provide an opportunity for examining an array in which the mutual coupling between adjacent elements should be quite small, and also for studying the behaviour of a T-junction splitter whose output arms are asymmetrically loaded. The return-loss sweep exhibits four strong resonances at 28.9, 31.8, 34.9 and 39.8 GHz, respectively. The principal resonance occurs at 39.8 GHz and minor resonances also appear at 30.9 and 37.4 GHz. The area scan shown in Fig. 21.18 measured at 34.9GHz corresponds to the only frequency at which any of the patches were strongly excited. This plot was thresholded lOdB above the noise floor of the detector in order to enhance the visibility of the regions of high excitation. It can be seen that only the top right-hand and bottom left-hand patches are strongly excited and also that both appear to be operating slightly below their natural resonance frequencies owing to the shift of the voltage null on the patch towards the feed point. From the slight asymmetry in the position of the VSWR maxima along the vertical arms of the primary splitter, it was found that the relative phase was close to 0,9n, and therefore 10% in error. Since the patches are grossly mismatched to the feed lines, the return-loss dips are probably caused by feeder resonance. This view is confirmed by Fig. 21.18, where it can be seen that the route between the two more strongly excited patches contains an integer number of voltage maxima and forces the primary T-junction to become a voltage minimum. The area scan corresponding to the resonance at 28.9GHz also showed that the route between the top left-hand patch and bottom right-hand patch was resonant at this frequency, whilst the primary T-junction became a voltage maximum in this case. The two patches are more weakly excited at 29.8 GHz because the natural patch resonance is much closer to the original frequency of 34.9 GHz than 28.9 GHz. The area scans (not shown) measured at 31.8 and 39.8 GHz suggest that line resonance can also occur between the pair of patches coupled by either the left-hand or the right-hand secondary splitters. Since the effective length of a patch is 112 at the natural resonance which occurs at approxmately 35.8 GHz, the patch element is physically shorter than 112 at 31.8 GHz and longer than 112 at 39.8 GHz. At frequencies greater or less than the half-width of the fundamental resonance, the edge discontinuities are no longer strongly coupled and can participate independently of one another in generating two additional
Microstrip field diagnostics
122 1
resonances in conjunction with some other discontinuity located elsewhere in the network. In the present example, the resonance at 31.8 GHz is associated with the relatively strong excitations observed at the feed-point edge of the lower lefthand patch and also the more distant edge of the upper left-hand patch. The principal return-loss dip at 39.8 GHz, however, is associated with the relatively high cross-polar T M , ,-mode excitations observed at the feed-point edge of the lower left-hand patch and the upper right-hand patch at this frequency. Furthermore, re-examination of Fig. 21.18 suggests that the return-loss dip observed at 34.9 GHz is also closely associated with the resonant length of line connecting the more distant edges of the lower left-hand patch and the upper right-hand patch as well as the proximity of the natural patch resonances to this frequency. Owing to the complexity of the observed resonance phenomena it would be quite difficult to design an array which exhibited only a single return-loss dip. Nevertheless, the physical insight gained by studying the mode patterns obtained at the various resonances of the structure does clearly identify which line lengths might profitably be adjusted in order to reduce the total number of resonant frequencies present in the system. The basic reason for the failure of the array geometry is due to the mismatch at the feed point of the patch elements, which leads to an imbalance of power division at the secondary splitters. The effect could, in principle, be compensated for by making the secondary feed line an integral number of half wavelengths long at the natural resonance frequency of the patch, and displacing the Tjunction one-eighth of a wavelength from the mid-point between the patches. Under these conditions the two branch lines form a parallel resonance circuit which should result in an equal division of power. Having established the probable cause of failure, the measurement procedure is repeated on the revised array geometry in order to confirm the original diagnosis. The entire process of empirical optimisation is repeated until the required performance has been achieved. In the hands of a skilled microwave engineer, a single one-dimensional scan along the axes of the feed lines could provide sufficient information for the optimisation of an array once the problem areas have been physically identified by a two-dimensional scan of the complete antenna. The pentagonal patch was designed by scaling the dimensions of the circularly polarised VHF antenna discussed in Reference 13 to a nominal frequency of 35 GHz. The return-loss sweep within the frequency range 26-40 GHz indicated the presence of three resonances, one of which was very weak. The strong resonances at 31.35 and 29.5 GHz exhibited return-loss dips of 3OdB abd 14dB, respectively. Area scans for the I E , ~ ' and relative phase distributions corresponding to these frequencies are shown in Figs. 21.19 and 21.20, where it may also be seen that the vertical microstrip feed line is offset a short distance from the apex of the pentagon. Examination of Fig. 21.19a indicates the presence of three voltage maxima of equal intensity which are equidistant from a deep
1222
Microstrip field diagnostics
minimum located at the centre of the patch. The large voltage gradients that exist in directions perpendicular to the edges of the patch suggest that this mode of excitation is not linearly polarised. The phase plot given in Fig. 21.19b indicates that the position of the voltage minimum also corresponds to the 'phase centre' of the antenna, which is the point from which all phase contours appear to diverge. In this particular example the phase levels are at 30" intervals and the software operates in the 180" phase boundary is range from - 180" through zero to + 180'. The represented by the broad contour that spirals out from the phase centre at the top of the Figure, and the small zigzag irregularities on it have no physical significance. It can be seen that the narrow basal edge of the pentagon has an almost constant relative phase of - 180" with respect to the feed point, which was arbitrarily set to zero phase. The intensity contour plot indicates the presence of three voltage maxima located at the vertices of an equilateral triangle inscribed within the pentagonal patch, and the fringe fields in the immediate vicinity of these maxima suffer a progressive phase shift of approximately 120". The phase gradient is particularly large along the two side edges of the pentagon. Viewed along the direction of radiation propagation, the lefthand rotational sense of the contours clearly indicates that this mode of resonance does, in fact, correspond to the left-hand circularly polarised mode discussed in Reference 13. The phase plot given in Fig. 21.20 for the resonance at 29.5 GHz shows that the basal edge has a constant phase of - 180°, whilst the two edges meeting at the apex now have a constant zero phase. The maximum phase gradient occurs approximately midway between the apex and base in a direction parallel to the axis of symmetry of the pentagon. This mode of resonance corresponds very closely to a simple linearly polarised rectangular patch mode. 21.11 Microstrip travelling-wave antenna
The final example of antenna analysis using the scanning-network probe is to a rampart-line array similar in type to that discussed in References 14 and 15. The rampart line is an interesting slow-wave structure because it radiates in the backward direction. The particular design shown here consists of ten meander sections which radiate a principal lobe at an angle of about 140" to the plane of the substrate. The width of the transmission line was increased towards the centre of the array so as to achieve a tapered aperture distribution as suggested in Reference 14. The principal return-loss dip for this antenna occurred at a frequency of 16.7 GHz and the area scan recorded at this frequency is shown in Fig. 21.21. Inspection of Fig. 21.21 shows that half of the structure receives little or no excitation, whilst the other half exhibits a significant standing-wave pattern. Theoretically, of course, this array should support a smoothly tapered voltage distribution which is larger at the two ends owing to the reduced width
Microstrip field diagnostics
1223
1224
Microstrip field diagnostics
Microstrip field diagnostics
of the transmission line. A colour-coded version of the same area scan also clearly shows an enhanced excitation at alternate corners of the rampart line. This rather unexpected result may be due in some way to the existence of mutual coupling between the relatively closely spaced parallel-line sections. The rampart-line antenna gives a very clear indication of the value of the area-scan technique in microstrip antenna diagnostics. A single two-dimensional scan has provided, in this instance, a considerable degree of physical insight into the problem areas of the design geometry. Comparable information could not possibly have been obtained from network-analyser measurements.
Fig. 21.21 IEZl2distribution for rampart-line antenna at 16.7GHz
21.12 Acknowledgments The author wishes to thank the SERC for the provision of a research grant which made this work possible. The Marconi Company is also gratefully acknowledged for supporting a CASE studentship award during the early stages of the programme. Finally, the author is much indebted to his research students,
1225
Dr. J. Whitehurst, Mr. A. Leggetter, and Mr. N. Piercy, for many hours of painstaking effort, and also to Mr. J. Taylor and Mr. L. Ellison for constructing the probe-transport mechanism.
21.13 References 1 DAHELE, J. S., and CULLEN, A. L.: 'Electric probe measurements on microstrip', IEEE Trans., 1980, MTT-28, p. 752 2 LADBROOKE, P. H.: 'A novel standing wave indicator in microstrip, Radio Electron. Engin., 1974,44, p. 273 3 NEUMANN, E. G.: 'Radiation from the free end of a dielectric rod transmission line', Z. Angew Physik., 1967, 24, p. 1 4 NEUMANN, E. G.: 'The electric field near a curved dielectric transmission line', NTZ, 1969, 3, p. 161 5 GINZTON, E. L.: 'Microwave measurements' (McGraw-Hill, 1957), pp. 249-271 6 MONTGOMERY, C. G.: 'Technique of microwave measurements' (McGraw-Hill, 1947) p. 485 7 SCHWARZ, S. E., and TURNER, C. W.: 'Measurement techniques for planar high frequer,cy circuits', IEEE Trans., 1986, MTT-34, pp. 463-467 8 HARRINGTON, R. F.: 'Time harmonic electromagnetic fields' (McGraw-Hill, 1961) 9 BAHL, I. J., and BHARTIA, P.: 'Microstrip antennas' (Artech House, 1980) 10 HELSZAJN, J., and JAMES, D. S.: 'Planar triangular resonators with magnetic walls', IEEE Trans., 1978, MTT-26, pp. 95-100 11 FRAYNE, P. G., and RIDDAWAY, C. J.: 'Resonance in self-oscillating antennas', Electron. Lett., 1986, 22, pp. 1269-1270 12 FRAYNE, P. G., and RIDDAWAY, C. J.: 'Resonance in an active millimetric conformal array antenna with quasi-optical feedback'. 5th Int. Conf. on Antennas and Propagation, York, ICAP 1987, p. 177 13 WEINSCHEL, H. D., and CARVER, K. R.: 'A medium gain circularly polarised microstrip UHF antenna for marine DCP communication to the GOES satellite system'. IEEE AP-S Symp. Digest., 1976, p. 391 14 HALL, P. S., WOOD, C., and JAMES, J. R.: 'Recent examples of conformal microstrip antenna arrays for aerospace applications'. 2nd Int. Conference on Antennas and Propagation, York, ICAP 1984, p. 397 15 HALL, P. S.: 'Microstrip linear array with polarisation control', IEE Proc., 1983,13OH, p. 215
Chapter 22
Microstrip antennas on a cylindrical surface E. V. Sohtell
22.1 Introduction Owing to their ability to conform to the underlying structure, microstrip antennas have a variety of applications to objects with a curved surface. The utilization can be, for example, on aircraft, missiles, ships, satellites etc. In many cases, where the radius of curvature is large, a planar theoretical approach is sufficient. However, when the radius of curvature is small, the curvature of the surface cannot be neglected. The purpose of this Chapter is to describe how theoretical design models, previously developed for planar structures, are extended to the cylindrical case, and to verify the theory with experimental results. A theoretical treatment of a microstrip patch on an infinitely long circular cylinder is presented in Section 22.2. The theory is used in the analysis of a single patch in Section 22.3. Measured results are shown for comparison. Section 22.4 describes the design of a complete phased array consisting of 32 patches. Input impedance, radiation patterns and mutual-coupling coefficients are displayed. The feed network for the array was designed and built by Dr. J.P. Starski, Division of Network Theory, Chalmers Univ. of Technology, Gothenburg.
22.2 Theoretical models for a patch on a cylinder This Section desciibes two theoretical models of the rectangular patch. They are useful both in calculating the input impedance and in finding the radiation pattern from the antenna. The description will concentrate on the radiation pattern from a cylindrical structure. The input impedance can in most cases be found very successfully by applying a planar theoretical approach [I]. An investigation of the influence of the curvature on the resonant frequency and the
1228
Microstrip antennas on a cylindrical surface
input inpedance was made by Luk et al. [2]. It was found that both the resistance and the susceptance of circumferentially polarised square patches vary with the cylinder radius. For axially polarised patches, on the other hand, only the resistance varies. In the cavity model, the patch is considered as a cavity bounded by two electric and four magnetic walls [3-51. From the modes set up in the cavity by the feed, the field distribution in the four magnetic wall are deduced. These field distributions are then used as sources for the radiation from the patch. The cavity model is developed for a rectangular patch on a cylinder in Section 22.2.1. The effect of the substrate surrounding the patch can be taken care of by solving the entire boundary-value problem, in which case the patch may be represented by a surface current on the substrate. When the appropriate integral equation is solved, with the feed probe or a microstripline as the source, the radiation patterns, as well as the input impedance, can be found [6]. Ashkenazy et al. used assumed surface currents in solving the boundary-value problem on a cylinder [7]. The latter description is what will be called the surface current model of the patch. This model will be discussed in Section 22.2.2. The two approaches described here are suitable for cylinders with a radius of up to 4 or 5 wavelengths. For larger cylinders the numerical evaluation becomes very time consuming and ray-tracing techniques are preferable [8].
Microstrip antennas on a cylindrical surface
where
*,(4,
z) =
aces (2) (y) COS
22.2.1 Cavity model of the patch The rectangular patch is modelled by two axial and two circumferential slots. The field distribution in the slots may be found by solving the boundary-value problem inside the cavity, with the feed as the source. The solution is described by a number of modes, which then gives rise to a set of field distributions in the side walls. These distributions are used as sources for the radiation from the patch. Special cases of radiation-pattern calculations are described in References 9 and 10. Internal fields The rectangular patch described by Fig. 22.1 is considered. The antenna is fed via a probe, which sets up a field underneath the patch. When the substrate is thin, we can assume that the E-field underneath the patch has only a p-component. Following the procedure for the planar case [3, 41, we derive the following expressions for the E- and H-fields:
2 C, Fig. 22.1 Axially polarised patch on a circular cylinder
and G~~ = sinc
(2)(e) sinc
p and q are the modal numbers: 0, 1, 2, - - - ;ko = 2n/Lo; E, is the relative dielectric constant of the substrate; +/, zfis the feed location; and A,, A, are the probe extensions in 4 and z for a rectangular probe (planar approximation). 6, = d/2R, z, d and R are given by Fig. 22.1. The effective loss tangent defl is incorporated to take care of all the losses in the cavity. Radiation losses and losses due to finite conductivity of the conductor, as well as losses in the
7230
Microstrip antennas on a cylindrical surface
Microstrip antennas on a cylindrical surface
7231
substrate, can be estimated using the procedure described for the planar case in Reference 11. Another way of describing the losses in the cavity is to use an impedance-boundary condition at the surrounding wall [4]. External fields Next, we want to find the radiation from the lossy cavity. The E-field in the cavity walls can be replaced by equivalent magnetic currents M, and MZ. When the substrate is thin compared to the wavelength, the magnetic currents are narrow and can be approximated by collapsed currents on the conducting cylinder. We may now replace the magnetic currents by flush-mounted slots in the cylinder. We thus end up with two axial and two circumferential slots in the ground plane. The field distribution along the four slots are considered to follow the distribution in the cavity (eqn. 22.1) [12]. The theoretical calculations carried out in this Chapter are all based on the assumption that the cylinder extends to infinity in both axial directions. A two-dimensional Fourier transform can therefore be applied in solving the boundary-value problem. In doing this we will have to make a suitable expansion of the field outside the cylinder and match to the known aperture distribution of a slot in the cylinder. The field from the aperture of a slot can be obtained from two orthogonal components of the vector potentials [13]. These components can be chosen as, for example, A, and F,. A denotes the magnetic and F the electric vector potential. The expressions for the axial components of the vector potentials are found by expanding both the field in the slot and the radiated fields outside the cylinder in cylindrical modes. The radiation condition at infinity indicates that Hankel functions of the second kind are to be used for an ep' time dependence. The tangential E-fields are matched in the slot and are set to zero on the rest of the cylinder. The following expressions are obtained for A, = - Azsin 0 and F, = - F. sin 0 in the far field when an asymptotic formula for the near-field/ far-field transformation is used [13]:
f
A, = exp(-jk0r) koV
"=-a
F, = exp ( -jko r) konr
,,-,
-
E$(n, k, cos 9) w y ( k oR sin e)
ejnbjn
where q is the free-space impedance. An appropriate Fourier transform is defined [I21 and the Fourier-transformed aperture fields are inserted into eqns. 2 2 . 8 ~and b. The radiated far field from each mode in the axial slots will now be given by
E
r
e
=
5
exp (- jkor) kocos O[exp (jkoz, cos 0) cos (qn) ZnZrR ( q n / ~ , ) ~- cos2e e-,kocos8~/2
z0
" &!J"cOs[n(4
-
11
* 4011
Hi2y(koR sin 9)
where the upper and the lower terms within the bracket are used for slots positioned at 4 = - 4, and 4 = 4,, respectively, and - z,/2 < z < zJ2.
+
The circumferential slots give rise to both components of the E-field. For each
P, we get
4 ( n . k0cose) HA2'(koR sin 0) sin 0 cos enEi(n, kocos 8) k,R sin20HA2y(ko R sin 0)
I
where g:(n, k:) and E$(n, kz) are the Fourier transforms of the slot fields Ei(q5) and E$(z). HA2)(z)is the Hankel function of the second kind and nth order, and HA2"(z) is the derivative with respect to the argument of the Hankel function. The radiated electric and magnetic fields are then found from the far-field approximations
where the upper and the lower terms within the bracket are used for slots positioned at z = + zd/2 and z = - zJ2, respectively, and - 4, < 4 < &. The origin in 4 and z is located in the centre of the patch in the expressions
7232
!
Microstrip antennas on a cylindrical surface
kOcod8-tqn/z,,,*
I
bpl(240)12 - n2
11
-10
where the H-field is given by eqns. 2 2 . 2 ~and b. The current densities on the patch are then represented as follows
J:pq
z, q = O zm/2 9 Z 0
240 n and P = 0 n = o , p + o
=
) (2) (y) (2)
H4,pq(4,Z) = - I,, sin - cos
J;,pq= - H q ( z) =
If z, is smaller than L/2, which is always the case for half- wavelength resonant patches, the only zero of the denominator will be for the combination q = 0, 0 = 90". A similar problem is encountered in eqns. 22.1 l a and b when both p and n are zero. A limiting value exists for these functions also. This is given in eqn. 22.13:
- jn[cos(pn) exp (-jn24,) -
7233
the interior fields in the cavity. This is a very crude approximation when the metal thickness is much larger than the skin depth of the metal. We only present an outline of the current method, the details can be found elsewhere [7, 121. Calculated results with an assumed current distribution will be shown in the next Section. The relation between the interior H-field and the surface current will be
given by eqns. 22.10 and 22.1 la, b. We add the contriubtions from the four slots and make a summation over all the cavity modes p, q to find the total field. All the above expressions contain an infinite summation, which is a sum of cylindrical modes in which the fields have been expanded. The number of cylindrical modes necessary for the summation to converge is dependent on the cylinder radius, the 0 angle and the 4 angle. In the circumferential slots there is also a dependence on the excitation mode. The number of terms is usually less than or around 2 kR. The coding of the formulas is fairly straightforward. However, at certain angles and for n = 0 care must be taken. In eqn. 22.10 special attention must be given for 0 angles where cos 0 = q1/2zm,since the denominator will be zero. The expression will have a limiting value, since the numerator also has a null for the same angle 0. It is found that jk, cos 0[exp (jkoz, cos 0) cos (qn) - 11 ( q n / ~ , ) ~- ~ C O S ~ B
Microstrip antennas on a cylindrical surface
cos
sin
(22.150) (22.156)
b is the cylinder radius including the substrate. The radiated far field from the patch is:
(22.13) and
Since the cylinder is considered infinite in the axial direction, the formulas are not valid for angles coinciding with the cylinder axis. The limit to as how close to the axis they can be used is actually set by the accuracy of the computer. A small-argument approximation for the Hankel function is needed for very small 0 angles, but the formulas are still valid as long as 0 is not precisely 0' or 180". Calculated radiation patterns can be found in Sections 22.3 and 22.4, where comparisons are also made with practical results. 22.2.2 Surface-current model We consider an infinitely long cylinder coated with a substrate. The patch is represented by axial and circumferential surface currents that have to be found by a solution of the integral equation for the problem. The fields in the substrate and in free space outside, as well as the currents on the patch, are expanded in cylindrical modes. The proper boundary conditions are satisfied and the resulting currents and fields are found. Alternatively, the cavity modes as deduced in the previous Section may be used to obtain the tangential H-field on the inside of the metal patch. When the 'metal is considered infinitely thin, the surface currents can be directly related to
E4(r74 , 0) = ko
where I
I:[
= M-'[:]
exp(-jk,r) nr
=
.
sin 0
1
j"ejn4 C,(n, kocos 0) (22.163)
n=-m
I:[]: :-
L[
M22
(22.17)
det(M) - M,,
J: and J; are the Fourier-transformed z-directed and 4-directed currents. The ekpressions for the elements in the M-matrix are given by Ashkenazy et al. [7]. The summation of cylindrical modes is similar to the summation for the expressions in the cavity model. However, the expressions are naturally more complicated since the substrate effects are included in the model. For every 0 angle, the Hankel function for three different arguments is necessary, from order zero up to as many modes as are required. It is also desirable to include a
1234
Microstrip antennas on a cylindrical surface
complex dielectric constant to take into account the dielectric losses. The pattern will otherwise show unnaturally large ripples in a 0 cut. A complex dielectric constant, however, leads to a complex argument in the Hankel functions. Routines with such facilities are unfortunately not available in all standard sub-routine packages. 22.3 Single-patch application
A study of the radiation performance of a single patch mounted on a circular dielectric-clad cylinder is described in this Section. Two different frequencies are applied, 2.615 GHz and 5.7 GHz. The element is oriented for axial as well as for circumferential polarisation. Radiation patterns in both 0- and &cuts are studied and measured patterns are compared to theoretically derived curves. Cross-polarisation levels are also of interest. Additional comparisons can be found in Reference 12.
1
Microstrip antennas on a cylindrical surface
1235
22.3.3 Radiation-pattern comparisons The cavity model (eqns. 22.10 and 22.1 la, b) and the surface-current model (eqns. 22.15-22.17) have been used in the theoretical calculations. Two patch sizes are examined here: one patch is 35 x 35 mm2and has a resonant frequency of 2,615GHz, and the other patch is nominally 15.2 x 15.2mm2 with a resonant frequency of 5.7 GHz. In the lower-frequency case, the cylinder has been covered with substrate all around in order to investigate the pattern behaviour in a complete q5 cut. Axially polarised patch at 5.7 GHz The H-plane radiation patterns for an element oriented for axial polarisation are shown in Fig. 22.2. The E,-field is the co-polar component in this diagram and
22.3.1 Mechanical design The cylinder radius is 0.1495m for all experiments described in this Section (1.3 1 and 2,851 at 2.615GHz and 5 7 G H z , respectively). The length of the cylinder is 0.635 m. The element is etched on a substrate which is easily curved about the cylinder. The substrate has a dielectric constant of 2.32 and a thickness of 3.18mm (118"). The loss tangent is given by the manufacturer, Tellite Co., to be 0.00015. The material is sensitive to heat, and, in applications where soldering is required, a low-temperature solder is recommended. This was tested for the soldering of the feed probe in this study. It was found, however, that the strength of the solder was not adequate for the kind of application where the antennas were connected and disconnected several times. A careful soldering with ordinary Pb/Sn solder was therefore made. An alternative feeding of the patch, e.g. microstrip feeding, could have been applied to avoid the soldering problem. In that case the radiation from the microstrip feed line has to be taken into account. 22.3.2 Measurements An anechoic chamber was used for all far field radiation-pattern measurements. The measurement room is equipped with standard instrumentation and has a measurement length of approximately 6 m. In this application, where the radiation pattern is broad, there are problems with reflections from objects nearby. The edge radition from the substrate caused additional difficulties. This radiation was reduced as much as possible by placing microwave absorbers as caps on the ends of the cylinder. An evaluation of the measurement room gave a peak-to-peak variation of the amplitude of around 1.6 dB at a level of - 10 dB, which indicates that the reflectivity level is about - 32 dB.
angle ?) Fig. 22.2 H-plane radiation pattern for an axially polarised patch at 5.7GH.z -measured 0 0 0 0 cavity model ( 5 modes) - - - surface-current model ( p , q = 0 , 1 and 2 , 0 )
the E+-field is the cross-polar component. The solid lines show the measured coand cross-polar levels. The broken lines are the computed fields with the surface-current model and the circles give the cavity-model prediction. The cavity model was used with five modes included, of which the p, q = 0, 1 and
7236
Microstrip antennas on a cylindrical surface
2, 0 modes dominate. The same two modes, with the level of the p, q = 2, 0 mode 40% of the dominant mode level, were also included in the surface-current model calculations. Both co-polar and cross-polar predictions agree very well with the measured curves. In the E-plane, i.e. in a 4 = 0' cut, we do not predict any cross-polarisation. The results of the measurements and calculations are given in Fig. 22.3. The measured cross-polar level is very low. The measured co-polar curve shows a
Microstrip antennas on a cylindrical surface
7237
models. The computed cross-polar curve derived via the surface-current model has used the excitation 1.0 and 0.4 for modes p, q = 1 , 0 and 0,2, respectively (the p, q = 0, 2 mode is the main contributor). The level is correct as it cuts through the measured edge-radiation ripple. We can observe in this measurement cut that the cross-polar-component ripples much heavier than the copolar-component ones. This is due not only to the lower power level, but also to the stronger E-plane field excitation. (This is the E-plane for the cross-polar component.) The cavity model has used five modes, but only two give a significantcontribution, the q = 1, 0 and 0, 2 modes.
b,
Fig. 22.3 E-plane radiation pattern for an axially polarised patch at 5 . 7 GHz -measured 0 0 0 0 cavity model (5 modes) --- surface-current model ( p , q = 0, 1 and 2. 0 )
ripple due to substrate edge radiation. This radiation also prevents the pattern from dropping down in the 0 = 0" and 0 = 180" directions. The same excitations as in the H-plane were used. Note the behaviour of the cavity-model prediction close to the cylinder axis. These peaks are caused by the sin 0 factor in the denominator of eqn. 22.1 l a for the 0:th cylindrical mode. Circumferentially polarised patch at 5.7 GHz Fig. 22.4 shows a comparison between the measured and computed curves for a circumferentially polarised patch in the H-plane (4 = 0'). The E6-component, i.e. the co-polar component, agreement is good for both theoretical
Fig. 22.4 H-plane radiation pattern for a circumferentially polarised patch at 5 7 G H z -measured 0 0 0 0 cavity model (5 modes) - - - surface-current model ( p, q = 1 , 0 and 0, 2)
The E-plane cut for the same patch is displayed in Fig. 22.5. Since the cylinder was not entirely covered with substrate, the measurements are not relevant outside an angle of approximately 100'. The surface-current model curve has a small ripple caused by circling waves around the cylinder. The shapes of both computed curves are symmetrical, whereas the probe excitation makes the measured curve slightly asymmetrical. The cross-polar level is low, which is expected.
7238
Microstrip antennas on a cylindrical surface
I
Circumferentially and axially polarised patches at 2,615 GHz Fig. 22.6 shows a complete 4 cut at 0 = 90°, i.e. in the E-plane for an element oriented for circumferential polarisation. It is interesting to note how well both theoretical models predict the interference from creeping waves circulating
Microstrip antennas on a cylindrical surface
around the cylinder. The amplitude of the interference is much higher when the patch is oriented for circumferential polarisation, compared to what is noted when the patch is rotated 90" (Fig. 22.7). An explanation for this is that the patch creates a stronger field along the ground plane in the E-plane compared to the H-plane. The asymmetry is due to the asymmetric probe location in 4. The cross-polar level is low, around - 35 dB, in the measured curve. This indicates that the probe is located exactly centered in the z-direction.
angle t)
angle
Fig. 22.5 E-plane radiation pattern for a circurnferentially polarised patch at 5.7GHz measured 0 0 0 0 cavity model (5 modes) - - - surface-current model ( p, q = 1 , 0 and 0 , 2)
Fig. 22.7
-
7239
t)
H-plane radiation pattern for an axially polarised patch at 261 GHz
-measured 0 0 0 0 cavity model (6 modes) ( p , q = 0, 1 )
- - - surface-current model
The co-polar component in the H-plane of an axially polarised patch is shown in Fig. 22.7. Only the dominant p, q = 0, 1 mode contributes visibly. The predicted 'back'-lobe, which is caused by the constructive interference from two waves travelling in opposite directions around the cylinder, only reaches a level of -47dB, as compared to - 18 dB in the circumferentially polarised patch case.
22.4 Array application
angle t) Fig. 22.6 E-plane radiation pattern for a circurnferentially polarised patch at 2.61 GHz measured 0 0 0 0 cavity model (6 modes) - - - surface-current model ( p, q = 1 , 0 and 0 , 2 )
-
0
22.4.1 General Microstrip antennas are very well suited to conformal array applications, and several projects have been reported in the literature [14-251. Sanford [I41 describes a phase-steered array, while References 15-21 report omnidirectional applications. A conical beam is produced by the cylindrical array in Reference 22, and a high-gain spherical array was studied by Dubost and Vinatier [23]. Various microstrip conformal arrays are briefly described by Munson [24] and a conical circularly polarised array with monopulse was reported by Newham
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Microstrip antennas on a cylindrical surface
Microstrip antennas on a cylindrical surface
[25]. Conformal printed dipole arrays have been analysed theoretically in References 26 and 27, and dipoles above a cylinder were investigated in terms of their active radition pattern in Reference 28. A bibliography of the recent literature on conformal antennas in general has been compiled by Hansen [29]. 22.4.2 Theoretical treatment ofjinite and injinite arrays A cylindrical-array antenna may be treated theoretically as an infinite array in the axial direction and an infinite periodic array in azimuth. As an alternative, an element-by-element approach may be used. When the number of elements is large, the infinite model is preferable, since.all the calculations may be performed by considering a single unit cell [28]. When the array is finite, the elements close to the edge behave differently from the centre elements, owing to the difference in mutual coupling. These edge effects must be taken into account in the design of small and moderately sized arrays, and also when very low sidelobes are required from a large array. Steyskal used an element-by-element approach for the analysis of a finite array of circular waveguides on a cylinder [30]. The same approach was also adopted by Pozar in a study of planar arrays of microstrip elements [31]. The radiation-pattern calculations of a finite-array antenna, using an element-by-element approach, involves the modelling of the antenna element and the incorporation of the mutual coupling. The modelling of the patch antenna was treated in the previous Section. A theoretical model for the mutual coupling between microstrip elements on a cylinder is not yet available; so in the array design described in this Section the measured S-matrix was incorporated to account for the mutual coupling. Since the measurement of the entire S-matrix is a very time-consuming, procedure and the accuracy is limited, an approximation is used. The idea is to assume that elements located similarly will couple the same way. For instance,. the two centre elements in one band are assumed to couple the same way as the two centre elements in another band, which might not be a bad approximation. However, when this reasoning is extended to be valid for the corner element and its closest neighbour in the same band, we have reason to believe that it is a poor approximation. Still, it will be shown that the approximation is acceptable in this application, where a sidelobe level of - 20 to - 30 dB is investigated. 22.4.3 Design of a phased array on C-band , In this Section we will describe the design of a microstrip antenna array on a cylindrical surface. The array is described in more detail in Reference 12 and the entire project was briefly reported by Sohtell and Starski [32]. The frequency of operation was set to 5.7 GHz. Beam steering f 30' was desired in azimuth, but as an extension of the program the possibility to steer the beam in elevation was also desirable. Another option was the incorporation of circular polarisation. The sidelobe level was to be controlled by using variable attenuators. The
1241
number of phase shifters and attenuators was limited to 8 in the first configuration. As in the design of a planar array, the size of the antenna, the element pattern, the type of element grid and the element separation will govern the characteristics of the far-field radiation pattern. Since the elements are placed on a curved surface, it is not possible to separate the element pattern from the array factor, which complicates the synthesis. In a beam-steering situation it is also essential to beware of the limits of the active angle of the array. The element pattern, the element grid and the active angle will be discussed below. The design will focus on the azimuth plane, since no restrictions were set on the radiation pattern in the elevation plane.
'
Antenna element According to the specifications, circular polarisation was required for a possible continuation of this project. There are several types of microstrip antennas that produce circular polarisation [5]. In this project, however, we wanted to be able to predict the radiation patterns theoretically as accurately as possible. An element which could easily be described in a cylindrical geometry was therefore wanted. In addition, we did not want any radiation from the feed network to interfere with the desired radiation. Consequently, a square-shaped probe-fed element was chosen. The dimensions of the element were predicted using standard methods available. The following simple formula for the resonant frequency of a patch on a curved surface is very useful [2]:
where 2R4, = 2R4, + h/& is the effectivecircumferential length of the patch and z, = z, h/& is the effective axial length. The actual dimensions of the patch are z, and 2R4,. R is the cylinder radius,pq is the mode number, h is the substrate height and E, the dielectric constant of the substrate. In our case we found that with E, = 2.32 and h = 3.18 mm, for a TM,, mode at 5.7 GHz, the length z, should be 15.18 mm. The dimensions of the microstrip element designed here are: axial length measured on the etched board is 15.10 0.05mm, and the width is 15.20 0.05mm. The measured return loss for this element is given in Fig. 22.8. The resonant frequency is 5.725GHz, which is exactly what eqn. 22.18 predicts. The bandwidth is -4.7% for a VSWR of 1.5.
+
+
+
Active angle The active angle of the cylinder can be seen from Fig. 22.9 to be limited by the beamwidth of the constituting elements. Beam steering to 0' and 30' is illustrated. Since the elements that were chosen for this array are a little smaller than 4 2 , a fairly broad beam was expected. To get an approximate idea of the beamwidth, a measured radiation pattern for a single element on a cylinder was
.
7242
Microstrip antennas on a cylindrical surface
Microstrip antennas on a cylindrical surface
studied. The element at one end of the array should not be too much out of phase when the beam is steered 30' in the other direction. The usable angle of the element studied was about 130" for 22' phase error and lOdB power loss.
0
5.2
I
I
I
I
I
I
I
I
5.7 Frequency (GHz)
Fig. 22.8 Measured return loss for an isolated probe-fed square patch
I
1
6.2
1243
An active angle smaller than 70" thus seemed necessary if all elements were to contribute to the main lobe for all steering angles without phase compensation. Element grid The specifications asked for beam steering _f 30' in elevation and azimuth with eight phase shifters. Steering of the beam in elevation requires more phase-shifters than beam-steering in azimuth, owing to the non-separable geometry. The array was therefore arranged to be steered in azimuth, in a first configuration, because of the limited number of phase shifters. The difference in beam steering in the two planes is discussed further in Section 22.4.4. The array was designed to allow for beam steering in both planes at the same time. A triangular-element lattice was chosen with a total of 32 elements. The elements were arranged in eight columns of four elements each. The power was thus first split into eight channels, each channel containing a phase shifter and an attenuator. The four elements in each column were uniformly fed with equal phase. The element separation was the next parameter to be found. On a planar surface, the discussion would proceed as follows. The largest separation between elements can be found in adiagonal plane. To be able to steer to 30" in this plane without introducing grating lobes, we would need an element separation smaller than 0.62. We do, however, know that the grating lobes are not as high and distinct in the azimuth cut, owing to the non-uniform element spacing [29]. The element separation in a diagonal plane was chosen to be 0.581, which gave a column/band separation of 0.4141 in q5 and z. The above considerations led to the choice of a cylinder diameter of approximately 0.3m. The actual radius of the cylinder used in the following measurements was 0.1495m (2.842 at 5.7 GHz) excluding the substrate. This resulted in an active angle of 63" when the substrate thickness was 3.18 mrn. A photograph of the array is shown in Fig. 22.10. 22.4.4 Measured performance
Fig. 22.9 Active angle in azimuth of a cylindrical array
Input impedance The cylinder with the array was placed in a small anechoic chamber built up by four walls covered with absorbers. The roof and the floor were not shielded. The room was examined for this application by moving the cylinder about in the room to find the in-and-out-of-phase interference of the reflections. An HP 8409B semi-automated network analyser was used to perform the measurements. The total error in the return-loss measurements was around f0.4dB and f 3" at the 25 dB level. All the neighbouring elements were terminated in matched loads during the measurements. The loads were all better than 20dB in return loss. Fig. 22.1 1 shows the return loss measured at all 32 input ports. The design centre frequency of 5.7 GHz is clearly demonstrated. A bandwidth of 100 MHz
1244
Microstrip antennas on a cylindrical surface
for a VSWR < 1.5 for all the elements was achieved. The variations in return loss are due to the etching, the probe locations, and the mutual coupling between the elements. Considering this, the result is very good. A tendency towards lower return loss was noted for the elements in the centre of the array.
Microstrip antennas on a cylindrical surface
7245
coupling heavily. The errors caused by surface-wave reflections at the edges of the board are not included in the estimations above. Fig. 22.12 gives the amplitude and phase of the measured mutual coupling at 5.7 GHz from a centre element to all the other elements and Fig. 22.13 shows the coupling from a corner element. A study of Figs. 22.12 and 22.13 gives the following information:
I
5.5
5.6
57 58 frequency (GHz)
5.9
Fig. 22.11 Measured return loss for 32 active elements
Fig. 22.10 32-element phased-array antenna
This is caused by the mutual coupling between the elements, since the patches were designed for optimum matching as isolated elements. Mutual co~~pling hetnwn rlw elements The same provisional anechoic chamber described previously was also used for the mutual-coupling measurements. The measurement error for these measurements was found to be less than f 0.4dB and 3" at a 20dB level. It was noted that the surface-wave radiation along the cylinder axis influenced the mutual
+
The coupling upwards from the centre element is stronger than the coupling downwards, except for the closest elements. The reason for this can probably be found in the second-order mutual-coupling effects, which are different owing to the asymmetric location of the element in the array. The E-plane coupling is stronger than the H-plane coupling for both elements, except for the centre element's coupling to the closest elements. The difference is very pronounced for the corner element. It is striking to see the difference in phase between the two planes. There are quite clearly two types of coupling involved. The surface-wave coupling is strongest in the E-plane. The radiation coupling, on the contrary, is probably stronger in the H-plane (cf. dipoles). This is also verified by far-field radiation-pattern computations made for single elements oriented for circumferential polarisation and elements oriented for axial polarisation (Section 22.3.3). It is shown that the surface wave radiated off the edge of the substrate is much stronger when the element is oriented for axial polarisation.
1246
Microstrip antennas on a cylindrical surface
A comparison between Figs. 22.12 and 22.13 shows that there are large differences in the measured amplitude and phase values for two-element combinations located similarly, which means that the mutual coupling is not only
t
%-vector
1
amplitude phase
Microstrip antennas on a cylindrical surface
1247
Feed network A block diagram of the feed network is shown in Fig. 22.14. The first power divider splits the power equally into eight channels, corrresponding to the eight columns of the array. In each channel there is a phase shifter, an attenuator and
1
amplitude phase
Fig. 22.12 Amplitude and phase of the measured mutual coupling from a centre element
Fig. 22.1 3 Amplitude and phase of the measured mutual coupling from a corner element
a function of distance and direction between the elements. The second-order coupling effects result in this difference. This should be remembered when the mutual coupling is included in the radiation-pattern calculations.
finally a 1:4 power splitter. The phase shifter can control the phase in steps of 45' between 0" and 360". The attenuator has an attenuation range of 0-40 dB continuously. The final power divider splits the power equally and with equal phase to the four elements in a column.
7248
Microstrip antennas o n a cylindrical surface
The computer-controlled phase shifter and attenuator are described by Starski and Albinsson in References 33 and 34, respectively. In order to be able to predict the radiation patterns of the array, it was important to know the total resulting phase and amplitude at each element. A
4 k?' Computer
-.
1:8
..
45'
90"
180'
0 -40 dB
Fig. 22.14 Block diagram of the feed network
thorough measurement of the complete feed nework was therefore made. The phase and amplitude at each one of the 32 ouput ports were measured as a function of phase-shifter setting and attenuation. These data were then recorded by a HP9816 computer and could be displayed during the antenna measurements. The values were used as input to the computer program for the prediction of the radiation patterns (see below). However, excitation errors due to reflections at the antenna elements were not compensated for. A discrepancy between the displayed values and the actual output values could also be expected owing to the fact that the semi-rigid cables after the measurement had to be bent to be attached to the elements. The total difference in phase and amplitude in the displayed values and the output values from the feed network is roughly f0.5dB and 7".
+
Antenna gain The antenna gain was measured in the anechoic chamber described in Section 22.3.2. The reflectivity level of the room is around - 40 dB for the entire array measurement. The feed network was set to give a main lobe in 4 = 0". The average power level at the elements was -25.0dB. An ideal power division would give - 15 dB, which means that 10 dB was lost in the feed network including the cables. This loss is mainly due to the phase shifters, which were not in their 0" state during the gain measurements. An increase in phase shift in the phase shifters results in an additional attenuation, and since the attenuation was not equal in all the channels, a compensating attenuation was applied in the leastattenuated channels. The measurements gave an antenna gain of 13.1 (k0.8)dB. Neglecting the feed loss, the antenna by itself has a gain of 23.1 dB. It should be pointed out that a constant amplitude over the aperture would give an equivalent taper which can be described by a function I/cos (4,) x g(4,,). The first term is due to the increased density of elements towards the edge, in a projected aperture plane. 4, is the 4 angle of the m th column, as measured from 4 = 0". g(4) is the
Microstrip antennas on a cylindrical surface
7249
element pattern, which can be approximated by cos(4) for small 4 angles. Consequently, we wanted an excitation with equal amplitudes to the elements during the antenna-gain measurement. An antenna gain of 23.1 (k043)dB gives an effective aperture A, of 16.3 [+3.3/-2.7]A2, using G = 4 ~ A , / 1 ~This . can be compared to the physical projected aperture of the array, which is 9.66A2. The actual aperture with a 112 margin around the printed array is 17.541'. The effective aperture of the array is thus approximately equal to the area of the array, including 142 around the printed pattern. Radiation patterns The cylinder was covered with substrate to a total height of 595 mm. In azimuth the substrate covered 620mm, corresponding to an angle of 230". Radiationpattern recordings outside the range 100" could therefore have been influenced bv the substrate edge. The calculated radiation patterns were all computed using the surface-current model of the patch (Section 22.2.2). The mutual coupling was incorporated using the mesured coupling coefficients from the centre element. In patterns where a cross-polar level is predicted, mode p, q = 2, 0, with an amplitude of 40% of the dominant mode (p, q = 0, 1) amplitude, was included.
-
+
Beam steering Let element number nm be excited by the current I,, = I(+,, z,,), where z, is the z-co-ordinate of then th band and 4, is the 4 angle of them th column. In order to steer the beam in a direction O0, 4,, the element excitation should be
I
- j k R ~ i n B ~ c o -&) s ( ~ ~ -jki,casOo
e (22.19) when the element phases are neglected. When we analyse this expression, we find that, to steer the beam in elevation 0, we need to calculate and change by individual amounts the phase of every element in the array. It is thus not possible to use one band as an entity, a so-called 'row and column' beam steering, the same way as in a planar array. A beam steering in azimuth only (0, = 90°), on the other hand, involves the phasing of the columns. Inrn
=
nm
Active-element patterns When a single element was excited, the surrounding elements were terminated in matched loads. The active-element patterns of a centre element and a corner element were recorded. Fig. 22.15 gives the predicted and measured radiation patterns for the centre element and Fig. 22.16 shows the radiation pattern for the corner element. The former is also compared to the radiation pattern of an isolated patch. Array patterns For the entire array, beam steering was performed in azimuth only. Fig. 22.17
7250 0
,
shows beam steering to 0°, 17O, 34", 55" and 63'. The element phases have been compensated for in the two latter diagrams. The recordings were made with the intention of putting as much power as possible into the main beam, but still keep a constant amplitude taper. None of the columns was therefore attenuated, although this would have helped to reduce the sidelobes.
I
I
-40
,
120
7251
Microstrip antennas on a cylindrical surface
Microstrip antennas on a cylindrical surface
I
I
I
90
60
30
I
I
I
0
30
60
I
I
90
120
I
I
I
I
angle (7
Fig. 22.15 Measured and predicted active radiation pattern for a centre element -measured - - - surface-current model, mutual coupling included . . . surface-current model, isolated element
angle Fig. 22.17 Beam steering to O", 7 7 , 344 55 and 6 3 in azimuth
-401
I
I
I
I
90
60
30
0
I
I
I
30
80
90
angle (7
I
I
120
150
Fig. 22.16 Measured and predicted active radiation pattern for a corner element -measured - - - surface-current model, mutual coupling included
The co- and cross-polar diagrams for a beam pointing in 0" are shown in Fig. 22.18. The sidelobe level for a constant-amplitude distribution is found to be - 13dB, which is also predicted. The cross-polar level is measured to be - 24 dB. The calculated results lie 3 dB below this value. The discrepancy is due to the fact that the cross-polar coupling has not been considered in the theoretical calculations and also because of the inaccurate feeding of the patches. The elements are sensitive to cross-polar components, since mode p, q = 1, 0 is resonant at the same frequency as the p, q = 0, 1 mode. A displacement of the feed probe only slightly will therefore cause cross-polarisation. Fig. 22.19 shows the co- and cross-polar curves when the beam is steered to 36". The patterns are predicted quite well with the theoretical model. The columns are all fed with equal amplitude. Pattern synthesis A good synthesis method is difficult to find for conformal arrays. The projected aperture method is the most commonly used [29, 351. Matrix inversion
-
7252
Microstrip antennas on a cylindrical surface
procedures were reported by Ziehm [36] and James [37] and an iterative method was developed by Guy [38] (also in Reference 39). We will show here the results of a projected aperture synthesis procedure. The sidelobes were reduced in an azimuth cut by using a sampled continuous Taylor distribution [40].
Microstrip antennas on a cylindrical surface
I
7253
the case of constant excitation and 0" beam steering. It should be pointed out that the reduced antenna gain is mainly due to the attenuation in the feed network, since the power in the outer channels is attenuated. A constant total power output would theoretically result in a loss of antenna gain of 0.1 dB for a 20 dB, and 1.4 dB for a 30 dB Taylor distribution, as compared to a constant distribution.
angle (7
Fig. 22.18 Measured and predicted rad~attonpattern with the mutual couplmg mcluded for a beam pointmg ~n0" measured co- and cross-polarlsatlon - - - surface-current model, co-polarlsatlon x x x surface-current model, cross-polar~sation
-
As mentioned earlier in this Section, the increased element density towards the edge of the array is approximately compensated for by the reduced element gain. As long as the angle is small, this is a reasonable approximation. A 30 dB Taylor distribution was applied, in order to reduce the sidelobes. The recorded and predicted radiation patterns are displayed in Fig. 22.20. The predicted pattern uses the excitation delivered by the feed network with the desired phases approximated the best that could be done with the 3 bit phase shifters. The mutual coupling is also included. Theoretical and measured curves agree very well in this diagram. A considerable sidelobe reduction was gained at the cost of lobe width and directivity. A reduced sidelobe level of a beam steered to 10" requires a new projection. The new projection leads to an asymmetrical element distribution. Consequently, a 'new calculation of element currents has to be done. A 20dB Taylor distribution applied to a beam steered to 10" gives the pattern shown in Fig. 22.21. The OdB level in both tapered diagrams is the level of the main lobe in
Fig. 22.1 9
Measured and predicted radiation pattern with the mutual coupling included for a beam pointing in 3 6 -measured co- and cross-polarisation - - - surface-current model, co-polarisation x x x surface-current model, cross-polarisation Source: E.V. Sohtell, 'Microstrip patch phased array on a cylinder', IEEE Int. Symp. Digest Antennas and Propagation, Vol. 111, 1988, pp 1152-1 155. @ (1 988) IEEE
22.5 Summary
Two theoretical models for the microstrip patch on a cylinder have been investigated in this Chapter. Both the cavity model and the surface-current model give a good description of the radiation properties of the patch. Apart from effects occurring for infinite-length cylinders in the theoretical models, and radiation off the substrate edge in the measurement case, the agreement between measured and theoretical curves is good. The cavity-model calculations require much less computer time than those performed with the surface-current model, and the higher-order modes are found quite easily with the cavity model. The
1254
Microstrip antennas on a cylindrical surface
Microstrip antennas on a cylindrical surface
1255
surface-current model does, however, give a better prediction of the radiation pattern for angles near the cylinder axis. It has been shown that the patch antenna is very well suited for application in a cylindrical phased array. The ease of fabrication and low cost make this type of array very attractive. Beam steering & 70' in azimuth is possible without commuting the active region. A three-step commutation will then provide coverage of 360" while maintaining a high antenna gain. It has also been shown that a theoretical model where the measured mutual coupling is included gives a good picture of the electrical performance of a patch array. Pattern synthesis may thus be performed with reasonable accuracy.
- - - - - - rO
22.6 References I 2 Fig. 22.20 Measured andpredicted radiation patterns with the mutual coupling included f o ~ a 3 0 dB Taylor distribution with the beam pointing in O'
-measured - - - surface-current model
Source: E.V. Sohtell. 'Microstrip patch phased array on a cylinder', IEEE Int. Symp. Digest Antennas and Propagation. Vol. 111. 1988, pp 1152-1 155. @ (1 988) IEEE
3 4 5 6 7
8
9
10 II 12
13 14 Fig. 22.21
Measured and predicted radiation patterns with the mutual coupling included for a 20dB Taylor distribution with the beam pointing in 1O'
-measured
- - - surface-current model
IS 16
KROWNE, C. M.: 'Cylindrical-rectangular microstrip antenna', IEEE Trans., 1983, AP-31, pp. 194-199 LUK, K. M., LEE, K. F., and DAHELE, J. S.: 'Input impedance and Q factors ofcylindricalrectangular microstrip patch antennas'. IEE Int. Conf. on Antennas and Propagation, Part 1, York, June 1986, pp. 95-98 LO, Y. T., SOLOMON, D., and RICHARDS, W. F.: 'Theory and experiment on microstrip antennas', IEEE Trans., 1979, AP-27, pp. 137-145. CARVER, K. R., and MINK, J. W.: 'Microstrip antenna technology', IEEE Trans., 1981, AP-29, pp. 2-24 JAMES, J. R., HALL, P. S., and WOOD, C.: 'Microstrip antenna theory and design' (Peter Peregrinus, 1981) NEWMAN, E. H., and TULYATHAN, P.: 'Analysis of microstrip antennas using moment methods', IEEE Trans., 1981, AP-29, pp. 47-53 ASHKENAZY, J., SHTRIKMAN, S., and TREVES, D.: 'Electric surface current model for the analysis of microstrip antennas on cylindrical bodies', IEEE Trans., 1985, AP-33, pp. 295-300 PATHAK, P. H., and KOUYOUMJIAN, R. G.: 'An analysis of the radiation from apertures in curved surfaces by the geometrical theory of diffraction', Proc. IEEE, 1974, 62, pp. 14381447 WU, KUANG-YUH, and KAUFFMAN, J. F.: 'Radiation pattern computations for cylindrical-rectangular microstrip antennas'. IEEE Int. Symp. Digest Antennas and Propagation, Vol. 1, 1983, pp. 39-42 JAKOBSEN, K. R.: 'The radiation from microstrip antennas mounted on two-dimensional objects', IEEE Trans.,1984, AP-32, pp. 1255-1259 PENARD, E.: ' ~ t u d ed'antennes imprimkes par la method de la caviti. Application au couplage'. D.Sc. Thesis, University of Rennes, 1982 SOHTELL, E. V.: 'Microwave antennas on cylindrical structures'. Technical Report 173, Ph.D. Dissertation, School of Electrical and Computer Engineering, Chalmers University of Technology, Sweden, Sept. 1987 HARRINGTON, R. F.: 'Time-harmonic electromagnetic fields' (McGraw-Hill, 1961) chap. 3 SANFORD, G. G.: 'Conformal microstrip phased array for aircraft tests with ATS-6'. IEEE Trans., 1978, AP-26, pp. 642-646 MUNSON, R. E.: 'Conformal microstrip antennas and microstrip phased arrays', IEEE Trans., 1974, AP-22, pp. 74-78 WEINSCHEL, H. D.: 'A cylindrical array of circularly polarized microstrip antenna'. IEEE Int. Symp. Digest Antennas and Propagation, 1975, pp. 177-180
1256
Microstrip antennas on a cylindrical surface
17 AGRAWAL, A. K.: 'Cylindrical array'. IEEE Int. Symp. Digest Antennas and Propagation, 1986, pp. 549-552 18 JAYAKUMAR, I., GARG, R., SARAP, B. K., and LAL, B.: 'A conformal cylindrical microstrip array for producing omnidirectional radiation pattern', IEEE Trans., 1986, AP-34, pp. 1258-1261 19 DUBOST, G., SAMSON, J., and FRIN. R.: 'Large bandwidth flat cylindrical array with circular polarisation and omnidirectional radiation', Electron. Lett., 1979, 15, pp. 102-103 20 OSTWALD, L. T., and GARVIN, C. W.: 'Microstrip command and telemetry antennas for communications technology satellite'. IEE Int. Conf. on Antennas for aircraft and spacecraft, London, 1975, pp. 217-22 21 WEINSCHEL, H. D., and WATERMAN, A.: 'Cylindrical microstrip array - C-band beacon antenna array with 48 rectangular radiating elements fed in phase'. Report AFGL-TR-830218, AD-A135 14414, July 1983 22 HALL, P. S., WOOD, C., and JAMES, J. R.: 'Recent examples of conformal microstrip antenna arays for aerospace applications', IEE Int. Conf. on Antennas and Propagation, York, 1981, pp. 397401 23 DUBOST, G., and VINATIER, C.: 'High gain array at I2GHz for telecommunications'. Int. URSI Symp. on Electromagnetic Waves, Munich, 1980, pp. 213A1-4 24 MUNSON, R. E.: 'Conformal microstrip communication antenna', IEEE Military Communications Conference, Monterey, 1986, pp. 23.3.14 25 NEWHAM, P.: 'Monolithic patch array antenna for small missile applications'. Military Microwaves, Conf. Proc. Brighton, England, 1986, pp. 335-340 26 LEE, K. S., and EICHMANN, G.: 'Elementary patterns for conformal dipole arrays mounted on dielectrically clad conducting cylinders', IEEE Trans., 1980, AP-28, pp. 81 1-18 27 ALEXOPOULOS, N. G., USLENGHI, P. L. E., and UZUNOGLU, N. K.: 'Microstrip dipoles on cylindrical structures', Electromagnetics, 1983, 3, pp. 31 1-326 28 HERPER, J. C., HESSEL, A,, and TOMASIC, B.: 'Element pattern of a cylindrical phased array. Part I: Theory', IEEE Trans., 1985, AP-33, pp. 259-272 29 HANSEN, R. C. (Ed.): 'Conformal antenna array: Design handbook'. AD A1 10091, Jan. 1982 30 STEYSKAL, H.: 'Analysis of circular waveguide arrays on cylinders', IEEE Trans., 1977, AP-25, pp. 610-616 31 POZAR, D. M.: 'Finite phased array of rectangular microstrip patches', IEEE Trans., 1986, AP-34, pp. 658-665 32 SOHTELL, E. V., and STARSKI, J. P.: 'Cylindrical microstrip patch phased array antenna - Chalscan C'. Military Microwaves Conf. Proc., Brighton, June 1986, pp. 317-322 33 STARSKI, J. P., and ALBINSSON, B.: 'Coupled transmission line as a DC isolating phase shifter network'. TR8407, Division of Network Theory, Chalmers Univ. of Technology, Sweden, Sept. 1984 34 STARSKI, J. P., and ALBINSSON, B.: 'An absorptive attenuator with optimised phase response'. TR8402, Division of Network Theory, Chalmers Univ. of Technology, Sweden, May 1984 35 RISZK, M. S. A. S., MORRIS, G., and CLIFTON, M. P.: 'Projected aperture synthesis method for the design of conformal array antennas'. IEE Int. Conf. on Antennas and Propagation, Coventry, 1985, pp. 48-52 36 ZIEHM, G.: 'Optimum directional pattern synthesis of circular arrays', Radio Electron. Engr., 1964, 28, pp. 341-355 37 JAMES, J. R.: 'Conformal antenna synthesis using spherical harmonic wavefunctions', Proc. IEE. 1975, 122, pp. 479486 38 GUY, R. F. E.: 'A synthesis technique for array antennas of general shape with various aperture constraints'. IEE Int. Conf. on Antennas and Propagation, Coventry 1985, pp. 35-39 39 GUY. R. F. E.: 'Power pattern synthesis of conformal arrays'. Military Microwaves, Conf. Proc., Brighton, 1986, pp. 341-346 40 BALANIS, C. A,: 'Antenna theory, analysis and design' (Harper & Row, NY, 1982)
Chapter 23
Extensions and variations t o the microstrip antenna concept P. S. Hall, A. Henderson, J. R. James
23.1 Introduction A large number of contributions to this handbook have described analytic or design aspects relating to single microstrip elements or their use in large microstrip arrays. This reflects a response to an important need for engineering developments in the communications, radar and navigation areas, where many of the ultimate uses of microstrip will be found. The number of ways of configuring a microstrip patch antenna, let alone the different array topologies, is seemingly vast, yet the fundamental performance limitations discussed in Chapter 1 are intrinsic in any microstrip antenna design. There we have cited bandwidth extension, radiation pattern control, efficiency and feeder architecture, substrate technology and manufacture etc., as major fundamental issues in design. Any one property can generally be optimised to a large degree, but only at the expense of the others, and copious illustrations are given throughout the Handbook. It is perhaps a sign of maturity in the microstrip antenna field that ways of combining microstrip printed technology with other constructional methods are now attracting attention. The central idea here is to sacrifice to some degree the manufacturing simplicity or the low profile or the choice of substrate materials and so on, in order to relax one or more of the above limitations fundamental to established microstrip technology. The concept of mixing technologies is well known in engineering design and is best described by considering specific examples. The purpose of this Chapter is to report various examples with which we have had particular design experience. Section 23.2 deals with two arrangements for exercising greater control of radiation patterns whilst maintaining the presence of simplistic microstrip patch antennas. First, in Section 23.2.1, the microstrip radiator is used as a feed element for a large - reflector antenna, thus combining the simplicity of the microstrip concept with the high efficiency and good sidelobe and cross-polarisation control properties of the reflector. Similarly the combination of dielectric spheres with patches (Section 23.2.2) is also seen to lead to improvements in pattern control with novel sparse array facilities, and a possible beam-switching
7258
Extensions.and variations to the microstrip antenna concept
technique is also realisable. Ways of satisfying multi-octave bandwidth demands are presented in Section 23.3, and the log-periodic concept in Section 23.3.1 is a particular demonstration of a significant improvement being made in one parameter, namely bandwidth, at the expense of another, in this case the physical area of the array; from this point of view, it is compatible with the findings elsewhere in the Handbook relating to the bandwidth-size trade off, but is, of course, an extreme case. A very new technique (Section 23.3.2) utilises the frequency-selective properties of a printed mesh and the fact that at low frequency a microstrip antenna can be composed of such a surface without impairing its performance. The outcome is a composite structure containing two sandwiched microstrip arrays, one radiating through the other and offering a dual-band aperture with multi-octave frequency separation. The problem of microstrip-line loss and its increase at millimetre wavelengths is noted in Section 23.4, and a hybrid dielectric/microstrip antenna is described to reduce feeder loss. The merits of this antenna structure, which combines the best properties of microstrip technology with dielectric-line technology, is discussed in the wider context of overall losses, which includes that associated with launching waves into the feeder. Finally in Section 23.5 we discuss the use of extreme values of substrate permittivity and also magnetic materials to create a multiplicity of engineering devices with quite different applications. In Section 23.5.1 we note the results of an investigation into the use of expanded-foam polystyrene substrates to reduce the cost of a large array for direct broadcasting reception from satellites. A novel robust electronic beam-scanning element for satellites using a magnetic overlay is described in Section 23.5.2. In contrast, the use of very high-permittivity substrates enables a reduced-size patch antenna to radiate into human tissue for cancer therapy, as described in Section 23.5.3.
23.2 Radiation pattern control 23.2.1 Reflector feeds Reflectors are well known for their good radiation pattern control, and when combined with high-precision horn-type feeds lead to low-sidelobe envelopes and low cross-polarisation over significant bandwidths. The horn is, however, considered to be the point of greatest complexity in a reflector antenna, and the need for simple antennas makes the implementation of the microstrip reflector feed attractive for many reasons. Their lightweight properties make them suitable for satellite multiple-beam applications [I] and the ease of circuit integration has resulted in investigations into their use as monopulse guidance antennas with integrated comparator systems [2]. Simple microstrip disc elements have been used to feed circularly symmetrical reflectors [3]. Small ground-plane sizes have to be used to reduce feed blockage. This results in some equalisation of the E- and H-plane feed patterns as shown in Fig. 23.1, and a consequent improvement in efficiency and cross-polarisation
Extensions and variations to the microstrip antenna concept
w
N
w
\O
-
0
I
N
G-
e a
f
B ob l o b N VN
'
I
7259
1260
Extensions and variations to the microstrip antenna concept
compared with that expected from patches on large ground planes. Table 23.1 indicates typical results obtained after optimisation of the ground-plane size. The need for a circularly symmetric feed pattern [4] implies a balanced magnetic
Extensions and variations to the microstrip antenna concept
1261
where
Em
=
E,
=
+ cos 8 cos 44 cos 0 sin 40 + cos 44 40
sin
(23.2)
where Em and E, are the radiation fields from the magnetic and electric sources, respectively, and the polarisation is in the y-direction. Substituting eqn. 23.2 into eqn. 23.1 and converting to reference and cross-polarised fields Ed and Em, respectively, gives E,~, EC,,
-90
-60
\30( 0
-30
, 30
= 1 =
+ cos e
(23.3)
0
- A-.
/ y
\.)
60
90 8 ldegl
(01
\
Fig. 23.2
1-120 0
I
-90 Ibl
-60
-30
Small magnetic dipole Small electric dipole
Geometry for calculation of fields due to magnetic and electric sources
--. .-.,
,
I
30
60
90
8 ldegl
Fig. 23.1 Measured radiation patterns of microstrip disc on circular ground plane Patch diameter = 16.4 mm; frequency = 5.89 GHz; substrate diameter = 32.8 mm, thickness = 3.18 mm, (hll, = 0.06). e, = 2 . 5
--
H plane
-.-.----
I
H plane plane
cross-polar Fig. 23.3 Patch and ring feed
and electric source as indicated in Fig. 23.2. The radiated field is given by E
=
Em
+ E,
(23.1)
which indicates zero cross-polarisation. Circular polarisation can be generated by a further pair of sources orthogonal to the first and excited in quadrature. However, for microstrip radiators the source is primarily magnetic. The ideal
1262
Extensions and variations to the microstrip antenna concept
Huygens source can be approached by various practical adaptations such as the finite ground plane noted above. A further example is to surround the disc by a quarter-wavelength-deep short-circuited annular ring [3, 41 as shown in Fig.
Extensions and variations to the microstrip antenna concept
7263
Feed-pattern symmetry can also be achieved by using small patch arrays [5], and the narrower beamwidths are more appropriate to feeding larger F/D reflectors or offset reflectors. Fig. 23.6 shows a typical four-element feed with a co-planar corporate feed circuit. A 4% bandwidth is achieved and typical patterns are shown in Fig. 23.7. The sidelobe asymmetry is primarily due to radiation from the feed lines. Reflector performance of between -20 and - 30 dB cross-polarisation level and about 66% efficiency are indicated in Table 23.1. Fig. 23.8 shows computed reflector patterns of this feed. Use of overlaid feed networks, although resulting in increased constructional complexity, reduces feed-line radiation and hence cross-polarisation, as shown in Fig. 23.9 and Table 23.1.
Fig. 23.4 Measured peak cross-polarisation of microstrip feeds -Disc on circular ground plane (Fig. 23.1) -- Patch and ring feed (Fig. 23.3) ---- Co-planar fed patch array (Fig. 23.6) Overlaid patch array (Fig. 23.9) f = f, is patch or array resonant frequency
€3 deg
Fig. 23.5
Measured radiation patterns of patch and ring feed Patch diameter d = 19.5 mm. gap width g = 2.25mm, ring width r = 9.0mm frequency = 5.2 GHz, substrate thickness h = 3.18mm ( h l l , = 0.06),E, = 2.5 H plane ---- E plane, upper curves co-polar; lower curves cross-polar
-
23.3. Fig. 23.4 indicates that the peak cross-polarisation is reduced by about 7 dB. Coupling to the slightly off-tuned annular resonant section also increases the feed bandwidth by up to 50%. A typical feed radiation pattern is shown in Fig. 23.5.
Fig. 23.6
Co-planar-fed patch arrays For F / D = 0.8reflector, patch size = 9.7 mm x 7.2mm, patch spacing = 17 mm, a = 45 mm, b = 60 mm, substrate h = 1.59mm ( h l l , = 0.06).E, = 2.32,frequency = 12.2GHz
It is clear that microstrip can be combined with reflectors to give antennas with good radiation pattern control and high gain over restricted bandwidths. The above examples illustrate the capabilities of this hybrid microstrip reflector antenna using mainly conventional microstrip concepts to realise the feed. There is no doubt much further scope for innovation and improvement, perhaps in the
1264
Extensions and variations to the microstrip antenna concept
Extensions and variations to the microstrip antenna concept
7265
forming of hybrid feeds. An illustration of this is the dielectric-sphere and patch feed [6], described in the next Section. An example of optimised use of basic patch elements within a dielectric-filled cylindrical cavity has also been given in
Fig. 23.8 Calculated radiation patterns of prime-focus-fed axi-symmetric reflector with linearly polarised patch array of Fig. 23.6 ( a ) E-plane ( b ) H-plane
Progress is also likely in the use of optimised array structures using the sequential rotation technique. Fig. 23.10 shows a 16-element array [q suitable for use as a feed for a high FjD reflector. The patches are circularly polarised and arranged with sequentially rotated feeding [8].A simplified feed structure compared with the conventional corporate network (Fig. 23.6) results in lower feed radiation. The close grouping of the patch input points means that four bends are obviated and the 180' phasing at the T-junction results in this source of unwanted radiation being directed into the main beam, hence reducing spillover and increasing efficiency. The changes in the feed-network radiation characteristics are illustrated in Fig. 23.1 1. Fig. 23.12 shows that array sidelobe levels are reduced by up to 10 dB by the new feed network, and that reductions can also be obtained by thinner substrates albeit at the cost of reduced bandwidth. Reductions in cross-polarisation are similar to those for sidelobes. Improvements in bandwidth are also noted using sequential rotation, with the higher-order modes associated with low-Q patches being suppressed, leading to the possibility of reflector feeds with bandwidths in excess of 10%.
1266
Extensions and variations to the rnicrostrip antenna concept
Extensions and variations to the rnicrostrip antenna concept
1267
23.2.2 Spherical dielectric overlays A truncated dielectric sphere is attached to a microstrip patch antenna as shown in Fig. 23.13. The composite structure is no longer of low profile and its manufacture is more complicated, but an additional dimension in radiation pattern control is achieved [6,9, 10, 1I]. The spherical-lens action occurs in the near field of the microstrip patch and can be approximately analysed [I I] by representing the patch radiator by Hertzian dipole elements at its perimeter and involving equivalent current sources on the sphere surface. The effect of the sphere on the patch resonant frequency and input impedance is of second order and readily allowed for. An example of the theoretical and measured radiation patterns are given in Fig. 23.14. As expected, the sphere tends to focus the broad patterns of the patch, with the resulting gain of the structure increasing with sphere diameter until a threshold diameter is reached. For spheres having relative permittivities of 2.3, the threshold was reached for a sphere diameter of about three free-space wavelengths and a gain of about 16.5 dBi. At larger diameters the field distribution over the sphere aperture departs from the illumination required for low sidelobes and narrow main beam. This is also confirmed by the analysis which allows for the dissipative losses in the sphere and the degree of truncation; progressively increasing the truncation also reduces the gain.
Fig. 23.9 Radiation patterns of overlaid patch array FID = 0.8, patch size = 1 2 . 0 mm x 8.0 mm, patch spacing = 1 8 mm. a = 5 6 mm, b = 5 0 rnm, patch height = 1.59 mm ( h l l = 0.06). feed height = 0.79 mm, 8, = 2.32, frequency = 10.6 GHz
-co-polar cross-polar
I
measured
I
-- co-polar ---- cross-polar the'w
Fig. 23.1 0 Silhouette of disc array for circular polarisation using sequentially rotated feeding Array details: E, = 2.32, substrate thickness = 1.59 mm = 0,05&, frequency = 12.0 GHz. patch spacing = 0.7&.
This new composite element offers greater freedom of design with regard to the equality of the E- and H-plane beamwidths, and there is also some suppression of the cross-polarisation levels of the patch antenna. These aspects are
1268
Extensions and variations t o the microstrip antenna concept
Extensions and variations to the microstrip antenna concept
II
1269
Fig. 23.13 Sketch of dielectric sphere overlaid on a microstrip patch antenna showing truncation of sphere
o', degrees
Fig. 23.1 1
Computed radiation patterns of feed network of array of 4 x 4 elements with disc radiation suppressed a Sequentially rotated feed b Conventional feed as Fig. 23.6 -co-polarised ---- cross-polarised 4 = 0' Patterns are normalised to peak radiation of array and feed together
array
as Fig. 23.10
/
-401 0
0.05
I
0.1
hlh, Fig. 23.1 2
Computed peak sidelobe level of feed radiation of 4 Array details as Fig. 23.6 and Fig. 23.10 -e,= 1.06---e,= 2.32
x
4-element array
Fig. 23.14 H-plane pattern of a rectangular patch element with overlaid sphere at 15.4 GHz Sphere radius a = 25 mm. 8, = 2.2. tanS, = 0.0003; microstrip substrate e ,, = 2.3, rand, = 0.0001. height = 0.79 mm, patch size = 5.9 mm x 5.9 mm -co-polar measured -.-.- co-polar, theory ---- cross-polar measured . . . . . co-polar pattern of patch alone, theory
1270
Extensions and variations to the microstrip antenna concept
0
9,' degrees
-90
-60
-30
0
30
60
I
L
Fig. 23.1 5
90 I
b
Measured radiation patterns of circular microstrip patch with overlaid truncated sphere at 1 1.98 GHz Sphere radius a = 11.1 mm. truncated sphere height h' = 0.92 x diameter, E,, = 2.2, tans, = 0,001; microstrip substrate E , ~= 2.3, tans2 = 0.001, height = 0.79 mm. patch radius = 8 . 5 mm, patch probe = 3.2 mm from centre. Element gain = 10.8 dBi. H -plane co-polar ---- H-plane cross-polar E-plane co-polar . . . . . E-plane cross-polar
-
a Amplitude b Phase centred at z = 7 mm from substrate groundplane
Extensions and variations to the microstrip antenna concept
1277
1272
'
I
Extensions and variations to the rnicrostrip antenna concept
,
,
I
t
,
,
Extensions and variations to the rnicrostrip antenna concept
1273
illustrated in the design [6] of a feed for a reflector antenna. The spherelpatch feed element was required to illuminate the reflector with E- and H-plane patterns of similar beamwidths over a bandwidth of 11.7-12.5 GHz. Crosspolarisation levels were maintained below - 15 dB while the phase deviation over the reflector illumination sector of 50" is small (Fig. 23.15). In another development of this antenna, orthogonal feeds were attached to the patch to facilitate circular polarisation. The weight of the spherejpatch exceeds that of a small microstrip array having the same gain, although the pattern control of the former is superior and is an attractive alternative to a horn feed. The deployment of the spherelpatch antenna in large arrays has some significance at millimetre wavelengths because the spheres can be constructed as a moulded planar radome. For arrays with moderate sidelobe levels sparse array techniques can be used, and an example is shown in Fig. 23.16. This arrangement offers a simplified feeder system for the patch antennas. When smaller spheres are overlaid on an array with conventional element spacing, there is some improvement in the cross-polarisation levels. These properties are summarised in Table 23.2. Another application of the dielectric overlays concerns a way of beam scanning by placing several microstrip patches beneath the sphere. Computations [ll] show the effect on the radiation patterns when three isolated quarterwavelength patch radiators are switched on and off. A beam swing of 25" is achieved which, without the sphere, would require many more microstrip patches plus a phase-shifter system. It is expected that the spherical dielectric overlay technique will find use in special applications demanding additional pattern control, and Dubost has subsequently described a cylindrical implementation using a dielectric-rod lens and a linear array [12].
23.3 Wide-bandwidth techniques
Fig. 23.1 6 Sparsely distributedpatch array with overlaidspheres at 90 GHz, with no truncation of spheres a Photographs of arrays with 6 4 and 16 elements b E-plane radiation patterns of 64-element array Element spacing = 2a = 6.35mm. h'12a = 1 .Or E,, = 2.2. tan 6, = 0.001, E,) = 2.3, tansr = 0.001. h = 0.127 mm, patch size = 1 .O mm x 1 .Omm. co-polar measured ---- co-polar theory . . . . . cross-polar measured
-
23.3.1 Log-periodic structures Microstrip antennas and arrays have bandwidth limitations that have been extensively documented. Owing to the inherent resonant action, patch antennas have bandwidths typically less than 10% [13, 311. Increases on this can be achieved by the use of thick patches with probe inductance compensation [14], stacked patches [I51 or the use of coplanar parasitic elements [16]. Even in these cases bandwidths are usually less than 30% but the use of log-periodic scaling of arrays of microstrip patches allows bandwidths of up to two octaves (120%) to be achieved. Applications of such wideband arrays include electronic warfare and wideband radar and measuring systems [17] in those cases where the low profile is an important system consideration. The log-periodic principle applied to microstrip patches [la, 191 is illustrated in Fig. 23.17, where the patch size and spacing increases along the array by a
1274
Extensions and variations to the microstrip antenna concept
Extensions and variations to the microstrip antenna concept
7275
region and the array or element pattern should have a null in the direction of the wave propagating along the array. These conditions can be met by most microstrip arrays. However, to ensure wideband action the propagation characteristic of the array should have no stop bands below the resonant frequency.
factor z, where:
where I, w and dare defined in Fig. 23.17 and the subscripts refer to the nth and (n f 1)th patches. In addition, the substrate thickness for each patch should be similarly scaled, effectively producing an array on a tapering substrate as shown in Fig. 23.17~.Such scaling will ensure that the array characteristics vary periodically with the logarithm of the frequency, provided certain conditions relating to the patch connection to the feed line are observed. This arrangement is the microstrip analogue of the log-periodic dipole array [20]. In both cases the elements close to resonance form an active region, giving rise to strong radiation, and hence attenuation of the travelling wave on the array.
ty L
-
H plane
x
input
feed
,patches
U I 0 2
.z
0
-1
pd lradsl
1
u,d
lnepers)
(b)
Fig. 23.17 Log-periodic electromagnetically coupled overlaid patch array a With scaled feed line and substrate b With uniform patch displacement p, substrate thicknesses h, and h, and feedline width w,
Criteria for successful log-periodic operation of series-fed arrays have been deduced. To prevent excitation of higher-order mode resonances in the lowfrequency elements beyond the active region, the array should be fed from the high-frequency end, should have high attenuation within and beyond the active
Fig. 23.18
( a ) Equivalent circuit of single overlaid patch as shown in Fig. 23.17 ( 6 ) Propagation characteristic of uniform overlaid patch array -calculated with mutual coupling--- calculated without mutual coupling 0 measured points I = 1 0 m m . w = 8 m m . p = 1 . 2 5 m m , d = 9 4 2 m m , w , = 2 . 5 m m , h,= 1,586 mm, h, = 0.793 mm, 8, = 2.32
The complex propagation constant 8' =
+ jy,, -sin kd 2 yo K Z kd 1 - j-sin r,
cos kd cos /?'d
=
fi
+ ju of a uniform array is given by
1276
Extensions and variations to the microstrip antenna concept
where adjacent-cell mutual coupling only is assumed. d is the array period length, Y,and k are the feed-line admittance and wave number respectively, and Y , , and Y,, are the self and mutual admittances of the array elements. Fig. 23.18 shows the equivalent circuit of the overlaid patch and the propagation characteristic of a uniform array of such patches, deduced using eqn. 23.5. k,, = 2~f/c is the free-space wave number. The normalised propagation constant pd is -a at zero frequency (kod = 0) due to the alternation in patch feeding. pd rises smoothly from - T to the resonant region at kod = 1.7, where heavy attenuation takes place owing to strong radiation. On the other hand, a stop band is noted in the propagation characteristic of a quarter-wavelength-line coupled patch array (Fig. 23.19). Similar characteristics have also been noted 1191for the
i
I 1
Extensions and variations to the microstrip antenna concept
1277
Fig. 23.20 shows the input return loss and gain of a 36-element overlaid patch log-periodic array designed for a near-broadside beam. Return loss is less than - 10 dB and the gain is greater than 8 dB over the bandwidth 4-16 G H z The
1
8
12
16
20 Freq.(GHz)
Fig. 23.19 Calculated propagation characteristic of quarter- wavelength line coupled patch array Array configuration and equivalent circuit of single period shown inset at top right and left, respectively I = 10mm. w = 8 m m t d = 9 ~ 8 2 m r n .w , = 2.5mm.h= 1.586mm.e, =2.32. w, = 0.5 mm, I, = 7.0 mm
comb-line array and the series-connected patch array [21], and it has been concluded that, for good log-periodic action, the patches need to be electromagnetically coupled to the feed line in some way. This introduces a series resonance into the element equivalent circuit which simulates that of the successful dipole log-periodic element. Such conclusions are, however, deduced from heuristic reasoning, and it may well be that other forms without coupling gaps may be discovered which also produce good log-periodic action.
(cl Fig. 23.20 36-element overlaid patch log-periodic array a Array silhouette b Measured input return loss IS,, I and transmission loss IS,, I measured --- calculated c Array gain -measured x calculated I, = 3.67 mrn, w, = 2.92 mm, dl = 3 6 7 mm, r, = 1.05. h, = 0.793mm, h, = 1,586mm. p = 1.25.8, = 2.32, T, = 1 .O Overall array size = 340 mm x 50 mm
-
calculated efficiency ranges from 85% to 70% across this band. Array analysis is based on an equivalent-circuit model of the array and reasonable agreement with theory is noted. Fig. 23.21 shows radiation patterns in the H-(longitudinal) plane. Significant narrowing of the beamwidth occurs at high frequencies. This
1278
Extensions and variations to the microstrip antenna concept
is believed to be due to the increased electrical thickness of the active-region patches at high frequencies, which reduces feed-line patch coupling, and hence increases the active-region length. The high cross-polarisation is also believed to be due to this effect. The lack of tapered substrate thickness is noted as the main limitation on the overall bandwidth of this log-periodic array.
Extensions and variations to the microstrip antenna concept
1279
Figs. 23.22 and 23.23 show results for the quarter-wavelength line coupled log-periodic array, the so-called quasi-log-periodic array [22], shown inset in Fig. 23.19. The array is constructed on a single uniform-thickness substrate. Fig. 23.22 shows input return loss and gain, and Fig. 23.23 shows E- and H-plane radiation patterns. A bandwidth of 22% was obtained for a practical antenna with five elements. frequency
2.6
2.8
3.0
, GHz
3.2
3.4
frequency, GHz Fig. 23.22 Performance of quasi log-periodic antenna; antenna shown inset in Fig. 2 3 . 1 9 a Measured and computed return loss as a function of frequency measured - - computed b Measured power gain in broadside direction as a function of frequency
-
Fig. 23.21 H-plane patterns of array of Fig. 23.22 ( a ) 4 GHz; ( b ) 16 GHz
-measured co-polar
--- calculated co-polar
-.-.-
measured cross-polar
The log-periodic principle can be also applied to microstrip to form endfire arrays [23], in contrast to the broadside-beam types described above. Applications here include mounting on nose cones of aerospace vehicles for a range
7280
Extensions and variations to the microstrip antenna concept
Extensions and variations to the microstrip antenna concept
n"
I
1281
of electronic-warfare functions. The key features in design are choice of element spacing and phasing and choice of element. The necessary close element spacing [24] and strong element radiation in the endfire direction are achieved by using quarter-wavelength shorted patches as shown in Fig. 23.24. These are parasitically coupled by tabs to the feed line to avoid stop bands [19]. Fig. 23.25 shows freq IGHzI
transrniss~on loss
frea IGHzI
return Loss Id01 N)
15
Fig. 23.23
dB Measured and computed co-polar radiation patterns of quasi log-periodic anten. na ( a ) E-plane pattern at 2.81 GHz ( b ) E-plane pattern at 2.87 GHz ( c ) H-plane pattern at 2.8 GHz -measured --- computed
short-circuit Fig. 23.24
Silhouette of endfire log-periodic microstrip patch array
Fig. 23.25 Performance of endfire log-periodic microstrip patch array a Transmission loss ---- measured --- computed b Measured return loss c Measured radiation patterns respectively, at: -4.25 GHz; --- 4.5 GHz; 4.75 GHz, . . . . .5.0 GHz.
the performance of an array which was designed for a 25% bandwidth. Similar performance trade-offs to those for the broadside log-periodic array are expected. as are limitations in overall bandwidth due to the use of flat substrates.
7282
Extensions and variations to the rnicrostrip antenna concept
23.3.2 Dichroic dual-function apertures There is a growing interest in apertures that can be used at different frequency bands, and for microstrip arrays this is most readily achieved by embodying dual-frequency patch elements in the array. The resulting band separation is generally small, but a multi-octave separation is now possible using the new dichroic microstrip concept [25-271 which permits two microstrip arrays to be sandwiched together as in Fig. 23.26. The innovation rests with array B composed of a printed mesh, which at f, is found to function as a conventional microstrip antenna. At frequency f,(> f,) the frequency-selective properties of the mesh render it 'transparent' to the radiation from array A. Typically f H f L
Fig. 23.28
Extensions and variations to the rnicrostrip antenna concept
1283
23.31 is a photograph showing its application. Many variations of the dichroic microstrip concept have been exploited including a rectangular mesh with integral-array feeders [29] and a novel window antenna [27l whereby both the ground plane and patches of a microstrip array are composed of frequency
Geometry of the dual-band dichroic array showing the frequency-selective surface array 6 superimposed on a microstrip array A
will be about 8 : l . The measured and computed radiation patterns of a mesh patch on a low-permittivity substrate are shown in Fig. 23.27, and apart from a higher input impedance the co- and cross-polar patterns are very similar to those of a conventional solid patch. A key issue is the degree of transparency experienced because the mesh patch is of limited size and furthermore is in the near field of the radiation sources. Computations using the NEC program 1281 and measurements establish, however, that the resulting transparency is surprisingly good, as the measurements in Fig. 23.28 show. A scattering analysis [29] gives further insight into the transparency, and establishes that the mesh perimeter has a significant effect, causing the ripple-interference pattern (Fig. 23.28). In the practical deployment of the dichroic concept there are many effects to consider which differ with the application, and numerous examples have been studied. The effect of a mesh on a 4 x 4 microstrip patch array is illustrated in Fig. 23.29, and the extension to higher-gain arrays in Fig. 23.30, which also shows an increase in sidelobe level due to scattering from the feeders of array B. The technique has been applied at millimetre wavelengths, and Fig.
Fig. 23.27 NEC-programme computations and measurements of square-mesh microstrip patch antennas. H-plane radiation pattern of a mesh patch with transmission-line feed (inset) a = 5.6cm; c = 1 cm, t = 0.1 cm, h = 0.06cm, frequency = 2.3GHz
}
I
measured
6,
---- computed E,
= I .05
= 1.0
(i) co-polar (ii) cross-polar
selective mesh, thus allowing the arrays to be used as an electromagnetic window at fH and as a conventional array at f,. Having introduced the dichroic microstrip concept, it is clear that much further exploitation remains using different geometries of mesh and substrate permittivities. The use of high-
7286
Extensions and variations to the microstrip antenna concept
Extensions and variations to the microstrip antenna concept
7287
has established several issues:
I
The increase in microstrip-line loss with frequency is not as excessive as originally contemplated. Travelling-wave dielectric antennas have lower loss than the microstrip counterparts, but control of radiation patterns is a problem. The lower transmission loss of dielectric antennas is negated by their incompatibility with waveguide feeds because of launcher radiation losses. Microstrip technology is the most attractive option up to 140 GHz, but there are some merits in the hybrid dielectric/microstrip linear array that combines the best features of microstrip and dielectric technologies. We will outline here the main features of the hybrid antenna, but first recapitulate briefly on the level and source of the increased microstrip-line loss at
Fig. 23.31
Photograph of 16 array removed.
x
16, 90 GHz array showing superimposed 2
waveguide Iaunc
Fig. 23.30 Measured H-plane radiationpatterns of a comb array A under a mesh-parch array, 6; mesh patch has a size a x a a = 7.95 cm, c = 1.1 1 cm. t = 0.48 cm, frequency = 17 GHz, E,, = 2.32, e, = 1.05, h, = 0.08 cm, h, = 0.6 cm, comb array size = 28 cm x 28 cm. (i)co-polar (ii) cross-polar without mesh-patch array --- with mesh-patch array
-
Fig. 23.32
Hybrid dielectriclmicrostrip antenna array
x
2, 9 GHz
1288
Extensions and variations to the microstrip antenna concept
millimetre wavelengths. A factor that has previously obscured the accurate measurement of microstrip loss at these higher frequencies is the leakage of radiation from the transitions attached to the line. A key contribution in the investigation [30] was the quantification, and hence separation, of the radiation from the dissipative loss. It was found that for RT Duroid substrates the loss at 90 GHz was 0.13 dB/1,, as opposed to 0.1 dB/L, at 20 GHz where 1, is the microstrip-line wavelength. Experiments and computations indicated that some loss reduction could be achieved by polishing the printed conductors to decrease surface roughness, but the practical implementation was unrealistic. Even less realistic in manufacture is the process of thickening the conductor so that its edges can be rounded. The hybrid dielectric/microstrip-antennaconcept aims at replacing the microstrip line in a linear array with an insular guide feeder; the practical arrangement is illustrated in Fig. 23.32. The microstrip patches electromagnetically couple to the insular guide feeder, and analysis and measurements establish that the array distribution is controlled by the feeder-patch separation. A summary of the array performance is given in Table 23.3 and a photograph of the structure in Fig. 23.33. The radiation pattern control is superior to that of a planar dielectric antenna, yet the low-transmission-loss qualities of the latter are preserved. The hybrid antenna only retains its advantage over a microstrip array when used in a compatible dielectric-feeder arrangement, and the test set-up in Fig. 23.32 with a waveguide/insular guide transition will lower the system efficiency owing to increased launcher loss. 23.5 Novel use of materials
23.5.1 Foam substrates for Iarge direct-broadcast-satellite domestic receiving arrays The use of expanded polystyrene foam for microstrip substrates is well known, and for a patch antenna it is generally beneficial in terms of the bandwidth and efficiency [31]. The use of a foam substrate in a large array appears to offer the outstanding advantage of a low-cost substrate, and this has recently been investigated [32,33]. Fig. 23.34 shows the laminar construction technique of the foam array. A distinct problem concerned the design of triplate corporate feeds for this electrically large array because the foam did not confine the feed fields as well as a plastic substrate and a significant radiation loss was experienced at the transition region between the corporate feed and antenna. The array specification was complicated by the requirement for a squinted beam and cikular polarisation, the latter being achieved using a polariser grid. Fig. 23.35 shows the measured radiation patterns. The pattern and bandwidth specifications were difficult to meet with a good margin, and the corporate feed loss contributed somewhat to the noise performance of the receiving system and increased the physical size of the array. A detailed comparison with conventional dish anten-
Extensions and variations to the microstrip antenna concept
1289
Table 23.3 Power budgets of 9 0 GHz hybrid linear microstrip patch antennas
(9
I
(ii)
Beamwidth, deg. (theory) (measured) Squint angle, deg (measured) Sidelobes, dB (measured) Cross-polar, dB (measured) Directivity*, dB Gain, dB (measured) Launcher loss, dB (theory) Mismatch loss, dB (measured) Feeder loss?, (theory) Resonator lossg*, dB (measured) Load loss*, dB Element spacing, mm Efficiency §, % (assuming no launcher or load loss) Efficiency" of microstrip array of same physical size, % ' Directivity = 10 log ( A / & cos (squint angle) dB; A = aperture area
t Calculated using 0.05 dB/& over 40 wavelengths '' From measurements on patch-resonator Q-factors '(i) Load loss = 24.2 - (17 + 2 + 0.04 + 2 + 0.97)
= 2.19 dB (ii) Load loss = 23.6 - (18 + 2 + 0.04 + 2 0.97) = 0.59 dB 5 (i) Efficiency = 24.2 - (17 + 2 + 2.19) = 3.01 dB = 50% (ii) Efficiency = 23.6 - (18 + 2 + 0.59) = 3.01 dB = 50% " Microstrip feeder of same physical length (39 wavelengths), loss = 0.1 3 dB/&, patch loss = 0.97 dB
+
1
1
1
1
1
CMs 1
1
1
1
E~
1
= 2, Z , = 50 R, line
1
Fig. 23.33 Photograph of 80-element 90 GHz hybrid dielectric/microstripantenna array
1290
Extensions and variations to the microstrip antenna concept
Extensions and variations to the microstrip antenna concept
7297
nas [33] is given in Table 23.4, illustrating the relative effects of noise due to antenna loss and the receiver noise. The conclusion for this particular application is that the use of a foam substrate leads to low costs but there is a compatibility problem with the feed arrangement, and the specification could be
H-plane
Fig. 23.35
Measured circularly polarisedradiationpatterns o f foam array at 17.9 GHz for four 33-finger combline sub-array with metal-plate polariser
Table 23.4 Comparison of antenna types and projected carrierlnoise ratios ( C I N ) at 17.9 GHz: NF = noise figure Fig. 23.34 Laminar construction o f foam microstrip array 1 Metal ground plane 2 Foam substrate 3 Combline array elements 4 Foam spacer 5 Polarising grid 6 Waterproof cover
more readily met using a higher-permittivity substrate and perhaps some lowerloss waveguide feeders for the longer lengths of feed. The feasibility then rests with manufacturing a substrate capable of robust stable operation at low cost. The array size, however, is very dependent on the noise performance of the receiver, and recent developments in semiconductors make possible a smaller
Large microstrip array
0.9 m dish
0.6 m dish
0.5 -4.56
- 8.07
5.2 -4.50
14.0 17.5 20.7
10.5 14.0 17.2
9.0 12.2 14.9
0.5
Antenna dissipation, dB Aperture capture area, dB m2 Total C/N, dB: 8 dB NF receiver 5 dB N F receiver 2.5 dB NF receiver
These figures assume: (a) 1.4 dB rain loss (b) 0.3 dB galactic noise (c) 160 W transmitted power (4 Antenna is modelled as a simple attenuator situated before receiver For C-MAC system, picture qualities are 'fair' for C / N > 9 and 'good' for C / N > 12
1292
Extensions and variations to the microstrip antenna concept
more efficient array, thus endorsing the feasibility of a flat plate DBS antenna. This research project [32, 331 has been a milestone in the development of a low-cost DBS array and clearly demonstrates the trade-offs between performance and cost. The additional difficulties of electronic beam scan are also highlighted.
Extensions and variations to the microstrip antenna concept
1293
23.5.3 Use of very-high-permittivity substrates in hyperthermia applicators Microstrip structures have also proved useful in the design of applicators to dispense high-power electromagnetic waves into human tissue in cancer
quor ter wavelength
section X - X Fig. 23.37 Hyperthermia applicator using quarter- wavelength microstrip patch
Fig. 23.36 Scanned microstrip patch antenna using thick ferrite slab a Construction of ferrite microstrip antenna showing co-ordinates b H-plane patterns of antennas e, = 10. e, = 13.8.p, p2 2. 1, 2a = 6 mm, frequency = 8.6 GHz
-
(ii) h, = 3 mm (iii)h2 = 3 mm magnetised Field strength of magnet was measured as 0.04 T in free space
23.5.2 Magnetic materials and beam scanning Magnetised substrates have been used as substrates for patch antennas [34]. More recently [35] a thick ferrite superstrate with an applied magnetic field, as shown in Fig. 23.36a, was devised and led to the creation of a beam that could be scanned between 15" (Fig. 23.366). An approximate analysis of the element illustrates the fundamental non-reciprocal action of the ferrite, but the precise behaviour embraces many effects including leaky-wave and surface-wave action in the ferrite slab. This type of element is of interest in certain communication applications demanding a robust construction, and the use of modem magnetic materials with temperature compensation will lead to a compact assembly.
*
Fig. 23.38 Photograph of microstrip hyperthermia applicatol
therapy. This fairly recent use of electromagnetic waves [36] necessitates the design of applicators that are well matched to the impedance of the human body and are compact in size for clinical convenience. An annular microstrip-loop
1294
Extensions and variations to the microstrip antenna concept
radiator has been devised [38] using plastic substrates, but the more recent compact applicators [36, 371 use a very high substrate permittivity. A sketch of a typical compact applicator is shown in Fig. 23.37 and a photograph in Fig. 23.38. In these designs the size reduction is achieved both by the high permittivity and the use of a quarter-wave as opposed to half-wave resonator. Further details are given in Table 23.5 for lower-frequency applicators. The penetration depth is a measure of performance, indicating the distance over which I/e2of the power is dispensed. Focused arrays of these applicators bring about an increased penetration depth. The compact applicator can be designed for a good stable input impedance match in operation without the use of additional matching elements, and further size reductions are possible at low frequencies by inserting ferrite material in the low-impedance regions of the substrate.
Table 23.5 Characteristics and performance of low-profile applicators
Applicator Material: 6, Pr
Element: quarter wavelength, cm Dimensions, cm Thickness, cm: Substrate Superstrate Frequency, MHz Net power for 235 W kg-' Penetration depth, cm (phantom)
A 30 1 7.5 15 x 15 x 4.5 2.2 2.2 200 156 4.0
B ' 30 2.5 7.5 15 x 15 x 4.5 2.2 2.2 120 406 4.3
23.6 Summary comment
The extensions and variations to the microstrip-antenna concept described are vastly different in application, and emphasise both the ingenuity that has already been experienced and the fund of innovative ideas that will continue to be created in future years. It was stated in Chapter 1 that the inspiration for innovation lies in the demands made by new systems, and this is well illustrated by the efforts on one hand to exert more control of radiation patterns, and on the other to increase bandwidth by an order. In each case one parameter is optimised at the expense of the others in a way which is compatible with the system constraints prevailing, but above all it is the microstrip technology that is diluted by other construction techniques to effect the desired optimisation. As already mentioned, it is a sign of maturity in a technology when a designer has learnt just how to exploit selectively its best features with confidence.
Extensions and variations to the microstrip antenna concept
7295
23.7 Acknowledgements
The authors would like to acknowledge the contribution to the work performed at RMCS and described in this chapter, of Dr G Andrasic, Dr C Hall, Dr C Prior and Mr R Johnson.
23.8 References I
I WOO, K.: 'Multiple beam antenna feed development'. IEEE Int. Symp. on Antennas and Propagation, Philidelphia, USA, 8-13 June, 1986, Vol. 1, p. 409-412 2 OLTMAN, H. G., WEEMS, D. M., LINDGREN, G. M., and WALTON, F. D.: 'Microstrip components for low cost millimetre wave seekers' In 'Millimetre and submillimetre wave propagation and circuits'. AGARD Conf. Proc. 245, pp. 27-1 to 27-9 3 HALL, P. S., and PRIOR, C. J.: 'Wide bandwidth microstrip reflector feed element'. 15th European Microwave Conference, Paris, Sept. 1985, p. 1039 4 HALL, P. S., and PRIOR, C. J.: 'Microstrip feeds for prime focus fed reflector antennas', IEE Proc., 1987, 134H, pp. 185-193 5 HALL, P. S., and PRIOR, C. J.: 'Microstrip array for reflector feed applications'. 14th European Microwave Conference, Liege, Sept. 1984, pp. 631-636 6 JAMES, J. R., HALL, C. M., HALL, P. S., and PRIOR, C. J.: 'Dielectric sphere reflector feed with microstrip excitation'. Proc. ISAP 1985, Tokyo, Aug. 1985, pp. 101-104 7 HALL, P. S., and HALL, C. M.: 'Coplanar corporate feed effects in microstrip patch array design', IEE Proc., 1988, 135H. pp. 180-186 8 TESHIROGI, T., TANAKA, M., and CHUJO, W.: 'Wideband circularly polarised array with sequential rotation', Proc. ISAP 85, Tokyo, Aug. 1985, pp. 117-120 9 HALL, C. M., ANDRASIC, G., and JAMES, J. R.: 'Microstrip planar arrays with dielectric sphere overlays', Electron Lett., 1985, 21, pp. 356-357 10 HALL, C. M., JAMES, J. R., and ANDRASIC, G.: 'Microstrip patch arrays with spherical dielectric overlays', Proc. Int. Conf. on Antennas and Propagation, Warwick University, IEE, April 1985, p. 89-93 11 JAMES, J. R., HALL, C. M., and ANDRASIC, G.: 'Microstrip elements and arrays with spherical dielectric overlays', IEE Proc., 1986, 133H, pp. 474482 12 DUBOST, G., and NICOLAS, M.: 'Broad angular coverage and large bandwidth antenna. 17th European Microwave Conference, Rome, Sept. 1987 13 JAMES, J. R., HENDERSON, A., and HALL, P. S.: 'Microstrip antenna performance is determined by substrate constraints', Microwave Syst. News, 1982, 2, pp. 73-84 14 HALL, P. S.: 'Probe compensation in thick microstrip patches', Electron Lett., 1987, 23, pp. 606-607 I5 HALL, P. S., WOOD, C., and GARRETT, C.: 'Wide bandwidth microstrip antennas for circuit integration', Electron. Lett., 1979, 15, pp. 458-460 16 KUMAR, G., and GUPTA, K. C.: 'Non-radiating edge and four edges gap coupled multiple resonator broad band microstrip antennas', IEEE Trans, 1985, AP-33, pp. 173-177 17 BENNETT, C. L., and ROSS, G. F.: 'Time domain electromagnetics and its applications', Proc. IEEE, 1978, 66, pp. 299-318 18 HALL, P. S.: 'New wideband microstrip antenna using log periodic technique', Electron Lett., 1980, 16, pp. 299-318 19 HALL, P. S.: 'Multi-octave bandwidth log periodic microstrip antenna array' Proc. IEE., 1986, 133 H, pp. 127-136 20 ISBELL, D. E.: 'Log periodic dipole arrays' IRE Trans., 1960, AP-8, pp. 260-267 21 DONG, W. R., and SENGUPTA, L. L.: 'A class of broad band patch microstrip travelling wave antennas', IEEE Trans., AP-32, (I), pp. 98-100
7296
Extensions and variations to the microstrip antenna concept
22 PUES, H., BOGAERS, J., PIECK, R., and VAN DE CAPELLE, A.: 'Wideband quasi log peripdic microstrip antenna', IEE Proc.. 1981, 128H, pp. 159-1 63 23 HALL, P. S., and SPARROW, A,: 'Microstrip log periodic antenna array with end fire beam', Electron Lett., 1987, 23, pp. 912-913 24 GREISER, J. W., and MAYS, P. E.: 'The bent backfire zigzag', IEEE Tram., 1964, AP-12, pp. 28 1-290 25 BOND, K., and SHELLEY, M. W.: 'Dual frequency antenna integration using invisible grating structures', IEE Proc., 1986, 133H. pp. 137-142 26 JAMES, J. R., and ANDRASIC, G,: 'Dichroic dual band microstrip array', Electron Letts., 1986, 22, pp. 1040-1042 27 ANDRASIC, G., and JAMES, J. R.: 'Microstrip window array', Electron. Lett., 1988,24, pp. 96-97 28 BURKE, G. J., and POGGIO, A. J.: 'Numerical electromagnetic code (NEC) method of moments', Tech. document 116, Naval Electronic Systems Command, July 1977 29 JAMES, J. R., and ANDRASIC, G.: 'Superimposed dichroic microstrip antenna arrays', IEE Proc., 1988, 135H. No 5, pp. 304-312 30 JAMES, J. R., and HENDERSON, A.: 'Planar millimetre wave antenna arrays' In BUTTON, K. I. (Ed.): 'Infra-red and millimetre waves'. Vol. 14: Millimetre components and techniquesPart V. (Academic Press, 1985), pp. 189-247 31 HENDERSON, A., JAMES, J. R., and HALL, C. M.: 'Bandwidth extension techniques in printed conformal antennas'. Military Microwaves Conference, Brighton, 1986, pp. 329-334 32 HENDERSON, A,, JAMES, J. R., HALL, P. S., STOTT, J. H., and BOARDMAN, D. H.: 'Investigation of a cost constrained 12 GHz flat plate antenna for DBS'. Proc. ICAP, Warwick, 1985, pp. 108-112 33 HENDERSON, A,, and JAMES, J. R.: 'Low cost flat plate array with squinted beam for DBS reception', Proc. IEE, 1987, lMH, pp. 509-514 34 DAS, N., CHOWDHURY, S. K., and CHAlTERJEE, J. S.: 'Circular microstrip antenna on ferromagnetic substrate', IEEE Trans, 1983, AP-31, pp. 188-190 35 HENDERSON, A., JAMES, J. R., and FRAY, A.: 'Magnetised microstrip antenna with pattern control' Electron. Lett., 1988, 24, pp. 45-47 36 JAMES, J. R., HENDERSON, A,, and JOHNSON, R. H.: 'Compact electromagnetic applicators'. In HAND, J. W., and JAMES, J. R. (Eds.): 'Physical techniques in clinical hyperthermia' (Research Studies Press, John Wiley, 1986), pp. 149-209 37 JAMES, I. R., HALL, C. M., and ANDRASIC, G.: 'Angled dual compact hyperthemic applicators', Proc. IEE, 1987, lMH, pp. 315-320 38 BAHL, I. J., BHARTIA, P., and STUCHLY, S. S.: 'Design of microstrip antennas covered with a dielectric layer', IEEE Trans., 1982, AP-30, pp. 314-318
Index
Abberation, 96 Acid, copper, 936 Activation energy, 875 Active angle, 1241 Active element pattern, 701,739, 1249 Active elements in a cylindrical array, 1249 Active impedance, 732 Active patches, 34 Active reflection coefficient, 708, 739 Additives, brightener, 936 Adhesion, 936 Adjustable height patch. 30 Admittance, aperture, 727 Aerospace systems, 1057 Air gap, adjustable, 193 Air-filled waveguide, 858 Airborne antenna, 1139 Airborne phased arrays, 802,810 Alumina substrates, 14, 1025 Aluminium, 93 1, 946 Aluminium foil, 1075 Amplitude distributions, 830 Analytical methods aperture radiation model, 583 cavity model, 458,580,1058,1228 Cohns method, 611 contour integral method, 472 desegmentation, 456,494 direct form of network analogue, 462
EMF,249 Filton Integration method, 285 integral equations, 715 method of moments, 364,708 moments method, 593 multiport network approach, 455 multiport network model, 462 network analysis, 488 plane wave spectrum method, 285 real-space integration method, 286
reciprocity method, 278 Richmonds reaction equation, 597 segmentation, 456,488 spectral domain approach, 590 steepest descent method, 278 surface current model, 1228 synthesis, 361 transmission line model, 456 variational method, 235 Wiener-Hopf method, 478 Angled slot array, 39 Anisotropy, 881, 909, 917 Annealed, 946 Annular ring, 25,879,1262 Annular slot, 111,611,1086 Annular slots attenuation coefficient, 614 guide wavelength, 611 impedance, 611 reflector planes, 617 Antennas conical, 601
DBS,859,861 dielectric, 1287 directly coupled three resonator, 507 hybrid microstrip, 580 integrated, 14 gap coupled multiresonator, 507 millimeter wave hybrid, 1285 multi-terminal, 236 open microstrip, 580 window, 1283 wraparound, 85 Antenna location, received signal fluctuations, 1084 Antennas for portable equipment, 1092 Aperture admittance, 727 Aperture blockage, 96, 104 Aperture coupled patches, 330
lndex
1298 lndex
Aperture coupling, 35, 332, 823 Aperture distribution, 762,821, 822, 825, 851 Aperture distribution Dolph-Chebyshev, 855 Aperture radiation analysis method, 583 Apertures, dichroic, 1282 Applications, 8 Array factor, 829 Array lattice rectangular, 706 triangular, 706, 1243 Array structures, 36 Arrays, 7,35 angled slots, 39 architecture, 745 asymmetric step, 39 bonding, 916 brick wall, 848 cascaded patch, 822 chain, 37, 763, 816 Chebyshev, 774 circularly polarised, 755,765 co-planar, 758 comb line, 37, 766, 822 composite element, 759,770 conformal, 795, 1153, 1227 conical, 1154 constant-conductance, 846 corner fed patches, 647 corporate-fed, 789 crank, 844 crank-line, 777 crank-type, 764 cross fed, 36, 655, 843 cross printed-dipole, 766 cross slot, 766 cylindrical, 34,765, 1227 DBS, 766,790,1288 design of planar, 622 discontinuity, 843 dual frequency, circular polarised, 802 dual polarised, 1073 electronically switched, spherical, 792 finite, 301, 731 flat, circular polarised, 765 four element, 1217 Franklin, 8 16, 848 Franklin line, 38 herringbone, 835 herringbone line, 38 infinite, 698, 731 lattice, 848
linear, 345,449 linear centre fed, 839 linearly polarised, 846 log periodic, 39, 387 microstrip, 443 millimeter wave, 1282 monopulse, 849, 1068, 1153 non uniform, 630 omnidirectional, 39, 382 parasitic, 801 parasitic patch, 825, 833 parasitically coupled, 37, 345 patch, 1263 planar, 345, 776,790 rampart, 816, 844 rampart line, 38,223, 763, 1222 recurrent sequential, 808 resonant, 769,816 scanning, 792 sector beam, 1081 sequential, 759, 788, 805 sequentially rotated, 12 series, 816 series fed patch, 515 series fed patches, 624 series-fed, 789, 8 18 series-fed circular polarised, 770 serpent, 816,833,843 serpent line, 38 sparse, 1273 spherical, 34,793, 1239 square patches, 1073 square-looptype, 764 squintless, 758,841 strip dipole and slot, 39 sub arrays, 655 synthesis, 662 tapered, 650 transposed, 821,822 travelling wave, 755, 762, 765, 769, 816,1222 triangle line, 38 two dimensional, 808 two sided, 746 untransposed, 821 wide bandwidth, 372 wideband, 804 wire grid, 848 Assemblies, 916 Asymmetric feeds, 797 Asymmetric step array, 39 Attachment mode, 433 Attenuation, 1016
Attenuators, 1241 Axial polarisation, 1239 Axial ratio, 723, 787, 1185 Axial-ratio bandwidth, 758,829, 859 Azimuthal modes, 53 Backward firing beams,834 Bag-moulding, 930 Balanced stripline, 1003 Bandwidth, 5, 11, 111, 128,219, 335, 338, 554,743,796,895 Bandwidth, 9 axial-ratio, 829, 859 extension, 9 gain, 823 VSWR, 118,823 Base-station antenna, 1083 Basis functions, 282 entire domain, 429, 437 Maxwell, 282 Maxwell, modified, 282 pulse, 282 subdomain, 282,437 subsectional, 423,440 Beam squint, 758 Beam steering, 1241, 1249, 1273 Beam-forming, adaptive, 862 Beams backward firing, 834 forward firing, 834 Beamwidth, 104 Bend measurement, 976 Bending, 916 Bends, 1168 Beryllia substrates, 1025 Bessel function, 1058, 1204 Bidirectional communications, 1107 Bismaleimide, 95 1 Bismaleimide-triazineepoxx878 Black copper oxide, 880 Blind spots, 336, 729 Blockage, aperture, 96 Boards, printed wiring, 916 Bolometer, 1194 Bonding lead, 952 thermal-compression, 938 thermosonic, 938 wire, ultrasonic systems, 938 Boundary conditions, 49, 115,395 Branch-line coupler, 854 Branching network, 825
1299
Brass, 946 Brick wall arrays, 848 Broadband microstrip antenna, 1083, 1086, 1129,1134 Broadband matching, 558 Built in antennas, 1092 Butler matrix, 855, 860, 1083 Cabin antenna, 1085 CAD, 14, 1031 Acline, 1033 Analop, 1036 Autoart, 1037 CADEC, 1033 CiAO, 1035 computer graphics, 1175 Esope, 1033 LINMIC, 1034 Mama, 1036 Micad, 1037 Micpatch, 1035 Microkop/Suspend, 1036 Micros, 1038 microstrip, 1001 microwave software applications, 1036 Midas, 1034 Multimatch, 1036 photoplots, 1175 Planim, 1036 S/Filsyn, 1037 Supercompact, 1033 techniques, 517 Temcad, 1039 Touchstone, 1032 Transcad, 1037 triplate, 1001 Fringing, 901 Capacitance, 901 Capacitive tuning, 329 Capacitors, 1040 Car telephones, 1079 Carbide, 922 Carbon fibre reinforced plastic, 1075 Cavity feeds, 859 ~ a v i t model, ; 112,458, 580, 884, 1058, 1228 Cavity-perturbation, 884 CCIR-TVRO conditions, 671 Central shorting pin, 85 Centred fed dipole, 287 Ceramic-PTFE, 953
1300 lndex
lndex
Chain array, 37, 763, 816, 940 Chain scission, 940 Chebyschev taper, 774, 1069 Chloride acid cupric, 949 alkaline cupric, 949 ferric, 949 Choke, peripheral, 104 Chokes, 97 Chromic-acid, 950 Circuit, etching, 1028 Circular array, 1127 Circular array feed, 1132 Circular array of slots, 1132 Circular array of strips, 1132 Circular microstrip discs, 1136 Circular patches, 45, 63, 111, 720, 1058, 1202 Circular polarisation, 5, 130, 219, 722, 744, 755,787, 846,848, 1127, 1132, 1261,1273 Circular polarised radiation, 824 Circular polariser, 766 Circulardisc patches, 756 Circular-patch array, 1113 Circular-patch-slot array, 1119 Circularly polarised, singly fed patches, 221 Circularly polarised arrays, 755,765 Circularly polarised circular patches, 232 Circularly polarised composite type patches, 222 Circularly polarised dipoles, 356 Circularly polarised elements, 12 Circularly polarised line antennas, 762 Circularly polarised patches, 27,499,821, 1218 Circulators, 1041 Circumferential polarisation, 1234 Co-axial feeds, 276 Co-planar arrays, 758 Co-planar coupling, 817 Co-planar feeds, 8 15 Co-polymers, 945 Coating, conformal, 950 Coaxial excitation, 432 Coaxial probe, 29, 433, 1194 Cohns method, 61 1 Collected volatile condensable materials (CVCM), 940 Colloidal, 88 1 Comb array, 37, 766, 822, 833 Combined feeds, 839 Comparator, monopulse, 859
Compensating hole transitions, 967 Components, 1039 Composite element, 755, 759, 770 Computational efficiency, 709 Computer graphics, 1175 Conductance edge, 476 radiation, 476, 554, 822, 835, 859 surface wave, 476 Conductivity, 879 Conductor, losses, 788, 790, 815, 1075 Conformal antenna, 1227 Conformal arrays, 795, 1153 Conformal mapping, 1008 Conical antennas, 601 Conical arrays, 1154 Conical beam, 1112, 1127, 1129, 1132, 1239 Conically depressed patch, 29 Connections, 332 Connector characterisation, 962 Connector test fixture, 963 Connectors, microstrip to coax, 1007 Constant-conductancearrays, 846 Contour integral method, 472 Coplanar line probes, 968 Coplanar stripline patch, 31 Copolymer substrates, 679 Corporate feeds, 301 Copper electroless, 935 Copper foil, 1075 Copper-Invar-copper, 946 Comer fed patches, 647 Comer reflector, 1082 Corporate feeds, 13, 35, 757,789, 816, 850, 1069,1288 Correction, end-fringing, 888 Correlation, 905 Corrugated ground plane, 28 Cosecant squared pattern, 671 Coupled triplate lines, 1169 Coupled-resonator, 340 Coupler branch-line, 854 hybrid-ring, 854 Coupling, 817, 887, 895, 897 Coupling agents, 875 aperture, 823 co-planar, 8 17 direct, 822 electromagnetic, 824 factor, 835
!
probe, 822 proximity, 8 18 Coupling gaps, 762 Coupling mechanisms, 816 Crank arrays, 764,777,844,1115 Cross-printed dipole arrays, 766 Cross fed arrays, 36,655,843 Cross patch, 501 Cross polarisation, 68,74,76, 100, 104, 590,1234 Cross slot arrays, 766, 1136 Crossed dipoles, 356 Crossed slot, 28 Crossover level, 793 Crystalline, 873, 878, 942 Current distributions, 112 magnetic, 726 sources, 112 Current sheet model, 731 Current-ribbon, 151 Cyanide, copper, 936 Cycling, wet/dry, 941 Cylindrical antenna, 1227 Cylindrical array, 1109 active-element, 1249 array feed, 1248 design, 1240 gain, 1248 impedance, 1243 mutual coupling, 1244 pattem synthesis, 1251 scanning, 1249 Cylindrical modes, 1230 Cylindrical near field scanning, 981 Cylindrical patches, 1227 Cylindrical wave propagation, 1072 Dantzig algorithm, 662 Data-relay satellite, 1146 DBS antennas, 766,790,859, 1112 De-smearing, 929 Decomposition, thermal, 919 Deformation, 924 Degenerate modes, 756 Dendrites, 879 Dents, 917 Desegmentation method, 456,494 Design procedure, series-feed, 836 Device attachment, 936 Diagnostics, 1159,1193.1214 Diagnostics, liquid crystal, 984
1301
Diagonal slot square patch, 499 Diagonally fed nearly square patch, 499 Dielectric antennas, 1287 losses, 788,815, 1016 Dielectric constant, 790, 897 Dielectric constant, effective, 481 Dielectric filling factor, 790 Dielectric image guide, 822, 858 Dielectric loss, 1075 Dielectric rod array, 39 Dielectric spheres, 3 1 Difference radiation pattem, 1068 Diffraction coefficient, 1069 Diffraction effects, 1069 Diodes, 1041 Dipole centre fed, 287 flat folded, 765 horizontal electric, 276,403 infinitesimal, 276 printed, 765 circularly polarised, 356 crossed, 356 efficiency, 367 EMC, 295 flat, 353 multiple, 299 mutual impedance, 359 parasitic, 759 polarisation, 361 printed, 706,732 stacked, 299 strip, 761 synthesis, 361 variable directivity, 372 Direct coupling, 822 Direct form of network analogue, 462 Direct-BroadcastSatellite, 1288 Directional coupler hybrid-ring, 855 rat-race, 855 Directivity, 127, 372, 554, 831 Directivity, linear arrays, 625 Directly coupled three resonator antenna disc,25,507,843,1258 Discontinuity arrays, 843 Discontinuity radiation, 791 Dispersion, microstrip, 1015 Dissipation, loss, 1285 Dissipation factor, 871, 878, 886, 895 Distribution amplitude, 830
1302 lndex
aperture, 825 Dolph-Chebyshev, 830 Taylor, 830 Dolph Chebyshev distributions, 830, 855 Dose rate, 940 Double tuning, 1064 Doubly diffracted field, 1069 Drills, 922 Dual aperture-fed patches, 823 Dual feeds, 219 Dual frequency circularly polarised arrays, 802 Dual ijarised array, 1073 Dual-fed circularly polarised patches, 220 Dual-frequency patches, 30, 188, 197,200, 312,313,796,802 Dual-polarisation patches, 3 12, 3 18 Ductility, 879, 936 Dust protection shield, 1063 Dyadic Green's function, 284,399 E-H antenna, 1083 Earth stations, 1112 Edge conductance, 476 effects, 1069 equivalent admittance network, 463 ground plane, 12, 731 non radiating, 481 Effective dielectric constant, 481 Effective loss tangent, 461 Effective permittivity two-layer medium, 196 Effective radius, 65, 137 Effective width, 115 Effects, environmental, 939 Efficiency, 5,13, 117,313,346,367,413, 554,781,837,1258 Efficiency computational, 709 measurement, 991 radiation, 9, 598, 734, 872 spill-over, 104 Elastic, 924 Electromagnetically coupled patch, 31 Electric current analysis method, 583 Electric dipole, 403 Electric shielding ring, 803 Electric source, 1260 Electric walls, 113 Electric-current source method, 762,765 Electric-field integral equation, 715, 726, 732
lndex
Electro-etch, 879 Electromagneticcoupling, 207, 797, 824 Electronically switched spherical arrays, 792 Electroplating, 935 Electrostatic charging, 1065 Element endfire, 749 tapered-slot, 751 Element factor, 831 Element grid, 1241 Element pattern, 732 Elliptical patch, 25, 182,235,756, 1129 Elliptical polarisation, 186 EM-field, far-zone, 117 EMC dipole, 295 EMF method, 249 End fringing, 887 Endfire arrays, 1279 Endfire elements, 749 Energy, confonnational, 88 1 Entiredomain basis functions, 429, 437 Environmental conditions, 875 Environmental effects, 679 Epoxy, 878,951 Equitriangular patches, 111 Equivalence . external, 47 internal, 49 Equivalent sources, 112 Equivalent circuit, 237, 728 Eauivalent circuit model., 769.. 776 Equivalent current sources, 114 Eauivalent edne admittance network. 463 ~quivalentmagnetic current, 116 Equivalent slot, 534 Equivalent surface currents, 49 Equivalent waveguide model, 817 Etch plasma, 929 sodium, 929 Etchant, 949 Etching, 1028 Eulers constant, 474 Excitation, coaxial, 432 Excitation field, 396 Excitation voltage, 784 Expansion functions, 53 External equivalence, 47 External matching circuits, 28 Fabric, 922 woven-glass, 935
Far-field approximations, 408 Feed isolation, 320 Feed structures, 35 Feeder of a cylindrical array, 1248 Feeds, 32, 756,767, 1001 3 dB hybrid, 220 architecture, 13 asymmetric, 797 cavity, 859 co-axial, 276 co-planer, 8 15 coaxial probe, 29 combined, 839 corporate, 13, 35, 306, 757, 816, 850, 1069 corporate, triplate, 1288 dual, 219 four point, 28 four-probe, 756 Lecher line, 353 microstrip line, 29 novel, 12 overlaid, 1263 parallel, 335, 757, 816, 825, 828 perpendicular, 747 phased array, 862,1248 radial waveguide, 859 rear, 758 reflector, 96 resonant, 835,1074 sequentially rotated, 36 series, 335,758,767,816,832 series compensated, 36 single, 219 spurious-radiation, 332 squintless, 832 stripline, 353 travelling-wave, 832 two-dimensional, 839 two-line, 276 Ferrimagnetic substrates, 1027 Ferrite superstrates, 1292 Fibres, glass, 922 Field, excitation, 396 Filler, ceramic, 922 Films, barrier, 930 Filton integration method, 285 Finite arrays, 301, 731 Finite ground plane, 12, 1069 Flat dipoles, 353 Flat folded dipole, 765 Floquet modes, 703 Flouborate, copper, 936
1303
Flush mounted antennas, 1092 Foam, 953 Foils adhesion, 875 aluminium, 1075 copper, 1075 electrodeposited, 879 rolled, 879 wrought, 879 Folded slots, 353 Forming rolls, 924 Forward firing beams, 834 Four element arrays, 1217 Four element sub-arrays, 805 Four point feeding, 28 Four-probe feeds, 756 Fourier Transform, 403,406,708, 716, 721,726 Franklin array, 38, 816, 848, 1105 Free radical, 941 Frequency, resonant, 895 Frequency agility, 187 Frequency diversity, 1084 Fringing fields, 113 Full sheet resonance test method, 884,897, 90 1 Fumes, 919 Functions testing, 53 triangular, 54 Future prospects, 1 GaAs substrate, 332 GaAs superstrate, 281 GaAs transitions, 968 Gain, 127, 554, 831 minimum coverage, 793 bandwidth, 823 factor, 104 Gain of a cylindrical array, 1248 Galerkin solution, 284 Gap coupled multiresonator antenna, 507 Gap-wupled patch, 8 17 Geometric optics field, 1069 Giotto spacecraft, 1061 Glass transition temperature, 875 Glossary, 24 Grain structure, 879 Grating lobes, 428, 826, 834, 1183 Green's function, 50, 116, 398, 41 1, 421, 426,462,695,726 dyadic, 399
lndex
1304 Index
planar configurations, 519 spectral domain, 327 Ground plane corrugated, 28 slot, 32 edge, 12,731 GTD, 1183 Guide dielectric image, 822 insular, 822 Gunn diode. 34 H-shaped patch, 26 Half-wave patch, 313, 817 Hand held message communication terminal, 1125 Handbook, 17 Hankel Transform, 406 Hankel function, 264, 473, 1230 Hard boundary diffraction coefficient, 1069 Herringbone array, 38, 835 Higher order modes, 356,787,796, 1058, 1129 Historical development, 1 History mechanical, 874 thermal, 874 Holes, burr-free, 922 Honeycomb substrate, 796 Horizontal dipole, 403 Humidity, 875 Huygens sources, 1262 Hybrid coupler, 1064,1081,1164 Hybrid microstrip antenna, 25, 580 Hybrid sources, 353 Hybrid-ring coupler, 854, 855 Hydrocarbon, 951 Hydrolysis, 875 Hydrophobic, 941 Hyperthermia applicator, 1293 Image, 116 Impedance active, 732 cylindrical array, 1243 input, 9, 118,439, 590, 708 matching, 655, 1190 matrix, 708,716 port matrix, 737,739 surface, 400 transformer, 1064
Incoherent radar, 1073 Indoor communications antenna, 1083 Indoor receiving antenna, 1084 Inductance feed probe, 329 Inductors, 1041 Infinite arrays, 698, 731 Infinite phased arrays, 698 Infinitesimal dipole, 276 Infra-red, 875 Input impedance, 9, 118,238,432,439, 708,875 admittance, 770 conductance, 554 Input resistance o f patches, 324 Inserted connector transitions, 967 Insular guide, 822 Integral equation, 47 Integral equation, electric-field, 715, 726, 732 Integrated antennas, 14 Integrated phased arrays, 742 Internal equivalence, 49 Iris, 906 Isolated power dividers, 852 Isolators, 1041 Junction effects, 1166
K connector transitions, 967 K', thermal coefficient of, 947 Kevlar epoxy, 1075 Land mobile satellite communications, 1127 Lattice arrays, 848 Launchers, 1287 Layer, resistive, 947 Leaky cavity, 119 Lecher line feeds, 353 Light, ultra-violet, 929 Limiting oxygen index, 919 Line analysis dielectric Green's function, 1020 Fourier transform, 1020 integral equations, 1020 TEM models, 1020 variational techniques, 1020 Line antenna, circularly polarised, 762 Linear arrays, 345,449
Linear centre fed arrays, 839 Linear polarisation, 130 Linear slots, 606 Linearly polarised arrays, 846 Lines dielectric, 1285 discontinuities, 762, 1017 losses, 624 open circuited, 1212 parallelaupled, 856 parameters, 971 parameter measurement, 970 synthesis, 1015 width, 943 Liquid crystal diagnostics, 984, 1058, 1159 Loading, reactive, 204, 826 Lobes, grating, 826, 834 Log periodic arrays, 39,387,834, 1273 Longitudinal polarisation, 822, 846 Lorentz's gauge, 398 Loss tangent, 117, 461 Losses, 174,407 conductor, 788,815,942,1075 dielectric, 1016, 1075 dissipation, 1285 line, 624 ohmic, 1016 radiation, 1016, 1075 reflection, 8 16 resistance, 887 resistive, 895 surface wave, 816, 1075 Low cost substrates, 674 Machining, 916 Magnetic current, 116,726,762 materials, 1292 source, 1260 walls, 113 Main beam direction, 781 Mandrel, 931 Manpack radars, 1079 Manufacture, 5,14 Marine radars, 1079 Maritime satellite communications, 1127 Matched terminations, 964 Matching, 5 Matching circuits external, 28 gaps, 28 Mated connector test method, 963
1305
Materials, magnetic, 1292 Mathematical modelling, 14 Matrix Butler, 861 excitation, 58 formulation, 50 impedance, 708,716 Maxson-Blass, 861 Maxon Blass matrix, 860 Maxwell basis functions, 282 Maxwell, modified basis functions, 282 Measurements, 957, 1006 bends, 976 efficiency, 991 line parameters, 970 radiometric, 993 resonant techniques, 976 T-junctions, 977 Melt point, crystalline, 879 Melt viscosity, 928 Metal failure, 934 Metallic ring transitions, 967 Method of moments, 282,295,364,401, 423,708 Metrology, 1193 Microstrip circuit realisation, 1028 impedance, 1013 line, 1004 materials and manufacture, 1023 Microstrip antenna hybrid, 25 frequency variable, 1092, 1101 post loaded, 1O92 quarter wavelength, 1092 window attached, 1092 Microstrip dispersion, 1015 Microstrip field diagnostics, 1193 Microstrip line, 537 Microstrip line feeds, 29 Millimetre wave hybrid antennas, 1285 Minimum coverage gain, 793 Mismatch thermal, 953 Mixed potential integral equation, 400 Mobile communications base stations, 1081 Mobile communications antenna, 1083 Mobile satellite communications, 800, 1142 Mobile systems, 1079 Modal expansional method, 235 Mode ambiguous, 901 Modelling mathematical, 14 Modelling accuracy, 16 Modes
1306
lndex
azimuthal, 53 degenerate, 756 higher order, 356, 787, 796, 1058 orthogonal, 221 parallel-plate, 8 16 resonant, 900 suppressing pins, 1065 transverse electric field, 887 unwanted, 258 Modularity, 744 Modulus, 953 Moisture, 875,941 Moments method, 593 Monopole probes, 1197 Monopulse arrays, 849, 1068, 1153 Monopulse comparator, 859 Moulding vacuum-bag, 926 Multi-terminal antenna, 236 Multibeam antenna, 1083, 1146 Multilayer substrates, 679,944 Multipath fading, 1096 Multiple beam-forming networks, 817, 859 Multiple dipoles, 299 Multiple feed point patches, 262 Multiple frequency patches, 320 Multiple layer patches, 30 Multiple tuning, 341 Multiport network approach, 455 Multiresonator patch, 507 Mutual coupling, 249, 306, 337.445. 561. Mutual coupling in a cylindrical array, 1244 Mutual coupling network, 464,482 Mutual impedance, 237,291,359,378 Narrow pin transitions, 967 Near field mapping 989 Near-field probes, 98 1 Network analysis techniques, 488 Networks multiple-beam-forming, 817 special-purpose, 859 Nitrogen, 930 Nodules, 879 Non radiating edge admittance network, 482 Non radiating edge characterisation, 481 Non uniform arrays, 630 Notched patch, 27,796 Numerical analysis, 16 Numerical techniques, 417
lndex
Off centred pin transitions, 967 Offset fed oatches. 221 Ohmic lo-, 101'6 Omnidirectional arrays, 382, 765 Open circuit end, 534 Open circuited lines, 1212 Open microstrip antennas, 580 Operational factors, 5 Optical modulator probe, 983 Optically tuned patches, 192 Orthogonal fields, 787 Orthogonal polarisation, 30 Overlaid feeds, 1263 Overlaid patches, 35, 1277 Pagers, 1092 Paired elements, 263,270, 758, 788, 804 Parallel feeds, 335, 757, 816, 825, 828 Parallel date resonator test method, 959 ~arallel-bu~led lines, 856 Parallel-plate modes, 8 16 Parallel-plate polariser, 766 Parallel-plate waveguide, 858 ~arasiticrarra~s, 80i Parasitic patches, 29,214,264, 797, 825, 833,1083,1086,1129 Parasitically coupled array, 37 Passivate, 950 Patch arrays, 822, 1263 Patches annular ring, 25, 111 apertureaupled, 330, 723 bandwidth, 111, 554 cavity model, 1228 circular, 45,63, 11I, 232, 580, 720, 1058, 1202 circulardisc, 756 circularly polarised, 27,499, 755, 821, 1218 composite type, 222 conically depressed, 29 coolanar strioline, 3 1 corner fed, 847 cross, 501 cylindrical, 1227 design, 557 diagonal slot square, 499 diaaonallv fed nearly square, 499 directivity, 554 disc, 1258 dual aperture-fed, 823 dual band circularly polarised, 1061
dual-fed, 220 dual-frequency, 30, 188, 197, 200, 312,313,796,802 dual-polarisation, 3 12, 3 18 efficiency, 554 electromagnetically coupled, 31,207, 797 elliptical, 25, 182, 235, 756 equitriangular, 111 gain, 554 Green's functions, 462 H shaped, 26 half-wavelength, 313 input conductance, 554 input resistance, 324 multiple feed points, 262 multiple frequency, 320 multiresonator, 507 mutual impedance, 378 notched, 27,796 offset fed, 221 optically tuned, 192 overlaid, 1277 paired, 263, 270, 804 parasitic, 214, 797 pentagon, 756 pentagonal, 25,505, 1218 piggy-back, 313 polarisation, 378 post-tuned, 3 15 probe-fed, 713,720 quarter wavelength, 313, 1154 rectangular, 111, 224,235,436, 553, 580, 1215,1234 rectangular, comer-fed, 756 rectangular ring, 26 resonant frequency, 324 short circuit, 374 short circuited, 353 short circuited ring, 346 shorted, 1281 singly fed, 221 slotted, 27 square, 25 square ring, 501 stacked, 29,320 stacked circular-disc, 197 star, 26 stepped, 29 strip line, 111 surface-current model, 1232 thick, 253 tilted slot, 756
1307
triangular, 25, 235, 1209 truncated comer, 27 truncated corner square, 499 two port, 51 1 wide, bandwidth, 320 wideband, 28, 796 Pattern, active element, 739 Pattern synthesis of cylindrical arrays, 1251 Peel strength, 937 Peel-test, 878 Pentagon patches, 25,505,756, 1218 Performance trade-offs, 7 Peripheral choke, 104 Permittivity complex, 872 effective, 48 1 relative, 871, 878, 881, 886, 895 very-high, 1293 Perpendicular feeds, 747 Persulfate, 949 Perturbation segment, 224 Perturbation cavity, 914 Phase centre, 96, 106, 1161 Phase constant, 779 Phase shifters, 864, 1081,1241 Phase shifters, Schiffmann, 848 Phased arrays, 378, 741, 802, 810, 862, 1241 Phased arrays infinite, 698 integrated, 742 Photolithographic techniques, 1002 Photomask, 888 adhesion, 9 18 Photoplots, 1175 Photoresist, 1029 Piggy-back patches, 313 Pinholes, 880 Pits, 917 Planar arrays, 345, 776, 790 Planar near field scanning, 981 Planar segments, characterisation by Z matrix, 467 Plane wave spectrum method, 285 Plastic substrates, 14, 1025 Platen-press, 929 Plating holes, 916 Point dipole approximation, 287 Poisson sum formula, 699 Polarisation, 5, 743, 783 Polarisation 45 deg, 821 axial, 1239
1308 lndex
circular, 5, 130,219, 722, 744, 755, 846,848,1261, 1273 circumferential, 1234 cross, 68, 74,76, 100, 104,590, 1234 ellipse, 1187 elliptical, 186 ellipticity, 231 linear, 130 longitudinal, 822, 846 orthogonal, 30 tracking, 755 transverse, 82 1, 846 Poles, surface wave, 697 Polyethylene, 873 Polymer fume fever, 919 Polymer systems, thermoset, 878 Polymerisation, 88 1 Polymides, 951 Polypropylene substrates, 678 Polypropylene-ethylenesubstrates, 679 Polytetraflouroethylene, 873 Post-tuned patches, 3 15 Posts, 235 Potential, 41 1 diffracted field, 397 scalar, 399, 405 vector, 50, 399,403,405 Power combiners, 8 16 Power dividers isolated, 852 rat race, 1069 split-tee, 852 three-port, 852 Wilkinson, 307, 852, 947, 1069 in-line, 850 Precision, 891 Press, platen, 926 Pressure vessel, 929 Printed dipoles, 706,732,765 Probe coupling, 822 Probe-fed patches, 71 3 Probes coaxial, 433, 1194 coplanar line, 968 errors, 1200 monopole, 1197 near-field, 981 optical modulator, 983 scanning network, 1195 short monopole, 982 small loop, 982 split coaxial balun, 982 square law, 983
lndex
wafer, 968 Processing, 916 Proximity coupling, 8 18 F'TFE, 873,881,919 ceramic, 884 glass fibre, 883 woven glass, 884 Pulse basis functions, 282 Pyrophosphate, copper, 936 Q factor, 111, 119, 128, 174, 324, 590, 593,796,887,895 Quarter wave resonance, 353 Quarter-wave patch, 3 13, 8 17 Quasi-log-periodic, 1279 Radar, 1105 Radar reflector, 1107 Radial waveguide feeds, 859 radiated, electric field, 41 1 Radiation circular polarised, 824 conductance, 8 17 cosmic, 940 damage, 941 dose, 941 efficiency, 9, 126, 598, 734 exposure, 939 feeds, 12 fields, 112 high-energy, 940 losses, 788,791, 1016, 1075 nuclear, 940 patterns, 122, 335, 449 resistance, 413 slot, 222 spurious, 353,743,816,824 ultra-violet, 941 unwanted, 787 Radiometric measurement, 993 Radius, effective, 65 Radome, 14,926,945, 1273 Railway antennas, 1087 Rampart array, 38, 763, 816, 844, 1222 Rat race hybrid, 855,1069 Reactance compensation, 761,823 Real space integration method, 286 Rear feeds, 758 Reciprocity method, 278 Rectangular array lattice, 706 Rectangular patch, 7,25, 111, 235,436,
1
553, 1215, 1234 Rectangular ring patch, 26 Rectangular-slot array, 1118 Reflect array, 33 Reflection coefficient active, 708, 739 Reflection losses, 816 Reflector feeds, 96, 1258 Relaxation synthesis, 662 Residue, 278 Resin poly(tetraflouroethy1ene)(PTFE), 879 polycyanate, 878 polyetherimide, 879 polyethersulfone, 879 polyimide, 878 polystyrene, 878 polysulfone, 879 triazine, 878 Resin laminates, 929 Resistance, radiation, 413 Resistive box terminations, 964 Resistive layer, 950 Resistivity, surface, 948 Resistors, 1040 Resonant arrays, 769,816 Resonant cavity, 111 Resonant feed networks, 835, 1074 Resonant frequency, 115,324,593 Resonant peak, 887 Resonant ring test method, 961 Resonant-mode, 117 Resonator microstrip, 914 stripline, 914 Resonator strip test method, 960 Richmonds reaction equation, 597 Rotation, sequential, 12,263, 828, 859 Rotman lenses, 860 Routers, 922 Rutile substrates, 1025 S-matrix, 1240 Safety, 916, 919 Sapphire substrates, 1025 Satellite ERS-I, 1073 ETS-V, 1112 NAVSTAR (GPS),1124 antennas, 1146 communications, 1136 systems, 1079 Scalar potential, 399, 405
1309
Scan angle, 785 Scan blindness, 700,709,719,723,731 Scan range, 743 Scanning a cylindrical array, 1249 Scanning arrays, 792 Scanning losses, 792 Scanning network probes, 1195 Scattering matrix, 702, 783 Scatterometer, 1073 Schartz-Christoffel transform, 1011 Schiffmann phase shifters, 848 Schotky barrier diode, 1194 Secondary su~eillanceradar, 1068 Sector beam array, 1081 Sector patterns, 664 Segmentation method, 456,488 Semi infinite substrate, 731 Semiconductor substrates, 1027 Sequential arrays, 12,36,263, 788, 805, 828,859,1142,1265 Series arrays, 816 Series compensated feeds, 36 Series fed patch arrays, 5 15 Series feeds, 335,758,767,816,832,789, 818 Series-fed circularly polarised arrays, 770 Series-feed design procedure, 836 Serpent array, 38,816, 833, 843 Shear, 937 Shipbourne antenna, 1136 Shock, thermal, 934 Short circuit patches, 25,346,353, 374, 1087,1281 Short monopole probe, 982 Shorting pin, 85 Sidelobe level, 5, 774 Simplex synthesis, 662 Single feeds, 219 Singly diffracted field, 1069 Skin effect, 943 Slot antenna, 1136 Slot combiner, 1084 Slotline transitions, 962 Slots annular, 6 11 crossed, 28 folded, 353 linear, 606 Slotted line measurements, 975 Slotted patch, 27 Small loop probe, 982 Smear, 923,934 Sodium-bisulphite, 950
1310 lndex
Solder reflow, 938 Solvents, 875 Sommerfeld equation, 276,285,407,417 Sources, hybrid, 353 Space diversity, 939, 1084 Sparse arrays, 1273 Spatial phase delay, 805 Special-purpose networks, 859 Specimen, test, 909,907 Spearal domain method, 265,327,404, 590 Spectral domain Green's function, 327 Spherical arrays, 34, 792, 793, 1134, 1239 Spherical dielectric overlays, 1267 Spherical near field scanning, 981 Spill-over efficiency, 104 Spiral, 30 Spiral slot, 33 Split coaxial balun probe, 982 Split-tee power dividers, 852 Splitters, Wilkinson, 356 Spurious radiation, 332, 353, 743,816, 824 Square law probe, 983 Square patch, 25 Square patch array, 1073, 1115 Square ring patch, 501 Square-loop-type arrays, 764 Squintless arrays, 758, 826, 832, 841 Stacked antenna, 312 Stacked circulardisc patches, 197 Stacked dipoles, 299 Stacked patches, 29,320 Stainless-steel, 946 Standing wave distribution, 887, 1199 Star patch, 26 Steepest descent method, 278,408 Stepped patch, 29 Strain, internal, 920 Strain relief, 920 Stress riser, 934 Strip combiner, 1084 Strip conductors, 275 Strip dipole, 761, 1132 Strip line patches, 111 Strip slot, 1132 Stripline, balanced, 1003 Stripline suspended, 8 16,823,857 thickness, 1011 triplate, 816, 823 feeds, 353 transitions, 962 resonator, 884
lndex
St~ctWes array, 36 feed, 35 Subarrays 2*2,759 four element, 805 two element, 804 Subdomain basis functions, 282,437 Subsectional basis functions, 423,440 Substrates, 15 alumina, 14, 1025 bending, 1177 beryllia, 1025 copolymer, 679 effects, 279 environmental effects, 679 ferrimagnetic, 1027 foam, 1288 GaAs, 332 honeycomb, 796 low cost, low loss, 674 materials, 871 measurements, 958 metal deposition, 1028 metallisation, 1027 multilayer, 679 non-woven glass-PTFE, 892 perpendicular, 337 plastic, 14, 1025 polypropylene, 678 polypropyleneethylene, 679 mtile, 1025 sapphire, 1025 semi infinite, 731 semiconductor, 1027 technology, 14 thick, 28, 113,275, 356 thickness, 74, 791 thick metal backed, 678 thin, 112 Sum radiation pattern, 1068 Summary, of chapters, 21 Summary, of topic areas, 18 Superstrate, 275, 597 GaAs, 281 teflon, 28 1 Superstrate effects, 281 Surface charge, 1196 current density, 1196 currents, 441 fields, 67 gradient, 52
resistivity, 117 tangent, 52 wave, 406,407,4 10 Surface analytical techniques, 1194 Surface current model, 1228 Surface currents, equivalent, 49 Surface field metrology, 1193 Surface impedance, 400 Surface resistivity, 815 Surface treatment, 879,929 Surface wave conductance, 476 Surface wave losses, 816 Surface wave poles, 593 Surface waves, 9, 12, 592, 600, 703, 728, 731,734,740,751 Surface waves circle diagram, 706 excitation, 116 loss, 1075 poles, 697 excitation, 127 Surveillance radars, 1079 Susceptance, edge, 479 Suspended stripline, 816, 823,857 Suspension, 881 Switchedelement spherical array, 1132 Synthesis, 361 Synthesis, lines, 1015 Synthesis methods, 662 Synthetic aperture radar antenna, 790, 1146
T junction, 977, 850, 1166 Tab patches, 30 Tapered absorbing film terminations, 964 Tapered arrays, 650 Taperedslot elements, 751 Taylor distribution, 830 Teflon superstrate, 281 Telemetry, 924 Temperature, 875,941 transition, 921 variation of K' with, 942 Terminations matched, 964 resistive box, 964 tapered absorbing film, 964 thin film pad, 964 Test method evaluation, 914 fluiddisplacement, 883 full-sheet-resonance.897
1311
mated connector, 963 microstripresonator, 893 parallel plate resonator, 959 resonant ring, 961 resonant-cavity perturbation, 906 resonator strip, 960 stripline-resonator, 882 stripline resonator test, 886 Testing functions, 53,427 Thermal paint, 1065 Thermalexpansion coefficient, 878, 936 Thermoplastic, 927 Thermoset, 927,941 Thick film, 1031 Thick patches, 253 Thick substrate, 28,275 Thin film pad terminations, 964 Three-faced array, 1111 Three-port power dividers, 852 Throwing power, 936 Tilt angle, 1188 Time-domain-reflectometry,979 TM210-mode microstrip antenna, 1129 Total mass loss (TML), 940 Toxity, 919 Tracking slope, 1188 Train antenna, 1087 Transistors, 1041 Transition, 942 Transition, crystalline, 881 Transition phase, 875 Transitions, 1288 compensating hole, 967 GaAs, 967 inserted connector, 967 K connector, 967 metallic ring, 967 narrow pin, 967 off centred pin, 967 slotline, 962 stripline, 962 thermal, 881 waveguide, 962 Transmission line analysis, 295, 527 Transmission line model, 112,317, 456, 769 Transmission lines, 1001 Transmission-line matrix method, 1023 Transportable earth station, 1125 Transposed arrays, 821 Transverse polarisation, 821, 846 Travelling wave arrays,' 13, 762, 765, 769, 816, 1222
1312 Index
Travelling wave feeds, 832 Travelling-wave array design, 777 Triangle line array, 38 Triangular array lattice, 706, 1243 Triangular functions, 54 Triangular patch, 25,235,1209 Triazene, 95 1 Triplate, 857 Triplate, balanced, 1003 Triplate CAD, 1001 Truncated corner patch, 27 Truncated corner square patch, 499 Tuned circuit, 9 Two element sub-arrays, 804 Two port patch, 511 Two sided arrays, 746 Two-dimensional feeds, 839 Two-line feeds, 276 Two-sided configuration, 332 UHF pagers, 1079 Uniform lines, 1006 Untransposed arrays, 821 Unwanted modes, 258 Unwanted radiation, 787 Unwanted waves, 762 Urban mobile communications, 1086 Vacuum outgassing, 939 Vacuum-bag, 929 Variational method, 235 Vector potential, 50, 399 Vehicle antennas, 1086 Very-high permittivity, 1293 Vim, 945 plated-through hole, 953 reliability of, 953 Visw-elastic, 873,920,924 Voids, 935 Voltage maxima, 88 Voltage vector, 716 VSWR bandwidth, Wafer probing, 968 Walls
electric, 113 magnetic, 113 Waveguide, 906 air-filled, 858 dielectric, 944 model, 817, 1023 parallel-plate, 858,897 simulator, 711,719 transitions, 962 Waves cylindrical, 1072 surface, 406,407,410,592,600,703, 73 1,734,740,75 1 unwanted, 762 Weathering, 941 Welding, 937 electron-beam, 938 laser, 938 parallel gap, 938 percussive arc, 938 resistance, 938 ultrasonic, 938 Wettability, 935 Wheeled vehicles, 1085 Wicking, 875,941 Wide bandwidth arrays, 372 Wide bandwidth patches, 28, 320,796 Widebandwidth, 324, 1273 Wideband arrays, 804 Wideband baluns, 968 Wideband techniques, 253 Wiener-Hopf method, 478 Wilkinson power dividers, 307, 356, 852, 1069 Window antennas, 1283 Wire grid arrays, 848 Wrap around antenna, 34,85 X-ray, 933
Z matrix arbitrary segments, 472 circular segments, 471 from Greens functions, 468 planer segments, 467 rectangular segments, 469
