Review of Antenna Concepts

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Introduction to Mobile Communications

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Types of antennas1

Wire antennas

There are various shapes of wire antennas such as straight wire, loop and helix.

Dipole

Loop

Helix

Wire Antennas

Aperture antennas antennas:

Some forms are the pyramidal horn, conical horn and rectangular waveguide. They can be covered with a dielectric material for protection from the environment.

Pyramidal Horn Conical Horn

Rectangular Waveguide

Aperture Antenna Configurations

1. Main reference: Antenna Antenna Theory: Analysis and Design, Design, 3rd Edition, Constantine Constantine A. Balanis Balanis (Arizona State Univ.), ISBN: 978-0-471-66782-7

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Microstrip patch antennas antennas

Popular for space born, and lately for commercial comm ercial applications. Consist of a metallic patch on a grounded substrate. The rectangular rectangular and circular patches are most common.

Rectangular patch ground plane

Dielectric Substrate

Circular Patch

Rectangular and Circular Microstrip patch antennas

Array antennas

Many applications require radiation characteristics that can not be met by a single s ingle element. In such cases, a number of elements in a certain electrical and geometrical arrangement may be used to approximate the desired radiation r adiation characteristics.

Microstrip Patch Array Aperture Array

Reflectors directors

Slotted Waveguide Array

Yagi-Uda Array

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Reflector Antennas

These are used when very high gain is important. .

Parabolic Reflectors

Corner reflector

Fundamental Parameters of Antennas Radiation Pattern

An antenna radiation pattern is defined as “A mathematical function or graphical representation of the radiation properties of the antenna as a function of space coordinates. z

elevation plane



coordinate system for antenna analysis

y

r  x azimuth plane

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Isotropic, Directional and Omni-directional Patterns An isotropic radiator: “a hypothetical lossless antenna having equal radiation in all directions”. Often taken as a reference for expressing the directive properties of actual antennas.

A directional antenna is one “having the property of radiating or receiving electromagnetic waves more effectively in some directions than others”. An omni-directional antenna is defined as an antenna whose radiation pattern is essentially non-directional in a given plane (say the azimuth plane) and directional in elevation.

Radiation Pattern Lobes A radiation lobe is “a portion of the radiation pattern bounded by regions of relatively weak radiation intensity”. A major lobe is defined as ”the radiation lobe containing the direction of maximum radiation”. A side lobe is “a radiation lobe in any direction other than the intended lobe”. A back lobe is “a radiation lobe whose axis makes an angle of approximately 180 degrees with respect to the beam of the antenna”.

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90

0.99667

120

60 0.7475

0.49834

150

30

0.24917

Radiation lobes of a hypothetical antenna pattern

180

0

210

330

240

300 270

linear plot of power pattern 1 0.9 0.8 0.7 y t i

Linear plot of a hypothetical [abs(sinx/x)] antenna pattern.

s n e t n i n o i t a i d a r

0.6 0.5 0.4 0.3 0.2 0.1 0 -4

-3

-2

-1

0

1

azimuth in radians

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2

3

4

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Field Regions Far-Field Region radiating near field region

R 1 = 0.62(D3/)1/2

reactive near field region D

R 2 = 2D2/

R 1 R 2

Radiation Power Density

The quantity used to describe the power associated with an electromagnetic wave is the instantaneous Poynting vector: w = e  h where w is the instantaneous Poynting vector (W/m2), e is the instantaneous electric field vector (V/m) and h is the magnetic field vector (A/m). Example The radial component of the radiated power density of an antenna is given by sin  W ra d = aˆ r W r = aˆ r A 0 ----------W/m2 2 r where a r is a unit radial vector, A 0 is the peak value of the power density. Determine the total radiated power. For a closed surface, choose a sphere of radius r. To find the total radiated power, integrate the radial component, of the power density, over the sur face of the

sphere. P ra d =

2

2 sin  a r A 0 -----------  aˆ r r sin   d   d  =  2 0 r

ˆ

0 

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2

 A 0

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Radian and Steradian

The measure of a plane angle is a radian. One radian is defined as the plane angle with its vertex at the centre of a circle of radius r that is subtended by an arc whose length is r. The measure of a solid angle is a steradian. One steradian is defined as the solid angle with its vertex at the center of a sphere of radius r that is subtended by a spherical surface area equal to that of a square with each side of length r. Radiation Intensity

Radiation intensity in a given direction is defined as “ the power radiated from an antenna per unit solid angle.” The radiation intensity is a far-field parameter. In mathematical form: 2

U = r W rad

where U is the radiation intensity (W/unit solid angle) and W rad is the radiation density (W/m2). U is also related to the far-zone electric field of the antenna by: 2

2 2 r U  ------  E   r     + E   r      2

where E and E are the far-zone electric field components, and

 is the intrinsic

impedance of the medium (   120  for free space). The total power is obtained by integrating the radiation intensity over the entire solid angle of 4 . 2



0 0 U sin  d  d 

P rad =

where d  = sin  d  d  is the element of solid angle. Example For the previous example, the power intensity is given by: 2 sin  U = r A 0 ----------- = A 0 sin  2 r and the radiated power can then be calculated as: 2

P ra d =



0 0

A 0  sin  

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2

2

 d   d  =  A0

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Directivity

This is defined as “The ratio of the radiation intensity in a given direction from the antenna to the radiation intensity averaged over all directions. If the direction is not specified, the direction of maximum intensity is implied.” In other words, the directivity of a non-isotropic antenna is equal to the ratio of its radiation intensity in a given direction over that of an isotropic source. U U 4  U D = ------- = ----------------- = ----------U 0 P ra d P rad  ----------  4  and when the direction is not specified, assume the direction of maximum directivity U ma x 4  U ma x D ma x = ------------- = -------------------U 0 P rad Example

The radial component of the radiated power density of an infinitesimal dipole of length L <<  is given by: 2

W rad = aˆ r W r = aˆ r A 0

-----------------sin   2

r

where a r is a unit radial vector, A 0 is the peak value of the power density, and  is the usual spherical coordinate. Determine the maximum directivity of the antenna, and express the directivity as a function of the directional angles  and . 2

2

The radiation intensity is given by U = r W r = A 0  sin   , which has a maximum at    . Therefore Umax = A0. The total radiated power is given by: 2

P ra d =



2 8 A 0  sin   sin   d   d  = A 0  ------  3 0

0 

Therefore, the maximum directivity is: 4  U ma x 4  A 0 3 ------------------------------------- D ma x = = = --P rad 2 8   ----- A 0  3

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and the directivity in any other direction is represented by: D = D 0  sin  

2

= 1.5  sin  

2

Another example

The directivity of a half-wave dipole is approximated by: 3

D = 1.67  sin   Therefore, the antenna’s maximum directivity is 1.67 (about 2.2 dB), and can be represented graphically as shown. 90

1.67

12 0

60

1.1133 15 0

30 0.55667

18 0

0

21 0

330

24 0

300 270

Directivity pattern of a half-wave dipole.

Gain

This is directly related to directivity, but takes into account the antenna efficiency. The absolute gain is defined as “the ratio of the intensity in a given direction to the radiation intensity that would be obtained if the power accepted by the antenna were radiated isotropically. The radiation intensity corresponding to the isotropically radiated power is equal to the power accepted (input) by the antenna divided by .” In other words:

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r ad ia ti on i nt en si ty U     gain = ------------------------------------------------------------------------------------------------------ = 4  -----------------P in  total input  accepted  power    4  

Reflection, conduction and dielectric losses

Antenna

output terminals (directivity reference)

input terminals (gain reference)

Reference Terminals and losses of an antenna Antenna Efficiency

The total antenna efficiency is used to account for losses at the input terminals and within the structure of the antenna. Losses may be due to 1) reflections caused by mismatch between the transmission line and the antenna. 2) I2R losses (conduction and dielectric in the antenna structure). The total efficiency can therefore be written as: e o = e r e cd =

2

 1 –   e cd

where  is the reflection coefficient at the input terminals of the antenna, and is given by: Z in – Z 0  = ------------------- Z in + Z 0 where Zin is the antenna input impedance, and Z 0 is the characteristic impedance of the transmission line. Example

A lossless half-wave dipole antenna, with input impedance of 73 ohms, is con-

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nected to a transmission line whose characteristic impedance is 50 ohms. The 3

antenna pattern is given approximately by U = B0  sin   . Find the overall maximum gain of this antenna. Half Power Beamwidth

Defined as “ In a plane containing the direction of the maximum of a beam, the angle between the two directions in which the radiation intensity is one half the maximum value of the beam”. There usually is a trade-off between the beam width and the sidelobe levels (narrower beamwidth goes with higher sidelobe levels). The resolution capability of an antenna (i.e. the ability to distinguish between two sources) is approximated by half the first null beamwidth. Bandwidth

Defined as “ The range of frequencies within which the performance of the antenna, with respect to some characteristic, conforms to a specific standard ” For broadband antennas, the bandwidth is usually expressed as the ratio of the upper-to-lower frequencies of acceptable operation. For example a 10:1 bandwidth indicates that the upper frequency is ten times greater than the lower operating frequency. For narrow-band antennas, the bandwidth is expressed as a percentage of the centre operating frequency of the antenna. E.g. a 5% bandwidth, for an antenna operating at 100 MHz indicates the antenna operation is acceptable over the range 97.5 to 102.5 MHz. Polarization

Polarization of the radiated wave is defined as “The property of an electromagnetic wave describing the time varying direction and relative magnitude of the electric field vector; specifically the figure traced as a function of time by the extremity of the vector at a fixed location in space, and the sense in which it is traced, as observed along the direction of propagation.” Polarization may be classified as linear, circular or elliptical. If the vector that describes the electric field at a point in space as a function of time is always directed along a line, the field is said to be linearly polarized. For circular polarization, the circle is traced in a clockwise or counter-clockwise sense. Clockwise rotation of the electric field vector is designated as right-hand

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polarization and counter-clockwise as left-hand polarization. Polarization Loss Factor and Efficiencies

In general the polarization of the receiving antenna will not be the same as the polarization of the incoming wave. This is generally stated as polarization mismatch. The amount of power extracted by the antenna under mismatch conditions will not be maximum. The polarization loss factor is defined as: PLF =

ˆw  ˆa

2

= cos  p

2

where  w and  a are the unit vector of the incident wave, and unit vector (polarization vector) of the receiving antenna respectively.  p is the angle between the two unit vectors. So if the antenna is polarization matched to the received wave, the PLF will be equal to unity. For orthogonal polarizations, PLF = 0.

 p

PLF = 1

PLF = cos

2

 p

 p

PLF = 0

PLF for transmitting and receiving aperture antennas

 p  p

PLF = 1

PLF = cos

2

 p

PLF = 0

PLF for transmitting and receiving linear wire antennas

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Input Impedance

This is defined as “the impedance presented by an antenna at its terminals, or the ratio of voltage to current at a pair of terminals, or the ratio of the appropriate com ponents of the electric to magnetic fields at a point.” The maximum power delivered to the antenna occurs when the antenna impedance presents a conjugate match to the source impedance. In this case, the power sup plied to the antenna will be equal to the power dissipated in the source resistance. The input impedance of an antenna is generally a function of frequency. Thus the antenna will be matched to the interconnecting transmission line and other associated equipment only within a bandwidth. Antenna effective Areas

The effective area (in a given direction) is defined as “ the ratio of the available power at the terminals of a receiving antenna, to the power flux density of a plane wave incident on the antenna (from that direction), assuming the wave being polarization matched to the antenna.” Friis Transmission Equation

(r , r ) (t, t) Transmitting antenna (Pt, Gt, Dt, ecdt,

t, ^t)

Receiving antenna (Pr , Gr , Dr , ecdr ,

r , ^r )

Geometrical Orientation of transmitting and Receiving antennas for Friis transmission formula

This equation relates the received signal power to the transmitter power, and various Tx and Rx antenna parameters as follows:

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P r = W t A r =



2 P t  -------------G t ------ G r = 2 4 4  R

2 P t 2 2 2  -------------  1 –  t  e cdt D t ------  1 –  r  e cdr D r ˆt  ˆr = 2 4 4  R

e cdt e cd r  1 –  t

2

  1 –  r

2

  2 D ˆ ˆ 2  --------- D              P 4  R t t t r r r t r t

P r 2 2 2   2 ----- = e cd t e cdr  1 –  t   1 –  r  ---------- D t   t   t  D   r   r  ˆt  ˆr  4  R r P t

When the Tx and Rx antennas are matched to their respective loads, and when the polarization of the Rx antenna is matched to the polarization of the incident wave, the above equation is reduced to: P r 2 2       ----- = e cdt e cd r ---------- D t   t   t  D   r   r  = ---------- G t   t   t  G   r   r   4  R  4  R r r P t 2    The factor ---------- is known as the free space loss factor and it accounts for the  4  R

spherical spreading of the energy by the antenna.

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Linear Arrays Two Element Array

z

1

Two Infinitesimal Dipoles

r 1

Equal magnitude excitations r

d/2



phase excitations differ by



r 2

y

2

r 1 z

1

d/2

r 

Far Field Observation d/2

2

y r 2

phase = /2

0 phase = /2

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The total field at the observation point is given by: total field = field due to the reference element  Array factor

 d j  --- + k --- cos  Array fa ctor = e

2

2



 d – j  --- + k --- cos  2 2 

+e

1 = 2 cos ---  kd cos  +   2

where k is the wavenumber and is given by 2

k = ------



The pattern of the array is obtained by the multiplication of the element pattern, and that of the array factor. By varying the relative phases of the feed current to the individual elements we are able to place nulls in the radiation pattern in certain directions. For example, to place a null in the phase of the elements to

 = 450 direction, we simply set the relative

  =  – ---------- when the element spacing is /4. 2 2

N-Element Linear Array; Uniform Amplitude and Spacing

z axis

The array factor is obtained by assuming all elements are point sources (which radiate uniformly in all directions).

r N

N

The element spacing is fixed. dcos() r 3



3 r 2

2 r 1

d

y-axis

1

Far Field Geometry of N-element Array of isotropic sources.

An array of identical elements all of identical magnitude and each with a progres-

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sive phase is referred to as a uniform array. The array factor for the geometrical configuration under consideration is: N sin  ----  2  AF = ---------------------1 sin  ---  2 

where it was assumed that the reference point is the physical center of the array.  = kd cos  +  The maximum value of the array factor above is equal to N, the number of elements. For convenience, the normalized array factor is defined as: N sin  ----  2  1 ----------------------- AF n = N 1 sin  ---  2 

Broadside Array

In many applications it is desirable to have the maximum radiation of an array directed normal to the axis of the array. To optimize the design, the maxima of the single element and of the array factor should both be directed toward q = 90 0. For broadside radiation, (i.e. a maximum for the array factor when q = 90 0) b is set to zero. In this case, the array factor becomes: N sin  ---- kd cos  2  1 ------------------------------------- AF n = N 1 sin  --- kd cos  2 

Example

Plot the array-factor patterns for a 10-element broadside array, with element spacings of /4

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Broadside Array Pattern: lambda/wavelength=1/4 0 degrees

10 dB

20 dB

30 dB

90 degrees

90 degrees

180 degrees

Array Factor Pattern of a 10-Element Linear, Uniform Amplitude Broadside Array. d = /4 and  = 0.

Ordinary End-Fire Array

It is sometimes desirable to direct the maximum radiation along the axis of the array, due for example to physical constraints. To direct the maximum radiation towards  = 00;

 = kd cos  +   = 0 = kd +  = 0   = – kd If the maximum is desired toward  = 1800, then:

 = kd cos  +   = 180 = – kd +  = 0   =

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End-Fire Array Pattern: beta = kd 0 degrees

10 dB

20 dB

30 dB

90 degrees

90 degrees

180 degrees

Array Factor Pattern of a 10-Element Linear, Uniform Amplitude End-Fire Array. d = /4 and  = +kd. Relating Power to Electric Field z

P d





elevation plane

L

y

r  azimuth plane

x

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Consider a small linear radiator of length L, placed coincident with the z-axis, and its centre is at the origin. If a current i 0 flows through this antenna, it launches electric and magnetic fields that can be expressed as:  d  i 0 L cos   1 c  j c  t – --c- E r = --------------------  ----- + -------------- e 2  0 c  d 2 j  c d 3   d  c c 2  – j  c  t – --c- E  = -------------------  -------- + ----- + -------------- e 4  0 c 2  d d 2 j  c d 3 

i 0 L sin   j  c

 d  c  j c  t – --c- H  = -------------------  -------- + ----- e 4  c  d d 2 

i 0 L sin   j  c

with E  = H r = H  = 0 . In the equations above, all 1  d terms represent the radiation field component, all 1  d 2 terms represent the induction field component and all the 1  d 3 represent the electrostatic field compoent. At distances far away from the antenna only the radiation field components are significant. In free space, the Power flux density, in W/m 2, is given by: P t G t EI RP E 2 P d = --------- = ------------ = ------------- 4  d 2 4  d 2

The gain of an antenna is related to the effective aperture by: 4  A e G = ------------

2

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Review of Antenna Concepts

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