ieee fractal antenna

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IEEE TRANSACTIONS ON ANTENNAS AND PROPAGATION, VOL. 60, NO. 7, JULY 2012

Communications Circularly Polarized Multiband Microstrip Antenna Using the Square and Giuseppe Peano Fractals Homayoon Oraizi and Shahram Hedayati Fig. 1. Configuration of the square fractal geometry. Abstract—By computer simulation and actual fabrication, it is demonstrated that multiband operation with circular polarization of radiation may be achieved by the combination of square and Giuseppe Peano fractal geometries realized on a two layer microstrip antenna. The antenna feed is designed by an electromagnetic coupling system. The proposed antenna configuration also achieves some degree of miniaturization, which makes it suitable for wireless applications. The antenna characteristics, such as return loss, axial ratio and radiation patterns achieved by the proposed structure attest to its effectiveness as a mobile radiator. Index Terms—Circular polarization, fractal antenna, microstrip, miniaturization.

Fig. 2. The generator of square fractal geometry.

I. INTRODUCTION Mandelbrot first introduced the fractal geometry in 1975 [1], in which each sub-section has the characteristics of the whole structure in a smaller scale. This is the basic property of self-similarity. Fractal geometries have been applied in various science and technologies, such as antennas and radiators. Generally, the utilization of fractal geometries in antennas tends to reduce their physical sizes and produce multiband response in their radiation characteristics. Since fractal structures have a repetitive geometry, they can generate long paths in a limited volume. Accordingly, we may refer to fractal geometries, such as the Koch, Minkowski, Hilbert and tree fractals [2], [5], which have been used for dipole and ring antennas. The property of self-similarity of fractal geometries is used to achieve multiband operations from fractal antennas and their space-filling property is used for the antenna miniaturization. [3], [4], [6]. Fractal geometries are used in radiating systems and even microwave devices to benefit from their interesting properties [6]. Since the generation of fractal configurations have an iterative procedure, then they can achieve long linear dimensions and high surface areas in a limited volume [5]. In this communication, a multiband antenna is introduced using the novel square and Giuseppe Peano fractals. It is designed for operation in the following bands: Global positioning system L1 (GPS 1.575 GHz); Hiper-Lan2 (High Performance Radio Local Area Network Type2) in the band 2.12–2.32 GHz; IEEE802.11b/g in the band from 2.4 to 2.484 GHz, which is one of the WLAN bands and IMT advanced system or forth generation (4G) mobile communication system in the band 4.6–5.2 GHz. We investigate the miniaturization and multi-banding [6] properties of the square fractal microstrip patch antenna. We also study the radiation properties of the combination Manuscript received December 22, 2010; revised December 27, 2011; accepted January 24, 2012. Date of publication April 30, 2012; date of current version July 02, 2012. The authors are with the Electrical Engineering Department, Iran University of Science and Technolog, Tehran 1684613114, Iran (e-mail: [email protected]. ir). Color versions of one or more of the figures in this communication are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TAP.2012.2196912

Fig. 3. Reflection coefficient of the initiator and first iteration square fractal.

of square and Peano fractals for the microstrip patch antenna with electromagnetically coupled feed systems. A prototype sample of the proposed fractal antenna is fabricated and measured. The miniaturization, multibanding and circular polarization of the proposed fractal antenna is verified by the simulation results and measurement data. II. COMBINATION OF THE SQUARE AND GIUSEPPE PEANO FRACTALS Consider the square fractal geometry in Figs. 1 and 2, where the initiator, first and second iterations are shown. We compare the radiation properties of the initiator and first iteration [5], where the parameters are selected as a = 2:3 mm and k2 = k1 = 2:5 for the resonance frequency of about 2.45 GHz. We select the substrate FR4 with dielectric constant "r = 4:4, height h = 1:6 mm and loss tangent tan = 0:02. The reflection coefficient of the initiator square fractal and the first iteration fractal are drawn in Fig. 3. Observe that although the size of the two squares are identical, but the resonance frequency of the first iteration is less than that of the initiator. The reason for lowering of resonance frequency with the reduction of parameter k1 is due to increase of the length of current path on the patch (L), as depicted in Fig. 5. Note that the n0 th iteration fractal has n separated regions, which resonate independently (ignoring the mutual coupling among them), and produce n + 1 fundamental resonance frequencies. For example, the first iteration fractal has two resonance frequencies, due to the inner

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Fig. 7. Implementation of the Peano fractal to the edges of square patch up to the second iteration.

Fig. 4. Reflection coefficient versus frequency for the first iteration square fractal.

Fig. 5. Surface currents on the patch for three distinct modes, (a) 1st mode (f = 2:4 GHz), (b) Spurious mode (f = 4:1 GHz), (c) 2nd mode (f = 6:7 GHz).

Fig. 6. Initiator and generator of the Giuseppe Peano fractal.

square and outer square rings. The surface current on the patch for three distinct modes are drawn in Fig. 5. Its return loss versus frequency is drawn in Fig. 4, where three resonance modes are shown. The middle resonance frequency (4.1 GHz) is due to the second resonance of the outer square ring. Observing the current distributions in Fig. 5, Note that (1) to (6) are derived based on the observations of the surface current distribution on the patch. This type of reasoning is also followed for the evaluation of the patch resonance frequency by measuring the length of current path between its nulls [2]. The resonance frequencies of the first iteration fractal of the square patch may be obtained by the following empirical relations:

= 2p"ce L1 c f2 = p 2 "e L2 f1

(1) (2)

where L1 and L2 are the average lengths of the current paths for the first and second resonance modes, which may be determined as:

= a + ka1 p a L2 = 2 : k2 L1

Fig. 8. Comparison of reflection coefficient of the Giuseppe fractal with other common fractals.

(3) (4)

These relations may be used for the design of antennas. Consider the initiator and generator of the Peano fractal as shown in Fig. 6. Application of such a fractal generation to the edges of square patch up to the second iteration is drawn in Fig. 7. In this section we investigate the possibilities and properties of the application of Giuseppe

Peano fractal geometry for the miniaturization of microstrip patch antennas and compare its performance with those of the usual fractals, such as Koch, Minkowski, Sierpinski and Tee-Type. The length of the Giuseppe Peano fractal patch perimeter increases, while its surface area remains constant without any more space occupation. Consequently the antenna miniaturization, maintenance of its gain and increase of its relative frequency bandwidth are achieved. The frequency response of S11 for several fractal geometries, such as Koch, Minkowski, Tee type and Giuseppe Peano (with their specified dimensions) are drawn in Fig. 8 for comparison. Observe that proposed Giuseppe Peano fractal geometry for the microstrip antenna produces comparatively a larger 10 dB return loss bandwidth with lower number of iterations, and also achieves better antenna miniaturization.

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Fig. 9. The proposed combination of square and Giuseppe Peano fractal with the electromagnetic coupling feed.

Fig. 10. A photograph of the fabricated fractal antenna.

Fig. 11. Reflection coefficient at the antenna feed point as S11 at three frequency bands (a) 1.5 GHz; (b) 2.5 GHZ; (c) 4.9 GHz.

III. ANTENNA DESIGN Novel fractal proposed antenna is shown in Fig. 9. It consists of two layers. The lower substrate is Rogers RT/Duroid 5880 (with "r = 2:2; h = 1:524 mm and tan = 0:0009) and the upper substrate is FR4 (with "r = 4:4; h = 1 mm and tan = 0:02). The feeding system is by electromagnetic coupling through a microstrip line on the lower substrate and the fractal patch is placed on the upper one. A photograph of the fabricated fractal antenna is shown in Fig. 10.

The average lengths of current paths for the first and second resonance modes L1 and L2 are derived experimentally:

L1 L2

= a + a + 32 (L1 + S1) = a + a + 3k21 (L1 + S 1) 1

2

(5)

3

4

(6)


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Fig. 13. Measurement of radiation patterns in the E- and H-planes at three frequency bands (a) 1.5 GHz; (b) 2.5 GHZ; (c) 4.9 GHz. Fig. 12. Axial ratio of the antenna at three frequency bands (a) 1.5 GHz; (b) 2.5 GHZ; (c) 4.9 GHz.

which are used for the antenna design. For the generation of circular polarization, a perturbation of electrical length is produced on the two perpendicular edges of the square patch, which are in the form of Giuseppe Peano fractals. The aim is to excite two orthogonal modes with a phase difference of 90 . The perturbations on the lengths of fractal edges on the outer square, namely S1, S2 and L1 and those on the inner square, namely S1=k1 ; S2=k1 and L1=k1 , are made

for the generation of circular polarization in the first and also second and third bands, respectively. These parameters are optimized for the achievement of axial ratio AR < 3 dB. The other parameters of structure are optimized for the desired impedance matching. Now the effects of variation of main parameters of the antenna structure, such as L1 and a4 are investigated. They should be modified for the increase of impedance bandwidth for operation in the bands, such as Hiper-Lan2 and IEEE802.11b/g. For this purpose, the primary antenna structure parameters are selected and a parametric study is conducted about the optimum values of L1 = 1:7 mm and a4 = 5 mm. the

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The measurement of radiation patterns in the E- and H-planes for the first, second and third bands are drawn in Fig. 13. The gain of the fractal antenna versus frequency across the operating bands is drawn in Fig. 14, which is quite good. IV. CONCLUSION

Fig. 14. The gain of the fractal antenna versus frequency in all application bands.

TABLE I COMPARE GIUSEPPE PEANO PERFORMANCE WITH USUAL FRACTALS

In this communication, a microstrip antenna is proposed as a combination of square and Giuseppe Peano fractals, which may produce three distinct frequency bands of operation with circular polarization. The antenna achieves some degree of miniaturization. The measured data and simulation results of the fabricated antenna for the return loss, axial ratio and radiation patterns attest to the effectiveness and suitability of the proposed fractal antenna for wireless applications. Observe that proposed Giuseppe Peano fractal geometry for the microstrip antenna produces comparatively a larger 10 dB bandwidth with lower number of iterations, and also achieves better antenna miniaturization.

REFERENCES

achieved responses of proposed antenna as reflection coefficient versus frequency are drawn in Fig. 11. The first and second resonance frequencies determine the length of outer and inner square sides (a1 and a3 ), respectively. The optimized values of parameters are given below: a1 = 30 mm, a2 = 15 mm, a3 = 10 mm, a4 = 5 mm, s1 = 4:3 mm, s2 = 3:9 mm, L1 = 1:7 mm. The size of the inner fractal teeth are one third (0.33) that of the outer one. The width and length of the feed line are 3.4 mm and 38 mm, respectively. A prototype model of the proposed fractal antenna is fabricated and measured. The simulation results and measurement data are compared in the following figures (Fig. 11). The reflection coefficient (as S11) at the antenna feed point across the individual S11 for the three distinct bands are shown in Fig. 11. Note that we have used substrates Rogers RT/Duroid 5880 and FR4 in the two layers. Substrate FR4 was used for more antenna miniaturization because of its higher dielectric constant ("r = 4:4). But it has higher losses, especially at high frequencies. This may accounted for the discrepancy between the simulation results and experimental data. Observe that the resonance frequency of the first iteration fractal antenna is actually 200 MHz lower than that of the corresponding simple square patch. Consequently, it is shown that some antenna miniaturization is achievable by the proposed fractal antenna. The bandwidth at the first resonance frequency (1.5 GHz) is 40 MHz, that at the second one (2.5 GHz) is 900 MHz and that at the third one (4.9 GHz) is 310 MHz. The circular polarization of radiation pattern is obtained by different lengths of teeth on the perpendicular sides of the square fractal (namely S1 and S2 in Fig. 8), which produce two orthogonal modes with 90 phase difference. The axial ratio of the antenna is drawn in Fig. 12. The bandwidth of circular polarizations at the first, second and third bands are 30, 40 and 50 MHz, respectively.

[1] D. H. Werner and R. Mittra, Frontiers in Electromagnetics. Piscataway, NJ: IEEE Press, 2000, pp. 48–81. [2] C. P. Baliarda, J. Romeu, and A. Cardama, “The Koch monopole: A small fractal antenna,” IEEE Trans. Antennas Propag., vol. 48, no. 11, Nov. 2000. [3] C. Puente-Baliaada, J. Romeu, R. Pous, and A. Cardama, “On the behavior of the Sierpinski multiband fractal antenna,” IEEE Trans. Antennas Propag., vol. 46, no. 4, Apr. 1998. [4] D. H. Werner and S. Ganguly, “An overview of fractal antenna engineering research,” IEEE Antennas Propag. Mag., vol. 45, no. 1, Feb. 2003. [5] J. P. Gianvittori and Y. Rahmat-Samii, “Fractal antenna: A novel antenna miniaturization technique, and applications,” IEEE Antennas Propag. Mag., vol. 44, no. 1, Feb. 2002. [6] M. Naghshvarian-Jahromi and N. Komjani, “Novel fractal monopole wideband antenna,” . Electromagn. Waves Applicat., vol. 22, no. 2–3, pp. 195–205, 2008.

ieee fractal antenna

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