Design of Elliptical Microstrip Patch Antenna using Genetic Algorithms

Simranjit Kaur Josan, J. S. Sohal Department of ECE,

Ludhiana College of Engineering and Technology Ludhiana, INDIA

simran_josan@yahoo.com

Balwinder Singh Dhaliwal Department of ECE

Guru Nanak Dev Engineering College Ludhiana, INDIA

bsdhaliwal@ymail.com

Abstract—In this paper, Genetic Algorithms (GA) has been applied to calculate the optimized parameters of Elliptical Microstrip antenna. The inputs to the problem are thickness of the substrate, eccentricity, dielectric constant and even mode frequency. The output obtained is the optimized semi- major axis length ‘a’ from which the other parameters i.e. semi-minor axis length and odd mode frequency are calculated. The results obtained by GA are compared with the targeted results. The results are in good agreement. GA results are also compared with IE3D simulation results. These results are also comparable and thus validate the GA based code.

Keywords-Elliptical microstrip patch antenna; Genetic Algorithms; Resonant frequency.

I. INTRODUCTION Micro-strip patch antennas are low profile, conformable to

planar and non-planar surfaces, simple and inexpensive to manufacture using modern printed-circuit technology, mechanically robust when mounted on rigid surfaces, compatible with MMIC designs, and when the particular patch shape and mode are selected they are very versatile in terms of resonant frequency, polarization, pattern and impedance [1]. The choice of shape of an antenna opens a whole new aspect of exploration in the field. In this work Elliptical Micro strip patch Antenna [EMSA] is being considered as this geometry presents greater potentials for low-profile antenna applications. The main advantage of elliptical patch geometry is that it gives dual resonant frequency owing to two modes i.e. even and odd mode [2, 3]. The involvement of complex functions in analysis of elliptical antenna makes it least analysed shape [2]. The analysis process has evolved from Variational method, Hammerstad formula to Mathieu's and modified Mathieu's function [2, 4]. The involvement of these methods and functions make mathematics of elliptical patch geometries tedious [4]. These approaches propose methods to calculate resonant frequency for even (fe) and odd (fo) modes as the function of input variables, which are the height of the dielectric substrate (h), dielectric constant (εr), and antenna dimensions (the major and the minor axis) [3, 4]. But reverse calculation of the antenna dimensions from the inputs like frequencies (fe, fo), height (h) and dielectric constant (εr) is not available in the literature [2].

In this paper, the antenna dimensions are determined by using Genetic Algorithms (GA). This approach shows a great promise in solving the complex synthesis equations and producing results at a faster pace compared to earlier known methods. Also this approach is better from ANN approach used previously by [2] as it does not require any training data at initial stage for calculation of parameters of the antenna.

II. DESIGN APPROACHES FOR ELLIPTICAL ANTENNA Fig. 1 shows the geometry of elliptical patch antenna with ‘a’ as semi-major and ‘b’ as semi-minor axis lengths, ‘h’ as the thickness of the substrate and ‘εr’ as the permittivity of dielectric substrate. The feed point is located along the 450 line between the major and minor axis of the elliptical patch.

Fig. 1: Geometry of Elliptical microstrip patch antenna.

In addition to dual frequency, the other advantages of elliptical shape include flexible design, freedom to change the dimensions like major/minor axis and eccentricity. Circular polarization (CP) can be achieved with single feed by locating the particular feed point on the elliptical patch. CP otherwise is possible by using multiple feeds or by using phase shifter radiators, both these methods increase the complexity of the structure [3]. The process of calculating the resonant frequency of the antenna when its dimension are given is known as Analysis process and the reverse i.e. calculating the dimensions of the antenna from given resonant frequency is known as Synthesis process. Different approaches like Variational method, Hammerstad formula, Mathieu's and modified Mathieu's function have been

hεr

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used to analyze the elliptical patch. Various methods like the Pentagon method, Corner fed rectangle method, Variations methods have been to obtain circular polarization [4]. Shen and later Yu have shown that circular polarization could be produced from the elliptical patch antenna by feeding it along a line 450 from its major axis [4]. The effects of fringe field at the edge of the elliptical patch and those of the dielectric substrate are taken into account in the calculation by [5]. The following equations given by [2] are used for analyzing elliptical patch antenna to find the resonant frequencies (fe, fo) from the input:

(1)

(2)

(3)

(4)

Where

a - Semi-major axis,

h - Height of dielectric substrate,

εr - Permittivity of dielectric substrate,

a eff - Effective semi-major axis,

e - Eccentricity of elliptical patch,

f11e,o - Dual-Resonance frequency,

q11e,o - Approximated Mathieu function of the dominant

TM11e,o mode.

III. PROPOSED APPROACH FOR SYNTHESIS OF ELLIPTICAL PATCH ANTENNA

The synthesis equations i.e. equations for finding semi major axis length ‘a’ are not available in the literature [2]. If analysis equations (1-4) mentioned above are rearranged to find ‘a’, then following equation is obtained:

Equation (5) obtained above is a typical equation which requires solving the logarithmic term in ‘a’. No conventional method is available to solve such an equation. One of the approaches [2] used artificial neural network to synthesize the antenna. However, the use of ANN requires some initial data to train the network.

The present work proposes use of Genetic Algorithms for synthesizing the elliptical antenna. Genetic Algorithms has already been used to optimize the parameters of rectangular micro strip patch antenna by [6]. In present paper, GA has been applied to calculate the optimized major axis of the elliptical patch for given value of eccentricity and other input parameters. The results are calculated and compared with those available in the literature. Also the obtained results are verified by IE3D simulations.

IV. BRIEF DESCRIPTION OF GENETIC ALGORITHMS Genetic Algorithm (GA) was first invented by John

Holland. GA provides an alternative method to solve problems, finding optimal parameters, which would otherwise be difficult for traditional methods. GA’s are search algorithms based on the mechanics of natural selection and natural genetics. With combined innovative flair of human search, GA’s are based on the theory “Survival of the Fittest” among string structures with a structured yet randomized information exchange. In every generation, a new set of creatures (strings) is created using bits and pieces of the fittest of the old; an occasional new part is tried for good measure. While randomized, genetic algorithms are no simple random walk. They efficiently exploit historical information to speculate on new search points with expected improved performance. GA is very efficient in exploring the entire search space or the solution space, which is large and complex. Genetic Algorithms are different from normal optimization and search procedures in following four ways [7]:

(i) GA’s work with coding of the parameter set, not the parameters themselves.

(ii) GA’s search from a population of points, not a single point.

(iii) GA’s use payoff (Objective function) information, not derivatives or other auxiliary knowledge.

(iv) GA’s are probabilistic transition rules, not deterministic rules.

The important parameters of GA can be summarized viz., • Reproduction - It is the process of copying the fitness

function or goodness of the function. • Crossover - this is an exchange of substrings

denoting chromosomes, for an optimization problem. It may be a single point cross over, two points cross over, cut and splice, uniform crossover or half uniform crossover.

• Mutation - the modification of bit strings in a single individual.

• Population size - the number of chromosomes (individuals) considered in one generation.

• Selection procedure – The selection of the individuals is based on random process/rating all individuals and selecting the best fit or filter solutions. Evaluation of the fitness criterion to choose which individuals from

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a population will go on to reproduce. Some general methods used are Roulette Wheel Selection and Tournament Selection.

• Number of generations - the maximum number of generations that the genetic algorithm can evolve into, before terminating.

• Termination – The algorithm terminates when one of

the following conditions is reached

Satisfactory solution

Fixed number of generations

When successive iterations no longer produce

better results

Manual inspection

For present work, the values used for the above mentioned parameters of GA, are listed in next section.

V. RESULTS & DISCUSSION Equation (4) for is used as the fitness function for GA. The unknown independent variable is semi major axis ‘a’. The population size is taken 20 individuals, and 200 generations are produced. The probability of crossover is set at 0.2, while the probability of mutation is equal to 0.01. Even mode resonant frequency , thickness of the substrate (h), dielectric constant (εr) and eccentricity (e) are given as inputs to GA, which gives the optimized value for the semi major axis ‘a’. Further from the value ‘a’, semi minor axis ‘b’ and odd mode resonant frequency ( ) is calculated.

The results tabulated below are generated for two different h values 0.3175 cm and 0.1575 cm. The eccentricity of elliptical patch is taken as constant value (0.2178) for the purpose of generating circular polarization [4]. Table 1 shows the % error in fo and ‘a’ when the inputs to GA are h = 0.3175 cm, and e = 0.2178, and εr = 2.48. Table 2 shows the % error in fo and ‘a’ when the inputs to GA are h = 0.1575 cm, and e = 0.2178, and εr = 2.48. The value of varies from 1 to 3.1 GHz. Table 1 and Table 2 show that the optimized semi major axis ‘a’ obtained using GA is in good agreement with the targeted results. Fig. 2 shows the best fitness value and best individual for one of the sample case ( = 1.0223) from table 1, the value of ‘a’ is obtained as 5.419.

Table 1: Comparison of GA results with Targeted results for input parameter εr = 2.48, h = 0.3175 cm, e = 0.2178

Input parameter

Targeted Results Using

equations(1-4)

GA Results % Error

(GHz)

a (cm) fo (GHz)

a (cm) fo (GHz)

a fo

1.0223 5.4192 1.0340 5.419 1.0340 0.0037 0 1.5376 3.5202 1.5552 3.52 1.5553 0.0057 0.0064 2.0734 2.5505 2.0972 2.551 2.0968 0.0196 0.0191 2.6060 1.9848 2.6349 1.984 2.6358 0.0403 0.0342 3.0538 1.6616 3.0888 1.662 3.0881 0.0241 0.0227

Table 2: Comparison of GA results with Targeted results for Input parameters εr = 2.48, h = 0.1575cm, e = 0.2178 Input

parame-ter

TargetedResults Using

equations(1-4)

GA Results % Error

(GHz)

a (cm) fo (GHz)

a (cm) fo (GHz) a fo

2.0435 2.7121 2.0669 2.712 2.0669 0.0037 0 2.5523 2.1465 2.5816 2.147 2.5810 0.0233 0.0232 3.0400 1.7828 3.0748 1.783 3.0745 0.0112 0.0098 1.0322 5.5000 1.0441 5.5 1.0441 0 0 1.5236 3.6818 1.5411 3.682 1.5411 0.0054 0

0 20 40 60 80 100 120 140 160 180 2000

5

10

15

Generation

Fitn

ess

valu

e

Best: 1.728e-005 Mean: 0.0011381

10

2

4

6

Number of variables (1)

Cur

rent

bes

t in

divi

dual

Current Best Individual

Best f itness

Mean f itness

Fig. 2 Best fitness value and Best individual plots for case 1 of table 1.

Some of the results from Table 1 and Table 2 are compared with the IE3D simulation results in Table 3, which shows that the results are comparable. The minor differences are due to simulation error. Feed is given along the line at an angle of 450 from major axis in the first quadrant.

Table 3: Comparison of GA results and Simulation results for e = 0.2178 and εr = 2.48

Input parameters

GA Results

Simulation Results Using

IE3D

h (cm)

a (cm)

(GHz)

fo (GHz)

(GHz)

fo (GHz)

0.3175 3.52 1.5376 1.5553 1.5132 1.5505 0.3175 1.984 2.6060 2.6358 2.8530 2.6115 0.3175 1.662 3.0538 3.0881 3.0418 3.0802 0.1575 5.500 1.0322 1.0441 1.0016 1.0197 0.1575 2.147 2.5523 2.5810 2.5254 2.5593 0.1575 1.783 3.0400 3.0745 3.0101 3.0440

Good circular polarization, S11, and Z parameter curves are observed for all the cases listed in the tables 3. For one sample case from table 3 (h=0.1575 cm, εr= 2.48, a= 5.500) the variation of impedance is shown in Fig. 3(a). The S11 is indicated in Fig. 3(b) which shows value of S11 as -18.1 dB at the frequency 1.0016 GHz. The radiation pattern is plotted in Fig. 3(c).

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Fig. 3(a) Impedance Variation

Fig. 3(b) S11 Curve

Fig. 3(c) Radiation pattern

VI. CONCLUSION

The results obtained by using Genetic Algorithms for elliptical micro strip patch antenna are in good agreement with the targeted results. The proposed algorithm requires less time and is very accurate. The simulated results validate the proposed approach. The complexity of synthesis of elliptical antenna is removed by using GA.

REFERENCES

[1] C. A. Balanis, Antenna Theory, John Wiley & Sons, Inc., 1997. [2] A. Aggarwal , D. Vakula and N.V.S.N. Sarna “Design of elliptical

micro strip patch antenna using ANN” PIERS proceedings China., September 2011, pp. 264-268.

[3] S.A. Long, L.C. Shen, D.H. Shaubert, F.G. Farrar, “An experimental study of circular polarized elliptical printed patch antenna” IEEE transaction on antennas and propagation Vol. 29, No.1, 1981, pp. 95-99.

[4] P. Mythili , A. Das , “Simple approach to determine resonant frequencies of micro strip antennas”. IEE Proceedings microwave antenna propagation Vol. 145, No.2, April 1998, pp 159-162.

[5] L.C. Shen, “The elliptical microstrip antenna with circular polarization” IEEE transactions on antennas and propagation, vol.AP-29, No.1, January 1981, PP 90-94.

[6] S.S. Patnaik, B. Khuntia, D.C. Panda and S. Devi “Calculation of optimized parameters of rectangular microstrip antenna using GA ” Microwave and optical technology letters USA vol 23 no. 4 , June 2003, PP 431-433.

[7] D.E. Goldberg, “Genetic Algorithms – in search Optimization & Machine learning.”,Pearson india 2004.

[8] N. Kumprasert, “Theoretical study of dual-resonant frequency and circular polarization of elliptical micro strip antennas," IEEE AP-S International Symposium,” Vol. 2, July 2000, PP 1015-1020.

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