Equivalent Circuit Modelling of an L-shaped Patch Antenna by Optimizing the Lumped Elements Using Differential Evolution Algorithm

Abdurrahim Toktas


L-shaped patch antenna (LPA) is formed by combining two monopole patch radiators. Proper modelling of a LPA using lumped elements is crucial in antenna design and analysis. In this study, a novel equivalent circuit (EC) modeling of an LPA using differential evolution (DE) optimization algorithm is presented. Two parallel branches each represents the monopole patch radiator compose the EC topology. In each branch, a serial resistance and inductance pair stands for patch conductor, a parallel resistance and capacitance pair symbolizes the dielectric substrate. The expressions of these eight lumped elements enclosing the antenna’s physical and electrical parameters accompanying with optimization variables are constituted considering the element definitions of microstrip transmission line (MTL). Return loss equation is derived through input impedance equation of the EC model. The variables are then optimally found by fitting the calculated return loss to the simulated results by DE algorithm. The proposed EC model is then verified through results of simulated and measured LPA. Moreover, real and imaginary parts of the EC input impedance are comparatively calculated. These show that the proposed EC model gives almost the same results in terms of important antenna parameters.


Antennas, patch antennas, L-shaped patch antennas, equivalent circuit model, optimization, differential evolution algorithm

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Submitted: 2017-05-16 00:28:28
Published: 2017-12-12 13:20:45
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W. F. Richards, Y. T. Lo and D. D. Harrisson, “An improved theory for microstrip antennas and applications,” IEEE T. Antenn. Propag., vol. 29, no. 1, pp. 38-46, 1981. doi: 10.1109/TAP.1981.1142524

A. K. Bhattacharyya and R. Garg, "Generalised transmission line model for microstrip patches," IEE Proc-H., vol. 132, no. 2, pp. 93-98, 1985. doi: 10.1049/ip-h-2:19850019

A. Toktas, M. B. Bicer, A. Akdagli and A. Kayabasi, “Simple formulas for calculating resonant frequencies of C and H shaped compact microstrip antennas obtained by using artificial bee colony algorithm,” J. Electromagn. Waves. App., vol. 25, no. 11-12, pp. 1718-1729, 2011. doi: 10.1163/156939311797164855

F. Yang, X.-X. Zhang, X. Ye and Y. Rahmat-Samii, "Wide-band E-shaped patch antennas for wireless communications," IEEE T. Antenn. Propag., vol. 49, no. 7, pp. 1094-1100, 2001. doi: 10.1109/8.933489

Z. N. Chen, “Radiation pattern of a probe fed L-shaped plate antenna,” Microw. Opt. Techn. Lett., vol. 27, no.6, pp. 410-413, 2000. doi: 10.1002/1098-2760(20001220)27:6<410::AID-MOP13>3.0.CO;2-Y

A. A. Deshmukh and G. Kumar, “Formulation of resonant frequency for compact rectangular microstrip antennas,” Microw. Opt. Techn. Lett., vol. 49, no. 2, pp. 498-501, 2007. doi: 10.1002/mop.22161

A. Toktas, M. B. Bicer, A. Kayabasi, D. Ustun, A. Akdagli. and K. Kurt, “A novel and simple expression to accurately calculate the resonant frequency of annular-ring microstrip antennas,” International Journal of Microwave and Wireless Technologies, vo. 7, no. 6, pp. 727– 733, 2015. doi: 10.1017/S1759078714000890

D. B. Davidson, “Computational electromagnetics for RF and microwave engineering,” Cambridge University Press, Cambridge, United Kingdom, 2005.

A. Taflove, “Computational electrodynamics: The finite-difference time domain method,” Artech House, Boston, 1995.

R. F. Harrington, “Field computation by moment methods,” IEEE Press, Piscataway, N.J., 1993.

E. Oñate, “Structural analysis with the finite element method. Linear Statics,” vol. 1 Basis and Solids, Springer, 2009.

K. C. Gupta, R. Garg, I. J. Bahl, and P. Bhartia, “Microstrip Lines and Slotlines,” 2nd Edition, Artech House, Boston, London, 1996.

R. Garg, P. Bhartia, I. Bahl, and A. Ittipiboon. “Microstrip antenna design handbook,”Artech House, Boston, London, 2003.

A. Singh, M. Aneesh, K. Kamakshi, A. Mishra, J. A. Ansari, “Analysis of F-shape microstrip line fed dualband antenna for WLAN applications,” Wirel. Netw., vol. 20, no. 1, pp. 133-140, 2014.

M. Ansarizadeh, A. Ghorbani, and R. A. Abd-Alhameed, "An approach to equivalent circuit modeling of rectangular microstrip antennas," Prog. Electromagn. Res. B, vol. 8, pp. 77-86, 2008.

K. Storn and K. Price, Differential evolution - A simple and efficient heuristic for global optimization over continuous spaces, J. Global Optim., vol. 11, no. 4, pp. 341–359, 1997. doi:10.1023/A:1008202821328

P. Rocca, G. Oliveri and A. Massa, “Differential evolution as applied to electromagnetics,” IEEE Antenn. Propag. Mag., vol. 53, no. 1, pp. 38–49, 2011.

G. R. DeJean and M. M. Tentzeris, "The application of lumped element equivalent circuits approach to the design of single-port microstrip antennas," IEEE T. Antenn. Propag., vol. 55, no. 9, pp. 2468-2472, 2007. doi: 10.1109/TAP.2007.904129

Y. Jawad , J. Hojin , K. Kwangho and N. Wansoo , “Design, analysis, and equivalent circuit modeling of dual band PIFA using a stub for performance enhancement”, J. Electromagn. Eng. Sci., vol. 3, no. 3, pp. 169-181, 2016. doi: 10.5515/JKIEES.2016.16.3.169

F. T. Ulaby, “Fundamentals of applied electromagnetics,” Prentice-Hall, Inc. Upper Saddle River, NJ, USA, 1997

A. Kayabasi, A. Toktas, A. Akdagli, M. B. Bicer, and D. Ustun, Applications of ANN and ANFIS to predict the resonant frequency of L-shaped compact microstrip antennas, The Applied Computational Electromagnetics Society (ACES), vo. 29, no. 6 , pp. 460-468, 2014.

M.V. Schneider, “Microstrip lines for microwave integrated circuits,” Bell Syst. Tech. J., vol. 48, no. 5, pp. 1421-144, 1969. doi: 10.1002/j.1538-7305.1969.tb04274.x

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