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

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) modelingof an LPAusing differential evolution (DE) optimization algorithmis presented. Two parallel brancheseach represents the monopole patch radiator compose the EC topology.In eachbranch, a serial resistance and inductance pair stands for patch conductor, a parallel resistance and capacitancepair symbolizes the dielectric substrate. The expressions of theseeightlumpedelementsenclosing the antenna’s physical and electrical parameters accompanyingwith optimization variables are constituted considering the element definitions of microstrip transmission line(MTL). Return loss equationis derived through input impedance equation of the EC model. The variables are then optimallyfoundby fitting the calculated return loss to the simulated results by DEalgorithm. The proposed ECmodelisthenverified through resultsof simulated andmeasured LPA.Moreover, real and imaginary parts of theECinput impedanceare comparatively calculated. Theseresults showthat the proposed EC model gives almost the same results in terms of important antenna parameters

PDF

___

[1] 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

[2] 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

[3] A.Toktas, M. B. Bicer, A. Akdagli and A. Kayabasi, “Simple formulas for calculating resonant frequencies of C and Hshaped 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

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

[5] 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::AIDMOP13>3.0.CO;2-Y

[6] 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

[7] 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

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

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

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

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

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

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

[14] 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.

[15] 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.

[16] A. Akdagli andA. Kayabasi, “An accurate computation method based on artificial neural networks with different learning algorithms for resonant frequency of annular ring microstrip antennas,” Journal of Computational Electronics, vol.13, no: 4, pp. 1014- 1019, 2014. doi: 10.1007/s10825-014-0624-6

[17] A. Kayabasiand A. Akdagli, “Predicting the resonant frequency of eshaped compact microstrip antennas by using ANFIS and SVM,” Wireless Personal Communications, vol. 82, no: 3, pp. 1893-1906, 2015, doi: 10.1007/s11277-015- 2321-6.

[18] A. Kayabasi and A. Akdagli, “Usage of ANN and ANFIS methods for computing resonant frequency of slot-loaded compact microstrip antennas,”Journal of the Faculty of Engineering and Architecture of Gazi University, vol.31, no: 1, pp. 105-117, 2016, Doi: 10.17341/gummfd.71495.

[19] 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

[20] 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.

[21] 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

[22] Y.Jawad , J.Hojin , K. Kwanghoand 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

[23] F. T. Ulaby, “Fundamentals of applied electromagnetics,” PrenticeHall, Inc. Upper Saddle River, NJ, USA, 1997

[24] 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.

[25] M.V. Schneider, “Microstriplines 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