volume | PIER Journals

Abstract

Ametho d based on concurrent neuro-fuzzy system (CNFS) is presented to calculate simultaneously the resonant frequencies of the rectangular, circular, and triangular microstrip antennas (MSAs). The CNFS comprises an artificial neural network (ANN) and an adaptive-network-based fuzzy inference system (ANFIS). In a CNFS, neural network assists the fuzzy system continuously (or vice versa) to compute the resonant frequency. The resonant frequency results of CNFS for the rectangular, circular, and triangular MSAs are in very good agreement with the experimental results available in the literature.

1. Bahl, I. J. and P. Bhartia, Microstrip Antennas, Artech House, Dedham, MA, 1980.

2. James, J. R., P. S. Hall, and C. Wood, Microstrip Antennas- Theory and Design, Peter Peregrisnus Ltd., London, 1981.

3. Garg, R., P. Bhartia, I. Bahl, and A. Ittipiboon, Microstrip Antenna Design Handbook, Artech House, Canton, MA, 2001.

4. Itoh, T. and R. Mittra, "Analysis of a microstrip disk resonator," Archiv fur Electronik und ¨ Ubertrugungstechnik, Vol. 27, 456-458, 1973.

5. Howell, J. Q., "Microstrip antennas," IEEE Trans.A ntennas Propagat., Vol. 23, 90-93, 1975.
doi:10.1109/TAP.1975.1141009

6. Hammerstad, E. O., "Equations for microstrip circuits design," Proceedings of the 5th European Microwave Conference, 268-272, 1975.

7. Helszajn, J. and D. S. James, "Planar triangular resonators with magnetic walls," IEEE Trans.Micr owave Theory Tech., Vol. 26, 95-100, 1978.
doi:10.1109/TMTT.1978.1129320

8. Carver, K. R., "Practical analytical techniques for the microstrip antenna," Proceedings of the Workshop on Printed Circuit Antenna Tech., 1-7, 1979.

9. Derneryd, A. G., "Analysis of the microstrip disk antenna element," IEEE Trans.A nten.Pr opagat., Vol. 27, 660-664, 1979.

10. Chew, W. C. and J. A. Kong, "Resonance of axial and non-axial symmetric modes in circular microstrip disk antenna," Proceedings of the IEEE AP-S Int.Symp osium, 621-625, 1980.

11. Sengupta, D. L., "Approximate expression for the resonant frequency of a rectangular patch antenna," Electronics Lett., Vol. 19, 834-835, 1983.
doi:10.1049/el:19830568

12. Dahele, J. S. and K. F. Lee, "Effect of substrate thickness on the performance of a circular-disk microstrip antenna," IEEE Trans. Antennas Propagat., Vol. 31, 358-364, 1983.
doi:10.1109/TAP.1983.1143037

13. Dahele, J. S. and K. F. Lee, "Theory and experiment on microstrip antennas with airgaps," IEE Proc.Micr owaves, Vol. 132, 455-460, 1985.

14. Chang, E., S. A. Long, and W. F. Richards, "An experimental investigation of electrically thick rectangular microstrip antennas," IEEE Trans.A ntennas Propagat., Vol. 34, 767-772, 1986.
doi:10.1109/TAP.1986.1143890

15. Garg, R. and S. A. Long, "Resonant frequency of electrically thick rectangular microstrip antennas," Electronics Lett., Vol. 23, 1149-1151, 1987.
doi:10.1049/el:19870801

16. Dahele, J. S. and K. F. Lee, "On the resonant frequencies of the triangular patch antenna," IEEE Trans.A ntennas Propagat., Vol. 35, 100-101, 1987.
doi:10.1109/TAP.1987.1143960

17. Chew, W. C. and Q. Liu, "Resonance frequency of a rectangular microstrip patch," IEEE Trans.A ntennas Propagat., Vol. 36, 1045-1056, 1988.
doi:10.1109/8.7216

18. Liu, Q. and W. C. Chew, "Curve-fitting formulas for fast determination of accurate resonant frequency of circular microstrip patches," IEE Proc.Micr owaves, Vol. 135, 289-292, 1988.

19. Abboud, F., J. P. Damiano, and A. Papiernik, "New determination of resonant frequency of circular disc microstrip antenna: Application to thick substrate," Electronics Lett., Vol. 24, 1104-1106, 1988.
doi:10.1049/el:19880750

20. Garg, R. and S. A. Long, "An improved formula for the resonant frequency of the triangular microstrip patch antenna," IEEE Trans.A ntennas Propagat., Vol. 36, 1988.

21. Gang, X., "On the resonant frequencies of microstrip antennas," IEEE Trans.A ntennas Propagat., Vol. 37, 245-247, 1989.
doi:10.1109/8.18712

22. Antoszkiewicz, K. and L. Shafai, "Impedance characteristics of circular microstrip patches," IEEE Trans.A ntennas Propagat., Vol. 38, 942-946, 1990.
doi:10.1109/8.55597

23. Chen, W., K. F. Lee, and J. S. Dahele, "Theoretical and experimental studies of the resonant frequencies of the equilateral triangular microstrip antenna," IEEE Trans.A ntennas Propagat., Vol. 40, 1253-1256, 1992.
doi:10.1109/8.182460

24. Roy, J. S. and B. Jecko, "Aform ula for the resonance frequencies of circular microstrip patch antennas satisfying CAD requirements," Int.J.Micr owave Millimeter-Wave Computer- Aided Eng., Vol. 3, 67-70, 1993.
doi:10.1002/mmce.4570030109

25. Guney, K., "Anew edge extension expression for the resonant frequency of electrically thick rectangular microstrip antennas," Int.J.Ele ctronics, Vol. 75, 767-770, 1993.
doi:10.1080/00207219308907154

26. Guney, K., "Resonant frequency of a triangular microstrip antenna," Microwave Opt.T echnol.L ett., Vol. 6, 555-557, 1993.
doi:10.1002/mop.4650060913

27. Guney, K., "Comments on: On the resonant frequencies of microstrip antennas," IEEE Trans.A ntennas Propagat., Vol. 42, 1363-1365, 1994.
doi:10.1109/8.318660

28. Guney, K., "Resonant frequency of electrically-thick circular microstrip antennas," Int.J.Ele ctronics, Vol. 77, 377-386, 1994.
doi:10.1080/00207219408926070

29. Lee, K. F. and Z. Fan, "CAD formulas for resonant frequencies of TM11 mode of circular patch antenna with or without superstrate," Microwave Opt.T ech.L ett., Vol. 7, 570-573, 1994.
doi:10.1002/mop.4650071212

30. Kara, M., "The resonant frequency of rectangular microstrip antenna elements with various substrate thicknesses," Microwave Opt.T echnol.L ett., Vol. 11, 55-59, 1996.
doi:10.1002/(SICI)1098-2760(19960205)11:2<55::AID-MOP1>3.0.CO;2-N

31. Kara, M., "Closed-form expressions for the resonant frequency of rectangular microstrip antenna elements with thick substrates," Microwave Opt.T echnol.L ett., Vol. 12, 131-136, 1996.
doi:10.1002/(SICI)1098-2760(19960620)12:3<131::AID-MOP4>3.0.CO;2-I

32. Gurel, C. S. and E. Yazgan, "Resonant frequency of an air gap tuned circular disc microstrip antenna," Int.J.Ele ctronics, Vol. 87, 973-979, 2000.
doi:10.1080/002072100404622

33. Gurel, C. S. and E. Yazgan, "New determination of dynamic permittivity and resonant frequency of tunable circular disk microstrip structures," Int.J.RF and Microwave Computer-Aided Eng., Vol. 10, 120-126, 2000.
doi:10.1002/(SICI)1099-047X(200003)10:2<120::AID-MMCE4>3.0.CO;2-6

34. Gurel, C. S. and E. Yazgan, "New computation of the resonant frequency of a tunable equilateral triangular microstrip patch," IEEE Trans.Micr owave Theory Tech., Vol. 48, 334-338, 2000.
doi:10.1109/22.826831

35. Guha, D. and J. Y. Siddiqui, "Resonant frequency of equilateral triangular microstrip antenna with and without air gap," IEEE Trans.A ntennas Propagat., Vol. 52, 2174-2177, 2004.
doi:10.1109/TAP.2004.832504

36. Guney, K., "Anew edge extension expression for the resonant frequency of rectangular microstrip antennas with thin and thick substrates," J.Communic ations Tech.and Electronics, Vol. 49, 49-53, 2004.

37. Angiulli, G. and M. Versaci, "Resonant frequency evaluation of microstrip antennas using a neural-fuzzy approach," IEEE Trans. Magnetics, Vol. 39, 1333-1336, 2003.
doi:10.1109/TMAG.2003.810172

38. Karaboga, D., K. Guney, N. Karaboga, and A. Kaplan, "Simple and accurate effective side length expression obtained by using a modified genetic algorithm for the resonant frequency of an equilateral triangular microstrip antenna," Int.J.Ele ctronics, Vol. 83, 99-108, 1997.
doi:10.1080/002072197135698

39. Akdagli, A. and K. Guney, "Effective patch radius expression obtained using a genetic algorithm for the resonant frequency of electrically thin and thick circular microstrip antennas," IEE Proc. Microwaves, Vol. 147, 156-159, 2000.

40. Karaboga, D., K. Guney, A. Kaplan, and A. Akdagli, "A new effective side length expression obtained using a modified tabu search algorithm for the resonant frequency of a triangular microstrip antenna," Int.J.RF and Microwave Computer-Aided Eng., Vol. 8, 4-10, 1998.
doi:10.1002/(SICI)1099-047X(199801)8:1<4::AID-MMCE2>3.0.CO;2-R

41. Karaboga, N., K. Guney, and A. Akdagli, "A new effective patch radius expression obtained by using a modified tabu search algorithm for the resonant frequency of electrically thick circular microstrip antenna," Int.J.Ele ctronics, Vol. 86, 825-835, 1999.
doi:10.1080/002072199133067

42. Sagiroglu, S. and K. Guney, "Calculation of resonant frequency for an equilateral triangular microstrip antenna with the use of artificial neural networks," Microwave Opt.T echnol.L ett., Vol. 14, 89-93, 1997.
doi:10.1002/(SICI)1098-2760(19970205)14:2<89::AID-MOP5>3.0.CO;2-H

43. Sagiroglu, S., K. Guney, and M. Erler, "Resonant frequency calculation for circular microstrip antennas using artificial neural networks," Int.J.RF and Microwave Computer-Aided Eng., Vol. 8, 270-277, 1998.
doi:10.1002/(SICI)1099-047X(199805)8:3<270::AID-MMCE10>3.0.CO;2-8

44. Karaboga, D.K. Guney, S. Sagiroglu, and M. Erler, "Neural computation of resonant frequency of electrically thin and thick rectangular microstrip antennas," IEE Proc.Micr owaves Antennas Propagat., Vol. 146, 155-159, 1999.

45. Guney, K., S. Sagiroglu, and M. Erler, "Comparison of neural networks for resonant frequency computation of electrically thin and thick rectangular microstrip antennas," J.of Electromagn. Waves and Appl., Vol. 15, 1121-1145, 2001.
doi:10.1163/156939301X00454

46. Ozer, S., K. Guney, and A. Kaplan, "Computation of the resonant frequency of electrically thin and thick rectangular microstrip antennas with the use of fuzzy inference systems," Int.J.RF and Microwave Computer-Aided Eng., Vol. 10, 108-119, 2000.
doi:10.1002/(SICI)1099-047X(200003)10:2<108::AID-MMCE3>3.0.CO;2-7

47. Guney, K. and N. Sarikaya, "Computation of resonant frequency for equilateral triangular microstrip antennas using adaptive neuro-fuzzy inference system," Int.J.RF and Microwave Computer-Aided Eng., Vol. 14, 134-143, 2004.
doi:10.1002/mmce.10125

48. Guney, K. and N. Sarikaya, "Adaptive neuro-fuzzy inference system for computing the resonant frequency of circular microstrip antenna," The Applied Computational Electromagnetics Society J., Vol. 19, 188-197, 2004.

49. Guney, K. and N. Sarikaya, "Adaptive neuro-fuzzy inference system for computing the resonant frequency of electrically thin and thick rectangular microstrip antennas," Int.J.Ele ctronics, Vol. 94, 833-844, 2007.
doi:10.1080/00207210701526317

50. Guney, K. and N. Sarikaya, "Resonant frequency calculation for circular microstrip antennas with a dielectric cover using adaptive network-based fuzzy inference system optimized by various algorithms," Progress In Electromagnetics Research, Vol. 72, 279-306, 2007.
doi:10.2528/PIER07031302

51. Guney, K. and N. Sarikaya, "Adaptive neuro-fuzzy inference system for computing the physical dimensions of electrically thin and thick rectangular microstrip antennas," Int.J.Infr ared and Millimeter Waves, Vol. 27, 219-233, 2006.
doi:10.1007/s10762-006-9070-2

52. Guney, K. and N. Sarikaya, "Multiple adaptive-network-based fuzzy inference system for the synthesis of rectangular microstrip antennas with thin and thick substrates," Int.J.RF and Microwave Computer-Aided Eng., Vol. 18, 359-375, 2008.
doi:10.1002/mmce.20294

53. Sagiroglu, S., K. Guney, and M. Erler, "Calculation of bandwidth for electrically thin and thick rectangular microstrip antennas with the use of multilayered perceptrons," Int.J.RF and Microwave Computer-Aided Eng., Vol. 9, 277-286, 1999.
doi:10.1002/(SICI)1099-047X(199905)9:3<277::AID-MMCE11>3.0.CO;2-3

54. Guney, K. and N. Sarikaya, "Artificial neural networks for calculating the input resistance of circular microstrip antennas," Microwave Opt.T echnol.L ett., Vol. 37, 107-111, 2003.
doi:10.1002/mop.10838

55. Guney, K. and S.S. Gultekin, "Acomparativ e study of neural networks for input resistance computation of electrically thin and thick rectangular microstrip antennas," J.Communic ations Tech. and Electronics, Vol. 52, 483-492, 2007.
doi:10.1134/S1064226907050014

56. Kaplan, A., K. Guney, and S. Ozer, "Fuzzy associative memories for the computation of the bandwidth of rectangular microstrip antennas with thin and thick substrates," Int.J.Ele ctronics, Vol. 88, 189-195, 2001.
doi:10.1080/00207210010002078

57. Guney, K. and N. Sarikaya, "Adaptive neuro-fuzzy inference system for the input resistance computation of rectangular microstrip antennas with thin and thick substrates," J.of Electromagn.Waves and Appl., Vol. 18, 23-39, 2004.
doi:10.1163/156939304322749599

58. Guney, K. and N. Sarikaya, "Input resistance calculation for circular microstrip antennas using adaptive neuro-fuzzy inference system," Int.J.Infr ared and Millimeter Waves, Vol. 25, 703-716, 2004.
doi:10.1023/B:IJIM.0000020756.48454.31

59. Guney, K. and N. Sarikaya, "Adaptive neuro-fuzzy inference system for the computation of the bandwidth of electrically thin and thick rectangular microstrip antennas," Electrical Eng., Vol. 88, 201-210, 2006.
doi:10.1007/s00202-004-0271-1

60. Guney, K. and N. Sarikaya, "Adaptive-network-based fuzzy inference system models for input resistance computation of circular microstrip antennas," Microwave Opt.T echnol.L ett., Vol. 50, 1253-1261, 2008.
doi:10.1002/mop.23354

61. Guney, K., S. Sagiroglu, and M. Erler, "Generalized neural method to determine resonant frequencies of various microstrip antennas," Int.J.RF and Microwave Computer-Aided Eng., Vol. 12, 131-139, 2002.
doi:10.1002/mmce.10006

62. Sagiroglu, S. and A. Kalinli, "Determining resonant frequencies of various microstrip antennas within a single neural model trained using parallel tabu search algorithm," Electromagnetics, Vol. 25, 551-565, 2005.
doi:10.1080/02726340591007013

63. Guney, K. and N. Sarikaya, "Ah ybrid method based on combining artificial neural network and fuzzy inference system for simultaneous computation of resonant frequencies of rectangular, circular, and triangular microstrip antennas," IEEE Trans. Antennas Propagat., Vol. 55, 659-668, 2007.
doi:10.1109/TAP.2007.891566

64. Jang, J.-S. R., "ANFIS: Adaptive-network-based fuzzy inference system," IEEE Trans.Systems, Vol. 23, 665-685, 1993.

65. Jang, J.-S. R., C. T. Sun, and E. Mizutani, Neuro-Fuzzy and Soft Computing: A Computational Approach to Learning and Machine Intelligence, Prentice-Hall, Upper Saddle River, NJ, 1997.

66. Mackay, D. J. C., "Bayesian interpolation," Neural Computation, Vol. 4, 415-447, 1992.
doi:10.1162/neco.1992.4.3.415

67. Guney, K., C. Yildiz, S. Kaya, and M. Turkmen, "Artificial neural networks for calculating the characteristic impedance of airsuspended trapezoidal and rectangular-shaped microshield lines," J.of Electromagn.Waves and Appl., Vol. 20, 1161-1174, 2006.
doi:10.1163/156939306777442917

68. Yildiz, C., K. Guney, M. Turkmen, and S. Kaya, "Neural models for coplanar strip line synthesis," Progress In Electromagnetics Research, Vol. 69, 127-144, 2007.
doi:10.2528/PIER06120802

69. Kaya, S., M. Turkmen, K. Guney, and C. Yildiz, "Neural models for the elliptic-and circular-shaped microshield lines," Progress In Electromagnetics Research B, Vol. 6, 169-181, 2008.

70. Turkmen, M., S. Kaya, C. Yildiz, and K. Guney, "Adaptive neurofuzzy models for conventional coplanar waveguides," Progress In Electromagnetics Research B, Vol. 6, 93-107, 2008.

71. Sarikaya, N., K. Guney, and C. Yildiz, "Adaptive neurofuzzy inference system for the computation of the characteristic impedance and the effective permittivity of the micro-coplanar strip line," Progress In Electromagnetics Research B, Vol. 6, 225-237, 2008.

72. Turkmen, I. and K. Guney, "Tabu search tracker with adaptive neuro-fuzzy inference system for multiple target tracking," Progress In Electromagnetics Research, Vol. 65, 169-185, 2006.
doi:10.2528/PIER06090601

73. Abraham, A., "Neuro fuzzy systems: State-of-the-art modeling techniques," Lecture Notes in Computer Science, 269-276, 2001.
doi:10.1007/3-540-45720-8_30

74. Abraham, A., "Adaptation of fuzzy inference system using neural learning," Fuzzy Systems Engineering: Theory and Practice (Studies in Fuzziness and Soft Computing), 53-83, 2005.

75. Maren, A. C., C. Harston, and R. Pap, Handbook of Neural Computing Applications, Academic Press, London, 1990.

76. Haykin, S., Neural Networks: A Comprehensive Foundation, Macmillan College Publishing Company, New York, 1994.

77. Guney, K., C. Yildiz, S. Kaya, and M. Turkmen, "Neural models for the V-shaped conductor-backed coplanar waveguides," Microwave Opt.T echnol.L ett., Vol. 49, 1294-1299, 2007.
doi:10.1002/mop.22473

78. Hagan, M. T. and M. Menjah, "Training feedforward networks with the Marquardt algorithm," IEEE Trans.Neur al Netw., Vol. 5, 989-993, 1994.
doi:10.1109/72.329697

79. Moller, M. F., "Ascaled conjugate gradient algorithm for fast supervised learning," Neural Networks, Vol. 6, 525-533, 1993.
doi:10.1016/S0893-6080(05)80056-5

80. Gill, P. E., W. Murray, and M. H. Wright, Practical Optimization, Academic Press, New York, 1981.

81. Fletcher, R. and C. M. Reeves, "Function minimization by conjugate gradients," Computer J., Vol. 7, 149-154, 1964.
doi:10.1093/comjnl/7.2.149

82. Levenberg, K., "Ametho d for the solution of certain nonlinear problems in least-squares," Quart.Appl.Math.II, 164-168, 1944.

83. Marquardt, D. W., "An algorithm for least-squares estimation of nonlinear parameters," SIAM J.Appl.Math., Vol. 11, 431-441, 1963.
doi:10.1137/0111030

84. Dennis, J. E., State of the Art in Numerical Analysis, Academic Press, 1977.

85. Spendley, W., G. R. Hext, and F. R. Himsworth, "Sequential application of simplex designs in optimization and evolutionary operation," Technometrics, Vol. 4, 441-461, 1962.
doi:10.2307/1266283

86. Nelder, J. A. and R. Mead, "A simplex method for function minimization," Computer J., Vol. 7, 308-313, 1965.

87. Holland, J., Adaptation in Natural and Artificial Systems, University of Michigan Press, MI, 1975.

88. Goldberg, D. E., Genetic Algorithms in Search, Optimization and Machine Learning, Addison-Wesley, Reading, MA, 1989.

89. Kennedy, J. and R. Eberhart, "Particle swarm optimization," Proceedings of the IEEE Int.Confer ence on Neural Networks, 1942-1948, 1995.

90. Eberhart, R. C. and J. Kennedy, "Anew optimizer using particle swarm theory," Proceedings of the Sixth International Symposium on Micro Machine and Human Science, 39-43, 1995.

Professor Kerim Guney

Dr. Nurcan Sarikaya