Vol. 48
Latest Volume
All Volumes
PIERM 115 [2023] PIERM 114 [2022] PIERM 113 [2022] PIERM 112 [2022] PIERM 111 [2022] PIERM 110 [2022] PIERM 109 [2022] PIERM 108 [2022] PIERM 107 [2022] PIERM 106 [2021] PIERM 105 [2021] PIERM 104 [2021] PIERM 103 [2021] PIERM 102 [2021] PIERM 101 [2021] PIERM 100 [2021] PIERM 99 [2021] PIERM 98 [2020] PIERM 97 [2020] PIERM 96 [2020] PIERM 95 [2020] PIERM 94 [2020] PIERM 93 [2020] PIERM 92 [2020] PIERM 91 [2020] PIERM 90 [2020] PIERM 89 [2020] PIERM 88 [2020] PIERM 87 [2019] PIERM 86 [2019] PIERM 85 [2019] PIERM 84 [2019] PIERM 83 [2019] PIERM 82 [2019] PIERM 81 [2019] PIERM 80 [2019] PIERM 79 [2019] PIERM 78 [2019] PIERM 77 [2019] PIERM 76 [2018] PIERM 75 [2018] PIERM 74 [2018] PIERM 73 [2018] PIERM 72 [2018] PIERM 71 [2018] PIERM 70 [2018] PIERM 69 [2018] PIERM 68 [2018] PIERM 67 [2018] PIERM 66 [2018] PIERM 65 [2018] PIERM 64 [2018] PIERM 63 [2018] PIERM 62 [2017] PIERM 61 [2017] PIERM 60 [2017] PIERM 59 [2017] PIERM 58 [2017] PIERM 57 [2017] PIERM 56 [2017] PIERM 55 [2017] PIERM 54 [2017] PIERM 53 [2017] PIERM 52 [2016] PIERM 51 [2016] PIERM 50 [2016] PIERM 49 [2016] PIERM 48 [2016] PIERM 47 [2016] PIERM 46 [2016] PIERM 45 [2016] PIERM 44 [2015] PIERM 43 [2015] PIERM 42 [2015] PIERM 41 [2015] PIERM 40 [2014] PIERM 39 [2014] PIERM 38 [2014] PIERM 37 [2014] PIERM 36 [2014] PIERM 35 [2014] PIERM 34 [2014] PIERM 33 [2013] PIERM 32 [2013] PIERM 31 [2013] PIERM 30 [2013] PIERM 29 [2013] PIERM 28 [2013] PIERM 27 [2012] PIERM 26 [2012] PIERM 25 [2012] PIERM 24 [2012] PIERM 23 [2012] PIERM 22 [2012] PIERM 21 [2011] PIERM 20 [2011] PIERM 19 [2011] PIERM 18 [2011] PIERM 17 [2011] PIERM 16 [2011] PIERM 14 [2010] PIERM 13 [2010] PIERM 12 [2010] PIERM 11 [2010] PIERM 10 [2009] PIERM 9 [2009] PIERM 8 [2009] PIERM 7 [2009] PIERM 6 [2009] PIERM 5 [2008] PIERM 4 [2008] PIERM 3 [2008] PIERM 2 [2008] PIERM 1 [2008]
2016-04-19
An Improved MoM -GEC Method for Fast and Accurate Computation of Transmission Planar Structures in Waveguides: Application to Planar Microstrip Lines
By
Progress In Electromagnetics Research M, Vol. 48, 9-24, 2016
Abstract
This paper presents a new hybridization between MoM-GEC and a MultiResolution analysis (MR) based on the use of wavelets functions as trial functions. The proposed approach is developed to speed up convergence, alleviate calculation and then provide a considerable gain in requirements (processing time and memory storage) because it generates a sparse linear system. The approach consists in calculating the total current and input impedance on an invariant metallic pattern through two steps. The first one consists in expressing the boundary conditions of the unknown electromagnetic current with a single electrical circuit using the Generalized Equivalent Circuit method (GEC) and then deduce an electromagnetic equation based on the impedance operator. The impedance operator used here is described using the local modal basis of the waveguide enclosing the studied structure. The second step consists in approximating the total current using orthonormal periodic wavelets as testing functions and the local modal basis of the waveguide as basis functions. The proposed approach allows fast calculation of such inner products through the use of the wavelets multiresolution (MR) analysis advantages, thus significantly reducing the required CPU-time for microstrip-type structure analysis [13, 14]. A sparse matrix is generated from the application of a threshold. A sparsely filled matrix is easier to store and invert [15, 16]. Based on this approach, we study the planar structures. The obtained results show good accuracy with the method of moments. Moreover, we prove considerable improvements in CPU time and memory storage achieved by the MR-GEC approach when studying these structures.
Citation
Nejla Oueslati Taoufik Aguili , "An Improved MoM -GEC Method for Fast and Accurate Computation of Transmission Planar Structures in Waveguides: Application to Planar Microstrip Lines," Progress In Electromagnetics Research M, Vol. 48, 9-24, 2016.
doi:10.2528/PIERM16030204
http://www.jpier.org/PIERM/pier.php?paper=16030204
References

1. Itoh, T. and M. Menzel, "A full-wave analysis method for open microstrip structures," IEEE Trans. Antennas Propagat., Vol. 29, 63-68, Jan. 1981.
doi:10.1109/TAP.1981.1142520

2. Baudrand, H., "Tridimensional methods in monolithic microwave integrated circuits," SMBO Brazilian Symposium NATAL, 183-192, Jul. 27-29, 1988.

3. Baudrand, H., "Representation by equivalent circuit of the integral methods in microwave passive elements," 20th EMC, Budapest, Sep. 10-14, 1990.

4. Harrington, R. F., Field Computation by Moment Methods, Wiley-IEEE Press, Apr. 1993.
doi:10.1109/9780470544631

5. Zhou, P. B., Numerical Analysis of Electromagnetic Field, 1st Ed., Springer, 1993.
doi:10.1007/978-3-642-50319-1

6. Mekkioui, Z. and H. Baudrand, "A full-wave analysis of uniform microstrip leaky-wave antenna with arbitrary metallic strips," Electromagnetics, Vol. 28, No. 4, 296-314, 2008.
doi:10.1080/02726340802040161

7. Aubert, H. and H. Baudrand, "L'Electromagnétisme par les schémas équivalents,", Cepaduès Editions, 2003.

8. Xiang, Z. and Y. Lu, "An effective wavelet matrix transform approach for efficient solutions of electromagnetic integral equations," IEEE Trans. Antennas Propagat., Vol. 45, Aug. 1997.

9. Loison, R., R. Gillard, J. Citerne, and G. Piton, "Application of the wavelet transform for the fast computation of a linear array of printed antennas," European Microwave Conf., Vol. 2, 301-304, Amsterdam, The Netherlands, 1998.

10. Oberschmidt, G. and A. F. Jacob, "Accelerated simulation of planar circuits by means of wavelets," European Microwave Conf., 305-310, Amsterdam, The Netherlands, 1998.

11. Wang, G. and G.-W. Pan, "Full wave analysis of microstrip expansion method," IEEE Trans. on Microw. Theory Tech., Vol. 43, No. I, 131-142, 1995.
doi:10.1109/22.362998

12. Chui, C. K. and E. Quak, "Wavelets on a bounded interval,", D. Braess and C. L. Schumaker, (eds.), ``Numerical methods of approximation theory,'' Vol. 9, 53--75, 1992.

13. Steinberg, B. Z. and Y. Leviatan, "On the use of wavelet expansions in the method of moments," IEEE Trans. Antennas Propagat., Vol. 41, No. 5, 610-619, 1993.
doi:10.1109/8.222280

14. Zhu, X., T. Sogaru, and L. Carin, "Three-dimensional biorthogonal multiresolution time-domain method and its application to electromagnetic scattering problems," IEEE Trans. Antennas Propagat., Vol. 51, No. 5, 1085-1092, May 2003.
doi:10.1109/TAP.2003.811527

15. Baudrand, H., Circuits Passifs en Hyperfréquences, Editions Cépaduès, Jan. 2001.

16. Aguili, T., "Modélisation des composants S. H. F planaires par la méthode des circuits équivalents généralisés,", Thesis, National Engineering School of Tunis ENIT, May 2000.

17. Wang, G., "On the utilization of periodic wavelet expansions in the moment methods," IEEE Trans. on Microw. Theory Tech., Vol. 43, No. 10, Oct. 1995.

18. Wang, G., "Application of wavelets on the interval to the analysis of thin-wire antennas and scatterers," IEEE Trans. Antennas Propagat., Vol. 45, No. 45, 885-893, May 1997.
doi:10.1109/8.575642

19. Pan, G. W. and X. Zhu, "The application of fast adaptive wavelet expansion method in the computation of parameter matrices of multiple lossy transmission lines," IEEE Trans. on Microw. Theory Tech., Vol. 1, 29-32, 1994.

20. Meyer, Y., "Ondelettes sur I'intervalle," Rev. Math. Iberoamer., Vol. 7, 115-143, 1991.
doi:10.4171/RMI/107

21. Baudrand, H., "Introduction au calcul des circuits microsondes,", Cepadues Ed., ENSEEIHT, Toulouse, 1994.

22. Boggess, F. and J. Narcowich, First Course in Wavelets with Fourier Analysis, Wiley, Oct. 2009.

23. Pan, G. W., Wavelets in Electromagnetics and Device Modeling, Wiley, New York, 2003.
doi:10.1002/0471433918

24. Daubechies, "Ten lectures on wavelets,", Society for Applied Mathematics Philadelphia, Pennsylvania, 1992.

25. Beylkin, G., R. R. Coifman, and V. Rokhlin, "Fast wavelet transforms and numerical algorithms - I,", Yale Univ. Tech. Rep., YALEU/DCS/RR-696, Aug. 1989, Commun. Pure Appl. Math., Vol. XLIV, 141-183, 1991.

26. Loison, R., "Utilisation de l'analyse multirésolution dans la méthode des moments. Application à la modélisation de réseaux d'antennes imprimées,", Ph.D. Thesis, National Institute of Applied Sciences, Jan. 2000.

27. Zhu, J., "Development of sensitivity analysis and optimization for microwave circuits and antennas in the frequency domain,", Master Thesis, Mcmaster University, Amilton, Ontario, Jun. 2006.

28. N'Gongo, R. S. and H. Baudrand, "Application of wave concept iterative procedure in planar circuits," Recent Res. Devel. Microwave Theory and Technique, Vol. 1, 187-197, 1999.

29. Beylkin, G., R. Coifman, and V. Rokhlin, "Fast wavelet transforms and numerical algorithms I," Comm. Pure Appl. Math., Vol. 44, 141-183, 1991.
doi:10.1002/cpa.3160440202

30. Alpert, B., R. Coifman, and V. Rokhlin, "Wavelet-like bases for the fast solution of second-kind integral equations," SIAM J. Sci. Comput., Vol. 14, No. 1, 159-184, Jan. 1993.
doi:10.1137/0914010

31. Beylkin, G., R. R. Coifman, and V. Rokhlin, "Fast wavelet transforms and numerical algorithms - I,", Yale Univ. Tech. Rep., YALEU/DCS/RR-696, Aug. 1989, Commun. Pure Appl. Math., Vol. XLIV, 141-183, 1991.

32. Alpert, B., R. Coifman, and V. Rokhlin, "Wavelet-like bases for the fast solution of second-kind integral equations," SIAM J. Sci. Comput., Vol. 14, No. 1, 159-184, Jan. 1993.
doi:10.1137/0914010

33. Chang, X. and L. Tsang, "Fast and broadband modeling method for multiple vias with irregular antipad in arbitrarily shaped power/ground planes in 3-D IC and packaging based on generalized foldy-lax equations," IEEE Transactions on Components, Packaging and Manufacturing Technology, Vol. 4, 685-696, 2014.
doi:10.1109/TCPMT.2013.2290897

34. Tsang, L. and S. Huang, "Modeling of vias sharing the same antipad in planar waveguide with boundary integral equation and group T matrix method," Progress In Electromagnetics Research, Vol. 152, 105-125, 2015.
doi:10.2528/PIER15072605