FAST SUMMATION OF DOUBLE INFINITE MODAL SERIES INVOLVED IN ANALYSIS OF SHIELDED MICROSTRIP CIRCUITS
Institute ofTelecommunications andAcoustics, Wrocław University of Technology
Wyb. Wyspiańskiego 27, 50-370 Wrocław, Poland
e-mail: Piotr.Slobodzian@pwr.wroc.pl
Received:
Rec. 14 November 2003
DOI: 10.12921/cmst.2004.10.01.101-109
OAI: oai:lib.psnc.pl:556
Abstract:
The paper addresses some aspects connected with computational methods involved in analysis of shielded microstrip circuits in the frame of the IE-MoM approach. The paper is focused on a method for efficient evaluation of double infinite modal series, which arise in the analysis of vertical metallizations embedded in a waveguide or cavity filled with a multilayer medium. Generally, the modal series converge very slowly, when treated in its original form, and from practical point of view it makes the IE-MoM approach inefficient. The rate of convergence of the modal series can be significantly increased by means of a transformation of the double infinite series into a fast converging single series. The transformation exploits the contour integral and the residue theorem method in conjunction with the well known Kummer’s transformation. The proposed method proved to be very efficient since it enables radical savings in computational time and this feature makes the method a good candidate for
practical purposes, especially for electromagnetic CAD tools.
References:
[1] J. C. Rautio and R. F. Harrington, An Electromagnetic Time-Harmonic Analysis of Shielded
Microstrip Circuits, IEEE Trans. Microwave Theory Tech., 35, 726-730 (1987).
[2] G. V. Eleftheriades, J. R. Mosig, and M. Guglielmi, A Fast Integral Equation Technique for Shielded Planar Circuits Defined on Nonuniform Meshes, IEEE Trans. Microwave Theory Tech., 44, 2293-2296 (1996).
[3] P. M. Słobodzian, A. Alvarez-Melcon, T. M. Grzegorczyk and F. E. Gardiol, Green’s function for vertical current sources embedded in uniform waveguides and cavities filled with multilayered media, Microwave Opt. Technol. Lett., 33, 186-191 (2002).
[4] P.M Słobodzian, On the dyadic Green’s function in the source region embedded in waveguides or cavitiesfilled with a stratified medium, Microwave Opt. Technol. Lett., 35 93-97 (2002).
[5] V. G. Celidze, Some methods for evaluation of double series and double integrals, Tbilisi University Press, Tbilisi, 1977 (inRussian).
[6] K. Knopp, Infinite series, PWN, Warsaw, 1956 (in Polish).
[7] P. M. Morse and H. Feshbach, Methods of theoretical physics, McGraw-Hill Book Co., Inc., New York, 1953.
The paper addresses some aspects connected with computational methods involved in analysis of shielded microstrip circuits in the frame of the IE-MoM approach. The paper is focused on a method for efficient evaluation of double infinite modal series, which arise in the analysis of vertical metallizations embedded in a waveguide or cavity filled with a multilayer medium. Generally, the modal series converge very slowly, when treated in its original form, and from practical point of view it makes the IE-MoM approach inefficient. The rate of convergence of the modal series can be significantly increased by means of a transformation of the double infinite series into a fast converging single series. The transformation exploits the contour integral and the residue theorem method in conjunction with the well known Kummer’s transformation. The proposed method proved to be very efficient since it enables radical savings in computational time and this feature makes the method a good candidate for
practical purposes, especially for electromagnetic CAD tools.
[1] J. C. Rautio and R. F. Harrington, An Electromagnetic Time-Harmonic Analysis of Shielded
Microstrip Circuits, IEEE Trans. Microwave Theory Tech., 35, 726-730 (1987).
[2] G. V. Eleftheriades, J. R. Mosig, and M. Guglielmi, A Fast Integral Equation Technique for Shielded Planar Circuits Defined on Nonuniform Meshes, IEEE Trans. Microwave Theory Tech., 44, 2293-2296 (1996).
[3] P. M. Słobodzian, A. Alvarez-Melcon, T. M. Grzegorczyk and F. E. Gardiol, Green’s function for vertical current sources embedded in uniform waveguides and cavities filled with multilayered media, Microwave Opt. Technol. Lett., 33, 186-191 (2002).
[4] P.M Słobodzian, On the dyadic Green’s function in the source region embedded in waveguides or cavitiesfilled with a stratified medium, Microwave Opt. Technol. Lett., 35 93-97 (2002).
[5] V. G. Celidze, Some methods for evaluation of double series and double integrals, Tbilisi University Press, Tbilisi, 1977 (inRussian).
[6] K. Knopp, Infinite series, PWN, Warsaw, 1956 (in Polish).
[7] P. M. Morse and H. Feshbach, Methods of theoretical physics, McGraw-Hill Book Co., Inc., New York, 1953.
