Fast Summation of Double Infinite Modal Series Involved in Analysis of Shielded Microstrip Circuits

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.

Fast summation of double infinite modal series using the Poisson summation formula

“…The double infinite modal series under consideration is associated with a diagonal entry of the MoM matrix resulting from the analysis of a vertical strip embedded in a rectangular cavity filled with an isotropic, linear medium [1]. The series has the following form ( ) and where, all the remaining quantities have been defined and described in [1].…”

“…The series has the following form ( ) and where, all the remaining quantities have been defined and described in [1]. As we can see, the series in Eq.…”

“…A method for its efficient summation, based on Kummer's transformation and the complex contour integral method, has been recently described in [1]. Unfortunately, the proposed method can not be directly applied to multiple-valued series with summand having branch points, which are not isolated singularities.…”

“…The method for series transformation, described in this paper, is adopted partly form [1] and consist of two stages.…”

“…Secondly, we shall discuss the possibility of the Poisson summation formula application. In order to demonstrate the proposed method for series transformation we shall apply it to one of the modal series, which has been already described in [1], namely the series 3 , Z which is a multiple-valued series.…”