Comparison between the Kummer´s transformation and Ewald method for the evaluation of the parallel plate Green´s functions

In this paper, we present a convergence and efficiency study of two different acceleration techniques for the evaluation of the parallel plate Green´s functions. The first technique is based on the extraction of the asymptotic terms of the spectral representation of the parallel plate Green´s functions by applying the Kummer´s transformation. The second technique is a straightforward reformulation of the 2-D Green´s functions for 1-D periodic structures to the parallel plate case. The PPW Green´s functions calculated by the two methods have been successfully applied to the analysis of a practical inductive microwave filter containing metallic and dielectric posts. The filter analysis technique is based on solving a surface integral equation by the MoM. The convenience of using one of the proposed acceleration technique or the other for the evaluation of each Green´s function components and its derivatives, necessary to solve the MoM problem, is properly justified