Influence of number of frequency points on rational function's zeroes and poles reliability in microwave filter tuning

Gulgowski, Jacek; Michalski, Jerzy Julian; Kacmajor, Tomasz

doi:10.1109/mikon.2012.6233531

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2023

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“…This operation in fact requires inverting a large matrix with polynomial elements, thus involving a symbolic engine, expensive and computationally intensive. Alternatively, the response of the network implementing the given coupling matrix is evaluated numerically and, via Cauchy's method [8], [9] or Vector Fitting [10], [11], the rational functions are then estimated, though subject to convergence and accuracy issues [12].…”

Section: Introductionmentioning

confidence: 99%

Analytical Derivation of Scattering and Admittance Rational Functions From Coupling Matrix

Oldoni

Macchiarella

Gentili

et al. 2023

IEEE Trans. Circuits Syst. II

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The coupling matrix provides an immediate tool to describe a network, widely used in the context of microwave filters. While several techniques exist to obtain and manipulate the coupling matrix for a given response, the opposite is traditionally achieved by numerically evaluating the response of the network at each frequency of interest and fitting the response to obtain the rational expressions embedding poles and zeros. The present manuscript instead proposes an analytic way to retrieve directly the admittance and scattering functions, as ratios of polynomials, from the coupling matrix. Applications include commercial software packages and more robust microwave filter optimizations during design.

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