Analytical Multiport Coupling Matrix Synthesis From Partial Fraction Expansions of S-Parameters

Coupling matrix has proven to be a very useful tool in the design of coupled-resonator networks. The existing analytical coupling matrix synthesis techniques include the steps of converting S-parameters into Y-parameters in explicit rational function forms and synthesizing a transversal coupling matrix from partial fraction expansions of Y-parameters. Such a synthesis procedure can hardly be applied to multiport networks because computing Y-parameter rational functions becomes much more challenging in multiport scenarios. This article introduces a new coupling matrix synthesis technique, where a multiport coupling matrix is directly synthesized from partial fraction expansions of S-parameter rational functions. Unlike traditional methods, there is no need to compute Y-parameter rational functions as an intermediate step. Analytical coupling matrix synthesis formulas are derived in this article. Two design examples, including a two-port bandstop filter and a four-port filtering coupler, are provided to demonstrate the applications of the novel synthesis procedure.