Coupling Matrix Synthesis With Repeated Poles in S-Parameters

Analytical coupling matrix synthesis techniques are essential to the accurate design of coupled-resonator networks. Conventional approaches synthesize coupling matrices from partial fraction expansions of Y-parameters. A recently proposed technique synthesizes multiport coupling matrices directly from partial fraction expansions of S-parameters. However, none of these works discusses coupling matrix synthesis problems with repeated poles in the rational characteristic functions. When the prescribed S-parameter rational functions have repeated poles, their partial fraction expansions take nonregular forms, requiring special treatment in the coupling matrix synthesis procedure. This article demonstrates such a situation by constructing a class of three-port S-parameter rational functions with repeated poles for diplexers. Then, it introduces a direct multiport coupling matrix synthesis technique from partial fraction expansions of these S-parameter rational functions. Two synthesis examples are provided to demonstrate the applications of the proposed method.