Constructing Three-Port <i>S</i>-Parameter Rational Functions for Coupling Matrix Synthesis of Contiguous-Band Diplexers

Diplexer synthesis is challenging due to the strong interaction between channels. Conventional synthesis techniques decompose a diplexer into two bandpass filters connected to a junction and try to restore Chebyshev characteristics for the channel filters. However, these methods do not work well when the two channels are contiguous. This work takes a different approach that tries to directly synthesize a three-port coupling matrix representing the whole diplexer. This article first investigates realizable conditions on three-port S-parameter rational functions and derives the constraints among the numerator and denominator polynomials. Then, it develops an iterative procedure based on a modified Remez-like algorithm to construct legitimate equi-ripple rational characteristic functions for diplexers. After that, a three-port coupling matrix can be synthesized from partial fraction expansions of S-parameters. The novel method can synthesize regular diplexers as well as contiguous-band diplexers. It allows the numbers of reflection zeros (RZs) and the return loss levels in the two passbands to be independently specified. Moreover, some finite-position transmission zeros (TZs) can be prescribed. The proposed method is validated by the synthesis and design of an asymmetric-response contiguous-band waveguide diplexer.