Frequency-Dependent Impedance Matching Synthesis Methodology for Filters or Matching Networks With Equiripple Responses
Santi Cano, Mario Faura, Laia García, J. Parrón, Pedro de Paco · IEEE Transactions on Microwave Theory and Techniques · 2026
Current synthesis techniques rely on either the low-pass prototype (LP) or direct bandpass (DB) representations to analyze filtering responses, each offering its own advantages. However, all these synthesis methods are carried out under the assumption that both the source and load terminations are constant impedances. This assumption is unrealistic for most RF filter designs, as they are often required to be matched to real devices with frequency-dependent impedances [$Z_{L}(f)$]. The problem can be interpreted as the interaction between two networks:$S_{A}$, representing the filter, and$S_{B}$, representing the$Z_{L}(f)$. When cascaded, these networks produce an overall response$S_{T}$. This article presents a direct synthesis approach for designing general Chebyshev filters terminated with a$Z_{L}(f)$at one port. The proposed approach employs a Remez-like algorithm to determine the characteristic polynomials of$S_{A}$such that, when cascaded with$S_{B}$, the overall response$S_{T}$exhibits an in-band quasi-equiripple behavior. Moreover, the proposed approach provides flexibility in controlling the return loss level ($RL_{T}$) of$S_{T}$, which is particularly useful for adjusting the out-of-band (OoB) rejection level and accommodating technological constraints in certain RF filters. The proposed method is validated through two examples with different optimality criteria: 1) an all-pole filter matched to an antenna booster, designed to approach the Bode–Fano limit by including the antenna’s reflection zero (RZ) within the quasi-equiripple response of$S_{T}$, thereby achieving the most optimal solution; and 2) a ladder filter matched to a real switch, designed excluding its RZs from$S_{T}$to obtain a suboptimal solution.