Synthesis of Inline Mixed Coupled Quasi-Elliptic Bandpass Filters Based on $\lambda/4$ Resonators

This paper proposes a general synthesis method for inline mixed coupled quasi-elliptic bandpass filters based on λ/4 resonators. Different from the conventional modeling with lumped and mixed inductive and capacitive coupling, the proposed mixed-coupling model here includes not only the coupling magnitudes, but also their paths' phases inside the mixed coupling. According to the presented formulation, there exists one lower side transmission zero for the capacitive-dominant mixed coupling. However, there are two transmission zeros in the upper stopband for the inductive-dominant case, and these two transmission zeros can be analytically synthesized with different coupling path ratios. The proposed synthesis method is then applied to design two second-order bandpass filters based on inductive-dominant coupled λ/4 resonators, resulting in two upper stopband transmission zeros. Furthermore, this synthesis method is extended to design two fourth-order quasi-elliptic bandpass filters with both inline capacitive- and inductive-dominant mixed couplings. Finally, the designed filters are fabricated and measured to provide successful verification on the proposed mixed coupling model approach.