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.