Trapezoid Topology for Dual-Mode Bandpass Filters

Presently, coupling topologies compatible with dual-mode resonator filters are restricted to either symmetric responses or asymmetric responses with up to N <tex-math notation="LaTeX"></tex-math> 2-1 transmission zeros (TZs). This article introduces a new coupling topology, the trapezoid topology, which is fully compatible with dual-mode resonator filters and capable of realizing both symmetric and asymmetric filter responses with up to N <tex-math notation="LaTeX"></tex-math> 2 TZs. The topology is categorized into two types: singly coupled and doubly coupled input and output (I/O) coupling structures. The available mixed configuration of single-and dual-mode resonators offers the advantage of suppressing harmonic resonances. This generic coupling topology can realize all possible out-of-band TZ arrangements. A mathematical formulation for numerically synthesizing trapezoid filters is also provided. The characteristic of multiple solutions offers users greater design flexibility. To validate the coupling topology and demonstrate its applicability to dual-mode resonator filters, two physical realization examples are presented: an electromagnetically designed 6-3-0 trapezoid filter realized by dual-mode dielectric resonators and a prototyped 8-4-0 trapezoid filter using circular waveguide dual-mode (CWDM) cavities. The simulated/measured filter responses align closely with the synthesized ones. Regarding practical designs, the criteria for selecting solutions and the sensitivities of TZs with respect to coupling elements are also discussed in detail.