Exhaustive Synthesis Framework of Dispersive Coupled Resonator Microwave Bandpass Filters

Coupled resonator bandpass filter with linearly dispersive couplings becomes popular in the industry for its known abilities in creating transmission zeros (TZs) and annihilating inconvenient couplings in physical realizations. The existing synthesis approaches for such filters mainly focus on manipulating certain local features of a dispersion-less coupling topology that reflects the filtering function, resulting in a handful of
ad-hoc
topologies. In this article, two propositions and a corollary are proposed, which lay the foundation of the exhaustive synthesis framework of dispersive coupled resonator bandpass filters that consists of exhaustive topology search for given filter characteristic and number of dispersive couplings and exhaustive real solution search for a given legitimate coupling topology with a specific filtering function. As the mathematical foundation, the two propositions are rigorously proved. A systematic pipeline is also introduced for easy adoption of the framework followed by various illustration examples concerning three application aspects of dispersive bandpass filters: creating TZs; rectifying coupling topology; and rearranging input/output (I/O) ports. A few new dispersive coupling topologies are also exhibited, including dispersive extended box, trapezoid, and grid topologies. A ceramic monoblock 6-4 filter with dispersive extended box is prototyped as an illustrative example, demonstrating the usefulness of the proposed exhaustive synthesis framework.