Extraction of Parallel-Coupled and End-Coupled TEM Resonator Networks from a Coupling Matrix in the Design of Coupled-Resonator Filters

Abstract

The paper presents theoretical formulas for the extraction of TEM network parameters from coupling matrices. Along with resonator couplings, the circuits realizing external couplings are also considered. The most common coupling techniques are investigated, i.e., parallel-coupled half-wave-long resonators and end-coupled half-wave-long resonators, for which appropriate design equations are derived. The considered approach of filter design allows for introducing the equivalent circuit of the designed filter prior to the electromagnetic analysis of the coupled resonators. This, in turn, provides better control of the design process and allows for designing the filter in a step-by-step process while constantly controlling the filter response. Moreover, knowing the equivalent circuit, one can use the known methods of, e.g., coupled-line section design, in calculating the couplings between the resonators instead of looking for the correct solution solely based on the electromagnetic calculations. Additionally, comparison of the filter’s response obtained by the proposed numerical calculations versus the filter response obtained with classic network synthesis methods, is given. Finally, an exemplary filter is designed with the use of the proposed approach and measured to show the possible application of the derived theoretical formulas.