General Coupling Matrix Synthesis Method for Microwave Resonator Filters of Arbitrary Topology

This letter presents a new approach to synthesize the resonator filters of an arbitrary topology. This method employs an optimization method based on the relation between the polynomial coefficients of the transfer function and those of the $S_{21}$ from the coupling matrix. Therefore, this new method can also be applied to self-equalized filters that were not considered in the conventional optimization methods. Two microwave filters, a symmetric 4-pole filter with four transmission zeros (TZs) and an asymmetric 8-pole filter with seven TZs, are synthesized using the present method for validation. Excellent agreement between the response of the transfer function and that of the synthesized $S_{21}$ from the coupling matrix is shown.