Analytical Coupled-Resonator Filter Synthesis Method by Extraction of Fully Canonical Second Order Blocks

This work presents an analytical method for extraction of cascaded fully canonical second order blocks, formed by two resonators with a direct input-output coupling that generates two transmission zeros. Starting from the transfer matrix of the complete network and the specification of the transmission zeros, the method finds a decomposition of the transfer polynomials into two new sets corresponding to the second order subnetwork and the remaining one. To do so, the general solution of the extracted block transfer matrix is computed at each transmission zero. Then, both solutions are used to solve the complete polynomials. In order to illustrate the use of the algorithm, an analytical synthesis of a seventh order filter with four transmission zeros is included. The network topology corresponds to two cascaded quadruplets sharing one resonator.