Coupling Matrix Reconfiguration Aided with a Start System Based on Simultaneous Diagonalization

In this paper, a start system is established based on the simultaneous diagonalization (SD) technique to assist in coupling matrix reconfiguration for non-classic filter topologies. SD can analytically find the congruent transform matrix to reconfigure arbitrary given topologies, including nonresonating nodes (NRNs) and frequency-dependent couplings (FDCs), to the transversal topology. Thus, it directly provides an analytical solution for the randomized start system. The proposed start system acts as the initial point of the homotopy continuation method, so the synthesis solution of specified non-classic filter topologies can be solved stably and efficiently. Two hybrid topologies with NRNs and FDCs are synthesized as examples to verify the proposed synthesis approach.