Synthesis of All-Resonator Multiplexers

This paper presents an iterative method to achieve a strong initial coupling matrix for triggering the subsequent matrix optimization of diplexers/multiplexers with all-resonator topologies. The method is based on the synthesis of a single channel filter in consideration of the estimated loading effect of other channels. The synthesis starts with the characteristic polynomials of each channel filter, obtaining corresponding input admittance, and extracting the equivalent circuit model. Two examples are used to demonstrate the synthesis process and validate the proposed technique. For most topologies, the iterative method converges after less than 20 iterations. The proposed method provides good initial values of the coupling matrix which can substantially reduce the optimization time to seconds, even for complicated topologies.