Exhaustive Synthesis of Microwave Filter Topologies Based on Total Degree Homotopy

In this paper, total degree homotopy is introduced to exhaustively synthesize microwave filter topologies. This is a reliable and efficient approach that can globally converge to all solutions of the target filter topologies in one run, with no need for repeating the algorithm with different randomized initial guesses. To further adapt to the features of filter topology reconfiguration, the operation that can eliminate the sign symmetry of coupling matrices and reduce computational complexity simultaneously is presented. To validate the proposed theories, one irregular fifth-order topology and one regular sixth-order topology followed by measurement results are synthesized as the examples.