A Synthesis Framework for Microwave Filter Topologies Utilizing Predetermined Reconfiguration Path

In this article, a general synthesis framework is proposed for microwave filter topologies incorporating cross-couplings, frequency-variant couplings (FVCs), and nonresonating nodes (NRNs). One coupling matrix (CM) and one capacitance matrix under the target topology are randomly initialized first. Through the symmetric matrices simultaneous diagonalization (SMSD) algorithm, the transformation matrix that reconfigures the initial two random matrices to any classic topology is then acquired analytically. Afterward, the reconfiguration path of this process can be predetermined directly by decomposing the transformation matrix via singular value decomposition (SVD) and Gaussian elimination (GE). Importantly, the reconfiguration path is only relevant to the target topology but independent of transmission zeros (TZs) frequencies and the return loss. Aided by the predetermined reconfiguration path, a more efficient optimization model is established to accelerate the synthesis of the target topology with a satisfactory response. Moreover, to further improve the optimization efficiency, the analytical gradient of the cost function is derived. Multiple synthesis examples are presented to validate the effectiveness of the proposed synthesis framework. Finally, a fifth-order coaxial cavity filter with three TZs is fabricated, and the synthesis, simulation, and measurement results collectively present a good agreement.