On the Search of the Coupling Matrix Synthesis Path Through Matrix Decomposition

The synthesis of nonconventional topologies has become the key enabler of next-generation filters. However, the coupling matrix (CM) reconfiguration path of noncanonical forms may become complex and difficult to trace, especially in high-order filters. As a consequence, the synthesis of this kind of networks is usually tackled by means of optimization and numerical interval methods. Although these synthesis methodologies have proven to be effective, for some cases they may take large amounts of time to get to the target topology. This work presents a methodology to extract the reconfiguration path of any target topology once the general transformation matrix is obtained, which is reproducible independently of the transfer function. This enables the option of using the powerful and rapid tool of CM reconfiguration. Moreover, this letter discusses the nonunique solution of a target topology with their reconfiguration path, which is strongly related to the eigenvalues of the network. Two different topologies are used as a vehicle to validate the presented methodology.