Rigorous Approach to Coupling Matrix Synthesis Problem With Arbitrary Topology

This work presents a mathematical procedure for solving coupling matrix synthesis problems with arbitrary topologies. A discussion on the properties of arbitrary response-preserving similarity transformations is provided. Based on this property, the proposed method rigorously addresses every possible coupling matrix complying with a desired target topology. This method applies to arbitrary target topologies, both redundant and non-redundant. In cases where there are an infinite number of solutions, this procedure yields a parameterized equation representing all such solutions.