On the Reconfiguration of Coupling Matrix

Abstract

In this article, a general coupling matrix reconfiguration approach is proposed considering arbitrary topology, frequency-dependent couplings (FDCs), and nonresonating nodes (NRNs). The principle is developed in two steps: 1) a systematic procedure is introduced to reconfigure an arbitrary coupling matrix into the transversal topology using the similarity transformation and the eigen decomposition of the coupling matrix; an analytical solution with excellent accuracy is achieved in this process and 2) a framework of coupling matrix reconfiguration is constructed as a much simpler inverse problem, which can be optimized with low computational cost. Both local and global optimization approaches are exploited for this problem. The proposed framework is general and applicable to various scenarios. To verify the proposed algorithm, three traditional coupling matrix examples, two FDCs-incorporated coupling matrix examples, an NRNs-incorporated coupling matrix example, and a five-pole waveguide filter implementation are presented, respectively.