General Theory of Coupled Characteristic Mode: An Eigen Subspace Approach

In this work, the problem of characteristic mode analysis using eigendecomposition of the method of moments impedance matrix has been simplified using the eigen-subspace approach. The idea behind the eigen-subspace arises from the physical properties of antenna or scatterers, where only a few eigenmodes are enough to characterize the antenna or scatterer. Therefore, entire space eigenanalysis is a waste of computational resources, and eigen-subspace analysis with few modes is good enough to characterize antennas and scatterers. It has been assumed that there is an eigen-subspace (or hyperplane) of coupled characteristic mode, which coincides with the eigen-hyperplane of uncoupled characteristic mode. We can say the coupled characteristic modes are linear combinations of isolated modes based on this assumption. The linear combination is mapped via modal coupling matrix. Using the modal coupling matrix, we can explain the behavior of arbitrarily shaped antennas and scatterers. A computationally efficient method is developed to compute coupled characteristic modes of two mutually coupled scatterers or antennas using the eigen-subspace. The method is summarized as a theorem of two-body coupled characteristic mode. The theorem of two-body coupled characteristic mode has been extended to the N-body coupled characteristic mode. Two algorithms have been developed for the two-body multimode coupled characteristic mode and N-body multimode coupled characteristic mode. Two numerical examples are provided to validate the proposed concepts.