Eigenvalue Crossing Avoidance in Characteristic Modes

The theory of characteristic modes (TCM) provides a set of eigenvalues and eigenvectors that are determined entirely by a structure's geometry at a particular frequency. When examining a design over a range of frequencies, consistent interpretation of the modal data is crucial. Here, we present a way of interpreting crossing avoidances observed when tracking characteristic-mode eigenvalue traces over frequency. Using the framework of coupled-mode theory, a method for decomposing a pair of characteristic modes into auxiliary modes is developed. The auxiliary modes have a degeneracy (eigenvalue crossing) and maintain continuity of modal current distributions through the coupling region of the original characteristic modes. We demonstrate several examples using our method on simple objects. Furthermore, we explore the effect of multiplicative noise and lumped reactive loading on induced crossing avoidance.