Deriving Characteristic Mode Eigenvalue Behavior Using Subduction of Group Representations

A method to derive features of modal eigenvalue traces from known and understood solutions is proposed. It utilizes the concept of subduction from point group theory to obtain the symmetry properties of a target structure from those of a structure with a higher order of symmetry. This is applied exemplary to the analytically known characteristic modes (CMs) of the spherical shell. The eigenvalue behavior of a cube in free space and a cuboid on a perfectly electrically conducting plane are continuously derived from this. In this process, formerly crossing eigenvalue traces are found to split up, forming a split trace crossing avoidance (STCA). This finding is used to explain indentations in eigenvalue traces observed for three-dimensional structures, that are of increasing interest in recent literature. The utility of this knowledge is exemplified through a demonstrator antenna design. The dimensions of the antenna structure are chosen so the STCA is outside the target frequency range, avoiding negative impacts on input matching and the frequency stability of the far field patterns.