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 is derived from it numerically. In this process, formerly crossing eigenvalue traces are found to split up, forming a macroscopic crossing avoidance (MACA). This finding is used to explain indentations in eigenvalue traces observed for 3-D structures, which are of increasing interest in recent literature. The utility of this knowledge is exemplified through a demonstrator antenna design. Here, the subduction procedure is used to analytically predict the eigenvalues of a cuboid on a perfectly electrically conducting plane. The a priori knowledge about the MACA is used to avoid its negative impact on input matching and the frequency stability of the far-field patterns, by choosing the dimensions of the antenna structure so the MACA is outside the target frequency range.