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.

I. Introduction

In recent years, the antenna literature has seen a resurgence of work centered around the theory of characteristic modes (TCM). Originally formulated by Garbacz in 1971 [1], the method was revisited and reformulated by Harrington and Mautz [2], [3]. Using the method-of-moments impedance matrix [4] of a perfectly conducting structure, one can use TCM to generate a set of modal currents with convenient properties. These modes are characterized entirely by the shape of the object, independent of any excitation. TCM has been the subject of application-focused review papers [5], [6] attempting to refine the popular understanding of the method and expand on what it offers the larger antenna engineering field. More recently, characteristic modes have been used in devising broadband equivalent circuit models of antennas [7], automated design resonant single- and multiband antennas [8], as well as enabling modal considerations of the antenna -factor [9], [10].