Analytical Representation of Characteristic Modes Decomposition

TL;DR

This paper presents an analytical formulation of characteristic modes based on a variational approach, providing deeper insight into modal behavior and practical tools for resonance analysis and code benchmarking.

Contribution

It introduces an explicit functional involving only currents in the spatial domain, enhancing understanding and application of characteristic modes theory.

Findings

Derived an explicit functional for characteristic modes

Analyzed modal behavior of canonical structures

Demonstrated applications in resonance and benchmarking

Abstract

Aspects of the theory of characteristic modes, based on their variational formulation, are presented and an explicit form of a related functional, involving only currents in a spatial domain, is derived. The new formulation leads to deeper insight into the modal behavior of radiating structures as demonstrated by a detailed analysis of three canonical structures: a dipole, an array of two dipoles and a loop, cylinder and a sphere. It is demonstrated that knowledge of the analytical functional can be utilized to solve important problems related to the theory of characteristic modes decomposition such as the resonance of inductive modes or the benchmarking of method of moments code.