Some numerical aspects of characteristic mode decomposition

Abstract

Nearly all practical applications of the theory of characteristic modes (CMs) involve the use of computational tools. Here in Paper 2 of this Series on CMs, we review the general transformations that move CMs from a continuous theoretical framework to a discrete representation compatible with numerical methods. We also review several key topics related to computational CMs, including modal tracking, dynamic range, code validation, electrically large problems, and non-PEC techniques.

Optimal Composition of Modal Currents for Minimal Quality Factor $Q$

“…A great advantage of the formula (30) is that only two modes with small eigenvalues (typically dominant mode and inductive mode with smallest eigenvalue) are needed and, thus, the notoriously known issue with the ill-conditioned weighting part of the matrix pencil in (22), R 0, is not challenged [56].…”

Optimal Currents on Arbitrarily Shaped Surfaces

“…Although straightforward, care should be taken when implementing the above procedure. The issue comes from the notoriously ill-conditioned matrix R [53], which results in only a few modes of ( 24), ( 26) being numerically stable on electrically small structures. Common algorithms, such as the generalized Schur decomposition or the implicitly restarted Arnoldi method as implemented in the Matlab [48], are often unable to generate modes satisfying (15) which ruins the theoretical reasoning below (27).…”

“…J (θ/ϕ) (r ) e jkr0•r dS (53) is the far-field radiation pattern projected in a given spherical direction [1]. Note that the observation directions θ 0 , ϕ 0 , r 0 are assumed constant during the integration (53).…”