Accurate and Efficient Evaluation of Characteristic Modes

Abstract

A new method to improve the accuracy and efficiency of characteristic mode (CM) decomposition for perfectly conducting bodies is presented. The method uses the expansion of the Green dyadic in spherical vector waves. This expansion is utilized in the method of moments (MoM) solution of the electric field integral equation (EFIE) to factorize the real part of the impedance matrix. The factorization is then employed in the computation of CMs, which improves the accuracy as well as the computational speed. An additional benefit is a rapid computation of far fields. The method can easily be integrated into existing MoM solvers. Several structures are investigated illustrating the improved accuracy and performance of the new method.

Upper bounds on absorption and scattering

“…Employing spherical wave decomposition, the symmetric positive definite radiation operator R 0 may be constructed [34] as where the inner dimension of the matrix S depends on the number of spherical harmonics used. The number of necessary spherical harmonics, and thus the rank of R 0 , may be approximated using the electrical size of the current support under consideration.…”

“…Although the bounds in (31), (34), and (37) are easily determined for an arbitrary shaped geometry, their explicit approximations depending only on resistivity ρ r , volume V , and free-space wavenumber k are of great interest [7]. Such approximation is possible in the limit of small electric sizes ka = 2πa/λ 1.…”

“…Such approximation is possible in the limit of small electric sizes ka = 2πa/λ 1. In this case it can be assumed that the summations in (31), (34) and (37) are dominated by the first term. If only this dominant term (n = 1) is kept, an analytical solution exists in all three cases and reads…”

“…τ,l = R (1) τ,l (ka) radial functions [56,34], and υ = (τ, s, m, l) a multi-index with s, l ∈ {1, 2}, m ∈ {0, . .…”

“…2πa) = (ka) −Bounds on absorption(31), scattering(34), and extinction (37) cross sections for spherical regions compared with realized cross sections of solid spheres and spherical shells homogeneously filled with resistivity (24) ρ r /a = 1 Ω and optimized reactance ρ i and shell thickness.…”