Theory and Computation of Substructure Characteristic Modes

TL;DR

This paper addresses substructure characteristic mode analysis by extending a scattering-matrix framework to arbitrary substructure design regions and backgrounds, enabling solver-agnostic evaluation. It introduces a generalized eigenproblem $S a_n = s_n S_b a_n$ whose eigenvectors define characteristic excitations and whose eigenvalues relate to modal scattering, with $f_n = S_b a_n$ giving the scattered field. The work proves equivalence to the conventional impedance-based substructure CM for lossless problems, demonstrates the approach on PEC and dielectric examples, and extends to infinite ground planes and complex materials. The approach enables analysis with any full-wave solver, scales favorably for large problems via matrix-free iterations and T-matrix hybridization, and has practical implications for antenna design in realistic backgrounds.

Abstract

The problem of substructure characteristic modes is developed using a scattering matrix-based formulation, generalizing subregion characteristic mode decomposition to arbitrary computational tools. It is shown that the modes of the scattering formulation are identical to the modes of the classical formulation based on the background Green's function for lossless systems under conditions where both formulations can be applied. The scattering formulation, however, opens a variety of new subregion scenarios unavailable within previous formulations, including cases with lumped or wave ports or subregions in circuits. Thanks to its scattering nature, the formulation is solver-agnostic with the possibility to utilize an arbitrary full-wave method.

Figures (12)

• Figure 1: Modal significances $|t_n|$ computed for a PEC geometry adapted from Ethier+McNamara2012 using the scattering-based formulation \ref{['eq:Seig']} with $\mathbf{S}_\mathrm{b}$ being unit matrix, i.e., $\mathbf{S}_\mathrm{b} = \mathbf{1}$, (solid lines), and the impedance-based formulation (dots) Harrington+Mautz1971. The dimensions read $\ell = 120\,\mathrm{mm}$, $w = 60\,\mathrm{mm}$, $h = 15\,\mathrm{mm}$, and $d = 30\,\mathrm{mm}$.
• Figure 2: Modal significances $|t_n|$ computed for the substructure $\varOmega_\mathrm{c}$ in the presence of the background scatterer $\varOmega_\mathrm{b}$. Both regions are PEC with dimensions identical to the structure in Fig. \ref{['fig:ethier-full']}. The impedance-based method relies on formulation Ethier+McNamara2012, while the scattering-based formulation relies on \ref{['eq:Seig']}.
• Figure 3: Sketch of the physical interpretation of scattering matrices $\mathbf{S}_\mathrm{b}$ and $\mathbf{S}$.
• Figure 4: Comparison between modal significances $|t_n|$ for the PIFA structure in Fig. \ref{['fig:ethier-full']} (solid) and a ground plane (dashed). No background is considered, i.e., $\mathbf{S}_\mathrm{b} = \mathbf{1}$. The colors are paired according to the similarity in radiation diagrams. When evaluating substructure characteristic modes in Fig. \ref{['fig:ethier-sub']}, the ground plane (dashed lines) is taken as a background. All dimensions are the same as in Fig. \ref{['fig:ethier-full']}.
• Figure 5: Modal significances $|t_n|$ computed for the substructure $\varOmega_\mathrm{c}$ in the presence of the background which contains scatterer $\varOmega_\mathrm{b}$ and a dielectric sphere filled with relative permittivity $\varepsilon_\mathrm{r} = 4$. The diameter of the sphere equals 180 mm and the distance between the sphere and the metallic structure is 30 mm. Other dimensions are identical to Fig. \ref{['fig:ethier-full']}. The impedance-based method relies on \ref{['eq:CMsubMoM']} and \ref{['eq:Zhybrid']}, while the scattering-based formulation relies on \ref{['eq:Seig']}.