General metallic-dielectric structures: A characteristic mode analysis using volume-surface formulations

In this article, the characteristic mode analysis (CMA) of general metallic-dielectric structures is performed using the volume-surface integral equation (VSIE). The whole-structure and substructure formulations for the CMA are presented and discussed. It is proven that only the substructure operator is symmetrical and therefore fulfills CMA's theoretic requirements. Such a symmetrical operator ensures that the computed eigencurrents are orthogonal and the eigenvalues are real numbers. Numerical analysis verifies that the substructure formulation yields more accurate results than the whole-structure one. A smartphone chassis on an FR-4 substrate and a split-ring resonator (SRR) on a Teflon substrate are analyzed using the presented method. The influence of the mesh size is discussed and it is shown that the volume mesh density increases at a rate similar to the surface mesh. In short, the volume-surface integral formulation with a substructure treatment is versatile, stable, and reasonably efficient for the CMA of thin metallicdielectric structures with planar or curved shapes.