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The theory of characteristic modes (TCM) is presented for arbitrarily shaped 3-D structures including perfect electric conductors (PECs) and homogeneous penetrable objects. It is shown that by properly expressing the weighting operator of the generalized eigenvalue equation in terms of the integral operators related to the radiated fields, TCM can be formulated directly for the surface integral equation formulation of the problem. This avoids symmetrization or other modifications of the equations. The eigenvalues are shown to be related to radiated, reactive, and dissipated power, and the corresponding far-field patterns are orthogonal. The previously introduced TCM formulations for PEC are special cases of this generalized TCM.

Resonances, i.e., extrema of the eigenvalues of characteristic modes for closed perfectly conducting objects are investigated. The characteristic modal solutions based on the electric, magnetic, and combined field integral operators (EFIO, MFIO, and CFIO) are studied and compared with analytical solutions for a sphere. All these formulations are found to capture both external (radiating) and internal (cavity) resonances predicted by the analytical expressions. At the internal resonances, the eigenvalues obtained with the EFIO- and MFIO-based approaches are not correct, and the corresponding modes are nonunique. These solutions also exhibit a strong duality between the electric (TM) and magnetic (TE) type modes. A connection is found between the external and internal resonances and the condition numbers of the matrices. The modal expansion of the CFIO-based solution is correct, even though it also experiences the nonuniqueness of the EFIO- and MFIO-based solutions.

©2018 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. The discretization by the Method of Moments (MoM) of electromagnetic integral equations, namely, the Electric Field Integral Equation (EFIE) for perfect electric conductors (PECs) and the Poggio-Miller-Chan-Harrington-Wu-Tsai (PMCHWT) integral formulation for penetrable objects, is usually carried out with divergence-conforming sets of basis functions. However, in the single-surface analysis of piecewise homogeneous composite objects the implementation of divergence-conforming sets around junction-edges, where several regions intersect, becomes convoluted. Recently, the monopolar-RWG discretization, discontinuous at edges, of the EFIE and the PMCHWT formulation has been proposed. In this paper we show how this facet-based scheme becomes well suited for the single-surface analysis of piecewise homogeneous composite objects without giving special attention to junction-edges.