Generalized Theory of Characteristic Modes

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.