Characteristic Mode Theory for PEC Bodies

Abstract

This chapter introduces the fundamental characteristic mode (CM) theory for perfectly electrically conducting (PEC) bodies. We will first formulate the electric field integral equation (EFIE) and magnetic field integral equation (MFIE) for PEC bodies from the Maxwell equation. The method of moments (MoM) is then applied to discretize the EFIE and MFIE into matrix equations. With the MoM impedance matrices, generalized eigenvalue equation is then developed by making use of the matrix properties, the Poynting's theorem, and the definitions for characteristic currents in the CM theory. Important CM properties, physical interpretations of many CM quantities, and their applications in antenna engineering are described in details. CM formulations based on the approximate magnetic field integral equation and combined field integral equation are also developed to offer much flexibility in the implementation of the CM theory. All these CM formulations provide similar CM analysis results. Following the CM theory are the algorithms for the solving of generalized eigenvalue equations and modal tracking across a wide frequency band. Numerical examples are finally presented to examine the numerical aspects of the CM theory and provide guidelines on how to implement the CM theory in computer code. Illustrative results are also given to show how to apply the CM theory in the analysis and design of antennas.