Heaviside Operational Calculus in Electromagnetic Image Theory

Abstract

The operational calculus originally introduced by Heaviside is shown to be directly applicable to forming image principles for various electromagnetic structures. the image expression is reduced to the compact form of a pseudo-differential operator applied to the original source function (for a point source this is the delta function). The final step is an interpretation of this result. For complicated operators an approximation can easily be done at this stage. The Heaviside method replaces previously applied, often heuristic, identification processes by a logical procedure. The method is first applied to symmetric and asymmetric transmission-line problems because they arise from three-dimensional physical problems. Two examples are worked through: the time-harmonic planar problem of two isotropic media and the elctrostatic problem of the sphere. Both examples give results which have been previously derived through more heuristic methods. A table of selected operational formulas is given as an appendix.