Conversion of Maxwell's Equations into Generalized Telegraphist's Equations*

Abstract

In this paper it is explained how Maxwell's field equations together with the appropriate boundary conditions may be converted into equations analogous to those for coupled transmission lines. This makes it possible to use the well-known techniques of dealing with transmission lines to solve certain field problems in those cases in which either the method of separating the variables fails or the boundary conditions are too complicated for the conventional method. For example, this method may be applied to studying waveguide to horn junctions, bending of waveguides, propagation of waves over an imperfect earth in the vicinity of the source, etc. Other applications are suggested in the course of the paper. On the theoretical side, this conversion of field equations into transmission line equations brings together two heretofore independent theories of wave propagation on wires, namely, Lord Kelvin's theory based on circuit concepts and Kirchhoff's laws and Mie's theory based on field concepts and Maxwell's equations. The “Generalized Telegraphist's Equations” derived in this paper differ from Kelvin's classical Telegraphist's Equations in two respects. Firstly, for a pair of conductors Kelvin obtained one pair of differential equations implying the existence of only one mode of propagation. For the same pair of conductors we obtain an infinite set of equations implying an infinite number of modes, from which Kelvin's equations are obtained by neglecting the