Transmission Line Theory Applied to Wave Guides and Cavity Resonators. I

Abstract

In Part I circuits consisting of hollow metal wave guides of arbitrary cross section are analyzed in terms of scalar and vector potential and stream functions in a form representing a generalization of the treatment of the conventional lines given by R. King. Completely hyperbolic solutions analogous to those given in the usual theory are obtained for the E and H modes; these yield general relations for the stream and potential distributions. Terminal, input, and characteristic impedances are defined for the wave guide or cavity resonator. The propagation constant is discussed, and it is demonstrated that the attenuation (constant) due to the imperfect metal walls of the pipe and the dielectrics in the guide are additive if the materials have low loss. The characteristic impedances for the two types of mode are considered, and general formulae for the practical conditions of operation are included. The analogy between this theory and that of the conventional line is discussed, and it is pointed out that the physical interpretations of results formally identical in the two cases are equivalent for a given mode and a particular cross section of pipe. The analogy breaks down, however, when one attempts to treat different modes and guides of different transverse dimensions at the same time, for example, in the problem of impedance matching. One advantage of the theory is that experimentally meaningful results may be obtained for general terminations which ordinarily cannot be handled analytically.