Author: W. Elwyn Williams

Publisher:

Published: 2015-08-05

Total Pages: 44

ISBN-13: 9781332200382

Excerpt from Step Discontinuities in Waveguides Problems involving discontinuities in waveguides are of great practical importance and a considerable amount of attention has been devoted to them in recent 3 rears, The two types of discontinuities that have been most extensively treated for a rectangular guide are the bifurcation of the guide by a semi infinite plane and a step discontinuity in the guide cross-section. The problem of the bifurcation may be solved in terms of known functions by applying the well-known Wiener-Hopf technique for solving integral equations. The methods for solving the problem of a step discontinuity which have appeared in the literature are, however, in no way based on the Wiener-Hopf approach. Two distinct methods have been employed; the first consists of expanding the field components on either side of the discontinuity in terms of the appropriate eigenfunctions for the region considered, and then matching the components across the plane of discontinuity. The second method used is the equivalent static approach as described in the Wave Guide Handbook. Since there is obviously a physical relationship between these two problems it is desirable to solve them both by the same method in order that the solution should display clearly the relationship between them, and this is the object of the present work. We therefore consider the application of the Wiener-Hopf technique to solve the problem of a step discontinuity in a parallel plate region (or, equivalently, the coupling of two parallel plate waveguides of different height). The problem is formulated as an acoustic one, but it could have been equally-well stated in electromagnetic terms by considering the case in which the only non-vanishing component of the magnetic field is parallel to the edges of the step. It is assumed that the fundamental mode is incident from the larger region on the step and, initially, that the dimensions of both regions concerned are taken to be such that only the fundamental mode may propagate without attenuation. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.