A Set of Second-Order Differential Equations Accociated with Reflections in Rectangular Wave Guides - Application to Guide Connected to Horn

N A companion paper 1 the disturbance produced by a corner in a rectangular wave guide is examined by transforming the system, conformally, into a straight guide. Although the medium in the straight guide is no longer uniform, an integral equation may be set up and approximate solutions obtained. In that paper the wave guide is assumed to have the same cross-section at + oo as at -- °°. When this is not so, a conformal transformation may still be used to transform the system into a straight guide provided one dimension of the original cross-section is constant. However, now some advantage appears to be gained by replacing the integral equation by a set of differential equations. Since two cases appear, corresponding to E and II corners, there are two sets of equations to be considered. These two sets of equations are studied in the present paper. After their derivation in Sections 1 and 2 several remarks are made in Section 3 concerning their solution, special emphasis being laid on the problem of determining the reflection coefficient. In the remainder of the paper the general theory is applied to a system formed by joining a rectangular wave guide to a horn, (with plane sides) flared in one direction. The reflection coefficients for sectoral horns flared in the planes of the electric and magnetic intensity, respectively, are given approximately by equations (6-1) and (7-1). These approximations assume the angle of flare to be small so that, as it turns out, only the first equations of the respective sets need be considered.