Propagation characteristics of rectangular corrugated waveguides

Abstract

The propagation characteristics of guided waves in a rectangular waveguide with transverse corrugations on all four walls is investigated both theoretically and experimentally. The theoretical solution obtained is an improvement on an earlier analysis, providing a basis for the assumption that the corrugated side walls of the guide act, very approximately, like a smooth metal-walled guide. It is also shown that the new solution, in contrast to the earlier solution, satisfies the impedance compatibility relation. List of principal symbolsa = inside width of main body region of rectangular waveguide b = inside height of main body region of rectangular waveguide h = slot depth in corrugated waveguide s = slot width in corrugated waveguide t = tooth thickness in corrugated waveguide p = s + t period of corrugations w = a + 2h d =b + 2h k = free space propagation phase constant k x = transverse x-directed phase constant of the propagating hybrid mode k y = transverse ^-directed phase constant of the propagating hybrid mode a x = propagation constant of the evanescent mode in the side-wall slots P y = propagation constant of the standing wave in the broad-wall slots P z = propagation constant of the propagating hybrid mode in the main body region A = field amplitude coefficient of the propagating hybrid modes B = field amplitude coefficient of the standing waves in the broad-wall slots C = field amplitude coefficient of the evanescent modes in the side-wall slots manufacture, as their construction is based on the machining of flat plates only. On the analytical side, corrugated waveguides of rectangular cross-section have received less attention than those of circular cross-section because of the greater difficulty in satisfying the boundary conditions when all four walls are corrugated [3]. The case when only one wall is corrugated, and slow waves propagate, has been well understood [4,5] for some time.The first solution for the four-corrugated-wall case, by Bryant [3] in 1969, effectively treated the case of corrugations on the broad walls alone, and did not strictly consider the sidewall corrugations, as was pointed out by Dybdal et al. [6] in 1970. In consequence, the solution thus obtained failed to satisfy the impedance compatibility relation [7], which must be satisfied by all correct separable modal solutions. Baldwin and Mclnnes [8] followed the method used by Bryant to analyse a rectangular horn with transverse corrugations along the broadwalls only. This is satisfactory where the rectangular horn is to receive linearly polarised waves, with the polarisation orthogonal to the corrugated walls. A horn of such construction had been shown previously by Lawrie and Peters [9] to have an E-plane radiation pattern with very low sidelobes.The purpose of this paper is to present a new analysis for the rectangular waveguide with transverse corrugations on all four walls. This takes account of the side-wall corrugations and the solution obtained satisfies the impedance compatibility relation.

Effective time domain analysis of periodic structures

“…generated by TEmn and TMmn of the smooth-walled waveguide with m-odd, n-even. For the first mode experimental results have been provided by Obaid et al [9]. There is overall agreement between all the results.…”

“…Moreover we have calculated the characteristics of the fourths and higher passbands of the sinusoidally corrugated slow wave structure which previous methods [1] have not permitted. [8] (dimensions in mm) and dispersion characteristics of the "odd-even" modes, a measurements [9], -calculations [8], x present method. …”