Calculation of electromagnetic fields and cutoff frequencies in waveguides with compound sections

Abstract

Electromagnetic fields and cutoff frequencies of various types in waveguides with compound sections are calculated by a method which takes into account singularities on the edge. The convergence of this method and the characteristics of numerical simulation on a computer are analyzed. The accuracy of the results and the collocability of fields along the boundaries between contiguous partial regions are evaluated. The characteristics of certain waveguides with compound sections are also examined. Waveguides with L, ~, H, T, O, rectangular-frame, and cruciform cross section (Fig. i) find various applications in microwave devices. The complexity of experimentally finalizing the design of devices with such waveguides makes it necessary to develop efficient methods of rather accurate calculation of electromagnetic fields and cutoff frequencies. The method of partial regions has found wide applications in the analysis of such structures. Usually, in the implementation of this method, the singularity in the field behavior near a sharp edge is omitted, which causes the slow convergence of this method. This deficiency can be overcome by approximating the field at the collocation boundary with a complete and orthogohal system of functions, each of which takes the singularity into account. We will consider only the L region (Fig. 2. By stipulating certain boundary conditions on the contour of this region, we can obtain the corresponding wave mode in a given waveguide [i]. For describing specific wave modes in these types of waveguides we will introduce indices n i (i = i, 2, 3, 4) denoting the boundary conditions at the contour of this region. Then n i = 0 when the boundary condition of an electric wall is stipulated on the i-th segment of the contour, and--n i = 1 when the boundary condition here is one of a magnetic wall. Our problem is to find the solution for the L region to the Helmholtz equation