Application of the method of integral equations based on the Lorentz lemma for calculation of matching transitions between rectangular waveguides with offset axes

Abstract

This work presents a brief description of the method of integral equations. Integral equations are obtained on the basis of the integral form of Lorentz's lemma using a non-standard physical approach. This method allows one to calculate the characteristics of various three-dimensional irregularities of the waveguide path. As an example of such irregularity, the considered transition between straight shielded waveguides with offset axes and with different transverse sizes. The main attention is paid to the description of the developed numerical-analytical algorithm for calculating the transmission characteristics of the matching transition. A procedure for obtaining an approximate record of the field components on the surface of an irregular region is presented, which makes it possible to take into account the curvature of the wave surface of an electromagnetic wave propagating in the guiding structure. In this case, the profile of the longitudinal section of the guiding structure can be described by any analytical functions. The concept of a 4W-fold comparison waveguide is introduced. In addition, this paper presents the results of calculating the frequency dependences of the transmission characteristics of the fundamental wave of waveguide transition at displacements of the axis of the second waveguide relative to the axis of the first waveguide by different values. The indicated transmission characteristics are found for single-mode and multimode modes of operation of the waveguide transition. In order to verify the results obtained, they have been compared with the results obtained using a modern licensed computer-aided design tool CST Microwave Studio. To demonstrate the possibility of solving the problem of “functional” optimization using the developed algorithm, the results of calculating the transmission characteristics of a waveguide transition between rectangular waveguides with cosine functions describing the profile of the longitudinal section of an irregular region have been presented. In order to indirectly substantiate the equivalence of the initial integral equations underlying the constructed algorithm and the problem of diffraction of an electromagnetic wave in a waveguide transition, a test problem of calculating the transmission characteristics of a stepped transition of two rectangular regular waveguides with different sizes has been solved. The calculation results have been compared with the results obtained on the basis of the electrodynamic substantiated method of half-inversion of the operator of the original boundary value problem. In addition to all the above, in order to assess the validity of the proposed method and the numerical-analytical algorithm built on its basis, a study of the convergence of the calculated results against the approximation number has been made.