THE NEW SOLUTION OF THE CANONICAL PROBLEM SCATTERING OF WAVEGUIDE MODES ON A CIRCULAR CONDUCTING CYLINDER

Abstract

By the method of product fields, generalized to matrix scattering operators, a strict solution to the problem of diffraction modes on inductive and capacitive pins in a rectangular waveguide is obtained. The square interaction region of the mod, which contains the conducting cylinder, is considered as a common part of several auxiliary regions that allow the separation of variables in the wave equation. In this area of communication, the complex amplitude of the field is represented as a superposition of cylindrical waves generated by the pin and wave modes that extend from the plane boundary surfaces. The application of matrix operator technology results in a mathematical model in the form of an operator transform (such as the "rules for drawing up tangents") for a generalized scattering matrix. The correctness of the resulting matrix model and the unconditional convergence of projective approximations to an exact solution are proved analytically. The results of numerical research of the coefficient of reflection of the main waveguide mode for capacitive pin in the wide range of frequency variation and geometry of the. communication domain are presented.