Multiple reflection method in problem of constructive synthesis of polarizers and phase shifters based on three non-dissipative inhomogeneities in waveguide

Abstract

The paper presents the results of developing an analytical method for constructive synthesis of waveguide polarizers and phase shifters based on three non-dissipative inhomogeneous elements. The analytical synthesis of such devices was carried out based on solving the problem of electromagnetic wave propagation in a waveguide segment with three non-dissipative inhomogeneities by the method of multiple reflections in the single-wave approximation. The proposed approach allowed us to obtain a clear physical substantiation of the mathematical formulation of conditions for the analytical synthesis of polarizers and phase shifters based on three non-dissipative inhomogeneities in a waveguide. As a result, simple formulas have been obtained that determine the parameters of phase-shifting elements and the electrical distance between them, at which there are no reflections and the desired phase shift is provided. The constructive synthesis of a polarizer is based on the conditions of equality of the required and real admittances of the reactive elements in the waveguide and their derivatives at the central frequency of the operating frequency range. As a result, the optimal geometric dimensions of the device structure were determined. As a result, the optimal geometric dimensions of the device structure are determined. It is shown that a polarizer based on three pins in a square waveguide can provide an operating frequency bandwidth of 10% with electromagnetic energy reflection of less than 1% and a differential phase shift of Δφ = 90° ± 1°, and an operating frequency bandwidth of up to 18% with an admissible reflection of 10% of energy and a differential phase shift of Δφ = 90° ± 2°. The theoretical results are confirmed by high-precision electrodynamic simulation and by experiments on the manufactured prototype of the original controlled X-band polarizer with the maximally flat phase-frequency characteristic based on three symmetrical metal pins inserted into a circular waveguide. The developed analytical method for the constructive synthesis of waveguide polarizers based on three inhomogeneities is intended both for independent use and for obtaining initial values of dimensions of the polarizing device to radically accelerate the search for a global extremum in the process of multiparameter optimization in the high-precision constructive synthesis of such a device at the electrodynamic level, taking into account higher types of waves and the interaction between inhomogeneities on higher types of waves.