# SCATTERING MATRICES OF LONGITUDINALLY COMPLICATED WAVEGUIDE STRUCTURES

## DOI:

https://doi.org/10.20535/2411-2976.22011.%25p## Abstract

An approach to the calculation of longitudinally complicated waveguide structures is developed based on integral equation method. A problem of electromagnetic wave diffraction on the complicated structure consisting of a great number of connected waveguide sections has been solved in rigorous formulation. The expressions for its generalized scattering matrices which order

is limited only by capabilities of computation technology are obtained. A designing technique for calculation of waveguide connections symmetrical with respect to the transverse plane passing through the middle of the structure perpendicularly to its longitudinal axis has been proposed. This technique is based on the solution of two simultaneous systems of linear algebraic equations with complex coefficients. The mathematical model of the symmetrical waveguide structure in the form of two simultaneous systems of linear algebraic equations with real coefficients is derived for estimation of single mode scattering matrix. The effectiveness of the proposed approach is illustrated by example of definition of mathematical models for calculation of scattering matrices of diaphragm of finite thickness and resonant enlargement between two circular waveguides. Proposed and known techniques for calculation of scattering matrices of these structures regarding the cost of computer time are compared. For the correct providing of this comparative analysis, the expressions for obtaining generalized scattering matrix of two circular waveguides junction are derived as a special case of scattering matrix of doubled discontinuity. It is shown that the proposed design technique based on the solution of simultaneous systems of linear algebraic equations which number is equaled to a number of discontinuities in waveguide structure ensures significant cost savings of computer time in comparison with the known approach based on the consecutive combining of generalized scattering matrices of separate junctions.

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