ON JUSTIFICATION OF A MATHEMATICAL MODEL FOR A PLANAR JUNCTION OF THREE WAVEGUIDES. PART I. E-PLANE PROBLEM

L. M. Onufriyenko, V. P. Chumachenko, Ya. V. Chumachenko

Abstract


In the paper, a mathematical model of an E-plane junction of three waveguides has been presented and justified. The coupling cavity of
the waveguide transformer in question has an arbitrary triangular shape. The problem of scattering of waveguide modes is formulated in the
form of a boundary-value problem for the Helmholtz equation with Neumann boundary conditions on the periphery of the unit, radiation
conductions in the waveguides and with the edge condition. The model is based on the specific trigonometric-series expansions of the field in
the triangular connecting region, which are constructed using the domain-product technique. It is suggested to consider the blocks of the matrix of the infinite system of linear equations, which arises in the course of solving the problem, in the capacity of operators in the sequence space of absolutely convergent series l1. It has been demonstrated that each such operator, describing the interaction of sides of the triangle, can be represented as a sum of a completely continuous operator and the contraction operator. It has been shown that in the space of sequences 1 1 1 (3) l1 = l ⊕l ⊕l the investigated system presents a functional equation with the Fredholm operator and that for almost all values of the frequency parameter the resulting equation is uniquely solvable in (3) l1 by means of the truncation method convergent in the norm of this space.

Keywords


waveguide discontinuities, domain-product technique, matrix-operator equations.

References


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DOI: https://doi.org/10.15588/1607-3274-2015-3-1



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