DOI: https://doi.org/10.15588/1607-3274-2015-4-1

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

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

Abstract

In the paper, a mathematical model of an H-plane three-port waveguide junction with an arbitrary-triangular coupling cavity has been
presented and justified. The problem of scattering of waveguide modes is formulated as a boundary-value problem for the Helmholtz equation
with the homogeneous Dirichlet boundary conditions on the periphery of the unit, radiation conductions in the waveguides and with the edge
condition. The model is based on a trigonometric-series representation of the sought-for field in the triangular connecting region, which is
constructed using the domain-product technique. The conventional expansion is revised to improve convergence properties of the used sine series. Properties of the infinite set of linear algebraic equations, which arises in the course of solving the problem, are studied. After simple modification, the system of equations is turned into an equivalent system, which is of the same kind as the system examined in the first part of the paper in analyzing the similar E-plane structure. In the space 1 1 1 (3) l1 = l ⊕l ⊕l (l1is the sequence space of absolutely convergent series), this fact allows to interpret the set of transformed equations as a single functional equation with the Fredholm operator and to prove that the derived equation has a unique solution, which can be found by means of the truncation method convergent in the norm of (3) l1 .

Keywords

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

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References

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Copyright (c) 2016 L. M. Onufriyenko, V. P. Chumachenko, Ya. V. Chumachenko 