ON THE THEORY OF AN E-PLANE WAVEGUIDE TRANSFORMER WITH THE N-FOLD ROTATIONAL SYMMETRY
Keywords:waveguide discontinuities, domain-product technique, matrix-operator equations.
AbstractThe mathematical justification of an earlier full-wave model for a symmetrical junction of N rectangular waveguides coupled in E-plane is presented in the paper. 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, and with the edge and radiation conductions. The model is based on the symmetry properties of the geometry and on trigonometric-series expansions of the field in the connecting region, which are constructed using the domain-product technique. It is suggested to consider N-infinite systems of linear equations (ISLE) with respect to expansion coefficients, which arise in the course of solving the problem, in the capacity of matrix-operator equations in the sequence space l1. The analysis has shown that an ISLE of the sort can have no more than one solution for almost all values of the frequency parameter. For 3 ≤ N ≤ 6, it has been found that operator of the ISLE can be presented as a sum of an identity operator, a contraction operator and a completely continuous operator. The obtained results allow considering the ISLE as a functional equation with the Fredholm operator. It has been proved that this equation is solvable in l1 by means of the truncation method convergent in the norm.
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Copyright (c) 2014 L. M. Onufriyenko, Ya. V. Chumachenko, V. P. Chumachenko
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