Özet:

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 . References Ващенко В. В. О выборе представления поля для базовой треугольной области в задачах моделирования H-плоскостных волноводных узлов / В. В. Ващенко, В. П. Чумаченко // Радіоелектроніка, інформатика, управління. – 2010. – № 1. – С. 5–9. 2. Chumachenko V. P. A GSM analysis of E-pane waveguide junctions filled with piecewise homogeneous dielectric / V. P. Chumachenko, V. V. Vashchenko // International Journal of Numerical Modelling: Electronic Networks, Devices and Fields. – 2012. – Vol. 25, No. 2. – P. 163–174. 3. Chumachenko V.P. Properties of some matrix operators appearing in the theory of planar aveguide junctions / V. P. Chumachenko // Telecommunications and Radio Engineering. – 2013. – Vol. 72, No. 6. – P. 469–484. 4. Онуфриенко Л. М. К обоснованию одной математической модели плоского соединения трех волноводов. Часть I. E-плоскостная задача / Л. М. Онуфриенко, В. П. Чумаченко, Я. В. Чумаченко // Радіоелектроніка, iнформатика, управління. – 2015. – №3(34). – С. 7–14. 5. Chumachenko V. P. Efficient field representation for polygonal region / V. P. Chumachenko // Electronics Letters. – 2001. – Vol. 37, No. 19. – P. 1164–1165. 6. Шестопалов В. П. Спектральная теория и возбуждение открытых структур / В. П. Шестопалов. – Киев : Наукова думка, 1987. – 288 с. 7. Chumachenko V. P. On linear independence of some function systems appearing in the theory of plane wave fields / V. P. Chumachenko // Telecommunications and Radio Engineering. – 2015. – Vol. 74, No. 4. – P. 281–296.

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