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Telecommunications and Radio Engineering
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ISSN Imprimir: 0040-2508
ISSN On-line: 1943-6009

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Telecommunications and Radio Engineering

DOI: 10.1615/TelecomRadEng.v72.i6.10
pages 461-467

GENERALIZED MODE‐MATCHING TECHNIQUE IN THE THEORY OF GUIDED WAVE DIFFRACTION.
PART 2: CONVERGENCE OF PROJECTION APPROXIMATIONS

I. V. Petrusenko
A. Usikov Institute of Radio Physics and Electronics, National Academy of Sciences of Ukraine; University of Customs Affair and Finances, 8, Rogaleva St., Dnepropetrovsk 49000, Ukraine
Yurii Konstantinovich Sirenko
O.Ya. Usikov Institute for Radio Physics and Electronics, National Academy of Sciences of Ukraine, 12, Academician Proskura St., Kharkiv 61085, Ukraine; V.N. Karazin Kharkiv National University, 4 Svobody Sq., Kharkiv 61022, Ukraine; L.N. Gumilyov Eurasian National University, 2, Satpayev St., Astana 010008, Republic of Kazakhstan

RESUMO

A rigorous justification of applicability of the truncation procedure to solution of infinite matrix equation of the mode‐matching technique still remains an open question throughout the years of its intensive use. The generalized mode‐matching technique suggested for solving the problems of mode diffraction by a step‐like discontinuity in a waveguide leads to the Fresnel formulas for matrix operators of wave reflection and transmission, rather than to standard infinite systems of linear algebraic equations. The present paper is aimed at constructing projection approximations for the mentioned operator‐based Fresnel formulas and investigating analytically the qualitative characteristics of their convergence. To that end the theory of operators in the Hilbert space is used. The unconditional strong convergence of the finitedimensional approximations of the operator‐based Fresnel formulas to the true scattering operators is proved analytically. The condition number of the truncated matrix equation is estimated. The obtained results can be used for a rigorous justification of the mode‐matching technique intended for efficient analysis of microwave devices.

Referências

  1. Polskiy, N.I., Projection methods in the applied mathematics.

  2. Gohberg, I.C. and Feldman, I.A., Convolutional equations and projection methods of their solution.

  3. Trenogin, V.A., Functional analysis.

  4. Luchka, A.Y. and Luchka, T.F., Origination and development of direct methods of mathematical physics.

  5. Petrusenko, I.V. and Sirenko, Yu.K., Generalized mode-matching technique in the theory of guided wave diffraction. Part 1: Fresnel formulas for scattering operators.

  6. Weyl, H., The classical groups: Their invariants and representations.

  7. Petrusenko, I.V. and Sirenko, Yu.K., Generalization of the power conservation law for scalar mode-diffraction problems.

  8. Petrusenko, I.V. and Sirenko, Yu.K., The lost "second Lorentz theorem" in the phasor domain.


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