Physics of Wave Processes and Radio SystemsPhysics of Wave Processes and Radio Systems1810-31892782-294XPovolzhskiy State University of Telecommunications and Informatics837210.18469/1810-3189.2020.23.4.8-18UnknownIntegral representations in boundary-value problems on calculation of devices of microwave and EHF bandsRaevskySergey B.physics@nntu.ruKapustinSergey A.physics@nntu.ruRaevskyAlexey S.physics@nntu.ruNizhny Novgorod State Technical University named after R.E. Alekseev1112202023481811022021Copyright © 2020, Raevsky S., Kapustin S., Raevsky A.2020<p>In the electrodynamic calculation of microwave (EHF) devices using methods that lead to algorithms in an open form, strict integral relations (representations) are very useful: Lorentz lemma, reciprocity theorem, orthogonality condition for eigenwaves, etc. of the results obtained, their convergence improves, and in some cases the calculation of characteristics that cannot be calculated without the indicated representations. Integral representations are a record of the equations of electrodynamics (in any unified form) and their solutions in one or another generalized form, linking in general the electromagnetic fields in electrodynamic structures described by boundary value problems. Integral views are used to control the results obtained; insome cases, they allow obtaining analytical solutions; lead to self-consistent problems that take into account the reverse effect of the radiation field on the primary sources; allow obtaining a priori information about the spectrum of possible solutions; solve associated problems as specific problems of arousal. Consideration of the phenomenon of complex resonance in this work shows that integral representations make it possible to establish a connection between non-self-adjointness and self-consistency of boundary value problems.</p>complex wavescomplex resonanceself-consistent problemdifferential equationsintegral equationкомплексные волныкомплексный резонанссамосогласованная задачадифференциальные уравненияинтегральные уравнения[Raevsky A.S. Electrodynamics of Guiding and Resonant Structures Described by Non-Self-Adjoint Boundary Value Problems: Dokt. fiz.-mat. sci. diss., Samara, 2004, 450 p. (In Russ.)][Vajnshtejn L.A. Electromagnetic Waves. Moscow: Radio i svjaz’, 1988, 440 p. (In Russ.)][Katsenelenbaum B.Z. High Frequency Electrodynamics. Moscow: Nauka, 1966, 240 p. (In Russ.)][Neganov V.A., Lemzhin M.I. Singular generalized Hallen equation for an electric vibrator. Physics of Wave Processes and Radio Systems, 2001, vol. 4, no. 1, pp. 40–43. (In Russ.)][Najmark M.A. Linear Differential Operators. Moscow: Nauka, 1969, 526 p. (In Russ.)][Mittra R., Li S. Analytical Methods of the Theory of Waveguides. Moscow: Mir, 1974, 327 p. (In Russ.)][Belov Ju.G. Calculation of critical frequencies and phase constant in an elliptical waveguide with a sinusoidal corrugation. Izv. vuzov SSSR Ser. Radioelektronika, 1977, vol. 20, no. 2, pp. 114–118. (In Russ.)][Katsenelenbaum B.Z. Theory of Irregular Waveguides with Slowly Varying Parameters. Moscow: AN SSSR, 1961, 213 p. (In Russ.)][Veselov G.I., Raevsky S.B. Layered Metal-Dielectric Waveguides. Moscow: Radio i svjaz’, 1988, 246 p. (In Russ.)]