S.А. Kapustin – Post-graduate Student,

Nizhny Novgorod State Technical University n.a. R.E. Alekseev

E-mail: kapustin_1994@mail.ru

N.А. Novoselova – Ph.D. (Eng.), Associate Professor,

Nizhny Novgorod State Technical University n.a. R.E. Alekseev

E-mail: physics@nntu.ru

A.A. Titarenko – Dr.Sc. (Eng.), Professor,

Nizhny Novgorod State Technical University n.a. R.E. Alekseev

E-mail: physics@nntu.ru

The article proposes modeling of complex resonance. A feature of complex resonance is its existence in the entire frequency band of the pair existence of complex waves. Since the power fluxes of the indicated complex waves are closed through the source, and their fields are localized near the latter, the complex resonance can be considered as an oscillation attached to the source.

The existence of intrinsic complex waves in the guiding structures is explained by a distributed power turn, then in the article, as one of the models of the phenomenon under consideration, a system of circuits closed through the source is proposed along which local energy transfer occurs in the guiding structure. In the source area, local power flows are summed. As a result, this region becomes equivalent to the resonator, and behaves in the range of pairwise excitation of conjugated complex waves as a band-pass filter. The study of the phenomenon of complex resonance is carried out on the basis of solving diffraction and excitation problems for a segment of an inhomogeneous guide structure loaded on both sides by uniformly filled waveguides that are matched at the ends. The solution of the excitation problem shows that independent, in principle, complex waves are excited in pairs by ordinary sources. Only with an appropriate choice of a source, for example, having the character of a longitudinal dependence of a current like a traveling wave, is it possible to separately excite the forward and backward complex waves or to predominantly excite one of them. Characterizing the phenomenon under consideration as a whole, we can say that complex resonance is detected in any range of existence of complex waves under the condition of their pairwise excitation in a segment of an inhomogeneous guiding structure, matched at the ends. Moreover, naturally, the mathematically indicated structure is described by a non-self-adjoint boundary-value problem. Since the condition of pairwise excitation of complex waves is provided by the source, it can be argued that complex resonance is realized in the presence of the latter. In a real situation, the matching condition is fulfilled approximately and has a frequency dependence, as a result of which the characteristics of the complex resonance are slightly different from ideal. With good agreement and with the exclusion of the frequency dependence of the exciting device, a complex resonance structure has a frequency response close to rectangular, which makes it very promising for use in the construction of bandpass filters.

Mathematically, the existence of complex resonance over the entire range of existence of complex waves is explained by the degeneracy (in this range) of the matrix of the characteristic equation of the vibrational system generated by the adjunction of the boundary value problem describing complex resonance. Since the emergence of Raman scattering requires pairwise excitation of complex waves, this resonance cannot exist without a source, that is, it is «attached» to the latter.

Experimental studies of complex resonance have led to the creation of microwave bandpass filters of a simple design with a theoretically calculated passband.

1. Veselov G.I., Raevskiy S.B. Sloistye metallo-dielektricheskie volnovody. M.: Radio i svyaz'. 1988.
2. Raevskiy A.S., Raevskiy S.B. Kompleksnye volny. M.: Radiotekhnika. 2010.
3. Ivanov A.E., Raevskiy S.B. Kompleksnyy rezonans v strukture na osnove kruglogo dvukhsloynogo ekranirovannogo volnovoda. Radiotekhnika i elektronika. 1991. T. 36. № 8. S. 1463–1468.
4. Raevskiy A.S., Raevskiy S.B. Kolebaniya i volny, prisoedinennye k istochniku. Radiotekhnika i elektronika. 2018. T. 63. № 1. S. 14–20.
5. Raevskiy A.S., Raevskiy S.B., Sedakov A.Yu. Kompleksnyy rezonans kak yavlenie, opisyvaemoe samosoglasovannoy prisoedinennoy kraevoy zadachey. Fizika volnovykh protsessov i radiotekhnicheskie sistemy. 2017. T. 20. № 3. S. 78–81.
6. Veselov G.I., Kalmyk V.A., Raevskiy S.B. Polosovoy fil'tr na dvukhsloynom kruglom ekranirovannom volnovode v rezhime kompleksnogo rezonansa. Izvestiya VUZov SSSR. Radiofizika. 1983. T. 26. № 8. S. 900–903.
7. A.s. №934561 (SSSR). Polosovoy fil'tr. Kalmyk V.A., Raevskiy S.B., Veselov G.I.
8. A.s. №1091262 (SSSR). Polosovoy fil'tr. Kalmyk V.A., Veselov G.I., Raevskiy S.B. [in Russian]