S.A. Kapustin – Post-graduate Student,

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

A.V. Lvutin – Post-graduate Student,

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

Yu.V. Raevskaya – Ph.D. (Eng.), Associate Professor,  

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

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

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

E-mail: physics@nntu.nnov.ru; Kapustin_1994@mail.ru

The type of complex eigenvalues depends on the features of the characteristic (dispersion) equations. The dispersion equations of dissipative electrodynamic structures are always complex (their solutions are complex quantities) because dissipative structures are described by non-self-adjoint operators, since the first self-adjointness condition is not satisfied for them. For structures without energy dissipation, self-adjointness is determined by the boundary conditions.

The article discusses the features of solutions to the dispersion equations of waves described by non-self-adjoint operators using the example of a circular two-layer shielded waveguide.

The numerical results presented in the article show a high «occupancy» of the spectrum with complex waves, thereby emphasizing the importance of complex eigenwaves in guiding structures described by non-self-adjoint boundary value problems.

The dispersion equation for the waves of nondissipative guiding structures have complex conjugate solutions that correspond to pairs of conjugate complex waves that form an oscillation attached to the source. This vibration forms a complex resonance.

Complex resonance, which has special properties: low Q-factor, which varies little over the frequency range, rectangular transmission characteristic of devices on sections of a circular two-layer shielded waveguide, calculated frequency transmission characteristic, open up significant prospects for using a circular two-layer shielded waveguide in the construction of resonators for paramagnetic resonance spectroscopes. Using a resonator on a segment of a circular two-layer shielded waveguide, it is possible to create a design of a rubidium discriminator that will significantly reduce the effect of microwave resonator parameters on the frequency of the standard and, at the same time, significantly simplify the structure of the latter by reducing the input signal power of the frequency multiplier. The proposed discriminator can be used in radio measuring technology in quantum frequency standards. In addition to the abovedescribed devices, resonators on sections of a circular two-layer shielded waveguide in the complex resonance mode can be successfully used in bandpass filters also due to the constant quality factor in the frequency range.

Kapustin S.A., Lvutin A.V., Raevskaya Yu.V., Titarenko A.A. Complex solutions of dispersion equations of non-selfadjocated edge electrodynamic boundary problems. Achievements of modern radioelectronics. 2020. V. 74. № 8. P. 48–55. DOI: 10.18127/j20700784-202008-05. [in Russian]

1. Raevskiy A.S., Raevskiy S.B. Kompleksnye volny. M.: Radiotekhnika. 2010. [in Russian]
2. Raevskiy A.S., Raevskiy S.B. Neodnorodnye napravlyayushchie struktury, opisyvaemye nesamosopryazhennymi operatorami. M.:  Radiotekhnika. 2004. [in Russian]
3. Veselov G.I., Raevskiy S.B. Sloistye metallo-dielektricheskie volnovody. M.: Radio i svyaz'. 1988. [in Russian]
4. Shevchenko V.V. Naglyadnaya klassifikatsiya voln, napravlyaemykh regulyarnymi otkrytymi volnovodami. Radiotekhnika i elektronika. 1969. T. 12. №10. S. 1768–1772. [in Russian]
5. Raevskiy A.S., Raevskiy S.B., Titarenko A.A. Osnovnaya osobennost' napravlyayushchikh struktur, opisyvaemykh nesamosopryazhennymi elektrodinamicheskimi operatorami. Pis'ma v zhurnal tekhnicheskoy fiziki. 2004. T. 30. № 1. S. 56–64. [in Russian]
6. Raevskaya Yu.V., Raevskiy S.B. Kraevye zadachi dlya prisoedinennykh voln. Antenny. 2019. №8 (262). S. 48–52. DOI: 10.18127/j03209601-201908-06. [in Russian]
7. Novoselova N.A., Raevskiy A.S., Raevskiy S.B., Shishkov G.I. Zadacha o vozbuzhdenii kompleksnykh voln kak prisoedinennaya.  Antenny. 2019. №1 (255). S. 31–35. DOI: 10.18127/j03209601-201901-04. [in Russian]
8. Kapustin S.A., Raevskiy S.B., Rudoyasova L.G. Svyazannye volny i kompleksnye volny, prisoedinennye k istochniku. Antenny. 2020.  № 1 (263). S. 41–48. DOI: 10.18127/j03209601-202001-06. [in Russian]