A. N. Dementyev – Ph.D. (Eng.), Associate Professor,

MIREA – Russian Technological University (Moscow)

E-mail: A.Dementev@tmnpo.ru

D. S. Klyuev – Dr.Sc. (Phys.-Math.), Head of Department of Radioelectronic Systems,

Volga State University of Telecommunications and Informatics (Samara)

E-mail: klyuevd@yandex.ru

A. M. Neshcheret – Ph.D. (Phys.-Math.), Head of Laboratory,

JSC “SIC RS” (Samara)

E-mail: nam@siprs.ru

O. V. Osipov – Dr.Sc. (Phys.-Math.), Vice-rector for Science and Innovation,

Volga State University of Telecommunications and Informatics (Samara)

E-mail: nanometa@yandex.ru

R. V. Sakhabudinov – Ph.D. (Eng.), Applicant,

Volga State University of Telecommunications and Informatics (Samara)

E-mail: serg-stapler1@yandex.ru

Currently, a promising approach to the modernization of antennas is the use of artificial composite materials – chiral metamaterials in their construction. Particularly interesting investigations are the studies of multi-element antenna arrays based on such chiral substrates, since the use of such antennas can increase the bandwidth in MIMO systems. In addition, these antennas have better electrical and mass-dimensional characteristics.

However, at the moment there are a number of difficulties associated with electrodynamic analysis and synthesis of such antennas based on chiral substrates. In particular, most of these studies are carried out using electrodynamic modeling systems such as FEKO, CST Studio, HFSS. The use of this approach to the study of antennas based on chiral metamaterials is usually associated with a number of features, the main of which are construction of correct models of the studied antennas and choice of the optimal sampling step. In addition, these software modeling systems are very demanding to computing resources. There are also other approaches to the study of antennas based on chiral metamaterials. In particular, electrodynamic analysis of a microstrip antenna with a rectangular radiator is presented in a number of works. The dependences of the resonant frequency, bandwidth, and input impedance are given. However, in this paper to calculate the characteristics of the antenna it was used Fredholm integral equation of the first kind, which is known to belong to the class of ill-posed mathematical problems in the sense of Hadamard.

This work deals with the electrodynamic analysis of the multielement antenna arrays with the substrate of the chiral metamaterial by the method of singular integral equations. The essence of this method is to obtain a singular integral representation of the electromagnetic field, which, when substituting boundary conditions on the radiating surface into it, passes into a singular integral equation, the numerical solution of which is a correct mathematical problem. In addition, since only part of the unknown function describing the distribution of the current density on the radiator is approximated (the rest part is calculated analytically), this method does not require large computational resources.

1. Buzov A.L., Klyuev D.S., Neshcheret A.M. Vozmozhnosti sovershenstvovaniya antennoj tekhniki putem ispol'zovaniya kiral'nykh metamaterialov. Fizika volnovykh protsessov i radiotekhnicheskie sistemy. 2018. № 3. T. 21. S. 66–72. [in Russian]
2. Neganov V.A., Osipov O.V. Otrazhayushchie, volnovedushchie i izluchayushchie struktury s kiral'nymi elementami. M.: Radio i svyaz'. 2006.
3. Badalov V.V., Belyaev S.O., Kopylov D.A., Neshcheret A.M. Issledovanie kharakteristik antennykh sistem na osnove metamaterialov v tselyakh obespecheniya elektromagnitnoj sovmestimosti sredstv radiosvyazi. Antenny. 2017. № 11. S. 31–38. [in Russian]
4. Bespalov A.N., Buzov A.L., Mishin D.V., Klyuev D.S., Neshcheret A.M. Mikropoloskovye antenny na osnove biizotropnykh i bianizotropnykh kiral'nykh metamaterialov v sistemakh MIMO. Radiotekhnika. 2019. № 3. S. 5–11. DOI 10.18127/j00338486-201903-01 [in Russian]
5. Buzov A.L., Klyuev D.S., Neshcheret A.M., Neganov V.A. Perspektivy ispol'zovaniya metamaterialov v antennakh novogo pokoleniya. Fizika volnovykh protsessov i radiotekhnicheskie sistemy. 2017. T. 20. № 3. S. 15–20. [in Russian]
6. Buzov A.L., Buzova M.A., Klyuev D.S., Mishin D.V., Neshcheret A.M. Raschet vkhodnogo soprotivleniya mikropoloskovoj antenny s podlozhkoj iz kiral'nogo metamateriala. Radiotekhnika i elektronika. 2018. № 11. T. 63. S. 1143–1148. DOI 10.1134/ S0033849418110037
7. Dement'ev A.N., Klyuev D.S., Neganov V.A., Sokolova Yu.V. Singulyarnye i gipersingulyarnye integral'nye uravneniya v teorii zerkal'nykh i poloskovykh antenn. M.: Radiotekhnika. 2015.
8. Neshcheret A.M. Analiz mikropoloskovykh antenn s podlozhkami iz kiral'nykh metamaterialov metodom singulyarnykh integral'nykh uravnenij. Fizika volnovykh protsessov i radiotekhnicheskie sistemy. 2018. № 4. T. 21. S. 6–16. [in Russian]