А. V. Bogoslovsky1, D. N. Borisov2, S. N. Razinkov3
1, 3 MESC of Air Forces “N.Е. Zhukоvsky and Yu.А. Gаgаrin Air Force Academy” (Vоrоnеzh, Russia)
2 Vоrоnеzh State University (Vоrоnеzh, Russia)

1 bogosandrej@yandex.ru, 2 borisov@sc.vsu.ru, 3 razinkovsergey@rambler.ru

To automate the movement and control the spatial orientation of mobile objects, it is necessary to develop antenna modules for high-precision positioning based on signals from global navigation satellite systems. It consists in the joint fulfillment of conflicting requirements for ensuring spatial frequency selectivity and miniaturization of receiving structures. Based on the conditions for preserving the mobile properties of carriers when placing consumer navigation equipment on their sides, it is advisable to use arrays of microstrip elements as antenna systems. The methodological basis for the analysis of antenna arrays is electrodynamic models that establish the relationship of structural parameters with signal reception characteristics.

The purpose of the article is construction of an electrodynamic model and study of the directional pattern of a flat microstrip antenna array.

In order to study characteristics of a flat array of microstrip vibrators placed on a substrate made from dielectric material with an infinitely extended thin perfectly conducting screen, using the method of integral equations from boundary conditions for superposition of an irradiating and secondary electric field, an edge problem is set for a system of antenna elements. Application of boundary conditions for superposition of received and scattered fields makes it possible to take into account electromagnetic connections in the array caused by secondary radiation. As a result of setting the effective dielectric constant of the excitation space, which depends on electrophysical properties, thickness of the substrate and dimensions of microstrip vibrators, as well as replacing receiving elements with equivalent electric vibrators in the form of perfectly conducting tubes with regular radii of cross sections and infinitely thin walls, a system of integral Hallen equations for equivalent electric array currents is obtained. Said currents are found in form of a set of discrete values, which is used to restore their distributions with controlled discrepancy of boundary conditions of the boundary problem, by partial inversion of operators of integral equations using the Krylov–Bogolyubov method. The directional pattern of the microstrip antenna array has been calculated from the distribution of equivalent currents; laws of change of directional properties of receiving structure at different number of elements are investigated.

On the basis of electrodynamic analysis of a flat microstrip antenna array, relationships of its directional pattern with design parameters are established. Estimates of improved spatial frequency fineness of receiving signals with increasing number of antenna elements have been obtained. The obtained results form a methodological basis for substantiating the technical appearance of receiving structures used in modules for high-precision positioning of mobile objects based on signals from global navigation satellite systems.

Bogoslovsky А.V., Borisov D.N., Razinkov S.N. Electrodynamic analysis of microstrip antenna arrays of high-precision positioning of mobile objects by signals of global navigation satellite systems. Antennas. 2025. № 5. P. 28–35. DOI: https://doi.org/10.18127/ j03209601-202505-03 (in Russian)

1. Aseev A.L., Vladimirov V.M., Fateev Yu.L. i dr. Issledovanie tochnostnykh kharakteristik antennykh modulej vysokotochnogo pozitsionirovaniya AM415 v uglomernykh izmereniyakh po signalam GLONASS/GPS. Vestnik Sibirskogo gosudarstvennogo aerokosmicheskogo universiteta. 2013. № 6 (52). S. 64–69. (in Russian)
2. Vladimirov V.M., Kondrat'ev A.S., Krylov Yu.V. i dr. Navigatsionnye kharakteristiki shchelevoj poloskovoj antenny vytekayushchej volny. Izvestiya vuzov. Fizika. 2012. № 8. S. 86–90. (in Russian)
3. Upravlenie i navedenie bespilotnykh letatel'nykh apparatov na osnove sovremennykh informatsionnykh tekhnologij. Pod red. M.N. Krasil'shchikova i G.G. Sebryakova. M.: FIZMATLIT. 2003. (in Russian)
4. Gusinskij A.V., Svirid M.S., Kondrashov D.A. i dr. Modelirovanie mikropoloskovoj antenny radiovysotomera dlya letatel'nogo apparata. Doklady Belorusskogo gosudarstvennogo universiteta informatiki i radioelektroniki. 2021. T. 19. № 5. S. 5–12. (in Russian)
5. Gabriel'yan D.D., Zvezdina M.Yu., Kas'yanov A.O. i dr. Antenny, SVCh-ustrojstva i ikh tekhnologii. Pod red. A.A. Kosogora. M.: FIZMATLIT. 2023. (in Russian)
6. Malevich I.Yu., Bobkov Yu.Yu., Kalenkovich E.N. i dr. Aktivnaya antenna dlya priema signalov sputnikovykh sistem GPS/GLONASS/ EGNOS. Doklady Belorusskogo gosudarstvennogo universiteta informatiki i radioelektroniki. 2013. № 6 (76). S. 19–23. (in Russian)
7. Panchenko B.A., Knyazev S.T., Nechaev Yu.B. i dr. Elektrodinamicheskij raschet poloskovykh antenn. M.: Radio i svyaz'. 2002. (in Russian)
8. Ulanovskij A.V., Kizimenko V.V. Modelirovanie mikropoloskovykh antennykh reshetok metodom integral'nykh uravnenij. Doklady Belorusskogo gosudarstvennogo universiteta informatiki i radioelektroniki. 2012. № 7 (69). S. 93–99. (in Russian)
9. Setukha A.V. Metod integral'nykh uravnenij v matematicheskoj fizike. M.: Izdatel'stvo MGU. 2023. (in Russian)
10. Neganov V.A., Pavlovskaya E.A., Yarovoj G.P. Izluchenie i difraktsiya elektromagnitnykh voln. Pod red. V.A. Neganova. M.: Radio i svyaz'. 2004. (in Russian)
11. Ponomarev L.I., Stepanenko V.I. Skaniruyushchie mnogochastotnye sovmeshchennye antennye reshetki. M.: Radiotekhnika. 2009. (in Russian)