Journal of Radio Electronics. eISSN 1684-1719. 2026. №5

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DOI: https://doi.org/10.30898/1684-1719.2026.5.7

CALCULATION OF AXIALLY SYMMETRIC MIRROR ANTENNA

BY INTEGRAL EQUATION METHOD

FOR BODIES OF REVOLUTION

E.I. Lavretski

Research Institute of Precise Constructions,

127490, Moscow, ul. Dekabristov, vladeniye 51

The paper was received April 3, 2026.

Abstract. For calculation of an axially symmetric Cassegrain antenna we use the electric field integral equation for body of revolution solved by the Galerkin method. For improvement of accuracy of integral equation numerical solution we introduced the new method for evaluation of double integrals with logarithmic singularity arising in matrix elements. Computation time and required memory of the electric field integral equation method for body of revolution are compared with those of integral equation method with RWG basis function and physical optics method with taking into account multiple reflections. It was shown in calculation of an axially symmetric Cassegrain antenna that the method of electric field integral equation for body of revolution provides the high accuracy, requires not much of RAM, computation time for the method approximately equals that of physical optics method with taking into account multiple reflections. With the help of the method of electric field integral equation for body of revolution we computed the Cassegrain antenna with a real horn feed when the electric surface currents on reflector, sub-reflector and the horn have been calculated in solving the integral equation. This calculation permits to take into account shadow effects by the horn feed on antenna characteristics. The calculation results at frequency 1.7 GHz are in coincidence with results of CST Microwave Studio-IE.

Key words: Cassegrain reflector antenna, electrical field integral equation for body of revolution (EFIE-BoR), physical optics method with taking into account multiple reflections.

Corresponding author: Lavretski Evgeny Izidorovich, e.lavretski@mail.ru

References

1. Vasil'ev E.N. Excitation of a smooth perfectly conducting body of revolution // Izv. vuzov SSSR. Ser. Radiofizika. – 1959. – Vol.2. – No.4. – P.588-601. (In Russian)

2. Markov G.T., Vasil'ev E.N. (eds.) Antennas of ballistic missiles, satellites and space stations. – Moscow: Dom tekhniki. – Vol.1. – 1960. – 335 p. (In Russian)

3. Vasil'ev E.N. Excitation of bodies of revolution. – Moscow: Radio i svyaz'. – 1987. – 272 p. (In Russian)

4. Fletcher K. Numerical methods based on the Galerkin method. – Moscow: Mir. – 1988. – 352 p. (In Russian)

5. Davydov A.G., Zakharov E.V., Pimenov Yu.V. Method for the numerical solution of problems of diffraction of electromagnetic waves on unclosed surfaces of revolution. // DAN SSSR. – 1983. – Vol.269. – No.2. – P.329-333. (In Russian)

6. Davydov A.G., Zakharov E.V., Pimenov Yu.V. Method for the numerical solution of problems of diffraction of electromagnetic waves on unclosed surfaces of arbitrary shape. // DAN SSSR. – 1984. – Vol.276. – No.1. – P.96-100. (In Russian)

7. Zakharov E.V., Davydov A.G., Khaleeva I.V. Integral equations with Hadamard kernels in diffraction problems. In: Current issues in applied mathematics. – Moscow: Izd-vo Moskovskogo universiteta. – 1989. – P.118-127. (In Russian)

8. Davydov A.G., Zakharov E.V., Pimenov Yu.V. Hypersingular integral equations in computational electrodynamics. In: Applied mathematics and informatics. – Moscow: MGU im. M.V. Lomonosova. – MAKS Press. – 2001. – No.9. – P.5-22. (In Russian)

9. Davydov A.G., Pimenov Yu.V. Software package EDEM3D for studying the electrodynamic characteristics of perfectly conducting three-dimensional objects. // Elektrodinamika SVCh i KVCh. – 1999. – Vol.7. – No.2. – P.24-26. (In Russian)

10. Davydov A.G., Pimenov Yu.V. Capabilities of the EDEM program for the development of antenna devices. // Antenny. – 2006. – No.12. – P.12-18. (In Russian)

11. Andreasen M. Scattering from bodies of revolution. // IEEE Trans. on Antennas and Propagation. – 1965. – Vol.10. – No.2. – P.303-310. https://doi.org/TAP.1965.1138406

12. Mautz J., Harrington R. H-field, E-field, and combined field solutions for bodies of revolution. // Interim technical report. – RADC-TR-77-109. – 1977. – 45 p.

13. Mautz J., Harrington R. An improved E-field solution for a conducting body of revolution. // Interim technical report. – RADC-TR-80-194. – 1980. – 71 p.

14. Glisson A., Wilton D. Simple and efficient numerical techniques for treating bodies of revolution. // Technical report. – RADC-TR-79-22. – 1979. – 129 p.

15. Gedney S., Mittra R. The use of the FFT for the efficient solution of the problem of electromagnetic scattering by a body of revolution. // IEEE Trans. on Antennas and Propagation. – 1990. – Vol.38. – No.3. – P.313-322. https://doi.org/10.1109/8.52253

16. Resende U., Moreira F., Pereira-Filho O. Efficient evaluation of singular integral equations in moment method analysis of bodies of revolution. // Journal of Microwaves, Optoelectronics and Electromagnetic Applications. – 2007. – Vol.6. – No. 2. – P.373-391.

17. Gustaffson M. Accurate and efficient evaluation of modal Green's functions. // Journal of Electromagnetic Waves. – 2010. – Vol.24. – No.10. – P.1291-1301. https://doi.org/10.1163/156939310791958752

18. Vaessen J., van Beurden M., Tijhuis A. Accurate and efficient computation of the modal Greens function arising in the electric-field integral equation for a body of revolution. // IEEE Trans. on Antennas and Propagation. – 2012. –Vol.60. – No.7. – P.3294-3304. https://doi.org/10.1109/TAP.2012.2196911

19. Epstein Ch., Greengard L., O’Neil M. A high-order wideband direct solver for electromagnetic scattering from bodies of revolution. // Journal of Computational Physics. – 2019. – Vol.387. – No.5. – P.205-229. https://doi.org/10.1016/j.jcp.2019.02.041

20. Garritano J., Kluger Y., Rokhlin V., Serkh K. On the efficient evaluation of the azimuthal Fourier components of the Green’s function for Helmholtz’s equation in cylindrical coordinates. // Journal of Computational Physics. – 2022. – Vol.471. https://doi.org/10.1016/j.jcp.2022.111585

21. Meincke P., Jorgenson E. Efficient BoR method of moments for rotationally symmetric antenna systems with offset illumination. // IEEE Antennas and Propagation Society International Symposium (APSURSI). – 06-11 July 2014. https://doi.org/10.1109/APS.2014.6905059

22. Markov G.T., Petrov B.M., Grudinskaya G.P. Electrodynamics and radio wave propagation. – Moscow: Sov. radio. – 1979. – 376 p. (In Russian)

23. Markov G.T., Chaplin A.F. Excitation of electromagnetic waves. – Moscow: Radio i svyaz'. – 1983. – 296 p. (In Russian)

24. Gibson W. The method of moments in electromagnetics. – Chapman & Hall. – 2008. – 272 p.

25. Korn G. Handbook of mathematics for scientists and engineers. – Moscow: Nauka. – 1977. – 831 p. (In Russian)

26. Rao S., Wilton D., Glisson A. Electromagnetic scattering by surfaces of arbitrary shape. // IEEE Trans. on Antennas and Propagation. – 1982. – Vol.30. No.3. – P.409-418. https://doi.org/10.1109/TAP.1982.1142818

27. Meleshko I., Lasyi P., Dovga Yu. Approximate method for calculating integrals with a logarithmic singularity. // Nauka i tekhnika. – 2012. – No.3. – P.47-50. (In Russian)

28. Lavretskii E.I., Chernyshov V.S. Calculation of a dual-reflector antenna using the physical optics method taking into account multiple reflections. // Journal of Radio Electronics. – 2022. – No.1. https://doi.org/10.30898/1684-1719.2022.1.5 (In Russian)

29. Lavretskii E.I., Chernyshov V.S. Calculation of a dual-reflector antenna taking into account the influence of supports by a rigorous method. // Journal of Radio Electronics. – 2023. – No. 6. https://doi.org/10.30898/1684-1719.2023.6.6 (In Russian)

30. Kurushin A.A. Design of microwave devices in CST Studio Suite. – Moscow: SOLON-Press. – 2023. – 428 p. (In Russian)

For citation:

Lavretski E.I. Calculation of axially symmetric mirror antenna by integral equation method for bodies of revolution // Journal of Radio Electronics. – 2026. – №. 5. https://doi.org/10.30898/1684-1719.2026.5.7 (In Russian)