Two approaches to solving the antenna synthesis problems according to the amplitude radiation pattern




nonlinear synthesis problem, linear antenna, amplitude radiation pattern, numerical simulation


A nonlinear synthesis problem according to given amplitude radiation pattern for plane aperture is considered in two ways. An analytical formula for the optimal current is obtained in the first approach. This current generates the amplitude radiation pattern which is close to the given one with the prescribed accuracy. The second approach consists of variational statement of synthesis problem. The numerical results illustrate that each method has advantages in the certain range of frequencies.


B. Minkovich, V. Yakovlev. Theory of Antenna Synthesis [in Russian]. Moscow: Sov. Radio, 1969.

A. G. Ramm, “Optimal solution of the problem of linear antenna synthesis,” Soviet Physics – Doklady, vol. 13, no 6, pp. 546-548, 1968.

A. G. Ramm, “On antenna synthesis theory,” in Antennas [in Russian]. Moscow: Svjaz, no. 5, pp. 35-46, 1969.

J. K. Butler, “Linear array synthesis for the best mean-square approximation of radiation patterns,” Radio Science, vol. 3, no. 5, pp. 447-450, 1968. DOI:

A. G. Ramm, “Signal estimation from incomplete data,” J. Math. Anal. Appl., vol. 125, pp. 267-271, 1987. DOI:

A. G. Ramm, A. I. Katsevich, The Radon Transform and Local Tomography. Boca Raton: CRC Press, 1996.

[[7] L. D. Bakhrakh, L. D. Kremenetskyi, Symthesis of Radiation Systems. Theory and Methods of Calculation [in Russian]. Moscow: Sov. Radio, 1974.

E. G. Zelkin, V. G. Sokolov, Methods of Antenna Synthesis. Phased Antenna Arrays and Antennas with Plane Apertures [in Russian]. Moscow: Sov. Radio, 1978.

M. I. Andriychuk, N. N. Voitovich, P. A. Savenko, V. P. Tkachuk, Antenna Synthesis by Amplitude Radiation Pattern [in Russian]. Kiev: Nauk. Dumka, 1993.

P. O. Savenko, Nonlinear Problems of Radiation System Synthesis [in Ukrainian]. Lviv: IAPMM of NASU, 2002.

P. O. Savenko, Nonlinear Problems of Radiation System Synthesis with Plane Aperture [in Ukrainian]. Lviv: IAPMM of NASU, 2014.

O. O. Bulatsyk, N. N. Voitovich, “Analytic solutions to a class of nonlinear integral equationconnected with modified phase problem,” Information Extraction and Processing, vol. 19, no. 95, pp. 33-39, 2003.

O. O. Bulatsyk, “Investigation of branching of solutions to nonlinear equation of the modyfied phase problem in the case of discrete Fourier transform,” Visnyk Lviv Univer. Ser. Prykl. Mat., Inform., vol. 7, pp. 20-32, 2003.

O. O. Bulatsyk, N. N. Voitovich, “Structure of phase-asymmetric solutions of circular antenna synthesis problem by amplitude radiation pattern with axially independent data,” Proc. of 2016 XXIst Int. Seminar/Workshop on Direct and Inverse Problems of Electromagnetic and Acoustic Wave Theory, DIPED, 26-29 Sept. 2016, Tbilisi, Georgia. IEEE, 2016, pp. 153-156. DOI:

O. O. Bulatsyk, B. Z. Katsenelenbaum, Y. P. Topolyuk, N. N. Voitovich, Phase Optomization Problems – Application in Wave Field Theory. Berlin: Wiley-WCH, 2010.

A. G. Ramm, M. I. Andriychuk, “Antenna synthesis by the modulus of diagram,” J. Advances Appl. Math., vol. 1, no. 1, pp. 1-10, 2016. DOI: