Numerical solution of nonlinear spectral problems in syhthesis theory of antennas with flat aperture

Authors

  • Petro O. Savenko Pidstryhach Institute of Applied Problems of Mechanics and Mathematics of National Academy of Sciences of Ukraine, Ukraine
  • Myroslava D. Tkach Pidstryhach Institute of Applied Problems of Mechanics and Mathematics of National Academy of Sciences of Ukraine, Ukraine

DOI:

https://doi.org/10.1109/ICATT.2017.7972590

Keywords:

nonlinear synthesis theory, spectral problem, connected component, initial solution, branching of solutions

Abstract

Numerical method for solving the nonlinear two-parameter spectral problems arising in nonlinear synthesis theory of antennas with a flat radiating aperture is considered. The numerical algorithms to find the connected components of the spectrum of linear homogeneous two-dimensional integral equations which describe the branching lines of solutions of synthesis problems of the flat apertures and antenna arrays according to the prescribed requirements to amplitude directivity pattern are constructed and justified. For the case of rectangular aperture the analysis of branching of the solutions of basic equations of synthesis with using the proposed method is presented. Results of numerical experiments are given.

References

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M. I. Andriychuk, N. N. Voitovich, P. A. Savenko, and V. P. Tkachuk, Antenna Synthesis According to Amplitude Directivity Pattern: Numerical Methods and Algorithms [in Russian]. Kiev: Naukova Dumka, 1993.

Petro Savenko, Lesya Klakovych, and Myroslava Tkach, Theory of Nonlinear Synthesis of Radiating Systems. LAP LAMBERT Academic Publishing, 2016.

P. O. Savenko, Nonlinear Problems of Radiating Systems Synthesis (Theory and Methods of Solution. Lviv: IAPMM, NASU, 2002.

P. A. Savenko and L. P. Protsakh, “Method of implicit function in solving the nonlinear spectral problem,” Izv. Vysch. Uch. Zaved. Mathematics, no. 11, pp. 41-44, 2007.

E. G. Zelkin and V. G. Sokolov, Synthesis Methods of Antenna Arrays and Antenna with Continuous Aperture [in Russian]. Moscow: Sov. Radio, 1980.

М. М. Vainberg and V. А. Trenogin, Theory of Branching of Solutions to Nonlinear Equations [in Russian]. Moscow: Nauka, 1969.

Published

2017-07-15

Issue

2017: ICATT-2017 - Proc. of XI Int. Conf. on Antenna Theory and Techniques

Section

General antenna theory, propagation, numerical and analytical methods