# Applying the concept of generating polynomials to the antenna synthesis problem by power criterion

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Abstract:

The antenna synthesis problem according to the prescribed power radiation pattern with the equality norm condition is considered. It is solved by the approach based on the concept of generating polynomials. The variational formulation, supplied by the Lagrange method of multipliers, is applied. The Lagrange--Euler equation for obtained functional is a nonlinear integral equation of the Hammerstein type. The polynomial approach is described for a
generalized equation of this type, which holds for different types of antennas. The modified Newton method is used for numerical solving of the respective systems of integro-transcendental equation. The approach is applied to the concrete problems related to the linear antenna, equidistant antenna array, and the circular aperture antenna. The numerical results are obtained and analyzed.

References:

- Bulatsyk O. O., Katsenelenbaum B. Z., Topolyuk Yu. P., Voitovich N. N. Phase Optimization Problems. WILEY-VCH, Weinheim (2010).
- Choni Yu. I. On antenna system synthesis according to given amplitude radiation pattern. Izv. Vyzov, Radioelectronika,
**11**, 12, 1325–1327 (1968), (In Russian). - Voitovich N. N. Antenna design for given pattern of amplitude of radiation (Semenov’s method). Radio Eng. and Electron.
**17**, 12, 2000–2005 (1972). - Voitovich N. N., Savenko P. A. Branching of solutions of the antenna synthesis problem based on a speciﬁed amplitude radiation pattern. Radio Eng. and Electron. Phys.
**20**, 1, 1–8 (1975). - Savenko P. A. Synthesis of linear antenna arrays with the prescribed amplitude pattern. Radiophys. and Quant. Electr.
**22**, 12, 1045–1049 (1979). - Andriychuk M. I., Voitovich N. N., Savenko P. A., Tkachuk V. P. Synthesis of Antennas according to Amplitude Directivity Pattern. Naukova Dumka, Kiev (1993), (In Russian).
- Savenko P. O. On structure of solution to problem of synthesis of linear antenna from a given radiation pattern. Radiophysics and Radioastronomy.
**5**,**4**, 405–415 (2000), (In Russian). - Savenko P. O. Nonlinear Problems of Radiating Systems. IAPMM NASU, Lviv (2002), (In Ukrainian).
- Savenko P. O. Nonlinear Synthesis Problems of Radiating Systems with Flat Aperture. IAPMM NASU, Lviv (2014), (In Ukrainian).
- Andriychuk M. I., Voitovich N. N. Antenna synthesis according to power radiation pattern with condition of norm equality. Direct and Inverse Problems of Electromagnetic and Acoustic Wave Theory (DIPED-2013). Proc. of Int. Seminar/Workshop. Lviv, 137–140 (2013).
- Voitovich N. N., Topolyuk Yu. P., Reshnyak O. O. Approximation of compactly supported functions with free phase by functions with bounded spectrum. Fields Institute Communications.
**25**, 531–541 (2000). - Voitovich N. N. Antenna synthesis by amplitude radiation pattern and modiﬁed phase problem. Appendix in: B. Z. Katsenelenbaum, Electromagnetic Fields – Restrictions and Approximation. WILEY-VCH, Weinheim, 195–233 (2003).
- Bulatsyk O. O. Complex polynomials representation of solutions to the antenna synthesis problem by the power pattern. Direct and Inverse Problems of Electromagnetic and Acoustic Wave Theory (DIPED-2013). Proc. of Int. Seminar/Workshop. Lviv, 166–170 (2013).
- Andriychuk M., Bulatsyk O., Voitovich N. Polynomial approach to linear antenna array synthesis problem according to power radiation pattern with restriction to its norm. Mathematical Methods in Electromagnetic Theory (MMET-2014). Proc. of 15th International Conference. Dnipropetrovsk, 36–38 (2014).
- Andriychuk M. I., Bulatsyk O. O., Voitovich N. N. Comparing different approaches to linear antenna synthesis problems according to power radiation pattern. Direct and Inverse Problems of Electromagnetic and Acoustic Wave Theory (DIPED-2014). Proc. of Int. Seminar/Workshop. Tbilisi, 15–18 (2014).
- Andriychuk M., Voytovych M. Modiﬁed Newton method for antenna power synthesis problem with ﬁxed norm of the pattern. Journal of Computational and Applied Mathematics.
**2**(116), 3–10 (2014). - Bulatsyk O. Extension of a class nonlinear Hammerstain integral equation with solutions represented by complex polynomials. Journal of Computational and Applied Mathematics.
**2**(116), 167–176 (2014).

Bibliography:

Math. Model. Comput. Vol.1, No.2, pp.121-134 (2014)