**6. References**


Fradin, A.Z. (1977). *Antenna-feeder devices*. M.Sviaz. Russia.

Harrington, R.F. (1968). *Field Computating by Moment Methods*. Macmillan, New York.

Markov, G.T. (1960). *Antennas.* M.-L. Gosenergoizdat. Russia.

*Radar Handbook*.(1970). M.I.Skolnik. EDITOR - IN - Chief. Mc Graw-Hill Company, 1970.

Rothammels, K. (1995). *Antennenbuch.* Franckh-Kosmos. Verlags-GmbH&Co., Stuttgart.

Sazonov, D.M and Shkolnikov, A.M. (1974).*The scattering of electromagnetic waves by a loaded antenna array*//Radiotechnology and Electronics. −1974. − № 4. pp.689-686.

**Chapter 0**

**Chapter 9**

**Synthesis of Antenna Systems According to the**

The problems of antenna synthesis, which use the amplitude RP as input information, are often used in the process of antenna design for many practical applications [4, 16, 27, 31]. In spite of the fact that the respective mathematical problems are ill-posed [32] and they have the branching solutions [29], the antenna synthesis according to the desired amplitude

As a rule, the branching of solutions depends on the properties of prescribed amplitude RP, geometrical and physical parameters of the considered antenna. The methods of nonlinear functional analysis [23] allowing to localize the branching solutions are applied for investigation of solutions and determination of their number and qualitative characteristics. Such approach too much simplifies determination of the optimal solutions by the numerical methods. The iterative processes for the numerical solving of the corresponding non-linear

In Section 2 we derive the main formulas for RP of antennas and introduce the objective functionals for the synthesis problem. Also in Section 2 we consider the variational statement

Section 3 contains the application of the proposed approach to several types of antennas. Depending on the restrictions which are imposed on the sought distribution of current or field in the antenna elements and type of antenna, the problems of amplitude-phase, amplitude, and phase synthesis are considered for the specific antennas. The methods of successive approximations are applied for solving the derived non-linear integral equations; the convergence of the elaborated methods is discussed. The direct optimization of the proposed functionals by the gradient methods is performed and successfully applied to

and reproduction in any medium, provided the original work is properly cited.

©2012 Andriychuk, licensee InTech. This is an open access chapter distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly

© 2012 The Author(s). Licensee InTech. This chapter is distributed under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution,

of problems and derive the fundamental nonlinear equations of the synthesis.

**Desired Amplitude Radiation Characteristics**

Mykhaylo Andriychuk

**1. Introduction**

http://dx.doi.org/10.5772/46164

Additional information is available at the end of the chapter

characteristics is very useful and perspective.

equations were elaborated in [3, 8, 11]. The Chapter is organized as follows.

solving the amplitude and phase synthesis problems.

cited.

In Section 4 conclusions are formulated.

Stratton, J.A. (1941). *Electromagnetic Theory*. McGraw-Hill.

Volakis, J.L. (2007). *Antenna Engineering Handbook*. Mc Graw-Hiil Companies.

Kazarin, A.N. , Runov, A.V. and Yurtsev, O.A. (1974). *Helix Antennas*. M. Sovetskoe radio. Russia.
