E.B. Ipatov, D.S. Lukin, E.A. Palkin

This work continues the development in the part of analysis and mathematical modeling characteristics polifokalnyh reflector antennas, with wide opportunities in the formation of complex patterns of radiation. The large number of focal points in this antenna system allows you to quickly change the direction of the main beam without turning the main reflector. They also have the ability to simultaneously send signals in multiple directions. Polifokalnye antenna are resistant to inhomogeneities in the external environment, as well as to various external influences. As an illustration of the problem in this paper we consider antennas with polynomial-profile of a reflector, which are provides the required characteristics of the radiation pattern. The paper presents the definitions for the identification of focusing points with different characteristics. These definitions are based on an analysis of critical points of the integrals, describing the wave field in the far field of antenna. Such analysis is based on the classification of critical points of parametric families of functions in accordance with the theory of singularities of smooth mappings (catastrophe theory). As examples of an algorithm for designing the antenna reflector, which is given by the mirror profile polynomial function of two variables. By changing the parameters of the polynomial, we can formulate analytical relations that guarantee the appearance of focal points with the desired characteristics. Solution to the problem of synthesis in this model, the reflector is reduced to the selection of the parameters of the polynomial satisfying these relations. Check the result of synthesis of the reflector shape was carried out by direct numerical simulation of the radiation pattern of the antenna. Using the above method of analysis for the design of reflector antennas greatly simplifies the algorithms of design. At the same time, the antennas with a complex profile of the reflector have a number of advantages in comparison with the parabolic and other frequently used reflectors. In particular, they allow you to scan a large range of angles in different planes. The classical parabolic antennas have the advantage only for small angles of the scan. The level of cross-polarization radiation for polynomial reflector is quite small, despite the fact that the reflector surface profile almost does not allow to assess in advance the depolarization of radiation. This method can be applied in the design of other aperture antenna systems.