Synthesis of the surface of reflector antenna for a given power pattern

Several problems of synthesis of reflector antennas for a given power pattern are considered. The antenna consists of a cylindrical reflector and radiation source. The problems are solved in the approximation of induced currents. Falling on the reflector, a nonuniform plane wave is supposed to be known in the first problem. The reflector surface is synthesized here. It produces an electromagnetic field with directivity, which is approximate to the given power pattern. The second problem consists in synthesis of the surface of a reflector antenna, where the falling cylindrical wave is formed by a certain excitation source with given directional characteristics. In the third problem, one more degree of freedom is added, i.e. both the shape of the reflector and directivity pattern of the antenna feed (radiation array) are synthesized. The variational statements of the problems are considered. Minimization of the corresponding functionals leads to a solution of the nonlinear integro-differential Euler equations. The methods of solution of the obtained equations are presented. Numerical results of synthesis are considered.