Synthesis and analysis of single shaped reflector antennas

Abstract

Introduction. Althou h eometrical optics (GO) is an asymptotic theory describyears constituted the foundation for synthesis of reflector antennas. While dual ing electromagnetic #e& of infinitely high frequencies only, it has for several reflectors are usually shaped to produce a certain aperture distribution leading to a pencil beam type pattern with high gain or low side lobes, etc., single reflectors field. In either of the cases, any design must necessarily be ver!fied by a diffracmay be syntheslsed to generate shaped beams by using the GO directly in the far tion analysis, because of the GO assumption made In the synthesis. In this paper we will demonstrate a numerical method for solving the synthesis problem for single reflector antennas. The technique has been found to be superior to what has reviously been applied, in particular because it returns the solution on a form wlich lends itself easily t o diffraction analysis. This is accomplished by solvin Westcott's synthesis problem usin a collocation method and an expansion of t l e reflector surface in bicubicspline?unctions. The theory will be resumed very briefly, and we wiU then present some results figuration, a reflector shaped to provide full earth coverage from a low orbitting from applying the developed synthesis and analysis programs to a particular consatellite. Formulation of the synthesis. As stated previously, the synthesis part of this study is based upon the work of Westcott (1983). To formulate the problem we of the coordinate system. The half angle subtended by the reflector at the feed is consider the reflector shown in fig. 1, illuminated by a feed located at the centre €Ic. Given the feed power densit pattern I(e,+), we require the reflector t o G(B. a) inside the far-field cone of half angle Of. Westcott showed that by using transform this pattern into a far-fie& pattern with a power density distribution an appropriate parametrization of the reflectoer surface one can derive a highly non-linear boundary value problem, the solution of which overns the reflector surface. He also showed how the non-linear problem couqd be linearized and solved by repeated solution of linear second order partial differential equations (POE'S).