Synthesis of a laterally displaced cluster feed for a reflector antenna with application to multiple beams and contoured patterns

When a feed is displaced from the focus of a reflector, phase distortion results in the effective aperture distribution, which in turn gives rise to secondary beam distortion. In multiple beam or contour beam antennas, the feed normally consists of an array of identical elements located on a triangular lattice. Taking advantage of this arrangement, a "cluster" of feed elements instead of a single element may be used to control each beam. By adjusting the relative excitations of the elements in a cluster, the aperture phase distortion due to the feed displacement may be partially compensated. Two general methods for synthesizing the excitations for a laterally displaced feed cluster are presented. In the first method the excitations are chosen to minimize the weighted phase error in the effective aperture by analytical means. The second method determines the excitations by a gradient optimization algorithm which minimizes the weighted error between an objective and the actual power patterns in the secondary pattern space. The first method is roughly two orders of magnitude more efficient computationally than the gradient optimization algorithm, but not as flexible in application or as precise. Numerical results are presented for cluster feed designs and their application to the synthesis of contour patterns.