A Shaped Reflector Antenna Design Approach for Contoured Beam Synthesis With Surface Curvature Constraints

An efficient B-spline curvature-based reflector shape synthesis technique for generating a continental US (CONUS) beam pattern is presented. The approach is based on representing a reflector as a set of curves that can be modified to alter the reflector's shape. Instead of directly optimizing the curves as done in other commercial software packages, the curvature is evaluated and represented using B-spline polynomials. The control points of each spline curve are defined as optimization variables, which generate new curvature profiles at each iteration. The set of curves with the corresponding curvature is synthesized using the natural equation method and is then used to construct the reflector surface. This two-step process of first optimizing the curvature and then reconstructing a reflector surface greatly facilitates the ability to impose constraints on surface curvature arising from the choice of the manufacturing process. Furthermore, no significant degradation in the convergence behavior was observed when including curvature bounds in the cost function. This makes the approach very attractive when compared to existing methods. In addition, this method can be applied to arbitrary reflector configurations of interest and be paired with any optimization method. The accuracy and validity of the proposed method are verified by multiple application examples.