Use of parabolic sections to shape the main reflector of omnidirectional dual-reflector antennas

This work presents a formulation for shaping the main reflector of an axis-symmetric dual reflector antenna designed to offer an omnidirectional coverage with an arbitrary radiation pattern in the vertical plane. The subreflector surface is generated by a hyperbola while the shaped main reflector is generated by a series of local parabolic sections sequentially concatenated. As case studies, two representative axis-displaced Cassegrainian configurations are synthesized to radiate, under GO principles, a cosecant radiation pattern in the elevation plane. For a rigorous antenna analysis, a hybrid technique based on Mode Matching and Method of Moments is employed.