Synthesis of cophase ring antennas according to a prescribed amplitude radiation pattern

A unified mathematical formulation is developed for two synthesis problems: (1) the search for the amplitude distribution of cophase currents in a ring array and (2) the search for the cophase field on the surface of a closed continuous planar antenna. A single numerical method is applied to both problems, and results are obtained for the synthesis of a planar circular antenna and a ring array consisting of 62 radiators situated on the periphery.