Application of the PTD to cross-polarization prediction in a shaped-reflector antenna

In recent years the physical theory of diffraction (PTD) has successfully been used to calculate the depolarizing effects of edges in the surfaces of planar and paraboloidal reflectors. These effects contribute to cross-polarized sidelobes in the radiation patterns of reflector antennas and in the PTD are calculated from an edge correction to the physical optics (PO) approximation to the induced current on the reflector surface. This approach is an attractive alternative to more rigorous moment methods for which the computational requirements rapidly increase as the size of the reflector increases in comparison to wavelength. However, earlier applications of the PTD to hyperboloidal reflectors were less successful, perhaps causing doubts about its effectiveness. In this paper first the accuracy of a PTD formulation is demonstrated in the case of a hyperboloidal reflector where previous PTD results are seen to be less accurate. The PTD formulation is then applied to obtain improved predictions of cross-polarization in a design for a shaped-reflector satellite antenna required to operate in both left- and right-hand circular polarizations. These results are shown to be much larger than for paraboloidal reflectors of similar size, suggesting that accurately evaluating edge effects may be necessary in designing shaped-reflector antennas for satellite applications.