New surface expansion for fast PO synthesis of shaped reflector antennas

Shaped reflector antennas are well established as the most attractive choice for satellite communications for the generation of fixed contoured beam due to their high efficiency on complex specified coverage. Several methods have been proposed to solve the problem of synthesising the shape of contoured beam reflector antennas. The most commonly used technique for designing shaped reflectors is a direct optimisation based on the far field evaluated by physical optics (PO). It involves an accurate diffraction analysis of the radiation of a surface defined by a set of numerical coefficients embedded inside an optimisation process, and it is time-consuming. We propose the use of a new surface expansion (B-spline functions) for the reflector which offers many advantages, among them are: faster synthesis (roughly 50 times faster compared to Zernike-based synthesis); the possibility to synthesise reflector shapes with any aperture boundaries (not restricted to elliptical/super-elliptical type); the possibility to incorporate constraints on curvature radius of the shaped surface, which is of a great interest for reflector manufacture; and the ability to connect with CAD software, since the representation is easily transformed into a Bezier surface representation