A new method of designing circularly symmetric shaped dual reflector antennas using distorted conics is presented. The surface of the shaped subreflector is expressed using a new set of equations employing differential geometry. The proposed equations require only a small number of parameters to accurately describe practical shaped subreflector surfaces. A geometrical optics (GO) based method is used to synthesize the shaped main reflector surface corresponding to the shaped subreflector. Using the proposed method, a shaped Cassegrain dual reflector system is designed. The field scattered from the subreflector is calculated using uniform geometrical theory of diffraction (UTD). Finally, a numerical example is provided showing how a shaped subreflector produces more uniform illumination over the main reflector aperture compared to an unshaped subreflector. 1. Introduction Reflector antennas are widely used in radars, radio astronomy, satellite communication and tracking, remote sensing, deep space communication, microwave and millimetre wave communications, and so forth [1–3]. The rapid developments in these fields have created demands for development of sophisticated reflector antenna configurations. There is also a corresponding demand for analytical, numerical, and experimental methods of design and analysis techniques of such antennas. The configuration of the reflectors depends heavily on the application. The dual reflector antennas are preferred in many applications because they allow convenient positioning of the feed antenna near the vertex of the main reflector and positioning of other bulky types of equipment behind the main reflector [3]. Also, the feed waveguide length is reduced [4]. They also have some significant electromagnetic advantage over single reflector systems [5]. Although many dual reflector configurations exist, the circularly symmetric dual reflector antennas remain one of the most popular choices for numerous applications [1]. One of the most common circularly symmetric dual reflector antennas is the Cassegrain antenna. The Cassegrain antenna is composed of a hyperboloidal subreflector and a paraboloidal main reflector. A feed antenna (usually a horn antenna) illuminates the subreflector which in turn illuminates the main reflector. The main reflector produces the radiated electric field that propagates into space. The radiation performance of the dual reflector antennas depends on the radiation characteristics of the feed and the geometrical shapes of the main reflector and the subreflector. Modern wireless communication and
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