A Time Domain analysis for a hyperbolic reflector antenna based on a mathematic continuation of ellipsoidal surface curvatures

A transient analysis of a hyperbolic reflector antenna is performed based on a mathematic continuation of surface curvatures of an ellipsoidal reflector antenna with the analysis previously performed in [1]. This work makes the time-domain (TD) analysis useful for the design of reflector antennas since both ellipsoidal and hyperbolic reflectors are widely used as sub-reflectors for dual-reflector antenna system. In particular, this work interprets the scattering phenomena in terms of reflected and diffracted fields with respect to the frameworks of geometrical theory of diffractions, and allows one to analyze the reflector based on the local scattering mechanism.