Analytic transient analysis of radiation from hyperboloid reflector antennas via surface curvature continuation of ellipsoidal surfaces

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. This work makes the time-domain 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 theories of diffraction, and allows one to analyse the reflector based on the local scattering mechanism.