Time domain analysis for ellipsoidal reflector antennas illuminated by a cosine-tapered and transient-step feed´s radiation

A time-domain (TD) analysis of ellipsoidal reflector antennas is presented to predict the transient scattered fields when it is illuminated by a cosine-tapered and transient-step feed radiation whose phase center is located at the nearby focus. A transient-step function of the feed´s radiation is considered because it will produce an impulsive response near the second focus of the reflector as interested in the applications of impulse-radiating antennas. This TD solution is in a closed form and remains valid both near and far from the reflector, and can be used via the convolution theorem to efficiently obtain the early time transient fields generated by the same ellipsoidal reflector antenna when it is illuminated by a realistic finite-energy pulse which emanates as a spherical wave from the focus. Numerical results are presented for the transient fields both near and far from the reflector.