TD-UTD Solutions for the Transient Radiation and Surface Fields of Pulsed Antennas Placed on PEC Smooth Convex Surfaces

A time-domain formulation of the uniform geometrical theory of diffraction (TD-UTD) is developed for predicting the transient radiation and surface fields of elemental pulsed antennas placed directly on a smooth perfectly conducting, arbitrary convex surface. The TD-UTD solution is obtained by employing an analytic time transform (ATT) for inverting into time the corresponding frequency domain UTD (FD-UTD) solution. An elemental antenna on the convex surface is excited by a step function in time and a TD-UTD solution is obtained first. The TD-UTD response to a more general pulsed excitation of the elemental current is then found via an efficient convolution of the TD-UTD solution for the step function excitation with the time derivative of the general pulsed excitation. In particular, this convolution integral is essentially evaluated in closed form after representing the time derivative of the general pulsed excitation by a small sum of simple signals whose frequency domain description is a sum of complex exponential functions. Some numerical examples are presented to illustrate the utility of these TD-UTD solutions for pulsed antennas on a convex body.