Spherical wave (multipole) expansion

The radiation from a time-dependent source distribution in free-space is analyzed using time-domain (TD) spherical wave (multipole) expansion. The multipole moment functions are calculated from the time-dependent source distribution. The series convergence rate in the near and far zone and the bounds on the near-zone reactive field are determined as functions of the source support and of the pulse length. The formulation involves a spherical transmission line representation that can be extended to more general spherical configurations. This formulation also describes the field and energy transmission mechanisms in a physically transparent fashion that will be used in a companion paper to define and explore fundamental concepts such as TD reactive energy and Q and to derive bounds on the antenna properties. Finally, the concepts discussed above are demonstrated numerically for pulsed radiation by a circular current disk. Index Terms - Antenna theory, near field, short-pulse electromagnetics, time-domain analysis.