Exact circuit analysis of spherical waves

A circuit representation for the impedance of spherical waves radiating from a spherical boundary was derived using a partial fraction expansion by Chu in order to establish gain bandwidth limitations for antennas. These circuits are derived directly from the recurrence relations for spherical Bessel functions. They provide an exact analog of the field solution both inside and outside of a spherical surface for any values of permittivity ( ) and permeability ( ). Since the circuits have the form of high-pass filters, they provide significant physical insight into scattering and radiation problems, suggest suitable asymptotic or approximate forms and allow circuit concepts and theorems to be brought to bear in order to solve specific configurations or to set general performance bounds. As an example of their application, compact computer programs for the radar cross section of conducting and dielectric spheres, the minimum \´s for antennas, the \´s and resonant frequencies of dielectric spheres and the induced current at the specular and shadow points of a conducting sphere are given. Other illustrative results are the short pulse responses of a solid dielectric and a dielectric-coated sphere computed using the circuit surge impedance and multiple reflection terms; and the response of a hypothetical scatterer in which the TE and TM modes are coupled.