On the exact theory of a prolate spheroidal receiving and scattering antenna

An exact formula for the current distribution I(η) along an unloaded (short-circuited terminals) prolate spheroidal receiving antenna of arbitrary eccentricity is derived when the incident field is a plane wave with the electric vector directed parallel to the major axis of the spheroid. A knowledge of the current I(0) and the input impedance Z0, derived earlier by Chu and Stratton, completely determines the receiving characteristics of the antenna when it is loaded by impedance ZL at η = 0. The current distribution along the antenna is obtained from Ampere's law by integrating the magnetic field at the surface of the spheroid around cross sections perpendicular to the major axis. This integration removes the azimuthal angular dependence providing sufficient simplification in the mathematics, so that the exact current distribution may be obtained from an equation involving a single infinite sum. The plane-wave scattering problem is completely formulated. It is shown that the solution for the scattered fields can be obtained only by solving simultaneous infinite matrix equations. Numerical results are presented that compare spheroidal antenna receiving current distributions to cylindrical antenna current distributions. Also the induced center currents are compared for a number of antenna-shape parameters. These reveal that thin cylindrical antenna theory may be extended past its theoretical limits of validity.