Evaluation of the quality factor of an electrically small antenna in spheroidal coordinates

A number of researchers have obtained expressions for the quality factor or "Q" of an antenna. Most of these authors treated the antenna as surrounded by a spherical surface. A spherical surface conforms to the geometry of very few antennas. Here we derive the corresponding expressions for the Q of an electrically small antenna surrounded by an spheroidal surface that is either prolate or oblate. In this way we can better treat the effects of aspect ratio. Prolate spheroids should better represent most antennas, which are long and thin. Oblate spheroids should represent antennas in the shape of a disk. We also present analytic expressions for the value of Q for spheroids in the limit of very small electrical length. The expressions become equal to that of the sphere in the appropriate limit. We explore some of the results from analytic expressions for prolate and oblate spheroids when compared to a sphere