Limits on the radiation Q of electrically small antennas restricted to oblong bounding regions

Expressions giving a lower limit on the radiation Q of electrically small antennas, based on the size of a bounding sphere, are well known in the literature. Many antennas are constrained to fit within elongated regions, and cannot effectively use the volume of the bounding sphere. In this paper, we present lower limits for the Q of vertically polarized antennas required to fit within regions bounded by a prolate spheroid. These limits are computed by determining equivalent circuits for the transverse magnetic prolate spheroidal wave functions outside the bounding spheroid, and then determining the Q for these circuits. As expected the minimum Q computed for these cases is higher than that based on bounding sphere, since the antenna volume is more restricted for a given maximum linear dimension.