An Exact Synthesis Procedure for Minimum Quality Factor Spherical Wire Antennas

A design procedure for minimum-Q spherical wire antennas of arbitrarily small electrical size is derived. Special cases of circularly polarized and self-tuned designs are investigated, where the latter is elliptically polarized and provides the lowest Q for any configuration of radiated spherical waves in the electrically small regime. The designs are tested in simulation to find that the polarizations agree with the theoretical predictions. The basis for these theoretical predictions — spherical wave expansion — also provides Q estimates which are attained in the self-tuned (lowest Q electrically small spherical wire) case over a range of electrical sizes for a large number of wires. For a more practical number of wires, a special case is synthesized with electrical size ka = 0.25 to obtain a quality factor which is 1.03 times the lower bound on spherical wire antenna Q, the lowest Q relative to this lower bound in the literature.