The Minimum Q for Spheroidally Shaped Objects: Extension to Cylindrically Shaped Objects and Comparison to Practical Antennas

The classic work of Chu and others has been extended to determine the minimum radiation Q for the TM case of electrically small antennas contained within a spheroid (prolate and oblate) with no energy stored inside. The results of numerical calculations have been used to give an analytic formula that can be used to determine the electrically small bound on Q_r as a function of aspect ratio for prolate and oblate spheroids. These formulas have been used to develop a lower bound for antennas contained within a cylinder, and a comparison has been made to several practical antennas as a function of aspect ratio. An antenna suggested by Wheeler is shown to have the best (lowest), Q_r of the antennas examined over a wide range of aspect ratios.