An Analytical Evaluation of The Quality Factor Qz for Dominant Spherical Modes

摘要

This paper describes an analytical evaluation of the quality factor Qz in aseparable system in which the vector potential is known. The proposed methoduses a potential definition of active and reactive power, implicitly avoidinginfinite entire space integration and extraction of radiation energy. As aresult, all the used quantities are finite, and the calculated Qz is alwaysnon-negative function of frequency. The theory is presented on the canonicalexample of the currents flowing on a spherical shell. The Qz for the dominantspherical TM and TE mode and their linear combination are found in closedforms, including both internal and external energies. The proposed analyticalmethod and its results are compared to previously published limits of thequality factor Q.