An analytical evaluation of the quality factor QZ for dominant spherical modes

This study describes an analytical evaluation of the quality factor Q_Z in a separable system in which the vector potential is known. The proposed method uses a potential definition of active and reactive power, implicitly avoiding infinite entire space integration and extraction of radiation energy. As a result, all the used quantities are finite, and the calculated Q_Z is always non-negative function of frequency. The theory is presented on the canonical example of the currents flowing on a spherical shell. The Q_Z for the dominant spherical transverse magnetic and transverse electric modes and their linear combination are found in closed forms, including both internal and external energies. The proposed analytical method and its results are compared with previously published limits of the quality factor Q.