Notes on the quality factor and bandwidth of radiating systems

This article attempts to clarify the concept of quality factor (Q) in connection with ideal radiating systems. Three different aspects are covered: Q (i) as a relation between the stored energy and radiated power in the modes corresponding to a given radiation field outside a spherical source volume, (ii) as a function of the measurable impedance or admittance and (iii) as a function of the bandwidth of a resonated system. The first approach yields a theoretical lower limit: the larger the sphere, the more inconceivable in practice. The second approach approximates the observable stored energy and incorporates the minimum energy necessary for the transport of energy from the feed point to the region outside the circumscribing sphere. The third method yields the antenna Q on condition that the input impedance corresponds to a single resonance phenomena.