On the Functional Relation Between Quality Factor and Fractional Bandwidth

The functional relation between the fractional bandwidth and the quality factor of a radiating system is investigated in this communication. Several widely used definitions of the quality factor are compared with two examples of RLC circuits that serve as a simplified model of a single-resonant antenna tuned to its resonance. It is demonstrated that for a first-order system, only the quality factor based on differentiation of the input impedance has unique proportionality to the fractional bandwidth, whereas, e.g., the classical definition of the quality factor, i.e., the ratio of the stored energy to the lost energy per one cycle, is not uniquely proportional to the fractional bandwidth. In addition, it is shown that for higher order systems, the quality factor based on differentiation of the input impedance ceases to be uniquely related to the fractional bandwidth.