Impedance, bandwidth, and Q of antennas

The purpose of this paper is twofold: (1) to derive an approximate expression for the bandwidth of a tuned antenna in terms of its input impedance that holds at every frequency, i.e., throughout its entire antiresonant and resonant frequency ranges; (2) to relate this expression for bandwidth to the antenna quality factor Q. The approximate expression for the bandwidth and its relationship to Q are both more generally applicable and more accurate than previous formulas. The validity and accuracy of the expressions are confirmed by the numerical solutions to straight-wire and wire-loop, lossy and lossless tuned antennas over a wide enough range of frequencies covering several resonant and antiresonant frequency bands. We show that the matched VSWR bandwidth is a more fundamental measure of bandwidth than conductance bandwidth because it exists in general for all frequencies at which an antenna is tuned. We also find that the Foster reactance theorem does not hold at all frequencies (whether or not the antenna is lossless). Although the general formula we derive for the bandwidth of an antenna involves the frequency derivative of resistance as well as the frequency derivative of reactance, quite remarkably, the half-power matched VSWR bandwidth of a general tuned lossy or lossless antenna is proven to approximately equal to 2/Q for all frequencies if Q/spl gsim/4.