Impedance, Bandwidth, and Q of Antennas

摘要

The primary purpose of this paper is twofold: first, to derive an approximate expression for the bandwidth of a tuned antenna in terms of its input impedance that holds at every frequency, that is, throughout the entire antiresonant as well as resonant frequency ranges of the antenna; and second, to relate this expression for bandwidth to the antenna quality factor Q. The definition of stored energy that we use to define the Q of an antenna is similar to that of previous authors 1-7. However, 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 to cover several resonant and antiresonant frequency bands. It is shown that the matched VSWR bandwidth is the 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 for antennas (whether or not the antenna is lossless) 8, SEC. 8-4. 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 2/Q for all frequencies if Q is greater than or approaches 4.