The inverse relationship between quality factor and bandwidth in multiple resonant antennas

Exact and approximate expressions for the quality factor (Q) and bandwidth of a general, tuned antenna were derived and presented in a previous article. An approximate, inverse relationship between Q and matched VSWR bandwidth was presented and was shown to be valid over a wide range of frequencies, encompassing many successive regions of resonances and antiresonances. Numerical results validating the inverse relationship between Q and matched VSWR bandwidth have been presented for a number of antennas including the electric dipole, the magnetic dipole (loop), and several electrically small designs. These antennas exhibit relatively narrow operating bandwidths and a single natural resonance or antiresonance within the defined bandwidth. Here, we seek to examine the limitations on the inverse relationship between Q and matched VSWR bandwidth for antennas that have relatively large operating bandwidths and that exhibit multiple resonances within the defined bandwidth. Specifically, we examine the inverse relationship between Q, defined in terms of the antenna's impedance properties, and the exact matched VSWR bandwidth for VSWRs ranging from 1.25 to 4.0