Bandwidth and the lower bound on Q for small wideband antennas

The lower bound on quality factor (Q) is a well known performance limit of electrically small, single TM or TE mode antennas that exhibit a single impedance resonance within their operating bandwidth. Since Q and matched VSWR bandwidth are inversely related, the lower bound on Q implies that there exists a corresponding upper bound on achievable matched VSWR bandwidth. Here, we examine the relationship between Q, the lower bound on Q and matched VSWR bandwidth for a reasonably small antenna that is designed to exhibit multiple resonances within a wide operating bandwidth. We show that the Q of the wideband antenna does not violate the lower bound, even though the matched VSWR bandwidth encompasses a range of frequencies containing multiple resonances and antiresonances