The Relationship Between Bandwidth and Quality Factor for Electrically Small Antennas Exhibiting Closely Spaced Resonances

Electrically small antennas typically exhibit a single resonance within their impedance bandwidth, the extents of which are defined by some choice of VSWR's. With as single resonance antenna, the inverse relationship between bandwidth and quality factor is well defined and holds over a wide range of frequencies. Additionally, both bandwidth and quality factor can be accurately approximated from the frequency derivatives of the antenna's impedance. In cases where the electrically small antenna exhibits multiple and very closely spaced resonances, the relationships between bandwidth and quality factor may not hold and it may not be possible to accurately determine these properties from the frequency derivatives of impedance. Here, we study the impedance, bandwidth and quality factors of an antenna design that exhibits closely spaced resonances and we examine the extent to which the relationships between these properties degrade.