On the inverse relationship between quality factor and bandwidth of small antennas

Relationship between the reflection coefficient bandwidth and quality factor (Q) of a small antenna is revisited using a simple frequency independent model. A tuned small antenna is considered in this case, which is modeled as either a series or a shunt RLC network. When the antenna resistance is matched with the characteristic impedance of the feed-line, both configurations lead to an identical relation, which is also interestingly identical to the well-known inverse bandwidth-Q formula for small antennas. However, this well-known formula is only applicable when the antenna is perfectly matched to its feed line. In this paper, a more general and yet simple form of this expression is derived, which can encompass the effect of mismatch between the antenna and its feed-line. Furthermore, we derive separate relations for the bandwidth-Q product, for both the loaded and unloaded cases. As an illustrative example, a microstrip patch antenna is considered to validate the results.