Quality Factor

The quality factor Q compares the resonant frequency of a system to the width of the frequency range over which it responds strongly. A high Q means the resonance is concentrated into a very narrow band, which usually happens when energy losses are small, while a low Q means the response is spread out because damping is stronger. In practice, Δf is often taken as the full width at half maximum of the resonance peak, so the ratio tells you how selective the circuit is around f_0.

Use this formula for resonant circuits, filters, antennas, and mechanical or acoustic resonators when you need to quantify how sharply they peak. It is especially useful when comparing tuning selectivity or estimating how much a circuit rejects nearby frequencies.

• Using the resonant frequency and bandwidth in different units, such as kHz and Hz, without converting first
• Confusing bandwidth with total passband edges instead of the half-power width Δf
• Assuming a larger Q means more power output rather than a narrower resonance