How does the Q factor relate to bandwidth in a resonant circuit?

• A. Q = BW / f0; higher Q means narrower bandwidth
• B. Q has no relation to bandwidth
• C. Q = f0 / BW; higher Q means narrower bandwidth
• D. Q = f0 / BW; higher Q means wider bandwidth

Answer: (C)

The Q factor measures how selective a resonant circuit is, by relating its center frequency to how wide the resonance is. It is defined as Q = f0 / Δf, where f0 is the resonant (center) frequency and Δf is the bandwidth over which the circuit resonates effectively (often the -3 dB bandwidth). Because Δf is in the denominator, increasing the bandwidth lowers Q, and decreasing the bandwidth raises Q. So a higher Q means a narrower, sharper resonance. That’s why the correct description is Q = f0 / BW, with higher Q corresponding to a smaller bandwidth. For clarity, if f0 is 1 MHz and BW is 10 kHz, Q = 100; increasing Q to 200 would shrink the bandwidth to 5 kHz, making the peak more selective.