Define the Q factor and its relation to bandwidth.

• A. Q = BW / f0
• B. High Q means broad bandwidth
• C. Q ≈ f0 / BW
• D. Damping increases Q

Answer: (C)

The Q factor tells you how sharply a system resonates. It is defined as the ratio of the resonant frequency to the bandwidth over which the system responds significantly. In practical terms, bandwidth is the width of the frequency range around the resonant frequency where the response remains appreciable (often defined by the half-power points). The relationship is Q ≈ f0 / BW, so the bandwidth is roughly BW ≈ f0 / Q.

This means a high Q gives a narrow bandwidth (the resonance is very selective), while a low Q gives a broad bandwidth (the resonance is less selective). In damping terms, more damping lowers Q and widens the bandwidth; less damping raises Q and narrows the bandwidth.

That’s why the correct statement expresses Q as the ratio f0 to BW. The other ideas mix up the relationship or the effect of damping: increasing damping does not raise Q, and a high Q corresponds to a narrower, not broader, bandwidth.