Define Q-factor of a resonant circuit and its relation to bandwidth.

• A. Q is the ratio of bandwidth to center frequency; high Q means broad resonance.
• B. Q is the product of center frequency and bandwidth.
• C. Q is the energy stored divided by energy dissipated per cycle.
• D. Q = f0 / BW; high Q implies a narrow, sharp resonance; low Q yields a broader resonance.

Answer: (D)

The Q-factor measures how selective or sharp the resonance of a circuit is. It compares how much energy the circuit can store to how much energy it loses, and in practical terms for a resonant circuit with a peak at f0, it is defined as Q = f0 divided by the bandwidth BW, where BW is the range of frequencies around f0 where the response remains strong (often down to half power). This means a high Q gives a small BW relative to f0, yielding a narrow, tall resonance, while a low Q gives a large BW and a broader resonance. The other descriptions miss this tight relationship: one reverses the ratio and would imply a broad resonance for a high Q; another multiplies f0 and BW, which isn’t how Q is defined; and the energy-based statement is related but not the standard simple form used for bandwidth, since the common practical definition is the ratio f0/BW.