Selectivity and bandwidth — does a lower quality factor (Q) produce a narrower bandwidth in a resonant circuit?

Introduction / Context:Quality factor Q and bandwidth are inversely related in linear resonant circuits. Designers rely on this relation to meet selectivity specifications in filters and tuned amplifiers.

Given Data / Assumptions:

• Single, lightly loaded resonant network with center frequency f0.
• Half-power bandwidth definition applies: BW = f2 − f1 where response is 3 dB down from the peak.

Concept / Approach:

The standard relation is Q = f0 / BW. Therefore BW = f0 / Q. As Q decreases, BW increases; as Q increases, BW decreases. Hence a lower Q gives a wider bandwidth, not a narrower one.

Step-by-Step Solution:

Verification / Alternative check:

Simulation or lab measurements of an RLC circuit show that increasing series resistance reduces Q and broadens the resonance curve, confirming the inverse relationship between Q and BW.

Why Other Options Are Wrong:

• The inverse relation holds for both series and parallel resonant forms under linear conditions.
• Zero resistance is unrealistic; however, practical resistance simply sets Q and hence BW by the same formula.
• Frequency range does not change the mathematical relationship.

Common Pitfalls:

Confusing sharpness of the peak (selectivity) with gain. Lower Q flattens and widens the resonance, even if peak amplitude also changes due to loading.

Final Answer:

False