Band-pass selectivity: In a series resonant band-pass filter, what happens to the bandwidth if the quality factor Q is reduced (lower Q)?

Introduction / Context:
The quality factor Q of a resonant circuit quantifies selectivity. For a band-pass filter, Q links the center (resonant) frequency and the bandwidth. Designers adjust Q to control how narrow or broad the passband is.

Given Data / Assumptions:

• Series resonant band-pass network.
• Q is decreased (lower Q).
• Standard definitions: Q = f0 / BW.

Concept / Approach:
The relationship BW = f0 / Q shows that, for a fixed resonant frequency f0, bandwidth is inversely proportional to Q. Therefore, lowering Q increases BW, which means the filter becomes less selective (broader passband).

Step-by-Step Reasoning:
Given Q decreasesBW = f0 / Q ⇒ BW increasesHence, the passband widens and selectivity reduces

Verification / Alternative check:
As Q → large, BW → small (very selective). As Q → small, BW → large (wide). This holds for both series and parallel tuned circuits (with topology-dependent impedance levels but the same proportionality).

Why Other Options Are Wrong:

• A higher resonant frequency: f0 is determined by L and C, not by Q directly.
• A smaller bandwidth: Opposite of the BW = f0 / Q relationship.
• A higher impedance: Not a general consequence of lowering Q in a series RLC; the key effect asked is bandwidth.

Common Pitfalls:
Confusing Q with gain or with impedance level. Q is predominantly a measure of selectivity and energy storage relative to loss in resonant systems.

Final Answer:
a larger bandwidth