Determining bandwidth of a resonant filter Is the bandwidth of a resonant (RLC) filter governed by both the quality factor Q and the resonant frequency f0 (for example, BW = f0 / Q)?

Introduction / Context:Bandwidth quantifies the width of the passband (or stopband) around resonance for band-pass or band-stop filters. The quality factor Q reflects how underdamped the resonance is. Their relationship guides component selection for target selectivity.

Given Data / Assumptions:

• Resonant frequency f0 for an RLC circuit.
• Quality factor Q defined as 2 * pi * (energy stored / energy dissipated per cycle) or, equivalently, f0 / BW for many resonant responses.
• Small-signal linear behavior.

Concept / Approach:

For classical second-order band-pass responses, BW = fH − fL and Q = f0 / BW, with f0 commonly near sqrt(fL * fH). This relation holds for both series and parallel RLC configurations when defined with standard half-power (−3 dB) points.

Step-by-Step Solution:

Verification / Alternative check:

Component-level: for a series RLC with R, L, C, Q ≈ (1/R) * sqrt(L/C) and f0 = 1 / (2 * pi * sqrt(L * C)). Substituting shows that BW depends on R through Q and on f0 via L and C, reinforcing the stated dependency.

Why Other Options Are Wrong:

• It is not limited to series or active filters; the relationship is generic for second-order resonances.
• No minimum Q such as 10 is required for the formula to hold; it is definitional.

Common Pitfalls:

Confusing absolute bandwidth with fractional bandwidth (BW / f0). Also, mixing peak voltage bandwidth with power bandwidth; standard practice uses half-power points for BW.

Final Answer:

True