RC low-pass filter terminology — for a single-pole RC low-pass network, is the bandwidth equal to the -3 dB cutoff frequency f_c?

Introduction / Context:
Bandwidth is a fundamental specification in filter design and signal processing. For simple, first-order filters, the definition is straightforward and often used in practical datasheets. This item ensures you understand how bandwidth relates to the -3 dB cutoff frequency in a single-pole RC low-pass network.

Given Data / Assumptions:

• First-order RC low-pass filter (one resistor, one capacitor).
• Cutoff frequency f_c defined at the magnitude response where output power is half the midband (voltage down by 3 dB): |H(f_c)| = 1/sqrt(2).
• “Bandwidth” refers to the range of frequencies for which the filter passes signals with minimal attenuation.

Concept / Approach:
By convention, for a first-order low-pass, the passband is taken from DC (0 Hz) up to the -3 dB point f_c. Since that interval length is simply f_c − 0, the bandwidth equals f_c. This contrasts with band-pass filters, where bandwidth is f_2 − f_1 between the two half-power frequencies.

Step-by-Step Solution:

Verification / Alternative check:
The -3 dB definition implies that below f_c the attenuation is less than or equal to 3 dB; since there is only one cutoff, this region’s width equals f_c. Many textbooks and manufacturer notes explicitly state BW = f_c for first-order low-pass sections.

Why Other Options Are Wrong:

• “Twice f_c” has no basis for a single-pole low-pass.
• “Defined only for high-pass” is incorrect; bandwidth is a universal metric.
• “Requires Q” applies to resonant second-order sections, not a first-order RC.

Common Pitfalls:
Confusing band-pass bandwidth (difference between two cutoffs) with low-pass bandwidth (single cutoff from DC).

Final Answer:
Correct — bandwidth equals f_c for a first-order RC low-pass filter.