For a low-pass filter, the rise time and the bandwidth are ...

For a low-pass filter, the rise time and the bandwidth are ...

• A. Directly proportional
• B. Inversely proportional
• C. Equal
• D. Unrelated

Answer: (B)

Rise time is about how fast the output can follow a step, and in a low-pass filter the speed is controlled by the filter’s time constant. For a simple one-pole RC low-pass, the rise time from 10% to 90% is t_r ≈ 2.2RC. The cutoff frequency (the bandwidth) is f_c = 1/(2πRC). Substituting RC gives t_r ≈ 2.2/(2π f_c) ≈ 0.35 / f_c. This shows rise time is inversely proportional to the bandwidth: wider bandwidth allows faster response (shorter rise time), while narrower bandwidth slows it down. That’s why the best description is that rise time and bandwidth are inversely related.