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RC Low-Pass: −3 dB Cutoff Frequency

A hidden low-pass RC. Sweep frequency, find where |H| = 1/√2, and report that cutoff f_c.

School· 22 min·Related simulator: Electricity & MagnetismRC Filter (LP / HP)

Goal

Determine f_c as the frequency where |V_out/V_in| = 1/√2 ≈ 0.707 (−3 dB).

Equipment

  • Low-pass RC (unknown R, C)
  • Function generator
  • AC voltmeters (in / out)

Experiment

Theory

For a first-order low-pass, |H| = 1/√(1+(f/f_c)²) with f_c = 1/(2πRC). At f = f_c the gain is 1/√2. The bench hides R, C, τ and f_c. A live voltmeter ratio |H| is the instrument — there is no −3 dB marker.

Procedure

  1. The network is a low-pass RC. R, C and f_c are hidden. You only change the drive frequency f.
  2. Watch the live |H| = |V_out/V_in|. Find the frequency where |H| is about 0.707. The bench does not mark the cutoff.
  3. Record that f. Repeat the hunt at least 6 times (you may start from different f).
  4. Take the mean of the f column and compare with the reference.

Conclusion

The mean cutoff agrees with 1/(2πRC). Main uncertainties: discrete frequency steps and judging |H| = 1/√2 by eye.