How RC filter cutoff frequency is calculated
An RC filter's cutoff is the frequency where the output has fallen to 1/√2 of the input (−3 dB) and the phase has shifted 45°. Beyond it a first-order filter rolls off at 20 dB per decade. A series RLC low-pass is second order: it rolls off at 40 dB per decade, and its Q decides whether the response is flat or peaks near resonance.
- RC cutoff:
fc = 1 / (2π·R·C) - Low-pass gain:
|H| = 1 / √(1 + (f/fc)²) - RLC resonance:
f₀ = 1 / (2π·√(L·C)),Q = √(L/C) / R
Worked example: anti-alias filter for an ADC
3.3 kΩ and 10 nF give a cutoff of 4.82 kHz and a 33 µs time constant. At 5 kHz, the Nyquist frequency of a 10 kS/s converter, the signal is only 3.2 dB down. A single RC pole is a weak anti-alias filter: use a higher-order filter or sample faster.
Good to know
- The source impedance adds to R, and a load across the output shifts the cutoff. Buffer the filter if either is significant.
- Capacitor tolerance moves the cutoff as much as resistor tolerance. Use C0G/NP0 parts where the frequency matters.
- A Q of 0.707 (Butterworth) is the flattest second-order response; above that the response peaks and rings on steps.
- Pro picks E12 and E24 parts for a target cutoff and plots the frequency response.