Electronics

RC Filters

First-order RC low-pass and high-pass filter design — cutoff, roll-off, and time constant.

Formulas

Cutoff frequency f_c1 / (2π R C)
Time constant τR · C
Gain at f_c−3 dB (0.707 × input)
Roll-off−20 dB/decade (first order)
Phase shift at f_c±45°

Low-pass

  • R in series, C to ground; output across C.
  • Passes DC to f_c; attenuates above.
  • Use for anti-aliasing before ADC, smoothing PWM to get DC.

High-pass

  • C in series, R to ground; output across R.
  • Blocks DC, passes above f_c.
  • Use for AC coupling, removing DC offsets.

Common f_c values

RCf_c
1 kΩ1 µF159 Hz
10 kΩ100 nF159 Hz
10 kΩ10 nF1.59 kHz
100 kΩ10 nF159 Hz
1 kΩ10 pF15.9 MHz
50 Ω1 nF3.18 MHz

Notes

  • RC filters are lossy in the passband (slight attenuation from the R). For unity passband use LC or active filters.
  • Never rely on a single RC stage to anti-alias a fast ADC — cascade or use active filters with steeper roll-off.
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