RC Filters
First-order RC low-pass and high-pass filter design — cutoff, roll-off, and time constant.
Reference
Formulas
- Cutoff frequency f_c
- 1 / (2π R C)
- Time constant τ
- R · 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
| R | C | f_c |
|---|---|---|
| 1 kΩ | 1 µF | 159 Hz |
| 10 kΩ | 100 nF | 159 Hz |
| 10 kΩ | 10 nF | 1.59 kHz |
| 100 kΩ | 10 nF | 159 Hz |
| 1 kΩ | 10 pF | 15.9 MHz |
| 50 Ω | 1 nF | 3.18 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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