RC filter — cutoff frequency
Low-pass filter — the frequency at which the output falls to −3 dB (0.707×).
SI prefixes accepted (4k7 / 1M / 10m / 220). Upper-case M = mega, lower-case m = milli
History
Formula
Time constant: τ = R × C [s]
At the cutoff frequency the output is −3 dB (≈0.707×)
Design notes
An RC filter is the simplest filter there is — one resistor and one capacitor. It turns up everywhere: noise removal, anti-alias filtering ahead of an ADC, supply decoupling and more.
Design notes:
• To raise the cutoff tenfold, divide either R or C by ten
• The fields accept SI prefixes (10k, 100n and so on)
• A low-pass filter passes everything below the cutoff and attenuates above it
The same R and C make a high-pass filter — just swap their positions.
When you need this
For single-pole filters made from one resistor and one capacitor — ADC anti-aliasing, sensor noise removal, reset timing, PWM smoothing. It reports cutoff frequency and time constant together, so you can reason in the frequency domain or the step response as suits the problem.
What cutoff frequency means
The cutoff fc = 1/(2πRC) is where the amplitude falls to −3dB (about 70.7%). It is not a wall; it is where the roll-off begins.
A single pole rolls off at 6dB per octave, or 20dB per decade. Ten times the cutoff frequency only gets you down to a tenth. Strong rejection needs more poles or a much lower cutoff.
Time constant and step response
| Elapsed | Settled to | Remaining error |
|---|---|---|
| 1 τ | 63.2 % | 36.8 % |
| 2 τ | 86.5 % | 13.5 % |
| 3 τ | 95.0 % | 5.0 % |
| 5 τ | 99.3 % | 0.7 % |
| 7 τ | 99.9 % | 0.1 % |
| 9 τ | 99.99 % | 0.01 % |
With a filter in front of an ADC, this table sets the minimum settling time between channels. For 12-bit accuracy (1/4096 ≈ 0.024%) you need at least 8τ after switching. On multiplexed designs this often becomes the limiting factor.
Worked example: ADC anti-aliasing
- Sampling a sensor at 1kHz, so Nyquist is 500Hz.
- To limit aliasing, target a cutoff around 150Hz.
- R = 10kΩ and C = 100nF give fc = 159.15Hz and a time constant of 1000µs.
- At 500Hz the attenuation is only about −10dB (a third) — that is all a single pole achieves.
- For better rejection, go to a higher-order filter, or oversample and decimate digitally, which is often more practical.
Choosing values
- Fix the resistor first. It follows from what the previous stage can drive and the input impedance of the next. In front of an ADC, 1–10kΩ is a comfortable range.
- Watch the capacitor dielectric. High-permittivity ceramics (X5R / X7R) lose capacitance under DC bias — some parts halve at half their rated voltage. That detunes the filter. Where accuracy matters, use C0G / NP0 or a part with substantial voltage headroom.
- Reconcile the filter resistor with the ADC. A larger resistor makes a low cutoff easier but starves the ADC sampling capacitor. If you raise the resistance, raise the capacitance enough that it acts as the charge source the ADC sees.
- Low-pass or high-pass is set by topology. fc is the same formula either way: capacitor to ground gives low-pass, capacitor in series gives high-pass.
Frequently asked questions
What does −3dB mean?
How much attenuation at ten times the cutoff?
Does cascading two RC stages give a sharper cutoff?
How bad is ceramic DC bias derating?
Standards and references
- IEC 60384-1 — Generic specification for fixed capacitors.
- EIA-198 — Temperature characteristic codes (C0G / X5R / X7R).
Last updated: 2026-08-29