RC filter calculator
Cutoff frequency and time constant of a first-order RC filter, with the attenuation and phase at a frequency you choose and the full magnitude response.
- Time constant τ = RC
- 100 µs A step response reaches 63.2 % of its final value at τ.
- Settling time, 5τ
- 500 µs Within 0.7 % of final value (1 − e^−5 = 99.3 %).
- Gain at the frequency of interest
- -16.07 dB
- Output / input at that frequency
- 0.1572
- Phase at that frequency
- -81 °
- Low-pass
- Chosen frequency
How this is calculated
fc = 1 / ( 2π · R · C ) τ = R · C Low-pass: |H| = 1 / sqrt( 1 + (f / fc)² ) phase = −atan( f / fc ) High-pass: |H| = (f / fc) / sqrt( 1 + (f / fc)² ) phase = 90° − atan( f / fc ) Gain (dB) = 20 · lg |H|
- Step response
- The output reaches 1 − e⁻¹ = 63.2 % of a step at t = τ, and 1 − e⁻⁵ = 99.3 % at 5τ.
- Roll-off
- −3.01 dB at fc, then 20 dB per decade (6 dB per octave) beyond it.
- Assumes
- A zero-impedance source and an unloaded output. A load resistance in parallel with the output lowers the gain and moves fc; buffer it or include it in R.
- Texas Instruments SLOA049D, Active Low-Pass Filter Design (Karki)Revision D, February 2023, section 3 (Equation 1) and section 9 (RC stage, Table 9-1)
- OpenStax, University Physics Volume 2 (Ling, Sanny, Moebs), section 10.5 RC Circuits2016
- OpenStax, University Physics Volume 2 (Ling, Sanny, Moebs), section 15.3 RLC Series Circuits with AC2016
Questions
1/(2π × 10 kΩ × 10 nF) = 1.592 kHz. The time constant is 100 µs, and at 10 kHz a low-pass passes 0.157 of the input, which is −16.1 dB.
τ = RC is the time for the capacitor to cover 63.2 % of a step change. After 5τ it is within 0.7 % of the final value, the usual figure for "settled".
No. At fc the output is 0.707 of the input (−3 dB) and the phase is −45° for a low-pass, +45° for a high-pass. A first-order filter only falls 20 dB per decade, so a signal 10 times above fc is still at one tenth amplitude.
Use a second-order filter: an LC filter or an active Sallen-Key stage falls 40 dB per decade. Cascading two RC stages without a buffer loads the first one and softens the corner.