RC Filter Calculator
Calculate cutoff frequency, time constant, impedance, and gain/phase characteristics for first-order filters.
| Decade | Frequency | Gain (dB) | Phase Shift |
|---|
RC Filters are simple passive networks that attenuate signal components outside a target frequency range.
Formulas:
- Cutoff Frequency (3dB):
fc = 1 / (2 * pi * R * C) - Gain (Vout/Vin):
1 / sqrt(1 + (f / fc)^2)(Low-Pass) - Phase Angle:
- arctan(f / fc)(Low-Pass)
Usage: Input resistance and capacitance to find the cutoff frequency. You can also simulate the filter's gain and phase shift at a specific operating frequency.
When you need it: Anti-aliasing in front of an ADC, smoothing a PWM output into an analog voltage, or knocking down high-frequency noise on a sensor line. The cutoff fc is the −3 dB point, where the signal is attenuated to about 70.7% of its input amplitude.
Worked example: R = 1.6 kΩ, C = 100 nF → fc = 1 / (2π × 1600 × 100e-9) ≈ 995 Hz. A single-pole low-pass rolls off at 20 dB/decade, so a tone at 10 kHz (≈10×fc) is attenuated roughly ten-fold.
Tips & gotchas:
- One RC gives only 20 dB/decade — cascade stages or use an active filter when you need steeper roll-off.
- For PWM→analog, put fc well below the PWM frequency (e.g.
fc ≈ f_pwm / 100) to keep ripple low. - Source and load impedance shift the effective cutoff — keep source resistance ≪ R ≪ load resistance.
- The time constant
τ = R × C(≈ 1/(2π·fc)) also sets settling time: about 5τ to reach 99% of the final value.