RC Filter Calculator
RC filters are the simplest analog filters, built from just a resistor and a capacitor. The cutoff frequency fc = 1/(2piRC) is where the output drops to 70.7% of the input (-3 dB). Below cutoff a low-pass filter passes signals through; above cutoff it attenuates them at 20 dB per decade.
An RC filter's behavior depends entirely on the relationship between the signal frequency and the cutoff frequency. The transfer function for a low-pass RC filter is:
|H(f)| = 1 / sqrt(1 + (f/fc)^2)
For a high-pass filter (swap R and C), the transfer function is:
|H(f)| = (f/fc) / sqrt(1 + (f/fc)^2)
- At f = fc: gain is -3 dB (70.7% voltage), phase is -45 degrees
- At f = 10 x fc: gain is about -20 dB (10% voltage) for low-pass
- At f = 0.1 x fc: gain is about -20 dB (10% voltage) for high-pass
The same R and C values set the time constant tau = RC, which governs the step response. A low-pass RC filter with a 1 kHz cutoff has a time constant of about 0.16 ms. This dual interpretation (frequency domain vs time domain) makes RC filters useful for both signal filtering and timing applications.
Common uses include smoothing power supplies, filtering ADC inputs, debouncing switches, coupling audio signals, and building anti-aliasing filters. For steeper rolloff, cascade multiple stages or use active filter topologies.