RC Low-Pass Filter

Formula

Description

A first-order RC low-pass filter passes signals below the cutoff frequency and attenuates signals above it. The cutoff frequency (also called the -3dB point or corner frequency) is where the output amplitude drops to 70.7% of the input (half power). Above this frequency, attenuation increases at 20 dB per decade (6 dB per octave). The filter consists of a series resistor followed by a capacitor to ground. At low frequencies, the capacitor impedance is high and most of the signal passes through. At high frequencies, the capacitor becomes a low impedance path to ground, shunting the signal.

Variables

• fc — Cutoff frequency at -3dB point (Hz)
• R — Resistance (Ω)
• C — Capacitance (F)

Practical Notes

First-order RC filters are used for anti-aliasing before ADCs, power supply decoupling, smoothing PWM signals into analog voltages, and removing high-frequency noise from sensor signals. For steeper rolloff, cascade multiple stages or use active filter topologies (Sallen-Key, multiple feedback). The phase shift at fc is -45 degrees.