RCfilter

An RC filter, or resistor-capacitor filter, is a basic passive electronic filter consisting of a single resistor and a single capacitor. It is a first-order network with a single reactive pole, providing a gradual change in signal strength with frequency. The behavior is governed by the time constant τ = RC, and the -3 dB cutoff frequency is fc = 1/(2πRC). The phase response also shifts with frequency, approaching -90 degrees above the cutoff for a low-pass configuration and approaching 0 to +90 degrees for a high-pass configuration.

Low-pass RC filter: In this configuration, the resistor is in series with the input and the capacitor is connected from the output node to ground, with the output taken across the capacitor. At low frequencies, the capacitor presents high impedance and the output follows the input; at high frequencies, the capacitor shunts the signal to ground and the output is attenuated. The magnitude response is |H(jω)| = 1/√(1+(ωRC)²) and the phase is -arctan(ωRC).

High-pass RC filter: The capacitor is in series with the input and the resistor is connected from the output node to ground, with the output taken across the resistor. At low frequencies, the capacitor blocks the signal and the output is small; at high frequencies, the output follows the input. The magnitude is |H(jω)| = ωRC/√(1+(ωRC)²) and the phase approaches +90 degrees at very low frequencies, transitioning toward 0 degrees at high frequencies.

Applications and limitations: RC filters are widely used for simple signal conditioning, anti-aliasing, audio shaping, and smoothing in power supplies. They are inexpensive and easy to implement but provide only first-order roll-off, so cascaded RC stages or buffered designs are used for steeper filters. Component tolerances and parasitics can affect performance, especially at higher frequencies.