Figure 1: In an RC low-pass filter, the resistor is in series and the capacitor shunts to ground. At low frequencies the capacitor has high impedance and Vout ≈ Vin. At high frequencies the capacitor shorts to ground.
Table of Contents
What Is an RC Filter?
An RC filter is the simplest and most widely used passive filter, consisting of just a resistor and capacitor. As a low-pass filter (R in series, C to ground), it passes low frequencies and attenuates high frequencies. As a high-pass filter (C in series, R to ground), it does the opposite. The cutoff frequency is fc = 1/(2πRC).
RC filters appear everywhere: audio tone controls, anti-aliasing before ADCs, DC blocking in amplifier coupling, power supply decoupling, and sensor signal conditioning. The Filter Cutoff Frequency Calculator handles RC alongside RL and LC types for quick comparison.
The Formula
At fc: XC = R, gain = −3 dB, phase = −45° (low-pass) or +45° (high-pass)
Worked Example — Audio Coupling
fc = 1/(2π × 10000 × 100×10−9) = 159.2 Hz
This blocks DC and frequencies below ~160 Hz, passing the audio signal above. The High Pass Filter Calculator provides detailed response curves.
Worked Example — Anti-Aliasing
R = 1/(2π × 10000 × 1×10−9) = 15.92 kΩ (use 15 kΩ standard)
Worked Example — Power Supply Decoupling
fc = 1/(2π × 10 × 100×10−6) = 159.2 Hz
A low fc ensures good filtering of mains ripple. The LC Filter Calculator can achieve even lower fc without the voltage drop of a resistor.
Loading Effects
An RC filter’s response changes if the load impedance is comparable to R. A low-impedance load in parallel with C effectively reduces R, raising fc. Always buffer the output with a high-impedance stage (op-amp follower) for predictable performance. The Active Filter Calculator incorporates buffering inherently.
Step Response
The time constant τ = RC determines how quickly the filter settles. After one τ, the output reaches 63.2% of its final value. After 5τ, it is within 1%. This is important for pulse and digital signals where settling time matters. The Crossover Calculator uses RC filter principles for speaker frequency division.
Capacitor Impedance Calculator: The Capacitor Impedance Calculator shows how capacitive reactance varies with frequency — the principle behind every RC filter.
Frequently Asked Questions
What does first-order vs second-order mean?
Can I use this for audio applications?
What is the phase shift at cutoff?
How do I make a bandpass filter?
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