What is an RC filter? Cutoff frequency and an example
A resistor and capacitor form a frequency-dependent voltage divider. The same two components can provide low-pass or high-pass behavior, depending on where the output is measured.
Low-pass and high-pass configurations
In an ideal series RC circuit, taking the output across the capacitor produces a low-pass filter. Low frequencies experience less attenuation; at higher frequencies, the capacitor reactance decreases and the output falls. Taking the output across the resistor produces a high-pass filter. Neither circuit abruptly removes every frequency beyond its cutoff.
Calculating the cutoff frequency
For an ideal unloaded first-order RC filter, fc = 1 / (2πRC). At cutoff, output amplitude is approximately 0.707 times the passband value, or about −3 dB. With R = 10 kΩ and C = 100 nF, RC = 0.001 seconds and fc ≈ 159 Hz. Use ohms and farads in the equation.
What does the time constant mean?
The time constant τ = RC describes how quickly the circuit responds. Following a voltage step, the capacitor voltage of an ideal low-pass circuit reaches approximately 63.2% of its final change after one time constant. Frequency response and step response describe the same R and C in two different ways.
Real circuit effects
Source resistance and the next stage’s input impedance become part of the divider. Component tolerances and operating conditions also matter. This small-signal example is not a mains protection circuit design.
The example assumes an ideal voltage source and a high-impedance load. An RC filter and an RC power snubber serve different design objectives.
Analog Devices — An Introduction to Electrical Filters ↗
Analog Devices — Low Pass and High Pass Filters ↗
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