RC filter formulas
fc = 1 / (2π·R·C) τ = R·C
low-pass: |H| = 1 / √(1 + (f/fc)²), φ = −atan(f/fc)
high-pass: |H| = (f/fc) / √(1 + (f/fc)²), φ = 90° − atan(f/fc)
At the cutoff frequency the output is 70.7 % of the input (−3 dB) and shifted by 45°. Above fc, a first-order low-pass falls by 20 dB per decade — ten times the frequency, one tenth the amplitude.
Example: R = 1.6 kΩ, C = 100 nF → fc ≈ 995 Hz, τ = 160 µs. A 1 kHz signal comes out at about 70 % amplitude.
Time constant and step response
τ = RC is how fast the capacitor follows a step: it reaches 63 % after one τ and about 99 % after five. See RC time constant: charge and decay.
Why simulate it?
The formula assumes an ideal source and no load. On a simulated oscilloscope you see the input and output together — the attenuation and the phase lag — and can change the frequency to watch the corner. Press Simulate this circuit to open the filter in CircuPilot with a signal generator and an oscilloscope already connected.
Step-by-step design: how to design an RC low-pass filter and simulate it with SPICE.
FAQ
How do I calculate the cutoff frequency of an RC filter?
f_c = 1 / (2π·R·C). For R = 10 kΩ and C = 100 nF, f_c ≈ 159 Hz. The same formula applies to low-pass and high-pass.
What is the difference between an RC low-pass and high-pass filter?
Only the order of the parts. Low-pass: resistor in series, capacitor to ground — passes slow signals. High-pass: capacitor in series, resistor to ground — blocks DC and passes fast signals.
Why is the output lower than the calculator says?
Usually the load: whatever you connect to the output forms a divider with the filter. Keep the load impedance at least ten times higher than R, or buffer it.