Science & engineering
First-order RC filter
Find the ideal cutoff, gain and phase of an unloaded RC low-pass or high-pass filter.
A clear answer. Here’s how.
For an ideal unloaded RC circuit, τ = RC and fc = 1/(2πRC). With x=2πfRC, low-pass gain = 1/√(1+x²), phase = −atan(x); high-pass gain = x/√(1+x²), phase = atan(1/x). Frequency is positive. Source/load impedance, component tolerances and parasitics are excluded.
See a worked example
Worked example
A fixed demonstration, separate from the values you enter above.
- Output topology
- Low-pass: output across capacitor
- Resistance (Ω)
- 1000
- Capacitance (µF)
- 0.1
- Frequency (Hz)
- 1000
Example result
- Cutoff frequency
- 1,591.54943092 Hz
- Time constant
- 0.0001 s
- Amplitude gain
- 0.846733015965
- Gain in decibels
- -1.44507011621 dB
- Output phase relative to input
- -32.1419076353 °