Sallen-Key Low-Pass Filter Calculator (Unity-Gain, Second Order)
Cut-off frequency, natural frequency, Q and passband peaking of a unity-gain Sallen-Key low-pass filter from its two resistors and two capacitors, and the C1 that makes it maximally flat.
Results
The dashed line marks the value you entered.
What this tool does
The Sallen-Key filter builds a second-order low-pass from an op-amp follower, two resistors and two capacitors. Its natural frequency is f₀ = 1 ÷ (2π √(R₁R₂C₁C₂)) but its Q depends on the ratio of the parts, Q = √(R₁R₂C₁C₂) ÷ (C₂(R₁ + R₂)), and the −3 dB point only equals f₀ when Q is 0.707. With equal resistors, C₁ = 2 C₂ gives that Butterworth response with no peaking; a bigger C₁ raises Q and makes the response peak, a smaller one lowers Q and rolls off earlier. C₁ is the capacitor going to the output, C₂ the one to ground.
Formula
f₀ = 1 ÷ (2π √(R₁R₂C₁C₂)) · Q = √(R₁R₂C₁C₂) ÷ (C₂(R₁ + R₂)) · Butterworth when C₁ = C₂ (R₁ + R₂)² ÷ (2R₁R₂)
Variables
| Symbol | Meaning | Unit |
|---|---|---|
r1 | Resistor R1 (from the input) | kΩ |
r2 | Resistor R2 (to the amplifier input) | kΩ |
c1 | Capacitor C1 (feedback, to the output) | nF |
c2 | Capacitor C2 (to ground) | nF |
F3 | Cut-off frequency (−3 dB) | Hz |
F0 | Natural frequency f₀ | Hz |
Q | Quality factor Q | — |
PK | Peaking above the pass-band level | dB |
CB | C1 that makes it Butterworth (Q = 0.707) | nF |
Worked example
- Resistor R1 (from the input)10 kΩ
- Resistor R2 (to the amplifier input)10 kΩ
- Capacitor C1 (feedback, to the output)22 nF
- Capacitor C2 (to ground)10 nF
- Cut-off frequency (−3 dB)1122.9 Hz
- Natural frequency f₀1073.0 Hz
- Quality factor Q0.742
- Peaking above the pass-band level0.04 dB
- C1 that makes it Butterworth (Q = 0.707)20.00 nF
Limitations
- Coverage and consumption figures vary between products. Take the values from the manufacturer's datasheet for the product you are actually using.
- The calculation runs at full precision and only the display is rounded. If you copy an intermediate value and retype it, small differences can appear.