Circuit Notebook Open the app

Signals & radio calculator, part of Premium

Sallen-Key filter

Sallen-Key filter: the circuit drawn with the example's values11kΩ11kΩ22nF10nF
Low-pass 1 kHz, Q 0.707: R 11 kΩ, C 22 nF / 10 nF

Feedback keeps the knee of two RC stages sharp; Q says how sharp: 0.7 is flat.

Opens in the app on 1 December, with Circuit Notebook 1.0 See it worked out

Part of Premium. It runs in your browser: nothing to install.

The example, worked out

Given

Filter
Low-pass
Cutoff frequency
1 kHz
Response
Butterworth (flat)
Capacitors around
10 nF
Resistor series
E24 (5 %)

Working

  1. equal resistors: the capacitors set Q
  2. then the resistors set the cutoff
  3. with the drawer values

Results

R1 = R211 kΩ
C1 (to the output)22 nF
C2 (to ground)10 nF
Cutoff you get975 Hz
Q you get0.742
−3 dB point1.02 kHz
Peaking0.036 dB

The formulas

  1. fc = 1 / (2π √(R1 R2 C1 C2))the cutoff of the second-order stage
  2. low-pass, R1 = R2: C1 / C2 = 4 Q²the capacitors set Q
  3. high-pass, C1 = C2: R2 / R1 = 4 Q²the resistors set Q

The usual traps

  • Capacitor tolerance moves Q as much as the resistors do.
  • An op-amp with too little gain-bandwidth bends the response near the cutoff.

Questions

How do I calculate the parts of a Sallen-Key filter?

fc = 1 / (2π √(R1 R2 C1 C2)): the cutoff of the second-order stage. low-pass, R1 = R2: C1 / C2 = 4 Q²: the capacitors set Q. high-pass, C1 = C2: R2 / R1 = 4 Q²: the resistors set Q.

What does it give for typical values?

Low-pass 1 kHz, Q 0.707: R 11 kΩ, C 22 nF / 10 nF. R1 = R2: 11 kΩ; C1 (to the output): 22 nF; C2 (to ground): 10 nF.

What are the usual mistakes?

Capacitor tolerance moves Q as much as the resistors do. An op-amp with too little gain-bandwidth bends the response near the cutoff.

In the app

Your circuit, drawn live

Change a value: the schematic redraws with your numbers on the parts.

The part you can buy

Results rounded to standard values (E12, E24, E96) and power ratings.

The working, shown

Every step written out. Try it first by hand, then check.

Into your notebook

One click puts the circuit on a sheet of your project.

Opens in the app on 1 December, with Circuit Notebook 1.0

Also in Signals & radio