3rd order Sallen-Key Low-pass Filter Design Tool

This page is a web calculator that design a 3rd order Sallen-Key low-pass filter. Use this utility to simulate the Transfer Function for filters at a given frequency, damping ratio ζ or values of R and C. The response of the filter is displayed on graphs, showing Bode diagram, Nyquist diagram, Impulse response and Step response.

Calculate the transfer function for 3rd order Sallen-Key low-pass filter with R and C values

Vi→ →Vo
Transfer function:
    Transfer function of 3rd order Sallen-Key low-pass filter


2nd order Sallen-Key low-pass filter tool, use also.
R1=Ω C1=F
R2=Ω C2=F
R3=Ω C3=F
p:pico, n:nano, u:micro, k:kilo, M:mega

Frequency analysis

Bode diagram
    Phase  Group delay
Nyquist diagram
Pole, zero
Phase margin
Oscillation analysis
Analysis on frequency range:
  f1=∼f2=[Hz] (optional)

Transient analysis

Step response
Impulse response
Overshoot
Final value of the step response
Analysis on time range:
  0∼[sec] (optional)


Calculate the R and C values for the Sallen-Key filter at a given frequency and damping ratio ζ

Vi→ →Vo
※ 3rd order filters are usually made from combinations of 1st and 2nd order filters following the equivalent block diagram.


Equivalent block diagram:

Vi→2πfc1

 s+2πfc1 
(2πfc2)2

 s2+2ζ(2πfc2)s+(2πfc2)2 
→Vo


Transfer function block diagram:



Select filter type

Set parameters of the equivalent block diagram
1st order filter:
  fc1=Hz
2nd order filter:
  fc2=Hz Damping ratio
ζ =

Butterworth filter
  Cut-off frequency
  fc=Hz
Chebyshev filter
  Characteristic frequency
  fc=Hz
  Gain ripple gr=dB
Bessel filter
  Characteristic frequency
  fc=Hz

C1 = F C2 = F
C1, C2 is optional. But when setting these capacitances, C1 and C2 of both are needed.

Select Capacitor Sequence:
Select Resistor Sequence:

Frequency analysis

Bode diagram
    Phase  Group delay
Nyquist diagram
Pole, zero
Phase margin
Oscillation analysis
Analysis on frequency range:
  f1=∼f2=[Hz] (optional)

Transient analysis

Step response
Impulse response
Overshoot
Final value of the step response
Analysis on time range:
  0∼[sec] (optional)