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Scientific Calculator  
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.
Filters
RC LPF
RC HPF
LR LPF
LR HPF
RLC LPF
RLC HPF
RLC BPF
RLC BEF
Sallen-Key LPF
Sallen-Key HPF
3rd order SallenKeyLPF
3rd order SallenKeyHPF
Multiple feedback LPF
Multiple feedback HPF
Multiple feedback BPF
3rd order Multiple feedback LPF
3rd order Multiple feedback HPF
TwinT notch
CR 2nd order LPF,HPF,BPF
Active filter


Filter index

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



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