(Sample) 3rd order Sallen-Key Low-pass Filter Design Tool - Result -

Calculated the Transfer Function for the 3rd order Sallen-Key Low-pass filter, displayed on graphs, showing Bode diagram, Nyquist diagram, Impulse response and Step response.

3rd order Sallen-Key filter

Vi→

→Vo

(Sample)Transfer Function:

G(s)=

133362301759 s3+6607.88013729s2+50305327.1219s+133362301759

R1 = 9.1kΩ
R2 = 68kΩ
R3 = 36kΩ
C1 = 0.033uF
C2 = 0.015uF
C3 = 680pF

Equivalent block diagram:

Vi(s)→

2πfc1  s+2πfc1

→

(2πfc2)2  s2+2ζ(2πfc2)s+(2πfc2)2

→Vo(s)

Cut-off frequency fc1, fc2 of equivalent block diagram:

fc1 = 538.768389471[Hz]
fc2 = 998.954448652[Hz]

Damping ratio ζ of equivalent block diagram:

ζ = 0.256722615545

Pole(s)

p = -256.454198869 +965.474616116i[Hz]
  |p|= 998.954448652[Hz]
p = -538.768389471[Hz]
  |p|= 538.768389471[Hz]
p = -256.454198869-965.474616116i[Hz]
  |p|= 998.954448652[Hz]

Phase margin

pm= 42.7[deg] (f =941.5[Hz])

Oscillation frequency

f = 965.474616116[Hz]

Overshoot (in absolute value)

The 1st peak  g_pk = 1.09 (t =0.00076[sec])
The 2nd peak  g_pk = 0.91 (t =0.0012[sec])
The 3rd peak  g_pk = 1.03 (t =0.0018[sec])

Final value of the step response (on the condition that the system converged when t goes to infinity)

g(∞) = 1

Frequency analysis

Transient analysis