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

Calculated the Transfer Function for the 3rd order Sallen-Key High-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)=

s3 s3+3710.78431373s2+7087418.30065s+6808278867.1

R1 = 5.1kΩ
R2 = 24kΩ
R3 = 120kΩ
C1 = 0.1uF
C2 = 0.01uF
C3 = 0.01uF

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 = 297.268553162[Hz]
fc2 = 303.860592855[Hz]

Damping ratio ζ of equivalent block diagram:

ζ = 0.482657376462

Pole(s)

p = -146.660556558 +266.123920459i[Hz]
  |p|= 303.860592855[Hz]
p = -297.268553162[Hz]
  |p|= 297.268553162[Hz]
p = -146.660556558-266.123920459i[Hz]
  |p|= 303.860592855[Hz]

Zero(s)

z = 0[Hz]
  |z|= 0[Hz]
z = -0[Hz]
  |z|= 0[Hz]
z = -0[Hz]
  |z|= 0[Hz]

Phase margin

pm= NAN[deg] (f =0[Hz])

Oscillation frequency

f = 266.123920459[Hz]

Overshoot (in absolute value)

The 1st peak  g_pk = -0.32 (t =0.00088[sec])
The 2nd peak  g_pk = 0.1 (t =0.0025[sec])
The 3rd peak  g_pk = -0.017 (t =0.0045[sec])

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

g(∞) = 0

Frequency analysis

Transient analysis