(Sample) 3rd order Multiple Feedback High-pass Filter Design Tool - Result -

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

3rd order Multiple Feedback Filter

Vi→

→Vo

(Sample)Transfer Function:

G(s)=

-0.969618616677s3 s3+13407.3521137s2+95087603.6433s+321567817529

R1 = 1000Ω
R2 = 10kΩ
R3 = 91kΩ
C1 = 0.15uF
C2 = 0.0047uF
C3 = 0.0047uF
C4 = 0.0047uF

Equivalent block diagram:

Vi(s)→

s  s+2πfc1

→

s2  s2+2ζ(2πfc2)s+(2πfc2)2

→Vo(s)

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

fc1 = 1018.68878553[Hz]
fc2 = 1128.09512887[Hz]

Damping ratio ζ of equivalent block diagram:

ζ = 0.494265753214

Pole(s)

p = -557.578788569 +980.665342673i[Hz]
  |p|= 1128.09512887[Hz]
p = -1018.68878553[Hz]
  |p|= 1018.68878553[Hz]
p = -557.578788569-980.665342673i[Hz]
  |p|= 1128.09512887[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 = 980.665342673[Hz]

Overshoot (in absolute value)

The 1st peak  g_pk = 0.31 (t =0.00024[sec])
The 2nd peak  g_pk = -0.098 (t =0.00068[sec])
The 3rd peak  g_pk = 0.014 (t =0.0012[sec])

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

g(∞) = 0

Filter gain at f=∞

k = -0.969618616677Times

Frequency analysis

Transient analysis