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

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(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+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

Filter gain at f=∞:
K=Times (K<0)

Select filter type Set parameters of the equivalent block diagram

1st filter:
f_c1=Hz
2nd filter:
f_c2=Hz	Damping ratio ζ=

Butterworth filter

Cut-off frequency fc=Hz

Chebyshev filter

Characteristic frequency fc=Hz
Gain ripple gr=dB

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)

Frequency analysis

Transient analysis

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