# (Sample)Multiple Feedback Band-pass Filter Design Tool - Result -

Calculated the Transfer Function for the multiple feedback band-pass filter, displayed on graphs, showing Bode diagram, Nyquist diagram, Impulse response and Step response.

## Multiple Feedback Band-pass Filter

 Vin(s)→ →Vout(s)
(Sample)Transfer Function:
 G(s)= -8912.65597148s s2+9238.72875092s+41335488.7073

R1 = 5.1kΩ
R2 = 20kΩ
R3 = 8.2kΩ
C1 = 0.022uF
C2 = 0.033uF

#### Center frequency

f0 = 1023.2498036[Hz]

#### Gain at center frequency f0

Gpk = -0.964705882353[times] (-0.312101466612)[dB]

#### Quality factor

Q = 0.695903982559

#### Damping ratio

ζ = 0.718489924661

#### Pole(s)

p = -735.194674297 +711.70847364i[Hz]
|p|= 1023.2498036[Hz]
p = -735.194674297-711.70847364i[Hz]
|p|= 1023.2498036[Hz]

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

#### Phase margin

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

#### Oscillation frequency

f = 711.70847364[Hz]

#### Overshoot (in absolute value)

The 1st peak  gpk = -0.63 (t =0.00017[sec])
The 2nd peak  gpk = 0.024 (t =0.00088[sec])
The 3rd peak  gpk = -0.00095 (t =0.0016[sec])

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

g(∞) = 0

f0=Hz
Gain K= at f0. (K<0)

### Q factor | Damping ratio ζ

Quality factor Q =
Damping ratio ζ =
 C1 = F C2 = F
C1, C2 is optional. But when setting these capacitances, C1 and C2 of both are needed to give following the equation
(C2/C1) > 4ζ 2|K| - 1

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