# (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]

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

g(∞) = 0

### Select filter type

Set parameters of the equivalent block diagram
 1st filter: fc1=Hz 2nd filter: fc2=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 response
Impulse response
Overshoot
Final value of the step response
Analysis on time range:
0∼[sec] (optional)