Op Amps for Everyone - The Repeater Builder's Technical ...

Low-Pass Filter Design
V IN
R 1
R 2
C 1
C 2
V OUT
R 3
R 4
Figure 16–15.
General Sallen-Key Low-Pass Filter
V IN
R 1
R 2
C 1
C 2
V OUT
Figure 16–16.
Unity-Gain Sallen-Key Low-Pass Filter
The transfer function of the circuit in Figure 16–15 is:
A(s)
A 0
1 c
C1 R1 R 2
1 A0 R1 C 2
s c 2 R 1
R 2
C 1
C 2
s 2
For the unity-gain circuit in Figure 16–16 (A 0 =1), the transfer function simplifies to:
A(s)
1
1 c C 1
R1 R 2
s c 2 R 1
R 2
C 1
C 2
s 2
The coefficient comparison between this transfer function and Equation 16–2 yields:
A 0
1
a 1
c C 1
R1 R 2
b 1
c 2 R 1
R 2
C 1
C 2
Given C 1 and C 2 , the resistor values for R 1 and R 2 are calculated through:
R 1,2
a 1 C 2 a 1 2 C 2
2 4b1 C 1
C 2
4f c C 1
C 2
Active Filter Design Techniques
16-15