"Chapter 1 - The Op Amp's Place in the World" - HTL Wien 10

V IN
Figure 16–15. General Sallen-Key Low-Pass Filter
V IN
Figure 16–16. Unity-Gain Sallen-Key Low-Pass Filter
R 1
R 1
The transfer function of the circuit in Figure 16–15 is:
A(s)
R 2
R 2
C 1
C 1
C 2
R 3
C 2
R 4
A 0
V OUT
V OUT
Active Filter Design Techniques
Low-Pass Filter Design
1 cC 1 R 1 R 2 1 A 0 R 1 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 cC 1 R 1 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 cC 1 R 1 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
4fcC 1 C 2
16-15