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

Low-Pass Filter Design
16.3.2.2 Multiple Feedback Topology
16-18
The MFB topology is commonly used in filters that have high Qs and require a high gain.
V IN
Figure 16–19. Second-Order MFB Low-Pass Filter
R 1
C 2
The transfer function of the circuit in Figure 16–19 is:
A(s)
R 2
R 3
C 1
R2 R1 V OUT
1 cC 1R 2 R 3 R 2 R 3
R 1 s c 2 C 1 C 2 R 2 R 3 s 2
Through coefficient comparison with Equation 16–2 one obtains the relation:
A 0 R 2
R 1
a 1 cC 1R 2 R 3 R 2 R 3
R 1
b 1 c 2 C 1 C 2 R 2 R 3
Given C 1 and C 2, and solving for the resistors R 1–R 3:
R 2
R 1 R 2
A 0
R 3
2 2
a1C2 a1 C2 4b1C1C 1 2 A 0
b 1
42 2
fc C1C2R2 4fcC 1 C 2