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

Active Filter Design Techniques
Band-Pass Filter Design
Because of the dependency between Q and A m, there are two options to solve for R 2: either
to set the gain at mid frequency:
R 2 2Am 1
1 Am
or to design for a specified Q:
R 2
2Q 1
Q
16.5.1.2 Multiple Feedback Topology
V IN
R 3
Figure 16–34. MFB Band-Pass
R 1
C
C
The MFB band-pass circuit in Figure 16–34 has the following transfer function:
A(s)
1 2R 1 R 3
R 1 R 3
R 2
R2R3 Cm·s
R1R3 V OUT
Cm·s R1R2R3 C R1R3 2 ·m 2 ·s2 The coefficient comparison with Equation 16–9, yields the following equations:
fm 1
mid-frequency:
2C
gain at f m:
filter quality:
bandwidth:
Am R 2
2R 1
Q fmR 2 C
B 1
R 2 C
R 1 R 3
R 1 R 2 R 3
The MFB band-pass allows to adjust Q, A m, and f m independently. Bandwidth and gain
factor do not depend on R 3. Therefore, R 3 can be used to modify the mid frequency with-
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