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

Band-Pass Filter Design
16-30
The graph shows that the frequency response of second-order band-pass filters gets
steeper with rising Q, thus making the filter more selective.
16.5.1.1 Sallen-Key Topology
V IN
Figure 16–33. Sallen-Key Band-Pass
R
C
C
2R
R
The Sallen-Key band-pass circuit in Figure 16–33 has the following transfer function:
A(s)
R 1
R 2
V OUT
G·RCm·s
1 RCm(3 G)·s R 2 C 2 m 2 ·s 2
Through coefficient comparison with Equation 16–10, obtain the following equations:
mid-frequency:
inner gain:
gain at f m:
filter quality:
fm 1
2RC
G 1 R 2
R 1
Am G
3 G
Q 1
3 G
The Sallen-Key circuit has the advantage that the quality factor (Q) can be varied via the
inner gain (G) without modifying the mid frequency (fm). A drawback is, however, that Q
and A m cannot be adjusted independently.
Care must be taken when G approaches the value of 3, because then A m becomes infinite
and causes the circuit to oscillate.
To set the mid frequency of the band-pass, specify f m and C and then solve for R:
R 1
2fmC