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Band-Pass Filter Design
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
R
V IN
R
C
C
2R
V OUT
R 1
R 2
Figure 16–33.
Sallen-Key Band-Pass
The Sallen-Key band-pass circuit in Figure 16–33 has the following transfer function:
A(s)
G·RC m·s
1 RC m (3 G)·s R 2 C 2 m2·s 2
Through coefficient comparison with Equation 16–10, obtain the following equations:
mid-frequency:
inner gain:
f m 1
2RC
G 1 R 2
R 1
gain at f A m
G
m:
3 G
filter quality: 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
2f m C
16-30