WOLFRAM NOTEBOOK

Sallen-Key Band-Pass Filter

​
low-pass
R
1
10000
Ω
R
2
10000
Ω
C
1
10
μF
C
2
10
μF
R
4
R
3
0
0.5
1
10
100
stages
1
high-pass
R
1
10000
Ω
R
2
10000
Ω
C
1
10
μF
C
2
10
μF
R
4
R
3
0
0.5
1
10
100
Stages
1
plot settings
​
center freq
1
10
100
BW (decades)
2
4
6
​
autoscale
max
0
min
-50
Bode plots
​
​
single high-pass
single low-pass
overall
​
​
Sallen–Key topology filters are second-order active filters whose simplicity makes them a popular choice for general filtering applications. In this Demonstration, Bode plots are produced for single-stage low-pass and high-pass filters or a combination of these filters, up to 10 stages each.

Details

The transfer function, cutoff frequency, and
Q
for low-pass and high-pass filters (with non-unity gain) are
1.
H
low
(s)=
K
2
(2πs)
(
R
1
R
2
C
1
C
2
)+(2πs)(
R
1
C
1
+
R
2
C
1
+
R
1
C
2
(1-K))+1
;
2.
H
high
(s)=
2
K(2πs)
R
1
R
2
C
1
C
2
2
(2πs)
(
R
1
R
2
C
1
C
2
)+(2πs)(
R
2
C
2
+
R
2
C
1
+
R
1
C
2
(1-K))+1
;
3.
Q
low
=
R
1
R
2
C
1
C
2
R
1
C
1
+
R
2
C
1
+
R
1
C
2
(1-K)
;
4.
Q
high
=
R
1
R
2
C
1
C
2
R
2
C
2
+
R
2
C
1
+
R
1
C
2
(1-K)
;
5.
f
0
=
1
2π
R
1
R
2
C
1
C
2
;
where
K=1+
R
4
R
3
and
R
1
,
R
2
,
R
3
,
R
4
,
C
1
,
C
2
are the resistances and capacitances.
For higher-order filters, the transfer funtions 1 and 2 are raised to the order of the filter. For a high-pass (low-pass) filter, set the order of the low-pass (high-pass) filter to "0".

References

[1] "Analysis of the Sallen–Key Architecture." Texas Instruments. (Sep 2002) http://www.ti.com/lit/an/sloa024b/sloa024b.pdf.

External Links

Permanent Citation

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