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

Practical Design Hints
V IN
16-50
C C
R 1
V MID
R 2
+V CC
C B
+V CC
R B
V OUT
R B
V IN
V MID
C 1 =C
Figure 16–50. Biasing a Sallen-Key and an MFB High-Pass Filter
16.8.2 Capacitor Selection
The tolerance of the selected capacitors and resistors depends on the filter sensitivity and
on the filter performance.
Sensitivity is the measure of the vulnerability of a filter’s performance to changes in component
values. The important filter parameters to consider are the corner frequency, f C,
and Q.
For example, when Q changes by ± 2% due to a ± 5% change in the capacitance value,
then the sensitivity of Q to capacity changes is expressed as: Q
s
2%
0.4
%
C 5% % . The
following sensitivity approximations apply to second-order Sallen-Key and MFB filters:
s Q
s
Q fc fc
s s 0.5
%
C R C R %
Although 0.5 %/% is a small difference from the ideal parameter, in the case of higher-order
filters, the combination of small Q and f C differences in each partial filter can significantly
modify the overall filter response from its intended characteristic.
Figures 16.51 and 16.52 show how an intended eighth-order Butterworth low-pass can
turn into a low-pass with Tschebyscheff characteristic mainly due to capacitance changes
from the partial filters.
Figure 16–51 shows the differences between the ideal and the actual frequency responses
of the four partial filters. The overall filter responses are shown in Figure 16–52.
C 2
C 3 =C
R 2
V MID
R 1
+V CC
V OUT