Note that this information provides insight on how to fine
tune the cutoff frequency, if necessary. It should be also
noted that R4 and R5 of each circuit also caused variations in
the pass band gain. Increasing R4 by ten percent, increased
the gain by 0.4 dB, while increasing R5 by ten percent,
decreased the gain by 0.4 dB.
Application Note (Continued)
TABLE 1.
Component Sensitivity Component Sensitivity
(LPF)
Ra
(LPF)
-1.2
-0.1
-1.1
+0.7
-1.5
-0.6
+0.6
(HPF)
Ca
(HPF)
-0.7
C1
Rb
-1.0
R2
R1
+0.1
-0.1
R3
C2
C3
R3
+0.1
-0.1
R4
R4
R5
R5
+0.1
10012836
Active filters are also sensitive to an op amp’s parameters
-Gain and Bandwidth, in particular. The LMV822/24 provide
a large gain and wide bandwidth. And DAAFs make excel-
lent use of these feature specifications.
FIGURE 10. Dual Amplifier, 3 kHz Low-Pass Active
Filter with a Butterworth Response and a Pass Band
Gain of Times Two
Single Amplifier versions require a large open-loop to
closed-loop gain ratio - approximately 50 to 1, at the Fc of
the filter response. Figure 12 shows an impressive photo-
graph of a network analyzer measurement (hp3577A). The
measurement was taken from a 300 kHz version of Figure
@
10. At 300 kHz, the open-loop to closed-loop gain ratio Fc
is about 5 to 1. This is 10 times lower than the 50 to 1 “rule
of thumb” for Single Amplifier Active Filters.
10012837
FIGURE 11. Dual Amplifier, 300 Hz High-Pass Active
Filter with a Butterworth Response and a Pass Band
Gain of Times Two
10012892
FIGURE 12. 300 kHz, Low-Pass Filter, Butterworth
Response as Measured by the HP3577A Network
Analyzer
Table 1 provides sensitivity measurements for a 10 MΩ load
condition. The left column shows the passive components
for the 3 kHz low-pass DAAF. The third column shows the
components for the 300 Hz high-pass DAAF. Their respec-
tive sensitivity measurements are shown to the right of each
component column. Their values consists of the percent
change in cutoff frequency (Fc) divided by the percent
change in component value. The lower the sensitivity value,
the better the performance.
In addition to performance, DAAFs are relatively easy to
design and implement. The design equations for the low-
pass and high-pass DAAFs are shown below. The first two
equation calculate the Fc and the circuit Quality Factor (Q)
for the LPF (Figure 10). The second two equations calculate
the Fc and Q for the HPF (Figure 11).
Each resistor value was changed by about 10 percent, and
this measured change was divided into the measured
change in Fc. A positive or negative sign in front of the
measured value, represents the direction Fc changes rela-
tive to components’ direction of change. For example, a
sensitivity value of negative 1.2, means that for a 1 percent
increase in component value, Fc decreases by 1.2 percent.
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