Table 1 provides sensitivity measurements for a 10 MΩload
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.
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.
Note that this information provides insight on how to fine
tune the cutoff frequency, if necessary. It should be also
noted that R
4
and R
5
of each circuit also caused variations in
the pass band gain. Increasing R
4
by ten percent, increased
the gain by 0.4 dB, while increasing R
5
by ten percent,
decreased the gain by 0.4 dB.
TABLE 1.
Component
(LPF) Sensitivity
(LPF) Component
(HPF) Sensitivity
(HPF)
R
a
-1.2 C
a
-0.7
C
1
-0.1 R
b
-1.0
R
2
-1.1 R
1
+0.1
R
3
+0.7 C
2
-0.1
C
3
-1.5 R
3
+0.1
R
4
-0.6 R
4
-0.1
R
5
+0.6 R
5
+0.1
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.
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 300kHz 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.
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
).
To simplify the design process, certain components are set
equal to each other. Refer to
Figure 10
and
Figure 11
. These
equal component values help to simplify the design equa-
tions as follows:
To illustrate the design process/implementation, a 3 kHz,
Butterworth response, low-pass filter DAAF (
Figure 10
)is
designed as follows:
1. Choose C
1
=C
3
=C=1nF
2. Choose R
4
=R
5
=1kΩ
3. Calculate R
a
and R
2
for the desired Fc as follows:
DS100128-37
FIGURE 11. Dual Amplifier, 300 Hz High-Pass Active
Filter with a Butterworth Response and a Pass Band
Gain of Times Two
DS100128-92
FIGURE 12. 300 kHz, Low-Pass Filter, Butterworth
Response as Measured by the HP3577A Network
Analyzer
LMV821 Single/ LMV822 Dual/ LMV824 Quad
www.national.com 14