the pass band gain. Increasing R
4
by ten percent, increased
the gain by 0.4 dB, while increasing R
5
by ten percent, de-
creased the gain by 0.4 dB.
TABLE 1.
Component (LPF)
R
a
C
1
R
2
R
3
C
3
R
4
R
5
Sensitivity (LPF)
-1.2
-0.1
-1.1
+0.7
-1.5
-0.6
+0.6
Component (HPF)
C
a
R
b
R
1
C
2
R
3
R
4
R
5
Sensitivity (HPF)
-0.7
-1.0
+0.1
-0.1
+0.1
-0.1
+0.1
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:
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.
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 = 1 nF
2. Choose R
4
= R
5
= 1 kΩ
3. Calculate R
a
and R
2
for the desired Fc as follows:
DS100128-92
FIGURE 12. 300 kHz, Low-Pass Filter, Butterworth
Response as Measured by the HP3577A Network
Analyzer
In addition to performance, DAAFs are relatively easy to de-
sign and implement. The design equations for the low-pass
and high-pass DAAFs are shown below. The first two equa-
tion 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).
4. Calculate R
3
for the desired Q. The desired Q for a Butter-
worth (Maximally Flat) response is 0.707 (45 degrees into
the s-plane). R
3
calculates as follows:
Notice that R
3
could also be calculated as 0.707 of R
a
or R
2.
The circuit was implemented and its cutoff frequency mea-
sured. The cutoff frequency measured at 2.92 kHz.
The circuit also showed good repeatability. Ten different
LMV822 samples were placed in the circuit. The correspond-
ing change in the cutoff frequency was less than a percent.
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