the pass band gain. Increasing R4 by ten percent, increased
the gain by 0.4 dB, while increasing R5 by ten percent, de-
creased the gain by 0.4 dB.
TABLE 1.
Component (HPF)
Component (LPF)
Sensitivity (LPF)
Sensitivity (HPF)
Ra
C1
R2
R3
C3
R4
R5
-1.2
-0.1
-1.1
+0.7
-1.5
-0.6
+0.6
Ca
Rb
R1
C2
R3
R4
R5
-0.7
-1.0
+0.1
-0.1
+0.1
-0.1
+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.
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:
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 C1 = C3 = C = 1 nF
2. Choose R4 = R5 = 1 kΩ
3. Calculate Ra and R2 for the desired Fc as follows:
DS100128-92
FIGURE 12. 300 kHz, Low-Pass Filter, Butterworth
Response as Measured by the HP3577A Network
Analyzer
4. Calculate R3 for the desired Q. The desired Q for a Butter-
worth (Maximally Flat) response is 0.707 (45 degrees into
the s-plane). R3 calculates as follows:
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).
Notice that R3 could also be calculated as 0.707 of Ra or R2.
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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