LMV821 datasheet(15/26 Pages) TI1

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Application Note (Continued)

Table 1 provides sensitivity measurements for a 10 M

Ω 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.

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 R5 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)

-1.2

-0.7

-0.1

-1.0

-1.1

+0.1

+0.7

-0.1

-1.5

+0.1

-0.6

-0.1

+0.6

+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 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.

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).

10012836

FIGURE 10. Dual Amplifier, 3 kHz Low-Pass Active

Filter with a Butterworth Response and a Pass Band

Gain of Times Two

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

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