LMV321 datasheet(16/27 Pages) NSC

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Application Notes (Continued)

Note that the single-op-amp active filters are used in to the

applications that require low quality factor, Q(

≤ 10), low

frequency (

≤ 5 kHz), and low gain (≤ 10), or a small value for

the product of gain times Q (

≤ 100). The op amp should have

an open loop voltage gain at the highest frequency of inter-

est at least 50 times larger than the gain of the filter at this

frequency. In addition, the selected op amp should have a

slew rate that meets the following requirement:

Slew Rate

≥ 0.5x(ω

HVOPP)x10

−6 V/µsec

where

H is the highest frequency of interest, and Vopp is the

output peak-to-peak voltage.

4.4.2 Sallen-Key 2nd-Order Active Low-Pass Filter

The Sallen-Key 2nd-order active low-pass filter is illustrated

in Figure 13. The dc gain of the filter is expressed as

(1)

Its transfer function is

(2)

The following paragraphs explain how to select values for

1,R2,R3,R4,C1, and C 2 for given filter requirements, such

as A

LP, Q, and f c.

The standard form for a 2nd-order low pass filter is

(3)

where

Q: Pole Quality Factor

C: Corner Frequency

Comparison between the Equation (2) and Equation (3)

yields

(4)

(5)

To reduce the required calculations in filter design, it is

convenient to introduce normalization into the components

and design parameters. To normalize, let

C =

n = 1rad/s,

and C

1 =C2 =Cn = 1F, and substitute these values into

Equation (4) and Equation (5). From Equation (4), we obtain

(6)

From Equation (5), we obtain

(7)

10006014

10006037

FIGURE 11. Simple Low-Pass Active Filter

10006015

FIGURE 12. Frequency Response of Simple Low-Pass

Active Filter in Figure 11

10006016

FIGURE 13. Sallen-Key 2nd-Order Active Low-Pass

Filter

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