Its transfer function is
Application Notes (Continued)
(2)
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10006016
FIGURE 13. Sallen-Key 2nd-Order Active Low-Pass
Filter
10006037
The following paragraphs explain how to select values for
R1, R2, R3, R4, C1, and C 2 for given filter requirements, such
as ALP, Q, and f c.
FIGURE 11. Simple Low-Pass Active Filter
The standard form for a 2nd-order low pass filter is
(3)
where
Q: Pole Quality Factor
ωC: Corner Frequency
Comparison between the Equation (2) and Equation (3)
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yields
FIGURE 12. Frequency Response of Simple Low-Pass
Active Filter in Figure 11
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 ≥ 0.5 x (ω HVOPP) x 10−6 V/µsec
where ωH is the highest frequency of interest, and Vopp is the
output peak-to-peak voltage.
(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 ωC = ωn = 1rad/s,
and C1 = C2 = Cn = 1F, and substitute these values into
Equation (4) and Equation (5). From Equation (4), we obtain
4.4.2 Sallen-Key 2nd-Order Active Low-Pass Filter
The Sallen-Key 2nd-order active low-pass filter is illustrated
(6)
in Figure 13. The dc gain of the filter is expressed as
From Equation (5), we obtain
(1)
(7)
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