ACTIVE FILTER
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
Simple Low-Pass Active Filter
The simple low-pass filter is shown in Figure 11. Its low-fre-
quency gain (ω → 0) is defined by −R3/R1. This allows low-
frequency gains other than unity to be obtained. The filter has
a −20 dB/decade roll-off after its corner frequency fc. R2
should be chosen equal to the parallel combination of R1 and
R3 to minimize errors due to bias current. The frequency re-
sponse of the filter is shown in Figure 12.
(1)
Its transfer function is
(2)
10006014
10006016
FIGURE 13. Sallen-Key 2nd-Order Active Low-Pass Filter
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 fc.
10006037
The standard form for a 2nd-order low pass filter is
FIGURE 11. Simple Low-Pass Active Filter
(3)
where
Q: Pole Quality Factor
ꢁꢁωC: Corner Frequency
A comparison between Equation 2 and Equation 3 yields
10006015
(4)
(5)
FIGURE 12. Frequency Response of Simple Low-Pass
Active Filter in Figure 11
Note that the single-op-amp active filters are used in the ap-
plications that require low quality factor, Q( ≤ 10), low fre-
quency (≤ 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 interest
at least 50 times larger than the gain of the filter at this fre-
quency. In addition, the selected op amp should have a slew
rate that meets the following requirement:
To reduce the required calculations in filter design, it is con-
venient to introduce normalization into the components and
design parameters. To normalize, let ωC = ωn = 1 rad/s, and
C1 = C2 = Cn = 1F, and substitute these values into Equation
4 and Equation 5. From Equation 4, we obtain
(6)
From Equation 5, we obtain
Slew Rate ≥ 0.5 × (ω HVOPP) × 10−6 V/µsec
where ωH is the highest frequency of interest, and VOPP is the
output peak-to-peak voltage.
(7)
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