Choosing the Feedback Circuit
10.2 Active filtering
Figure 72. Low-pass active filtering. Sallen-Key
C1
R1
IN
R2
+
C2
TS615
_
OUT
25Ω
Rfb
RG
910Ω
TS615
From the resistors Rfb and RG we can directly calculate the gain of the filter in a classical, non-inverting
amplification configuration:
AV = g = 1 + R--R---f-g-b--
We assume the following expression as the response of the system:
Tjω = V---V--o--i--un---j-t-ωj--ω--- = 1-----+-----2----ζ----ω-j----ω--g--c-----+-------(--ω--j----ω---c-----)--2---2----
The cutoff frequency is not gain-dependent and so becomes:
ωc
=
------------------1-------------------
R1R2C1C2
The damping factor is calculated by the following expression:
ζ = 12-- ωc(C1R1 + C1R2 + C2R1 – C1R1g)
The higher the gain the more sensitive the damping factor is. When the gain is higher than 1, it is
preferable to use some very stable resistor and capacitor values. In the case of R1=R2:
ζ = 2----C-----2-----–----C-----1----R--R-------f--g--b----
2 C1C2
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