TSH350_07 Datasheet, PDF (18/22 Pages) STMicroelectronics – 550MHz low noise current feedback amplifier

Active filtering
8
Active filtering
Figure 35. Low-pass active filtering, Sallen-Key
C1
R1
IN
R2
+
C2
_
R_fb
R_G
910
TSH350
OUT
100
18/22
From the resistors R_fb and R_G we can directly calculate the gain of the filter in a classic non-
inverting amplification configuration:
A_V
=
g
=
1 + -^R----^f--^b-
R_g
We assume the following expression as the response of the system:
T_jω
=
V_-----o_----u_---t_--j-ω-
Vin_jω
=
-------------------^g---------------------
1
+
2
ζ-_ω^j--^ω-_c
+
(_---j_--ω_---)_--²_-
ω_c2
The cut-off frequency is not gain-dependent and so becomes:
ω_c
=
------------------¹------------------
R1R2C1C2
The damping factor is calculated by the following expression:
ζ
=
1_--
2
ω_c
(
C₁
R₁
+
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=R:
ζ = ²----^C-----²----–----^C-----¹---^{R--R--------f-g}--^b--
2 C₁C₂
Due to a limited selection of values of capacitors in comparison with resistors, we can set
C1=C2=C, so that:
ζ = ²----^R-----²----–----^R-----¹---^{R--R--------f-g}--^b--
2 R₁R₂