RHF330 Datasheet, PDF (19/22 Pages) STMicroelectronics – Rad-hard 1 GHz low noise operational amplifier

RHF330
8
Active filtering
Active filtering
Figure 33. Low-pass active filtering, Sallen-Key
C1
R1
IN
R2
+
C2
_
R_fb
R_G
OUT
100 Ω
AM00840
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 is 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 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 capacitor values in comparison with the resistors, we can set
C1=C2=C, so that:
ζ = ²----^R-----²----–----^R-----¹---^{R--R--------f-g}--^b--
2 R₁R₂
Doc ID 15576 Rev 3
19/22