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SBOS426B – NOVEMBER 2008 – REVISED AUGUST 2010
illustrates both noninverting (Figure
and inverting (Figure
op amp circuit
configurations with gain. In circuit configurations with
gain, the feedback network resistors also contribute
noise. The current noise of the op amp reacts with
the feedback resistors to create additional noise
components.
A) Noise in Noninverting Gain Configuration
R
2
The feedback resistor values can generally be
chosen to make these noise sources negligible. Note
that low-impedance feedback resistors load the
output of the amplifier. The equations for total noise
are shown for both configurations.
Noise at the output:
2
2
R
1
E
O
E
O
= 1 +
2
R
2
R
1
e
n
+ e
1
+ e
2
+ (i
n
R
2
) + e
S
+ (i
n
R
S
)
2
2
2
2
2
2
1+
R
2
R
1
Where e
S
=
Ö
4kTR
S
´
1 +
R
S
e
1
=
Ö
4kTR
1
´
V
S
R
2
R
1
R
2
R
1
= thermal noise of R
S
= thermal noise of R
1
e
2
=
Ö
4kTR
2
= thermal noise of R
2
B) Noise in Inverting Gain Configuration
R
2
Noise at the output:
2
R
1
E
O
2
E
O
= 1+
R
2
R
1
+ R
S
e
n
+ e
1
+ e
2
+ (i
n
R
2
) + e
S
2
2
2
2
2
R
S
Where e
S
=
Ö
4kTR
S
´
R
2
R
1
+ R
S
R
2
R
1
+ R
S
= thermal noise of R
S
V
S
e
1
=
Ö
4kTR
1
´
= thermal noise of R
1
e
2
=
Ö
4kTR
2
= thermal noise of R
2
NOTE: For the OPA209 series op amps at 1kHz, e
n
= 2.2nV/√Hz and I
n
= 530fA/√Hz.
Figure 34. Noise Calculation in Gain Configurations
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