Datasheet

Data Sheet ADA4940-1/ADA4940-2
Rev. C | Page 23 of 32
APPLICATIONS INFORMATION
ANALYZING AN APPLICATION CIRCUIT
The ADA4940-1/ADA4940-2 use open-loop gain and negative
feedback to force their differential and common-mode output
voltages in such a way as to minimize the differential and common-
mode error voltages. The differential error voltage is defined as
the voltage between the differential inputs labeled +IN and −IN (see
Figure 61). For most purposes, this voltage can be assumed to be
zero. Similarly, the difference between the actual output common-
mode voltage and the voltage applied to V
OCM
can also be assumed
to be zero. Starting from these two assumptions, any application
circuit can be analyzed.
SETTING THE CLOSED-LOOP GAIN
The differential mode gain of the circuit in Figure 61 can be
determined by
G
F
dm
IN
dmOUT
R
R
V
V
=
,
,
This assumes that the input resistors (R
G
) and feedback resistors
(R
F
) on each side are equal.
ESTIMATING THE OUTPUT NOISE VOLTAGE
The differential output noise of the ADA4940-1/ADA4940-2 can
be estimated using the noise model in Figure 63. The input-referred
noise voltage density, v
nIN
, is modeled as a differential input, and
the noise currents, i
nIN−
and i
nIN+
, appear between each input and
ground. The noise currents are assumed to be equal and produce
a voltage across the parallel combination of the gain and feedback
resistances. v
nCM
is the noise voltage density at the V
OCM
pin. Each
of the four resistors contributes (4kTR
x
)
1/2
. Table 14 summarizes
the input noise sources, the multiplication factors, and the
output-referred noise density terms. For more noise calculation
information, go to the Analog Devices Differential Amplifier
Calculator (DiffAmpCalc™), click ADIDiffAmpCalculator.zip
and follow the on-screen prompts.
ADA4940-1/
ADA4940-2
+
R
F2
V
nOD
V
nCM
V
OCM
V
nIN
R
F1
R
G2
R
G1
V
nRF1
V
nRF2
V
nRG1
V
nRG2
i
nIN+
i
nIN–
08452-050
Figure 63. ADA4940-1/ADA4940-2 Noise Model
As with conventional op amp, the output noise voltage densities
can be estimated by multiplying the input-referred terms at +IN
and −IN by the appropriate output factor,
where:
( )
21
N
ββ
G
+
=
2
is the circuit noise gain.
G1
F1
G1
1
R
R
R
β
+
=
and
G2
F2
G2
2
RR
R
β
+
=
are the feedback factors.
When R
F1
/R
G1
= R
F2
/R
G2
, then β1 = β2 = β, and the noise gain
becomes
G
F
N
R
R
β
G +== 1
1
Note that the output noise from V
OCM
goes to zero in this case.
The total differential output noise density, v
nOD
, is the root-sum-
square of the individual output noise terms.
∑
=
=
8
1i
2
nOinOD
v
v
Table 14. Output Noise Voltage Density Calculations
Input Noise Contribution Input Noise Term
Input Noise
Voltage Density
Output
Multiplication Factor
Output-Referred Noise
Voltage Density Term
Differential Input v
nIN
v
nIN
G
N
v
nO1
= G
N
(v
nIN
)
Inverting Input i
nIN−
i
nIN−
× (R
G2
||R
F2
) G
N
v
nO2
= G
N
[i
nIN−
× (R
G2
||R
F2
)]
Noninverting Input i
nIN+
i
nIN+
× (R
G1
||R
F1
) G
N
v
nO3
= G
N
[i
nIN+
× (R
G1
||R
F1
)]
V
OCM
Input v
nCM
v
nCM
G
N
(β
1
− β
2
) v
nO4
= G
N
(β
1
− β
2
)(v
nCM
)
Gain Resistor R
G1
v
nRG1
(4kTR
G1
)
1/2
G
N
(1 − β
2
) v
nO5
= G
N
(1 − β
2
)(4kTR
G1
)
1/2
Gain Resistor R
G2
v
nRG2
(4kTR
G2
)
1/2
G
N
(1 − β
1
) v
nO6
= G
N
(1 − β
1
)(4kTR
G2
)
1/2
Feedback Resistor R
F1
v
nRF1
(4kTR
F1
)
1/2
1 v
nO7
= (4kTR
F1
)
1/2
Feedback Resistor R
F2
v
nRF2
(4kTR
F2
)
1/2
1 v
nO8
= (4kTR
F2
)
1/2