
Data Sheet
ADA4940-1/ADA4940-2
Rev. C | Page 23 of 32
APPLICATIONS INFORMATION
ANALYZING AN APPLICATION CIRCUIT
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 VOCM 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 i
n Figure 61 can be
determined by
G
F
dm
IN
dm
OUT
R
V
=
,
This assumes that the input resistors (RG) and feedback resistors
(RF) on each side are equal.
ESTIMATING THE OUTPUT NOISE VOLTAGE
be estimated using the noise model i
n Figure 63. The input-referred
noise voltage density, vnIN, is modeled as a differential input, and
the noise currents, inIN and inIN+, 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. vnCM is the noise voltage density at the VOCM pin. Each
of the four resistors contributes (4kTRx)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
and follow the on-screen prompts.
ADA4940-1/
ADA4940-2
+
RF2
VnOD
VnCM
VOCM
VnIN
RF1
RG2
RG1
VnRF1
VnRF2
VnRG1
VnRG2
inIN+
inIN–
08452-
050
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:
(
)
2
1
N
β
G
+
=
2
is the circuit noise gain.
G1
F1
G1
1
R
β
+
=
and
G2
F2
G2
2
R
β
+
=
are the feedback factors.
When RF1/RG1 = RF2/RG2, then β1 = β2 = β, and the noise gain
becomes
G
F
N
R
β
G
+
=
1
Note that the output noise from VOCM goes to zero in this case.
The total differential output noise density, vnOD, is the root-sum-
square of the individual output noise terms.
∑
=
8
1
i
2
nOi
nOD
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
vnIN
GN
vnO1 = GN (vnIN)
Inverting Input
inIN
inIN × (RG2||RF2)
GN
vnO2 = GN [inIN × (RG2||RF2)]
Noninverting Input
inIN+
inIN+ × (RG1||RF1)
GN
vnO3 = GN [inIN+ × (RG1||RF1)]
VOCM Input
vnCM
GN (β1 β2)
vnO4 = GN (β1 β2)(vnCM)
Gain Resistor RG1
vnRG1
(4kTRG1)1/2
GN (1 β2)
vnO5 = GN (1 β2)(4kTRG1)1/2
Gain Resistor RG2
vnRG2
(4kTRG2)1/2
GN (1 β1)
vnO6 = GN (1 β1)(4kTRG2)1/2
Feedback Resistor RF1
vnRF1
(4kTRF1)1/2
1
vnO7 = (4kTRF1)1/2
Feedback Resistor RF2
vnRF2
(4kTRF2)1/2
1
vnO8 = (4kTRF2)1/2