Datasheet
ADA4939-1/ADA4939-2
Rev. 0 | Page 18 of 24
Table 11. Output Noise Voltage Density Calculations for Matched Feedback Networks
Input Noise Contribution Input Noise Term
Input Noise
Voltage Density
Output
Multiplication Factor
Differential Output 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
F2
) 1 v
nO2
= (i
nIN
)(R
F2
)
Noninverting Input i
nIN
i
nIN
× (R
F1
) 1 v
nO3
= (i
nIN
)(R
F1
)
V
OCM
Input v
nCM
v
nCM
0 v
nO4
= 0
Gain Resistor R
G1
v
nRG1
(4kTR
G1
)
1/2
R
F1
/R
G1
v
nO5
= (R
F1
/R
G1
)(4kTR
G1
)
1/2
Gain Resistor R
G2
v
nRG2
(4kTR
G2
)
1/2
R
F2
/R
G2
v
nO6
= (R
F2
/R
G2
)(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
Table 12. Differential Input, DC-Coupled
Nominal Gain (dB) R
F
(Ω) R
G
(Ω) R
IN, dm
(Ω) Differential Output Noise Density (nV/√Hz)
6 402 200 400 9.7
10 402 127 254 12.4
14 402 80.6 161 16.6
Table 13. Single-Ended Ground-Referenced Input, DC-Coupled, R
S
= 50 Ω
Nominal Gain (dB) R
F
(Ω) R
G1
(Ω) R
T
(Ω) R
IN, cm
(Ω) R
G2
(Ω)
1
Differential Output Noise Density (nV/√Hz)
6 402 200 60.4 301 228 9.1
10 402 127 66.5 205 155 11.1
14 402 80.6 76.8 138 111 13.5
1
R
G2
= R
G1
+ (R
S
||R
T
).
Similar to the case of a 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
RR
R
β
+
=
and
G2
F2
G2
2
RR
R
β
+
=
are the feedback factors.
When the feedback factors are matched, R
F1
/R
G1
= R
F2
/R
G2
, 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
vv
Table 12 and Table 13 list several common gain settings,
associated resistor values, input impedance, and output noise
density for both balanced and unbalanced input configurations.
IMPACT OF MISMATCHES IN THE FEEDBACK
NETWORKS
As previously mentioned, even if the external feedback networks
(R
F
/R
G
) are mismatched, the internal common-mode feedback
loop still forces the outputs to remain balanced. The amplitudes
of the signals at each output remain equal and 180° out of phase.
The input-to-output differential mode gain varies proportionately
to the feedback mismatch, but the output balance is unaffected.
The gain from the V
OCM
pin to V
O, dm
is equal to
2(β1 − β2)/(β1 + β2)
When β1 = β2, this term goes to zero and there is no differential
output voltage due to the voltage on the V
OCM
input (including
noise). The extreme case occurs when one loop is open and the
other has 100% feedback; in this case, the gain from V
OCM
input
to V
O, dm
is either +2 or −2, depending on which loop is closed. The
feedback loops are nominally matched to within 1% in most
applications, and the output noise and offsets due to the V
OCM
input are negligible. If the loops are intentionally mismatched by a
large amount, it is necessary to include the gain term from V
OCM
to V
O, dm
and account for the extra noise. For example, if β1 = 0.5
and β2 = 0.25, the gain from V
OCM
to V
O, dm
is 0.67. If the V
OCM
pin
is set to 2.5 V, a differential offset voltage is present at the output of
(2.5 V)(0.67) = 1.67 V. The differential output noise contribution is
(7.5 nV/√Hz)(0.67) = 5 nV/√Hz. Both of these results are
undesirable in most applications; therefore, it is best to use
nominally matched feedback factors.