
AD8139
APPLICATIONS
ESTIMATING NOISE, GAIN, AND BANDWIDTH
WITH MATCHED FEEDBACK NETWORKS
Estimating Output Noise Voltage
The total output noise is calculated as the root-sum-squared
total of several statistically independent sources. Since the
sources are statistically independent, the contributions of each
must be individually included in the root-sum-square calcula-
tion. Table 6 lists recommended resistor values and estimates of
bandwidth and output differential voltage noise for various
closed-loop gains. For most applications, 1% resistors are
sufficient.
Table 6. Recommended Values of Gain-Setting Resistors and
Voltage Noise for Various Closed-Loop Gains
3 dB
Bandwidth
(MHz)
1
200
200
400
2
200
400
160
5
200
1 k
53
10
200
2 k
26
The differential output voltage noise contains contributions
from the AD8139’s input voltage noise and input current noise
as well as those from the external feedback networks.
Rev. A | Page 19 of 24
Gain
R
G
()
R
F
()
Total Output
Noise (nV/√Hz)
5.8
9.3
19.7
37
The contribution from the input voltage noise spectral density
is computed as
+
=
G
F
n
R
R
v
Vo_n
1
, or equivalently, v
n
/β
(7)
where
v
n
is defined as the input-referred differential voltage
noise. This equation is the same as that of traditional op amps.
The contribution from the input current noise of each input is
computed as
(
)
F
i
Vo_n
=
2
n
R
(8)
where
i
n
is defined as the input noise current of one input. Each
input needs to be treated separately since the two input currents
are statistically independent processes.
The contribution from each
R
G
is computed as
=
G
F
G
R
R
kTR
Vo_n
4
3
(9)
This result can be intuitively viewed as the thermal noise of
each
R
G
multiplied by the magnitude of the differential gain.
The contribution from each
R
F
is computed as
F
kTR
n
Vo
4
4
_
=
(10)
Voltage Gain
The behavior of the node voltages of the single-ended-to-
differential output topology can be deduced from the previous
definitions. Referring to Figure 57, (C
F
= 0) and setting
V
IN
= 0
one can write
F
ON
AP
G
AP
IP
R
V
V
R
V
V
=
(11)
+
=
=
G
F
G
OP
AP
AN
R
R
R
V
V
V
(12)
Solving the above two equations and setting
V
IP
to
V
i
gives the
gain relationship for
V
O, dm
/
V
i
.
i
G
F
dm
O,
ON
OP
V
R
R
V
V
V
=
=
(13)
An inverting configuration with the same gain magnitude can
be implemented by simply applying the input signal to V
IN
and
setting V
IP
= 0. For a balanced differential input, the gain from
V
IN, dm
to
V
O, dm
is also equal to
R
F
/
R
G
, where V
IN, dm
=
V
IP
V
IN
.
Feedback Factor Notation
When working with differential amplifiers, it is convenient to
introduce the feedback factor β, which is defined as
G
F
G
R
R
R
+
=
β
(14)
This notation is consistent with conventional feedback analysis
and is very useful, particularly when the two feedback loops are
not matched.
Input Common-Mode Voltage
The linear range of the V
AN
and V
AP
terminals extends to within
approximately 1 V of either supply rail. Since V
AN
and V
AP
are
essentially equal to each other, they are both equal to the ampli-
fier’s input common-mode voltage. Their range is indicated in
the Specifications tables as input common-mode range. The
voltage at V
AN
and V
AP
for the connection diagram in Figure 57
can be expressed as
=
=
=
ACM
V
V
(
AP
AN
V
V
×
+
+
+
2
×
+
OCM
V
G
F
G
IN
IP
G
F
F
R
R
R
V
R
R
R
)
(15)
where
V
ACM
is the common-mode voltage present at the
amplifier input terminals.