AD8139 AD [Analog Devices], AD8139 Datasheet - Page 19

• Manufacturer Part Number: AD8139
• Description: Low Noise Rail-to-Rail Differential ADC Driver
• Manufacturer: AD [Analog Devices]

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
Gain
1
2
5
10
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.
The contribution from the input voltage noise spectral density
is computed as
where v
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
where i
input needs to be treated separately since the two input currents
are statistically independent processes.
The contribution from each R
This result can be intuitively viewed as the thermal noise of
each R
Vo_n
Vo_n =
Vo_n
G
n
n
multiplied by the magnitude of the differential gain.
is defined as the input noise current of one input. Each
is defined as the input-referred differential voltage
R
200
200
200
200
1
3
2
G
=
(Ω)
=
v
i
n
n
4
( )
⎛
⎜
⎝
kTR
R
1
F
+
R
200
400
1 k
2 k
R
R
G
F
(Ω)
F
G
⎛
⎜
⎝
⎞
⎟
⎠
R
R
, or equivalently, v
G
F
⎞
⎟
⎠
G
3 dB
Bandwidth
(MHz)
400
160
53
26
is computed as
n
/β
Total Output
Noise (nV/√Hz)
5.8
9.3
19.7
37
Rev. A | Page 19 of 24
(7)
(8)
(9)
The contribution from each R
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
one can write
Solving the above two equations and setting V
gain relationship for V
An inverting configuration with the same gain magnitude can
be implemented by simply applying the input signal to V
setting V
V
Feedback Factor Notation
When working with differential amplifiers, it is convenient to
introduce the feedback factor β, which is defined as
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
approximately 1 V of either supply rail. Since V
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
can be expressed as
where V
amplifier input terminals.
IN, dm
Vo
V
V
β
V
⎛
⎜
⎝
V
to V
OP
AN
R
AN
IP
=
_
F
ACM
R
IP
−
R
R
−
n
=
=
+
G
O, dm
V
= 0. For a balanced differential input, the gain from
F
F
4
V
V
V
AN
R
R
is the common-mode voltage present at the
AP
+
=
ON
AP
AP
G
G
and V
is also equal to R
R
×
=
=
G
=
=
4
(
kTR
V
V
V
V
V
AP
O,
ACM
IP
OP
AP
dm
R
+
F
2
−
⎡
⎢
⎣
O, dm
for the connection diagram in Figure 57
F
V
V
R
=
=
IN
AN
ON
F
/ V
R
R
R
+
)
G
G
and V
F
⎞
⎟
⎠
i
R
.
V
+
F
G
i
is computed as
F
⎛
⎜
⎝
⎤
⎥
⎦
/ R
R
AP
G
F
R
, where V
terminals extends to within
+
G
F
R
= 0) and setting V
G
×
V
OCM
IN, dm
IP
AN
to V
⎞
⎟
⎠
= V
and V
i
AD8139
gives the
IP
− V
AP
IN
IN
are
and
= 0
IN
(10)
(11)
(12)
(13)
(14)
(15)
.