AD8139
APPLICATIONS
ESTIMATING NOISE, GAIN, AND BANDWIDTH
WITH MATCHED FEEDBACK NETWORKS
The contribution from each RF is computed as
Vo_n4 = 4kTRF
(10)
Estimating Output Noise Voltage
Voltage Gain
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.
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, (CF = 0) and setting VIN = 0
one can write
VIP −VAP
V
AP −VON
RF
=
(11)
(12)
RG
RG
RF + RG
⎡
⎤
Table 6. Recommended Values of Gain-Setting Resistors and
Voltage Noise for Various Closed-Loop Gains
3 dB
VAN =VAP = VOP
⎢
⎥
⎣
⎦
Solving the above two equations and setting VIP to Vi gives the
gain relationship for VO, dm/Vi.
Bandwidth
(MHz)
Total Output
Noise (nV/√Hz)
Gain
RG (Ω)
200
200
200
200
RF (Ω)
200
400
1 k
1
2
5
10
400
160
53
5.8
9.3
19.7
37
RF
RG
VOP − VON = VO, dm
=
V
(13)
i
2 k
26
An inverting configuration with the same gain magnitude can
be implemented by simply applying the input signal to VIN and
setting VIP = 0. For a balanced differential input, the gain from
VIN, dm to VO, dm is also equal to RF/RG, where VIN, dm = VIP − VIN.
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.
Feedback Factor Notation
When working with differential amplifiers, it is convenient to
introduce the feedback factor β, which is defined as
The contribution from the input voltage noise spectral density
is computed as
RG
RF + RG
RF
RG
⎛
⎞
⎟
β =
(14)
Vo_n1 = vn 1+
, or equivalently, v /β
(7)
⎜
n
⎝
⎠
This notation is consistent with conventional feedback analysis
and is very useful, particularly when the two feedback loops are
not matched.
where vn 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
Input Common-Mode Voltage
The linear range of the VAN and VAP terminals extends to within
approximately 1 V of either supply rail. Since VAN and VAP 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 VAN and VAP for the connection diagram in Figure 57
can be expressed as
Vo_n2 = in
(
RF
)
(8)
where in 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 RG is computed as
VAN =VAP =VACM
=
R
RG
⎛
⎜
⎞
⎟
F
Vo_n3 = 4kTRG
(9)
RF
(VIP +V )
RG
RF + RG
⎛
⎜
⎞
⎟
⎛
⎜
⎞
⎟
IN
×
+
×VOCM
(15)
⎝
⎠
RF + RG
2
⎝
⎠
⎝
⎠
This result can be intuitively viewed as the thermal noise of
each RG multiplied by the magnitude of the differential gain.
where VACM is the common-mode voltage present at the
amplifier input terminals.
Rev. A | Page 19 of 24
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