AD8139
APPLICATIONS
Voltage Gain
ESTIMATING NOISE, GAIN, AND BANDWIDTH
WITH MATCHED FEEDBACK NETWORKS
The behavior of the node voltages of the single-ended-to-
differential output topology can be deduced from the previous
definitions. Referring to Figure 59, (CF = 0) and setting VIN = 0,
one can write
Estimating Output Noise Voltage
The total output noise is calculated as the root-sum-squared
total of several statistically independent sources. Because the
sources are statistically independent, the contributions of each
must be individually included in the root-sum-square calculation.
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.
VIP −VAP VAP −VON
=
(11)
RG
RF
RG
⎡
⎤
VAN =VAP = VOP
(12)
⎢
⎥
RF + RG
⎣
⎦
Solving the above two equations and setting VIP to Vi gives the
gain relationship for VO, dm/Vi.
Table 6. Recommended Values of Gain-Setting Resistors and
Voltage Noise for Various Closed-Loop Gains
RF
RG
VOP − VON = VO, dm
=
V
(13)
i
3 dB
Total Output
Gain RG (Ω) RF (Ω) Bandwidth (MHz) Noise (nV/√Hz)
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.
1
200
200
200
200
200
400
1 k
400
160
53
5.8
9.3
19.7
37
2
5
10
2 k
26
Feedback Factor Notation
When working with differential amplifiers, it is convenient to
introduce the feedback factor β, which is defined as
The differential output voltage noise contains contributions
from the input voltage noise and input current noise of the
AD8139 as well as those from the external feedback networks.
RG
RF + RG
β =
(14)
The contribution from the input voltage noise spectral density
is computed as
This notation is consistent with conventional feedback analysis
and is very useful, particularly when the two feedback loops are
not matched.
⎛
⎜
⎝
⎞
⎟
⎟
⎠
RF
RG
⎜
Vo_n1 = vn 1+
, or equivalently, vn/β
(7)
Input Common-Mode Voltage
where vn is defined as the input-referred differential voltage
noise. This equation is the same as that of traditional op amps.
The linear range of the VAN and VAP terminals extends to within
approximately 1 V of either supply rail. Because VAN and VAP are
essentially equal to each other, they are both equal to the input
common-mode voltage of the amplifier. 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 59
can be expressed as
The contribution from the input current noise of each input is
computed 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 because the two
input currents are statistically independent processes.
VAN =VAP =VACM
=
RF
RF + RG
(VIP +V )
RG
RF + RG
⎛
⎜
⎞
⎟
⎛
⎜
⎞
⎟
The contribution from each RG is computed as
IN
×
+
×VOCM
(15)
2
⎝
⎠
⎝
⎠
⎛
⎜
⎜
⎝
⎞
⎟
⎟
⎠
RF
RG
Vo_n3 = 4kTRG
(9)
where VACM is the common-mode voltage present at the
amplifier input terminals.
This result can be intuitively viewed as the thermal noise of
each RG multiplied by the magnitude of the differential gain.
Using the β notation, Equation 15 can be written as follows:
V
ACM = βVOCM + (1 − β)VICM
or equivalently,
ACM = VICM + β(VOCM − VICM
(16)
(17)
The contribution from each RF is computed as
Vo_n4 = √4kTRF
(10)
V
)
where VICM is the common-mode voltage of the input signal,
that is, VICM = VIP + VIN/2.
Rev. B | Page 19 of 24
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