AD8137
Data Sheet
Rev. E | Page 24 of 32
The differential output voltage noise contains contributions
from th
e AD8137’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
+
=
G
F
n
R
v
Vo_n
1
, or equivalently, vn/β
(7)
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
( )
F
n R
i
Vo_n =
2
(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.
The contribution from each RG is computed as
=
G
F
G
R
TR
Vo_n
k
4
3
(9)
This result can be intuitively viewed as the thermal noise of
each RG multiplied by the magnitude of the differential gain.
The contribution from each RF is computed as
F
TR
Vo_n
k
4
4 =
(10)
Voltage Gain
The behavior of the node voltages of the single-ended-to-
differential output topology can be deduced from the signal
setting VIN = 0, one can write:
F
ON
AP
G
AP
IP
R
V
R
V
=
(11)
+
=
G
F
G
OP
AP
AN
R
V
(12)
Solving the previous two equations and setting VIP to Vi gives
the gain relationship for VO, dm/Vi.
i
G
F
dm
O,
ON
OP
V
R
V
=
(13)
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.
Feedback Factor Notation
When working with differential drivers, it is convenient to
introduce the feedback factor β, which is defined as
G
F
G
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 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 amplifier’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 64 can be expressed as
VAN = VAP = VACM =
(
)
×
+
+
×
+
OCM
G
F
G
IN
IP
G
F
V
R
V
R
2
(15)
where VACM is the common-mode voltage present at the amplifier
input terminals.
Using the β notation, Equation (15) can be written as
VACM = βVOCM + (1 β)VICM
(16)
or equivalently,
VACM = VICM + β(VOCM VICM)
(17)
where VICM is the common-mode voltage of the input signal,
that is
2
IN
IP
ICM
V
+
≡
For proper operation, the voltages at VAN and VAP must stay
within their respective linear ranges.
Calculating Input Impedance
whether the amplifier is being driven by a single-ended or a
differential signal source. For balanced differential input
signals, the differential input impedance (RIN, dm) is simply
RIN, dm = 2RG
(18)
For a single-ended signal (for example, when VIN is grounded
and the input signal drives VIP), the input impedance becomes
)
(
2
1
F
G
F
G
IN
R
+
=
(19)