Datasheet

AD8137 Data Sheet
Rev. E | Page 24 of 32
The differential output voltage noise contains contributions
from the 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
R
vVo_n 11
, 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
n
RiVo_n =2
(8)
where i
n
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 R
G
is computed as






=
G
F
G
R
R
TRVo_n k43
(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
TRVo_n k44 =
(10)
Voltage Gain
The behavior of the node voltages of the single-ended-to-
differential output topology can be deduced from the signal
definitions and Figure 64. Referring to Figure 64, C
F
= 0 and
setting V
IN
= 0, one can write:
F
ONAP
G
AP
IP
R
VV
R
VV −
=
−
(11)






+
==
G
F
G
OPAPAN
RR
R
VVV
(12)
Solving the previous two equations and setting V
IP
to V
i
gives
the gain relationship for V
O, dm
/V
i
.
i
G
F
dmO,
ONOP
V
R
R
VVV ==−
(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 drivers, it is convenient to
introduce the feedback factor β, which is defined as
G
F
G
RR
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. Because V
AN
and V
AP
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 V
AN
and V
AP
for the connection diagram in Figure 64 can be
expressed as
V
AN
= V
AP
= V
ACM
=
( )








×
+
+








+
×
+
OCM
G
F
GINIP
G
F
F
V
RR
R
VV
RR
R
2
(15)
where V
ACM
is the common-mode voltage present at the amplifier
input terminals.
Using the β notation, Equation (15) can be written as
V
ACM
= βV
OCM
+ (1 − β)V
ICM
(16)
or equivalently,
V
ACM
= V
ICM
+ β(V
OCM
− V
ICM
) (17)
where V
ICM
is the common-mode voltage of the input signal,
that is
2
INIP
ICM
VV
V
+
≡
For proper operation, the voltages at V
AN
and V
AP
must stay
within their respective linear ranges.
Calculating Input Impedance
The input impedance of the circuit in Figure 64 depends on
whether the amplifier is being driven by a single-ended or a
differential signal source. For balanced differential input
signals, the differential input impedance (R
IN, dm
) is simply
R
IN, dm
= 2R
G
(18)
For a single-ended signal (for example, when V
IN
is grounded
and the input signal drives V
IP
), the input impedance becomes
)(2
1
F
G
F
G
IN
RR
R
R
R
+
−
=
(19)