Datasheet

AD8571/AD8572/AD8574
Rev. E | Page 15 of 24
AUTO-ZERO PHASE
In this phase, all ΦA
X
switches are closed, and all ΦB switches
are open. Here, the nulling amplifier is taken out of the gain
loop by shorting its two inputs together. Of course, there is a
degree of offset voltage, shown as V
OSA
, inherent in the nulling
amplifier, that maintains a potential difference between the +IN
and −IN inputs. The nulling amplifier feedback loop is closed
through ΦA
2
, and V
OSA
appears at the output of the nulling
amplifier and on C
M1
, an internal capacitor in the AD857x.
Mathematically, this can be expressed in the time domain as
V
OA
[t] = A
A
V
OSA
[t] − B
A
V
OA
[t] (1)
This can also be expressed as
[]
[]
A
OSAA
OA
B
tVA
tV
+
=
1
(2)
The previous equations show that the offset voltage of the nulling
amplifier times a gain factor appears at the output of the nulling
amplifier and thus on the C
M1
capacitor.
AMPLIFICATION PHASE
When the ΦB switches close and the ΦA
X
switches open for
the amplification phase, the offset voltage remains on CM1 and
essentially corrects any error from the nulling amplifier. The
voltage across C
M1
is designated as V
NA
. The potential difference
between the two inputs to the primary amplifier is designated as
V
IN
, or V
IN
= (V
IN+
− V
IN−
). The output of the nulling amplifier
can then be expressed as
V
OA
[t] = A
A
(V
IN
[t] − V
OSA
[t]) − B
A
V
NA
[t] (3)
Because ΦA
X
is now open and there is no place for C
M1
to
discharge, the voltage (V
NA
) at the present time (t) is equal to
the voltage at the output of the nulling amp (V
OA
) at the time when
ΦA
X
is closed. If the period of the autocorrection switching
frequency is designated as T
S
, the amplifier switches between
phases every 0.5 × T
S
. Therefore, in the amplification phase
[]
⎥
⎦
⎤
⎢
⎣
⎡
−=
SNANA
TtVtV
2
1
(4)
and substituting Equation 4 and Equation 2 into Equation 3 yields
[] [] []
A
SOSAAA
OSAA
IN
AOA
B
TtVBA
tVAtVAtV
+
⎥
⎦
⎤
⎢
⎣
⎡
−
−+=
1
2
1
(5)
For the sake of simplification, it can be assumed that the auto-
correction frequency is much faster than any potential change
in V
OSA
or V
OSB
. This is a good assumption because changes in
offset voltage are a function of temperature variation or long-
term wear time, both of which are much slower than the
auto-zero clock frequency of the AD857x, which effectively
makes the V
OS
time invariant, and Equation 5 can be rewritten as
[] []
(
)
A
OSAAAOSAAA
IN
AOA
B
VBAVBA
tVAtV
+
−
+
+=
1
1
(6)
or
[] []
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
+
+=
A
OSA
IN
AOA
B
V
tVAtV
1
(7)
Here, the auto-zeroing becomes apparent. Note that the V
OS
term is reduced by a factor of 1 + B
A
, which shows how the
nulling amplifier has greatly reduced its own offset voltage error
even before correcting the primary amplifier. Therefore, the
primary amplifier output voltage is the voltage at the output of the
AD857x amplifier. It is equal to
V
OUT
[t] = A
B
(V
IN
[t] + V
OSB
) + B
B
V
NB
(8)
In the amplification phase, V
OA
= V
NB
, so this can be rewritten as
[
]
[] []
⎥
⎥
⎦
⎤
⎢
⎢
⎣
⎡
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
+
+++
=
A
OSA
IN
A
B
OSB
BINB
OUT
B
V
tVABVAtVA
tV
1
(9)
Combining terms yield
[
]
[]
()
OSB
B
A
OSA
B
A
B
A
BIN
OUT
VA
B
VBA
BAAtV
tV
+
+
++
=
1
(10)
The AD857x architecture is optimized in such a way that
A
A
= A
B
, B
A
= B
B
, and B
A
>> 1. In addition, the gain product to
A
A
B
B
is much greater than A
B
. Therefore, Equation 10 can be
simplified to
V
OUT
[t] = V
IN
[t]A
A
B
A
+ A
A
(V
OSA
+ V
OSB
) (11)
Most obvious is the gain product of both the primary and nulling
amplifiers. This A
A
B
A
term is what gives the AD857x its extremely
high open-loop gain. To understand how V
OSA
and V
OSB
relate to
the overall effective input offset voltage of the complete amplifier,
set up the generic amplifier equation of
V
OUT
= k × (V
IN
+ V
OS, EFF
) (12)
where:
k is the open-loop gain of an amplifier.
V
OS, EFF
is its effective offset voltage.
Putting Equation 12 into the form of Equation 11 gives
V
OUT
[t] = V
IN
[t]A
A
B
A
+ V
OS, EFF
A
A
B
A
(13)