Datasheet
REV. C–10–
AD8011
(error current times the open-loop inverting input resistance) that
results (see Figure 7), a more exact low frequency closed-loop
transfer function can be described as
A
G
GR
T
R
T
G
G
A
R
T
V
I
O
F
OO
F
O
=
+
×
+
=
++11
for noninverting (G is positive).
A
V
O
F
O
G
G
A
R
T
=
++1
1 –
for inverting (G is negative).
where G is the ideal gain as previously described. With R
I
= T
O
/A
O
(open-loop inverting input resistance), the second expression
(positive G) clearly relates to the classical voltage feedback op amp
equation with T
O
omitted due to its relatively much higher value
and thus insignificant effect. A
O
and T
O
are the open-loop dc
voltage and transresistance gains of the amplifier, respectively.
These key transfer variables can be described as
A
Rg
mf
A
g
mc
R
O
=
××
×
12
1
1
|
|
( – )
and
T
RA
O
=
×
12
2
|
|
Therefore
R
g
mc
R
g
mf
I
=
×
×
1
1
2
–
where g
mc
is the positive feedback transconductance (not shown)
and 1/g
mf
is the thermal emitter resistance of devices D1/D2 and
Q3/Q4. The g
mc
× R1 product has a design value that results in a
negative dc open-loop gain of typically –2500 V/V (see Figure 8).
R
S
L
N
T
O
(s)
A
O
(s)
V
P
Z
I
IE
L
I
R
N
C
P
R
F
+V
S
–V
S
L
S
R
L
C
L
V
O
L
S
Z
I
= OPEN LOOP INPUT IMPEDANCE = C
I
|| R
L
Figure 7. Z
I
= Open-Loop Input Impedance
Though atypical of conventional CF or VF amps, this negative
open-loop voltage gain results in an input referred error term
(V
P
–V
O
/G = G/A
O
+ R
F
/T
O
) that will typically be negative for G,
greater than +3/–4. As an example, for G = 10, A
O
= –2500,
and T
O
= 1.2 MΩ, results in an error of –3 mV using the A
V
derivation above.
This analysis assumes perfect current sources and infinite transistor
V
A
s. (Q3, Q4 output conductances are assumed zero.) These
assumptions result in actual versus model open-loop voltage gain
and associated input referred error terms being less accurate for
low gain (G) noninverting operation at the frequencies below the
open-loop pole of the AD8011. This is primarily a result of the
input signal (V
P
) modulating the output conductances of Q3/Q4,
resulting in R
I
less negative than derived here. For inverting
operation, the actual versus model dc error terms are relatively
much less.
1E+03 1E+04 1E+05 1E+06 1E+07 1E+08 1E+09
80
70
60
50
40
20
10
FREQUENCY (Hz)
30
GAIN (dB ⍀)
–90
PHASE (Degrees)
–100
–110
–120
–160
PHASE
GAIN
0
–10
–20
–30
–170
–180
–190
–200
–130
–140
–150
A
O
(s)
Figure 8. Open-Loop Voltage Gain and Phase
AC TRANSFER CHARACTERISTICS
The ac small signal transfer derivations below are based on a
simplified single-pole model. Though inaccurate at frequencies
approaching the closed-loop BW (CLBW) of the AD8011 at low
noninverting external gains, they still provide a fair approxima-
tion and an intuitive understanding of its primary ac small signal
characteristics.
For inverting operation and high noninverting gains, these
transfer equations provide a good approximation to the actual
ac performance of the device.
To accurately quantify the V
O
versus V
P
relationship, A
O
(s)
and T
O
(s) need to be derived. This can be seen by the following
nonexpanded noninverting gain relationship
VsVs
G
G
As
R
Ts
OP
O
F
O
()/ ()
[] []
=
++1
with
As
Rg
mf
A
g
mc
R
S
g
mc
R
O
()
||
–
–
=
××
×
×
12
11
1
11
τ
where R1 is the input resistance to A2/A2B, and τ1 (equal to
CD ⫻ R1 ⫻ A2) is the open-loop dominate time constant,
and
T
s
AR
s
O
()
||
=
×
+
21
2
11τ