Datasheet

MAX4207
Precision Transimpedance Logarithmic
Amplifier with Over 5 Decades of Dynamic Range
10 ______________________________________________________________________________________
Total Error
Total error (TE) is defined as the deviation of the output
voltage, V
LOGV1
, from the ideal transfer function (see
the Transfer Function section):
TE is a combination of the associated gain, input offset
current, input bias current, output offset voltage, and
transfer characteristic nonlinearity (log conformity)
errors:
where V
LC
and V
OSOUT
are the log conformity and out-
put offset voltages, respectively. Output offset is defined
as the offset occurring at the output of the MAX4207
when equal currents are presented to I
LOG
and I
REF
.
Because the MAX4207 is configured with a gain of K =
-0.25V/decade, a 4 should multiply the (±V
LC
±V
OSOUT
)
term, if V
LC
and V
OSOUT
were derived from this default
configuration.
I
BIAS1
and I
BIAS2
are currents in the order of 20pA, sig-
nificantly smaller than I
LOG
and I
REF
, and can therefore
be eliminated:
Expanding this expression:
The first term of this expression is the ideal component
of V
LOGV1
. The remainder of the expression is the TE:
In the second term, one can generally remove the
products relating to ∆K, because ∆K is generally much
less than 1. Hence, a good approximation for TE is
given by:
As an example, consider the following situation:
Full-scale input = 5V
I
LOG
= 100µA
I
REF
= 100nA
K = 1 ±5% V/decade (note that the uncommitted ampli-
fier is configured for a gain of 4)
V
LC
= ±5mV (obtained from the Electrical Characteristics
table)
V
OSOUT
= ±2mV (typ), and T
A
= +25°C.
TE K K
I
I
VV
LOG
REF
LC OSOUT
≅ ±






±± ±
()








∆ log
10
4
TE K K
I
I
KKVV
LOG
REF
LC OSOUT
≅ ±






±+±±
()
∆∆log ( )
10
41
VK
I
I
KK
I
I
KKVV
LOGV
LOG
REF
LOG
REF
LC OSOUT
210 10
41
≅






±






±+±±
()
log log
()
∆
∆
VKK
I
I
VV
LOGV
LOG
REF
LC OSOUT210
14≅ ±






±± ±
()








()log∆
VKK
II
II
VV
LOGV
LOG BIAS
REF BIAS
LC OSOUT210
1
2
14=±






±± ±
()








()log∆
-
-
VVTE
LOGV IDEAL1
=±
IDEAL TRANSFER FUNCTION
WITH VARYING K
MAX4207 fig03
CURRENT RATIO (I
LOG
/I
REF
)
NORMALIZED OUTPUT VOLTAGE (V)
100
1100.10.01
-2
-3
-1
0
1
2
3
4
-4
0.001 1000
V
OUT
= K LOG (I
LOG
/I
REF
)
K = 1
K = 0.5
K = 0.25
K = -0.25
K = -0.5
K = -1
Figure 3. Ideal Transfer Function with Varying K
IDEAL TRANSFER FUNCTION
WITH VARYING I
REF
MAX4207 fig04
I
LOG
(A)
OUTPUT VOLTAGE (V)
100µ
1µ 10µ100n10n
-1.0
-0.5
0
0.5
1.0
1.5
-1.5
1n 1m
K = -0.25
I
REF
= 100µA
I
REF
= 10nA
I
REF
= 1µA
Figure 4. Ideal Transfer Function with Varying I
REF