MAX4207 Maxim, MAX4207 Datasheet - Page 10

• Manufacturer Part Number: MAX4207
• Description: The MAX4207 logarithmic amplifier computes the log ratio of an input current relative to a reference current (externally or internally generated) and provides a corresponding voltage output with a default -0
• Manufacturer: Maxim

Precision Transimpedance Logarithmic
Amplifier with Over 5 Decades of Dynamic Range
Figure 3. Ideal Transfer Function with Varying K
Total error (TE) is defined as the deviation of the output
voltage, V
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
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
Because the MAX4207 is configured with a gain of K =
-0.25V/decade, a 4 should multiply the (±V
term, if V
configuration.
I
nificantly smaller than I
be eliminated:
Expanding this expression:
10
BIAS1
V
V
LOGV
LOGV
______________________________________________________________________________________
and I
2
2
LC
=
LC
≅
K
LOGV1
K
(
and V
-3
1
BIAS2
-1
-2
-4
and V
4
3
2
0
(
1
±
1
0.001
±
∆
V
K
∆
OUT
, from the ideal transfer function (see
V
) log
OSOUT
K




are currents in the order of 20pA, sig-
LOGV
0.01
OSOUT
IDEAL TRANSFER FUNCTION
= K LOG (I
) log




CURRENT RATIO (I
10
WITH VARYING K
LOG



10
0.1
1
I
I
LOG
LOG BIAS
are the log conformity and out-
=
REF BIAS
K = -0.25
K = -0.5
K = -1
were derived from this default



V
/I
I
I
LOG
REF
IDEAL
REF
and I
-
1
-
)
I
I
K = 1
K = 0.5
K = 0.25
LOG

 ±

10
REF
2
/I
±
1
REF
4

 ±

TE
(
)
, and can therefore
±
100
4
V
(
LC
±
V
LOG
LC
1000
LC
±
Total Error
V
±
OSOUT
±V
V
and I
OSOUT
OSOUT
REF
)




)




)
.
The first term of this expression is the ideal component
of V
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
I
K = 1 ±5% V/decade (note that the uncommitted ampli-
fier is configured for a gain of 4)
V
table)
V
Figure 4. Ideal Transfer Function with Varying I REF
LOG
REF
LC
OSOUT
TE
LOGV1
= ±5mV (obtained from the Electrical Characteristics
TE
= 100nA
≅ ±
= 100µA
V
LOGV
≅ ±
K K
= ±2mV (typ), and T
∆
. The remainder of the expression is the TE:
K
-0.5
-1.0
-1.5
1.5
1.0
0.5




log
2
0
∆ log
1n
≅
±
K
10
K
4 1
I
REF
K
log



(
IDEAL TRANSFER FUNCTION
10n
= 10nA
I
10
I
LOG
REF
10
+



WITH VARYING I
∆
I



I
100n
LOG
REF
K

 ±

I
I
LOG
REF
)
I
REF
(
±
I
4 1
LOG
= 1µA
V

 ±

K
1µ
A
LC

 ±

(
(A)
= +25°C.
4
+
±
K K
(
10µ
±
∆
∆
V
REF
V
OSOUT
K
I
LC
REF
)
log
K = -0.25
(
100µ
= 100µA
±
±
V
10
V
LC
OSOUT
)



1m
I
±
I
LOG
REF
V
OSOUT



)




)