MAX4206
Precision Transimpedance Logarithmic
Amplifier with Over 5 Decades of Dynamic Range
12 ______________________________________________________________________________________
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 Character-
istics table)
V
OSOUT
= ±2mV (typ)
T
A
= +25°C
Substituting into the total error approximation,
TE ≅ ± (1V/decade)(0.05log
10
(100µA/100nA)
±4 (±5mV ±2mV) = ±[0.15V ±4(±7mV)]
As a worst case, one finds TE ≅ ±178mV or ±3.6% of
full scale.
When expressed as a voltage, TE increases in proportion
with an increase in gain as the contributing errors are
defined at a specific gain. Calibration using a look-up
table eliminates the effects of gain and output offset
errors, leaving conformity error as the only factor con-
tributing to total error. For further accuracy, consider tem-
perature monitoring as part of the calibration process.
Applications Information
Input Current Range
Five decades of input current across a 10nA to 1mA
range are acceptable for I
LOG
and I
REF
. The effects of
leakage currents increase as I
LOG
and I
REF
fall below
10nA. Bandwidth decreases at low I
LOG
values (see
the Frequency Response and Noise Considerations
section). As I
LOG
and I
REF
increase to 1mA or higher,
transistors become less logarithmic in nature. The
MAX4206 incorporates leakage current compensation
and high-current correction circuits to compensate for
these errors.
Frequency Compensation
The MAX4206’s frequency response is a function of the
input current magnitude and the selected compensation
network at LOGIIN and REFIIN. The compensation net-
work comprised of C
COMP
and R
COMP
ensures stability
over the specified range of input currents by introducing
an additional pole/zero to the system. For the typical
application, select C
COMP
= 100pF and R
COMP
= 100Ω.
Where high bandwidth at low current is required, C
COMP
= 32pF and R
COMP
= 330Ω are suitable compen-
sation values.
