Datasheet
MAX4206
Precision Transimpedance Logarithmic
Amplifier with Over 5 Decades of Dynamic Range
10 ______________________________________________________________________________________
Detailed Description
Theory
Figure 2 shows a simplified model of a logarithmic
amplifier. Two transistors convert the currents applied
at LOGIIN and REFIIN to logarithmic voltages accord-
ing to the following equation:
where:
V
BE
= base-emitter voltage of a bipolar transistor
k = 1.381 x 10
-23
J/K
T = absolute temperature (K)
q = 1.602 x 10
–19
C
I
C
= collector current
I
S
= reverse saturation current
The logarithmic amplifier compares V
BE1
to the refer-
ence voltage V
BE2
, which is a logarithmic voltage for a
known reference current, I
REF
. The temperature depen-
dencies of a logarithmic amplifier relate to the thermal
voltage, (kT/q), and I
S
. Matched transistors eliminate
the I
S
temperature dependence of the amplifier in the
following manner:
VVV
kT
q
I
I
kT
q
I
I
kT
q
I
I
I
I
kT
q
I
I
OUT BE BE
LOG
S
REF
S
LOG
S
REF
S
LOG
REF
= −
=
−
=
−
=
12
ln ln
ln ln
ln
=
()
=×
kT
q
I
I
K
I
I
see Figure
LOG
REF
LOG
REF
ln( ) log
log ( )
10
3
10
10
V
kT
q
I
I
BE
C
S
=
ln
MAX4206
LOGIIN
CMVIN
V
CC
REFIIN
V
CC
CURRENT
CORRECTION
V
CC
LOGV1
SCALE
OSADJ
LOGV2
V
CC
V
CC
REFISET
CURRENT MIRROR
CMVOUTREFVOUT
REFIOUT
GND
V
EE
0.5V
1.238V
V
EE
V
EE
SUMMING
AMPLIFIER
AND
TEMPERATURE
COMPENSATION
Figure 1. Functional Diagram