Datasheet
www.ti.com
LOG102
9
SBOS211B
A
2
A
1
I
1
Q
1
Q
2
V
OUT
= (1V) LOG
I
1
I
2
I
2
I
1
I
2
++
––
R
2
V
OUT
V
L
R
1
V
BE
1
V
BE
2
also
VV
RR
R
I
I
V
RR
R
nV
I
I
OUT
L
OUT
T
=
+
=
=
+
12
1
2
12 1
2
1
1
log
log
Using the base-emitter voltage relationship of matched
bipolar transistors, the LOG102 establishes a logarith-
mic function of input current ratios. Beginning with the
base-emitter voltage defined as
VV
I
I
where V
kT
q
BE T
C
S
T
==ln :
k = Boltzmann’s constant = 1.381 • 10
–23
T = Absolute temperature in degrees Kelvin
q = Electron charge = 1.602 • 10
–19
Coulombs
I
C
= Collector current
I
S
= Reverse saturation current
From the circuit in Figure 11, we see that
VV V
LBE BE
=
12
–
Substituting (1) into (2) yields
VV
I
I
V
I
I
LT
S
T
S
=
1
1
1
2
2
2
ln – ln
If the transistors are matched and isothermal and
V
TI
= V
T2
, then (3) becomes:
VV
I
I
I
I
VV
I
I
and ce
xx
VnV
I
I
LT
SS
LT
LT
=
=
=
=
1
12
1
2
10
1
2
23
ln – ln
ln sin
ln . log
log
where n = 2.3
INSIDE THE LOG102
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(9)
(10)
(11)
FIGURE 11. Simplified Model of Log Amplifier.
(8)
or
It should be noted that the temperature dependance
associated with V
T
= kT/q is internally compensated on
the LOG102 by making R
1
a temperature sensitive resis-
tor with the required positive temperature coefficient.
USING A LARGER REFERENCE VOLTAGE
REDUCES OFFSET ERRORS
Using a larger reference voltage to create the reference
current minimizes errors due to the LOG102’s input offset
voltage. Maintaining an increasing output voltage as a func-
tion of increasing photodiode current is also important in
many optical sensing applications. All zeros from the A/D
converter output represent zero or low scale photodiode
current. Inputting the reference current into I
1
, and designing
I
REF
such that it is as large or larger than the expected
maximum photodiode current is accomplished using this
requirement. The LOG102 configured with the reference
current connecting I
1
and the photodiode current connecting
to I
2
is shown in Figure 12. A
3
is configured as a level shifter
with inverting gain and is used to scale the photodiode
current directly into the A/D input voltage range.
The wide dynamic range of the LOG102 is useful for measuring
avalanche photodiode current (APD) (see Figure 13).