Datasheet

LOG112, 2112
11
SBOS246D
www.ti.com
also
VV
RR
R
OUT
L
=
+
12
1
(9)
V
RR
R
nV
I
I
OUT
T
=
+
12
1
1
2
log
(10)
or
V V LOG
I
I
OUT
=






(. )05
1
2
(11)
Using the base-emitter voltage relationship of matched
bipolar transistors, the LOG112 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 :
(1)
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 12:
VV V
LBE BE
=
12
–
(2)
Substituting (1) into (2) yields:
VV
I
I
V
I
I
LT
S
T
S
=
1
1
1
2
2
2
ln – ln
(3)
If the transistors are matched and isothermal and
V
TI
= V
T2
, then (3) becomes:
VV
I
I
I
I
LT
SS
=






1
12
ln –ln
(4)
VV
I
I
and ce
LT
= ln sin
1
2
(5)
ln . logxx= 23
10
(6)
VnV
I
I
LT
= log
1
2
(7)
where n = 2.3 (8)
INSIDE THE LOG112
FIGURE 13. Simplified Model of a Log Amplifier.
A
2
A
1
I
1
Q
1
Q
2
I
2
I
1
I
2
++
––
R
2
V
OUT
V
L
R
1
V
BE
1
V
BE
2
V
OUT
= (0.5V)LOG
I
1
I
2






NOTE: R
1
is a metal resistor used to compensate for gain
over temperature.
DEFINITION OF TERMS
TRANSFER FUNCTION
The ideal transfer function is:
V
LOGOUT
= (0.5V)LOG (I
1
/I
2
)
Figure 14 shows the graphical representation of the transfer
over valid operating range for the LOG112 and LOG2112.
ACCURACY
Accuracy considerations for a log ratio amplifier are some-
what more complicated than for other amplifiers. This is
because the transfer function is nonlinear and has two
inputs, each of which can vary over a wide dynamic range.
The accuracy for any combination of inputs is determined
from the total error specification.
TOTAL ERROR
The total error is the deviation (expressed in mV) of the actual
output from the ideal output of V
LOGOUT
= (0.5V)LOG (I
1
/I
2
).
Thus,
V
LOGOUT(ACTUAL)
= V
LOGOUT(IDEAL)
± Total Error (6)
It represents the sum of all the individual components of error
normally associated with the log amp when operated in the
current input mode. The worst-case error for any given ratio
of I
1
/I
2
is the largest of the two errors when I
1
and I
2
are
considered separately. Temperature can affect total error.
FIGURE 14. Transfer Function with Varying I
2
and I
1
.
3.0
3.5
2.0
2.5
1.0
1.5
0.5
0
–3.0
–3.5
–2.0
–2.5
–1.0
–0.5
–1.5
1nA
10nA
100nA
1µA
10
µA
100
µA
1mA
10m
A
100pA
V
OUT
(V)
I
2
= 100pA
I
2
= 1nA
I
2
= 10nA
I
2
=
100nA
I
2
= 1
µA
I
2
= 10
µA
I
2
= 100
µA
I
2
= 1m
A
I
1
V
LOGOUT
= (0.5V)LOG (I
1
/I
2
)