LOG102 Datasheet, PDF (9/15 Pages) Texas Instruments – LOGARITHMIC AND LOG RATIO AMPLIFIER

INSIDE THE LOG102
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
V_BE
=
V_T
ln
I_C
I_S
where :
V_T
=
kT
q
(1)
k = Boltzman’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
V_L = V_BE1 – V_BE2
(2)
Substituting (1) into (2) yields
V_L
=
V_T1
ln
I₁
I_S1
– V_T2
ln ^{I 2}
I_S2
(3)
If the transistors are matched and isothermal and
V_TI = V_T2, then (3) becomes:
V_L
=
V_T1

^ln

I₁
I_S
–
ln
I₂
I_S



(4)
V_L
=
V_T
ln ^I1
I₂
and since
(5)
ln x = 2.3 log₁₀ x
(6)
V_L
=
n
V_T
log ^I1
I₂
(7)
where n = 2.3
(8)
also
V_OUT
=
V_L
R₁ + R₂
R1
(9)
= log ^I1
(10)
I₂
or
V_OUT
=
R₁ + R₂
R1
n
V_T
log
I₁
I₂
(11)
I₁
I₁
Q_{1 –}
– ^Q2
+
+
V_BE1 V_BE2
I₂
A₂
V_OUT
A₁
V_OUT = (1V) LOG
I₁
I₂
R₂
I₂
V_L
R₁
FIGURE 11. Simplified Model of Log Amplifier.
It should be noted that the temperature dependance
associated with V_T = kT/q is internally compensated on
the LOG102 by making R₁ 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 I₁, 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 I₁ and the photodiode current connecting
to I₂ is shown in Figure 12. A₃ 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).
LOG102
SBOS211A
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