LOG100 Datasheet, PDF (5/9 Pages) Burr-Brown (TI) – Precision LOGARITHMIC AND LOG RATIO AMPLIFIER

THEORY OF OPERATION
The base-emitter voltage of a bipolar transistor is
V_BE = V_T l n
I_C
I_S
KT
where: V_T = _q
(1)
K = Boltzman’s constant = 1.381 x 10^–23
T = Absolute temperature in degrees Kelvin
q = Electron charge = 1.602 x 10^–19 Coulombs
I_C = Collector current
I_S = Reverse saturation current
From the circuit in Figure 1, we see that
V_OUT' = V_BE1 – V_BE2
(2)
Substituting (1) into (2) yields
V_OUT' = V_T1 l n
I₁
I_S1
– V_T2
ln
I₁
I_S2
(3)
If the transistors are matched and isothermal and V_T1 = V_T2,
then (3) becomes:
V_OUT' = V_T [ l n
I_{1 – l n}
I_S
I_{2 ]}
I
S
(4)
V_OUT' = V_T ln
I₁
I
and since
(5)
2
ln x = 2.3 log₁₀ x
(6)
I
V_OUT' = n V_T log
1
I
(7)
2
where n = 2.3
(8)
also
V_OUT = V_OUT'
R₁ + R₂
R₁
(9)
=
R₁ + R₂
R
n V_T log
I₁
I
(10)
or
1
2
V_OUT = K log
I₁
I₂
(11)
It should be noted that the temperature dependance associ-
ated with V_T = KT/q is compensated by making R₁ a
temperature sensitive resistor with the required positive
temperature coefficient.
DEFINITION OF TERMS
TRANSFER FUNCTION
The ideal transfer function is V_OUT = K log
I₁
I
where:
2
K = the scale factor with units of volts/decade
I₁ = numerator input current
I₂ = denominator input current.
ACCURACY
Accuracy considerations for a log ratio amplifier are some-
what more complicated than for other amplifiers. The reason
is that 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.
10
K=5
K=3
8
6
4
K=1
2
1nA 10nA 100nA
I₁
0
1µA 10µA 100µA 1mA
–2
–4
–6
V_OUT = K LOG
I₁
I₂
–8
I₂ = 1µA
–10
Fixed value of I₂.
FIGURE 2. Transfer Function with Varying K and I₁.
I₁
I₁
Q_{1 –}
– ^Q2
+
+
V_BE1 V_BE2
I₂
A₂
V_OUT
A₁
V_OUT = K LOG
I₁
I₂
R₂
I₂
V_OUT
R₁
FIGURE 1. Simplified Model of Log Amplifier.
10
I₂ = 10nA
I₂ = 1µA
8
6
4
I₂ = 100µA
2
1nA 10nA 100nA 1µA 10µA 100µA 1mA I₁
0
–2
–4
–6
V_OUT = K LOG
I₁
I₂
K=3
–8
Fixed value of K.
–10
FIGURE 3. Transfer Function with Varying I and I .
2
1
®
5
LOG100