LOG104_14 Datasheet, PDF (10/15 Pages) Texas Instruments – LOGARITHMIC AND LOG RATIO AMPLIFIER

INDIVIDUAL ERROR COMPONENTS
The ideal transfer function with current input is:
V_OUT
=
(0.5V) •
log ^I1
I₂
(8)
The actual transfer function with the major components of
error is:
V_OUT
= (0.5V) (1± ∆K) log
I₁ – I_B1
I₂ – I_B2
± Nm ± V_{OS O}
(9)
The individual component of error is:
∆K = gain accuracy (0.15%, typ), as specified in
specification table.
I_B1 = bias current of A₁ (5pA, typ)
I_B2 = bias current of A₂ (5pA, typ)
N = log conformity error (0.01%, 0.06%, typ)
0.01% for n = 5, 0.06% for n = 7.5
V_OSO = output offset voltage (3mV, typ)
m = number of decades over which N is specified:
Example: what is the error when
I₁ = 1µA and I₂ = 100nA
(10)
V_OUT
=
(0.5
±
0.0015)
log
10 ^−6
10 ^−7
− 5 • 10^−12
− 5 • 10^−12
± (2)(0.0001)5 ± 3.0mV
= 0.5055V
(11)
Since the ideal output is 0.5V, the error as a percent of
reading is
% error = ^0.5055 • 100% = 1.1%
0.5
(12)
For the case of voltage inputs, the actual transfer function is
( ) ( ) V_OUT =
0.5V
1± ∆K log
V₁
R₁
– I_B1
±
E_OS1
R₁
V₂
R₂
– I_B2
± ^EOS2
R₂
± Nm ± V_OSO
(13)
Where
E_{OS1 and} E_OS2
R₁
R₂
are considered to be zero for large
values of resistance from external input current sources.
10
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LOG104
SBOS243C