LOG102 Datasheet, PDF (11/15 Pages) Texas Instruments – LOGARITHMIC AND LOG RATIO AMPLIFIER

DEFINITION OF TERMS
TRANSFER FUNCTION
The ideal transfer function is:
V_OUT = 1V • logI₁/I₂
(5)
Figure 14 shows the graphical representation of the transfer
over valid operating range for the LOG102.
3
2
I 2^{= 1nA}
I
=
2
10nA
1
10nA 100nA 1µA 10µA 100µA 1mA I₁
0
I
= ^100nA
2
I
=
2
1^µA
I 2^{= 10µA}
I
=
2
100^µA
I
=
2
1mA
Dashed Line = Greater
Supply Voltage Requirement
V_OUT = (1V) • LOG
I₁
I₂
–3
FIGURE 14. Transfer Function with Varying I₂ and I₁.
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_OUT = 1V • log(I₁/I₂).
Thus,
V_{OUT (ACTUAL)} = V_{OUT (IDEAL)} ± Total Error.
(5)
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 I₁/I₂ is the largest of the two errors when I₁ and I₂ are
considered separately; and is shown in Table I. Temperature
can affect total error.
I₂
(maximum
error)⁽¹⁾
100nA
(25mV)
1µA
(20mV)
10µA
(25mV)
10nA
(30mV)
I₁ (maximum error)⁽¹⁾
100nA
(25mV)
30mV
25mV
30mV
25mV
30mV
25mV
NOTE: (1) Maximum errors are in parenthesis.
TABLE I. I₁/I₂ and Maximum Errors.
1µA
(20mV)
25mV
20mV
25mV
ERRORS RTO AND RTI
As with any transfer function, errors generated by the func-
tion itself may be Referred-to-Output (RTO) or Referred-to-
Input (RTI). In this respect, log amps have a unique property:
Given some error voltage at the log amp’s output, that error
corresponds to a constant percent of the input regardless of
the actual input level.
LOG CONFORMITY
For the LOG102, log conformity is calculated the same as
linearity and is plotted I₁/I₂ on a semi-log scale. In many
applications, log conformity is the most important specifica-
tion. This is true because bias current errors are negligible
(1pA compared to input currents of 1nA and above) and the
scale factor and offset errors may be trimmed to zero or
removed by system calibration. This leaves log conformity as
the major source of error.
Log conformity is defined as the peak deviation from the best
fit straight line of the V_OUT versus log (I₁/I₂) curve. This is
expressed as a percent of ideal full-scale output. Thus, the
nonlinearity error expressed in volts over m decades is:
V_{OUT (NONLIN)} = 1V/dec • 2Nm V
(6)
where N is the log conformity error, in percent.
INDIVIDUAL ERROR COMPONENTS
The ideal transfer function with current input is:
V_OUT
=
(1V) •
log ^I1
I₂
(7)
The actual transfer function with the major components of
error is:
V_OUT
= (1V) (1± ∆K) log
I₁ – I_B1
I₂ – I_B2
± 2Nm ± V_{OS OUT}
(8)
The individual component of error is:
∆K = gain accuracy (0.3%, 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 (0.04%, 0.15%, typ)
0.04% for n = 5, 0.15% for n = 6
V_{OS OUT} = output offset voltage (1mV, typ)
n = number of decades over which N is specified:
Example: what is the error when
I₁ = 1µA and I₂ = 100nA
(9)
V_OUT
= (1± 0.003) log
10 ^–6
10 ^–7
– 5 • 10^–12
– 5 • 10^–12
± (2)(0.0004) 5 ± 0.3mV
LOG102
SBOS211A
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