LOG101 Datasheet, PDF (9/13 Pages) Burr-Brown (TI) – Precision LOGARITHMIC AND LOG RATIO AMPLIFIER

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.
(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 I₁/I₂ is the largest of the two errors when I₁ and I₂ are
considered separately. Temperature can affect total error.
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.
USING A LARGER REFERENCE VOLTAGE
REDUCES OFFSET ERRORS
Using a larger reference voltage to create the reference
current minimizes errors due to the LOG101’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 LOG101 configured with the reference
current connecting I₁ and the photodiode current connecting
to I₂ is shown in Figure 13. The OPA703 is configured as a
level shifter with inverting gain and is used to scale the
photodiode current directly into the A/D converter input
voltage range.
The wide dynamic range of the LOG101 is also useful for
measuring avalanche photodiode current (APD) (see Figure 14).
LOG CONFORMITY
For the LOG101, 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 because bias current errors are negligible
(5pA compared to input currents of 100pA 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: ₍₇₎
V_OUT(NONLIN) = 1V/dec • 2NmV
where N is the log conformity error, in percent.
INDIVIDUAL ERROR COMPONENTS
The ideal transfer function with current input is:
(8)
V_OUT
=
(1V) •
log ^I1
I₂
The actual transfer function with the major components of
error is:
(9)
V_OUT
= (1V) (1± ∆K) log
I₁ – I_B1
I₂ – I_B2
± 2Nm ± V_{OS O}
I_REF =
V_REF
R₁
I_REF
R₁
V_REF
I_PHOTO
I_MIN to I_MAX
I₁
1
( ) ^VOUT ^{= V}REF ^–
R_{2 • (1V)LOG}
R₃
I_REF
I_PHOTO
C_C
Q₁
Q₂
A₂
A₁
R₂
V_OUT
3
I₂
8
LOG101
6
R₃
OPA703
V_MIN to V_MAX
A/D
Converter
R₂
R₃
FIGURE 13. Technique for Using Full-Scale Reference Current Such that V_OUT Increases with Increasing Photodiode Current.
LOG101
SBOS242B
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