7.1.1.1 Logarithmic Conformity Error

The LOG200 current-input logarithmic conversions, as well as the input and gain resistors of the LOG200

output-stage difference amplifier, have some inherent mismatches (both initially and across temperature) that

appear as errors at the system level. These errors are subdivided into three categories: offset error, gain or

scaling factor error, and logarithmic or log conformity error (LCE). The LCE is a nonlinear error that is measured

after the offset and gain errors have been calibrated, and is similar in many ways to the integrated nonlinearity

error of an ADC or DAC. The LCE describes the difference between the expected value and measured value

due to random nonideal behavior within the device. The LCE is defined in one of two possible ways: either as an

immediate error (with units of volts) or as a maximum error envelope (expressed as a percentage). Typically, a

plot of input current or logarithmic current (logarithmic scale) vs output voltage (linear scale) is used for the data

set, as in Figure 7-3.

I1 Input Current ( A)

0.01

0.1

1

10

100

1000

10000

-0.6

-0.3

0

0.3

0.6

0.9

1.2

Figure 7-3. OUTA Voltage vs I1 Input Current

First, a best-fit line is established to describe the device transfer function. The slope of this line as compared

to the nominal scaling factor, K, establishes the scaling factor error, and the intercept of the line establishes the

offset error. Next, the difference of the measured device output as compared to the point on the best-fit line

is calculated for a given input condition (point on the X axis). For any given point, the result is the immediate

logarithmic conformity error, and the value differs depending on the data range across that the best-fit line was

established. For example, at high input currents, the LOG200 experiences self-heating due to the increased

power dissipation through parasitic resistances, and these thermal effects result in higher apparent LCE within

the 100µA to 10mA current range than is measured within the 10nA to 100µA current range.

I1 Input Current ( A)

0.01

0.1

1

10

100

1000

10000

-4

-2

0

2

4

6

8

Figure 7-4. Logarithmic Conformity Error vs I1 Input Current

Individually calculating the LCE for every possible input condition is not practical. The LCE expressed as an

error envelope is more useful to circuit designers. This calculation conveys the maximum LCE expected across

a given input range as a percentage of the expected full-scale output voltage. The calculation involves iterating

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LOG200

SBOSA28A – AUGUST 2023 – REVISED DECEMBER 2024

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