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 8-3.

10 nA to 100 µA

Figure 8-3 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 100-µA to 10-mA current range than is measured within the 10-nA to 100-µA current range.

10 nA to 100 µA

Figure 8-4 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 across a set of all measured immediate LCE values for a given range. The difference of the maximum and minimum values is then halved and normalized with a division by the output voltage span of the measurement (the difference of the maximum output voltage and minimum output voltage, typically at the two endpoints of the data set), to express LCE as a percentage of the full-scale range:

The LCE envelope can then be expressed in dB through the following relationship, where the factor of 20 is associated with amplitude. For expression in terms of optical power, this factor is 10.