This paper gives results concerning the measurement of differential and integral nonlinearity of ADC's using the histogram method with a sine wave input Signal. w e specify the amount of overdrive required as a function of the noise level a function of the desired accuracy, the desired confidence level, as to achieve the desired accuracy in individual DNL values with 99% confidence, we expect 1% of the DNL values (or approximately 10 of them) to be out of tolerance. This means Will be measured with an error greater than the and the desired accuracy and the number of samples required as that there is a high probability that the worst DNL and the noise level. An analysis o f the effect on the results of harmonic distortion of the applied signal is given. The error analysis assumes a mixture of coherent and random sampling rather than pure random sampling.
JSA
BACKGROUND AND NOTATIONA . General Notation throughout:The following general notation and definitions will be used N = number of bits of the ADC. The output codes of the ADC are integers between 0 and 2N -1 (inclusive).
T[k]= kth transition level. The voltage level at which the ADC will produce an output code of k -1 or less 50% of the time and an outputof k or more 50% of the time. w [ k ] = T [ k + 1 1 -T[k] = the kth code bin width. v Q The reduced full-scale voltage, V , is the difference between the last and first transition levels and is one code bin width smaller than what is commonly called the full-scale voltage. Additional parameters relating to the ADC depend on the Gain and Offset, which have nonunique definitions. The gain and offset are parameters of a straight-line fit to T[k] versus k , and will have different values depending on how the fit is done. The general relation used to define gain and offset is = T[2N -11 -T[1] = the reduced full-scale voltage = V / ( a N -2) = the average code bin width. of the ADC.G . T [ k ] where G VOS = the offset voltage, nominally 0,= the residual error.= the gain, nominally 1,The fit might be done to minimize the sums of the squares of the residuals, to minimize the maximum residual, to make the residuals zero at the end points, or by some other method. Different methods yield slightly different values for the gain, --. . . IEEE Log Number 9302072.the offset, and the residuals.
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