Influence of Frequency Errors in the Variance of the Cumulative Histogram

Abstract—In this paper, the calculation of the variance in the number of counts of the cumulative histogram used for the char-acterization of analog-to-digital converters (ADCs) with the his-togram method is presented. All cases of frequency error, number of periods of the stimulus signal, and number of samples are con-sidered, making this approach more general than the traditional one, used by the IEEE 1057-1994 standard, where only a limited frequency-error range is considered, leading to a value of 0.2 for the variance. Furthermore, this value is an average over all cumu-lative histogram bins, instead of a worst-case value, leading to an underestimation of the variance for some of those bins. The exact knowledge of this variance allows for a more efficient test of ADCs and a more precise determination of the uncertainty of the test result. This calculation was achieved by determining the dependence of the number of counts on the sample phases, on the transition voltage between codes, and on the stimulus signal phase. Index Terms—ADC test, analog–digital conversion, frequency error, histogram