Variance of the cumulative histogram of ADCs due to frequency errors

The variance in the number of counts of the cumulative histogram, used for the characterization of analog-to-digital converters (ADCs) with the histogram method, is calculated without any restrictions regarding the magnitude of the frequency errors on the stimulus and sampling signals, number of periods of the stimulus signal, and number of samples. The formulation adopted allows a graphical interpretation of the problem that helps future developments still needed in this particular subject. 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. Numerical simulation and experimental results that validate the theory are shown.