Bias of the independently based gain and offset error in ADC testing using the histogram method

When normally distributed additive noise is present on the test setup, it leads to a bias on the values of estimated gain and offset error of analog-to-digital converters when estimated using the Histogram Test Method. It is shown that the offset estimation is unbiased while the gain estimation can have up to 5% bias for values of signal-tonoise ratio as low as 10 dB. It is also shown that this bias is not dependent on the number of samples acquired. An approximate analytical expression, in closed form, is proposed for rapid estimation of gain error. It considers the signal-to-noise ratio as well as the amount of overdrive used. The analytical derivations made are validated using simulated data using a Monte Carlo procedure. The same procedure is used with experimental data obtained with a real data acquisition system to validate the results obtained.

Automated summary

When there is normally distributed additive noise on the test setup, the Histogram Test Method for estimating the gain and offset error of analog-to-digital converters may result in bias. The study shows that the offset estimation is unbiased, but the gain estimation can have up to 5% bias even at low signal-to-noise ratios of 10 dB. The bias is found to be independent of the number of acquired samples. An approximate analytical expression is proposed for rapidly estimating gain error, taking into account the signal-to-noise ratio and overdrive used. The analytical derivations are validated using simulated data and experimental data obtained with a real data acquisition system.