Modelling ADC nonlinearity in Monte Carlo procedures for uncertainty estimation

Monte Carlo procedures can be successfully employed to evaluate the uncertainty of measurements performed by digitally processing sampled data, provided that the uncertainties affecting the input samples are modelled correctly. The static nonlinearity is the most difficult error to be modelled, since the technical specifications afforded by the manufacturers of the acquisition systems usually are not sufficient to describe the nonlinearity curve over the entire input range. Thus, suitable assumptions are needed and approximations are unavoidable. This paper focuses on measurements systems based in plug-in data acquisition boards, which are generally based on successive approximation register A/D converters. A behavioural model is presented, according to which the overall nonlinearity is divided into two contributions: a smooth component, responsible for the macroscopic error trend in the output domain, and a component with sudden variation in the scale of values. Theoretical fundamentals of the methods are reported and experimental results highlighting the reliability of the proposed approach are discussed.