Normalization and correction of the integral nonlinearity error of an analog-to-digital converter: the advantage of a projective measurement model over a traditional model

The article considers the normalization and correction of the error of analog-to-digital converters taking into account the integral nonlinearity of their conversion function. Integral nonlinearity is a key parameter limiting the accuracy and quality of analog-todigital conversion in modern applications. Linear normalization of the error of an analog-to-digital converter, taking into account only additive and multiplicative components, is insufficient for high-precision systems, where integral nonlinearity plays a significant role.

Currently, there is no generally accepted algorithm for correcting the error of the integral nonlinearity of analog-to-digital converters. Also, there is no unified conversion function that would include linear conversion as a special case and simultaneously take into account the integral nonlinearity. For the normalization and correction of the limiting error band of analog-to-digital converters, it is proposed to use a projective measurement model. It is shown that the integral nonlinearity can be approximated by the nonlinearity of the projective conversion. A distinctive feature of the projective model is its ability to directly account for nonlinearities in conversion characteristics, eliminating their linearization or consideration as sources of error. Unlike the normalization formula in the linear model, the error bandwidth normalization formula corresponding to the projective measurement model accounts for integral nonlinearity as a separate term, hence its terminology as extended. Using examples of the characteristics of real analog-to-digital converters, the advantage of using the projective model over the traditional linear model is demonstrated. The projective model is particularly relevant for correcting the systematic measurement error bandwidth based on the generalized equation of projective measurement conversion, which includes the linear measurement equation as a special case. The results obtained are useful for metrologists, developers of analog-to-digital converters, and measurement systems. 

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