A/D converters with midpoint correction

The analog to digital converter (ADC) has been widely used in modern electronic systems and instruments. Characterizing and improving the performances of ADCs has been an active research area for years based on IEEE Standard 1241 (2001), B.E. Peetz et al. (1982), J. Doernberg et al. (1984), G. Chiorboli et al. (1996) and N. Giaquinto et al. (1996). In this paper, we introduce a simple algorithm, namely, the midpoint correction algorithm, to improve the signal to noise ratio (SNR) performance of an ADC with nonlinearity errors. The residual mean square error (MSE) after the application of the midpoint correction algorithm is obtained in closed form. An approximate equation governing the relationship between the residual mean square error of an ADC and the normalized mean square error (MSE_DNL) of the residual differential nonlinearity (DNL) is also derived. It can be shown that MSE ≅ (q²/12)*(1+3*MSE_DNL), where q is the quantization step-size of an ideal ADC. Computer simulation results are also presented to validate the theoretical results.