Digital inversion of nonlinear deterministic characteristics of ΣΔ modulators: a mapping approach

We give a general approach to the problem of digital inversion of nonlinear deterministic characteristics in a /spl Sigma//spl Delta/ modulator. This consists of going back to the elementary definition of a /spl Sigma//spl Delta/ modulator as a mapping. The difficulty of this approach is that this inversion leads to a whole set of solutions. However, it turns out that the output in an ideal /spl Sigma//spl Delta/ modulator coincides with the geometric center of this set. While this is no longer the case in the presence of nonlinear analog imperfections, a general scheme for their digital compensation can be defined by systematically providing as final output the true geometric center of the set. As a preliminary validation, we show the remarkable efficiency of this general correction scheme in the case of static ADC-DAC deviations.