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 ΣΔ modulator. This consists of going back to the elementary definition of a ΣΔ 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 ΣΔ 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