Non-linearities modelling and post-compensation in continuous-time ΣΔ modulators

The authors present a post-compensation technique for continuous-time (CT) ΣΔ modulators based on efficient finite-order Volterra models. At first, the authors develop a behavioural model for a CT sigma–delta modulator (SDM). This model includes non-linear and non-ideal behaviour and leads to a finite Volterra representation of the SDM. Then, they derive and discuss two novel compensation blocks that are special cases of Volterra models. These models, a memory polynomial (MP) and a modified generalised memory polynomial (MGMP), can be interpreted as generalisations of classical block-based non-linear models, like Hammerstein and Wiener systems, respectively. The authors show that the MGMP compensator offers a better distortion cancellation because of the inclusion of cross-terms at the output of the model, at the price of increasing complexity. Simulation results, based on a transistor level circuit model for the SDM, show a good agreement between the SDM and the developed models. In addition, the authors also verify good performance of the proposed compensators.