On the synthesis and optimization of cascaded continuous-time Sigma-Delta modulators

Up to now, there exist two completely different approaches for the synthesis of cascaded CT Sigma-Delta modulators. While the first method is based on a DT prototype and thus on the application of a DT-to-CT transformation, the second one is entirely performed in the CT domain. In this contribution, the method of lifting will be applied to overcome the disadvantages afflicted with the first method (e.g. less ideal anti-aliasing filter performance, increased circuit complexity) and to establish a time efficient DT simulation model for the second method. Thereby, optimal modulator coefficients as well as optimal digital cancellation filters for an arbitrary cascaded CT modulator can be simulated in an efficient and rapid manner. For illustrative purposes, the complete synthesis procedure is demonstrated by the example of a 2-1-1 cascaded CT modulator.