Accurate Time-Domain Simulation of Continuous-Time Sigma-Delta Modulators

In this paper we present a methodology for the simulation of continuous-time sigma-delta converters. This method, based on a fixed-step algorithm, permits not only a time-domain simulation of the modulator output but also the simulation of intermediary signals. The method is based on the discretization of the continuous-time models and the use of a discrete simulator such as Simulink, which is more efficient than an analog simulator. By using filters with a sampling frequency higher than the modulator output frequency, the model can simulate input signals with a bandwidth which is higher than half the modulator sampling frequency. The transformation is exact in terms of Noise Transfer Function and asymptotically exact in terms of Signal Transfer Function (the Transfer Function from the modulator input to each stage filter output rapidly tends to the continuous-time model transfer function when the number of steps increases).