A High-Efficient Algorithm For The Simulation Of Sigma-Delta Modulator

In the integrated circuit design, Sigma-Delta modulators are widely used for high precision data conversion between analog and digital domain. Because of the structure of Sigma-Delta modulators, the simulation has its own special difficulties. General purpose simulation tools are not suitable. They can't meet the needs of high efficiency. To obtain the performance characteristics of modulators, such as Signal-to-Noise, they have to be simulated over tens of thousands of clock cycles. If the structure of modulator is complicated, it takes several hours or even a few days. The simulation is important. The difficulties above bring much probem in the design of high-resolution modulators.The paper studies efficent simulation methods for Sigma-Delta modulators. It describes simplely the principle of Sigma-Delta modulator, summarizes the commonly used simulation methods. Simulation methods for SDMs can be classified to three levals: behavioral, circuit level simulation and transistor level simulation. In this paper, the basic principle and difference of Sigma-Delta modulator about the three levels is given. Circuit level simulation could get a better balance between the accuracy and speed. The main work of the paper is to present the sampled data simulation which allows the analysis of non-ideal in the circuit level simulation. Based on the sampled data simulation of linear circuits, the effect of nonlinear elements can be simulated with iteration. We can improve the accuracy, shorten the time of computation, and then obtain the high accuracy. The detail principle of simulation algorithm is given, including the formulation of circuits, the process of iteration and the numerical inverse Laplace transforms which solve linear networks formulation.Adopting the above algorithm, this paper gives the simulation results of different circuits. The circuits are continues-time Sigma-Delta modulator, switched-capacitor integrators and switched capacitor Sigma-Delta modulators. The experiment results are given in the numerical and graphic forms. At the same time, the MATLAB and SPICE results are compared, indicating the merits of using the simulation method.