A comparison of simulation methods for continuous time sigma delta modulators

Abstract

Continuous time (CT) sigma delta modulators are mixed signal systems that are commonly simulated at a system level using SPICE macro modeling, solving differential equations, implementing difference equations based on impulse invariance and using Simulink. In this paper, the delta transform (forward Euler method), the bilinear transform (trapezoidal rule), the midpoint integration method, a variation on the use of impulse invariance and Simpson's rule are used to determine difference equations which are used to simulate CT sigma delta modulators. The accuracy and speed of these methods are compared to Simulink models of CT sigma delta modulators with respect to the modulator's signal to quantization noise ratio and the elapsed time of each simulation.