Methods for Simulating Continuous Time Delta Sigma Modulators

Abstract

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