Nonlinear Dynamics of Bandpass Sigma-Delta Modulation — An Investigation by Means of the Critical Lines Tool

Bandpass sigma-delta modulation is a technique used to convert high-frequency narrowband electronic signals from analog form to digital, or vice versa. It is a fundamentally nonlinear technique, and therefore can be analyzed only approximately by application of linear analysis. The aim of this work is to present certain results concerning the dynamical behavior of bandpass sigma-delta modulators with zero input based on application of methods of nonlinear dynamics and noninvertible map theory. We will consider the effect of certain circuit imperfections on the behavior of the system, and will also consider the effect of operating in a chaotic regime. While many of our results arise from application of standard methods of nonlinear dynamics, we will emphasize in particular those results that can be obtained by application of the critical lines tool of Mira. The paper, therefore, has two aims: To investigate the nonlinear behavior of bandpass sigma-delta modulators and to provide a demonstration of the applicability of the critical lines tool to a system of engineering importance.