Discontinuous piecewise-linear discrete-time dynamics - maps with gaps in electronic systems

Purpose - Many important electronic systems are modelled by discrete-time equations with nonlinearities that are discontinuous and piecewise-linear, often arising as a result of quantization. Approximations based on linearization - the standard engineering response to nonlinearity are often quite unhelpful in these systems, because of the form of the nonlinearity. Certain methods and results have been developed over a number of years for the analysis of discontinuous pieewise-linear discrete-time dynamics. The aim of this tutorial paper is to review that body of knowledge, and to show how it can be applied to representative electronic systems. Design/methodology/approach - The paper uses an important electronic circuit the Sigma Delta modulator as a central example, and considers the dynamical behaviour exhibited by this circuit and related circuits. Findings - The circuits under investigation exhibit complex forms of behaviour that can be explained by the application of methods of nonlinear discrete-time dynamics. Originality/value - This paper is intended to provide a brief introduction to the body of research that exists into the behaviour of nonlinear discrete-time circuits and systems with discontinuous piecewise-linear nonlinearities.