GLOBAL STABILITY, LIMIT CYCLES AND CHAOTIC BEHAVIORS OF SECOND ORDER INTERPOLATIVE SIGMA DELTA MODULATORS

Author:

HO CHARLOTTE YUK-FAN1,LING BINGO WING-KUEN2,REISS JOSHUA D.3,YU XINGHUO4

Affiliation:

1. School of Mathematical Sciences, Queen Mary, University of London, Mile End Road, London E1 4NS, United Kingdom

2. School of Engineering, University of Lincoln, Lincoln, Lincolnshire LN6 7TS, United Kingdom

3. Department of Electronic Engineering, Queen Mary, University of London, Mile End Road, London E1 4NS, United Kingdom

4. School of Electrical and Computer Engineering, Royal Melbourne Institute of Technology, GPO Box 2476V, Melbourne, VIC 3001, Australia

Abstract

It is well known that second order lowpass interpolative sigma delta modulators (SDMs) may suffer from instability and limit cycle problems when the magnitudes of the input signals are at large and at intermediate levels, respectively. In order to solve these problems, we propose to replace the second order lowpass interpolative SDMs to a specific class of second order bandpass interpolative SDMs with the natural frequencies of the loop filters very close to zero. The global stability property of this class of second order bandpass interpolative SDMs is characterized and some interesting phenomena are discussed. Besides, conditions for the occurrence of limit cycle and fractal behaviors are also derived, so that these unwanted behaviors will not happen or can be avoided. Moreover, it is found that these bandpass SDMs may exhibit irregular and conical-like chaotic patterns on the phase plane. By utilizing these chaotic behaviors, these bandpass SDMs can achieve higher signal-to-noise ratio (SNR) and tonal suppression than those of the original lowpass SDMs.

Publisher

World Scientific Pub Co Pte Lt

Subject

Applied Mathematics,Modelling and Simulation,Engineering (miscellaneous)

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