Ho, Yuk-Fan and Ling, Wing-Kuen and Reiss, Joshua . and Yu, Xinghuo (2011) Global stability, limit cycles and chaotic behaviors of second order interpolative sigma delta modulators. International Journal of Bifurcation and Chaos, 21 (6). pp. 1755-1772. ISSN 0218-1274

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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.

Item Type:	Article
Additional Information:	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.
Keywords:	Second order interpolative sigma delta modulators, fractal behavior, limit cycle behavior, chaotic behavior, global stability.
Subjects:	H Engineering > H310 Dynamics
Divisions:	College of Sciences > Faculty of Science > Lincoln School of Engineering
Depositing User:	Wing-Kuen Ling
Date Deposited:	10 Sep 2010 09:12
Last Modified:	13 Mar 2013 08:45
URI:	http://eprints.lincoln.ac.uk/id/eprint/3284

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