Nonlinear behaviors of bandpass sigma-delta modulators with stable system matrices

Ho, C, Ling, B, Reiss, J and Yu, X 2006, 'Nonlinear behaviors of bandpass sigma-delta modulators with stable system matrices', IEEE Transactions on Circuits and Systems. Part 2: Express Briefs, vol. 53, pp. 1240-1244.


Document type: Journal Article
Collection: Journal Articles

Title Nonlinear behaviors of bandpass sigma-delta modulators with stable system matrices
Author(s) Ho, C
Ling, B
Reiss, J
Yu, X
Year 2006
Journal name IEEE Transactions on Circuits and Systems. Part 2: Express Briefs
Volume number 53
Start page 1240
End page 1244
Total pages 5
Publisher IEEE
Abstract It has been established that a class of bandpass sigma delta modulators (SDMs) may exhibit state space dynamics which are represented by elliptical or fractal patterns confined within trapezoidal regions when the system matrices are marginally stable. It is found that fractal patterns may also be exhibited in the phase plane when the system matrices are strictly stable. This occurs when the sets of initial conditions corresponding to convergent or limit cycle behavior do not cover the whole phase plane. Based on the derived analytical results, some interesting results are found. If the bandpass SDM exhibits periodic output, then the period of the symbolic sequence must equal the limiting period of the state space variables. Second, if the state vector converges to some fixed points on the phase portrait, these fixed points do not depend directly on the initial conditions.
Keyword(s) Dynamics
Chaos
DOI - identifier 10.1109/TCSII.2006.882805
Copyright notice ©2005 IEEE
ISSN 1057-7130
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