Representation of sigma-delta modulators as continuous systems for analysis of their effect on chaotic signals

Gary Ushaw; S. McLaughlin; David Thomas Hughes; Bernard Mulgrew

doi:10.1117/12.162668

18 November 1993 Representation of sigma-delta modulators as continuous systems for analysis of their effect on chaotic signals

Gary Ushaw, S. McLaughlin, David Thomas Hughes, Bernard Mulgrew

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Proceedings Volume 2038, Chaos in Communications; (1993) https://doi.org/10.1117/12.162668
Event: SPIE's 1993 International Symposium on Optics, Imaging, and Instrumentation, 1993, San Diego, CA, United States

Abstract

Sigma-Delta Modulation ((Sigma) (Delta) M) has attracted a great deal of interest as a method of analogue to digital conversion (ADC). This paper introduces a method of analysis for (Sigma) (Delta) M based on replacing the non-linear quantizer with a continuous element. Conventionally, analysis of sigma-delta modulation has been in the discrete domain, often treating the quantizer as a simple additive noise source, which has led to limited success in understanding the processes involved. However, the only truly discrete element in the circuit is the quantizer so if this could be represented accurately enough as a continuous element then a new form of analysis may be possible. A representation of the one-bit quantizer as a hyperbolic tangent function with a sufficiently steep gradient in the crossover region is proposed.

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Gary Ushaw, S. McLaughlin, David Thomas Hughes, and Bernard Mulgrew "Representation of sigma-delta modulators as continuous systems for analysis of their effect on chaotic signals", Proc. SPIE 2038, Chaos in Communications, (18 November 1993); https://doi.org/10.1117/12.162668

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