Nonlinear-Stability Analysis of Higher Order Δ–Σ Modulators for DC and Sinusoidal Inputs

Article

Lota, J., Al-Janabi, Mohammed and Kale, Izzet 2008. Nonlinear-Stability Analysis of Higher Order Δ–Σ Modulators for DC and Sinusoidal Inputs. IEEE Transactions on Instrumentation and Measurement. 57 (3), pp. 530-542.
AuthorsLota, J., Al-Janabi, Mohammed and Kale, Izzet
Abstract

Abstract—The present work that exists on predicting the stability of Δ–Σ modulators is confined to DC input signals and unity quantizer gains. This poses a limitation for numerous Δ–Σ modulator applications. The proposed research work gives the stability curves for DC, sine, and dual sinusoidal inputs for any value of the quantizer gain. The maximum stable input limits for third-, fourth-, and fifth-order Chebyshev-Type-II-based Δ–Σ modulators are established using the describing-function method for DC and sinusoidal inputs. Closed-form mathematical expressions for the gains of the quantizer for higher order Δ–Σ modulators whose inputs are two concurrent sinusoids are derived from first principles. The derived stability curves are shown to agree reasonably well with the simulation results for different types of input signals and amplitudes.

KeywordsDC and sinusoidal inputs; nonlinear; quantizer gain; stability; Δ–Σ modulators
JournalIEEE Transactions on Instrumentation and Measurement
Journal citation57 (3), pp. 530-542
ISSN0018-9456
Year2008
PublisherIEEE
Publisher's version
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CC BY-ND
Web address (URL)http://dx.doi.org/10.1109/TIM.2007.911640
Publication dates
PrintMar 2008
Publication process dates
Deposited11 Oct 2009
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Citation:
Lota, J. Al-Janabi, M., Kale, I. (2008) ‘Nonlinear-Stability Analysis of Higher Order Δ–Σ Modulators for DC and Sinusoidal Inputs’ IEEE Transactions on Instrumentation and Measurement 57 (3) 530-542.

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