Stability analysis of the second order ΣΔ modulator

Steiner, Philip; Yang, Wei

doi:10.1109/iscas.1994.409383

Cited by 14 publications

(11 citation statements)

References 4 publications

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“…Experimentation with the variable-input positively invariant set algorithm [21] yielded results which are in accordance with observations made by other researchers [22], namely that if the input range is too broad, the modulator is not stable and positively invariant sets do not exist. Fig.…”

Section: Time-varying Input-resultssupporting

confidence: 89%

An algorithm for computing convex positively invariant sets for delta-sigma modulators

Schreier¹,

Goodson²,

Zhang³

1997

IEEE Trans. Circuits Syst. I

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Computational geometry is used to locate convex positively invariant sets for delta-sigma modulators. The existence of a positively invariant set implies the stability of the modulator and yields rigorous state bounds. Convex positively invariant sets for single-bit modulators up to order four, with a restricted class of time-varying inputs, have been found. MAT-LAB code implementing the proposed algorithm is available from ftp: //next242.ece.orst.edu/pub/delsig.tar.Z.

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Section: Time-varying Input-resultssupporting

confidence: 89%

An algorithm for computing convex positively invariant sets for delta-sigma modulators

Schreier¹,

Goodson²,

Zhang³

1997

IEEE Trans. Circuits Syst. I

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“…One technique is to model the quantizer as a threshold function in the state equations, which gets complicated for higher-order Δ-Σ modulators and is limited to 1 st -and 2 nd -order Δ-Σ modulators [1]. Another approach to simplify the analysis has been to assume a DC input to the Δ-Σ modulator [2]- [7]. In [8], separate signal and quantization noise nonlinear gains have been used for the stability analysis of 2 nd -and 3 rd -order Δ-Σ modulators for DC and sinusoidal inputs using the root locus approach.…”

Section: A Literature Review-limitations Of Existing Approachesmentioning

confidence: 99%

Nonlinear Stability Prediction of Multibit Delta–Sigma Modulators for Sinusoidal Inputs

Lota

Al-Janabi

Kale

2014

IEEE Trans. Instrum. Meas.

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“…One technique is to model the quantizer as a threshold function in the state equations. The analysis, however, gets complicated for higher order ∆-Σ modulators and has therefore been limited to the first-and second-order ∆-Σ modulators [1]- [4]. For higher order ∆-Σ modulators, linearized modeling is a method that has been found to be useful for performance analysis [5], [6], [8], wherein the 1-bit quantizer is modeled as a linear gain and an additive noise source.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear-Stability Analysis of Higher Order $\Delta$ –$\Sigma$ Modulators for DC and Sinusoidal Inputs

Lota

Al-Janabi

Kale

2008

IEEE Trans. Instrum. Meas.

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Abstract-The present work that exists on predicting the stability of ∆-Σ modulators is confined to DC input signals and unity quantizer gains. This poses a limitation for numerous ∆-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 ∆-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 ∆-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.Index Terms-DC and sinusoidal inputs, nonlinear, quantizer gain, stability, ∆-Σ modulators.

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Stability analysis of the second order ΣΔ modulator

Cited by 14 publications

References 4 publications

An algorithm for computing convex positively invariant sets for delta-sigma modulators

An algorithm for computing convex positively invariant sets for delta-sigma modulators

Nonlinear Stability Prediction of Multibit Delta–Sigma Modulators for Sinusoidal Inputs

Nonlinear-Stability Analysis of Higher Order $\Delta$ –$\Sigma$ Modulators for DC and Sinusoidal Inputs

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