An analysis of nonlinear behavior in delta - sigma modulators
Sasan H. Ardalan,J.J. Paulos +1 more
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TLDR
This paper introduces a new method of analysis for deltasigma modulators based on modeling the nonlinear quantizer with a linearized gain, obtained by minimizing a mean-square-error criterion, followed by an additive noise source representing distortion components.Abstract:
This paper introduces a new method of analysis for deltasigma modulators based on modeling the nonlinear quantizer with a linearized gain, obtained by minimizing a mean-square-error criterion [7], followed by an additive noise source representing distortion components. In the paper, input signal amplitude dependencies of delta-sigma modulator stability and signal-to-noise ratio are analyzed. It is shown that due to the nonlinearity of the quantizer, the signal-to-noise ratio of the modulator may decrease as the input amplitude increases prior to saturation. Also, a stable third-order delta-sigma modulator may become unstable by increasing the input amplitude beyond a certain threshold. Both of these phenomena are explained by the nonlinear analysis of this paper. The analysis is carried out for both dc and sinusoidal excitations.read more
Figures
Fig. 6. Minimum Mean Square Error Linearized Gain Modeling of Nonlinearity 
Fig. 23 Nyquist Plot 3rd Order Modulator «11=0.1, (12=0.1, (13=1.0) 
Fig. 16. Calculated SNR for 2nd and 3rd Order Modulator, ~: =256 
Fig. 21. Calculated Variances at Quantizer Input, 2nd Order Sinusoidal Input 
Fig. 22 Nyquist Plot 2nd Order Modulator (Q(=O.5, Q2=1.0)
Citations
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Granular quantization noise in the first-order delta-sigma modulator
TL;DR: In this article, a unified approach to analyzing the granular quantization error of the first-order Delta Sigma modulator is presented, which handles many of the previously analyzed input sequences in addition to a large class of new input sequences.
Proceedings ArticleDOI
Invariant sets for general second-order low-pass delta-sigma modulators with DC inputs
TL;DR: In this paper, the authors describe analytic and algorithmic methods for finding invariant sets of second-order delta-sigma modulators with DC inputs, which yield rigorous theoretical bounds on the state variables.
DC stability analysis of high-order, lowpass /spl
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High-order single-stage single-bit oversampling A/D converter stabilized with local feedback loops
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TL;DR: An overview of 1-bit audio processing is presented in this article, where several characteristics of the sigma-delta modulator (SDM) are discussed, as well as some simple design methodologies of SDMs.
References
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Journal ArticleDOI
A Use of Double Integration in Sigma Delta Modulation
TL;DR: A modulator that employs double integration and two-level quantization is easy to implement and is tolerant of parameter variation.
Journal ArticleDOI
Nonlinear Control Engineering
TL;DR: In this paper, a nonlinear control engineering (NCE) approach is proposed to solve the problem of NCE in the context of NCLE, where NCE is applied to control engineering.
Book ChapterDOI
The Structure of Quantization Noise from Sigma-Delta Modulation
James C. Candy,O. Benjamin +1 more
TL;DR: Simple algebraic expressions for this modulation noise and its spectrum in terms of the input amplitude are derived and can be useful for designing oversampled analog to digital converters that use sigma-delta modulation for the primary conversion.
Journal ArticleDOI
Design Methodology for ΣΔM
B. Agrawal,K. Shenoi +1 more
TL;DR: In this paper, a design methodology based on correspondence between performance requirements, mathematical parameters, and circuit parameters of a sigma-delta modulator is presented, which will guide a design engineer in selecting the circuit parameters based on system requirements, in translating paper design directly into LSI design, in predicting the effect of component sensitivity, and in analyzing the operations of the sigmoid modulator, which is viewed as a device which distributes the noise power, determined by peak SNR, over a much broader band, compared to signal bandwidth, shapes and amplifies it,