An analysis of nonlinear behavior in delta - sigma modulators
Sasan H. Ardalan,J.J. Paulos +1 more
Reads0
Chats0
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
More filters
Journal ArticleDOI
An empirical study of high-order single-bit delta-sigma modulators
TL;DR: Plots of the maximum signal-to-noise ratio (SNR) achievable with a given modulator order and oversampling ratio (OSR) are presented and can be used to determine the modulator orders required to achieve a given SNR or to check the tightness of theoretical bounds.
Proceedings ArticleDOI
Evaluation and improvement of Boolean comparison method based on binary decision diagrams
TL;DR: The results show that binary decision diagrams (BDD) with the proposed ordering method can verify almost all benchmark circuits in less than several central processor unit (CPU) minutes, which is one hundred times faster than times reported in the literature.
Journal ArticleDOI
Sigma-Delta Modulators: Tutorial Overview, Design Guide, and State-of-the-Art Survey
TL;DR: A review of the state of the art on nanometer CMOS implementations is described, giving a survey of cutting-edge ΣΔ architectures, with emphasis on their application to the next generation of wireless telecom systems.
Journal ArticleDOI
Global stability of relay feedback systems
TL;DR: Conditions in the form of linear matrix inequalities (LMIs) are presented that guarantee global asymptotic stability of limit cycles induced by relays with hysteresis in feedback with linear time-invariant (LTI) stable systems, leading to belief that globally stable limit cycles of RFS frequently have quadratic surface Lyapunov functions.
Journal ArticleDOI
Optimal parameters for /spl Delta//spl Sigma/ modulator topologies
TL;DR: A graph showing the maximal achievable performance of each topology as a function of the oversampling ratio is presented, offering a valuable help for the design of analog-to-digital converters.
References
More filters
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,