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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Proceedings ArticleDOI
On the stability and configuration of sigma delta modulators
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TL;DR: A stability analysis of ordinary differential equations to represent a continuous sigma delta modulator, with particular reference being made to values representing the gains of the feedback loop and the integrator leakage in the circuit.
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A mechanism for the detection and removal of limit cycles in the operation of sigma delta modulators
Joshua D. Reiss,M.B. Sandier +1 more
TL;DR: This work presents a more effective method for detecting and removing unwanted limit cycles, which destroys the periodicity of sigma-delta ADC modulator's output sequence and, thereby, removes the limit cycles.
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Efficient Computation of the LF/HF Ratio in Heart Rate Variability Analysis Based on Bitstream Filtering
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Proceedings ArticleDOI
Stability analysis of higher-order delta-sigma modulators using the describing function method
TL;DR: The maximum stable input limits for third-, fourth- and fifth-order Chebyshev Type II based Delta-Sigma modulators are established and these results are useful for optimising the design of higher-order Delta- Sigma modulators.
Journal ArticleDOI
Impact of finite impulse response digital-toanalogue converter delay on the stability of continuous-time sigma-delta modulators with pulse-with modulation in the feedback path
F. Colodro,Antonio Torralba +1 more
TL;DR: Here, it is shown that PWM-SDMs with an order greater than 2 can be designed maintaining the low sensitivity of multiple feedback architectures to a delay in the outer loop.
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,