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Understanding Delta-Sigma Data Converters

TL;DR: This chapter discusses the design and simulation of delta-sigma modulator systems, and some of the considerations for implementation considerations for [Delta][Sigma] ADCs.
Abstract: Chapter 1: Introduction.Chapter 2: The first-order delta-sigma modulator.Chapter 3: The second-order delta-sigma modulator.Chapter 4: Higher-order delta-sigma modulation.Chapter 5: Bandpass and quadrature delta-sigma modulation.Chapter 6: Implementation considerations for [Delta][Sigma] ADCs.Chapter 7: Delta-sigma DACs.Chapter 8: High-level design and simulation.Chapter 9: Example modulator systems.Appendix A: Spectral estimation.Appendix B: The delta-sigma toolbox.Appendix C: Noise in switched-capacitor delta-sigma data converters.

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Citations
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Journal ArticleDOI
TL;DR: It is shown that /spl Sigma//spl Delta/ quantization of a unit-norm finite frame expansion in /spl Ropf//sup d/ achieves approximation error, and one is able to bound the mean squared error (MSE) by an order of 1/N/sup 2/.
Abstract: The K-level Sigma-Delta (/spl Sigma//spl Delta/) scheme with step size /spl delta/ is introduced as a technique for quantizing finite frame expansions for /spl Ropf//sup d/. Error estimates for various quantized frame expansions are derived, and, in particular, it is shown that /spl Sigma//spl Delta/ quantization of a unit-norm finite frame expansion in /spl Ropf//sup d/ achieves approximation error where N is the frame size, and the frame variation /spl sigma/(F,p) is a quantity which reflects the dependence of the /spl Sigma//spl Delta/ scheme on the frame. Here /spl par//spl middot//spl par/ is the d-dimensional Euclidean 2-norm. Lower bounds and refined upper bounds are derived for certain specific cases. As a direct consequence of these error bounds one is able to bound the mean squared error (MSE) by an order of 1/N/sup 2/. When dealing with sufficiently redundant frame expansions, this represents a significant improvement over classical pulse-code modulation (PCM) quantization, which only has MSE of order 1/N under certain nonrigorous statistical assumptions. /spl Sigma//spl Delta/ also achieves the optimal MSE order for PCM with consistent reconstruction.

153 citations


Cites background from "Understanding Delta-Sigma Data Conv..."

  • ..., see [31], [38], is to assume that the state variables in the scheme (13) are independent and identically distributed uniform random variables with zero mean and variance ....

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Journal ArticleDOI
TL;DR: In this article, the authors proposed a sensor concept for temperature, humidity, and gas detection on plastic substrates, suitable for mobile applications, like smart RFID tags, and demonstrated the possibility of developing gas sensors on humidity sensitive substrates.
Abstract: Temperature, gas and humidity resistive/capacitive sensors on plastic substrates, suitable for mobile applications, like smart RFID tags, have been produced and investigated. The sensor concept is providing simple, versatile and low power solutions for temperature, humidity and gas detection. The device structure was devised together with the data evaluation strategies based on the latest generation ΣΔ analog (resistance and capacitance) to digital converters. The possibility of developing gas sensors on humidity sensitive substrates, having temperature corrected responses is demonstrated. The proposed sensor is aimed to evolve towards “flexible and full plastic” implementations.

146 citations

Journal ArticleDOI
TL;DR: This paper derives a closed form expression for the performance of a class of dynamic quantizers in the form of a linear difference equation such that the system composed of a given linear plant and the quantizer is an optimal approximation of the givenlinear plant in the sense of the input-output relation.

144 citations

Journal ArticleDOI
TL;DR: In this paper, the effects of synchronous demodulation and electrostatic quadrature compensation performed with a dc voltage on the final zero-rate output (ZRO) of a vibratory microgyroscope are studied.
Abstract: In this paper, issues related to the zero-rate output (ZRO) of a vibratory microgyroscope are studied. Different sources of the ZRO are discussed and how the effect of each source can be minimized and their stability improved is described. The effects of synchronous demodulation and electrostatic quadrature compensation performed with a dc voltage on the final ZRO are analyzed. Ways to implement the control loop for electrostatic quadrature compensation performed with a dc voltage are described, concentrating on a case where the compensation voltage is generated with a digital-to-analog converter and the controller is digital. In particular, extending the resolution with SigmaDelta techniques is studied. The experimental work shows the feasibility of the implemented quadrature compensation loop and analyzes the ZRO sources of one particular gyroscope implementation. How to perform the ZRO measurements in such a way that the various sources can be distinguished from each other is also described.

141 citations


Cites background or methods from "Understanding Delta-Sigma Data Conv..."

  • ...In the system, the gyroscope output signals are converted into the digital domain with bandpass (BP) ADCs ([10], Ch....

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  • ...If the ADC is a -type converter [4], [8], [10], then with a dc input signal, the input voltage can be revealed with unlimited resolution by integrating it for a long enough time....

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  • ...In the system, the gyroscope output signals are converted into the digital domain with bandpass (BP) ADCs ([10], Ch. 5) after analog signal processing....

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  • ...T. Salo is also acknowledged for implementing the bandpass ADCs used in the system....

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Proceedings ArticleDOI
01 Dec 2009
TL;DR: The transmitter optimization for the flat multi-input multi-output (MIMO) channel under nonlinear distortion from the digital-to-analog converters (DACs) is studied, taking into account the effects of the transmitter nonlinearities.
Abstract: We study the transmitter optimization for the flat multi-input multi-output (MIMO) channel under nonlinear distortion from the digital-to-analog converters (DACs). Our design is based on a minimum mean square error (MMSE) approach, taking into account the effects of the transmitter nonlinearities. Our derivation does not make use of the assumption of uncorrelated white distortion (quantization) errors and considers the correlations of the quantization error with the other signals of the system. Through simulation, we compare the new optimized linear transmitter to previously proposed linear transmitter designs when operating under DACs in terms of uncoded BER.

139 citations


Cites background from "Understanding Delta-Sigma Data Conv..."

  • ...In fact, in order to reduce circuit complexity and save power and area, low resolution DACs have to be employed [4]....

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References
More filters
Journal ArticleDOI
TL;DR: Higher order modulators are shown not only to greatly reduce oversampling requirements for high-resolution conversion applications, but also to randomize the quantization noise, avoiding the need for dithering.
Abstract: Oversampling interpolative coding has been demonstrated to be an effective technique for high-resolution analog-to-digital (A/D) conversion that is tolerant of process imperfections. A novel topology for constructing stable interpolative modulators of arbitrary order is described. Analysis of this topology shows that with proper design of the modulator coefficients, stability is not a limitation to higher order modulators. Furthermore, complete control over placement of the poles and zeros of the quantization noise response allows treatment of the modulation process as a high-pass filter for quantization noise. Higher order modulators are shown not only to greatly reduce oversampling requirements for high-resolution conversion applications, but also to randomize the quantization noise, avoiding the need for dithering. An experimental fourth-order modulator breadboard demonstrates stability and feasibility, achieving a 90-dB dynamic range over the 20-kHz audio bandwidth with a sampling rate of 2.1 MHz. A generalized simulation software package has been developed to mimic time-domain behavior for oversampling modulators. Circuit design specifications for integrated circuit implementation can be deduced from analysis of simulated data. >

399 citations

Journal ArticleDOI
James C. Candy1
TL;DR: It is shown that digital filters comprising cascades of integrate-and-dump functions can match the structure of the noise from sigma delta modulation to provide decimation with negligible loss of signal-to-noise ratio.
Abstract: Decimation is an important component of oversampled analog-to-digital conversion. It transforms the digitally modulated signal from short words occurring at high sampling rate to longer words at the Nyquist rate. Here we are concerned with the initial stage of decimation, where the word rate decreases to about four times the Nyquist rate. We show that digital filters comprising cascades of integrate-and-dump functions can match the structure of the noise from sigma delta modulation to provide decimation with negligible loss of signal-to-noise ratio. Explicit formulas evaluate particular tradeoffs between modulation rate, signal-to-noise ratio, length of digital words, and complexity of the modulating and decimating functions.

342 citations

Journal ArticleDOI
TL;DR: 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.

284 citations

Book ChapterDOI
James C. Candy1, O. Benjamin1
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.
Abstract: When the sampling rate of a sigma-delta modulator far exceeds the frequencies of the input signal, its modulation noise is highly correlated with the amplitude of the input. We derive simple algebraic expressions for this noise and its spectrum in terms of the input amplitude. The results agree with measurements taken on a breadboard circuit. This work can be useful for designing oversampled analog to digital converters that use sigma-delta modulation for the primary conversion.

255 citations

Journal ArticleDOI
01 Mar 1993
TL;DR: The modulator of a bandpass analog/digital (A/D) converter, with 63 dB signal/noise for broadcast AM bandwidth signals centered at 455 kHz, has been implemented by modifying a commercial digital-audio sigma-delta ( Sigma Delta ) converter.
Abstract: The modulator of a bandpass analog/digital (A/D) converter, with 63 dB signal/noise for broadcast AM bandwidth signals centered at 455 kHz, has been implemented by modifying a commercial digital-audio sigma-delta ( Sigma Delta ) converter. It is the first reported fully monolithic implementation of bandpass noise shaping and has applications to digital radio. >

211 citations