Book•
Understanding Delta-Sigma Data Converters
08 Nov 2004-
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.
Citations
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17 Apr 2018
TL;DR: In this paper, the ∆Σ-Signal-verarbeitung (DSSV) is prasentiert, which reduziert den Umsetzungsaufwand digitaler Regelungsstrukturen bei gleichbleibender Regelqualititat.
Abstract: Die erreichbare Regelgute einer digitalen Regelungstruktur ist nicht ausschlieslich abhangig vom Regelalgorithmus, sondern wird ebenso durch die Eigenschaften des digitalen Zielssystems beeinflusst. Im Rahmen dieses Beitrages wird ein neuartiger Ansatz zur digitalen Signalverarbeitung prasentiert, die ∆Σ-Signalverarbeitung (DSSV). Dieser reduziert den Umsetzungsaufwand digitaler Regelungsstrukturen bei gleichbleibender Regelqualititat. Die Gegenuberstellung der DSSV mit der klassischen digitalen Signalverabreitung erfolgt durch eine Implementierung einer oberschwingungsbehafteten Stromeinpragung in eine Synchronmaschine
1 citations
TL;DR: The possibility of using a single digital ΔΣ modulator to simultaneously encode the two channels of a stereo signal is illustrated and if one channel is unused, it lets the other get improved dynamic range and SNR.
Abstract: The possibility of using a single digital {\Delta}{\Sigma} modulator to simultaneously encode the two channels of a stereo signal is illustrated. From the modulated stream, the two channels can be recovered with minimal processing and no cross-talk. Notably, demultiplexing does not affect the sample-depth so that, after it, one still has a data stream suitable for directly driving a power bridge and convertible into analog by mere low-pass filtering. Furthermore, the approach is very flexible and if one channel is unused, it lets the other get improved dynamic range and SNR. The approach can take advantage of recent techniques for the design of {\Delta}{\Sigma} modulators, including methods for psychoacoustically optimal distribution of quantization noise. Code is available to replicate the proposed examples and as a general computer aided design tool.
1 citations
Cites background or methods from "Understanding Delta-Sigma Data Conv..."
...Under common assumptions, a relationship exists between STF, NTF and the internal filtering structures inside the modulator such that, once STF (z) and NTF (z) are assigned, the modulator functionality is fully defined (even if the actual implementation and arrangement of the filters can vary) [6]....
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...Specifically, doubling the OSR improves the noise floor by approximately 3 dB + 6 dB · (modulator order), which is an expected result [6]....
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...The benchmark coders have a 20 kHz bandwidth, half the order, and are designed with the same technique (Schreiers’ synthesizeNTF [6]) and OSR as those under test, getting a 2.56 MHz sample rate....
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...Tests run for multiple modulator orders, using Schreier’s synthesizeNTF [6] (in (a), γ = 1....
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...To have NTF (z) highly attenuating in B, it must be allowed to amplify elsewhere (so that the net result appears like moving noise from one frequency region to another) [6]....
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01 Jan 2010
TL;DR: The research toward the development of high speed and high resolution analog-to-digital converters (ADCs) has been equally driven by the demand of high-speed wire line and wireless networks.
Abstract: In recent years, the research toward the development of high speed and high resolution analog-to-digital converters (ADCs) has been equally driven by the demand of high-speed wire line and wireless ...
1 citations
Additional excerpts
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TL;DR: A new magnitude-only transfer-function modeling framework for SDM architectures, which is based on output noise spectrum and produces a stable LTI NTF approximation model, based on a phase reconstruction and a rational transfer- function fitting step, using the Vector Fitting algorithm.
Abstract: Sigma delta modulators importance is unambiguous in many applications. Since they are inherently non-linear systems, they are often approximately linearized to allow for the derivation of their theoretical Noise-Transfer-Function (NTF). SDM NTF is used for both analyzing and synthesizing them. Although linearization is the standard approach for its derivation, there do exist SDM architectures to which it cannot be applied. The aim of this paper is twofold: To provide a general framework for deriving the NTF for all SDM architectures, and, to use it to evaluate the accuracy of the standard theoretical NTF approximation for those SDM architectures accepting linearization. To this end, we introduce a new magnitude-only transfer-function modeling framework for SDM architectures, which is based on output noise spectrum and produces a stable LTI NTF approximation model. This framework is based on a phase reconstruction and a rational transfer-function fitting step, using the Vector Fitting algorithm. To show its applicability, we used it to derive NTF models for SDMs at system level and at RTL. Finally, the generality of our approach is demonstrated by deriving experimental NTF for a class of SDMs without standard linearized models.
1 citations
Cites background from "Understanding Delta-Sigma Data Conv..."
...Typically, L is selected so that STF is very close to unity and NTF is very close to zero within the useful signal bandwidth, and, the loop is stable [18,19]....
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...The purpose of the SDM is to pass the input signal to its output, representing it with the resolution of the quatizer, which can be 1 or more bits, and with the minimum possible quality loss [18]....
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...SDM synthesis is equivalent to the selection of an NTF that maximizes the signal-to-quantization-noise ratio (SQNR) [18] in the frequency band of interest, while ensuring stability and reasonable hardware complexity....
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...under the assumption that the quantization error is approximately uniformly distributed white noise for realistic input signals [18]....
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...The choice of sinusoidal excitation signals for SDM NTF excitation is standard in the literature [18,42]....
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01 Nov 2013
TL;DR: It is shown that the figure-of-merit (FOM) of such designs can be lower than designs using oversampling by a factor of integer powers of two, and the same optimization approach can be used for other low voltage low power portable audio applications.
Abstract: This paper presents power optimization of a sigma-delta (ΣΔ) modulator based digital-to-analog converter (DAC) for hearing-aid audio back-end application. In a number of state-of-the-art publications the oversampling ratio (OSR) of the ΣΔ modulator is chosen as a factor of integer power of two. The reason given is the simplicity of the interpolation filter (IF) block. However, being able to choose OSR factors of integer powers of two only, might be restricting and not necessarily optimal. Therefore the ΣΔ modulator based DAC designs with multistage IF that include a stage performing oversampling by a factor of 3 are investigated. This new design freedom is used to lower the operating frequency of the whole DAC and save considerable amount of power. It is shown that the figure-of-merit (FOM) of such designs can be lower than designs using oversampling by a factor of integer powers of two. The same optimization approach can be used for other low voltage low power portable audio applications (mobile phones, notebook computers etc.).
1 citations
Cites background or methods from "Understanding Delta-Sigma Data Conv..."
...The third stage is designed as a 3 order cascaded-integrator-comb (CIC) filter and the fourth stage as a second order CIC filter [8]....
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...5 is used as advised in [8] the modulator will reach only 89 dB peak SQNR, which is below the specification of Section II....
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...There are more precise figures of merit for modulators used in other works [8]....
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References
More filters
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
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
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
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
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