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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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Book ChapterDOI
01 Jan 2019
TL;DR: This chapter focuses on specific system-level simulations of the simplest Sigma-Delta modulator, to be referred as MOD1, formed by a first-order loop filter and a single-bit quantizer, using MATLAB and Simulink as the tools used to explore the properties of MOD1.
Abstract: This chapter focuses on specific system-level simulations of the simplest Sigma-Delta modulator, to be referred as MOD1, formed by a first-order loop filter and a single-bit quantizer. The aim of this chapter is to help beginners make the important leap from theory to actually understand the significance of the subtle concepts that are essential to becoming confident in designing a successful modulator. As mentioned, MATLAB® and Simulink® are the tools used to explore the properties of MOD1. Therefore, after a brief description of the Simulink® model provided in the Toolbox accompanying this book, a step-by-step set of practical exercises is proposed. Specifically, the reader will be able to observe the time domain waveforms of the modulator in response to both DC and sinewave inputs as well as noise shaping in the frequency domain via fast Fourier transform (FFT). A number of non-ideal effects are studied such as tones, dead zones, and saturation. Further, the prevention of the non-idealities discussed is investigated, mainly through the use of dither. Some simple mathematics is used as an aid in presenting the theoretical concepts, and for results evaluation, however, formula proofs are generally avoided in order to keep the focus on the results themselves and a rather practical approach to the subject. The interested reader is encouraged to consult the references for complete mathematical derivations.
01 Jan 2012

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

  • ...Therefore, the sampling frequency fs is equal to 250MHz, and the signal bandwidth fBW is equal to 5MHz, the OSR is about 25 using the following equation [15]:...

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  • ...oversampling ratio and the loop-filter order [15]....

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Journal ArticleDOI
TL;DR: The proposed concept of modulators as heuristic optimizers for circulant unconstrained discrete quadratic programming (C-UDQP) is revisited, compared to previous results and exact optimization techniques.
Abstract: A recent result on the potential of $\Delta \!\Sigma $ modulators ( $\Delta \!\Sigma $ Ms) as heuristic optimizers for circulant unconstrained discrete quadratic programming (C-UDQP) is revisited, bridging it with current developments on the design of $\Delta \!\Sigma $ Ms by semi-definite programming (SDP). This provides an efficient strategy by which one can design a $\Delta \!\Sigma \text{M}$ and its input signal from a C-UDQP specification so that the solution of the C-UDQP problem can be found in the $\Delta \!\Sigma \text{M}$ output, all with almost no manual intervention. The proposed concept is validated by simulation-based experiments on a benchmark case, comparing the new strategy to previous results and exact optimization techniques.
DOI
01 May 2020
TL;DR: In this approach, a high speed and simple structure dynamic element matching (DEM) based on homogenization and time-division is designed and merged into one complex DAC for quadrature mismatch cancelation which leads to near-perfect I/Q balance.
Abstract: This paper proposes a new mismatch cancelation technique for quadrature delta-sigma modulators (QDSM). In this approach, a high speed and simple structure dynamic element matching (DEM) based on homogenization and time-division (HTD) is designed. In addition, I and Q digital-to-analog converters (DACs) are merged into one complex DAC (C_DAC) for quadrature mismatch cancelation which leads to near-perfect I/Q balance. A third-order multi-bit continuous-time (CT) QDSM for a WCDMA LOW-IF receiver is designed and implemented in 180 nm CMOS technology to investigate the effects of the proposed DEM. The proposed DEM method and DWA algorithm are applied to the QDSM with 2% mismatch errors in DAC cells and compared two outputs PSD effects. Simulation results show that the modulator achieves a signal-to-noise ratio (SNR) of 74 dB and 74.2 dB for the proposed method and DWA, respectively, while the proposed method is simpler and faster than the data weighted averaging (DWA) algorithm.

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

  • ...In [11], a DWA algorithm has been implemented in a new method and its pointer has been randomly added....

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Book ChapterDOI
01 Jan 2017
TL;DR: In this article, the authors compared two wideband MASH implementations in a 28 nm CMOS process and their properties and performances are discussed based on the architectural differences and a unique circuit block in continuous-time MASH, a continuous time residue generation circuit is discussed in detail.
Abstract: BW = f s/(2 OSR). As this equation indicates, wideband ΣΔ ADCs having bandwidths in the hundreds of MHz require clock frequencies in the GHz range even to obtain a relatively low OSR of ten. In such low-OSR systems, MASH architectures achieve better power efficiency than traditional single-loop ΣΔ ADCs. Nanometer CMOS process technologies enable continuous-time ΣΔ ADCs operating at GHz clock frequencies. However, the combination of continuous-time and low-OSR at a GHz clock frequency presents new challenges. In this paper, ΣΔ ADCs including the traditional single-loop and MASH, are reviewed in the context of wideband wireless applications with out-of-band blockers. A unique circuit block in continuous-time MASH, a continuous-time residue generation circuit, is discussed in detail. Two wideband MASH implementations in a 28 nm CMOS process are compared and their properties and performances are discussed based on the architectural differences.

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

  • ...The power efficiency of each ADC can be quantified via the thermal noise figure-of-merit FOM DDRC 10 log10(BW/P) [1]....

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  • ...where the OSR is the oversampling ratio, fS is the sampling frequency, and BW is the raw bandwidth of the † ADC [1]....

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  • ...In the case of † ADCs, the overall gain is frequency dependent and represented as a transfer function L0 while a transfer function L1 is used to represent the frequency-dependent gain of the feedback path [1]....

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References
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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