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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09 Jul 2017
TL;DR: All-digital frequency synthesis using two low-pass single-bit Multi-Step Look-Ahead sigma-delta modultors (MSLASDMs) is presented, showcasing the performance advantage of using MSLA SDMs instead of conventional ones.
Abstract: All-digital frequency synthesis using two low-pass single-bit Multi-Step Look-Ahead sigma-delta modultors (MSLA SDMs) is presented. MSLA SDMs provide better noise shaping characteristics, i.e. SNDR and bandwidth, than conventional SDMs at the cost of higher hardware complexity. The balance between complexity and performance is adjusted by the number of look-ahead steps, which is an additional design parameter. The frequency synthesizer system is comprised of two identical low-pass single-bit MSLA SDMs. Their inputs are orthogonal sinusoidals generated by a direct digital synthesizer (DDS). The frequency range of the synthesizer using a single clock signal is determined by the oversampling ratio (OSR) of the SDMs. A lower OSR results in a wider frequency range, but reduces the output SNDR. System-level simulation results of the frequency synthesizer are presented, showcasing the performance advantage of using MSLA SDMs instead of conventional ones.
4 citations
Cites methods from "Understanding Delta-Sigma Data Conv..."
...1 is easily derived from that of the low-pass MSLA SDMs using the well-known transformation z → −z2 for the NTF of bandpass SDMs [5], i....
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TL;DR: NTF design and optimization methods which are particularly useful in audio applications are reviewed.
Abstract: The parameters of sigma-delta audio DAC depend mainly on digital sigma-delta
modulator’s features, especially on its noise transfer function (NTF). Many methods
of design and optimization of the loop filter’s coefficients in sigma-delta modulators
have been proposed so far. These methods enable the designer to get suitable noise
transfer functions for specific application. This paper reviews NTF design and optimization
methods which are particularly useful in audio applications.
4 citations
Cites background from "Understanding Delta-Sigma Data Conv..."
...(23) Requirement that ∣∣DEN(ejθ)∣∣ should be maximally flat around θ = 0 is equivalent to the condition that DEN(z) ·DEN(1/z) should be maximally flat around z = 1 (Schreier, Temes, 2005):...
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TL;DR: In this article, Sobolev duals are introduced for finite frames for road quantization and shown to provide a high precision linear reconstruction procedure for Sigma-Delta (Σ∆) quantization of finite frames.
Abstract: A new class of alternative dual frames is introduced in the setting of finite frames for Rd. These dual frames, called Sobolev duals, provide a high precision linear reconstruction procedure for Sigma-Delta (Σ∆) quantization of finite frames. The main result is summarized as follows: reconstruction with Sobolev duals enables stable rth order Sigma-Delta schemes to achieve deterministic approximation error of order O(N−r) for a wide class of finite frames of size N . This asymptotic order is generally not achievable with canonical dual frames. Moreover, Sobolev dual reconstruction leads to minimal mean squared error under the classical white noise assumption.
4 citations
TL;DR: A method to design a discrete-time NTF from a normalized analog highpass filter in which the coefficients of the characteristic polynomial of the squared-magnitude function of the filter are optimized to minimize the energy in the band of interest.
Abstract: One of the popular methods of designing a noise transfer function (NTF) used in the synthesis of a delta–sigma modulator (DSM) is to optimally place its zeros across the signal band of interest while minimizing the in-band noise power. The distribution of the poles of the NTF is considered secondary. In this brief, we provide a method to design a discrete-time NTF from a normalized analog highpass filter in which the coefficients of the characteristic polynomial of the squared-magnitude function of the filter are optimized to minimize the energy in the band of interest, in addition to satisfying the realizability constraints required to synthesize a DSM. We compare the performance of the NTFs designed using our method with those designed using one of the well-known methods in terms of the signal-to-quantization noise ratio (SQNR). It is shown that the SQNR of the NTFs designed using our method is higher than that of the NTFs designed using the well-known methods.
4 citations
Cites methods from "Understanding Delta-Sigma Data Conv..."
...INTRODUCTION DELTA-SIGMA Modulation has been known to provide high-resolution analog-to-digital conversion and digitalto-analog conversion [1]....
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...REQUIREMENTS OF A NOISE TRANSFER FUNCTION A general DSM with a single quantizer and loop filters L0(z) and L1(z) [1] is shown in Fig....
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TL;DR: In this article , a 3-0 sturdy-multi-stage noise-shaping (SMASH) continuous-time (CT) incremental delta-sigma analog-to-digital converter (ADC) is presented.
Abstract: This article shows the design of a wideband 3-0 sturdy-multi-stage noise-shaping (SMASH) continuous-time (CT) incremental delta–sigma (I- $\boldsymbol {\Delta \Sigma }$ ) analog-to-digital converter (ADC). The two stages’ quantizers (QTZs) are implemented by a single re-configurable multibit (MB) asynchronous (A)SAR ADC. The digital-to-analog converter (DAC) nonlinearities are suppressed by reconfiguring the asynchronous successive-approximation register (ASAR) ADC from 2 to 5 b, and correspondingly, the DACs dynamically switch from 1.5- to 4-b tri-level outputs within each Nyquist conversion cycle. This results in a DAC-calibration-free MB operation. A two-tap FIR filter is implemented in the feedback DACs to reduce jitter requirements in the initial 1.5-b cycles. Through the design representation, a detailed fundamental comparison between an X-0 SMASH architecture and an X-order single-loop modulator is discussed. This discussion highlights the introduction of an efficient tri-level combination between the MSB and the LSBs of the ASAR QTZ. The resulting SMASH CT I- $\boldsymbol {\Delta \Sigma }$ modulator was fabricated in 28-nm CMOS technology with an active area of 0.125 mm2. It achieves 97-dB spurious-free dynamic range (SFDR) without calibration, 89-dB dynamic range (DR), and 81.2-dB SNDR in a 1-MHz bandwidth (BW). It consumes 3.6 mW from a single 0.9-V supply. The design shows very good robustness across different tested samples, supply variations, and across temperatures from −20 °C to 80 °C.
4 citations
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