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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02 Oct 2009
TL;DR: A new modified DWA structure is presented, which results in a completely first order mismatch noise shaping while solving in band tone problem, and its modified version can also be used in bandpass applications.
Abstract: In order to reduce mismatch error of a DAC used in a multibit delta-sigma some dynamic element matching (DEM) algorithms have been proposed before, from which Data-Weighted-Averaging (DWA) method is more hardware efficient and widely used. Unfortunately, DWA technique loses its functionalities for periodic signals which cannot be practically avoided. Many improvements have been suggested to minimize in band tone generated by DWA algorithm, but they cause limited performance compared with an ideal first order DEM. This paper presents a new modified DWA structure, which results in a completely first order mismatch noise shaping while solving in band tone problem. Simulations are presented for a 3rd-order lowpass delta sigma. However, its modified version can also be used in bandpass applications.
15 citations
Cites background from "Understanding Delta-Sigma Data Conv..."
...Unfortunately, DWA technique loses its functionalities for periodic signals which cannot be practically avoided....
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TL;DR: A reconfigurable 65-nm continuous-time low-pass delta-sigma modulator that improves the linearity of the flash, while also increasing the highest sampling rate and bandwidth of the modulator.
Abstract: A reconfigurable 65-nm continuous-time low-pass delta-sigma modulator operates with a sampling frequency from 491 MHz to 1536 MHz, a signal bandwidth from 10 MHz to 100 MHz, and a dynamic range of 754 dB to 628 dB, respectively Flash ADC calibration and reference shuffling with zipper rotation are used to improve the linearity of the flash, while also increasing the highest sampling rate and bandwidth of the modulator Dynamic element matching using a randomized incremented pointer improves the linearity of the DAC
15 citations
TL;DR: A design flow for ΔΣ modulators is illustrated, allowing quantization noise to be shaped according to an arbitrary weighting profile, based on finite-impulse-response noise transfer functions, possibly with high order.
Abstract: A design flow for {\Delta}{\Sigma} modulators is illustrated, allowing quantization noise to be shaped according to an arbitrary weighting profile. Being based on FIR NTFs, possibly with high order, the flow is best suited for digital architectures. The work builds on a recent proposal where the modulator is matched to the reconstruction filter, showing that this type of optimization can benefit a wide range of applications where noise (including in-band noise) is known to have a different impact at different frequencies. The design of a multiband modulator, a modulator avoiding DC noise, and an audio modulator capable of distributing quantization artifacts according to a psychoacoustic model are discussed as examples. A software toolbox is provided as a general design aid and to replicate the proposed results.
15 citations
Cites background or methods from "Understanding Delta-Sigma Data Conv..."
...CMQ states that uniform quantization can be approximately modeled as the superimposition of noise, white in spectrum, independent from the quantized signal and uniformly distributed within [−∆/2,+∆/2], where ∆ is the quantization step....
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...This is not possible with conventional flows [5], [7], [8], which merely distinguish between the signal band and outof-band frequencies, aiming just at concentrating noise in the latter....
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...It holds relatively well whenever the modulator input signal is “busy” [5]....
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...2(b) shows the magnitude response of a tenthorder FIR NTF obtained by the proposed approach and compares it to that of a second-order NTF obtained by DELSIG’s synthesizeNTF [5]....
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...Together with the Classical Model of Quantization (CMQ) [5], this allows the modulator behavior to be expressed by two items: the signal transfer function (STF), from input u(nT ) to...
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01 Jan 2008
TL;DR: This work addresses a well known problem of unwanted spurious tones in the modulator’s output spectrum by proposing means for guaranteeing that the output period will never be shorter than a prescribed minimum value for all constant inputs.
Abstract: Digital delta-sigma modulators are used in a broad range of modern electronic sub-systems, including oversampled digital-to-analogue converters, class-D amplifiers and fractional-N frequency synthesizers. This work addresses a well known problem of unwanted spurious tones in the modulator’s output spectrum. When a delta-sigma modulator works with a constant input, the output signal can be periodic, where short periods lead to strong deterministic tones. In this work we propose means for guaranteeing that the output period will never be shorter than a prescribed minimum value for all constant inputs. This allows a relationship to be formulated between the modulator’s bus width and the spurious-free range, thereby making it possible to trade output spectrum quality for hardware consumption. The second problem addressed in this thesis is related to the finite accuracy of frequencies generated in delta-sigma fractional-N frequency synthesis. The synthesized frequencies are usually approximated with an accuracy that is dependent on the modulator’s bus width. We propose a solution which allows frequencies to be generated exactly and removes the problem of a constant phase drift. This solution, which is applicable to a broad range of digital delta-sigma modulator architectures, replaces the traditionally used truncation quantizer with a variable modulus quantizer. The modulus, provided by a separate input, defines the denominator of the rational output mean. The thesis concludes with a practical example of a delta-sigma modulator used in a fractionalN frequency synthesizer designed to meet the strict accuracy requirements of a GSM base station transceiver. Here we optimize and compare a traditional modulator and a variable modulus design in order to minimize hardware consumption. The example illustrates the use made of the relationship between the spurious-free range and the modulator’s bus width, and the practical use of the variable modulus functionality.
15 citations
TL;DR: Tellegen's theorem is used to demonstrate interreciprocity in LPTV networks with sampled outputs, and enables the determination of the equivalent LTI filters from multiple sources in the LPTV network to the sampled output, using just one time-domain simulation.
Abstract: We consider a linear periodically time-varying (LPTV) network (varying with frequency f
s
) excited by an input x(t). We show (using frequency-domain arguments) that if its output is sampled at f
s
, one can find a linear time-invariant (LTI) filter, which, when excited by x(t) and output sampled at f
s
, yields the same sequence as the LPTV network. We then use Tellegen's theorem to demonstrate interreciprocity in LPTV networks with sampled outputs. This enables the determination of the equivalent LTI filters from multiple sources in the LPTV network to the sampled output, using just one time-domain simulation. A first-order continuous-time delta sigma modulator is used to illustrate the theory.
15 citations
Cites result from "Understanding Delta-Sigma Data Conv..."
...Note the simplicity with which this result was obtained, when compared to a more conventional way of establishing this [13]....
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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