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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TL;DR: I have been always interested on the inner mechanisms that generate new innovative ideas: the valuable one generated by applying and refining ideas already formulated by others, and the one, which is not ahead the state-of-the-art simply because it opens new avenues to the human knowledge.
Abstract: I have been always interested on the inner mechanisms that generate new innovative ideas. In reality, we have two kinds of innovative results: the valuable one generated by applying and refining ideas already formulated by others, and the one, which is not ahead the state-of-the-art simply because it opens new avenues to the human knowledge. Both categories are relevant especially the first one because it produces astonishing numbers. For that category the essence of innovation is advancing the state-of-the-art by an extent that is measured with solid and well-defined parameters (or figures of merit). The other category is fuzzy: the new avenues are not well defined and, in some cases, they are dead-end roads. However, the second type of scientific activity fascinates me much more than the first one because it corresponds to the road marked by creative people. Obviously, in our discipline it not possible to invent something by totally groping in the dark; in some sense we don't have basic research; it is necessary to create new things by having in mind problems and necessities valuable for the scientific progress. However, these kinds of creative contributions, even if incremental, do not follow a step-by-step approach but look ahead of any logic, linear and engineering flow.
38 citations
01 Dec 2007
TL;DR: An upper bound of the performance of dynamic quantizers is derived as a closed form and an optimal dynamic quantizer is provided, which is a solution to the problem, in an analytical way, by a numerical simulation.
Abstract: This paper addresses a problem of finding an optimal dynamic quantizer in a given feedback control loop with discrete-valued signal constraints. First, an upper bound of the performance of dynamic quantizers is derived as a closed form. Based on this, we next provide an optimal dynamic quantizer, which is a solution to the problem, in an analytical way. Finally, the validity of the optimal dynamic quantizer is demonstrated by a numerical simulation.
38 citations
Cites methods from "Understanding Delta-Sigma Data Conv..."
...For the discretevalued input control, several quantizers have been proposed: the locational optimization based quantizer [14], the receding horizon quantizer [15], the ∆Σ modulator [16], and the ∆modulation algorithm [17]....
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Patent•
02 May 2008TL;DR: In this paper, an analog-to-digital delta sigma modulator with a duty cycle modulator and a finite impulse response (FIR) filter in a main-loop feedback path is presented.
Abstract: A signal processing system includes an analog-to-digital delta sigma modulator with a duty cycle modulator and a finite impulse response (FIR) filter in a main loop feedback path of the delta sigma modulator. The duty cycle modulator and FIR filter can provide high performance filtering in the main loop feedback path. To prevent instability in the main loop caused by the duty cycle modulator and FIR filter, the delta sigma modulator also includes a stabilizer loop. Transfer functions of the main loop and the stabilizer loop combine to achieve a target transfer function for the analog-to-digital delta sigma modulator that provides for stable operation of the analog-to-digital delta sigma modulator. In at least one embodiment, the stabilizer loop includes a stabilizer path that provides output data directly to an integrator of the main loop filter.
37 citations
01 Jan 2011
TL;DR: This paper gives an intuitive understanding, as well as an analytical basis, for computing the signal transfer function of CTDSMs with SC DACs, and proposes power-efficient circuit techniques to improve alias rejection in such modulators.
Abstract: Continuous-time modulators (CTDSMs) with switched-capacitor (SC) feedback digital-to-analog converters (DACs) are relatively less sensitive to clock jitter when compared to converters that use non-return-to-zero feedback DACs. How- ever, as we show in this paper, using an SC DAC can seriously compromise the alias rejection of the modulator, thereby nullifying one of the principal advantages of continuous-time operation. We give an intuitive understanding, as well as an analytical basis, for computing the signal transfer function of CTDSMs with SC DACs. We propose power-efficient circuit techniques to improve alias rejection in such modulators and give experimental results that illustrate some of our ideas. Index Terms—Aliasing, analog-digital (A/D) conversion, anti-aliasing, assisted opamp, continuous-time, digital-to-analog conversion (DAC), feedforward, NRZ, oversampling, rejection, sigma-delta, switched capacitor, time varying.
37 citations
TL;DR: A method for bandpass cancellation of the quantization noise occurring in high efficiency, envelope pulsed transmitter architectures-or carrier bursting is introduced and the performance-trend predictions made by the theoretical framework in terms of efficiency and spectral purity are evaluated.
Abstract: This paper introduces a method for bandpass cancellation of the quantization noise occurring in high efficiency, envelope pulsed transmitter architectures-or carrier bursting. An equivalent complex baseband model of the proposed system, including the -modulator and cancellation signal generation, is developed. Analysis of the baseband model is performed, leading to analytical expressions of the power amplifier drain efficiency, assuming the use of an ideal class B power amplifier. These expressions are further used to study the impact of key system parameters, i.e. the compensation signal variance and clipping probability, on the class B power amplifier drain efficiency and signal-to-noise ratio. The paper concludes with simulations followed by practical measurements in order to validate the functionality of the method and to evaluate the performance-trend predictions made by the theoretical framework in terms of efficiency and spectral purity.
37 citations
Cites background from "Understanding Delta-Sigma Data Conv..."
...One advantage of such multi-level architecture over the binary case is that following classical -modulation theory [34]...
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...where [34], in which for the quantizer defined in (2)....
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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