INTERNATIONAL JOURNAL OF CIRCUIT THEORY AND APPLICATIONS, VOL. 25, 317—318 (1997) GUEST EDITORIAL DELTA—SIGMA MODULATORS AND NOISE SHAPING: CURRENT STATUS, RECENT DEVELOPMENTS AND FUTURE TRENDS ORLA FEELY1* AND RICHARD SCHREIER2 1 Department of Electronic and Electrical Engineering, University College Dublin, Dublin 4, Ireland 2 Analog Devices Inc., 804 Woburn Street, Wilmington, MA 01887, U.S.A. The past decade has witnessed an explosive growth in the applications of delta—sigma (or sigma—delta—the two terms are interchangeable) modulation and related techniques. The most obvious manifestation of this to the general public has been in digital audio, where in the mid-1980s the ever-increasing number of bits of resolution claimed by competing manufacturers was suddenly, and puzzlingly, interrupted by the appearance of ‘one-bit’ products. The parallel appearance of the word ‘oversampling’ provided the clue as to why this apparently backward step was actually progressive—although delta—sigma converters use low-resolution samples to reproduce a signal, they provide many more per second than conventional converters. The output of the delta—sigma modulator can then be filtered and decimated to retrieve a high-resolution signal. Although the concepts underlying delta—sigma modulation were first published in the early 1960s, it was with the arrival of VLSI technology in the 1980s that data converters based on these principles became commercially feasible. These converters relax constraints on analogue component accuracy by increasing demands on sampling speed and digital processing—a trade-off that is very well suited to the characteristics of today’s CMOS technology. As a result, delta—sigma data converters have become the converters of choice in a wide variety of applications, notably digital telephony, digital audio and instrumentation. Progress in this area has been dramatic and can be loosely grouped into three overlapping areas. The area of circuit design has seen the development of a variety of modulator topologies to meet a growing range of applications, supported by the development of new CAD tools. The original delta—sigma modulators consisted of a filter and a one-bit quantizer connected in a feedback loop in such a way as to shape the quantization noise away from low frequencies. Among the important extensions to this basic topology we now have multiloop systems, which employ multiple feedback loops around a single quantizer; multistage systems, which employ a cascade of basic modulators; multibit systems, in which the quantizer is no longer restricted to one bit (recent and highly promising systems of this type employ noise shaping in a second manner, this time to the DAC errors within the loop); and bandpass systems, which operate on highfrequency narrowband signals. The second of our loose groupings deals with the theory of delta—sigma systems. The most common form of analysis replaces the quantizer with a noise source and then treats the modulator as a two-input linear system. This technique yields much useful insight, but it fails to take into account the true non-linear nature of the system and thus fails to account for such important effects as tonal behaviour and modulator instability. In a sense, delta—sigma systems are particularly simple non-linear systems—typically of low order and with the non-linearity often just a single discontinuity — but underneath this facade of simplicity can lie fiendishly complex dynamics. Many contributions have been made in the arena of delta—sigma theory, but many opportunities still exist for the interested researcher. * Correspondence to: Orla Feely, Department of Electronic and Electrical Engineering, University College Dublin, Dublin 4, Ireland. Email: orla.feely@ucd.ie CCC 0098—9886/97/050317—02$17.50 ( 1997 by John Wiley & Sons, Ltd. 318 GUEST EDITORIAL The third and more recent area involves the application of delta—sigma techniques in ‘unusual’ areas, by which we mean areas other than data conversion. That these techniques have widespread applicability should not be surprising—for example, the standard half-toning procedure by which grey-scale images are represented by black dots on a white background is just one-bit oversampling, with the eye providing the requisite lowpass filtering. Many such applications are usefully viewed from the delta—sigma perspective, with the advances already made in delta—sigma theory and design proving useful in areas such as image processing, signal generation and clock jitter reduction. This is an area that will undoubtedly continue to grow, with delta—sigma and noise-shaping principles finding application in more and more areas of engineering and science. The research literature on delta—sigma modulation is expanding very rapidly, with material on the subject now finding its way into undergraduate textbooks. Two excellent introductions to the area are contained in References 1 and 2. Reference 1 presents a collection of (pre-1991) papers on the subject, together with a tutorial introduction, while the more recent volume2 contains contributions from a number of experts on various theoretical and practical issues associated with delta—sigma modulators, again with a tutorial introduction. Given the importance of delta—sigma modulation and noise-shaping techniques, this special issue is particularly timely and the diversity of the papers is representative of the diversity of the field. In the area of circuit design, Medeiro et al. describe the design of a state-of-the-art low-power second-order modulator with the aid of a special-purpose CAD methodology. Lindfors et al. propose a hardware-efficient dynamic element-matching technique for the reduction of the effect of DAC non-linearity in a multibit bandpass modulator. The section on theory of delta—sigma systems comprises two tutorial papers and one presenting new results. Feely gives a tutorial introduction to non-linear dynamics and chaos and summarizes the ways in which this theory has been applied to delta—sigma systems. Thao summarizes the results obtained from the application of deterministic analysis to the problem of signal reconstruction for delta—sigma systems. Petkov and Davies study the non-linear oscillations arising in a bandpass delta—sigma modulator with constant input. The papers on unusual architectures and applications of delta—sigma techniques demonstrate the diversity of research in this area. Veillette and Roberts describe the use of delta—sigma oscillators in generating singleand multitone signals for applications in test, control and communications. Birru proposes a recursive deconvolution technique which allows the delta—sigma modulator within a DAC to operate at a lower speed. Bit-flipping techniques are applied by Magrath and Sandler to reduce the transition rate in a delta—sigma modulator for power DAC applications. Finally Abeysekera explains the similarity between the delta—sigma technique and the technique of pulse stuffing, widely used in digital communication networks, and thereby proposes techniques for jitter reduction in pulse-stuffing synchronizers. It is hoped that the papers in this special issue will provide a valuable resource for designers and researchers already working in the area and will alert others to the increasingly diverse, and rewarding, nature of research in this arena. REFERENCES 1. J. C. Candy and G. C. Temes (eds) Oversampling Delta—Sigma Data Converters, IEEE, New York, 1992. 2. S. R. Norsworthy, R. Schreier and G. C. Temes (eds) Delta—Sigma Data Converters: ¹heory, Simulation and Design, IEEE, New York, 1996. . Int. J. Circ. Theor. Appl., Vol. 25, 317—318 (1997) ( 1997 by John Wiley and Sons, Ltd.

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