Preface

Sigma-Delta modulators (Ms) have become one of the best choices for the implementation of analog/digital interfaces integrated in CMOS technologies. Compared to other kinds of analog-to-digital converters (ADCs), Ms cover the widest conversion region of the resolution-versus-bandwidth plane, being the most efficient solution to digitize very diverse types of signals in an increasing number of application scenarios, which span from high-resolution low-bandwidth data conversion (like digital audio, sensor interfaces, and instrumentation) to ultra-low power biomedical systems and medium-resolution broadband wireless communications. This versatility, together with their robustness and their simplicity in many practical situations, has motivated that more and more engineers today consider Ms as a first choice for their research projects and their industrial products.

The first idea underlying the operation of Ms was patented by Cutler in 1960 [1], although its application to the construction of data converters was first reported in the published literature by Inose et al in 1962 [2]. The operation of Ms is relatively simple to describe, although sometimes difficult to analyze. Essentially, the fundamental principle behind Ms is based on the combination of two signal processing techniques, namely oversampling and quantization noise shaping. The former consists of taking the signal samples at a higher rate than the one dictated by the Nyquist sampling theorem. These samples are commonly quantized with a large error by using a low-resolution quantizer. The resulting oversampled quantization error is filtered in the modulator feedback loop, so that its frequency spectrum is shaped in such a way that a large portion of its power is pushed out of the signal band, where it is removed by a digital filter. The outcome of the combined action of oversampling and noise shaping allows Ms to achieve a high-precision digitization by using a low-resolution coarse quantizer. Therefore, unlike other kinds of ADC architectures that require high-precision analog circuits, Ms trade the accuracy of their analog circuitry by the speed of digital signal processing, thus achieving a higher degree of insensitivity to circuit error mechanisms and potentially benefiting from CMOS technology evolution towards the nanometer scale.

Prompted by the mentioned benefits and fueled by technology downscaling and industry trends in consumer digital electronics, the original concept of noise shaping described above has evolved over the last five decades through many M generations, giving rise to a pleiad of architectures, circuit and system design techniques, and a number of Integrated Circuits (ICs), which have pushed the state-of-the-art on Ms forward, yielding to innovative research results and successful industry products. All these advances and research works have lead (and continue doing so) to a vast amount of technical literature. Indeed, since the publication of pioneer works like the widely cited papers written by Candy [3, 4] and Boser and Wooley [5], the number of publications has increased significantly including hundreds of patents, thousands of research papers, some tutorial papers [6–8], as well as tens of introductory and specialized monographs [9–29]. However, with so much material and abundance of technical information published, many designers—particularly novel designers and also some experienced designers focused on a specific subtopic of Ms—may become disoriented and lost. This has motivated some authors to put all these pieces of information together in a comprehensive and systematic way.

Apart from the earlier books aiming to catalogue the existing publications on Ms [9], one of the first attempts to present a guide for M designers is the book edited by Norsworthy et al in 1997 [10], also known as “the yellow book” by the M community. This book deals with a number of important subjects in Ms and it was contributed by a number of experts in the field, thus making it more difficult to present its contents in a coherent and consistent way. With this objective in mind, some authors have put their effort on writing tutorial monographs dealing with the systematic design of Ms.

Among others, the book written by Schreier and Temes, published in 2005 [21], often named “the green book”, has become one of the most popular books on converters. This book provides an excellent and comprehensive treatment of Ms, their operating principles, and main architectures, presenting several design examples constructed using the well-known Schreier's MATLAB toolbox [30]. Although some examples of continuous-time (CT) circuit implementations are given, the book mainly focuses on system-level description, considering a switched-capacitor (SC) implementation. Some other remarkable examples are the book written by Medeiro et al in 1999 [13]—focused on the systematic design of SC Ms—and the book of Ortmanns and Gerfers [22] published in 2006, which is still one of the most complete monographs on CT Ms reported to date. All these books, as well as other monographs reported in the technical literature, give a partial view of Ms, paying more attention to some particular aspects of the design of Ms, and/or a type of architecture, circuit technique, or application.

In this scenario, this book attempts to cover some of these knowledge gaps, by providing a broader and systematic description of the universe of Ms, their diverse types of architectures, circuit techniques, analysis and synthesis methods and CAD tools, as well as their practical design considerations. From this perspective, the book has a twofold purpose. First, it constitutes a unique monograph that results from compiling the enormous number of technical and research works reported to date on the topic of Ms, and presents the results of such a compilation in a didactical, pedagogical, and intuitive style. The second main objective and a key feature of this book is to serve as a practical guide for designers, putting emphasis on explaining practical design issues involved in the whole design flow of Ms: from specifications to chip implementation and characterization. To this end, a top-down approach is followed, presenting the contents in a hierarchical way; that is, going from theoretical fundamentals, system-level design equations, and behavioral models to circuit, transistor-level, and physical implementation, in order to provide readers the necessary understanding and insight into the recent advances, trends, and challenges involved in the design of state-of-the-art ICs.

Indeed, it is the top-down approach adopted in this book that inspires the hierarchical way in which the contents are organized. Thus, following this introduction, Chapter 1 begins from top, giving an introductory survey of Ms, their principles of operation, fundamental architectures, analysis and synthesis methods, as well as a taxonomical description of the diverse variety of practical M topologies, the nature of signal (low-pass and band-pass), as well as the dynamics involved (either discrete-time or continuous-time). In this chapter Ms are considered ideal systems, except for their inherent quantization error. Chapter 2 descends one level in the modulator hierarchy to analyze the effect of main circuit error mechanisms as well as architectural and timing nonidealities, considered in both SC and CT circuit implementations. The mathematical models, analytical procedures, and design guidelines described in this chapter provide sufficient understanding of the main practical problems affecting the performance of Ms in practice.

The knowledge derived from the first two chapters is presented in this book as an essential part of the systematic top-down/bottom-up synthesis methodology of Ms, that is described in Chapter 3. This chapter analyzes different strategies for the high-level modeling and simulation of Ms, focusing on the so-called behavioral modeling and simulation techniques. A step-by-step procedure to develop efficient behavioral models in the MATLAB/SIMULINK environment is described and illustrated with a number of examples of the main M building-block models. As an application, a time-domain behavioral simulator named SIMSIDES, is described and applied to the high-level sizing and verification of some case studies. The contents of this chapter are extended and complemented in Appendixes A and B. Appendix A gives a more complete user guide of SIMSIDES and Appendix B provides an overview of all behavioral models and libraries included in this simulator.

Chapter 4 moves farther down from the system-level description given in previous chapters to the circuit and physical level. This chapter provides a number of necessary design recommendations and practical recipes to complete the design flow of a M, showing the step-by-step methodology to transform a behavioral-model description given in Chapter 3 into an electrical schematic initially based on macromodels, and then implemented with transistors, and finally concluding the design cycle with the layout and chip implementation. Plenty of examples, case studies, and simulation test benches are given to illustrate the practical issues and design considerations addressed in the chapter, that cover from electrical analysis and simulation using SPICE-like simulators to layout design considerations, chip prototyping, and experimental measurements of Ms in the laboratory.

To conclude the book, Chapter 5 gives an overview of the state-of-the-art M ICs, comparing their performance with Nyquist-rate ADCs. Overall, more than 300 state-of-the-art IC references have been studied in detail and considered in this review, including papers published from 1990 to June 2012. Therefore, following the practical philosophy that inspires this book, the diverse families of state-of-the-art M architectures and circuit techniques are exhaustively analyzed and compared to extract practical and empirical design guidelines from the statistical data, trying to identify the incoming trends, design challenges, as well as the solutions proposed by cutting-edge ICs that are in the frontiers of Ms.

The book contents are addressed and structured for a large audience: from senior designers who want to acquire a deeper and updated insight into Ms, to nonexperienced undergraduate students who are looking for a comprehensive, uniform, and self-contained reference into this hot topic. Bearing this in mind, the style and main purpose of the book is to serve also as an educational and reference textbook for undergraduate and graduate students. Indeed, the book is based on a number of graduate courses given by the authors, including master and doctorate degree programs, invited lectures, and IEEE conference tutorials. All these materials have been adapted and updated so that a large portion of the book can be also used (and indeed it has been used) in both undergraduate and graduate courses.

However, in spite of the encyclopedic nature of the book, it is impossible to give an exhaustive description of all the topics contained in the thousands of publications dealing with Ms. Instead, the book tries to cover the main subtopics, providing sufficient insight to understand the other ones, that are just overviewed and sometimes even omitted. In order to try to palliate these unavoidable deficiencies, an exhaustive list of specific references is included at the end of each chapter. Overall, the book contains around 500 selected references in order to guide readers to increase their understanding of the diverse research topics dealing with the world.

The huge amount of information contained in the book is complemented and updated with a number of electronic resources, that have been prepared by the authors and are freely available on the Web. To this purpose, all the data analyzed in the state-of-the-art survey presented in Chapter 5 have been collected in a spreadsheet, which is available at http://www.imse-cnm.csic.es/∼jrosa/CMOS-SDMs-Survey-IMSE-JMdelaRosa.xlsx. This database is periodically kept up to date and aims to be a complement to the popular Murmann's ADC survey data collection [31]. In addition, a fully functional version of the time-domain behavioral simulator SIMSIDES is freely available on demand at http://www.imse-cnm.csic.es/simsides. The simulator includes a number of examples, containing the case studies presented in the book and many more examples and demos. Apart from the SIMSIDES software, the majority of examples and test benches of different CAD tools used throughout the book are also available on the Web at www.wiley.com/go/delarosa_converters.

Last but not least, it is important to mention that the aforementioned web sites will be regularly updated with new pieces of information and updated material related to the state-of-the-art M ICs, SIMSIDES examples and demos, as well as new inputs provided by us and hopefully by our readers. Therefore, your feedback is very important and very welcomed!

We hope that you enjoy reading this book as much as we have enjoyed writing it.

José M. de la Rosa and Rocío del Río
Sevilla, October 2012

References

[1] C. C. Cutler, “Transmission System Employing Quantization,” US Patent No. 2,927,962, 1960.

[2] H. Inose, Y. Yasuda, and J. Murakami, “A Telemetering System by Code Modulation—- Modulation,” IRE Transactions on Space Electronics and Telemetry, vol. 8, pp. 204–209, September 1962.

[3] J. Candy and O. J. Benjamin, “The Structure of Quantization Noise from Sigma-Delta Modulation,” IEEE Transactions on Communications, pp. 1316–1323, 1981.

[4] J. Candy, “A Use of Double Integration in Sigma-Delta Modulation,” IEEE Transactions on Communications, vol. 33, pp. 249–258, March 1985.

[5] B. E. Boser and B. A. Wooley, “The Design of Sigma-Delta Modulation Analog-to-Digital Converters,” IEEE Journal of Solid-State Circuits, vol. 23, pp. 1298–1308, December 1988.

[6] P. M. Aziz et al., “An Overview of Sigma-Delta Converters,” IEEE Signal Processing Magazine, vol. 13, pp. 61–84, January 1996.

[7] I. Galton, “Delta-Sigma Data Conversion in Wireless Transceivers,” IEEE Transactions on Microwave Theory and Techniques, vol. 50, pp. 302–315, January 2002.

[8] J. M. de la Rosa, “Sigma-Delta Modulators: Tutorial Overview, Design Guide, and State-of-the-Art Survey,” IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 58, pp. 1–21, January 2011.

[9] J. Candy and G. Temes, Oversampling Delta-Sigma Data Converters: Theory, Design and Simulation, IEEE Press, 1991.

[10] S. R. Norsworthy, R. Schreier, and G. C. Temes, Delta-Sigma Data Converters: Theory, Design and Simulation, IEEE Press, 1997.

[11] J. Cherry and W. Snelgrove, Continuous-Time Delta-Sigma Modulators for High-Speed A/D Conversion, Kluwer Academic Publishers, 1999.

[12] J. V. Engelen and R. van de Plassche, BandPass Sigma-Delta Modulators: Stability Analysis, Performance and Design Aspects, Kluwer Academic Publishers, 1999.

[13] F. Medeiro, B. Pérez-Verdù, and A. Rodríguez-Vázquez, Top-Down Design of High-Performance Sigma-Delta Modulators, Kluwer Academic Publishers, 1999.

[14] V. Peluso, M. Steyaert, and W. Sansen, Design of Low-Voltage Low-Power CMOS Delta-Sigma A/D Converters, Kluwer Academic Publishers, 1999.

[15] S. Rabii and B. A. Wooley, The Design of Low-Voltage, Low-Power Sigma-Delta Modulators, Kluwer Academic Publishers, 1999.

[16] L. Breems and J. H. Huijsing, Continuous-Time Sigma-Delta Modulation for A/D Conversion in Radio Receivers, Kluwer Academic Publishers, 2001.

[17] Y. Geerts, M. Steyaert, and W. Sansen, Design of Multi-bit Delta-Sigma A/D Converters, Kluwer Academic Publishers, 2002.

[18] J. M. de la Rosa, B. Pérez-Verdú, and A. Rodríguez-Vázquez, Systematic Design of CMOS Switched-Current Bandpass Sigma-Delta Modulators for Digital Communication Chips, Kluwer Academic Publishers, 2002.

[19] M. Kozak and I. Kale, Oversampling Delta-Sigma Modulators, Springer, 2003.

[20] O. Bajdechi and J. Huising, Systematic Design of Sigma-Delta Analog-to-Digital Converters, Kluwer Academic Publishers, 2004.

[21] R. Schreier and G. C. Temes, Understanding Delta-Sigma Data Converters, Wiley-IEEE Press, 2005.

[22] M. Ortmanns and F. Gerfers, Continuous-Time Sigma-Delta A/D Conversion: Fundamentals, Performance Limits and Robust Implementations, Springer, 2006.

[23] K. Philips and A. H. M. van Roermund, Sigma Delta A/D Conversion for Signal Conditioning, Springer, 2006.

[24] R. del Río, F. Medeiro, B. Pérez-Verdú, J. M. de la Rosa, and A. Rodríguez-Vázquez, CMOS Cascade Modulators for Sensors and Telecom: Error Analysis and Practical Design, Springer, 2006.

[25] L. Yao, M. Steyaert, and W. Sansen, Low-Power Low-Voltage Sigma-Delta Modulators in Nanometer CMOS, Springer, 2006.

[26] P. G. R. Silva and J. H. Huijsing, High Resolution IF-to-Baseband ADC for Car Radios, Springer, 2008.

[27] R. H. van Veldhoven and A. H. M. van Roermund, Robust Sigma Delta Converters, Springer, 2011.

[28] A. Morgado, R. del Río, and J. M. de la Rosa, Nanometer CMOS Sigma-Delta Modulators for Software Defined Radio, Springer, 2011.

[29] E. Janssens and A. van Roermund, Look-Ahead Based Sigma-Delta Modulation, Springer, 2011.

[30] R. Schreier, The Delta-Sigma Toolbox v. 7.3. [Online]. Available: http://www.mathworks.com/matlabcentral/fileexchange/19, 2009.

[31] B. Murmann, ADC Performance Survey 1997–2012. [Online]. Available: http://www.stanford.edu/∼murmann/adcsurvey.html, 2012.