This book proposes a new approach to circuit simulation that is still in its infancy. The reason for publishing this work as a monograph at this time is to quickly distribute these ideas to the research community for further study. The book is based on a doctoral dissertation undertaken at MIT between 1982 and 1985. In 1982 the author joined a research group that was applying bounding techniques to simple VLSI timing analysis models. The conviction that bounding analysis could also be successfully applied to sophisticated digital MOS circuit models led to the research presented here. Acknowledgments 'me author would like to acknowledge many helpful discussions and much support from his research group at MIT, including Lance Glasser, John Wyatt, Jr. , and Paul Penfield, Jr. Many others have also contributed to this work in some way, including Albert Ruchli, Mark Horowitz, Rich Zippel, Chtis Terman, Jacob White, Mark Matson, Bob Armstrong, Steve McCormick, Cyrus Bamji, John Wroclawski, Omar Wing, Gary Dare, Paul Bassett, and Rick LaMaire. The author would like to give special thanks to his wife, Deborra, for her support and many contributions to the presentation of this research. The author would also like to thank his parents for their encouragement, and IBM for its financial support of t,I-Jis project through a graduate fellowship. THE BOUNDING APPROACH TO VLSI CIRCUIT SIMULATION 1. INTRODUCTION The VLSI revolution of the 1970's has created a need for new circuit analysis techniques.

This book provides comprehensive coverage of the recent advances in symbolic analysis techniques for design automation of nanometer VLSI systems. The presentation is organized in parts of fundamentals, basic implementation methods and applications for VLSI design. Topics emphasized include statistical timing and crosstalk analysis, statistical and parallel analysis, performance bound analysis and behavioral modeling for analog integrated circuits. Among the recent advances, the Binary Decision Diagram (BDD) based approaches are studied in depth. The BDD-based hierarchical symbolic analysis approaches, have essentially broken the analog circuit size barrier.

Circuit simulation has become an essential tool in circuit design and without it's aid, analogue and mixed-signal IC design would be impossible. However the applicability and limitations of circuit simulators have not been generally well understood and this book now provides a clear and easy to follow explanation of their function. The material covered includes the algorithms used in circuit simulation and the numerical techniques needed for linear and non-linear DC analysis, transient analysis and AC analysis. The book goes on to explain the numeric methods to include sensitivity and tolerance analysis and optimisation of component values for circuit design. The final part deals with logic simulation and mixed-signal simulation algorithms. There are comprehensive and detailed descriptions of the numerical methods and the material is presented in a way that provides for the needs of both experienced engineers who wish to extend their knowledge of current tools and techniques, and of advanced students and researchers who wish to develop new simulators.

The summer school on VLSf GAD Tools and Applications was held from July 21 through August 1, 1986 at Beatenberg in the beautiful Bernese Oberland in Switzerland. The meeting was given under the auspices of IFIP WG 10. 6 VLSI, and it was sponsored by the Swiss Federal Institute of Technology Zurich, Switzerland. Eighty-one professionals were invited to participate in the summer school, including 18 lecturers. The 81 participants came from the following countries: Australia (1), Denmark (1), Federal Republic of Germany (12), France (3), Italy (4), Norway (1), South Korea (1), Sweden (5), United Kingdom (1), United States of America (13), and Switzerland (39). Our goal in the planning for the summer school was to introduce the audience into the realities of CAD tools and their applications to VLSI design. This book contains articles by all 18 invited speakers that lectured at the summer school. The reader should realize that it was not intended to publish a textbook. However, the chapters in this book are more or less self-contained treatments of the particular subjects. Chapters 1 and 2 give a broad introduction to VLSI Design. Simulation tools and their algorithmic foundations are treated in Chapters 3 to 5 and 17. Chapters 6 to 9 provide an excellent treatment of modern layout tools. The use of CAD tools and trends in the design of 32-bit microprocessors are the topics of Chapters 10 through 16. Important aspects in VLSI testing and testing strategies are given in Chapters 18 and 19.