Asymptotic Waveform Evaluation

The intense drive for signal integrity has been at the forefront ofrapid and new developments in CAD algorithms. Thousands ofengineers, intent on achieving the best design possible, use SPICE on a daily basis for analog simulation and general circuit analysis. But the strained demand for high data speeds, coupled with miniaturizationon an unprecedented scale, has highlighted the previously negligible effects of interconnects; effects which are not always handled appro priately by the present levels of SPICE. Signals at these higher speeds may be degraded by long interconnect lengths compared to the increasingly shorter sig nal rise times. Interconnect structures can be diverse (pins, connectors, leads, microstrips, striplines, etc. ) and present at any of the hierarchical packaging levels: integrated circuits, printed circuit boards, multi-chip modules or sys tem backplanes. Analysis of these effects in any CAD package has become a necessity. Asymptotic waveform evaluation (AWE) and other moment matching tech niques have recently proven useful in the analysis of interconnect structures and various networks containing large linear structures with nonlinear termi nations. Previously, all that was available to the designer was a full SPICE simulation or a quick but uncertain timing estimation. Moment matching, used in linear systems analysis as a method of model reduction, describes a method to extract a small set of dominant poles from a large network. The information is obtained from the Taylor series coefficients (moments) of that system.

Model order reduction (MOR) techniques reduce the complexity of VLSI designs, paving the way to higher operating speeds and smaller feature sizes. This book presents a systematic introduction to, and treatment of, the key MOR methods employed in general linear circuits, using real-world examples to illustrate the advantages and disadvantages of each algorithm. Following a review of traditional projection-based techniques, coverage progresses to more advanced MOR methods for VLSI design, including HMOR, passive truncated balanced realization (TBR) methods, efficient inductance modeling via the VPEC model, and structure-preserving MOR techniques. Where possible, numerical methods are approached from the CAD engineer's perspective, avoiding complex mathematics and allowing the reader to take on real design problems and develop more effective tools. With practical examples and over 100 illustrations, this book is suitable for researchers and graduate students of electrical and computer engineering, as well as practitioners working in the VLSI design industry.

Digital Timing Macromodeling for VLSI Design Verification first of all provides an extensive history of the development of simulation techniques. It presents detailed discussion of the various techniques implemented in circuit, timing, fast-timing, switch-level timing, switch-level, and gate-level simulation. It also discusses mixed-mode simulation and interconnection analysis methods. The review in Chapter 2 gives an understanding of the advantages and disadvantages of the many techniques applied in modern digital macromodels. The book also presents a wide variety of techniques for performing nonlinear macromodeling of digital MOS subcircuits which address a large number of shortcomings in existing digital MOS macromodels. Specifically, the techniques address the device model detail, transistor coupling capacitance, effective channel length modulation, series transistor reduction, effective transconductance, input terminal dependence, gate parasitic capacitance, the body effect, the impact of parasitic RC-interconnects, and the effect of transmission gates. The techniques address major sources of errors in existing macromodeling techniques, which must be addressed if macromodeling is to be accepted in commercial CAD tools by chip designers. The techniques presented in Chapters 4-6 can be implemented in other macromodels, and are demonstrated using the macromodel presented in Chapter 3. The new techniques are validated over an extremely wide range of operating conditions: much wider than has been presented for previous macromodels, thus demonstrating the wide range of applicability of these techniques.

The idea for this book originated during the workshop “Model order reduction, coupled problems and optimization” held at the Lorentz Center in Leiden from S- tember 19–23, 2005. During one of the discussion sessions, it became clear that a book describing the state of the art in model order reduction, starting from the very basics and containing an overview of all relevant techniques, would be of great use for students, young researchers starting in the ?eld, and experienced researchers. The observation that most of the theory on model order reduction is scattered over many good papers, making it dif?cult to ?nd a good starting point, was supported by most of the participants. Moreover, most of the speakers at the workshop were willing to contribute to the book that is now in front of you. The goal of this book, as de?ned during the discussion sessions at the workshop, is three-fold: ?rst, it should describe the basics of model order reduction. Second, both general and more specialized model order reduction techniques for linear and nonlinear systems should be covered, including the use of several related numerical techniques. Third, the use of model order reduction techniques in practical appli- tions and current research aspects should be discussed. We have organized the book according to these goals. In Part I, the rationale behind model order reduction is explained, and an overview of the most common methods is described.

As the complexity of electronic systems continues to increase, the micro-electronic industry depends upon automation and simulations to adapt quickly to market changes and new technologies. Compiled from chapters contributed to CRC's best-selling VLSI Handbook, this volume of the Principles and Applications in Engineering series covers a broad rang

Over the years, the fundamentals of VLSI technology have evolved to include a wide range of topics and a broad range of practices. To encompass such a vast amount of knowledge, The VLSI Handbook focuses on the key concepts, models, and equations that enable the electrical engineer to analyze, design, and predict the behavior of very large-scale integrated circuits. It provides the most up-to-date information on IC technology you can find. Using frequent examples, the Handbook stresses the fundamental theory behind professional applications. Focusing not only on the traditional design methods, it contains all relevant sources of information and tools to assist you in performing your job. This includes software, databases, standards, seminars, conferences and more. The VLSI Handbook answers all your needs in one comprehensive volume at a level that will enlighten and refresh the knowledge of experienced engineers and educate the novice. This one-source reference keeps you current on new techniques and procedures and serves as a review for standard practice. It will be your first choice when looking for a solution.

This volume documents the research carried out by visiting scientists attached to the Institute for Mathematical Sciences (IMS) at the National University of Singapore and the Institute of High Performance Computing (IHPC) under the program “Advances and Mathematical Issues in Large Scale Simulation.” From 2002 to 2003, researchers from various countries gathered to initiate interesting and innovative work on various themes related to multiscale simulation and fast algorithms. Today, modeling and simulation are used extensively to solve complex problems and to reduce the use of experimentation during the design and analysis stage. It is important to know the various issues that have to be considered in the successful development of computational methodologies for such work. This volume is a compilation of the research by various visiting scientists in the area of modeling and multiscale simulation. Each article covers a major project and documents how computational methodology, mathematical modeling, high performance computing and simulation are combined in a multiscale scheme to solve a variety of complex problems. Some of these include the design, synthesis, processing, characterization and manufacture of nanomaterials and nanostructures, new algorithms for computational work, and grid computing. Through the included examples, readers can realize the vast potential of computational modeling and large scale simulation for the solution of problems in a variety of disciplines and applications. Contents:Methods of Multiscale Modeling in Mechanics (W A Curtin)Efficient and Accurate Boundary Methods for Computational Optics (C Hafner & J Smajic)Finite Element Modeling of Periodic Structures (Z Lou & J-M Jin)Factorization of Potential and Field Distributions without Utilizing the Addition Theorem (A-R Baghi-Wadji & E Li)Virtualization-Aware Application Framework for Hierarchical Multiscale Simulations on a Grid (A Nakano et al.)Molecular Dynamics Simulation and Local Quantities (T Ikeshoji)Recent Advances in Modeling and Simulation of High-Speed Interconnects (M Nakhla & R Achar)Multiscale Modeling of Degradation and Failure of Interconnect Lines Driven by Electromigration and Stress Gradients (R Atkinson & A M Cuitiño) Readership: Engineers, scientists and graduate students who need further insights into the applications and power of computational methodology for the solution of a wide array of problems. Keywords:Large Scale Simulation;High Performance Computing;Multiscale Simulation;Fast Algorithms;Computational MethodologyKey Features:Provides insight into the applications and power of computational methodology in solving a wide array of complex problems