Reduced Order Modeling And Analysis For Vlsi Rlc Interconnect

Symbolic analysis is an intriguing topic in VLSI designs. The analysis methods are crucial for the applications to the parasitic reduction and analog circuit evaluation. However, analyzing circuits symbolically remains a challenging research issue. Therefore, in this book, we survey the recent results as the progress of on-going works rather than as the solution of the field. For parasitic reduction, we approximate a huge amount of electrical parameters into a simplified RLC network. This reduction allows us to handle very large integrated circuits with given memory capacity and CPU time. A symbolic analysis approach reduces the circuit according to the network topology. Thus, the designer can maintain the meaning of the original network and perform the analysis hierarchically. For analog circuit designs, symbolic analysis provides the relation between the tunable parameters and the characteristics of the circuit. The analysis allows us to optimize the circuit behavior. The book is divided into three parts. Part I touches on the basics of circuit analysis in time domain and in s domain. For an s domain expression, the Taylor's expansion with s approaching infinity is equivalent to the time domain solution after the inverse Laplace transform. On the other hand, the Taylor's expansion when s approaches zero derives the moments of the output responses in time domain. Part II focuses on the techniques for parasitic reduction. In Chapter 2, we present the approximation methods to match the first few moments with reduced circuit orders. In Chapter 3, we apply the Y-Delta transformation to reduce the dynamic linear network. The method finds the exact values of the low order coefficients of the numerator and denominator of the transfer function and thus matches part of the moments. In Chapter 4, we handle two major issues of the Y-Delta transformation: common factors in fractional expressions and round-off errors. Chapter 5 explains the stability of the reduced expression, in particular the Ruth-Hurwitz Criterion. We make an effort to describe the proof of the Criterion because the details are omitted in most of the contemporary textbooks. In Chapter 6, we present techniques to synthesize circuits to approximate the reduced expressions after the transformation. In Part III, we discuss symbolic generation of the determinants and cofactors for the application to analog designs. In Chapter 7, we depict the classical topological analysis approach. In Chapter 8, we describe a determinant decision diagram approach that exploits the sparsity of the matrix to accelerate the computation. In Chapter 9, we take only significant terms when we search through determinant decision diagram to approximate the solution. In Chapter 10, we extend the determinant decision diagram to a hierarchical model. The construction of the modules through the hierarchy is similar to the Y-Delta transformation in the sense that a byproduct of common factors appears in the numerator and denominator. Therefore, we describe the method to prune the common factors.

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.

This book presents an updated selection of the most representative contributions to the 2nd and 3rd IEEE Workshops on Signal Propagation on Interconnects (SPI) which were held in Travemtinde (Baltic See Side), Germany, May 13-15, 1998, and in Titisee-Neustadt (Black Forest), Germany, May 19-21, 1999. This publication addresses the need of developers and researchers in the field of VLSI chip and package design. It offers a survey of current problems regarding the influence of interconnect effects on the electrical performance of electronic circuits and suggests innovative solutions. In this sense the present book represents a continua tion and a supplement to the first book "Signal Propagation on Interconnects", Kluwer Academic Publishers, 1998. The papers in this book cover a wide area of research directions: Beneath the des cription of general trends they deal with the solution of signal integrity problems, the modeling of interconnects, parameter extraction using calculations and measurements and last but not least actual problems in the field of optical interconnects.

For the new millenium, Wai-Kai Chen introduced a monumental reference for the design, analysis, and prediction of VLSI circuits: The VLSI Handbook. Still a valuable tool for dealing with the most dynamic field in engineering, this second edition includes 13 sections comprising nearly 100 chapters focused on the key concepts, models, and equations. Written by a stellar international panel of expert contributors, this handbook is a reliable, comprehensive resource for real answers to practical problems. It emphasizes fundamental theory underlying professional applications and also reflects key areas of industrial and research focus. WHAT'S IN THE SECOND EDITION? Sections on... Low-power electronics and design VLSI signal processing Chapters on... CMOS fabrication Content-addressable memory Compound semiconductor RF circuits High-speed circuit design principles SiGe HBT technology Bipolar junction transistor amplifiers Performance modeling and analysis using SystemC Design languages, expanded from two chapters to twelve Testing of digital systems Structured for convenient navigation and loaded with practical solutions, The VLSI Handbook, Second Edition remains the first choice for answers to the problems and challenges faced daily in engineering practice.

Modeling and Simulation of High Speed VLSI Interconnects brings together in one place important contributions and state-of-the-art research results in this rapidly advancing area. Modeling and Simulation of High Speed VLSI Interconnects serves as an excellent reference, providing insight into some of the most important issues in the field.

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.

Simulation based on mathematical models plays a major role in computer aided design of integrated circuits (ICs). Decreasing structure sizes, increasing packing densities and driving frequencies require the use of refined mathematical models, and to take into account secondary, parasitic effects. This leads to very high dimensional problems which nowadays require simulation times too large for the short time-to-market demands in industry. Modern Model Order Reduction (MOR) techniques present a way out of this dilemma in providing surrogate models which keep the main characteristics of the device while requiring a significantly lower simulation time than the full model. With Model Reduction for Circuit Simulation we survey the state of the art in the challenging research field of MOR for ICs, and also address its future research directions. Special emphasis is taken on aspects stemming from miniturisations to the nano scale. Contributions cover complexity reduction using e.g., balanced truncation, Krylov-techniques or POD approaches. For semiconductor applications a focus is on generalising current techniques to differential-algebraic equations, on including design parameters, on preserving stability, and on including nonlinearity by means of piecewise linearisations along solution trajectories (TPWL) and interpolation techniques for nonlinear parts. Furthermore the influence of interconnects and power grids on the physical properties of the device is considered, and also top-down system design approaches in which detailed block descriptions are combined with behavioral models. Further topics consider MOR and the combination of approaches from optimisation and statistics, and the inclusion of PDE models with emphasis on MOR for the resulting partial differential algebraic systems. The methods which currently are being developed have also relevance in other application areas such as mechanical multibody systems, and systems arising in chemistry and to biology. The current number of books in the area of MOR for ICs is very limited, so that this volume helps to fill a gap in providing the state of the art material, and to stimulate further research in this area of MOR. Model Reduction for Circuit Simulation also reflects and documents the vivid interaction between three active research projects in this area, namely the EU-Marie Curie Action ToK project O-MOORE-NICE (members in Belgium, The Netherlands and Germany), the EU-Marie Curie Action RTN-project COMSON (members in The Netherlands, Italy, Germany, and Romania), and the German federal project System reduction in nano-electronics (SyreNe).

This book gathers selected high-quality research papers presented at the Eighth International Congress on Information and Communication Technology, held at Brunel University, London, on 20–23 February 2023. It discusses emerging topics pertaining to information and communication technology (ICT) for managerial applications, e-governance, e-agriculture, e-education and computing technologies, the Internet of Things (IoT) and e-mining. Written by respected experts and researchers working on ICT, the book offers a valuable asset for young researchers involved in advanced studies. The work is presented in four volumes.