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Krylov Subspace Techniques for Circuit and Interconnect Analysis (5Hr)

M. Nakhla   and   R. Achar

(ISBN 0-9731047-5-9; First Edition: May 1, 2002; Omniz Global Knowledge Corporation)

This multimedia book provides a comprehensive treatment of recently developed model-reduction strategies based on Krylov subspace techniques and their application to simulation of large high-speed interconnect subnetworks. Building from the very basic concepts, the book unravels the mystery of model-order reduction and Krylov-subspace techniques through dazzling animations.

The book provides an in-depth coverage of various related algorithms such as Arnoldi, PRIMA etc. as well as related issues such as accuracy, stability and passivity preservation etc. It covers both cases of single and multiport network reductions. The book also provides literature reviews, numerous examples, illustrations, and necessary relations/derivations. The book has been developed in an easy-to-understand style and with in-depth coverage.

The material presented is useful for designers, application engineers, CAD tool developers as well as to those interested in understanding model-order reduction and signal integrity issues in high-speed circuits. The book is also useful to the math community where the complex issue of model-order reduction using Krylov-subspace techniques is presented in the most revealing form with the help of intense multimedia presentations. This CD based multimedia book contains approximately five hours of intense multimedia presentations.


  1. Introduction and Basic Concepts

  2. Krylov-Subspace Techniques

  3. Circuit (Single Port) Reduction

  4. Multiport Reduction and Passivity Preservation

  5. Exam-1;    Exam-2;      Exam-3

  6. References

I. Introduction and Basic Concepts

1. High-Speed Design Issues
2. Review of Circuit Simulation
3. Interconnect Simulation Issues
    * Mixed Frequency/Time Difficulty
    * CPU Expense
4. Exam

5. References

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II. Krylov-Subspace Techniques

1. Basic Concepts
    * Upper Hessenberg (UH) Matrix
    * Eigenvalues Through Direct Similarity Transformation
       * Example
       * Disadvantages
2. Krylov-Subspace Methods
3. Arnoldi Algorithm for Partial Reduction to UH form
    * Step - I Step - II Step - III
    * Summary of the Algorithm
4. Exam;         

5. References

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III. Circuit (Single Port) Reduction

1. Single Port Circuit Equations
2. Circuit Reduction Using Arnoldi Algorithm
3. Accuracy Issues
4. Example

5. Exam         

6. References

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IV. Multiport Reduction and Passivity Preservation

1. Formulation of Multiport Networks

    * Example
2. Reduction of Multiport Equations
    * Block Moments
    * Block Krylov-Subspace

       * Example
    * Multiport Reduced Model
3. Passivity Preservation
    * Review of Passivity Properties
    * Passive Reduction Using Congruent Transformation
    * Example
4. MNA Formulation for Passive Reduction; Example
5. Summary of Passive Reduction/Macromodeling
6. Exam         

7. References

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V. Exam

There are three complete exams in this book which are designed to test the level of one's understanding after completing the study. The questions are such that they broadly cover the material taught in the course and are formulated to reinforce the concepts learnt during the study. The solutions, corrected paper and the final marks are provided after the completion of the exam.

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VI. References

A Comprehensive list of related references in the leading IEEE international journals and conferences is provided.

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Copyright 2002, Omniz Global Knowledge Corporation. All rights reserved.
Revised: 07/20/2002

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