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Model-Reduction Algorithms

       (Principles, AWE, CFH & Macromodeling) (6Hr)

M. Nakhla   and   R. Achar

(ISBN 0-9731047-3-2; First Edition: May 1, 2002; Omniz Global Knowledge Corporation)

This multimedia book provides a comprehensive treatment of recently developed model-reduction algorithms and their application to analysis of high-speed circuits and interconnects. Starting with the fundamentals, the book unravels the mystery of model-reduction algorithms through dazzling animations and multimedia presentations. The topics cover the broad area of model-reduction algorithms, Asymptotic Waveform Evaluation (AWE) and Complex Frequency Hopping (CFH). The book also provides detailed coverage of macromodeling techniques, including the synthesis of differential equations from reduced-order models and also synthesis of SPICE compatible netlists from differential equations.

The book starts with the basics of model-reduction algorithms, such as the concept of moments, Padé approximation and model-reduction issues (stability, passivity accuracy etc.) and proceeds to present the recent advances and their application to circuit/interconnect simulation. The material presented is accompanied with illustrative animations, reinforced with the audio. The book also provides literature reviews, numerous examples, 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 as well as to those interested in understanding model-order reduction and signal integrity issues in high-speed designs. The book is also useful to the math community where the complex issue of model-order reduction is presented in the most revealing form with the help of intense multimedia presentations. This CD based multimedia book contains approximately six hours of intense multimedia presentations.


  1. Principles of Model-Reduction Techniques

  2. Asymptotic Waveform Evaluation (AWE)

  3. Complex Frequency Hopping (CFH)

  4. Macromodeling and Transient Analysis

  5. Exam-1;    Exam-2; Exam-3;    Exam-4

  6. References

I. Principles of Model-Reduction Techniques

1. Model-Reduction - The Concept
2. Model-Reduction - Dominant Poles
    * Impulse Response
    * Systems with Complex Poles
3. Model-Reduction - Requirements
    * Accuracy
    * Stability
    * Passivity
    * CPU efficiency
4. Model-reduction - Classification of Algorithms
    * Direct Padé Based Techniques
    * Indirect Padé Based Techniques
5. Exam;     Test-Match;      References

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II. Asymptotic Waveform Evaluation (AWE)

1) AWE - The Concept
2) Padé Approximation
    * Taylor Series & Definition of Moments; Example
    * Rational Approximation
    * Example of Padé Approximation
    * Comparison of Taylor v/s Padé Approximation
    * Pole-Residue Model;  Example
3) Application to Circuit Analysis, Example
4) Computation of Circuit Moments, Example
5) Summary of The Algorithm

6. Exam;     Test-Match;      References

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III. Complex Frequency Hopping (CFH)

1. Limitations of Single Expansion Techniques
2. Complex Frequency Hopping
3. Theory of Shifted Moments and Poles
4. Generalized Computation of Circuit Moments
    * Transmission-Line Moments
5. Search Algorithms
    * Transfer-Function Based Search
    * Poles Based Search
6. Multiport Network Analysis
7. Block CFH

8. Exam,     Test-Match,     References

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IV. Macromodeling and Transient Analysis

1. Impulse Response
2. Transient Response - Linear Circuits
    * Unit-Step Response
    * Unit-Ramp Response
    * Response Due to Arbitrary Piece-Wise Linear Inputs
    * Example-1,   Example-2,   Example-3
3. Macromodeling
    * Ordinary Differential Equations (ODEs)
    * Complex Poles
    * Example-4,   Example-5,   Example-6
    * Example-7,   Example-8
4. Conversion of ODEs to SPICE Netlist
5. Transient Analysis - Nonlinear Circuits

6. Exam,     Test-Match,     References

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V. Exam

There are four 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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