Fast Algorithm for Transient Analysis of Distributed ... VLSI Very Large Scale Integrated Circuit RLCG

  • View
    0

  • Download
    0

Embed Size (px)

Text of Fast Algorithm for Transient Analysis of Distributed ... VLSI Very Large Scale Integrated Circuit...

  • Fast Algorithm for Transient Analysis of

    D istributed Interconnects Including

    Driver and Load Circuits

    by

    Lidija Filipovic

    A thesis submitted to the Faculty of Graduate Studies and Research in partial

    fulfillment of the requirements for the degree of Master of Applied Sciences

    Ottawa-Carleton Institute for Electrical and Computer Engineering

    Department of Electronics

    Faculty of Engineering

    Carleton University

    Ottawa, Ontario, Canada

    September 2007

    © Lidija Filipovic 2007

    Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

  • Library and Archives Canada

    Bibliotheque et Archives Canada

    Published Heritage Branch

    395 Wellington Street Ottawa ON K1A 0N4 Canada

    Your file Votre reference ISBN: 978-0-494-33644-1 Our file Notre reference ISBN: 978-0-494-33644-1

    Direction du Patrimoine de I'edition

    395, rue Wellington Ottawa ON K1A 0N4 Canada

    NOTICE: The author has granted a non­ exclusive license allowing Library and Archives Canada to reproduce, publish, archive, preserve, conserve, communicate to the public by telecommunication or on the Internet, loan, distribute and sell theses worldwide, for commercial or non­ commercial purposes, in microform, paper, electronic and/or any other formats.

    AVIS: L'auteur a accorde une licence non exclusive permettant a la Bibliotheque et Archives Canada de reproduire, publier, archiver, sauvegarder, conserver, transmettre au public par telecommunication ou par I'lnternet, preter, distribuer et vendre des theses partout dans le monde, a des fins commerciales ou autres, sur support microforme, papier, electronique et/ou autres formats.

    The author retains copyright ownership and moral rights in this thesis. Neither the thesis nor substantial extracts from it may be printed or otherwise reproduced without the author's permission.

    L'auteur conserve la propriete du droit d'auteur et des droits moraux qui protege cette these. Ni la these ni des extraits substantiels de celle-ci ne doivent etre imprimes ou autrement reproduits sans son autorisation.

    In compliance with the Canadian Privacy Act some supporting forms may have been removed from this thesis.

    While these forms may be included in the document page count, their removal does not represent any loss of content from the thesis.

    Conformement a la loi canadienne sur la protection de la vie privee, quelques formulaires secondaires ont ete enleves de cette these.

    Bien que ces formulaires aient inclus dans la pagination, il n'y aura aucun contenu manquant.

    i * i

    Canada Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

  • Abstract

    Rapid advances in integrated circuit technology, such as, the ever-increasing signal

    speed, complex functionality, larger circuits and shrinking device sizes, have dras­

    tically increased the need for fast and accurate interconnect analysis. At higher

    frequencies, the conventional lumped models become inadequate in describing the in­

    terconnect performance and distributed transmission line models become necessary.

    In this thesis, an efficient algorithm is introduced for time-domain simulation of in­

    terconnects including driver and load. Presented approach extracts transfer function

    definition of output signals in terms of pole-residue based time-domain macromod­

    els. The new algorithm is suitable for a repetitive type of environment, where the

    transient responses need to be estimated for varying loads and drivers, quickly. The

    proposed method yields significant speed-up compared to the MNA type analysis of

    distributed networks with load and driver. Several numerical examples are presented

    to demonstrate its validity and efficiency.

    i

    Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

  • Acknowledgements

    I would like to express my most sincere gratitude to my mentors and supervisors Prof.

    Ram Achar. and Prof. Michel Nakhla. Their tireless support and encouragement

    have made this work an enriching and enjoyable experience. It has been my pleasure

    to be advised and guided by you.

    Furthermore, I would like to thank and acknowledge my colleagues in the CAD

    group at Carleton University. A special thanks are due to Dharmendra Saraswat

    and Andrew Charest for many helpful discussions.

    ii

    Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

  • Contents

    1 Introduction 1

    1.1 Background and M o tiv a tio n ....................................................................... 1

    1.2 C on tribu tions................................................................................................. 4

    1.3 Organization of the T h e s is .......................................................................... 4

    2 Interconnects 6

    2.1 Interconnect M odelling................................................................................. 6

    2.1.1 Lumped M odels.................................................................................. 8

    2.1.2 Distributed M o d els ........................................................................... 9

    2.1.3 Full-Wave M odels............................................................................... 10

    2.2 Interconnect Simulation ............................................................................. 11

    2.2.1 Modified Nodal Analysis (MNA) ................................................... 11

    2.2.2 Time-Domain Sim ulation.................................................................. 16

    3 Transmission Line M acrom odeling 18

    iii

    Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

  • 3.1 Method of Characteristics (M o C ) ............................................................ 18

    3.2 Macromodeling Issues................................................................................... 21

    3.2.1 S ta b ility .............................................................................................. 22

    3.2.2 Causality .......................................................................................... 22

    3.2.3 Passiv ity .............................................................................................. 23

    3.2.4 E ffic iency .......................................................................................... 24

    3.3 Matrix Rational Approximation (MRA) ............................................... 24

    3.3.1 Time-Domain Simulation Using MRA M acrom odels................ 29

    3.3.2 MRA Macromodel P ro p e r tie s ....................................................... 32

    3.4 DEPACT: Delay-Extraction Based Passive Compact Transmission-Line

    Macromodeling A lg o rith m .......................................................................... 33

    3.4.1 Time-Domain Simulation Using DEPACT Macromodel . . . . 35

    3.4.2 DEPACT Macromodel P ro p e rtie s ................................................. 38

    3.5 Simulation Issues in the Presence of Driver and L o a d ......................... 38

    4 Proposed Closed-form M odel for Transient Analysis o f MTL w ith

    Driver and Load Circuits 40

    4.1 Interconnect Macromodel............................................................................ 41

    4.2 Output Evaluation with L o a d ................................................................... 43

    4.3 Output Evaluation with Both Driver and L oad ...................................... 48

    4.4 Transient Response C o m p u ta tio n ............................................................ 50

    iv

    Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

  • 4.5 Analysis of Multiconductor Transmission L ines...................................... 51

    4.6 Numerical E x a m p le s ................................................................................... 53

    4.6.1 Example 1: Single Transmission L in e ................................... 53

    4.6.2 Example 2: Single Transmission Line with Complex Driver and

    L o a d .................................................................................................... 54

    4.6.3 Example 3: Multiconductor Transmission Line Network . . . . 61

    5 Performance Improvem ents and the Special Cases o f the Proposed

    Algorithm 65

    5.1 Fast Pole Computation for Low-Order Macromodels............................. 66

    5.1.1 Cubic P o lynom ials ................................................................... 67

    5.1.2 Quartic P o lynom ials ................................................................ 68

    5.1.3 Quintic Polynomials ......................................................................... 70

    5.2 Braodband and Long Delay Interconnect Macromodeling Issues . . . 72

    5.3 Distributed RC In te rco n n ec ts ................................................................... 73

    5.3.1 RC Distributed Transmission Line M acrom odel................ 74

    5.3.2 RC

View more