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Interconnect 03 - Interconnect Modeling

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    OutlineRecall of required material from ignal ! " tem t#eor"

    L$I " tem% con&olution% Laplace tran form

    $ran fer function% impedance% admittanceMain ignal : delta% tep% ramp% aturated ramp and t#eir re pon e

    'i tri(uted interconnect R) line'eri&ation of #eat tran fer equationSolution in *domain and time domain +,it#out proof-)ompari on to lumped ingle* egment model

    Interconnect a an R)*tree'ela" and tran ition time repre entation

    $ran fer function of R)*tree and it propertie . L/*filter Moment and repre entation in *domain.ero*pole and re idua*pole repre entation. 'ominant pole.lmore dela". /enfield*Ru(in tein (ound . lmore dela" formula proof.2 . 'ela" metric (a ed on moment .

    $ran ition time modelinglmore dela" for general input)entral moment and t#eir relation to momentRepre entation of re pon e a a pro(a(ilit" di tri(ution.2lpert e timation for recei&er lope. 'ela" and lope e pre ion (a ed on momentplicit output lope calculation for inge R)* tage

    'ri&er*recei&er interaction'ri&er modeling. 5*equation2dmittance and impedance calculationffecti&e capacitance and algorit#m for it calculation.Repre entation of load a 6/I*model7.$,o* tep dela" appro imation

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    Recall 8 L$I " temL$I: Linear $ime In&ariant

    Linear : t#e re pon e to linear com(ination of input ignalproduce linear com(ination of re pon e$ime In&ariant : S#ift of input ignal in time cau e t#eame #ift of output ignal

    L$I " tem re pon e i o(tained (" con&olution :

    ,#ere i impul e re pon e

    ( ) ( ) ( ) y t h t x t = ( )h t

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    Recall 8 *domainLaplace tran form of t#e ignal:

    $#e Laplace tran form of impul e re pon e i " tem tran fer function:

    undamental relation (et,een time*domain and *domain:

    { }

    { }0

    ( )

    (

    ( )

    (

    )

    () ))

    ( st

    st

    x t e dt

    x t e dt

    x

    s

    t X

    X x

    s

    t

    +

    +

    = =

    = =

    L

    L

    Two-sided

    One-sided (regular)

    { })( () t H s h=L

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    a ic input ,a&eform'irac impul e +delta- function:

    ;ea&i ide tep function:

    Ramp function:

    Saturated ramp function:

    ( ) , 0;

    0, 0.

    t

    t t

    + ==

    ( ) ( ) 0, 0;

    1, 0.

    t t

    d t u t

    up


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