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8/9/2019 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
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