Interconnect Modeling & Analysis

Transcription

1 EE9 VS tcoct d by tcoct odg & y ot of u Ro t Dfto of ot t dt t t dt t t dt t t!! -t ot dt t t! Not tt Eo dy t ooto otg o of u ut

2 EE9 VS tcoct d by Dt of t c b xd to tf fucto N Exd oud dt t d t: -t d oxto d oxto of ty /: Ο b b b -t d oxto << N: Fout cott by tcg ot to cout &

3 EE9 VS tcoct d by 3 G ot tcg cu Bc d: tc t ot t codto tc.. ˆ o ˆ o ˆ fo ˆ ˆ of ot ˆ Ο Ο W -: out Rdu & o Q codto t ˆ tc ft - ot EQ

4 EE9 VS tcoct Bc St fo ot tcg St : out ot - - of St : So o- uto of EQ to gt :o :du St 3: Gt oxt fo ˆ t t t St 4: c d t -4 f cy fo btt ccucy t oot of ot tcg od ot coutto tt D y o tfod ut D ccut Rcu coutto bd o t t ct ot coutto ot tcg tod ytotc Wfo Euto WE [g- Ro D 9] -o tod [ootz 984] [Go-Zou SS 93]... d by 4

5 EE9 VS tcoct B of ot outto by D y cb to g R to Ud ytotc Wfo Euto WE [g-ro D 9] Rt ud t-t ccut by yt of ft-od dfft uto: x& Gx bu y x x t ccut b cut d otg G t oy t to t oy t ccto d ducto bu t xctto fo ddt ouc y t outut of tt f Fucto u zo t codto d fo c tfo: X GX bu Y X X U Y dot c tfo of x u y cty f fucto: Y U G t bty but fxd xo ot uc tt G o-gu G G b b d by 5

6 EE9 VS tcoct d by 6 yo Exo d ot Exo of bout : Rcu ot coutto: K u u G b G u b u G u u u yo Exo d ot ot d Exo of oud Rcu ot coutto: K u G u b G u b u G u u u

7 EE9 VS tcoct ttto of ot outto out: u G b W ut to D y: ttg x & otg ducto V d og ccto cout cut toug ducto d otg co ccto ot ot: ducto Votg ouc cto ut ouc V ± V ± V V ttto of ot outto ot d V ± out: G u u W ut to D y: ttg x & u otg ouc of ducto cut ouc of ccto xt xctto cout cut toug ducto d otg co ccto ot ot: ducto Votg ouc cto ut ouc V ± d by 7

8 EE9 VS tcoct ttto of ot outto ot d out: u G u W ut to D y: ttg x u ot cut toug ducto d otg co ccto xt xctto cout otg ouc of ducto d cut ouc of ccto ot: ducto Votg ouc cto ut ouc V ± V ± ot outto by D y fo D y to cout t -t od ot otg co > t -t od ot of cut co > t -t od ot of D y: odfd od y ud og WE -tbu coxty to cout ot u to t -t od: t coxty of D y d by 8

9 EE9 VS tcoct dtg d Ddtg of ot outto by D y Rcu coutto of cto u ffct c t tx G U-fctod xcty oc outto of u cood to cto tto t tx og to gcto coodg to gu of t gt bout u ot outto fo R ot tcoct R t Exot c tuctu of G d tc to cout ot o bc oc: Rcu ot coutto [Yu-Ku VS 95] ct ot coutto [og-ko D 97] Bot ud gty dfft dfto of ot t t dt! W cotu to u t dfto bfo t t dt! d by 9

10 EE9 VS tcoct B of ot outto fo R W gt odd ud R t Dfto: ubt ootd t od R c tfo of V c tfo of t od of od tc bt od d ductc bt od d cctc t od cut fo to otg co - t od ot of od o ouc R f Fucto fo R y K t od : t t fo oot to od R Z R tot tc o t tot ductc V V R V o t Votg do fo oot to od : f fucto: Z V V Z d by

11 EE9 VS tcoct d by Rcu Fou fo ot Exdg to yo : Z f fucto: R R Rcu fou fo ot: f f f R Df -t od gtd cctc of : Rcu Fou fo ot ot d o tt: oot d f oot d f f f R Df -t od gtd cctc ubt Sty t dfto of Eo dy Euty: R

12 EE9 VS tcoct Rcu ot outto fo R [Yu-Ku VS 95] tz --t d -t od ot out ot fo od to od uccy Botto-u t t : O fo od out -t od gtd cctc out t -t od gtd cctc ubt o-do t t ; O fo od out t ot t c ccto od R coxty to cout ot u to t -t od O ct ot outto [og-ko D 97] tt t t oc uc [Ku-Yu VS 95] u ttc t tooogy o utb fo tcoct y Not utb fo t tooogy otzto ft c odfcto of t tooogy d to cout -t od ot ct udt of ot o utb fo t otzto got tt cotuct tooogy botto-u fo odfy t t tooogy udt t tf fucto fo cty d by

13 EE9 VS tcoct B fo Botto-U ot outto od t coutto of ot fo u ogy ubt g ubt t ot ubt d t t ootd t od u Dfto: ~ u~ tf - t od ot of od og og ubt ubt tf u fucto of od og ubt - t od g td cctc of ubt - t od ot of od ubt - t od g td cctc of ubt u ubt fucto of od ubt u u Botto-U ot outto t tf fucto ~ fo ubt d ot-gtd cctc of ubt: u fo K fo K g ubt cout tf fucto u~ d gtd cctc cuy: R N tf fucto fo od u ~ u~ ~ fo K fo K N ot-gtd cctc of u : fo K u cd u R u u d by 3

14 EE9 VS tcoct oxty y of ct ot outto u tooogy od oxty du to c dg: O ot t coxty: O f t od of tt t coxty O ot tcg by WE [g-ro D 9] Rc t tf fucto obtd fo ccut t bty but fxd xo ot uc tt G o-gu G G W tx dgozb SËS Ë dg K N S Ë S f g N f g : coc of o b d by 4

15 EE9 VS tcoct d by 5 -t d oxto d oxto of ty /: Ο b b b -t d oxto << N: Eut to fdg ducd-od tx R uc tt gu of R coc of t oxtg o fo t og yt ytotc Wfo Euto Rc EQ: t ] [ ] [ dg K Ë V V V V V

16 EE9 VS tcoct d by 6 ytotc Wfo Euto ot d Rt EQ: t Ë V V V VË R ] [ ] [ ] [ K K K Sog fo : Ë V V V R Nd to cout t o ft Stuctu of tx R tx: fo R coud b tx of t bo tuctu ccttc uto: ] gcto [ Egu Not tt: cttc uto bco t doto of :

17 EE9 VS tcoct d by 7 Sog fo tx R od utcto of R o 3 oduc R oduc Sog fo tx R ot d ft utcto of R o R oduc 3 Eutg t :

18 EE9 VS tcoct d by 8 Suy of WE St : out ot coc of dd o ccucy ut; ctc 5 futy ud St : So yt of uto by Gu to to gt St 3: So t ccttc uto of R to dt t oxt o St 4: So fo du V Nuc tto of WE Du to cu coutto of ot og to gcto coodg to gu of tx t gt bout u ot tx ud WE bco dy codtod cg ub of o do ot o ccucy Ub to tt t ccucy of t oxtg od Rd tcu ot utc d to y utotcy d y b couttoy x

19 EE9 VS tcoct d by 9 d oxto czo tod V [Fd-Fud D 95] Bc d of o-ytc czo tod: od t gt d ft Kyo ubc } { ft Kyo ubc } { Kyo ubc Rgt K K y czo cuo to gt fo... : o uc of b-otogo b cto fo ft d gt Kyo ubc K d K cty uc of o-ytc tdgo czo tc c tx tto of b-otogo octo of oto K d K Egu of oxt to of t g tx dtg: od dct coutto of ot Nucy obut fo g-od d oxto No-ytc czo tod St : d St d St δ η ρ η ρ Fo do: St : out δ St : St 3: St 4: ρ δ δ γ η δ δ β δ α St γ α β α ˆ ˆ St ˆ ˆ d ˆ ˆ St η ρ η ρ

20 EE9 VS tcoct d by R o czo tod Bdo occu f o cout δ Do by ozo yt ub δ y ut uc tbty ob c b dd by ug o-cd oo-d t of t czo cuo f tx ytc d t ttg cto d dtc t o ytc czo tod o ytc czo tod cot tc t x ub of ot Oy f of t ot c b tcd ot of czo Vcto czo cto: } d { } { B-otogoty: f f δ oof by ducto: γ α η β α ρ β α ρ γ α η β α γ α η ρ f : β α ρ f < :

21 EE9 VS tcoct d by ot of czo Vcto ot d t K K } { } { B of Kyo ubc: ] [ ] [ W V dg δ δ δ V W D ot of czo tc czo tc: fo Rto to tx : o ot coot d t coot - cto o coodt t ~ W W V V η ρ α η γ η γ α η γ α α ρ β ρ β α ρ β α ~ d O O O O O O O O O O O O Rto bt czo tc: ~ D D

22 EE9 VS tcoct d by octo of czo to d t tx tto of b-otogo of oto d t t bt oxto to t of tcg t x ub of ot Rc tt " " Fo to of czo tc d ~ W W η η η W ~ η V ρ ρ ~ " " V W D V W η ρδ ρ ηδ ρ η octo of czo to d ot d -t od d oxto Ο

23 EE9 VS tcoct Egdcooto of - S Ë S Ë dg K S Ë S ì µυ µ υ µ υ õ :cocof o y ut f o of t gu zo V got St : Ru t of t czo oc to obt t tdgo tx St : out gdcooto - SË S Ë dg K St ì S d õ S St 3: out t o d du of µ υ St d fo µ υ t f t t t o d by 3

24 EE9 VS tcoct R o V got Ru ougy t out of coutto o WE Dotg cot t U fctozto of G c d to b coutd oy oc Nd tot of coutto of d out coutto WE Nucy o obut t WE V got c b ud to obt boud fo t ooxto o Exo ot co uc tt πf x t fucy g of tt [ f x ] V fy t to t coc of od got fo Kyo Subc [S t. D 96] od oy t gt Kyo ubc: K { } y t od oc d to d to oduc fo : O uc of otoo od cto tt t Kyo ubc K uc of -by- u bg tdgo u tgu tc c tx tto of otogo octo of oto t Kyo ubc od oc c otooty by ug cuc tt o ou cto ucy ot but t coug oxt tf fucto tc oy ot d by 4

25 EE9 VS tcoct St : St ˆ Fo do: St : St : St 3: out f t od oc t ˆ t to Kyo ubc K ˆ St t St ˆ St 4: Fo do: St xutd t ˆ d ˆ ˆ t bg tx U bg tx Rto to tx : Fo V V t t [ V ] t t t 3 O t t 3 33 O t O O O t t t t d by 5

26 EE9 VS tcoct od-bd Rducd-Od odg od oc tc oy ot V V V fo < V Ο od-bd ducd-od odg ot doxto t oy d-ty oxto ob to fo to-dd od oc to obt d-oxto but too x tx-d czo V [Fd-Fud D 95] tfc bt o d ubto o coctd t o-ot WE V d od-bd oc u c-ud tf fucto fo g ot -ut -outut to c b yzd by tx of c-do tf fucto tfc c b odd by obtg d oxto fo c of ut d outut ug WE V o odbd oc outto cot c dy t t z of tfc ddu oxt tf fucto coutd ty tout g foto V ud boc czo got to cout tx d oxto to t t tx-ud tf fucto utouy d by 6

27 EE9 VS tcoct tx f Fucto Rt -ut -outut ud tt ccut by yt of ft-od dfft uto: x& Gx Bu y x B N N u cto of ut fucto d y t cto of uo outut fucto f fucto tx: Y U G t bty but fxd xo ot uc tt G o-gu R G G B B tx d oxto Exo of tx tf fucto : -t d oxto << N: d t cd t ot o o t of Ο Ο Nd boc czo tod to cty cout R d by 7

28 EE9 VS tcoct Boc Kyo Subc od ot ut g ttg cto but ut ttg cto: gt d ft ttg cto tc R d Dfto of gt d ft boc Kyo tc N K R [ R R R R] K [ N ] K R K : -t do gt ft boc Kyo ubc t ubc d by t ft y ddt cou of t tx KR K Boc czo cotuct to uc of b-otogo b cto V { } d W { } fo ft d gt boc Kyo ubc K R d K Stc of Boc czo tod St : R [ ] d [ ] St uxy cto ˆ fo K ˆ fo K Fo do: ˆ ˆ St : out d ˆ ˆ St : out uxy cto ˆ ˆ St 3: Botogo z ˆ gt ou czo cto St 4: ˆ gt ou czo cto Botogo z xt czo cto ˆ xt czo cto ˆ gt gt d by 8

29 EE9 VS tcoct czo tx d Rducd-Od od Boc czo tod o oduc to czo ~ tc d d bdd tc ub-dgo d ~ u-dgo ub-dgo d u-dgo ot dtc to t d czo cto t c of g-cto czo tod ud ducd-od od x& Gx Bu y x x& x Ru y x U -z cto d to oxt.. tct x t gt Kyo ubc V x V d V d& V d Ru d& d W Ru y V d y V d oxt t og yt t yt cobd t t t of t yt fo uto Stb d Rducd-Od od Stb d to c gt o gy t t bob Db to gutd tb ducd-od od fo g R ccut to u ucc of uto ttcy ytc tx d to b tcty tb f t gu gt o-ot t ytc tx d to b gt -dft dft f fo y o-zo cto x x x o tt f t ytc tx gt dft t tb od gu d coodg gcto x x x x x x x d by 9

30 EE9 VS tcoct Stb d Rducd-Od od Rducd-od od bd o od d ytc czo tod tb f t tx gt -dft x x x V V x V x V x tx G ot y gt -dft G d g ot -dft Rducd-od od bd o o-ytc czo tod c t b utb f t d oxt gtd fo tb ccut u of coguc tfoto o -dft tc B Q Q B cogut to oodt-fod od tod [S t. D 96] Bc d: f gt -dft tx B ytc t BB gt -dft x BBx x B Bx Bx Bx tx G ot y gt -dft od cg of coodt: ~ x x x& Gx Bu G x x Bu G x& x G x G G x~ & x~ G G Bu ~ x fo od cuo bd o tfod yt tx: ~ G Bu d by 3

31 EE9 VS tcoct o y by oguc foto [K-Yg D 97] d oxto u tt tcg o-od ot oduc dot o ot gut t gt ctu of o oxtd u of t bc d of coguc tfoto of -dft tc foto bd o oy fctozto foto bd o Egdcooto Dct o y o to of o of t R to bt dc d u-cfd xu fucy R Nto ducto ut to dog of g-fucy o Sz of ducd R to dd oy o t ub of ofucy o foud G G cut Dcto c tfo of ud t-t ccut: G x Bu b tto d od t t of tc uc tt G x b G G G x G : ot tc : t t od tc dcb cocto og : octo tc d t od dcb cocto og ot dcb bc bt ot d by 3

32 EE9 VS tcoct tx f Fucto f fucto t t ot dg ot dc dttc: x b G G G G ot of ub-tc G G : f t u of t to d ccto ot t c dgo ty of G d ot d gt t o u to t u of t bout u of t off-dgo t t coodg o odto uffct but ot cy to u tt t tc o-gt dft ot -dft ot cod ductc c tx oud ot tfy t codto toug y t b o-gt dft d t tod c t b d f c t od dc t to ot od G ot dft o d Egu o of occu G gu Eu to t outo to t gzd gu ob: G Sc G ytc ot dft ytc ot -dft t gu d ot fo t o d t zo o t g-fucy o to of gu o tfoto toducd to ot d t utd o to duc t z of t to d by 3

33 EE9 VS tcoct d by 33 foto by oy Fctozto ot G to dtty tx by oy fctozto c xt c G ot dft t G X X G GX X G G G X G Nd to fo gy o t cctc tx to do utd o W ot ffct dc bo c o cotbuto to t ft to ot foto by Egdcooto gcto :otou tx of gu tx of :dgo U Ë UËU Ë X X G G X X G U X " " " " " t N N N " of t dgo - t d " - t o of t G

34 EE9 VS tcoct Eto of Utd o G G" " " " " Ë Ec o octd t g t od Utd o dod by cuttg t coodg t od Eut to og t coodg o d cou G d Eut to og t coodg gcto U bfo t tfoto fod Wc o oud do? G xu fucy ω c d xu o ε c 3 3 f cut-off gu c dfd by ε ω ω t o ε of dog < c boudd by ε c ˆ ω ω ε x [ ] ω [ ω ω ] c c ω ω c c c c c outto of o U ytc czo tod to cout uc of czo cto V d czo tx Egu of o Rtz u oxt gu of ou of U o Rtz cto obtd by V Z Z t gcto of U t czo t ct otogozto Rtz u uuy cogd ft to xt gu of ddto cto ccutd ut to g Rtz u t cfd g cogd od o of otogoty c o cogc of t dot gu d ct got of dot gu o coy cd o ut occuc of gu to b foud d by 34