Tzong-Lin Wu, Ph.D. Department of Electrical Engineering National Taiwan University. Introduction Transmission lines equations for coupled lines

Transcription

1 Crossalk Tong-in Wu Ph.D. Deparen of Elecrical Engineering Naional Taiwan Universiy Topics: nroducion Transission lines equaions for coupled lines syerical lines and syerically driven hoogeneous ediu syerical lines in hoogeneous ediu syerical lines and asyerical driven Qualiaive descripion of crossalk Terinaions Measureen of crossalk paraeers How crossalk noise can be reduced

2 nroducion Three characerisics:. Polariy of noise a near end is opposie o ha a he far end.. Noise duraion a near end is larger han ha a he far end. 3. Noise agniude a near end is saller han ha a he far end. 3 nroducion : Physical eoery of Coupled ines Two kind of coupling:. nducive coupling. Capaciive coupling 4

3 nroducion: cross-alk echanis of he inducive coupling Qualiaive undersanding of he coupling echanis How abou he cross-alk echanis of he capaciive coupling?? 5 A Driving signal B A B D C C Tp Tp C C C everse coupling nducive Tr Derivaive of inpu signal negaive Toal coupled areas are he sae ise and fall ies sae as inpu Forward coupling Capaciive Tp A B Tr D C Tp D 6 3

4 Coupled lines equaions Δ Δ Δ ' Δ C Δ C [ Δ Δ] 7 Coupled lines equaions Marix fors where C d d d C d l l N M O l l Q P N M O Q P c c N M O c c Q P N M O Q ' C C C P ' C C C NM C C C C O QP : self-inducance per uni lengh of line and when isolaed : uual inducance beween line and C : capaciance o ND of line and when isolaed ** C : uual capaciance beween line and 8 4

5 Coupled lines equaions Capaciance arix C C C C C C C g inducance arix For uli-conducor coupled lines C C C C C Capaciance arix CN C N NN nducance arix N N NN 9 Coupled lines equaions e 0 e 0 e 0 e 0 jω γ jω γ jω γ jω γ γ jω 0 0 γ jωc 0 0 γ A 0 0 ω CC C C A C [ ] C C C C de A γ 0 ω for nonrivial soluions The γcan be solved wih wo possible soluions 0 5

6 Syerical lines and syerical driven Condiions: balanced lines C C The balanced lines are driven by coon ode or differenial ode only Characerisics: Propagaion delay per-uni lengh: τ ± ± C C Characerisic ipedance Z Z k Z C C k 0e k Z C C k 0o c c where k k c : agneic coupling coefficien C : capaciive coupling coefficien C Syerical lines and syerical driven Z 0 e τ Z 0 o τ 6

7 Syerical lines and syerical driven Microsrip exaple 3 Syerical lines and syerical driven anoher definiion for even and odd ode Coupling Facor 0logZ Z Ze Zo/Ze Zo Noe: 4 7

8 Physical concep for he even-ode and odd ode ipedance Odd ode - and - odd C C C C C odd g Z odd C C C odd odd TD C C C odd odd odd 5 Physical concep for he even-ode and odd ode ipedance Even ode and even Ceven C0 C C Z even C C C even even TD C C C odd even even 6 8

9 pedance rends for he even- and odd-odes Wha ipedance behaviors do you see? 7 pedance rends for he even- and odd-odes. High-ipedance races exhibi significanly ore ipedance variaion han do he lower-ipedance race because he reference planes are uch farher in relaion o he signal spacing.. A saller spacing he single-line ipedance is lower han he arge. This is because he adjacen races increase he selfcapaciance of he race and effecively lower is ipedance even when hey are no acive. 3. Higher coupling he races behave he larger variaion even- and odd- ipedances will have. 8 9

10 Muual coupling rends for he icrosrip and sripline Muual parasiic fall off exponenially wih race-race spacing 9 Exaple by siulaion: Please copare he coupling characerisics for he hree cases: Ze Zo 0 0

11 Effec of swiching paerns on ransission line Crossalk induced fligh ie and signal inegriy variaions Wha phenoena do you see?? Swiching paern

12 Effec of swiching paerns on ransission line As he swiching paerns are in even-ode: Over-driven behavior is seen Overshooing. onger propagaion delay is seen. As he swiching paers are in odd-ode: Under-driven behavior is seen Undershooing. Shorer propagaion delay is seen. Why?? 3 Effec of swiching paerns on ransission line Even-ode paern ipedance changed fro Z 0 o Z e > Z 0. overdriven when Z e > Z s. Slower propagaion velociy. Odd-ode paern ipedance changed fro Z 0 o Z odd < Z 0. under driven when Z odd < Z s. Faser propagaion velociy. 4

13 Effec of swiching paerns on ransission line Siulaing races in a uliconducor syse using a single-line equivalen odel SEM Targe race is line. Please find he equivalen ipedance and ie delay Z eff C C C 3 3 TD C C C eff 3 3?? 5 Effec of swiching paerns on ransission line TD C C C eff 3 3 Z eff C C C

14 Exaple by TD easureen: 7 Exaple by TD easureen: quesion one?? 8 4

15 Exaple by TD easureen: quesion one?? Differenial ipedance D.. is 50Ω wihou ND plane And abou 00Ωwih ND plane. Why?? 9 Firs half: wo races refer each oher like a wised line and C Second half: wo races refer he ND plane uual coupling is quie sall k k c 0 so D..*Z odd Z

16 Exaple by TD easureen: quesion wo?? Wha s he variaion of he differenial ipedance For he differenial pair crossing he slo? 3 Exaple by TD easureen: quesion wo?? The gap behaves like a high ipedance disconinuiy which Will cause reflecions. 3 6

17 Hoogeneous Mediu Condiions: eal no Quasi- TEM ode propagaing on he ransission lines Characerisics: Propagaion delay per-uni lengh: τ τ τ0 k where k k kccoupling coefficien k : For uual inducance coupling C kc CC : For uual capaciance coupling 33 Syerical ines on Hoogeneous Mediu Condiions: balanced lines C C The balanced lines are driven by coon ode or differenial ode only τ τ Characerisics: Characerisic ipedance Z Z where Z Z 0e 0o C 34 7

18 Exaple: hoogeneous coupled line Please copare he coupling characerisics for he hree cases:. K. Ze 3. Zo

19 A Qui: Please copare heir Z e Z o e o and C. a b ε 4.5 ε 4.5 ε 4.5 ε.5 ε 4.5 ε Syerical ines and asyerically driven Asyerical driven Π -Terinaions: Z 0e 3 Z0eZ0 Z Z Z0o / / 3 o 0e 0o erinae even ode erinae odd ode 38 9

20 Syerical ines and asyerically driven Z 0o T - erinaions erinae odd ode 3 Z0e Z0o erinae even ode Z 3 0e 39 perfec Terinaion for Differenial Transission ine. Wha are heir values of he resisance?. Wha are heir advanages and disadvanages? Bridge Terinaion AC Terinaion Single ended erinaion 40 0

21 perfec Terinaion for Differenial Transission ine Z o Bridge Terinaion Z o Z o Z o Z o AC Terinaion Single ended erinaion 4 perfec Terinaion for Differenial Transission ine Bridge:. Odd ode is copleely absorbed. Even ode is copleely refleced 3. Only one resisance is used. Single-ended. Odd ode is copleely absorbed. Even ode has he reflecion coefficien T Zo Ze/ZoZe 3. The exra daping of he even ode coss an addiional resisance. AC Odd ode is copleely absorbed Even ode is copleely refleced a low frequency bu has he reflecion T Zo Ze/ZoZe a high frequency. 3. Copared o bridge ype even ode is aenuaed wihou increasing saic power dissipaion. 4. Needing hree coponens. 4

22 Exaple: Terinaion for Differenial Transission ine 43 Exaple: Terinaion for Differenial Transission ine A siple bridge erinaion 44

23 Exaple: Terinaion for Differenial Transission ine A siple bridge erinaion bu Unbalance driving Differenial signal is sill good Coon signal on each line is oscillaing 45 Exaple: Terinaion for Differenial Transission ine A Pi-erinaion for unbalance driving Coon-ode is daped 46 3

24 Exaple: Terinaion for Differenial Transission ine Coon-ode resonance Differenial pair excied by coon-ode signal 47 Exaple: Terinaion for Differenial Transission ine Single-ended erinaion for Unbalanced driving Beer han bridge erinaion 48 4

25 Exaple: Terinaion for Differenial Transission ine AC T-erinaion for Unbalanced driving 49 Exaple: Terinaion for Differenial Transission ine Bridge erinaion a he far end and Series erinaion a he near end. Power saving. dea of DS 50 5

26 Exaple: Terinaion for Differenial Transission ine Bridge erinaion a he far end and Series erinaion a he near end For DS case 5 Exaple: Effecs of Terinaion Neworks on Signal-nduced EM fro he Shields of Fibre Channel Cables Operaing in he b/s egie 000 EEE EMC Syposiu 5 6

27 Exaple: Effecs of Terinaion Neworks on Signal-nduced EM fro he Shields of Fibre Channel Cables Operaing in he b/s egie Measureen of S for boh differenial ode and coon ode Terinaion effec is reduced for high frequency range 53 Exaple: Effecs of Terinaion Neworks on Signal-nduced EM fro he Shields of Fibre Channel Cables Operaing in he b/s egie EM differenial Why he erinaion effec is degraded a high frequency range? 54 7

28 Quaniaive descripion of crossalk Capaciive coupling nducive Coupling x K x d d τ x f f in see appendix 7. K K f b x K [ τx τx T ] b b in in d f he coupled lines are syerical CZ ns / c : Forward coupling coefficien Z CZ 4τ Z diensionless : Backward coupling coefficien 55 Quaniaive descripion of crossalk n he loosely coupled syse k k c << Z and τ C C is accurae enough τ CZ τ K f k kc τz τ Kb CZ k kc 4τ Z 4. is clear ha he backward coupling can be reduced by decreasing he uual coupling and C or by increasing he coupling o ground C and C.. The forward crossalk is ero for wo idenical lines in hoogeneous ediu. no easy in pracical circuis 56 8

29 Crossalk for a rap sep driver [ f f T ] in r 57 Crossalk for a rap sep driver Forward crossalk a he far end: l K l d d T f f in d K l f Td < < Td Tr T 0 elsewhere Backward crossalk a he near end f T r < T d r 0 K [ T ] b b in in d bax Kb f T r > T d l T K K bax τ b T r r b 58 9

30 SPCE siulaion of crossalk 59 Measureen of coupling coefficien Frequency doain : exaple AMBUS MM Connecor Tes odule design 60 30

31 Measureen of coupling coefficien Frequency doain : AMBUS MM Connecor Calibraion Open shor load 6 Measureen of coupling coefficien Frequency doain : exaple AMBUS MM Connecor Theory uual capaciance Open circui!! ow freq. assupion The slope of S f a low frequency is aking o copue he C 6 3

32 Measureen of coupling coefficien Frequency doain : exaple AMBUS MM Connecor Theory uual inducance Shor circui!! The slope of S f a low frequency is aking o copue he 63 Measureen of coupling coefficien Frequency doain : exaple AMBUS MM Connecor Measureen seup 64 3

33 Differenial pedance Measureen by TD/TDT They have good EMS uniy and EM nerference Perforance. 65 Differenial pedance Measureen by TD/TDT Equivalen circuis of he differenial inerconnecs: Type 66 33

34 Differenial pedance Measureen by TD/TDT Equivalen circuis of he differenial inerconnecs: Type Negaive ipedance no pracical Advanage is i is a rigorous equivalen circui. Disadvanage is only valid in hree conducor inerconnecs. 67 Differenial pedance Measureen by TD/TDT Equivalen circuis of he differenial inerconnecs: Type 68 34

35 Differenial pedance Measureen by TD/TDT Measureen Principle 69 Differenial pedance Measureen by TD/TDT Coparison of he equivalen odel by he SPCE 70 35

36 A Final Quesion: Can you explain why 7 How o reduce crossalk noise Space ou signal rouing oue-void channels adjacen o criical nes ncrease coupling o ground un orhogonal raher han parallel Provide he hoogeneous ediu Using he slowes riseie and falling ie 7 36

37 0. Three conducor lines and crossalk Tie Doain Crossalk S Frequency-doain Crossalk a. Two conducors ransission lines has no crossalk proble. n order o have crossalk we need o have hree or ore conducors. b. eneraor S ± s NE NE _ 0 ecepor FE FE _ 73 c. The generaor circui consiss of he generaor conducor and reference conducor and has curren along he conducors and volage beween he. The and will generae EM fields and inerac wih he recepor circui. d. The objecive in a crossalk analysis is o deerine he near-end volage NE and far-end volage FE given he cross-secional diension and he erinaion characerisics S S NE FE

38 e. Two ype of crossalk analysis Tie-doain crossalk : predic FE and NE given S. Frequency-doain crossalk : predic jw and jw given FE NE S cos w φ. S f. For sipliciy we will assue ha he ediu surrounding he conducors for hese configuraions is hoogeneous. Closed-for expressions for he per-uni-lengh paraeers for he lines in inhoogeneous ediu such as icrosrip lines are difficul o deerine. 75 Transission ine Equaions a. Assue only TEM ode presen on he aerials so line volages and as well as line currens and can be uniquely defined. b. Equivalen circui of TEM-ode on 3-conducor aerial : Δ Δ O Δ Δ Δ Δ Δ C Δ C Δ Δ C Δ Δ Δ _ Δ _ Δ Δ 76 38

39 39 77 n arix ers : C C C C C C O O O O [ ] [ ] C { 78 c. Soluions n ie doain i is a difficul proble. When 0 lossless lines here are exac soluions in SPCE. n frequency doain he exac soluions for above aerial equaions are possible we will show he exac soluion for lossless case. O O O O where C C C C C C C {

40 Noe: n frequency doain he equaions > d Z d d Y d where Z jw Y jwc e e jw { e } jw { e } The per-uni-lengh paraeers nernal paraeers : O and inernal inducance are no dependen on he line configuraions. a. For aerial in hoogeneous ediu με C C με C με v Exaple : Three-conducor line C C C C C C v C v C C v C C v μσ μσ 80 40

41 4 8 Wide-Separaion Approxiaion for Wires a. Magneic flux of a curren-carrying wire hrough a surface volage beween wo poins for a charge-carrying wire 0 ln μ π ϕ ϕ a b q ba 0 ln q ba πε 8 b. Paraeers of hree-conducor ransission lines nducance : o ϕ ϕ ϕ ϕ ϕ ϕ ϕ

42 . generaor d recepor r W r W d d ND rwo. Self inducance d r W ϕ r WO μ0 d ln π r W μ 0 d ln π rwr μ0 d ln π r WO WO μ 0 d ln π rwr WO Muual inducance d r W Capaciance d d r WO r W ϕ C q C C C C C P q pq p μ0 d ln π d μ0 d ln π d q q C p p μ0 d ln π r d r WO WO 84 4

43 P q q 0 P q q 0 P q q 0 q q 0. Self capaciance q d r W _ r WO P d ln πε0 r W d ln πε 0 rwr d ln πε0 r WO WO q 85. Muual capaciance q d r W _ d d r W P d ln πε0 d d ln πε0 d d r WO d ln πε0 r WO r WO q reference 86 43

44 ln 4 ln ; ln ln ln ln ln S h h S S S S S S S S r h h h r h W W π μ π μ π μ π μ ϕ π μ π μ π μ ϕ c. Exaple r W r W ϕ ϕ h h h h S S S S Frequency-Doain Seady Sae Crossalk eneral Soluion : a. b. C Y Z Y Z jw jw where d d d d YZ ZY YZ ZY general Noe :in d d d d

45 45 89 YZ r YZ T r YZT T T 0 0 : of he eigenvalues is of he eigenvecors is where diagonalied r r such ha a ransforaion arix find we can if 0 0 e e e e r r r r d d odal curren le d d r r r r YZT T T YZ T T 90 3 c. d. ± ± ± ± ± ± r r r r r e e where for in arix 0 0. e e e e Te T ZTr Tr Y ZTr r YZT T e Tre Y Y e e T T r r r r r r by d d Z Z Tr T Z YZ Y YZ c see below for deail

46 上式的 Tr T YZ - YZ Tr T T YZT r r T YZTr Tr T YZ Tr T Tr T YZ siilar o he scalar resuls Z Z YZ y e. Solving he four unknowns and - by he erinaion condiion 0 S ZS0 Z S S 0 0 where S Z S Z 0 0 NE 0 FE 9 a 0 0 Z T C 0 T - - Z T Z T - - C S S a Z T e e C r r - T e e r r - Z T e e Z T e C r r - r C S C S r C e C - - and e r - Z Z T Z Z T S - r Z Z T Z Z Te 0 can be solved. 9 46

47 Exac Soluion for ossless ines in Hoogeneous Media a. for lossless line : 0 and Z jw Y jwc YZ w C w με β diagonal arix where C με for ho ogeneous ransission lines. w T r jβ j v b. can be shown ha : jπ 0 S jw C λ α S D k jπ NE FE jwc C λ S DC NE FE k α NE NE DC en NE FE S FE NEFE jw jwc D en NE FE NE FE FE DC DC 93 where : αsα ααs α α α α D C S w τ τ k jwcs τ τ sin β C cos β S β en S S C k coupling coefficien k C C C C S τ ie consan C C S S τ ie consan C C NE FE NE FE NE FE 94 47

48 S DC S DC DC exciaion a generaor circui S S ZC v k Characerisic ipedances C C of each circui in he presence of he oher circui. ZC v k C C S NE FE αs α αs α ZC ZC ZC ZC if α < low ipedance load. α > high ipedance load. 95 nducive and Capaciive coupling a. Two reasonable assupions The line is elecrically shor. i. e. λ β C cos ζ The generaor and recepor circuis are weakly coupled. k D jwτ jwτ en if w is sall hen D en 96 48

49 b. NE NEFE jw jwc NE DC DC NE FE NE FE FE NE FE jw jwc FE DC DC NE FE NE FE NE NE _ jw DC jwc DC FE FE _ d jw DC DC ef d d d jwcdc C DC C d d which is he independen curren source due o he volage of generaor Crossalk is he superposiion of wo coponens; One is inducive coupling he oher one is capaciive coupling. c. nuiively : When low-ipedance load high curren low volage he inducive coupling is doinan. When high-ipedance load low curren high volage he capaciive coupling is doinan