Crosstalk

吳瑞北

Rm. 340, Department of Electrical Engineering

E-mail: rbwu@ew.ee.ntu.edu.tw

url: cc.ee.ntu.edu.tw/~rbwu

S. H. Hall et al., High-Speed Digital Design, Chap.4

N. N. Rao, Elements of Engineering Electromagnetics, Sec. 6.7. 1

R. B. Wu

What will you learn

• Physical insight to inductive & capacitive coupling

• Definition of L and C matrices of multi-coupled tx-lines

• Electrical parameter extraction for coupled tx-lines

• Phenomenological description of crosstalk noise by

weakly coupling analysis

• Analytic derivation for crosstalk noise by model analysis

• Construction of equivalent SPICE circuit for transient

simulation of ideal coupled tx-lines

• Novel designs for minimization of crosstalk noise:

matched termination, guard trace, spiral delay line.

2

R. B. Wu

Contents

• Two mechanisms that Cause Crosstalk

• Crosstalk-induced Noise

• Even/Odd Mode Decomposition

• Modal Analysis

• Simulation in SPICE

• Design Issues

3

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MCM Structures Typical Conductor Cross-section Typical via-size and pitch

4

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Example

5

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Crosstalk is caused by energy coupling from one line to another via:

Mutual capacitance (electric field)

Mutual inductance (magnetic field)

Zs

Zo

Zo

Zo

Mutual Capacitance, Cm Mutual Inductance, Lm

Zs

Zo

Zo

Zo

Cm

Lm

near

far

near

far

6

Mutual Inductance and Capacitance

R. B. Wu

Mutual L induces current from a driven line onto a quiet line

by magnetic field。

drivernoise m

dIV L

dtGround

driver victim

G.H. Shiue

Mutual Inductance

7

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Mutual C is coupling of two conductors via electric field

drivernoise m

dVI C

dt

driver victim

Ground

G.H. Shiue

Mutual Capacitance

8

R. B. Wu

Circuit is distributed into N segments

K1

L11(1)

L22(1)

C1G(1)

C12(1) K1

L11(2)

L22(2)

C1G(2)

C12(2)

C2G(2) C2G(1)

K1

L11(N)

L22(N)

C1G(N)

C12(n)

C2G(N)

C1G C2G

C12

2211

12

LL

LK

Line 1

Line 2

Line 1 Line 2

9

Crosstalk Model by “Equivalent Circuit”

R. B. Wu

Inductance matrix: LNN = self inductance of line N per unit length

LMN = mutual inductance between lines M and N

[L] =

NNN

N

LL

LL

LLL

1

2221

11211 ...

10

Inductance Matrix

R. B. Wu

Capacitance matrix: CNN = self capacitance of line N per unit length where:

CNG = Capacitance between line N and ground

CMN = Mutual capacitance between lines M and N

[C] =

11 12 1

21 22

1

... N

N NN

C C C

C C

C C

NN NG mutualsC C C

11 1 12GC C C

For example, for 2 line circuit:

11

Capacitance Matrix

R. B. Wu

Numerical Techniques

CAP1 CAP2 - microstrip

CAP3 – triplate

CAP4 – e.g. CPW

Geometry of lines:

width, separation, thickness, height,

substrate, etc.

C2D

Electrical parameters:

capacitance matrix [C]

Inductance matrix [L]

• Based on IE formulation

and MoM

• Exact integration formulae

• Four versions are available

W. T. Weeks, “Calculation of coefficients of capacitance of multiconductor transmission

lines in the presence of a dielectric interface,” IEEE T-MTT, Jan. 1970. 12

R. B. Wu

CAP2 Example

13

Crosstalk Induced Noise

15

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Circuit element representing transfer of energy

dt

dILV mLm

dt

dVCI mCm

Mutual inductance induces current on victim line opposite of driving current (Lenz’s Law)

Mutual capacitance passes current through mutual capacitance that flows in both directions on the victim line

16

Mechanism of coupling

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Coupled currents on victim line sum to produce near and far end crosstalk noise

Crosstalk Induced Noi

Zs

Zo

Zo

Zo

Zs

Zo

Zo

Zo

ICm Lm

near

far

near

far

ILm

LmCmfarLmCmnear IIIIII

17

Coupled Currents

R. B. Wu

Near end crosstalk is always positive Currents from Lm and Cm always add & flow into the node.

For PCB’s, far end crosstalk is “usually” negative Current due to Lm larger than current due to Cm

Note that far and crosstalk can be positive or nullified.

Driven Line

Un-driven Line “victim”

Driver

Zs

Zo

Zo

Zo

Near End

Far End

18

Voltage Profile of Coupled Noise

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V

Time = 0

Zo

Near end crosstalk pulse at T=0 (Inear)

Far end crosstalk pulse at T=0 (Ifar) TD

2TD

~Tr

~Tr

far end

crosstalk

Near end

crosstalk

Zo

V

Time = 2TD

Zo Near end current

terminated at T=2TD

Zo

Zo

V

Time= 1/2 TD

Zo

V

Time= TD

Zo Far end of current

terminated at T=TD

19

Graphical Explanation

R. B. Wu

Crosstalk Equations

Driven Line

Un-driven Line “victim”

Driver

Zs

Zo

Zo

Zo

Near End

Far End

Driven Line

Un-driven Line “victim”

Driver

Zs

Zo

Zo

Near End

Far End

LCXTD

C

C

L

LVA MMinput

4

2

input M M

r

V TD L CB

T L C

TD

2TD

Tr ~Tr Tr

A B

TD

2TD

Tr ~Tr ~Tr

A B

C

C

L

LVA MMinput

4

CB2

1

input M M

r

V TD L CC

T L C

C

Terminated Victim

Far End

Open Victim

20

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Driven Line

Un-driven Line “victim”

Driver

Zs

Zo

Zo

Near End

Far End

Near End Open Victim

TD

2TD

Tr Tr Tr

A

B

C

3TD

C

C

L

LVA MMinput

2

2

input M M

r

V TD L CB

T L C

C

C

L

LVC MMinput

4

The Crosstalk noise characteristics are dependent on the termination of the victim line

21

Crosstalk Equations -2

R. B. Wu

Calculate near and far end crosstalk-induced noise magnitudes and

sketch the waveforms of circuit:

Vsource=2V, Trise = 100ps.

Length of line is 2 inches. Assume all terminations are 70 Ohms.

Assume the following capacitance and inductance matrix: L = nH / inch C = pF / inch Characteristic impedance is: Therefore the system has matched termination. (Vinput = 1.0V), crosstalk noise magnitudes can be calculated as follows:

9.869 2.103

2.103 9.869

2.051 0.239

0.239 2.051

4.69051.2

869.9

11

11

pF

nH

C

LZO

v R1 R2

22

Example

R. B. Wu

1212

11 11

1 2.103 0.2390.082

4 4 9.869 2.051

input

near

V CL VV V

L C

1212

11 11

TD 1 *280ps 2.103 0.2390.137

2 2*100ps 9.869 2.051

input

far

rise

V CL VV V

T L C

Near end crosstalk voltage amplitude:

Far end crosstalk voltage amplitude:

Thus,

100ps/div

20

0m

V/d

iv

Propagation delay of the 2 inch line is:

2inch* (9.869nH*2.051pF 0.28ns=280psTD X LC

23

Example (cont.)

Even/Odd Mode Decomposition

24

R. B. Wu

Coupling Effects on Tx-line Parameters

Key Topics:

Odd and Even Mode Characteristics

Microstrip vs. Stripline

Modal Termination Techniques

Modal Impedance’s for more than 2 lines

Effect of Switching Patterns

Single Line Equivalent Model (SLEM)

25

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Field Distribution

• Differential and common mode signals have different field

distribution, impedance and propagation velocity.

26

Differential mode common mode

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EM Fields btw two coupled lines interacts with

each other. These interactions affect the

impedance and delay of tx-line

A 2-conductor system has 2 propagation modes

Even Mode (Both lines driven in phase)

Odd Mode (Lines driven 180o out of phase)

Field interaction causes the system electrical

characteristics to be dependent on the patterns.

Even Mode

Odd Mode

27

Odd/Even Transmission Modes

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Potential difference btw conductors lead to increase of effective C equal to Cm

Magnetic Field:

Odd mode

Electric Field:

Odd mode

+1 -1 +1 -1

Because currents flow in opposite directions, total L is reduced by Lm

Drive (I)

Drive (-I)

Induced (-ILm) Induced (ILm)

V

-I

Lm dt

dILmL

dt

IdLm

dt

dILV

)(

)(

I

28

Odd Mode Transmission

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121111 LLLLL modd

Mutual Inductance:

Consider the circuit:

dt

dIL

dt

dILV

dt

dIL

dt

dILV

mO

mO

122

211

Since the signals for odd-mode switching are always opposite, I1 = -I2 and

V1 = -V2, so that:

dt

dILL

dt

IdL

dt

dILV

dt

dILL

dt

IdL

dt

dILV

mOmO

mOmO

2222

1111

)()(

)()(

Thus, since LO = L11 = L22,

equivalent inductance seen in an odd-mode environment is reduced by

mutual inductance. 29

Derivation of Odd Mode Inductance

I1

I2

L11

L22

V2

V1

2211LL

LK m

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mmgodd CCCCC 111 2

Mutual Capacitance:

Consider the circuit:

C2g

C1g Cm

V2

V2 C1g = C2g = CO = C11 – |C12 |

So,

dt

dVC

dt

dVCC

dt

VVdC

dt

dVCI

dt

dVC

dt

dVCC

dt

VVdC

dt

dVCI

mmOmO

mmOmO

121222

212111

)()(

)()(

And again, I1 = -I2 and V1 = -V2, so that:

dt

dVCC

dt

VVdC

dt

dVCI

dt

dVCC

dt

VVdC

dt

dVCI

mOmO

mgmO

22222

11

1111

)2())((

)2())((

Thus,

eq. capacitance for odd mode switching increases. 30

Derivation of Odd Mode Capacitance

R. B. Wu

Impedance:

11 12

11 12

oddodd

odd

L L LZ

C C C

11 12 11 12( )( )odd odd oddTD L C L L C C

Propagation Delay:

Explain why.

31

Odd Mode Transmission Characteristics

Note: 2differential oddZ Z

R. B. Wu

Since conductors are at equal potential, effective C is reduced by Cm

Because currents flow in same direction, total L is increased by Lm

Drive (I)

Drive (I)

Induced (ILm) Induced (ILm)

V

I

Lm dt

dILmL

dt

IdLm

dt

dILV

)(

)(

I

Electric Field:

Even mode

Magnetic Field:

Even mode

+1 +1 +1 +1

32

Even Mode Transmission

R. B. Wu

Impedance:

11 12

11 12

eveneven

even

L L LZ

C C C

11 12 11 12( )( )even even evenTD L C L L C C

Propagation Delay:

35

Even Mode Transmission Characteristics

Note: even oddZ Z

Note:

for microstrip lines

for strip lines

even odd

even odd

TD TD

TD TD

R. B. Wu

Variations in Impedance - microstip

2.4r

w ws

d

tw/d = 1,1.5,2

w/d = 1,1.5,2

t = 0,0.4,0.7,1 mil

0 1 2 3

s/d

20

40

60

80

100Z

Im

ped

an

ce

(

)

Zeven

Zodd

Ref:吳瑞北、薛光華等，磁碟容錯陣列控制電路板之訊號整合度分析 ，普安案研究計畫報告，民92年2月，第2章。 36

R. B. Wu

Single-Line Eq. Model (SLEM)

• Goal:

– Determine effective crosstalk-induced impedance & delay variation for a multi-conductor system.

– Eestimate worst-case crosstalk effects during a bus design prior to actual layout

• SLEM

22 21 232,eff.

22 12 23

2,eff. 22 21 23 22 12 23

; L L L

ZC C C

TD L L L C C C

22 21 232,eff.

22 12 23

2,eff. 22 21 23 22 12 23

; L L L

ZC C C

TD L L L C C C

37

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Effects on SI & Velocity – on microstrip

Rem: No velocity variations due to crosstalk in striplines.

38

Modal Analysis

39

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Model Decomposition Theory

• For coupled lines, ;

z t z t

v L i i C v

Transformation: = , = ;V m I mv M v i M i

1

1

;

;

z t z t

z t z t

V m I m m m m m V I

I m V m m m m m I V

M v L M i v L i L M LM

M i C M v i C v C M CM

, both diagonal;

is eigenmatrix of

m m

-1

m m V V V

L C

L C = M LC M M LC

, , ,

, , ,

modal impedance ;

velocity 1

m i m ii m ii

pm i m ii m ii

Z L C

L C

40

R. B. Wu

Modal Analysis Procedure

• Find MV, eigenvectors of LC (fairs if LC is diagonal)

• Find MI, eigenvectors of CL,

– usually take

• Use MV and MI to calculate modal inductance,

capacitance, voltages, and currents

• Calculate modal impedances and velocities

• Carry out traditional tx-line analysis for each mode

• Convert modal quantities back into line quantities.

1T

I VM M

41

s.t. =T T T Tm V I m m mv i v M M i v i

R. B. Wu

Input waveforms Even mode (as seen on line 1)

Odd mode (Line 1)

v2

v1

Probe point

Delay difference due to modal velocity differences

Impedance difference

V1

V2

Line 1

Line2

42

Odd/Even Mode Comparison for Coupled Microstrips

R. B. Wu

Symmetric Coupled Lines

1

1][ 11

C

C

k

kCC

1

1][ 11

L

L

k

kLL

1 1 1 11 1 ;

1 1 1 12 2

V IM M

1

11

1

11

1 0 ;

0 1

1 0

0 1

L

L

C

C

kL

k

kC

k

m V I

m I V

L M LM

C M CM

11

11

1

,1 0 ,1 01

1

,2 0 ,2 01

0 0 11 11

modal characteristics: (1: odd; 2: even)

; 1 1

; 1 1 ;

where ; 1

L

C

L

C

k

m m L Ck

k

m m L Ck

L

C

Z Z k k

Z Z k k

Z L C

,1 0 ,2note: m mZ Z Z 43

V

Edge of driving signal

Far end

Near end crosstalk pulse

Far end crosstalk pulse

Near end

R. B. Wu

Equivalent Tx-Lines for Modes

• Modal decomposition

• Equivalent tx-line

• Modal voltages at both ends:

1

,s

02 1 1 2( ) ( ) ( )

0 1 1 0 2s su t u t u t

m Vv v M v

,

,

,

, , , , ,

,

,

, , ,

,

2near end: (0, ) ( ) 1 ( ) ;

far end: ( , ) 1 ( );

m i

m i

m i

m i m in L i s i m in

m i s

m i

m i L i m in

m i s

Zv t v t v t

Z Z

Zv t v t

Z Z

, ,

, ,

, ,

; L m i s m i

L i s i

L m i s m i

Z Z Z Z

Z Z Z Z

44

R. B. Wu

Line Voltages at Both Ends

• Line voltages at both ends

• Near end crosstalk

• Far end crosstalk

,11 1

2at 0 or ,22

( )( ) 1 1( )

( )( ) 1 1

m

zm

v tv tt

v tv t

V mv M v

,2 ,1

2

,2 ,1

(0, ) ( ) for 0 2m m

m s m s

Z Zv t u t t T

Z Z Z Z

,2 ,1,2 ,1

2

,2 ,2 ,1 ,1

2 ( ) 2 ( )( , ) for 3

( ) ( )

m mL m L m

m s m L m s m L

Z Z u t Z Z u tv t T t T

Z Z Z Z Z Z Z Z

,,2

,2 ,2 ,2 ,1 ,1 ,1

,2 ,1

2 21 1

( ) ( )m im

m L s m L s

m s m s

Z Zu t u t

Z Z Z Z

45

R. B. Wu

Exact Crosstalk at Matched Load

• Zero far end noise ==>

• Crosstalk noise (with matched load)

,1 ,2

,1 ,2

(i)

(ii) choose

m m C L

m m s L s L eq

k k

Z Z Z Z Z Z Z

,1 ,2 0 eq m mZ Z Z Z

,2 ,1

,2 ,1

,2 ,1

2,2 ,1,2 ,1

,2 ,1

0

2 2

,2 ,1

2 2 22

24

12

2( , ) ( ) ( )

( ) ( )

(0, ) ( ) ( ) ( )

( ) ( )

m m

m m

m m eq

m mm mm m

L C

eq

m m

Z Z Z

Z Z Z Z

k k

Zv t u t u t

Z Z

u t u t

v t u t u t u t

u t u t

46

R. B. Wu

Far End Crosstalk Noise – Short Line

• Case 1: || << tr;

,2 ,1212( , ) ( ) ( )

m mv t u t u t

,2 ,1

0

0

even odd

(1 )(1 ) (1 )(1 )

( )

m m

L C L C

L C

k k k k

k k

0 ,2 ,1

0 00

2

)

12

(2 2

( , ) ( ) ( ) ( )

( ) ( )

m m

L Ckk

v t u t t t

u t u t

2a pulse of value , width L C

r s r

k k Tt u t

47

R. B. Wu

Far End Crosstalk Noise – Long Line

• Case 2: || > tr

(long line or short risetime)

,2 ,1212( , ) ( ) ( )

m mv t u t u t

,2 ,1 0even odd ( )m m L Ck k

12 2( , ) : a pulse of value

and width

sv t u

48

R. B. Wu

Remarks

• NEN occurs because odd (even) mode has smaller (larger)

launched voltage and positive (negative) reflected wave.

• FEN occurs because even and odd modes arrives at a

different time.

• Under matched load, modal analysis yields same results

with weakly coupling analysis at near end.

• At far end, weakly coupling analysis fails for long line or

shorter risetime, while modal analysis is still applicable and

yield correct results.

• Modal analysis can apply to more complicated cases, i.e.,

asymmetric, multiple, lossy coupled lines, etc.

49

Simulation in SPICE

50

R. B. Wu

Eq-ckt Model in SPICE (1)

2*"3"*67 elements SPICE #67t

TD10 segments #

670psps/in134LTD

(nH/in)97.0

7.09 (pF/in);

1.21.0

1.01.2

ps100 5in,length :Ex.

r

1111

C

LC

tr

51

R. B. Wu

Eq. ckt by Even/Odd Decomposition

52

1 1 1 11 1 ;

1 1 1 12 2

V IM M

= , = ;V m I mv M v i M i

Eq. circuit

1 1 11 2 2 2

1 1 12 2 2 2

( ) (1 )

( ) (1 )

o e o e o

o e e o e

v v v v v v

v v v v v v

Line 1

Line 2

AV1

AV2

BV1

BV2

Coupled lines

mode 1

mode 2

AV1 BV1

AV2BV2

oddZ ,0

evenZ ,0 even

odd

Ai1

Bi2

Bi1Aoi , Boi ,

Bei ,Aei ,

AoV , BoV ,

AeV ,2

1

BeV ,AeV ,

AoV ,2

11

Aoi ,2

11

Aei ,

2

1

AeV ,2

11

AoV ,

2

1

Aei ,2

11

Aoi ,

2

1

BeV ,2

1BoV ,

2

11

Boi ,2

11

Bei ,

2

1

BoV ,2

1BeV ,

2

11

Bei ,2

11

Boi ,

2

1

De-coupled lines

R. B. Wu

Crosstalk Simulation in SPICE

Parameters

[C], [L]

SPICE

subcircuit

Driver, Receiver

circuits

TRANS

SPICE

53

R. B. Wu

Equivalent SPICE Subcircuit (2)

F. Romeo and M. Santomauro, “Time-domain simulation of n coupled transmission lines,”

IEEE Trans. Microwave Theory Tech., vol. 35, pp. 131-136, Feb. 1987. 54

R. B. Wu

TRANS Example

55

R. B. Wu

Simulation Results

56

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Measurement and Simulation

57

30

Unit: mil

1.3

16 in.

3

i/p

o/p

NEN

FEN

εr=5

R. B. Wu

Further Reading -1 • A. Feller, et al., “Crosstalk and reflections in high-speed digital

systems,” 1965 Fall Jt. AFIPS, pp. 511-525.

• A. J. Gruodis and C. S. Chang, “Coupled lossy transmission line characterization and simulation,” IBM J. R&D, pp. 25-41, Jan. 1981.

• F. Romeo et al., “Time-domain simulation of n coupled transmission lines,” IEEE T-MTT, vol. 35, pp. 131-136, Feb. 1987.

• R. B. Wu & F. L. Chao, “Laddering wave in serpentine delay line,” IEEE T-AdvP, vol. 18, pp. 644-650, Nov. 1995.

• R. B. Wu & F. L. Chao, "Flat spiral delay line design with minimum crosstalk penalty," IEEE T-AdvP, vol. 19, pp. 397-402, May 1996.

• Y.-S. Cheng & R. B. Wu, “Enhanced microstrip guard trace for ringing noise suppression using a dielectric superstrate,” IEEE T-AdvP, vol. 33, pp. 961-968, Nov. 2010.

• G.-H. Shiue, et al., “Ground bounce noise induced by crosstalk noise for two parallel ground planes with a narrow open-stub line and adjacent signal traces in multilayer package structure,” IEEE T-CPMT, vol. 4, pp. 870-881, May 2014.

58

R. B. Wu

Further Reading -2

• J. Bernal, et al., “Crosstalk in coupled microstrip lines with a top

cover,” IEEE T-EMC, vol. 56, pp. 375-384, Apr. 2014.

• G.-H. Shiue, et al., “Ground bounce noise induced by crosstalk noise

for two parallel ground planes with a narrow open-stub line and

adjacent signal traces in multilayer package structure,” IEEE T-CPMT,

vol. 4, pp. 870-881, May 2014.

• M. S. Halligan and D. G. Beetner, “Maximum crosstalk estimation in

weakly coupled transmission lines”, IEEE T-EMC, vol. 56, pp. 736-

744, Jun. 2014.

• M. S. Halligan and D. G. Beetner, “Maximum crosstalk estimation in

lossless and homogeneous transmission lines,” IEEE T-MTT, vol. 62,

pp. 1953-1961, Sept. 2014.

• F. Grassi, et al., “On mode conversion in geometrically unbalanced

differential lines and its analogy with crosstalk,” IEEE T-CPMT, vol.

57, pp. 283-291, April 2015.

59

R. B. Wu

Further Reading -3

• G. Li, et al., “Measurement-based modeling and worst-case estimation of

crosstalk inside an aircraft cable connector,” IEEE T-EMC, vol.57,

pp.827-835, Aug. 2015.

• R. Araneo, et al., “Modal propagation and crosstalk analysis in coupled

graphene nano-ribbons,” IEEE T-EMC, vol. 57, pp. 726-733, Aug. 2015.

• A. Chada, et al., “Crosstalk impact of periodic coupled routing on eye

opening of high speed links in PCBs,“ IEEE T-EMC, vol. 57, pp. 1676-

1689, Oct. 2015.

• V. Ramesh Kumar, et al., “An unconditionally stable FDTD model for

crosstalk analysis of VLSI interconnects,” IEEE T-CPMT, vol. 5, pp.

1810-1817, Dec. 2015.

• B. R. Huang, et al., “Far-end crosstalk noise reduction using decoupling

capacitor,” IEEE T-EMC, vol. 58, pp. 836-848, June 2016.

• F. Grassi, et al., "Crosstalk and mode conversion in adjacent differential

lines," IEEE T-EMC, vol. 58, pp. 877-886, June 2016.

•

60