© H. Heck 2008Section 5.31 Module 5:Advanced Transmission Lines Topic 3: Crosstalk OGI EE564 Howard Heck

© H. Heck 2008 Section 5.3 1

Module 5: Advanced Transmission LinesTopic 3: Crosstalk

OGI EE564

Howard Heck


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64 Where Are We?

1. Introduction

2. Transmission Line Basics

3. Analysis Tools

4. Metrics & Methodology

5. Advanced Transmission Lines1. Losses

2. Intersymbol Interference (ISI)

3. Crosstalk

4. Frequency Domain Analysis

5. 2 Port Networks & S-Parameters

6. Multi-Gb/s Signaling

7. Special Topics


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64 Contents

Introduction Circuit Models

Mutual Inductance Mutual Capacitance

Effective Impedance and Velocity Coupling Matrices

Noise Coupling On Passive Lines Coupling Coefficient Forward and Backward Crosstalk Crosstalk on Passive Lines – Example

Implementation Considerations Homogeneous and Non-Homogeneous Media Printed Circuit Boards Minimization Techniques Lossy Lines

Summary References


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64 Introduction

Recall the T.E.M. mode single line:

Two adjacent lines have two possible T.E.M. modes:Even mode – excited in phase with equal amplitudes.

HE E

H

EH

Even ModeEven Mode Odd ModeOdd Mode

Odd mode – driven 180º out of phase with equal amplitudes.


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64 Introduction #2

In general, for a system of n transmission lines, there are n possible TEM modes.

When the fields from adjacent transmission line interact with each other, we get crosstalk.

Crosstalk can have the following impacts:1. The characteristics (Z0, vp) of the driven lines

are altered.

2. Noise is coupled onto passive lines.


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64 Circuit Model

Single line (lossless): 2 coupled lines:

L0

C0

L0

C0

L0

C0

L0

C0

L0

C0

C0

L0

C0

CmLm

L0Line 1

Line 2

The mutual inductance, Lm, causes the current in line 1

to induce a voltage on line 2 :

The mutual capacitance, Cm, causes the voltage on

line 1 to induce a current in line 2 :

dtdILV m

12 [5.3.1]

I C dVdtm2

1 [5.3.2]


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64 Mutual Inductance

L0

L0

Lm

I1

I2

+ V1 -

+ V2 -

dt

dIL

dt

dILV m

`2`101 [5.3.3]

dt

dIL

dt

dILV m

`1`202 [5.3.4]

dt

dILLVV m 021 [5.3.5]

If the lines are driven in odd mode, . Then dI

dt

dI

dt

dI

dt1 2` `

modd LLL 0 [5.3.8] dt

dILLVV m 021 [5.3.7]

Effective inductances: L L Leven odd 0

dI

dt

dI

dt

dI

dt1 2` ` If the lines are driven in even mode, . Then

meven LLL 0 [5.3.6]


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64 Mutual Capacitance

Recall the even mode field diagram. Some fringing fields are lost due to overlap between electrical field lines. So, even mode capacitance is less than the total capacitance of a single PCB trace.

In a multi-conductor PCB, the effective capacitances obey the relationship, , where C0 is the total capacitance of the line.

C0

C0

Cm

V2

V1

I1

I2

[5.3.9]

dt

dVC

dt

dVCC

dt

VVdC

dt

dVCI mmm

`2`10

`21`101

[5.3.10]

dt

dVC

dt

dVCC

dt

VVdC

dt

dVCI mmm

`1`20

`12`202

[5.3.11]dt

dVCII 021 [5.3.12]0CCeven

Odd mode, . Then dV

dt

dV

dt

dV

dt1 2` `

[5.3.13] dt

dVCCII m2021 [5.3.14]modd CCC 20

C C Ceven odd 0

dV

dt

dV

dt

dV

dt1 2` ` Even mode, . Then


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64 Effective Impedance and Velocity

Even mode:

Odd mode:

m

pCCL

v

00

1[5.3.16]

eveneven

evenpCL

v1

, [5.3.18]even

eveneven C

LZ ,0 [5.3.17]

oddodd

oddpCL

v1

, [5.3.20]odd

oddodd C

LZ ,0 [5.3.19]

Since and , we get:oddmeven CCCC 0 L L Leven odd 0 Z Z Zeven odd0 0 0, ,

What about vp?

Typically, for microstrips.Since all fields are contained within the dielectric

medium, there is no effect on p for striplines.

v v vp even p p odd, ,

mCC

LZ

0

00 [5.3.15] Recall:


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64 Coupling Matrices

Capacitance:

1 2

Cs1 Cs2

C12

CQ

VV

111

1 02

CQ

VV

222

2 01

CQ

VV

121

2 01

CQ

VV

212

1 02

Q

Q

C C

C C

V

V1

2

11 12

21 22

1

2

[5.3.21]

whereTotal capacitance

(C0 + Cm)

Mutual capacitance(Cm)

Note, Cii is the total capacitance capacitance (sum of capacitance to ground plus mutual capacitances). Mathematically : C C Cs11 1 12 12222 CCC s and


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64 Coupling Matrices #2

Inductance:

Recall even and odd modes:

[5.3.22]

dtdI

dtdI

LL

LL

V

V

2

1

2221

1211

2

1

where L11 and L22 are self inductances

L12 and L21 are mutual inductances

C C C

C Codd m

even

0

0

2 L L L

L L Lodd m

even m

0

0

Apply the matrices to the even and odd mode equations:

1211121210 2 CCCCCCCC smodd [5.3.26]

1211121210 CCCCCCC seven [5.3.25]

12110 LLLLL modd [5.3.24]

12110 LLLLL meven [5.3.23]

where C0 = Cs1 (total capacitance to ground)


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64 Coupling Matrics – n Line System

Inductance matrix: L L L

L L

L L

N

N NN

11 12 1

21 22

1

Capacitance matrix: C C C

C C

C C

N

N NN

11 12 1

21 22

1

Lii = self inductance of line i

Lij = mutual inductance between lines i and j

Cii = total capacitance seen by line i

= capacitance of conductor i to ground plus all

mutual capacitances to other lines.Cij = mutual capacitance between conductors i and j


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64 Effective Impedance & Velocity Again

The effective inductance and capacitance can be calculated using the matrices for arbitrary switching patterns.

For lines switching in-phase (even mode), inductances add, capacitances subtract.

For lines switching out-of-phase (odd mode), inductances subtract, capacitances add.

From this, the effective impedance and propagation velocity can be approximated.


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64 Lossless Example

Network:Network:

PCB trace cross-section:PCB trace cross-section:

0.005"0.005"

0.005"

0.0007"

0.0074"

0.002"

r = 4.0

LC matrices:LC matrices:

innHL /632.10191.1

191.1350.10

inpFC /553.2217.0

217.0553.2

60

60

Coupling

Line 1

Line 260

60


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64 Lossless Example #2

Out-of-PhaseOut-of-Phase

5.57217.0553.2

191.135.101

1

inpF

innHZ odd

111 911.1217.0553.2191.135.10 ftnsinpFinnHodd

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 2 4 6 8time [ns]

volt

age

[V] D10.862V

0.997V

D2

0.138V0.003V

R1

0.981V 1.000V

R2

0.019V 0.000V1.93ns

Coupled ModelCoupled Model Single Line Eq. ModelSingle Line Eq. Model

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 2 4 6 8time [ns]

volt

age

[V]

R

0.996V

D

0.939V

1.000V

1.912ns


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64 Lossless Example #3

In-PhaseIn-Phase

3.70217.0553.2

191.135.101

1

inpF

innHZ even

111 970.1217.0553.2191.135.10 ftnsinpFinnHeven

Coupled ModelCoupled Model Single Line Eq. ModelSingle Line Eq. Model

D1

1.100V1.001V

R1

0.990V

1.000V

R2D2

0 2 4 6 8time [ns]

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

volt

age

[V]

1.95ns-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 2 4 6 8time [ns]

volt

age

[V]

DR

1.039V

0.998V

1.000V

1.97ns


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64 Noise Coupling Mechanism

2IC

IC IC ILIC + IL IC - IL

The total backward current is IC + IL. The total forward current is IC – IL.

Lm induces current IL traveling backward on the victim line.

IC splits into equal components traveling forward & backward in the victim line.

Current IC flows through the mutual capacitance from the driven line to the victim line.

Z0

Z0

Z0 Z0

VS

L0

L0

LmCm


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64 Coupling Coefficients

The capacitive coupling coefficient is the ratio of the mutual capacitances to the total capacitance:

K

C

CCj

iji j

jj

[5.3.37]

The inductive coupling coefficient is the ratio of the mutual inductances to the self inductance of the transmission line:

K

L

LLj

iji j

jj

[5.3.38]

We can rewrite the coupling coefficient from equation [5.3.36] in terms of the capacitive and inductive coupling coefficients:

KK K

vC L

2

[5.3.39]


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64 Forward & Backward Crosstalk

We have seen that TEM modes cause forward & backward coupled waves. How does that show up as noise at the ends of the network?

Noise currents (IC and IL) are proportional to the edge rate of the

signal (dV/dt). IC has 2 equal components traveling in opposite directions.

IL has 1 component traveling backward.

Z0

Z0

Z0

Z0

Z0

Z0Z0Vin(t)

VC

VL

IC

IL

VC

VL

IC

IL

Cm Lm

Noise voltages VL has a backward

component with the same polarity as VC and a forward component which has the opposite polarity from VC.

Therefore, VL subtracts from VC in the forward direction, but adds to VC in the backward direction.


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64 Far End (Forward) Crosstalk

Forward coupling coefficient:

0000 2

1

22 L

L

C

C

vL

L

C

CKKK mm

p

mmdLC

dF

[5.3.40]

where: d is the transmission line propagation delay per

unit length which equals 1/vp (propagation velocity).

Recall and . ThendZL 00 0

0 ZC d

K Z CL

ZF mm

1

2 00

[5.3.41]


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64 Far End (Forward) Crosstalk #2

Far end crosstalk noise:

[5.3.42]

where: l is the coupled line length and

Substitute:

[5.3.44]

V t K l

dV t t

dtfe Fd

dV t t

dt

V

td swing

r

[5.3.43]

V t K l

dV t t

dtZ C

L

Zl

V

tfe Fd

mm swing

r

1

2 00

V tV l

tZ C

L

Zfeswing

rm

m

2 00

[5.3.45]

Pulse width of the noise:)(or fr ttPW [5.3.46]


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64 Near End (Backward) Crosstalk

Backward Coupling Coefficient:

[5.3.47]

Near end crosstalk pulse width:

[5.3.49]

[5.3.48]

00

00 4

1

4

1

4

1

Z

LCZ

L

L

C

CKKK m

mmm

LCB

Near End Crosstalk Noise:

2for

2for 2

rdswingB

rdd

r

swingB

ne tlVK

tll

t

VK

tV

Non-saturated

Saturated

PW l td 2


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64 Near End vs. Far End Crosstalk

The magnitude of the backward (near end) crosstalk coefficient is greater than that of forward (far end) crosstalk.

The pulse width of backward crosstalk is greater than that of forward crosstalk.

Why do we care about near end crosstalk?


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64 Crosstalk Noise Example

Using the coupled lines from the even/odd mode example:

0 2 4 6 8time [ns]

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2v

olt

ag

e [

V]

D1

R1D2

R2

0.119V

-0.490V

0.981V 1.000V

1.93ns

3.86ns


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64 Crosstalk Noise Example #2

The forward coupled pulse: appears at the receiver at the same time as the driven signal. has the opposite polarity from the driven signal. has a pulse width equal to the rise time of the signal

The backward coupled noise pulse: appears at the driver as soon as the driven signal propagates

onto the coupled lines. has the same polarity as the driven signal. has a pulse width of twice the prop delay.

0 2 4 6 8time [ns]

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

volt

age

[V] D1

R1D2R2

0.119V

-0.490V

0.981V 1.000V

1.93ns

3.86ns


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64 Crosstalk in Homogenous Media

Relationship between inductive & capacitive coupling matrices:

Where I is the identity matrix. Therefore, .

L Cv

Ip

1

2

L C 1

Relationship of KC and KL:

From it follows that . KC = KL. L C 1C

C

L

Lm m

[5.3.50]

Forward Crosstalk:

Backward Crosstalk:

Kt

K KFd

C L 2

0

K K K KB C L C 1

4

1

2 [5.3.52]

[5.3.51]


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64

Crosstalk on Non-Homogeneous Media Relationship between inductive & capacitive coupling

matrices: L C 1

Relationship of KC and KL: KC KL C

C

L

Lm m

Forward Crosstalk:

Backward Crosstalk:

KF 0

K KB F


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64 Crosstalk in Printed Circuit Boards

Param Xtalk

r

t

w

s

h

ws

w

t

h1

h2

r

What other parts of the interconnect can act as sources of crosstalk?


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64 Techniques for Minimizing Crosstalk

In general, striplines have less crosstalk than microstrips, due to the presence of the second reference plane.This is not always true. To design a stripline to the

same impedance as a microstrip may require you to increase h for the stripline. This can actually cause the crosstalk to be higher for the stripline.

Increase s:For speeds of 100 MHz or higher: s 2wFor speeds of 200 MHz or higher: s 3w

Decrease h:For 133 MHz & higher: h w.


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64

Techniques for Minimizing Crosstalk #2

Limit the coupled trace length.Remember, crosstalk can occur between adjacent

layers, too. Keep adjacent layers far apart. Route lines on adjacent layers orthogonally, if possible.

Add “shielding”:Route “guard” traces between signal traces on PCBs.

• Be careful with this one. You must tie use vias to connect the guard traces to the adjacent reference layer at frequent points.

Lots of ground I/O in connectors and packages.

Use resistor packs instead of resistor networks. VTT

S1

S4

S3

S2

VTT

S1

S4

S3

S2 S5

S7

S6


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64 Summary

Crosstalk arises from mutual capacitance and inductance between transmission lines.

Crosstalk alters the impedance and propagation velocity of transmission lines, and creates noise on quiet lines.

Crosstalk can be expressed in terms of the ratios of mutual capacitance to the total capacitance and mutual inductance to the self inductance.

Crosstalk noise travels in both directions.


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64 References

S. Hall, G. Hall, and J. McCall, High Speed Digital System Design, John Wiley & Sons, Inc. (Wiley Interscience), 2000, 1st edition.

H. Johnson and M. Graham, High-Speed Signal Propagation: Advanced Black Magic, Chapters 2 & 3, Prentice Hall, 2003, 1st edition, ISBN 0-13-084408-X.

W. Dally and J. Poulton, Digital Systems Engineering, Chapters 4.3 & 11, Cambridge University Press, 1998.

H.B.Bakoglu, Circuits, Interconnections, and Packaging for VLSI, Addison Wesley, 1990.


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64 References #2

H. Johnson and M. Graham, High Speed Digital Design: A Handbook of Black Magic, PTR Prentice Hall, 1993.

R. Poon, Computer Circuits Electrical Design, Prentice Hall, 1st edition, 1995.

R.E. Matick, Transmission Lines for Digital and Communication Networks, IEEE Press, 1995.

“Line Driving and System Design,” National Semiconductor Application Note AN-991, April 1995.

K.M. True, “Data Transmission Lines and Their Characteristics,” National Semiconductor Application Note AN-806, February 1996.


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64

Noise Coupling from an Impedance Point of View

Coupling occurs when the initial wave travelling on the active line reaches point z.

The noise waves are the sum of the even and odd propagation modes.

We can derive a coupled noise coefficient as a function of the even and odd mode impedances.

z

z

Ve

Vo

Ie

Io

Ve

Vo

Ie

Io

= 1

Active (Driven) Line

Passive (Quiet) Line


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64 Noise Coupling #2

Define coupling coefficient: At z:

Substitute:

Apply KCL at z:

Substitute:

Use Ohm’s law:

Substitute:

KV

VvQ

A

oeQ VVV

oeA VVV

KV V

V Vve o

e o

ooo ZIV 0

eee ZIV 0

KI Z I Z

I Z I Zve e o o

e e o o

0 0

0 0

III oe

oeQ III 0

KZ Z

Z Zve o

e o

0 0

0 0

[5.3.4a]

[5.3.3a]

[5.3.2a]

[5.3.1a]

[5.3.8a]

[5.3.7a]

[5.3.6a][5.3.5a]

[5.3.10a]

[5.3.9a]

z

z

Ve

Vo

Ie

Io

Ve

Vo

Ie

Io

= 1

Active (Driven) Line

Passive (Quiet) Line

Documents

© H. Heck 2008Section 5.31 Module 5:Advanced Transmission Lines Topic 3: Crosstalk OGI EE564 Howard Heck