ECE 497 JS Lecture - 06 Coupled Linesjsa.ece.illinois.edu/ece497js/Lect_06.pdf · 2013. 3. 23. ·...

1Copyright © by Jose E. Schutt-Aine , All Rights ReservedECE 497-JS, Spring 2004

ECE 497 JS Lecture - 06Coupled Lines

Spring 2004

Jose E. Schutt-AineElectrical & Computer Engineering

University of [email protected]


Signal Integrity

Crosstalk Dispersion Attenuation

Reflection Distortion Loss

Delta I Noise Ground Bounce Radiation

Sense Line

Drive Line

Drive Line

Crosstalk Crosstalk NoiseNoise


TEM PROPAGATION

L

∆z

C

I

V

+

-

z

Zo βZ1 Z2

Vs


Telegrapher’s Equations

L: Inductance per unit length.

C: Capacitance per unit length.

L

∆z

C

I

V

+

-

V ILz t

∂ ∂− =∂ ∂

I VCz t∂ ∂

− =∂ ∂


50 Ωline 1

line 2

50 Ω

line 1

line 2

50 Ωline 1

line 2

line 1

line 2

Crosstalk noise depends on termination


50 Ωline 1

line 2

50 Ω

line 1

line 2

line 1

line 2

tr = 1 ns tr = 7 ns

Crosstalk depends on signal rise time


tr = 1 ns tr = 7 ns

Crosstalk depends on signal rise time

50 Ωline 1

line 2

line 1

line 2

line 1

line 2


Coupled Transmission Lines

εr

w s

h

Cs

V1

V2

I1

I2

Cs

Cm Lm


1 1 211 12

V I IL Lz t t

∂ ∂ ∂∂ ∂ ∂

− = +

1 1 211 12

I V VC Cz t t

∂ ∂ ∂∂ ∂ ∂

− = +

2 1 221 22

I V VC Cz t t

∂ ∂ ∂∂ ∂ ∂

− = +

Telegraphers Equations for Coupled Transmission Lines

Maxwellian Form

2 1 221 22

V I IL Lz t t

∂ ∂ ∂∂ ∂ ∂

− = +


1 1 2s m

V I IL Lz t t

∂ ∂ ∂∂ ∂ ∂

− = +

2 1 2m s

V I IL Lz t t

∂ ∂ ∂∂ ∂ ∂

− = +

1 1 1 2s m m

I V V VC C Cz t t t

∂ ∂ ∂ ∂∂ ∂ ∂ ∂

− = + −

2 1 2 2m m s

I V V VC C Cz t t t

∂ ∂ ∂ ∂∂ ∂ ∂ ∂

− = − + +

Telegraphers Equations for Coupled Transmission Lines

Physical form


Relations Between Physical and Maxwellian Parameters

(symmetric lines)

L11 = L22 = Ls

L12 = L21 = Lm

C11 = C22 = Cs+Cm

C12 = C21 = - Cm


( )11 12e eV IL L

z t∂ ∂

− = +∂ ∂

( )11 12e eI IC Cz t

∂ ∂− = +∂ ∂

Add voltageand currentequations

Ze = L11 + L12C11 + C12

= Ls + LmCs

ve = 1(L11 + L12 )(C11 + C12 )

= 1(Ls + Lm )Cs

Ve : Even mode voltage

Ie : Even mode current

Ve = 12

V1 + V2( )

Ie = 12

I1 + I2( )

Impedance

velocity

Even Mode


Subtract voltageand currentequations

Vd : Odd mode voltage

Id : Odd mode current

Impedance

velocity

Odd Mode

( )11 12d dV IL L

z t∂ ∂

− = −∂ ∂

( )11 12d dI IC Cz t

∂ ∂− = −∂ ∂

( )d 1 21V2

V V= −

( )d 1 21I2

I I= −

11 12d

11 12 2Z = = s m

s m

L L L LC C C C

− −

− +

d11 12 11 12

1 1v = = ( )( ) ( )( 2 )s m s mL L C C L L C C− − − +


+1 +1

EVEN

+1 -1

ODD

Mode Excitation


PHYSICAL SIGNIFICANCE OF EVEN- ANDODD-MODE IMPEDANCES

* Ze and Zd are the wave resistance seen by the even and odd mode travelling signals respectively.

V1 = Z11 I1 + Z12 I2

V2 = Z21 I1 + Z22 I2

* The impedance of each line is no longer describedby a single characteristic impedance; instead, we have


Even-Mode Impedance: ZeImpedance seen by wave propagating through the coupled-line system when excitation is symmetric (1, 1).

Odd-Mode Impedance: ZdImpedance seen by wave propagating through the coupled-line system when excitation is anti-symmetric (1, -1).

Common-Mode Impedance: Zc = 0.5ZeImpedance seen by a pair of line and a common return by a common signal.

Differential Impedance: Zdiff = 2ZdImpedance seen across a pair of lines by differential mode signal.

Definitions


EVEN AND ODD-MODE IMPEDANCES

Z11, Z22 : Self Impedances

Z12, Z21 : Mutual Impedances

For symmetrical lines,

Z11 = Z22 and Z12 = Z21


EXAMPLE(Microstrip)

εr = 4.3Zs = 56.4 Ω

Single LineDielectric height = 6 milsWidth = 8 mils

εr = 4.3

Coupled LinesHeight = 6 milsWidth = 8 milsSpacing = 12 mils

Ze = 68.1 Ω Zd = 40.8 ΩZ11 = 54.4 Ω Z12 = 13.6 Ω


( ,0) ( ,0) ( ,0) ( ,0)e d e dtdr

e d e d

a t a t a t a tIZ Z Z Z

= + + −

( ,0) ( ,0)tdr e dV a t a t= −da ( ,0) 0t =

= 2

tdr e

tdr

V ZI

Even Mode

coaxial line

Zgline 1

line 2

Zg

stepgenerator

Vb

Vf IT

+

-VT I2

I1

reference plane tied to ground

e g1Z = 2( ) Z1

e

e

ρρ

+−

e 2v =

e

lτ


coaxial line

Zg

Zg

stepgenerator

Vb

Vf line 1

line 2

IT

VTI2 reference plane floating

+-

I1

[ ]tdr e d e dV = a (t,0)+a (t,0)- a (t,0)-a (t,0) f bV V= +

tdr ( ,0) ( ,0)I = e d

e d

a t a tZ Z

+

tdr

( ,0) ( ,0)I =- e d

e d

a t a tZ Z

−

ae(t,0) = 0, VtdrItdr

= 2Zd

dd

1 1 2l, v = 2 1

dd g

d

Z Zρρ τ

+= −

Odd Mode


EXTRACT INDUCTANCE AND CAPACITANCE COEFFICIENTS

s1L = + 2

e d

e d

Z Zv v

1s

e e

CZ v

=

m 1L = - 2

e d

e d

Z Zv v

m 1 1 1C = - 2 e e d dZ v Z v

d s eZ < Z < Z


20

40

60

80

100

120

4 6 8 10 12 14 16 18Spacing (mils)

Even-Mode Impedanceh=3 milsh=5 milsh=7 mils

h=10 milsh=14 mils

h=21 mils

Ze(

Ω)

Measured even-mode impedance


20

25

30

35

40

45

50

4 6 8 10 12 14 16 18Spacing (mils)

Odd-Mode Impedanceh=3 mils

h=5 mils

h=7 mils

h=10 mils

h=14 mils

h=21 mils

Zd

(Ω

)

Measured odd-mode impedance


0.158

0.16

0.162

0.164

0.166

0.168

0.17

4 6 8 10 12 14 16 18Spacing (mils)

Even-Mode velocityh=3 mils

h=5 mils

h=7 mils

h=10 mils

h=14 mils

h=21 mils

v e(m/n

s)

Measured even-mode velocity


0.175

0.18

0.185

0.19

0.195

0.2

0.205

0.21

4 6 8 10 12 14 16 18Spacing (mils)

Odd-Mode Velocity

h=3 milsh=5 mils

h=7 mils

h=10 milsh=14 milsh=21 mils

vd(m

/ns)

Measured odd-mode velocity


0

50

100

150

200

250

4 6 8 10 12 14 16 18Spacing (mils)

Mutual Inductance h=3 mils

h=5 mils

h=7 mils

h=10 mils

h=14 mils

h=21 mils

Lm

(nH

/m)

Measured mutual inductance


10

15

20

25

30

35

40

4 6 8 10 12 14 16 18Spacing (mils)

Mutual Capacitance h=3 mils

h=5 mils

h=7 milsh=10 mils

h=14 mils

h=21 mils

Cm

(pF/

m)

Measured mutual capacitance


40

50

60

70

80

90

100

110

10 20 30 40 50

Typical Even & Odd Mode Impedances

ZevenZodd

Zeve

n, Z

odd

(Ohm

s)

Distance (mils)

Even & Odd Mode Impedances


Microstrip : Inhomogeneous structure, odd and even-mode velocities must have different values.

Stripline : Homogeneous configuration, odd and even-mode velocities have approximately the same values.

Modal Velocities in Stripline and Microstrip


Microstrip vs Stripline

Microstrip (h =8 mils)w = 8 milsεr = 4.32Ls = 377 nH/mCs = 82 pF/mLm = 131 nH/mCm = 23 pF/mve = 0.155 m/nsvd = 0.178 m/ns

Stripline (h =16 mils)w = 8 milsεr = 4.32Ls = 466 nH/mCs = 86 pF/mLm = 109 nH/mCm = 26 pF/mve = 0.142 m/nsvd = 0.142 m/ns

50 Ω

50 Ω


-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

Vol

ts

microstrip

C

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

Vol

ts

stripline

C

50 Ω

50 Ω

Microstrip vs Stripline

Sense line response at near end

Probe


1( ) e e d d

j z j z j z j zv v v v

e e d d

even odd

V z A e B e A e B eω ω ω ω

− + − +

= + + +1442443 1442443

2 ( ) e e d d


e e d d

even odd

V z A e B e A e B eω ω ω ω

− + − +

= + − −1442443 1442443

Zs1

Zs2 ZL2

ZL1line 1

line 2

General Solution for Voltages


11 1( ) e e d d


e e d de d

even odd

I z A e B e A e B eZ Z

ω ω ω ω− + − +

= − + − 144424443 14444244443

21 1( ) e e d d


e e d de d

even odd

I z A e B e A e B eZ Z

ω ω ω ω− + − +

= − − − 144424443 14444244443

Zs1

Zs2 ZL2

ZL1line 1

line 2

General Solution for Currents


odd

even

First reflection

even

even

odd

odd

Second reflection

odd

odd

odd

oddeven

even

even

even

Zs1

Zs2 ZL2

ZL1line 1

line 2

Coupling of Modes (asymmetric load)


Coupling of Modes(symmetric load)

Zs

Zs ZL

ZLline 1

line 2

odd

even

First reflection

even

odd

Second reflection

odd

even


-0.2

0

0.2

0.4

0.6

0.8

1

Vol

ts

0 5 10 15 20 25 30

Time (ns)

Drive Line at Near End

35 40

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

Vol

ts

0 5 10 15 20 25 30

Time (ns)

Sense Line at Near End

35 40

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ECE 497 JS Lecture - 06 Coupled Linesjsa.ece.illinois.edu/ece497js/Lect_06.pdf · 2013. 3. 23. ·...

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