Couple Dtl

8/17/2019 Couple Dtl

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ECE 451 – Jose Schutt ‐ Aine 1

ECE 451

Coupled Lines

Jose E. Schutt-Aine

Electrical & Computer Engineering

University of Illinois

[email protected]


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Signal Integrity

Crosstalk Dispersion AttenuationReflection Distortion Loss

Delta I Noise Ground Bounce Radiation

Sense Line

Drive Line

Drive Line

Crosstalk Noise


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TEM

PROPAGATION

L

z

C

I

V

+

-

z

Z o Z1 Z2

Vs


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Telegrapher’s Equations

L: Inductance per unit length.

C : Capacitance per unit length.

L

z

C

I

V

+

-

V I L z t

I V C

z t


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50 line 1

line 2

50

line 1

line 2

50 line 1

line 2

line 1

line 2

Crosstalk noise depends on termination


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50 line 1

line 2

50

line 1

line 2

line 1

line 2

tr = 1 ns tr = 7 ns

Crosstalk depends on signal rise time


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50 line 1

line 2

50

line 1

line 2

line 1

line 2

tr = 1 ns tr = 7 ns



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tr = 1 ns tr = 7 ns


50 line 1

line 2

line 1

line 2

line 1

line 2


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Coupled Transmission Lines

r

ws

h

Cs

V1

V2

I1

I2

Cs

Cm

Lm


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1 1 211 12

V I I L L

z t t

1 1 211 12

I V V C C

z t t

2 1 221 22

I V V C C z t t

Telegraphers Equations for Coupled Transmission Lines

Maxwellian Form

2 1 221 22

V I I L L

z t t


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1 1 2s m

V I I L L

z t t

2 1 2m s

V I I L L

z t t

1 1 1 2s m m

I V V V C C C

z t t t

2 1 2 2m m s

I V V V C C C z t t t

Telegraphers Equations for Coupled Transmission Lines

Physical form


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Relations Between Physical

and Maxwellian Parameters

(symmetric lines)

L11 = L22 = Ls

L12 = L21 = Lm

C11 = C22 = Cs+Cm

C12 = C21 = - Cm


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11 12e eV I L L

z t

11 12e e I I

C C z t

Add voltage

and current

equations

Z e

= L11 + L12

C 11 + C 12=

Ls + Lm

C s

ve =1

(L11 + L12 )(C 11 + C 12 )=

1

(Ls + Lm )C s

Ve : Even mode voltage

Ie : Even mode current

V e =1

2V 1 + V 2( )

I e =1

2 I 1 + I 2( )

Impedance

velocity

Even Mode


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Subtract voltage

and current

equations

Vd : Odd mode voltage

Id : Odd mode current

Impedance

velocity

Odd Mode

11 12d d V I L L

z t

11 12d d I I

C C z t

d 1 21

V2

V V

d 1 21I2

I I

11 12

d 11 12 2

Z = = s m

s m

L L L L

C C C C

d

11 12 11 12

1 1v = =

( )( ) ( )( 2 )s m s m L L C C L L C C


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+1 +1

EVEN

+1 -1

ODD

Mode Excitation


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PHYSICAL SIGNIFICANCE OF EVEN- AND

ODD-MODE IMPEDANCES

* Ze and Zd are the wave resistance seen by the even

and odd mode travelling signals respectively.

V 1 = Z 11 I 1 + Z 12 I 2

V 2 = Z 21 I 1 + Z 22 I 2

* The impedance of each line is no longer described

by a single characteristic impedance; instead, we have


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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


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EVEN AND ODD-MODE IMPEDANCES

Z11, Z22 : Self Impedances

Z12, Z21 : Mutual Impedances

For symmetrical lines,

Z11 = Z22 and Z12 = Z21


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EXAMPLE

(Microstrip)

r = 4.3Zs = 56.4

Single Line

Dielectric height = 6 mils

Width = 8 mils

r = 4.3

Coupled Lines

Height = 6 mils

Width = 8 milsSpacing = 12 mils

Ze = 68.1 Zd = 40.8

Z11 = 54.4 Z12 = 13.6


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( ,0) ( ,0) ( ,0) ( ,0)e d e d tdr

e d e d

a t a t a t a t I

Z Z Z Z

( ,0) ( ,0)tdr e d V a t a t d a ( ,0) 0t

= 2

tdr e

tdr

V Z

I

Even Mode

coaxial line

Zg

line 1

line 2

Zg

stepgenerator

V b

Vf IT

+

-VT I2

I1

reference plane tied to ground

e g

1

Z = 2( ) Z1

e

e

e

2

v =e

l


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coaxial line

Zg

Zg

stepgenerator

V b

Vf line 1

line 2

IT

VTI2 reference plane floating

+

-

I1

tdr e d e d V = 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 t

Z Z

tdr

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

e d

a t a t

Z Z

ae(t,0) = 0 ,

V tdr

I tdr = 2 Z d

d

d

1 1 2l, v =

2 1

d d g

d

Z Z

Odd Mode


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EXTRACT INDUCTANCE AND

CAPACITANCE COEFFICIENTS

s

1L = +

2

e d

e d

Z Z

v v

1s

e e

C Z v

m

1L = -

2

e d

e d

Z Z

v v

m

1 1 1C = -

2 e e d d Z v Z v

d s eZ < Z < Z


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20

40

60

80

100

120

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

Even-Mode Impedanceh=3 mils

h=5 mils

h=7 mils

h=10 mils

h=14 mils

h=21 mils

Z e (

)

Measured even-mode impedance


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20

25

30

35

40

45

50

4 6 8 10 12 14 16 18

Spacing (mils)

Odd-Mode Impedanceh=3 mils

h=5 mils

h=7 mils

h=10 mils

h=14 mils

h=21 mils

Z d (

)

Measured odd-mode impedance


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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


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0.175

0.18

0.185

0.19

0.195

0.2

0.205

0.21

4 6 8 10 12 14 16 18

Spacing (mils)

Odd-Mode Velocity

h=3 mils

h=5 mils

h=7 mils

h=10 mils

h=14 mils

h=21 mils

v d

( m / n

s )

Measured odd-mode velocity


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0

50

100

150

200

250

4 6 8 10 12 14 16 18

Spacing (mils)

Mutual Inductance h=3 mils

h=5 mils

h=7 mils

h=10 mils

h=14 mils

h=21 mils

L m ( n

H / m )

Measured mutual inductance


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10

15

20

25

30

35

40

4 6 8 10 12 14 16 18

Spacing (mils)

Mutual Capacitance h=3 milsh=5 mils

h=7 mils

h=10 mils

h=14 mils

h=21 mils

C m

( p F /

m )

Measured mutual capacitance


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40

50

60

70

80

90

100

110

10 20 30 40 50

Typical Even & Odd Mode Impedances

ZevenZodd

Z e v e n ,

Z o d d ( O h m s )

Distance (mils)

Even & Odd Mode Impedances


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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


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Microstrip vs Stripline

Microstrip (h =8 mils)

w = 8 mils

r = 4.32Ls = 377 nH/mCs = 82 pF/m

Lm = 131 nH/m

Cm = 23 pF/mve = 0.155 m/ns

vd = 0.178 m/ns

Stripline (h =16 mils)

w = 8 mils

r = 4.32Ls = 466 nH/mCs = 86 pF/m

Lm = 109 nH/m

Cm = 26 pF/mve = 0.142 m/ns

vd = 0.142 m/ns

50

50


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-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

V o l t s

microstrip

C

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

V o l t s

stripline

C

50

50

Microstrip vs Stripline

Sense line response at near end

Probe


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1( ) e e d d

j z j z j z j z

v v v v

e e d d

even odd V z A e B e A e B e

2 ( ) e e d d

j z j z j z j z

v v v v

e e d d

even odd

V z A e B e A e B e

Zs1

Zs2 ZL2

ZL1line 1

line 2

General Solution for Voltages


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1

1 1

( ) e e d d

j z j z j z j z

v v v v

e e d d e d

even odd

I z A e B e A e B e Z Z

2

1 1( ) e e d d

j z j z j z j zv v v v

e e d d

e d

even odd

I z A e B e A e B e Z Z

Zs1

Zs2 ZL2

ZL1line 1

line 2

General Solution for Currents


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odd

even

First reflection

even

even

odd

odd

Second reflection

odd

odd

odd

odd

even

even

even

even

Zs1

Zs2 ZL2

ZL1line 1

line 2

Coupling of Modes

(asymmetric load)


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Coupling of Modes

(symmetric load)

Zs

Zs ZL

ZLline 1

line 2

odd

even

First reflection

even

odd

Second reflection

odd

even


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-0.2

0

0.2

0.4

0.6

0.8

1

V o l t s

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

V o l t s

0 5 10 15 20 25 30

Time (ns)

Sense Line at Near End

35 40


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1 2 3

31 1 211 12 13

V I V V C C C

z t t t

32 1 221 22 23

V I V V C C C

z t t t

3 31 231 32 33

I V V V C C C

z t t t

31 1 211 12 13

I V I I L L L

z t t t

32 1 221 22 23

I V I I L L L

z t t t

3 31 231 32 33

V I I I L L L

z t t t

Three‐Line Microstrip

h i Al h d


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11 13( )V I

L L z t

11 13( ) I V

C C z t

Subtract (1c) from (1a) and (2c) from (2a), we get

This defines the Alpha mode with:

1 3V V V 1 3 I I I and

The wave impedance of that mode is:

11 13

11 13

L L Z

C C

and the velocity is 11 13 11 13

1u

L L C C

Three‐Line – Alpha Mode

Th Li M d l D iti


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In order to determine the next mode, assume that

1 2 3V V V V

1 2 3 I I I I

31 211 21 31 12 22 32 13 23 33V I I I

L L L L L L L L L z t t t

31 211 21 31 12 22 32 13 23 33 I V V V

C C C C C C C C C z t t t

By reciprocity L32

= L23 , L

21= L

12, L

13= L

31

By symmetry, L12

= L23

Also by approximation, L22 L11 , L11+L13 L11

Three‐Line – Modal Decomposition


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31 211 12 13 12 112V I I I

L L L L L z t t t

In order to balance the right-hand side into I, we need to have

12 11 2 11 12 13 2 11 12 22 L L I L L L I L L I

2

12 122 L L

or 2

Therefore the other two modes are defined as

The Beta mode with

Three‐Line – Modal Decomposition

Th Li B t M d


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The Beta mode with

1 2 32V V V V

1 2 32 I I I I

The characteristic impedance of the Beta mode is:

11 12 13

11 12 13

22

L L L Z C C C

and propagation velocity of the Beta mode is

11 12 13 11 12 131

2 2

u

L L L C C C

Three‐Line – Beta Mode

Three Line Delta Mode


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The Delta mode is defined such that

1 2 32V V V V

1 2 32 I I I I

The characteristic impedance of the Delta mode is

11 12 13

11 12 13

22

L L L Z C C C

The propagation velocity of the Delta mode is:

11 12 13 11 12 131

2 2

u

L L L C C C

Three‐Line – Delta Mode


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1 0 1

1 2 1

1 2 1

E

1 2 3

Alpha mode

Beta mode*

Delta mode*

Symmetric 3‐Line Microstrip

In summary: we have 3 modes for the 3-line system

*neglecting coupling between nonadjacent lines

C l W id


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1 2 3

r = 4.3

113 17 5

( / ) 16 53 16

5 17 113

C pF m

346 162 67

( / ) 152 683 152

67 162 346

L nH m

0.45 0.12 0.45

0.5 0 0.50.45 0.87 0.45

E

0.44 0.49 0.44

0.5 0 0.50.10 0.88 0.10

H

Coplanar Waveguide

Co la a Wa e uide


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73 0 0

( ) 0 48 0

0 0 94

m Z

56 23 8

( ) 22 119 22

8 23 56

c Z

0.15 0 0

( / ) 0 0.17 00 0 0.18

pv m ns

1 2 3

r = 4.3

Coplanar Waveguide


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WS' S'WS

r h

2S k

S W

( ) : Complete Elliptic Integral of the first kind K k

'( ) ( ')K k K k

2 1/ 2' (1 )k k

30 '( ) (ohm)( )1

2

ocp

r

K k Z K k

1/ 22

1cp

r

v c

Coplanar Waveguide


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S WW

r h

120 '( ) (ohm)

( )1

2

ocs

r

K k Z

K k

Coplanar Strips

Q lit ti C i


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Characteristic Microstrip Coplanar Wguide Coplanar strips

eff * ~6.5 ~5 ~5

Power handling High Medium Medium

Radiation loss Low Medium Medium

Unloaded Q High Medium Low or High

Dispersion Small Medium Medium

Mounting (shunt) Hard Easy Easy

Mounting (series) Easy Easy Easy

* Assuming r =10 and h=0.025 inch

Qualitative Comparison

V Transmission Line


50/58


2p

h

w

dielectric

ground

signal strip

a s issio i e

V Li Ch i i I d


51/58


0

50

100

150

200

250

0 0.1 0.2 0.3 0.4 0.5 0.6

w/h

CHARACTERISTIC IMPEDANCE

30º

37.5º

45º52.5º

60º

Microstrip

0.7 0.8 0.9 1

Z o ( o h m s )

Calculated values of the characteristic impedance for a single-line v-strip structure as a

function of width-to-height ratio w/h. The relative dielectric constant is r = 2.55.

V‐Line Characteristic Impedance

V Li Eff ti P itti it


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1.8

1.85

1.9

1.95

2

2.05

2.1

2.15

2.2

0 0.1 0.2 0.3 0.4 0.5 0.6

w/h

EFFECTIVE PERMITTIVITY

30º

37.5º

45º

52.5º

60º

Microstrip

0.7 0.8 0.9 1

E f f e c t i v e R e l a

t i v e D i e l e c t r i c C o n s t a n t

Calculated values of the effective relative dielectric constant for a single-line

v-strip structure as a function of width-to-height ratio w/h.

The relative dielectric constant is r = 2.55

V‐Line – Effective Permittivity

Th Li V T i i Li


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h

y

x

Region2

Region3

Region4

Region6

Region1

Region5

2pw

dielectricground surface

signal strip

s

Three‐Line – V Transmission Line

V‐Line and Microstrip


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74.00 -0.97 -0.23

C (pF/m) = -0.97 74.07 -0.97

-0.23 -0.97 74.00

425.84 20.35 7.00

L (nH/m) = 20.36 422.85 20.36

7.00 20.35 425.84

52.49 -5.90 -0.57

C (pF/m) = -5.90 53.27 -5.90

-0.57 -5.90 52.49

609.74 113.46 41.79

L (nH/m) = 113.54 607.67 113.54

41.79 113.46 609.74

Microstrip V-line

Comparison of the inductance and capacitance matrices

between a three-line v-line and microstrip structures.

The parameters are p/h = 0.8 mils, w/h = 0.6 and r = 4.0.

h

y

x

Region2

Region3

Region4

Region6

Region1

Region5

2pw

dielectricground surface

signal strip

s1 2 3

i e a i o ip

V Li C li C ffi i


55/58

ECE 451

– Jose

Schutt

‐ Aine 55

0

50

100

150

200

250

300

350

0 0.2 0.4 0.6 0.8 1 1.2s/h

Mutual Inductance

V-line

microstrip

L m

( n H / m )

0

5

10

15

20

2530

35

40

0 0.2 0.4 0.6 0.8 1 1.2s/h

Mutual Capacitance

V-line

microstrip

C m

( p F / m )

Plot of mutual inductance (top) and mutual capacitance (bottom) versus spacing-to-height ratiofor v-line and microstrip configurations. The parameters are w/h = 0.24, r = 4.0.

V‐Line: Coupling Coefficients


56/58

ECE 451

– Jose

Schutt

‐ Aine 56

0

0.1

0.2

0.3

0.4

0.5

0.6

0 0.2 0.4 0.6 0.8 1 1.2s/h

Coupling Coefficient

V-line

microstrip

K v

Plot of the coupling coefficient versus spacing-to-height ratio for v-line and microstrip configurations.

The parameters are w/h = 0.24, r = 4.0.

V‐Line vs Microstrip: Coupling Coefficients

Advantages of V‐Line


57/58

ECE 451

– Jose

Schutt

‐ Aine 57

0.5

0.6

0.7

0.8

0.9

1

1 3 5 7 9 11 13 15 17

microstrip

V-60

V-30

Frequency (GHz)

Line

arAttenua

tion

Propagation Function

2p

h

w

dielectric

ground

signal strip

Advantages of V Line

* Higher bandwidth

* Lower crosstalk

* Better transition

ground reference

ground reference

d i e l e c

t r i c

s u b s

t r a t e

signal strip

Advantages of V‐Line

I


58/58

ECE 451

– Jose

Schutt

‐ Aine 58

-8

-7

-6

-5

-4

-3

-2

-1

0

0 5 10 15 20 25

Insertion Loss

Vline

Microstrip 2 0 * l o g 1 0 * | S 2 1 |

Frequency (GHz)

V‐Line vs Microstrip: Insertion Loss

Couple Dtl

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