ECE 497 JS Lecture -04 Lossy Linesjsa.ece.illinois.edu/ece497js/Lect_04.pdfLossy Lines Spring 2004...

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

ECE 497 JS Lecture -04Lossy Lines

Spring 2004

Jose E. Schutt-AineElectrical & Computer Engineering

University of [email protected]


Metallic Conductors

Length

σArea

Re sist an ce : R

Package level:W=3 milsR=0.0045 Ω/mm

R = Le ng thσ Are a

Submicron level:W=0.25 micronsR=422 Ω/mm


Metal Conductivityσ (Ω-1 m−1 ×10-7)

Silver 6.1Copper 5.8Gold 3.5Aluminum 1.8Tungsten 1.8Brass 1.5Solder 0.7Lead 0.5Mercury 0.1

Metallic Conductors


RF SOURCE

Loss in Transmission Lines


δ

Low Frequency High Frequency Very High Frequency

Skin Effect in Transmission Lines


. .

Magnitude of current density

y

σ

w

t

e

D

V

J = Joe- y /d e

- jy / d

d

Skin Effect in Microstrip

εr


The electric field in a material medium propagates as

z

Eoe−γz = Eoe−αze− jβz

where γ = α + jβ. We also have

γ = ω µε(1+jσ

ωε) .

Skin EffectSkin Effect

Wint

δs

δs

Hint

CURRENT AREAS


−∂V∂z

= (R+ jωL)I = ZI

−∂I∂z

= (G+ jωC)V = YV

Lossy Transmission LineL

∆z

C

I

V

+

-

G

R

Telegraphers Equation


z

R, L, G, C,

Lossy Transmission Line

forward wave

backward wave


Lossy Transmission Line

( ) z j zV z Ae eα β− −= z j zBe eα β+ ++

1( ) z j z

o

I z Ae eZ

α β− − = z j zBe eα β+ +−

( )( )j R j L G j Cγ α β ω ω= + = + +( )( )o

R j LZ

G j Cωω

+=

+

z

Zo βZ1 Z2

Vslg


l

Zin

R

C

R : series resistance per unit lengthC : shunt capacitance per unit length

in

coth (1 )2Z =

(1 )2

Rl CRl jR

Rl C jR

ω

ω

+

+

inarg(Z ) 45≈ oFor very high ω,

RC Transmission Line


l

Zin

R

C

2

2 << RCl

ωIf then

in1 1Z + = +

2 2T

T

Rl RjCl jCω ω

=

RT = Rl : total resistanceCT = Cl : total capacitance

RC Transmission Line


ChipChip--Level Interconnect DelayLevel Interconnect DelayLine

-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Vol

ts

0 0.4 0.8 1.2 1.6 2Time (ns)

Far End Response

BoardVLSISubmicronDeep Submicron

-0.1

0.175

0.45

0.725

1

0 0.4

Vol

ts

0.8 1.2 1.6 2Time (ns)

Near End Response


Pulse Characteristics: rise time: 100 ps fall time: 100 ps pulse width: 4ns

Line Characteristics length : 3 mm near end termination: 50 Ω far end termination 65 Ω

LogicthresholdLogic

threshold


Effect of Losses in TLEffect of Losses in TL

- Signal attenuation

- Dispersion

- Rise time degradation-0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Vol

ts0 0.4 0.8 1.2 1.6 2

Time (ns)

Far End Response


( )( )( )( ) j R j L G j Cγ α ωω β ω ω= + = + +

15Copyright © by Jose E. Schutt-Aine , All Rights ReservedECE 497-JS, Spring 2004 Source: Allied Electronics, Inc.

Connectors


1 20

2( , ) k kf

k o

x klV x t T V tv

∞

=

+= Γ Γ −

∑

11 2

0

2( 1)( , ) k kb

k o

x k lV x t T V tv

∞+

=

− += Γ Γ −

∑

( , ) ( , ) ( , )f bV x t V x t V x t= +

Transmission Line SolutionsTime Domain


+

-

Vg

-x=0

ZgZg

ZL

x=l

time

volta

ge

1

0

2( 1)1 2( 0, ) ( )2

k k cg L j g

k c o

k l lV x t V t V tv v

∞+

=

+= = + Γ Γ − −

∑

0

2 2 k k cL j c g

k c o

kl lV tv v

∞

=

+ Γ Γ Γ − −

∑

21 2 2( 0, ) [ ( ) ( - ) ( - - )] 2

cc L

o c o

ll lV x t u t u t u tv v v

= = + Γ + ΓAtx=0

TDR Equations


Time Domain Reflectometry

coaxial line

Zg

Zg

stepgenerator

Vb

Vfmicrostrip line


Network Analyzer


L

C/2 C/2

R

oP = (R + j L)(1 + j CZ /2)ω ω

oY = j CZ /2ω

112S =

2 2o

o o

P YZ YPZ P YZ YP

− −+ + + 21

2S = 2 2

o

o o

ZZ P YZ YP+ + +

21 2 (1 - )oA Z S=

11 21 11

21 11 21 11

2Y = 4 2

o

o o

A S S Z S AS Z S S Z S A A

− −+ + + 21 21 - 2 (1 ) oP A YS Z S Y= +

Low-Frequency TL Approximation


c opper m i c r os t r i p w =5 m i l l=2 0 .2 cm

f i be r gl a s s s ubs t r a t e SMA conne c t or

0.94

0.95

0.96

0.97

0.98

0.99

1

0 0.02 0.04 0.06 0.08 0.1

Microstrip

I n

Frequency (GHz)

5

10

15

20

25

30

0 0.02 0.04 0.06 0.08 0.1

Microstrip

R e

Frequency (GHz)

- Network analyzer measurement of S parameters

- Use de-embedding scheme

- Use extraction algorithm

Microstrip Characterization


CABLE CHARACTERIZATION

Scattering parameter determination.

2

21 2 2

(1 ) 1

XSX

− Γ=

− Γ

2

11 2 2

(1 ) 1

XSX

− Γ=

− ΓdX e γ−=

c o

c o

Z ZZ Z

−Γ =

+

cR j LZG j C

ωω

+=

+( )( ) R j L G j Cγ ω ω= + +


- dX=e j d de eγ β α− −=

2 1Q QΓ = + −

( )( )

11 21

11 211d S S

X eS S

γ− + − Γ= =

− +

2 211 21

11

12

S SQ

S− +

=

Re cR Zγ=

c1 ImZ L γω

=

Re c

GZγ

=

1 Im c

CZγ

ω=

TL Extraction Formulas


Low-Loss Approximation

R Lω<<

G Cω<<

If we assume

and

c

R + j =2 2Z p

R C LC jL v

ωγ ω≅ +

c

R2Z

α ≅pv

ωβ ≅

cLZC

≅


pdv φω

= −∆∆

p

dv

φω

∆= −

∆

( )2 lncZ XR

d= −

( )ln Xd

α = −

TL Extraction Formulas


0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0.55

0 0.02 0.04 0.06 0.08 0.1

Category 5/ 100-meter

Simulation

Measurement

S11

Mag

nitu

de

Frequency (GHz)

-50

-40

-30

-20

-10

0

10

20

30

0 0.02 0.04 0.06 0.08 0.1


Simulation

Measurement

S11

Phas

e (d

eg)

Frequency (GHz)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 0.02 0.04 0.06 0.08 0.1


Simulation

Measurement

S21

Mag

nitu

de

Frequency (GHz)-200

-150

-100

-50

0

50

100

150

200

0 0.02 0.04 0.06 0.08 0.1


Simulation

Measurement

S21

Phas

e (d

eg)

Frequency (GHz)

Category-5 Cable


0

0.1

0.2

0.3

0.4

0.5

0.6

0 0.05 0.1 0.15 0.2

Category 5/ 1-meter

Simulation

Measurement

S11

Mag

nitu

de

Frequency (GHz)-200

-150

-100

-50

0

50

100

150

0 0.05 0.1 0.15 0.2

Category 5/ 1-meter

Simulation

Measurement

S11

Phas

e (d

eg)

Frequency (GHz)

0.65

0.7

0.75

0.8

0.85

0.9

0.95

1

0 0.05 0.1 0.15 0.2

Category 5/ 1-meter

Simulation

Measurement

S21

mag

nitu

de

Frequency (GHz)-200

-150

-100

-50

0

50

100

150

200

0 0.05 0.1 0.15 0.2

Category 5/ 1-meter

Simulation

Measurement

S21

phas

e (d

eg)

Frequency (GHz)

Category-5 Cable


0

1

2

3

4

5

6

0 0.02 0.04 0.06 0.08 0.1


Res

ista

nce

(Ohm

s/m

)

Frequency (GHz)0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.02 0.04 0.06 0.08 0.1


Vel

ocity

Rat

io

Frequency (GHz)

Category-5 Cable


( ) * psR f R f=

*r ro rsv v v f= +

( ) ( )skin skinZ R f j L R j R Lω ω= + = + +

Cable Loss Model

Category 5 100 0.724 -0.165 15.38 0.482 0.224-Ga 100 0.678 1.157 29.03 0.593 0.1Category 3 100 0.705 11.06 12.31 0.473 0.01 SMA 50 0.700 0.113 7.94 0.415 0.2

Zo vro vrs Rs p fmax(W) (m/ns) (m/ns-GHz) (Ω/m-GHzp) (GHz)


cableZs = 50 Ω

Vs

open

near end far end

Time-Domain Simulations


-0.5

0

0.5

1

1.5

2

0 500 1000 1500 2000

22GA/Cu/4-cond Near End

volts

Time (ns)

-0.5

0

0.5

1

1.5

2

2.5

3

0 500 1000 1500 2000

22GA/Cu/4-cond Far End

volts

Time (ns)

Pulse Propagation (CAT-5)


-0.5

0

0.5

1

1.5

2

0 500 1000 1500 2000 2500 3000 3500

MP/CM Shielded Near Endvo

lts

Time (ns)

-0.5

0

0.5

1

1.5

0 500 1000 1500 2000 2500 3000 3500

MP/CM Shielded Far End

volts

Time (ns)

Pulse Propagation (MP/CM)


-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 500 1000 1500 2000

RG174 Near End

volts

Time (ns)

-0.2

0

0.2

0.4

0.6

0.8

1

1.2

1.4

0 500 1000 1500 2000

RG174

volts

Time (ns)

Pulse Propagation (RG174)

ECE 497 JS Lecture -04 Lossy Linesjsa.ece.illinois.edu/ece497js/Lect_04.pdfLossy Lines Spring 2004...

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Transcript of ECE 497 JS Lecture -04 Lossy Linesjsa.ece.illinois.edu/ece497js/Lect_04.pdfLossy Lines Spring 2004...