ens466 week11.final

8/9/2019 ENS466 Week11.Final

1/13

11/20

ENS/ELT466

TelecommunicationSystemsLab

Fall2013

Week11 Nov.19

TransmissionLines&RF

Techniques

TelecommunicationSystemsLab(ENS466)

Fall2013

Week11 Nov.19


2/13

11/20

RadioFrequencies

Classification Frequency(f) Wavelength()

Lowfrequency(LF) 30KHz300KHz 10km1km

Mediumfrequency(MF) 300KHz3MHz 1km100m

Highfrequency(HF) 3MHz30MHz 100m10m

Veryhighfrequency(VHF) 30MHz300MHz 10m1m

Ultrahighfrequency(UHF) 300MHz3GHz 1m10cm

Superhighfrequency(SHF) 3GHz30GHz 10cm1cm

Extremelyhighfrequency(EHF) 30GHz300GHz 1cm1mm mmwaves

shortwaves

microwaves

mediumwaveslongwaves

DataTransferRate

Inweek5,weintroducedradiofrequency(RF)wavesandmicrowaves,whichare

electromagnetic(EM)waveswithfrequenciesfrom3x104 Hzto3x1011 Hz.

Higherfrequenciesoffermorebandwidthfordatatransmission,buttheyrequire

specialtechniquesindevicedesignandcircuitwiring.

Wavelengthvs.WireLengthWhenEMwavestravelthroughvacuumorair,theirvelocityisclosetothespeedof

lightinavacuum,c,andtheirwavelengthisgivenby:

c

f

8299,792,458 m/sec 3 10 m/secc x

Onceadeviceorawirebecomesaslongasafractionofawavelength(sayL~/10),thewavescrestswillreachdifferentpartsofthedeviceatdifferenttimes,

invalidatinglowfrequencyanalysisandrequiringtheuseofRFtechniques.

Forexample,ifa1kmwireisusedtoconnectahometoatelephoneswitchingoffice,

lowfrequencytechniquescannotbeusedforf>30kHz. Abreadboardcircuitinthe

labmayuseonly~1morsooftotalwiring,suggestingalimitof30MHz,butthe

inductancesandcapacitancesinthecircuitcontributedelaysaswell,makingthelimit

lower,ontheorderofafewMHz.


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GuidedWavesEMwavescanalsopropagatealongwires,inwhichcasetheyarecalledguided

waves.

Many

cases

of

interest

involve

two

conductors

whose

cross

section

and

spacingaremaintainedconstantalongtheirlength. Examplesofsuchtransmission

lines

includetwinleadandcoaxialcable:

Coaxial

cable

is

the

workhorse

of

RF

systems,

including

cable

TV

distribution

networks,labinstruments,andmobilephonetowerwiring. Coaxialcableishighly

resistanttoelectricalinterferencefromexternalfields.

twinlead coaxialcable

PropagationVelocityMaxwellsequationscanbeusedtosolveforthespeedofEMwavesinatransmission

line.

r

cv

Foracoaxialcablewithidealconductorsandnonmagneticinsulators,theformulais:

where isthedielectricconstant(a.k.a.relativepermittivity)ofthedielectric

material.r


4/13

11/20

TransmissionLineCircuitModelThecircuitmodelofauniform(lossless)

transmission

line

consists

of

identical

LC

sectionsgangedtogether. Aseachsection

chargesup,itpassesthewavealongtothe

nextsection.

1v

LC

Withinthiscircuitmodel,thepropagation

velocityis:

where istheinductanceperunitlength

and isthecapacitanceperunitlengthof

theparticularcableused.

L

C

DelayExampleIfacellphonetransmitterisconnectedtoitsantennabya200mRG8A/Ucable

whoseinductanceis73.75nH/ft andwhosecapacitanceperunitlengthis29.5pF/ft,

howmuchtimedelaydosignalsexperienceinthecable?

9 12

1

200 39.3773.75 10 29.5 10

12

0.97

x xt x LC

v LC

t

t s

Whenapplyingtheformulas,makesureyourlengthandtimeunitsareconsistent!


5/13

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CharacteristicImpedanceSolvingMaxwellsequationsforguidedwavesrevealsaconsistentrelationbetween

the

current

flowing

in

the

conductors

and

the

voltage

between

them,

defining

the

characteristic

impedance

(Z0)ofthetransmissionline. Likethewavevelocity,Z0dependsonthesizeandpositionoftheconductorsandthedielectrics. Foranideal

coaxialcable,thecharacteristicimpedanceis:

0 10 0

138log

r

D LZ or Z

d C

wheredisthediameteroftheinnerconductorandDistheinnerdiameterofthe

outerconductor.

Z0istiedtomanyimportantpropertiesofthecableitself,aswellasaffectingthe

circuitstowhichthecableisattached.

AttenuationTheattenuationorlossofRFcables,oftenstatedindB/m,riseswithfrequency. This

isduetoskineffectintheconductorsaswellasdielectriclosses. Theattenuationis

alsohigherinsmallercables.

AttenuationalsodependsontheZ0ofthecoaxialcable.

from microwaves101.comdB/meter@

f=10GHz

d=0.25

Frequency(MHz)

Attenuation(dB/km)

d=0.102

d=0.032

Thismeansatradeoffbetweencableweight/flexibility/costandattenuation.


6/13

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Z0ExampleWhatisthecharacteristicimpedanceofacablewhosecenterconductorhasa

diameter

of

0.0362,

whose

shield

has

an

inner

diameter

of

0.1175,

and

whose

dielectrichasarelativepermittivityof2.0?

Infact,thisisastandardsizeofsemirigidcoppercoaxusuallyreferredtobyits

outerdiameterof0.141.

Generally,labinstrumentsandRFinterconnectsuseZ0=50,whilecableTVsystemsuseZ0=75.

D

d0 10 10

0

138 138 0.1175log log

0.03622

138.511 49.9

1.414

r

DZ

d

Z

Matched(NonResonant)LineWhentheloadimpedanceattachedtotheendofthetransmissionlineispurely

resistiveandequaltoZ0,thereisnoreflectionandalloftheRFpowerisdeliveredto

theload.

Z0Zin=Z0 RL=Z0

TheimpedanceZinseenbythesourceispurelyresistiveandequaltoZ0regardlessof

thelinelengthx orfrequency.

lengthx


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Mismatched(Resonant)LineWhentheloadimpedanceattachedtotheendofthetransmissionlineisnotequalto

Z0,

reflections

occur.

Part

(or

all)

of

the

RF

power

is

reflected

back

to

the

source.

IfRL>Z0thereflectionwillhavethesamesignastheincidentwave,butifRL< Z0the

reflectionwillhaveinvertedsign.

Z0Zin=?? RL>Z0

Z0Zin=?? RLZ0

ProblemslikethisareoftensolvedbytheuseofagraphiccalculatorcalledtheSmith

chart. (Note:wewillnotstudySmithchartsinthisclass.)

0

0

0

tan 2

tan 2

L

TL

in

L

TL

xZ jZ

Z Z

xZ jZ


8/13

11/20

QuarterWaveTransformerAstheelectricallengthofthemismatchedtransmissionlineapproachesonequarter

of

a

wave

(i.e.

x

TL/4)

the

input

impedance

Zinbecomes

:

Thus,anysourceresistancecanbematchedtoanyloadresistance(foraspecific

frequency)byinsertingaTL/4 transmissionline sectionwithimpedanceZ0,where:

00in

L

ZZ Z

Z

0 in LZ Z Z

Thisincludesthecasewherethesourceitselfisanothertransmissionline.

StandingWavesTravelingwave+backreflection=standingwave.

time=0

time=1T/8

time=2T/8

time=3T/8

time=4T/8

time=5T/8

time=6T/8

time=7T/8

distance0/2

openckt

voltagewaves currentwaves

foldbackfor

reflectedwave

Thesumofthetraveling

wavesintheforward&

backwarddirectionsisa

wavethatjustoscillates

inthesameplace.


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StandingWaves(II)Reflectionfromashortcircuitcreatesstandingwaveswithvoltage&current

interchanged.

time=0

time=1T/8

time=2T/8

time=3T/8

time=4T/8

time=5T/8

time=6T/8

time=7T/8

distance0/2

shortckt

currentwaves voltagewaves

foldbackfor

reflectedwave

Thestandingwavefrom

ashortcircuithas

voltagenullsatx=0,

x=/2,x=,...

VSWRAlthoughmismatchedlinescanbeusefulinsomesituations,reflectionsin

communicationchannelsaregenerallyabadthing. Reflectionsduetomismatch

cause:

lossofsignalpower

Instabilityofsourceswhenbackwardpoweriscoupledintothem

Overloadingoflines

Multipathinterferencefrommultiplereflectionpoints.

max

min

1

1

VVSWR

V

MismatchreflectionsareoftencharacterizedbytheVSWR

(voltage

standing

wave

ratio),givenby:

whereisthereflectioncoefficientdefinedearlier. NotethatVSWRis1foraperfectmatchand foranopenorashortcircuit.


10/13

11/20

MaximumFrequency MultimodingAtlowfrequencies,thereisonlyonepossiblesolutionforMaxwellsequationsin

coaxial

cable.

However,

as

the

frequency

rises

beyond

the

single

mode

cutoff,

additionalsolutions(modes)appearwithdifferentvelocitiesandcharacteristic

impedances.

Inthemultimoderegion,pulsesbecomedistortedandreflectionsarepractically

impossibletoeliminate,socoaxisrarelyusedatthosefrequencies. Thesinglemode

cutoffforanidealcoaxisapproximately:

min

max2

2

TL

r r

D d cf

D d

The

practical

effect

of

this

formula

is

that

smaller

coax

diameters

must

be

used

at

higherfrequencies,leadingtohigherlosspermeterandlowermaximumpower

rating.

CoaxConnectors

from microwaves101.com

Justlikethecablesthemselves,coaxconnectorsgetsmallerastheworkingfrequency

goesup:

Thehighestfrequencyconnectorsarethemostdelicate theymustbekeptcleanand

neverovertightened. Torquewrenchesarerequiredforinstrumentgraderesults.


11/13

11/20

Striplines (RFonBoard)Coaxialcableisnotsuitedtomicrofabrication,somonolithicICs&printedcircuit

boards

need

a

different

solution.

Two

of

the

most

common

are

microstrip line

and

coplanarwaveguide:

metalguide

structures

dielectric

substrate

metal

groundplane

microstrip line coplanarwaveguide

Summary ATRFandmicrowavefrequencies,wemustaccountforthephysicalsizeof

componentsandsystems.

Guidedwavesareelectromagneticwavesthatpropagatealongapairedconductorstructurecalledatransmissionline.

Eachtypeoftransmissionlinestructurehasapropagationvelocityvsomewhatlowerthanc(thespeedoflightinavacuum)andacharacteristicimpedanceZ0.

Themostcommontransmissionlineatradiofrequenciesisthecoaxialcable. Ithas

Theattenuation(dB/m)ofatransmissionlineincreasesasitsconductorsgetsmaller.

When

Z0of

the

line

matches

the

load

resistance

(non

resonant

line),

all

the

power

istransferredtotheload,thereisnostandingwave,andtheVSWR=1.

WhenZ0ofthelinedoesnot matchtheloadresistance(resonantline),someorallpowerisreflected,theVSWR>1,andastandingwaveoccurs.

ThemaximumfrequencyatwhichagivenT.L.isusefulissetbytheonsetofhighermodes.

OnPCboardsandmicrowaveICs,microstrip lineandcoplanarwaveguidemaybeused.

0 10

138log

r

D LZ

d C

1

r

cv

LC


12/13

11/20

ENS466/ELT466 Assignments LabReport:

Labreport#11willcoverLabAssignment11(thisweekslab);itisdueatthestart

ofclasson11/26. Reading:

tobepostedonBlackBoard.

Nextweek:

FiberOpticsandLaserSafety

NewIEEEStudentChapter@CSIIEEE(theInstituteofElectricalandElectronicsEngineers)istheworldsleadingprofessionalsocietyforelectronicengineering.

Localchapteractivitiesareagreatwaytomeetpeopleandlearnaboutdifferentbranchesofthefield. (andafreelunchissometimesincluded!)


13/13

11/20

Backups/Alternates

TelecommunicationSystemsLab

(ENS466)

Fall2013

PSDsofBinaryFormats

(unipolar)NRZ

randomdata

PSD

(unipolar)NRZ

101010...

PSD

Manchestercode

randomdata

f1

bT

2

bT

Millercode

randomdata

f1

bT

2

bT

PSD=PowerSpectralDensity;sinc(x)=sin(x)/x.

ens466 week11.final

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