8/9/2019 ENS466 Week11.Final
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ENS/ELT466
TelecommunicationSystemsLab
Fall2013
Week11 Nov.19
TransmissionLines&RF
Techniques
TelecommunicationSystemsLab(ENS466)
Fall2013
Week11 Nov.19
8/9/2019 ENS466 Week11.Final
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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
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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!
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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.
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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
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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¤t
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.
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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.
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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
8/9/2019 ENS466 Week11.Final
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ENS466/ELT466 Assignments LabReport:
Labreport#11willcoverLabAssignment11(thisweekslab);itisdueatthestart
ofclasson11/26. Reading:
tobepostedonBlackBoard.
Nextweek:
FiberOpticsandLaserSafety
NewIEEEStudentChapter@CSIIEEE(theInstituteofElectricalandElectronicsEngineers)istheworldsleadingprofessionalsocietyforelectronicengineering.
Localchapteractivitiesareagreatwaytomeetpeopleandlearnaboutdifferentbranchesofthefield. (andafreelunchissometimesincluded!)
8/9/2019 ENS466 Week11.Final
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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.
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