COMMUNICATION CABLES TRANSMISSION DATA.docx
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COMMUNICATION CABLES TRANSMISSION DATA.docx
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COMMUNICATIONCABLESTRANSMISSIONDATA
COMMUNICATIONCABLESTRANSMISSIONDATA
PrimaryConstants
Inatransmissionline,thePRIMARYCONSTANTSare:
∙R=resistance
∙G=conductance
∙L=inductance
∙C=capacitance
∙ResistanceR-Allowingfortheresistanceofbothwires,butneglectinghelixlosses,theresistanceofatwistedpair,is:
R=43.9/d2ohmsperkilometer
whered=wirediameterinmillimeters
R=0.002074/d2ohmsper100feet
whered=wirediameterininches
Atcarrierandradiofrequenciesitisnecessarytoconsidertheskineffect.Thenforashieldedtwincable:
R=
0.127*106*√fρ1
d
+6.38*106*ρ1
d2
+0.506*106h2√fρ8
D8*(1–h4)
ohmsperkilometer
-where:
f=frequencyinMegahertz
ρ1=resistivityofconductorsinohms-centimeter
ρ8=resistivityofshieldinohms-centimeter
d=diameterofconductorinmillimeters
D=axialseparationofconductorsinmillimeters
D8=internaldiameterofshieldinmillimeters
h=D/D8
g=d/2D
OR
R=
152√fρ1
d
+301ρ1
d2
+607h2√fρ8
D8*(1–h4)
ohmsper100feet
-where:
d=diameterofconductorsininches
D=axialseparationofconductorsininches
D8=internaldiameterofshieldininches
Theothersymbolsareasinthepreviousformula,and,inparticular,ρ1andρ8areinohms-centimeter.
∙ConductanceG–Thisisahypotheticalshuntorleakageresistanceperunitlengthandrepresentshighfrequencydielectriclosses.
G=
2πf104tanδC
siemensperkilometer
-where:
f=frequencyinMegahertz
tanδ=dissapationfactorofthedielectric
C=capacitanceinfaradsperkilometer
Note:
WhenthevalueofGisrequiredinsiemensper100feet,thevalueofCshouldexpressedinfaradsper100feet.
∙InductanceL–TheinductanceofapairfromDCthroughtheVFregionis:
L=
(920*10-6)log10(2D/d)
+(1.0*10-4)
henriesperkilometer
L=
(28.0*10-6)log10(2D/d)
+(3.04*10-6)
henriesper100feet
-where:
D=axialseparationofconductors
d=diameterofconductors
Atcarrierandradiofrequencies,theinductanceisdependentuponthefrequency.
Thenforashieldedtwincable:
L=
(920*10-6)log10((1-h)/(g(1+h2)))
+32.8R
2πf
henriesperkilometer
L=
(28.0*10-6)log10((1-h2)/(g(1+h2)))
+R/(2πf)
henriesper100feet
∙CapacitanceC–Inamultipaircable,thecapacitancebetweenthetwoconductorsofapairisdifficulttoreducetoageneralformulasinceeachpairissurroundedbyothersprovidingapartialshield,andtheratioofcopperspacetoairanddielectricspacevaries.Asanapproximation:
C=
0.0121∈e
/
log10((D+√(D2-d2))/d)
microfaradsperkilometer
OR
C=
368∈e
/
log10((D+√(D2-d2))/d)
picofaradsper100feet
--where:
∈e=effectivedielectricconstant≈2.2
D=axialseparationofconductors
d=diameterofeachconductor
Themutualcapacitanceofapairinamultipairtelephonecableisnominally0.083microfaradspermile(0.052microfaradsperkilometer).Forlowcapacitancecables,thevaluesare0.066microfaradspermileand0.041microfaradsperkilometerrespectively.Thesearenominalaveragevalues.RMSdeviationsfromthesevaluesarequotedasfollows:
∙TransverseDeviation–ThestandardorRMSdeviationofthemutualcapacitancevaluesofindividualpairsfromtheaveragewithinthesamelengthofcable.
∙LongitudinalDeviation–ThestandardorRMSdeviationoftheaveragemutualcapacitancevaluesforanyparticularlengthofcablefromthegrandaverageofalargenumberoflengths.
CoaxialCable:
C=
(0.0241∈)/(log10(D/d))
microfaradsperkilometer
OR
C=
(736∈)/(log10(D/d))
picofaradsper100feet
-where:
∈=dielectricconstant
D=innerdiameterofouterconductor
D=outerdiameterofinnerconductor
SecondaryConstants
TheSECONDARYCONSTANTSare:
γ=propagationconstant
α=attenuationconstant
β=phaseconstant
v=velocityofpropagation
Z=impedance
∙PropagationConstantistheexponentofthevectorratioofthesignalvalueatthetwoendsofunitlengthoflinethroughwhichthesignalistransmitted,thatis:
·Es/Er=eγ
-where:
Es=sendingendvoltage
Er=receivingendvoltage
∙AttenuationisameasureofthelossofsignalamplitudeperunitlengthandmaybeexpressedinNepersperkilometerordecibelsper100feet.Thefollowingrelationshipsaregivenforconvenienceinmakingconversions:
·1Neper=8.686decibels
1Mile=1.609kilometers
1Kilometer=3281feet
1Neperperkilometer=0.2647decibelsper100feet
∙PhaseConstantisthechangeofphaseangleofthewaveperunitlength,andmaybeexpressedinradiansperkilometer.
∙Velocityisthespeedofpropagationofthesignalalongthelineandmaybeexpressedinkilometerspersecond.Itcanalsobequotedasavelocityratioto,orpercentageof,thespeedoffreespacepropagation–c.
·Arelatedconstantisthetransmittime,ie:
timerequiredtotravelunitdistance.Forexample,inasolidpolyethyleneinsulatedcableathighfrequenciesthetransittimeis5.05nanosecondspermeteror1.54nanosecondsperfoot.
∙Impedanceisthevectorratioofinputvoltagetoinputcurrentathighfrequency,forauniformlongand/orcorrectlyterminatedline,inohmsanddegrees.Thisisthe"characteristic"or"surgeimpedance"oftheline.Itisdependantoncross-sectionaldimensionsonlyandnotonlengthofline,assumingtherearenoreflections.
Ifyouwouldliketoseemoreinfoonthevariousconstantsusedandtheirindividualformulae,orindividualformulaforattenuationand/orimpedanceof;coaxialand/orshieldedtwincable,pleasefeelfreetodosoonour‘ContactingUs’page.
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SpecialCharacteristics
Crosstalk
Crosstalkisameasureoftherelativestrengthofdesiredsignalinonepairversusthestrengthofinduced,undesiredsignalinanotherpair.
Generallyspeaking,fromthelowerfrequenciestoaroundthethreehundredkilohertz(300Khz)region,twistedpairsissuperiortocoaxialcable.Athigherfrequencies,coaxialcableismorepreferrable.
Twistedpairsdeteriorateincrosstalkasthefrequencyincreases.Thisisduetotheelctromagneticcouplinginducedbythesidebysidewire,orpair,layout.
Conversely,coaxialcableimprovesincrosstalkasthefrequencyincreasebecauseofskineffect.Thisisactuallyenhancedastheskineffectisoutsidetheactualconductor(thegroundsheathofthecoaxcable).Anyreductionofsignalorcrosstalkinfluenceisminimizedbythesegregationoftheconductorsbythegroundsheath(s).
Crosstalkismeasuredindecibels.Itcanbemeasuredateitherthenear-endorfar-end,ofthecircuit,overtherangeoffrequenciesofinterest.Ingeneral,far-endcrosstalkismorecritical.Thisisbecause,atthesource,thesignalappliedtotheconductorisnormallyatit’sgreatestpotential,andduetothelengthofcable,thesignalhasdecreasedmakingitmoresusceptibletointerference.
Theapproximaterelationshipwithlengthis:
CrosstalkindBforlengthB=CrosstalkindBlengthA
20log10(lengthB/lengthA)
Factorscontributingtocrosstalkinpairedcableareresistanceunbalanceandcapacitorunbalance.
Sidetogroundunbalancecontibutestonoise.
Pair-to-PairorSide-to-SideCapacitanceUnbalance
Thepairsneednotbelaidspiral-fourorstar-quadasshown.Theaboveisapictorialrepresentationonly.
PercentageResistanceUnbalanceofaPair
%Unbalance=((higherwireresistance–lowerwireresistance)/lowerwireresistance)*100
Side-to-GroundUnbalance
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ImpedanceRegularity
Inhighfrequencycables,theimpedancevariesnotjustwithfrequency,butaloswiththedistanceofthecablerun.Thisisduetosmallirregularitiesinthematerialand/ormanufactureofthecable.
PulseEchoTests(knownaEchoTest)andStructuralReturnLoss(knownasSRL).
Pulsetestsdetectindividual,localchangesofimpedancealongthecable.
SRLtestsdetectperiodicirregularities.
(Note:
AtaplantIworkedin,wehadasubdivisionoftheSRLtests.Thisgroupedfrequenciesintworanges.Thein-housenamesweusedwereSingingReturnLoss–High[SRL-Hi]andSingingReturnLoss–Low[SRL-Lo].IfyoueverheartheSRLpipedoveraspeaker,theinducednoisecouldbeconstruedasinging–keepthevolumelow.Onelastwordhere;thedesignationofhighandlowwerewithrespecttostandardtelephoneresponserangesof200Hzthrough5Khz)
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SkinEffect
Athighfrequencies,conductorresstsancesareincreasedbyaphenomenonknownasskineffect.Currentseeksthepathofleastresistance.Inductivereactanceislessnearerthesurface(s)ofconductorscontainingthefield.Currentcrowdstowardtheoutersurfaceoftheinnerconductor(s)andtheinnersurfaceoftheouterconductororshield.
Currentintensityfallsoffexponentiallywithdepth.Thedepthofpenetration-δ-isthedepthatwhichthecurrentintensityhasfallento1/eofit’svalueatthesurface,wheree=2.718.
Atthreeandfourtimesthedepthofpenetration,thecurrentintensityis5and2percentofthatotthesurface,respectively.
Wherethediameteroftheconductorislargecomparedtothedepthofpenetration,thetotalcurrentisgivenbythesurfacecurrentintensitytimesthedepthofpenetration.
=
100(/f)
millimeters
=
100(/f)
inches
Whereρ=resistivityinohm-centimeter
=1.72*10-6forcopper
or=2.83*10-6foraluminum
μ=magneticpermeability
=1forb
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