信號完整性LosslessTransmissionLine初中教育

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信號完整性LosslessTransmissionLine-初中教育

ZSωp,p1

jω?p

2

?+:=Sourceimpedanceofthedriver:parametervectorpmustcontain:p0=1(type),p1=seriesresistance(?),p2=seriesinductance(H)

Youcanaddparameterstomakethesourceandloadimpedancesascomplicatedasyoulike.Propertiesofthetransmissionline,sourceandload

rad/s

Calculationtrick:offsetthezerothfrequency

slightlyfromDCtoavoidpide-by-zerosingularities

rad/s

Hz

FrequenciesusedtosampleFouriertransformfunctions

IndextofrequencypointsindexHorizontalaxisfortimeplots3.6.6LosslessTransmissionLine

TheoverallcircuitgainGofalongtransmission-lineconfigurationcandiffersubstantiallyfromH,whereHrepresentstheone-wayattenuationofsignalsmovingfromendtoendacrossthetransmissionline.EvenincaseswhereHisrelativelywell-behaved,theoverallcircuitperformancecansometimessufferfromterribleresonance.

TherearethreeclassicwaystostabilizethepropagationfunctionofanLCtransmissionline,eliminatingtheundesirableresonance.Eachcaseusesaresistiveterminationtodeliveracircuitgainproportionaltotheone-waytransmissionlinepropagationfunctionH(w)(see[3.14]).InthecaseofarelativelyshortLCtransmissionline(suchasnormallyusedonaprinted-circuitcardforhigh-speeddigitalsignals)the

propagationfunctionHispracticallyflatwithlinearphase,indicatingthelineitselfactsasnothingmorethanatime-delayelementwithaminoramountofattenuation.

Presumingthattheattenuation(andpossiblydistortion)ofH(w)fallswithinacceptablebounds,aproperlyterminatedLC-modetransmissionlinemaybeoperatedsatisfactorilyatanylength.

Table4.2Examplecode(page250)

?T1010

12??:=sSamplingresolutionDesiredsimulationtime

Tlen1010

9

??:=s

Lengthofsamplevector(mustbeapoweroftwo)integer

n01,N1?..:=indexIndextotimepointss

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3.6.6LosslessTransmissionLine.mcd

[3.98]

11SSCLCL1

122GZZZHHHHZZZ??=

?

+?+++

??

ThethreeclassicterminationstylesappearinFigure3.24.TheoverallcircuitgainGforeachisderivedfrom

[3.17],repeatedhereforconvenience.

Equation3.98,OverallCircuitGain

3pF

50ohmspload35031012??

:=Impedanceofload(inshuntwithendofline)

type3length,mv0,m/sZ0=50ohmsθ0(notused)pline202π?109?00501.4457108?.12

:=Transmissionlineparameters

R0(notused)ω0(notused)RDC(notused)type23nH10ohmspsource1103109??

:=Sourceimpedanceofthedriver

type1Particularpropertiesofthistransmissionlineexample

Ashuntloadimpedance:parametervectorpmustcontain:p0=3(type),p1=shuntresistance(?),p2=shuntcapacitance(F)

Atransmissionline:parametervectorpmustcontain:p0=2(type),p5=characteristicimpedance(aconstantrealvalueinohms),p6=velocityofpropagation(m/s).Argumentp7representsthelengthoftheline(m).

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3.6.6LosslessTransmissionLine.mcd

ThefunctionG,implementedinMathCadnotation

4.6UsefulFourierTransformPairs

Pulseofwidthb

AsyouprogressinyouruseofMathCadyouwilleventuallytomakeafunctionlikethisthattakesbasanargumentandreturnsafrequency-domainvector.ThedefinitionofparameterizedfunctionsthatreturnvectorsrequiressomeMathCadtrickery.Theideaistofirstdefineageneralfunctioninthefreqeuncydomainusingcontinuousarguments.Thendefineanewfunctionthatevaluatesthegeneralfunctionatavectorofspecificfrequencies,givenbyvectorω.

InMathCadsyntax,thearrowoverthefunctionPulB_continuousindicatesthatitistobeevaluatedateverypointinthevectorωandtheresultreturnedshallbeformattedasavector.

PulBbPulB_continuousωb,

→????????:=Pulseofwidtha·(N·?T)

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PulNaPulN_continuousωa,

→????????:=ClockwaveformwithMcompletecycles

ClkNMClkN_continuousωM,

→????????:=Thedelayoperatorshiftsrightbyamountτ.Thisfunctionlookssimplerthantheothersbecauseitdoesn'trequirean"if-then"clause,soIcandirectlyapplythevector-evaluationoverbaroperatoronthecontinuous-freqeuncydefinitionofthefunction.Thefunctionsthatcontain"if-then"clausesarenot

directlycompatiblewiththeoverbaroperator,whichiswhytheyareimplementedintwosteps.

Dlyτe

j?ω?τ?→??:=Linear-rampLPFwith10-90%rise/falltimer

LinrrLinr_continuousωr,

→????????:=QuadrQuad_continuousωr,

→????????:=(c)2023HowardJohnsonandSignal

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GaussianLPFwith10-90%rise/falltimer

GausrGaus_continuousωr,

→

????????:=Table4.2ExampleCode(continued)

Excitationrise/falltime(s)

r10010

12

??:=Excitationisacombinationofthepulsefunctionwithawaveshapingfilter,in