Signal Integrity.pdf

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1、SignalIntegrity345Chapter8SignalIntegrityThedataratesatwhichseriallinkstypicallyoperateareveryoftengreaterthantheinherentbandwidthcapabilitiesofthechannelwhichconnectsthetransmitterdevicetothereceiverdevice.Signalintegrityanalysisisthereforerequiredtodeterminewhetherthesignalbeingtrans

2、mitted,asdistortedbythechannel,isrecoverablebythereceiver.Thischapterfocusesonthetypesandsourcesofjitterindetail.Signalintegrityanalysistechniquesaredescribedusingbothcircuitsimulationandstatisticalanalysistechniques.8.1ProbabilityDensityFunctionsAprobabilitydensityfunction(PDF)defines

3、theprobabilityofasamplexhavingacertainvaluefortheuniverseofpossiblevaluesofx.Inthecontextofjitter,xisdefinedasthetimingdeviationofagivenedgeofthesignal,andp(x)istheprobabilityofthesignaledgehavingthisamountofdeviation.Beforediscussingthevariouscontributorstojitter,itisusefultoreviewthe

4、mathematicsbehindtwocommonPDFs:thePDFforaGaussiandistribution,andthePDFforadual-Diracdistribution.8.1.1GaussianDistributionTheGaussiandistributioniswellstudiedinthefieldofprobabilityandstatis-tics.Itcanbeusedtocharacterizemanynaturallyoccurringphysicalphenomenaanditdoesagoodjobofrepres

5、entingtherandomjittercomponentofserialdatatransitions.AGaussiandistributionisdefinedbytwovalues:themean,representedbythe“”symbol,andthestandarddeviation,representedbythe“"”symbol.Themeanisthecentralpositionofthecurveonthex-axis,andthestandarddeviationisameasureofthewidthofthedistribut

6、ion.Bydefinition,theGaussiandistribu-tionisunbounded,meaningthatnomatterhowfaravalueisfromthemeanvalue,thereisanonzeroprobabilityofencounteringanoccurrenceatthatvalue.Fig.8.1illustratesaPDFforaGaussiandistributionforwhich=0,"=1.ThePDFcorrespondingtoFig.8.1isdefinedbythefollowingequati

7、on:2τ−•----------2112σ(8.1)p()τσ,=----------⋅⋅---e2πσwhere$=(x–),representingthedifferencebetweentheamountofdeviationofagivenedgetransition(x)andthemeanofthedistribution().Thep($,")functionspecifiestheprobabilitydistributionandcanbeintegratedbetweentwolimitstodeterminetheprobabilit