群时延的原理Group_delay

1©2005CiscoSystems,Inc.Allrightsreserved.GroupDelayCiscoPublicTheBasics•Considerthe6MHzspectrumoccupiedbyananalogTVchannelordigitallymodulatedsignal,the5-42MHzupstreamspectrum,oranyspecifiedbandwidthorpassbandastheequivalentofabandpassfilter.Bandpassfilterequivalent2©2005CiscoSystems,Inc.Allrightsreserved.GroupDelayCiscoPublicTheBasics•AsignaltakesacertainamountoftimetopassthroughafilterThetransittimethroughthefilterisafunctionofthefilter’svelocityofpropagation(alsocalledvelocityfactor)Velocityofpropagationisthespeedthatanelectromagneticsignaltravelsthroughsomemedium,usuallyexpressedasapercentageofthespeedoflightinavacuumTransittimeandvelocityofpropagation3©2005CiscoSystems,Inc.Allrightsreserved.GroupDelayCiscoPublicTheBasics•InmanyinstancesthevelocityofpropagationthroughafiltervarieswithfrequencyThevelocityofpropagationmaybegreaterinthecenterofthefilter’spassband,butslowernearthebandedges-3dBpointPassbandcenterVelocityofpropagationversusfrequency4©2005CiscoSystems,Inc.Allrightsreserved.GroupDelayCiscoPublicTheBasics•Thefinitetimerequiredforasignaltopassthroughafilter—oranydeviceforthatmatter—iscalleddelayAbsolutedelayisthedelayasignalexperiencespassingthroughthedeviceatsomereferencefrequencyDelayandabsolutedelay5©2005CiscoSystems,Inc.Allrightsreserved.GroupDelayCiscoPublicTheBasics•Ifdelaythroughafilterisplottedonagraphoffrequency(x-axis)versustimedelay(y-axis),theplotoftenhasaparabola-orbathtub-likeshapeFrequencyTimedelay012345Delayversusfrequency6©2005CiscoSystems,Inc.Allrightsreserved.GroupDelayCiscoPublicTheBasics•Theuppertraceshowsmagnitudeversusfrequency:thefilter’sbandpasscharacteristics.Thex-axisisfrequency,they-axisisamplitude.•Thelowertraceshowsgroupdelayversusfrequency.Thex-axisisfrequency,they-axisistime.Notethebathtub-likeshapeofthecurve.NetworkanalyzerplotofCh.T8bandpassfilterGraphiccourtesyofHoltzman,Inc.7©2005CiscoSystems,Inc.Allrightsreserved.GroupDelayCiscoPublicTheBasics•Ifpropagationortransittimethroughadeviceisthesameatallfrequencies,phaseissaidtobelinearwithrespecttofrequencyIfphasechangesuniformlywithfrequency,anoutputsignalwillbeidenticaltotheinputsignal—exceptthatitwillhaveatimeshiftbecauseoftheuniformdelaythroughthedevice•Ifpropagationortransittimethroughadeviceisdifferentatdifferentfrequencies,theresultisdelayshiftornon-linearphaseshiftIfphasechangesnon-linearlywithfrequency,theoutputsignalwillbedistortedPhaseversusfrequency8©2005CiscoSystems,Inc.Allrightsreserved.GroupDelayCiscoPublicTheBasics•Delaydistortion—alsoknownasphasedistortion—isusuallyexpressedinunitsoftime:milliseconds(ms),microseconds(µs)ornanoseconds(ns)relativetoareferencefrequency•Phasedistortionisrelatedtophasedelay•Phasedistortionismeasuredusingaparametercalledenvelopedelaydistortion,orgroupdelaydistortionDelayandphasedistortion9©2005CiscoSystems,Inc.Allrightsreserved.GroupDelayCiscoPublicTheFormalDefinitionGroupdelayis“thederivativeofradianphasewithrespecttoradianfrequency.Itisequaltothephasedelayforanidealnon-dispersivedelaydevice,butmaydiffergreatlyinactualdeviceswherethereisarippleinthephaseversusfrequencycharacteristic.”IEEEStandardDictionaryofElectricalandElectronicsTerms10©2005CiscoSystems,Inc.Allrightsreserved.GroupDelayCiscoPublicTheMath(Yikes!)whereGDisgroupdelayvariation,φisphaseinradians,andωisfrequencyinradianspersecondddGD•Initssimplestmathematicalrepresentation…•Forthepurists,groupdelayalsoisdefined)()(•Andyetanotherdefinitionis)()()(jeHddddD11©2005CiscoSystems,Inc.Allrightsreserved.GroupDelayCiscoPublicTheTranslation(Whew!)•Ifphaseversusfrequencyisnon-linear,groupdelayexists.•Inasystem,network,deviceorcomponentwithnogroupdelay,allfrequenciesaretransmittedthroughthesystem,network,deviceorcomponentinthesameamountoftime—thatis,withequaltimedelay.•Ifgroupdelayexists,signalsatsomefrequenciestravelfasterthansignalsatotherfrequencies.12©2005CiscoSystems,Inc.Allrightsreserved.GroupDelayCiscoPublicExamplecourtesyofHoltzman,Inc.TheAnalogyImagineagroupofrunnerswithidenticalathleticabilitiesonasmooth,flattrack…Alloftheathletesarriveatthefinishlineatexactlythesametimeandwithequaltimedelayfromoneendofthetracktotheother!13©2005CiscoSystems,Inc.Allrightsreserved.GroupDelayCiscoPublicGroupDelay:AnAnalogyNowlet’ssubstituteagroupofRFsignalsfortheathletes.Here,the“track”istheequivalentofafilter’spassband.FrequencyTimeAllofthefrequenciesarriveatthedestinationatexactlythesametimeandwithequaltimedelaythroughthefilterpassband!14©2005CiscoSystems,Inc.Allrightsreserved.GroupDelayCiscoPublicExamplecourtesyofHoltzman,Inc.GroupDelay:AnAnalogyBacktoathletes,butnowtherearesomethathavetorunintheditchesnexttothetrack.Someathletestakealittlelongerthanotherstoarriveatthefinishline.Theirtimedelayfromoneendofthetracktotheotherisunequal.15©2005CiscoSystems,Inc.Allrightsreserved.GroupDelayCiscoPublicGroupDelay:AnAnalogySubstituteRFsignalsfortheathletesagain.The“track”isafilter’spassband,the“ditches”arethefilter’sbandedges.FrequencyTimeTimedifference(unequaltimedelaythroughthefilter)16©2005CiscoSystems,Inc.Allr