Lab7AMRadio

RichardLiuandBrodyKellish

IhaveadheredtotheDukeCommunityStandardincompletingthisassignment.

Objectives

Inthislabassignment,weexploredtheprocessofamplitudemodulation.Welearnedhowtomodulateacarriersignalinordertotransmitinformationinthemodulatedsignal,aswellashowtorecoverthistransmittedinformationuponreceipt.Tothisend,wealsocreatedabasicdemodulatorcircuit(essentiallyanenvelopedetectorfortheinputvoltagesignal),thatweusedtorecovertheAMwave.WeusedthemodulationfunctiononthefunctiongeneratortocreateandtransmitanAMwavewithaveryshortrange.Bytuningasmall,portableAMradiotothecorrectfrequency,wewereabletohearourAMsignal.WethenusedourenvelopedetectortodemodulatetheAMsignalanddisplayitontheoscilloscope.Background

Inthislab,wefocusedprimarilyonamplitudemodulation/demodulation,theprocessesusedinAMradiototransmitsignals.Bymodulatingacarriersignalwiththedesiredmessagesignal,wecancreateasignalthathasthesamefrequencyasthecarriersignal,butthathasanamplitudethatfollowsthefrequencyofthemodulatingmessagesignal.Thisprocessisillustratedinthefollowingdiagramprovidedinthelabhandout.Inthefigure,m(t)isthemessagesignal,andc(t)isthecarriersignal.Asisclearfromthefigure,theeffectofthemodulationistovarytheamplitudeofthecarriersignalaccordingtothemessagesignal(creatinganamplitudeenvelope).

Inordertoextractthismessagesignalfromthemodulatedcarriersignal,wecanutilizeasimplecapacitivefilterknownasanenvelopedetector.Theoutputoftheenvelopedetectoreffectivelytracestheamplitudeofthemodulatedcarriersignal.However,inordertoachievethedesiredbehavior,wemustchoosecomponentvaluessuchthatthetimeconstantofthecircuitallowsforthevoltageacrossthecapacitortotracethevoltageoftheinputmodulatedsignalinordertoachieveaccuratedemodulation,andrecoveryofthemessagesignal.

Exercise1:AMSignalinTimeandFrequencyDomainsProcedure

First,wesetthefunctiongeneratortooutputa50kHzsinusoidalsignalwithapeaktopeakvoltageof1V.Wethenconnectedthefunctiongeneratortotheoscilloscope,sothatwecouldviewtheoutputsignal.WemadesurethatthehorizontalscaleoftheoscilloscopewassuchthatwecouldseeseveralperiodsoftheAMsignal.WeusedtheAMmodulationfeatureonthefunctiongeneratortocreateasinusoidalmodulating(message)signal.Inordertodoso,wehadtosettheshapeoftheAMwavetoSINE,selecttheINTmodulationtype(thefunctiongeneratoritselfproducesthemodulationsignalinternally),andsettheparametersofthisinternallygeneratedsignaltothefollowing:

kHzfm = 1

(Index of Modulation) 0 =

Withthesemodulationsettings,wesavedtheoscilloscopedisplaytoanimagefile.Thisscreenshotshowsjusttheunmodulatedcarriersignal,sincethevalueof was0.Next,we set equalto0.50(50%).Again,weadjustedtheoscilloscopehorizontalscaletosee severalperiodsofthewave,andsavedanotherscreenshotofthedisplay,thistimeshowingthemodulatedAMsignalatthenewmodulationfactor.WeusedtheoscilloscopetomeasuretheminimumandmaximumvoltagesoftheAMsignal,andthencalculatedtheexperimentalusingthefollowingequation:

= V + Vmax minV Vmax min

Thecalculatedvalueofshouldbeclose(ifnotequalto)0.50,whichwasthemodulationfactorwespecified.Ourcalculatedvaluesofcanbefoundintheresultssection.Next,weusedtheFFT(FastFourierTransform)functionontheoscilloscopetoviewthefrequencydomainofthesignal.Wesetthecenterfrequencyoftheoscilloscopeplottobethecarrierfrequency,andadjustedthefrequencyspanto10kHztoensurethatwecouldseetheentireregionofinterest.WetookascreenshotoftheFFTplot(alongwiththecorrespondingtimedomainsignal),takingspecialcaretonotethepresenceofthreepeaksinthefrequencyplotone(thelargestpeak)at50kHz(thecarrierfrequency)andtwomore(oneoneithersideofthecarrierfrequency),locatedat501kHz.Wethenchangedthevaluesofthecarrierfrequencyandthemodulationfrequency.OurobservationsarenotedintheDiscussion.Finally,werepeatedthestepsaboveforthreedifferentvaluesofthemodulationfactor.Weusedvaluesof0.15,0.80,and1.15tocompare,repeatingthecalculationsfortheobservedateachmodulationfactorspecified.Thescreenshots/calculationsfor=0,=0.50,andthecalculationsforallothertrialscanbefoundintheResults.Sinceallwearechanginginthese

trialsisthemodulationfactor,thefrequencyspectrumplotswillnotchangeforeachvalueof.Results

ScreenshotsoftheoscilloscopedisplaysforeachAMsignal(withthecorrespondingFFTplot),alongwiththecalculationsofthemodulationfactorcanbefoundbelow.Weperformedtheexperimentformodulationvaluesof0,0.50,0.15,0.80,and1.15(thismodulationfactorissignificantinthatitisgreaterthanoneseetheDiscussionformoredetails).=0

NoFFTwasprovidedforthistrial,sincetheAMsignalisapure,unmodulatedsinusoid

AMSignal50kHzCarrier,1kHzMod, =0

.0097 = V + Vmax min

V Vmax min = 2.09V + 2.05V2.09V 2.05V = 0 0

=0.50 Notethepresenceofthreepeaks,locatedatthefrequenciesdescribedinthe

procedure.

AMSignal50kHzCarrier,1kHzMod, =0.50

.57 .50 = V + Vmax minV Vmax min = 0.80V + 0.22V

0.80V 0.22V = 0 0 =0.15

.18 .15 = V + Vmax minV Vmax min = 0.58V 0.40V0.58V + 0.40V = 0 0

=0.80

.77 .80 = V + Vmax minV Vmax min = 0.775V 0.10V0.775V + 0.10V = 0 0

=1.15

.11 .15 = V + Vmax minV Vmax min = 1.00V (0.05V )1.00V + (0.05V ) = 1 1

Inthistrial,itisimportanttonotethatthevalueofVminisnegative.Discussion

Howmanypeaksdidyouexpecttoseeandwheredidyouexpecttoseethemonthefrequencyaxis(inregardstothe=0.50modulatedsignal)?Wesawthreepeaksinthefrequencyspectrum.Thelargestpeakwaslocatedatthecarrierfrequency(50kHz)withtwosmaller,identicalpeaksat49kHzand51kHz.Thesethreepeakswouldalsoberepeatedatthesamelocationonthenegativefrequencyaxis.Changethefrequencyofthemodulatingsignalandobservehowthespectrumchanges.Noteyourobservations.Whenwechangedthefrequencyofthemodulatingsignalfrom1kHzto2kHz,wesawthatthetwopeaksoneithersideofthecarrierfrequency(50kHz)movedfartherawayfromthecarrierfrequency.Thatis,thevaluesoccurredat502kHz(48kHzand52kHz).Thiscanbeseeninthefollowingscreenshot.

Noticethatthemodulatingfrequencypeaksoccurfartherfromthecarrierfrequencypeaks

Changethefrequencyofthecarriersignalandobservehowthespectrumchanges.Noteyourobservations.

Whenwechangedthefrequencyofthecarriersignalfrom50kHzto51kHz(whilekeepingthemodulatingsignalfrequencyat1kHz)wesawthethreepeaksshiftedtotherightby1kHz.Thecarrierfrequencypeakoccursat51kHz,andthemodulatingsignalfrequencypeaksoccurat50kHzand52kHz.

Noticetheshift1kHztotherightofthethreepeaks

Writeabriefparagraphonhowweshouldchoosethemodulatingfactor.Themodulatingfactor,asageneralruleofthumb,shouldalwaysbelessthan1.AswecanseefromthegraphsintheResultssection,whenthemodulatingfactorisgreaterthanone,thereissomecrossoverintheresultingAMsignal,asisdepictedinthefollowingdiagram.

Figuretakenfromhttp://en.wikipedia.org/wiki/Amplitude_modulation

Whenthiscrossoveroccurs,itbecomesimpossibletoaccuratelyrecoverthemodulatingsignalwithanenvelopedetector.Theenvelopeofthefunctionappearstobecomposedoftwodifferentperiodfunctions,wheninreality,thevaluesoftheenvelopecrossattheAmplitude=0axis,causingdistortionintheAMsignal.Thus,weneverwantamodulationfactorgreaterthan1,inordertoavoidthiscrossoverintheAMwave.Thisisknownasovermodulation.Thevalueofthemodulationfactor(whenitisbetween0and1)determinesthedeepnessofthevalleysintheAMwave.Conclusions

AmplitudeModulationproducesasignalwithfrequencycontentatthecarrierfrequency,fc,andatadistance(positiveandnegativedistance,thatis)offmawayfromthecarrierfrequency,wherefmisthefrequencyofthemodulatingsignal.Moresimply,thefrequencycontentoccursatfc,fc+fm,andfcfm.Additionally,theindexofmodulationmustalwaysbelessthanonetoensurethatnodistortionoccursinthereconstructionofthemessage(modulating)signal.Themodulationfactordetermineshowmuchthemaximumandminimumpeakvoltagesdiffer,andthus,ahighermodulationfactorwillresultinanoutputsignalwithdeepervalleysbetweenthepeaks.ThemodulationfactorcanbeeasilycomputedfrominspectionofthegraphofanAMsignal,bythefollowingformula:

= V + Vmax minV Vmax min

Exercise2:UsinganExternalModulatingSignalProcedure

Inthisexercise,weusedthesame50kHzcarriersinusoidasinthepreviousexercise.However,bychoosingtoplaymusicastheinputmodulationinsteadofamonotone,wewereabletoseetheAMsignalasitmodulatesasignalwithdynamicfrequencies.Withthefunctiongeneratorstillconnectedtotheoscilloscope,wesetthescaleontheoscilloscopeproperlysothatwecouldseemultipleperiodsoftheAMsignal.WethensetthefunctiongeneratortoEXTAMmodulation(externalmodulationinput).Thisallowedustoconnectanaudiocabletothebackofthefunctiongeneratortobeusedastheinputtotheoscilloscopemodulationfunction.Weconnectedtheaudiooutputfromamobilephonelineouttothemodulationinputofthefunctiongenerator.Weplayedavarietyofsongsfromthephone,andobservedthebehavioroftheAMsignalontheoscilloscopeinboththefrequencyandtimedomains.Ascreenshotoftheamplitudemodulatedsignal,alongwithitsFFT(adjustedforscale)areshownbelowintheResultssection.

Results

ThisscreenshotrepresentsaninstantaneouscaptureoftheAMwaveforminreality,theenvelope(alongwiththecorrespondingFFTplot)isconstantlychanginginrealtimealongwiththemusicbeingplayed.Wenoticeintheplot,thefrequencyforthecarrierwaveformisclear(50kHz)whilethefrequenciesforthemodulatedmusicinputaredynamicandcontainsmanypeaksofvaryingamplitudes.Thisistobeexpected,asthemusicsignaliscomposedofaudiocontentatmanydifferentfrequenciesandwithdifferentvolumes.Wealsoobservethesamesymmetryaboutthecarrierfrequencyasinthelastexample,whichistobeexpectedalthoughthemodulatingsignalisnolongerapuresinusoid,weshouldstillseethesamepropertiesforeachindividualmodulatingsinusoidintheaudioinput(thismakesintuitivesenseifwethinkofthemusicsignalasaweightedsumofindividualsinusoids,eachcontributingindependentlytotheoverallfrequencyspectrumofthesignal).Discussion

Answerthefollowingquestionsreferringtotheoscilloscopedisplay:a.Whatarethefrequencyrangesofthetwosidebands?b.Arethesidebandsmirrorimagesofeachother?Thefrequencyrangesofthetwosidebandsareapproximately52.557.5kHzand42.547.5kHz.Thesidebandsaremirrorimagesofoneanother.

Conclusions

Thebiggesttakeawayfromthisexercisewasthatevenwhentheinputmodulationsignalisdynamicandnotjustamonotone,theFFTplotoftheAMsignalisstillsymmetricalandhasclearsidebands,whicharemirroredacrossthefrequencyofthecarriersignal.Intuitively,thismakessensetous,asmusicisjustasuperpositionofsignalsofdifferingfrequenciesandamplitudes.Thus,weexpecttoseethatrepresentedinourFFT,whichwedid.Exercise3:BroadcastingYourSignalProcedure

Inthissegmentofthelab,weaimedtocreateasimpleAMradiostationbybroadcastingmusicviaamplitudemodulatedsignals.Onthefunctiongenerator,wesetthecarriersignaltohaveafrequencyof1000kHzandapeaktopeakvoltageof1.5Vwith50%modulation.WechosetoplaythesongCollardGreensbySchoolboyQ,asitinvolvedawiderangeoffrequencies,sothatwemayseetheeffectofamplitudemodulationonlowandhighfrequencycontent.However,withtheaforementionedsettings,wedidnothearanythingonourportableAMradio,despitevaryingthedistancebetweentheportableradiototheantennafromveryclosetorelativelyfar,andcyclingthroughallpossiblestations(partofthisfailuremayhavebeenduetoadysfunctionalportableAMradio).AfterswappingouttheAMradioforafunctionalone,wealsochangedthepeaktopeakvoltageofthecarriersignalto2V,aswepredictedthatitwouldcreateastrongeroutputsignal,andthus,wouldcreateaclearerradiostation.Withthesechanges,wewereabletohearthesongrelativelyclearly.Results

ThemostsignificantresultweobservedwastheeffectofchangingthepeaktopeakvoltageoftheAMwaveform.Forlowervoltages,wewerestillabletoheartherecoveredmusic,albeitfaintlyandwithafairamountofstaticnoise.Asweincreasedthevoltage(firstfrom1.5Vto2.0V),wenoticedthatthemusicbecameslightlylouder,andthus,easiertohear.Aswecontinuedtoincreasethepeaktopeakvoltage,weheardanoticeabledifferenceinvolume.Wedidnotnoticeanydifferenceintherangeofbroadcastwhenchangingthepeaktopeakvoltage,butthatcouldbejustduetolackofproperequipment.Discussion

Howfarcanyoumoveawayfromthetransmitterandstillrecognizethemusicsignalfromyourstation?

Themaximumrangeofthebroadcastwasonlyafewcentimeters(510cm).Thesignalwasstrongestwhentheantenna(anauxiliarycable)wasnearlytouchingtheportableAMradio.Askyourpartnertochangethepeaktopeakvalueofthecarriersignal.a.Didthestrengthofthereceivedsignalchange?b.Didthefidelityofthereceivedsignalchange?Whenwechangedthepeaktopeakvalueofourcarriersignalfrom1.5Vto2.0V,themusicwentfrombeingveryfainttorecognizable.Similarly,anotherincreasefrom2.0Vto2.5Vmadethemusiccleareragain.Asfarasourearscouldhear,therewasnonoticeablechangeinthefidelityofthesignalthestaticthatweheardwasamplifiedalongwiththevolumeofthemusicitself.Conclusions

ThisexercisetaughtushowwecouldapplyamplitudemodulationintherealworldtotransmitandrecoverinformationusingAMwaves.Welearnedthatitisindeedpossibletoretrieveamodulatedinputclearlyexamplesofsuchapplicationsincluderadiostationsaswellastwowayradiosandwirelessinternet.However,oneareawherewecouldhaveimproveduponinthisexercisewasincreasingtherangeofbroadcastofoursignal.Ourrangeofbroadcastwasextremelysmall(about510cmaslistedabove),andifwehadmoretime,wecouldhavetriedtoadjustvariouspropertiestoseeifwecouldpossiblyincreasetherangewiththeequipmentthatwasavailable.Exercise4:AMDemodulationUsinganEnvelopeDetectorProcedure

ForthisexerciseweconstructedanenvelopedetectorusinganRCcircuit.Thecircuitwasbuiltaccordingtothebelowdiagram.

Forourcircuitcomponents,wechosea2000resistoranda50nFcapacitor(howwecametochoosethesevaluesisexplainedintheDiscussionsection).

Usingthefunctiongenerator,wecreatedaninternallymodulatedAMwaveformwithacarrierfrequencyof100kHz,peaktopeakvoltage5Vandamodulationindexof0.5.Ourmodulatingwaveformhadafrequencyof1kHz,andwasasimple,puresinusoid(thismadeiteasiertoviewourresultsontheoscilloscopelaterintheexperiment).WethenattachedtheoscilloscopeprobesacrosstheresistorRstovisualizetheAMwaveformitselfoftheenvelopedetector,andtookseveralscreenshotstoshowthecharacteristicbehaviorofthesystem.WealsomeasuredtheoutputacrosstheresistorR(thevoltageacrossRisequaltothevoltageacrossC,giventhattheyareconnectedinparallel)inordertomeasuretheoutputoftheenvelopedetector..Results

AMWaveformTimeandFrequencySpectra(Input)

Intheabovefigure,weseethesamecharacteristicFFTofanAMwaveformasinthefirstexperiment.Thatis,thefrequencyspectrumhaspeaksatthecarrierfrequencyfc=100kHz,andfc fm,wherefm(thefrequencyofthemodulatingsignal)isequalto1kHz. EnvelopeDetectorTimeandFrequencySpectra(Output)

Inthissecondfigure,whichwetookfromtheoscilloscopewhentheleadswereconnectedacrosstheoutputresistorR,wedonotseethetraditionalAMwaveform.Instead,wefoundthattheoutputsignalcontainedapeakat1kHz(thefrequencyofthemodulatingsignal),alongwithsomeartifactsthatoccurevery1kHz.Itwouldappearthatourenvelopedetectorfunctionedcorrectly,asthemodulatingsignalwaseffectivelyrecovered(albeitslightlyattenuated,althoughthisistobeexpected,duetothepresenceoftheRsresistor,whichdropsthevoltageoftheinputsignal).Discussion

Howmanypeaksdoyouobserveinthespectrum?Wherearetheylocated?Isthisexpected/unexpected?Inthepowerspectrum,weobserve3peaks.Oneisat100kHzandtheothertwoareat99kHzand101kHz.ThisisexactlywhatweexpecttoseeintheoriginalAMwaveform.Commentonthetwotimedomainsignalsthatyouobserved(Q1andQ5).ThetimedomainrepresentationoftheAMwaveformisexactlyhowwewouldexpectittolookweseethecarrierwave,apuresinusoidat100kHz,whoseamplitudevaries(byafactorof0.50)accordingtothemodulatingsignal,whichwasapuresinusoidat1kHz.Thetimedomainplotoftheenvelopedetectoroutputsignalappearstobethemodulatingsignalitselfthatis,apuresinusoidat1kHz,albeitslightlyattenuated.Whatdidyouexpectthesignalattheoutputoftheenvelopedetectortolooklike?Haveyourecoveredyouroriginalsignal?

Weexpectedtoseeasinglesinusoidat1kHz.Uponinspectionofourfigure,wedidrecoverthissignal,butwealsoseesomereplicasofthesignalthatoccurevery1kHz(theseharmonicsarelikelyartifactsofthebehaviorofthesimplecircuititself).Commentonthetwofrequencydomainrepresentations(Q3andQ7).TheAMwaveformshowsthecharacteristicthreepeaks,centeredatthecarrierfrequency,adistancefmawayfromthecarrierfrequencyinthepositiveandnegativedirections.Intheenvelopedetector,wewouldideallyexpectasinglepeakat1kHz,butsincethisisanimperfectenvelopedetector,weseesmallerpeaksthatoccurevery1kHz.Theseartifactscouldbeduetointerferenceoranimperfectlyconstructedcircuit,ormayjustbeafunctionoftherelativesimplicityofthisenvelopedetectorcircuit.Relateyourfrequencydomainobservationstoyourtimedomainobservationsoftheinputandoutputsignals.Lookingfirstatthefrequencydomainrepresentations,wenoticeseveralthingsbetweentheinputandtheoutput.WeexpecttheinputAMsignaltohaveapeakat100kHzandsidebandsat100 1kHz.Essentially,thatisindeedwhatweobserved.However,aperfectenvelope detectorwouldgiveanoutputthatisamonotonesinusoid,withfrequencydomainrepresentationofasinglepeakat1kHz.However,weobservethatalthoughthereisapeakat1kHz,therearealsopeaksat2kHz,3kHz,4kHz,etc.Thiscanbeattributedtovariousimperfectionsintheenvelopedetectorconstruct.Translatingtheseobservationstothetimedomain,weseethattheinitialsignalisaarchetypalexampleofanamplitudemodulatedsignal,andfrequencyof1.4083kHzatteststhattheoriginalmonotonehasindeedbeenmodulated.Theoutputfromtheenvelopedetectorresemblesasinusoidandhasafrequencyof1.003kHz.Becausetheaforementionedartifactsoccuratmultiplesof1kHz,ourfundamentalfrequencyisstill1kHzandouroscilloscopedatamatchesourexpectations.Theartifactsareeasyenoughtoremove,buttheyillustratethatwehave,infact,reconstructedthebasicmodulatingsignal.DescribeindetailhowyouselectedthevalueofRandCforyourcircuit.Justifyyourselectionintermsofthesignalparameters(e.g.,carrierfrequency,messagecontent).WewereinstructedtocreateanRCcircuitthathadatimeconstant suchthat

.Thesevaluesaresignificantinthattheyrepresenttheperiodsofthecarrier1100000