Basic_Concepts_in_RF_Design

ICE669(H.J.Yoo)BasicConceptsinRFDesignICE669(H.J.Yoo)NonlinearsystemsLinearsystem–outputcanbeexpressedasalinearcombinationofinputs–otherwise,nonlinearnonzeroinitialconditionsorfiniteoffsetsmakesystemnonlinearTimeinvariantsystem–timeinvariant:timeshiftininputresultsinthesametimeshiftinoutputDifferentialorbalancedsystem–systemwithodd-symmetry–noevenorderharmonicsExample–(b)nonlineartime-variantsystem–(c)lineartime-variantsystemalinearsystemcangeneratefrequencycomponentsthatdonotexistintheinputsignal
   



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ωω



ττ−→−→



Razavi98ICE669(H.J.Yoo)GainCompressionMemoryless,nonlinearsystem–ForanonlinearsystemthatcanbeapproximatedHarmonics–Evenorderharmonicsresultfromαjwithevenj–AmplitudeofnthharmonicconsistsofatermproportionaltoAnandothertermsproportionaltohigherpowerofA–NeglectinglatterforsmallA,nthharmonicgrowinproportiontoAnGainCompression–Smallsignalgainvarieswithinputlevel–Mostcircuits,outputiscompressiveorsaturating→occursifα30–SmallsignalgainisadecreasingfunctionofA–1-dBcompressionpoint:inputsignallevelthatcausessmall-signalgaintodropby1dB–Measureofmaximumapplicableinputsignal–Around-20to-25dBm(63.2to35.6mVppin50Ωsystem)intypicalfront-endRFamplifiers








ααα++≈












ωαωαωαααωωαωαωαωαωαωαω           


++++=++++=++==







ααααα=−=+−−Razavi98ICE669(H.J.Yoo)DesensitizationandCrossModulationDesensitizationandBlocking–DesensitizationProblemwhenprocessweak,desiredsignalwithastronginterfererWeaksignalcanexperiencesmallergainaslargesignaltendstoreduceaveragegainGainbecomesadecreasingfunctionofA2–ForsufficientlylargeA2,gaindropstozero→“blocked”–InRFdesign,“blockingsignal”usuallyreferstointerferersthatdesensitizeacircuitthoughgaindoesnotfalltozero–ManyRFreceiversrequiretowithstandblockingsignals60to70dBhigherthanthewantedsignalCrossModulation–Phenomenonthatoccurswhenaweakandastronginterfererpassthroughanonlinearsystem–Amplitudeofinterferermodulatestheamplitudeofweaksignal–From(1),ifamplitudeofinterfererismodulatedby–Desiredsignalattheoutputcontainsamplitudemodulationatωmand2ωm–CommoncaseofcrossmodulationAmplifiersthatmustsimultaneouslyprocessmanyindependentsignalchannel—e.g.,CATVtransmittersFullduplexCDMAsystems—requestforsuper-linearLNA!!++=+++=++=+=









ωααωααααααωω    









  

ωω+!++++×+=



ωωωαα   


Razavi98ICE669(H.J.Yoo)IntermodulationIntermodulation–whentwosignalswithdifferentfrequenciesareappliedtoanonlinearsystem–theoutputingeneralexhibitssomecomponentsthatarenotharmonicsoftheinputfrequenciesThird-orderIM(TOI)–ifthedifferencebetweenω1andω2issmall,thecomponentat2ω1-ω2and2ω2-ω1appearinthevicinityofω1andω2–intypicaltwo-tonetest,A1=A2–Corruptionofasignalduetointermodulationbetweentwointerferersaweaksignalwithtwostronginterferers







        






















ωωαωωαωωωωαωωαωωωωαωωαωωωαααωαααωωω−++±=−++±=−++±=+++++=  









αααωω++=+=Razavi98ICE669(H.J.Yoo)Third-orderInterceptPoint(IP3)Third-orderinterceptpoint(IP3)–IIP3andOIP3RelationshipbetweenA1-dBandAIP3CalculationofIP3withoutextrapolationExample⋅⋅⋅+−+−++++=+=







      





ωωαωωαωααωααωω


αααααα=∴=!

−≈=−≈=
 
  
    
 
=−≈==


Razavi98ICE669(H.J.Yoo)IP3ofCascadedNonlinearStagesOverallIIP3ofcascadedstages–forworst-caseestimate,–Asα1increases,theoverallIP3decreaseswithhighergaininthefirststage,thesecondstagesenseslargerinputlevels,therebyproducingmuchgreaterIM3product–Sinceeachstagehasanarrowpassband,out-of-bandsignalsareheavilyattenuated–forthreeormorestages(Powers&gainsinrealvalue,notindB)–Forgaingreaterthan1,theIP3oflatterstagebecomesincreasinglycritical[][][]



















#βαβααβαβαβαβααβαβααααβαααβαααββββααα++=∴++++=++++++++=++=++=



















!







αββαβαβαβααβα++=++=

α+≈⋅⋅⋅+++≈⋅⋅⋅+++≈






  βααRazavi98ICE669(H.J.Yoo)AdjacentChannelPowerRejection(ACPR)ACPR–AdjacentchannelpowerrejectionOrigin–IntermodulationProblem–Leadtohigherinbandnoisepower–Signalpowerleakagetotheadjacentchannel→degradeadjacentchannel(usedbyothers)S/NratioCDMAACPR–Measurespectralpowerofthechannel(1.23MHzbandwidth)–Measureupperandlowerband