- 1. Engr.Tehseen Ahsan Lecturer, Electrical Engineering Department EE-307 Electronic Systems Design HITEC University Taxila Cantt, Pakistan Amplifier Frequency Response (Part 2)
- 2. The Bode Plot AplotofdBvoltagegainversusfrequencyonsemilogpaperiscalledaBodePlot. AgeneralizedBodeplotforanRCcircuitlikethatshowninfigure10-23(a)appearsinpart(b) 2
- 3. The Bode Plot continue… Theidealresponsecurveisshowninblue.Noticethatitisflat(0dB)downtocriticalfrequencyatwhichpointthegaindropsat-20dB/decade. Abovefcarethemidrangefrequencies.Theactualresponsecurveisshowninred. Theactualresponsecurvedecreasesgraduallyinmidrangeandisdownto-3dBatthecriticalfrequency. Often,theidealresponseisusedtosimplifyamplifieranalysis Thecriticalfrequencyatwhichthecurvebreaksintoa-20dB/decadedropissometimescalledthelowerbreakfrequency. 3
- 4. Total Low-Frequency Response of an Amplifier Let’slookatthecombinedeffectofthethreeHigh-passRCcircuitsinaBJTamplifier. EachcircuithasacriticalfrequencydeterminedbyRandCvalues. ThecriticalfrequenciesofthethreeRCcircuitsarenotnecessarilyallequal. IfoneoftheRCcircuitshasacritical(break)frequencyhigherthantheothertwothenitisthedominantRCcircuit. Thedominantcircuitdeterminesthefrequencyatwhichtheoverallgainofamplifierbeginstodropat-20dB/decade. Theothercircuitseachcauseanadditional-20dB/decaderoll-offbelowtheirrespectivecritical(break)frequencies. 4
- 5. Total Low-Frequency Response of an Amplifier continue… 5
- 6. Total Low-Frequency Response of an Amplifier continue… RefertoBodeplotinfigure10-25whichshowsthesuperimposedidealresponsesforthreeRCcircuits(greenLines)ofaBJTamplifier. EachRCcircuithasadifferentcriticalfrequency. TheinputRCcircuitisdominant(highestfc)inthiscase,andthebypassRCcircuithasthelowestfc.Theoverallresponseisshownastheblueline. 6
- 7. Total Low-Frequency Response of an Amplifier continue… 7
- 8. Total Low-Frequency Response of an Amplifier continue… RefertotheBodeplotinfigure10-26allRCcircuitshavethesamecriticalfrequency,theresponsecurvehasonebreakpointatthatvalueoffc,andthevoltagegainrollsoffat-60dB/decadebelowthatvalue. Inthiscasethegainisat-9dBbelowthemidrangevoltagegain(-3dBforeachRCcircuit). 8
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- 12. 10-4 High-Frequency Amplifier Response Wehaveseenthecouplingandbypasscapacitorsaffectthevoltagegainofanamplifieratlowerfrequencieswherethereactancesofthecouplingandbypasscapacitorsaresignificant. Inmidrangeofanamplifier,theeffectsofthecapacitorsareminimalandcanbeneglected. Ifthefrequencyisincreasedsufficiently,apointisreachedwherethetransistor’sinternalcapacitancesbegantohaveasignificanteffectonthegain. 12
- 14. BJT Amplifiers continue… Noticethatthecouplingandbypasscapacitorsaretreatedaseffectiveshortsanddon’tappearinequivalentcircuit. TheinternalcapacitancesCbeandCbc,whicharesignificantonlyathighfrequencies,doappearinthediagram. CbeissometimescalledinputcapacitanceCib,andCbcissometimescalledoutputcapacitanceCob. CbeisspecifiedondatasheetsatacertainvalueofVBE. OftenthedatasheetwilllistCibasCiboandCobasCobo. Theoastheletterinthesubscriptindicatesthecapacitanceismeasuredwiththebaseopen. 14
- 15. Miller’s Theorem in High-Frequency Analysis (in BJT Amplifiers) Cin(Miller)=Cbc(Av+1) Cout(Miller)=Cbc(Av+1/Av) ThesetwoMillercapacitances(Cin(Miller)&Cout(Miller))createahigh-frequencyinputRCcircuitandahigh-frequencyoutputRCcircuit. Becausethecapacitancesgotogroundandthereforeactaslow-passfilters. 15IdealModelbecausestraycapacitancesduetocircuitinterconnectionsareneglected
- 16. The Input RC Circuit Athighfrequencies,theinputcircuitisshowninfig10-33(a) whereRin(base)=βacr'e16
- 17. The Input RC Circuit continue… Asthefrequencyincreases,thecapacitivereactancebecomessmaller.Thiscausesthesignalvoltageatbasetodecrease,sotheamplifier’svoltagegaindecreases. Thereasonforthisisthatthecapacitanceandresistanceactasavoltagedividerand,asthefrequencyincreases,morevoltageisdroppedacrosstheresistanceandlessacrosscapacitance. Atthecriticalfrequency,thegainis3dBlessthanitsmidrangevalue. Thecriticalhighfrequency,fc,isthefrequencyatwhichthecapacitivereactanceisequaltothetotalresistance. XCtot=Rth=Rout=Rs∥R1∥R2∥βacr'e 17
- 18. The Input RC Circuit continue… 18Upper critical Frequency
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- 22. Phase Shift of the Input RC Circuit Becausetheoutputvoltageofahigh-frequencyinputRCcircuitisacrossthecapacitor,theoutputvoltagelagstheinput.Thephaseangleisexpressedas Atthecriticalfrequencyfc,thephaseangleis45˚withthebase(output)voltagelaggingtheinputsignal. Asthefrequencyincreasesabove,thephaseangleincreasesabove45˚andapproaches90˚whenthefrequencyissufficientlyhigh. 22
- 23. The Output RC circuit Thehigh-frequencyoutputRCcircuitisformedbytheMilleroutputcapacitanceandtheresistancelookinginatthecollectorasshowninfigure10-36(a). 23
- 24. The Output RC circuit continue… Cout(Miller)=Cbc(Av+1/Av) Ifthevoltagegainisatleast10,thenCout(Miller)≈Cbc. Thecriticalfrequencyisdeterminedas JustlikeinputRCcircuit,theoutputRCcircuitreducesthegainby3dBatthecriticalfrequency.Whenthefrequencygoesabovethecriticalvalue,thegaindropsat-20dB/decaderate.ThephaseangleintroducedbyoutputRCcircuitis 24Where Rc = RC ∥RL
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- 27. FET Amplifiers Theapproachtothehigh-frequencyanalysisofaFETamplifierissimilartothatofaBJT. ThebasicdifferencesarethespecificationsoftheinternalFETcapacitancesandthedeterminationoftheinputresistance.Figure10-39(a)showsaJFETcommon-sourceamplifierusedtoillustratehigh-frequencyanalysis. 27
- 28. FET Amplifiers Continue… Ahigh-frequencyequivalentcircuitfortheamplifierisshowninfigure10-39(b). Thecouplingandbypasscapacitorsareassumedtohavenegligiblereactancesandareconsideredtobeshorts. TheinternalcapacitancesCgsandCgdappearintheequivalentcircuitbecausetheirreactancesaresignificantathighfrequencies. 28
- 29. Values of Cgs, Cgd, and Cds FETdatasheetsdonotnormallyprovidevaluesforCgs,Cgd, orCds. InsteadthreeothervaluesareusuallyspecifiedwiththehelpofthemyoucaneasilycalculateCgs,Cgd,andCds. Cgd=Crss Cgs=Ciss-Crss Cds=Coss-Crss Cossisnotspecifiedasoftenastheothervaluesondatasheets. IncaseswhereCossisnotavailable,youmusteitherassumeavalueorneglectCds. 29Ciss = the input capacitanceCrss = the reverse transfer capacitanceCoss= the output capacitance
- 30. Miller’s Theorem in High-Frequency Analysis (in FET Amplifiers) Cin(Miller)=Cgd(Av+1) Cout(Miller)=Cgd(Av+1/Av) ThesetwoMillercapacitances(Cin(Miller)&Cout(Miller))createahigh-frequencyinputRCcircuitandahigh-frequencyoutputRCcircuit. Botharelow-passfilterswhichproducephaselag. 30
- 31. The Input RC Circuit Thehigh-frequencyinputcircuitformsalow-passtypeoffilterandisshowninfig-10-41(a). 31
- 32. The Input RC Circuit Continue… SincebothRGandRin(gate)ofFETsareextremelyhigh, thereforecontrollingresistancefortheinputcircuitistheresistanceoftheinputsourceRsaslongasRs<<Rin. ThisisbecauseRsappearsinparallelwithRinwhenThevenin’stheoremisapplied. ThesimplifiedinputRCcircuitappearsinfigure10-41(b). Thecriticalfrequencyis: 32
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- 35. The Output RC circuit Thehigh-frequencyoutputRCcircuitisformedbytheMilleroutputcapacitanceandtheresistancelookinginatthedrainasshowninfigure10-43(a). 35
- 36. The Output RC circuit continue… Cout(Miller)=Cgd(Av+1/Av) Ifthevoltagegainisatleast10,thenCout(Miller)≈Cgd. Thecriticalfrequencyisdeterminedas Theoutputcircuitproducesaphaseshiftof36Where Rd = RD ∥RL
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- 38. Total High-Frequency Response of an Amplifier Wehavealreadyseenthat,twoRCcircuits(Cin(Miller)& Cout(Miller))createdbytheinternaltransistorcapacitancesinfluencethehigh-frequencyresponseofbothBJTandFET. Asthefrequencyincreasesandreachesthehighendofitsmidrangevalues,oneoftheRCcircuitwillcausetheamplifier’sgaintobegindroppingoff. Thefrequencyatwhichthisoccursisthedominantcriticalfrequency;itisthelowerofthetwocriticalfrequencies. Anidealhigh-frequencyBodeplotisshowninfigure10- 44(a)nextslide.Itshowsthefirstbreakpointatfcu(input) wherethevoltagegainbeginstorolloffat-20dB/decade.Atfcu(output),thegainbeginsdroppingat-40dB/decadebecauseeachRCcircuitisaddinga-20dB/decaderoll-off38
- 39. Total High-Frequency Response of an Amplifier continue… Figure10-44(b)showsanon-idealBodeplotwherethevoltagegainisactually-3dBbelowmidrangeatfcu(input). OtherpossibilitiesarethattheoutputRCcircuitisdominantorbothcircuitshavethesamecriticalfrequency. 39
- 40. 10-5 Total Amplifier Frequency Response Figure10-45(b)nextslideshowsageneralizedidealBodeplotfortheBJTamplifierinfig10-45(a)nextslide. Thethreebreakpointsatthelowercriticalfrequencies(fcl1,fcl2, andfcl3)areproducedbythreelow-frequencyRCcircuitsformedbythecouplingandbypasscapacitors. Thetwobreakpointsatthehighercriticalfrequencies(fcu1andfcu2)areproducedbytwohigh-frequencyRCcircuitsformedbythetransistor'sinternalcapacitances. Thetwodominantcriticalfrequenciesfcl3(fcl(dom))andfcu1(fcu(dom)) areofourinterestinfig10-45(b). Thesetwofrequenciesarewherethevoltagegainoftheamplifieris3dBbelowitsmidrangevalue. Thesedominantfrequenciesarereferredtoasthelowercriticalfrequencyfcl(dom),andtheuppercriticalfrequency,fcu(dom).40
- 41. Total Amplifier Frequency Response Continue… 41
- 42. Total Amplifier Frequency Response Continue… Theupperandlowercriticalfrequenciesaresometimescalledthehalf-powerfrequencies.Thisisduetothefactthattheoutputpowerofanamplifieratitscriticalfrequenciesisone-halfofitsmidrangepower(asdiscussedpreviously). Alsostartingwiththefactthattheoutputvoltageis70.7%ofitsmidrangevalueatthecriticalfrequencies. 42
- 43. Bandwidth Anamplifiernormallyoperateswithsignalfrequenciesbetweenfcl(dom)andfcu(dom). Whentheinputsignalfrequencyisatfcl(dom)orfcu(dom),theoutputsignallevelis70.7%ofitsmidrangevalue. Ifthesignalfrequencydropsbelowfcl(dom),thegainandthustheoutputsignalleveldrops20dB/decadeuntilthenextcriticalfrequencyisreached. Thesameoccurswhenthesignalfrequencygoesabovefcu(dom). Therange(band)offrequencieslyingbetweenfcl(dom)andfcu(dom)isdefinedasthebandwidthoftheamplifierasshowninfigure10- 46nextslide. Onlythedominantcriticalfrequenciesappearintheresponsecurvebecausetheydeterminethebandwidth. 43
- 44. Bandwidth Continue… Theamplifier’sbandwidthisexpressedinunitsofhertzas BW=fcu(dom)-fcl(dom) Ideally,allsignalfrequencieslyinginamplifier’sbandwidthareamplifiedequally.i.e,ifa10mVrmssignalisappliedtoanamplifierwithavoltagegainof20,itisamplifiedto200mVrmsforallfrequenciesinthebandwidth. 44
- 45. Unity-Bandwidth Product Onecharacteristicofamplifiersisthattheproductofvoltagegainandbandwidthisalwaysconstantwhentherollis-20dB/decade. Thischaracteristiciscalledgain-bandwidthproduct. Let’sassumethatthelowercriticalfrequencyofaparticularamplifierismuchlessthantheuppercriticalfrequency. fcl(dom)<<fcu(dom) Thebandwidthcanbeapproximatedas BW=fcu(dom)-fcl(dom)≈fcu45
- 47. Unity-Gain Frequency Continue… Noticethatfcl(dom)isneglectedbecauseitissomuchsmallerthanfcu(dom),andthebandwidthapproximatelyequalsfcu(dom). Beginningatfcu(dom),thegainrollsoffuntilunitygain(0dB)isreached. Thefrequencyatwhichtheamplifier’sgainis1iscalledtheunity- gainfrequency,fT. ThesignificanceoffTisthatitalwaysequalsthemidrangevoltagegaintimesthebandwidthandisconstantforagiventransistor. fT=AV(mid)BW Forthecaseshowninfig10-47,fT=AV(mid)fcu47
- 48. 10-6 Frequency Response of Multistage Amplifiers Whenamplifierstagesarecascadedtoformamultistageamplifier(morethanonestageamplifier),thedominantfrequencyresponseisdeterminedbytheresponsesoftheindividualstages. Therearetwocasestoconsider: 1.Eachstagehasadifferentlowercriticalfrequencyandadifferentuppercriticalfrequency. 2.EachStagehasthesamelowercriticalfrequencyandthesameuppercriticalfrequency. DifferentCriticalFrequencies Whenthelowercriticalfrequency,fcl(dom),ofeachamplifierstageisdifferent,thedominantlowercriticalfrequency,f'cl(dom),equalsthecriticalfrequencyofthestagewiththehighestfcl(dom). Whentheuppercriticalfrequency,fcu(dom),ofeachamplifierstageisdifferent,thedominantuppercriticalfrequency,f'cu(dom),equalsthecriticalfrequencyofthestagewiththelowestfcu(dom). 48
- 49. Frequency Response of Multistage Amplifiers Continue… OverallBandwidth ThebandwidthofamultistageamplifierisBW=f'cu(dom)-f'cl(dom) EqualCriticalFrequencies Wheneachamplifierstageinamultistagearrangementhasequalcriticalfrequencies,youmaythinkthatthedominantcriticalfrequencyisequaltothecriticalfrequencyofeachstage.Thisisnotthecasehowever. Samelowercriticalfrequencies SameHighercriticalfrequencies Where“n”isthenumberofstagesofamultistageamplifier. 49
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