Amplifier frequency response(part 2) floyd 7 ed

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)
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3. The Bode Plot continue…
Theidealresponsecurveisshowninblue.Noticethatitisflat(0dB)downtocriticalfrequencyatwhichpointthegaindropsat-20dB/decade.
Abovefcarethemidrangefrequencies.Theactualresponsecurveisshowninred.
Theactualresponsecurvedecreasesgraduallyinmidrangeandisdownto-3dBatthecriticalfrequency.
Often,theidealresponseisusedtosimplifyamplifieranalysis
Thecriticalfrequencyatwhichthecurvebreaksintoa-20dB/decadedropissometimescalledthelowerbreakfrequency.
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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.
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13. BJT Amplifiers
Ahigh-frequencyacequivalentcircuitfortheBJTamplifierinfig10-31(a)isshowninfig10-31(b).
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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
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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).
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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).
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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

46. Unity-Gain Frequency
ThesimplifiedBodeplotforthecondition(discussedinpreviousslide)isshowninfig10-4746

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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