The document discusses the frequency response of amplifiers and how different circuit elements affect gain and phase shift at different frequencies. It introduces several key concepts: 1. The input, output, and bypass circuits each form RC networks that attenuate gain and introduce phase shift at lower frequencies. 2. The critical frequency is where gain drops by 3 dB (-3 dB point) and occurs when the capacitive reactance equals the resistance in each RC network. 3. Gain rolls off at -20 dB per decade below each critical frequency. Phase shift also increases at lower frequencies through each RC network. 4. Miller's theorem is used to analyze the effect of internal transistor capacitances at higher frequencies. The

1. Engr.Tehseen Ahsan
Lecturer, Electrical Engineering Department
EE-307 Electronic Systems Design
HITEC University Taxila Cantt, Pakistan
Amplifier Frequency Response (Part 1)

2. 10.1 Introduction
Previouslyweneglectedtheeffectsofinputfrequencyonanamplifier’soperationduetocapacitiveelementsinthecircuitinordertofocusonotherconcepts(inEE-205)
Thecouplingandbypasscapacitorswereconsideredtobeidealshortsandtheinternaltransistorcapacitanceswereconsideredtobeidealopens.Thistreatmentisvalidwhenthefrequencyisinanamplifier’smidrange.
Sincecapacitivereactanceisinverselyproportionaltotheinputfrequency.Whenthefrequencyislowenough,thecouplingandbypasscapacitorscannolongerbeconsideredasshortsbecausetheirreactancesarelargeenoughtohaveasignificanteffect.
2

3. 10.1 Introduction continue…
Also,whenthefrequencyishighenough,theinternaltransistorcapacitancescannolongerbeconsideredasopensbecausetheirreactancesbecomesmallenoughtohaveasignificanteffectonamplifieroperation.
Frequencyresponseofanamplifieristhechangeingainorphaseshiftoveraspecifiedrangeofinputsignalfrequencies.
3

4. Effect of Coupling Capacitors
Sincecapacitivereactanceisinverselyproportionaltofrequency.Atlowerfrequencies(AudioFrequenciesbelow10Hz)-capacitivelycoupledamplifierssuchasthoseinfigure10-1havelessvoltagegainthantheyhaveathigherfrequencies.ThereasonisthatatlowerfrequenciesmoresignalisdroppedacrossC1andC3becausetheirreactancesarehigher.Thishighersignalvoltagedropatlowerfrequenciesreducesthevoltagegain.AlsoaphaseshiftisintroducedbythecouplingcapacitorsbecauseC1formsaleadcircuitwithRinoftheamplifierandC3formsaleadcircuitwithRLinparallelRCwithorRD
RecallanRCcircuit(OutputvoltageacrossRleadstheinputvoltageinphase) 4

5. Effect of Coupling Capacitors continue.. 5

6. Effect of Bypass Capacitors
Atlowfrequencies,thereactanceofthebypasscapacitorC2infigure10-1,becomessignificantandtheemitter(orFETsourceterminal)isnolongeratacground.ThecapacitivereactanceXC2inparallelwithRE(orRS)createsanimpedancethatreducesthegain.
Forexamplewhenthefrequencyissufficientlyhigh,XC=OΩandthevoltagegainoftheCEamplifierisAv=RC/r'e.AtLowerfrequencies,XC>>OΩandthevoltagegainisAv=RC/(r'e+Ze)
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7. Effect of Internal Transistor Capacitors
Athighfrequenciesthecouplingandbypasscapacitorsbecomeeffectiveacshortsanddonotaffectanamplifier’sresponse.Internaltransistorcapacitances,howeverdocomeintoplay,reducinganamplifier’sgainandintroducingphaseshiftasthesignalfrequencyincreases.
Infigure10-3,inthecaseofBJT,Cbeisthebase-emitterjunctioncapacitanceandCbcisthebase-collectorjunctioncapacitance7

8. Effect of Internal Transistor Capacitors continue…
Atlowerfrequencies,theinternalcapacitanceshaveaveryhighreactancethereforetheylooklikeopensandhavenoeffectonthetransistor’sperformance.
Asthefrequencygoesup,theinternalcapacitivereactancesgodownandatsomepointtheybegintohaveasignificanteffectonthetransistor’sgain.
WhenthereactanceofCbebecomessmallenough,asignificantamountofvoltagedropislostduetovoltagedividereffectofthesignalsourceresistanceandthereactanceCbeasillustratedinfigure10-4(a)
WhenthereactanceofCbcbecomessmallenough,asignificantamountofvoltageisfedbackoutofphasewithinput(-vefeedback),thuseffectivelyreducingthevoltagegainasshowninfigure10-4(b)
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9. Effect of Internal Transistor Capacitors continue… 9

10. Miller’s Theorem
Itisusedtosimplifytheanalysisofinvertingamplifiersathighfrequencieswheretheinternalcapacitancesareimportant.
ThecapacitanceCbcbetweentheinput(base)andoutput(collector) isshowninfigure10-5(a)inageneralizedform.
AvistheabsolutevoltagegainoftheamplifierandCrepresentsCbc
Miller’stheoremstatesthatCeffectivelyappearsasacapacitancefrominputtogroundasshowninfigure10-5(b)thatcanbeexpressedasfollows:Cin(Miller)=C(Av+1)…..(1)
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11. Miller’s Theorem continue…
Equation1showsthatCbchasamuchgreaterimpactoninputcapacitancethanitsactualvalue.IfCbc=6pFandamplifiergainis50thenCin(Miller)=306pF.
Figure10.6showshowthiseffectiveinputcapacitanceappearsintheactualacequivalentcircuitinparallelwithCbe11

12. Miller’s Theorem continue…
Miller’stheoremalsostatesthatCeffectivelyappearsasacapacitancefromoutputtogroundasshowninFigure10.5(b),thatcanbeexpressedasfollows:Cout(Miller)=C(Av+1/Av)….(2)
Equation2indicatesthatifthevoltagegainis10orgreaterCout(Miller)=C=Cbcbecause(Av+1/Av)isapproximatelyequalto112

13. 10.2 The Decibel
Decibelsareaformofgainmeasurementandarecommonlyusedtoexpressamplifierresponse.
Thedecibelisalogarithmicmeasurementoftheratioofonepowertoanotheroronevoltagetoanother.
Powergainisexpressedindecibels(dB)asAp(dB)=10logApwhereApistheactualpowergain,Pout/Pin
Voltagegainisexpressedindecibels(dB)asAv(dB)=20logAv
IfAvisgreaterthan1,thedBgainispositiveandifAvislessthan1, thedBgainisnegativeandisusuallycalledattenuation. 13

14. O dB Reference
ItisoftenconvenientinamplifierstoassignacertainvalueofgainastheOdBreference.
Thisdoesnotmeanthatactualvoltagegainis1(0dB);itmeansthatthereferencegain,nomatterwhatitsactualvalue,isusedasareferencewithwhichtocompareothervaluesofgainandisthereassigneda0dBvalue.
Manyamplifiersexhibitamaximumgainoveracertainrangeoffrequenciesandareducedgainatfrequenciesbelowandabovethisrange.
Themaximumgainoccursfortherangeoffrequenciesbetweentheupperandlowercriticalfrequenciesandiscalledmidrangegain, whichisassigneda0dBvalue. 14

15. O dB Reference continue…
Anyvalueofgainbelowthisrangecanbereferencedto0dBandexpressedasanegativedBvalue.
Figure10-7illustratesanormalizedgain-versus-fequencycurveshowingseveraldBpoints.Thetermnormalizedmeansthatthemidrangevoltagegainisassignedavalueof1or0dB. 15Mid range voltage gain is 100Gainatacertainfrequencybelowmidrangeis50thusthereducedvoltagegaincanbeexpressedas20log(50/100)=20log(0.5)= -6dB

16. O dB Reference continue…
Table10-1showshowdoublingorhalvingvoltagegainstranslatesintodecibelvalues.Noticethateverytimethevoltagegainisdoubled,thedecibelvalueincreasesby6dBandeverytimethegainishalved,thedBvaluedecreasesby6dB. 16

17. The Critical Frequency
Alsocalledcutofforcornerfrequencyisthefrequencyatwhichtheoutputpowerdropstoone-halfofitsmidrangevalue.Thiscorrespondstoa3dBreductioninpowergain,asexpressedindBbyAp(dB)=10log(0.5)=-3dB
Theoutputvoltageis70.7%ofitsmidrangevalueatcriticalfrequencyandexpressedindBasAv(dB)=20log(0.707)=-3dB
Thevoltagegainisdownto3dBoris70.7%ofitsmidrangevalueandatthesamefrequency,thepowerisone-halfofitsmidrangevalue. 17

18. Power Measurement in dBm
ThedBmisaunitformeasuringpowerlevelsreferencedto1mW.
PositivedBmvaluesrepresentpowerlevelsabove1mWandnegativedBmvaluesrepresentpowerlevelsbelow1mW.
Each3dBmincreasecorrespondstoadoublingofthepower,anda3dBmdecreasecorrespondstoahalvingthepower.Seetable10-218

19. 10-3 Low Frequency Amplifier Response
“Wewillexaminehowthevoltagegainandphaseshiftofacapacitivelycoupledamplifierareaffectedbyfrequenciesbelow(belowmidrange)whichthereactanceofthecouplingcapacitorsbecometoolargetoneglect.” 19

20. BJT Amplifiers
AtypicalcapacitivelycoupledCEamplifierisshowninFigure10-8.
Assumingthatcouplingandbypasscapacitorsareidealshortsatthemidrangesignalfrequency,wecandeterminethemidrangevoltagegainusingequation(1),whereRc=RC∥RD
Av(mid)=Rc/r'e……(1) 20

21. BJT Amplifiers Continue…
TheBJTamplifierinfig10-8hasthreehigh-passRCcircuitsthataffectitsgainasthefrequencyisreducedbelowmidrange.
Thethreehigh-passRCcircuitsinlow-frequencyacequivalentcircuitisshowninFig10-9.
Unliketheacequivalentcircuitusedpreviouslywhichrepresentedmidrangeresponse(XC=OΩ),thelow-frequencyequivalentcircuitretainsthecouplingandbypasscapacitorsbecauseXCisnotsmallenoughtoneglectwhenthesignalfrequencyissufficientlylow. 21

22. The Input RC Circuit
TheinputRCcircuitisformedbyC1andtheamplifier’sinputresistanceasshowninfig10-10
Asthesignalfrequencydecreasesincreases.ThiscauseslessvoltageacrossRinbecausemorevoltageisdroppedacrossC1andconsequentlytheoverallvoltagegainoftheamplifierisreduced. 22

23. The Input RC Circuit Continue…
TheVbaseinfig10-10(neglectingtheinternalresistanceoftheinputsource)canbestatedas
Asmentionedpreviously,acriticalpointintheamplifier’sresponseoccurswhentheoutputvoltageis70.7%ofitsmidrangevalue.ThisconditionoccursintheinputRCcircuitwhenXC1=Rin23
Attenuation / Attenuation factor

24. Lower Critical Frequency
Theconditionwherethegainisdown3dBislogicallycalledthe-3dBpointoftheamplifierresponse;theoverallgainis3dBlessthanatmidrangefrequenciesbecauseoftheattenuationoftheinputRCcircuit.
Thefrequency,fc,atwhichthisconditionoccursiscalledlowercriticalfrequency(lowercutofffrequency,lowercornerfrequency)andcanbecalculatedasfollows: 24

25. 25

26. Voltage Gain Roll-off at low frequencies
TheinputRCcircuitreducestheoverallvoltagegainofanamplifierby3dBwhenthefrequencyisreducedtothecriticalvaluefc.
Asthefrequencycontinuestodecreasebelowfc,theoverallvoltagegainalsocontinuestodecrease.
Therateofdecreaseinvoltagegainwithfrequencyiscalledroll- off.
Foreachtentimesreductioninfrequencybelowfc,thereisa20dBreductioninthevoltagegain. 26

27. Voltage Gain Roll-off at low frequencies Continue…
Let’sconsiderafrequencythatisone-tenthofthecriticalfrequency(f=0.1fc).SinceXC1=Rinatfc,thenXC1=10Rinat0.1fcbecauseoftheinverserelationshipofXC1andfc.TheattenuationoftheinputRCcircuitis,therefore, 27

28. dB/decade
Aten-timeschangeinfrequencyiscalledadecade.
ForinputRCcircuit,theattenuationisreducedby20dBforeachdecadethatthefrequencydecreasesbelowthecriticalfrequency.
Thiscausestheoverallvoltagegaintodrop20dBperdecade.
Figure10-11showsagraphofdBvoltageversusfrequency.
28Frequencyisreducedtoone-hundredthoffc(atwo-decadedecrease)i. e,20log(0.01)=-40dB

29. 29

30. Phase Shift in the Input RC Circuit
Inadditiontoreducingvoltagegain,theinputRCcircuitalsocausesanincreasingphaseshiftthroughanamplifierasthefrequencydecreases.
Atmidrangefrequencies,thephaseshiftthroughtheinputRCcircuitisapproximatelyzerobecauseXC1=0Ω.
AtlowerfrequencieshighervaluesofXC1causesaphaseshifttobeintroducedandtheoutputvoltage(basevoltage),VboftheRCcircuitleadstheinputvoltageVin.
ThephaseangleinaninputRCcircuitisexpressedas(Recallaccircuittheory) 30

31. Phase Shift in the Input RC Circuit Continue…
AcontinuationofthisanalysisrevealsthatthephaseshiftthroughtheinputRCcircuitapproaches90˚asthefrequencyapproacheszero. 31

32. The Output RC Circuit 32Fig10-8isformedbyC3,theresistancelookinginatthecollectorandtheloadresistanceRL
ForRout,lookinginatthecollector,thetransistoristreatedasanidealcurrentsource(withinfiniteinternalresistance)
ThevenizethecircuittotheleftofcapacitorC3producesanequivalentvoltagesourceequaltothecollectorvoltageandaseriesresistanceequaltoRC

33. The Output RC Circuit Continue…
ThecriticalfrequencyoftheoutputRCcircuitisgivenby
TheeffectoftheoutputRCcircuitontheamplifiervoltagegainissimilartothatoftheinputRCcircuit.
Asthesignalfrequencydecreases,XC3increases.ThiscauseslessvoltageacrosstheloadresistancebecausemorevoltageisdroppedacrossC3.
PhaseshiftintheOutputRCCircuitThephaseangleintheoutputRCcircuitis33

34. 34

35. The Bypass RC Circuit 35Amplifier voltage gain Av=Rc/r'e
Amplifier voltage gain Av=Rc/(r'e+Ze)

36. The Bypass RC Circuit Continue…
36ThebypassRCcircuitisformedbyC2andtheresistancelookinginattheemitterRin(emitter) Rin(emitter)isderivedbyfirstapplyingThevenin’stheoremlookingfromthebaseofthetransistortowardstheinputsourceVin.Thisresultsinanequivalentresistance(Rth)andanequivalentvoltagesource(Vth(1))inserieswiththebaseasshowninfig10-16(c)nextslide.

37. The Bypass RC Circuit Continue… 37Rin(emitter) is determined with equivalent input source shorted and is expressed as

38. The Bypass RC Circuit Continue… 38LookingfromcapacitorC2, Rth/βac+r'eisinparallelwithRE
Thevenizingagain,wegettheequivalentRCcircuit.ThecriticalfrequencyforthisequivalentbypassRCcircuitis

39. 39

40. FET Amplifiers
Azero-biasedD-MOSFETamplifierwithcapacitivecouplingontheinputandoutputshowninfigure10-18,youhavelearnedpreviouslythatthemidrangevoltagegainofazero-biasedamplifieris
Thisisthegainatfrequencieshighenoughsothatthecapacitivereactancesareapproximatelyzero40

41. FET Amplifiers Continue…
Theamplifierinfig10-18hasonlytwohigh-passRCcircuitsthatinfluenceitslow-frequencyresponse.
OneRCcircuitisformedbytheinputcouplingcapacitorC1andtheinputresistanceasshowninfig-10-19.
ThesecondRCcircuitisformedbytheoutputcouplingcapacitorC2andtheoutputresistancelookinginatthedrain41

42. The Input RC Circuit
JustlikeBJTamplifier,thereactanceoftheinputcouplingcapacitorincreasesasthefrequencydecreaseswhenXC1=Rin,thegainisdown3dBbelowitsmidrange.Thelowestcriticalfrequencyis42

43. 43

44. The Output RC Circuit 44
2ndRCcircuitisformedbyacouplingcapacitorC2andtheoutputresistancelookinginatthedrain
JustlikeBJT,theFETisalsotreatedasacurrentsourceTheTheveninequivalentofthecircuittotheleftofC2

45. The Output RC Circuit Continue…
ThecriticalfrequencyforthisRCcircuitis
Thephaseangleinthelow-frequencyoutputRCcircuitis
Againatthecriticalfrequency,thephaseangleis45˚andapproaches90˚asthefrequencyapproacheszero.
TheeffectoftheoutputRCcircuitontheamplifier’svoltagegainbelowthemidrangeissimilartothatofinputRCcircuit. 45

46. 46

47. Reference(s) 47
Chapter 1O: “Electronic Devices”, by Thomas L .Floyd, 7thEdition.