EE 40458 Power Gain and Amplifier Designhscdlab/pages/courses/microwaves/EE...Power Gain •Power...
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EE 40458 Power Gain and Amplifier Design 10/31/2017
Transcript of EE 40458 Power Gain and Amplifier Designhscdlab/pages/courses/microwaves/EE...Power Gain •Power...
EE40458PowerGainandAmplifierDesign
10/31/2017
Motivation
• Briefrecap:– We’vestudiedmatchingnetworks(severaltypes,howtodesignthem,bandwidth,howtheywork,etc…)
– Studiednetworkanalysistechniques(matriceswithS,ABCD,…;flowgraphs,etc.)
– Butwhy?Ultimategoal:designacircuitthatdoessomethinguseful
• Amplifiersareagoodstartingpoint– Usefulformany(all?)systems– Fundamentalprinciplescanbeappliedtoothercircuits
Design/AnalysisApproach• Couldapproachdesignmanyways– “Regular”circuitdesign:useequivalentcircuitmodel(hybrid-π,Tmodel)
– We’lltakeanalternative:treatactivedeviceas(known)2-portS-matrix
• Thisapproachallowsustobemoregeneral(resultswillapplymorewidely)– Example:we’llbeabletoprojectwhatthehighestgainpossibleis,whetherornotthecircuitisstable(i.e.,willitoscillate?);notalwayssoobviousfromequivalentcircuitswithoutalotofwork
– Sidebonus:we’llgettoseewhatfeaturesofS-matricesaredesirableforcircuits;helpuschoosedevices
Amplifiers– It’s(Mostly)AboutGain
• Frompreviousclasses—ofcoursegainisthekeything• Butitisn’tquitesosimpleforhigh-frequencysystems• Recall:from“regular”circuitdesign:gainwas(mostly)voltagegainAv;sometimes(morerarely)currentgain– Butyoudon’treallyneedanamplifierforeitherofthese!
– Atransformercanproducevoltagegain(andalotofit…)
– Moregenerally,amatchingnetworktradesvoltagegainforcurrentgain(orvisa-versa)
• Whatdoamplifiersreallydo,then?– Powergainisthekeyfeature:notjustvoltageorcurrentinisolation
PowerGain
• Powergain:notquitesosimpleasitmightlook:
• OK—butwhatisPout andPin,exactly?Thereareseveral(useful)possibilities,weneedtobeclearwhichwemean–Withvoltage,currentgaintheseambiguitiesarelesstroublesome
Gain = PoutPin
PowerGain– Definitions• Sinceinput,outputpowercanbedefineddifferentways,
multipledefinitionsforpowergain(notjustonegain;thereareseveraldifferentalternatives!)
GP =PLPin
=Power delivered to load
Power delivered (absorbed by) network
GT =PLPavs
=Power delivered to load
Power available from source
GA =PavnPavs
=Power available from networkPower available from source
PowerGain- Comparisons• GP:“operatingpowergain,”
most obvious,butnotallthatuseful
• GA:“availablegain,”goodbaselineforcomparisons,showswhatperformanceispossible
• GT:“transducergain,”mostusefulinsystemcontext,analysis• What’sthedifferenceamongthese?
– Doyoucountwhatactuallygetsintothenetwork(Pin)orwhatcouldhavegottenin(Pavs)?
– Sameideaatoutput(PLvs.Pavs)– Degreeofmismatchisthe
difference
GP =PLPin
=Power delivered to load
Power delivered (absorbed by) network
GT =PLPavs
=Power delivered to load
Power available from source
GA =PavnPavs
=Power available from networkPower available from source
DistinctionsAmongPowerGainDefinitions
• Howmuchpoweristransferreddependsontheimpedances/reflectioncoefficients:
• Pin:powercarriedbya1,minusthatreflectedoff(b1)
• Pavs:what’sthemostpoweryoucouldgetfromthesource(ifitwereconjugately matched)?
• Pavn:what’sthemostpoweravailablefromS?
• PL:powerdissipatedinZL
NumericalComparisons?• Howdothesethreedefinitionscompareintermsof
magnitude?
• GA>GT (becausePL <Pavn frommismatch)• GP >GT (becausePin <Pavs…)• ButnotclearifGP,GA larger…dependsonrelativedegreeof
source,loadmismatch• Canderiveeachgainfromflowgraph:
GT =PLPavs
; GP =PLPin; GA =
PavnPavs
PowerGainExpressions• Powergains:
• Where:
GT =1− ΓS
2
1−ΓinΓS
S212 1− ΓL
2
1− S22ΓL2 =
1− ΓS2
1− S11ΓS
S212 1− ΓL
2
1−ΓoutΓL2
GP =1
1− Γin2 S21
2 1− ΓL2
1− S22ΓL2
GA =1− ΓS
2
1− S11ΓS2 S21
2 11− Γout
2
Γin = S11 +S12S21ΓL
1− S22ΓL
Γout = S22 +S12S21ΓS
1− S11ΓS
AmplifierDesign
• Withthesedefinitions,wecanstartdesigningforreal
• Severalusefulspecialcasesfordesigns:–Maximumgain– Specifiedgain(i.e.tradelowergainformorebandwidth)
– Lownoise• Let’sdoanexampleofeachonetoseehowtheywork
DesignforMaximumGain
• Formaximumgain:wanttoconjugately matchboththeinputandoutput—simultaneously
• Mathematically:
– Note:canworkwithreflectioncoefficientssinceZ<->G asa1-to-1map
– Also,inthiscase,GT =GA;maximizingpowerinandout
Γin = ΓS*
Γout = ΓL*
MaximumGainDesign,Cont.
• So:howtodesign?– Basicidea:
– Ourjob:• MakeinputmatchingnetworkpresentGs*=Gin
• MakeoutputmatchingnetworkpresentGL*=Gout
• (Soitisreallyjustaboutmakingmatchingnetworks—oncethecorrect“targets”forGS,GL arefound)
MaximumGainDesign,Cont.• Designapproach:knowinput,outputmustbeconjugately
matched.So:
• Butwealsoknow
• So:GS dependsonGL (andvisa-versa)– MustsolveforbothGS andGL simultaneously(asinglesolutionthat
satisfiesalltheconstraints)– Bookgoesthroughthealgebrainsomedetail…
Γin = ΓS*
Γout = ΓL*
Γin = S11 +S12S21ΓL
1− S22ΓL
Γout = S22 +S12S21ΓS
1− S11ΓS
MaximumGainDesign,Cont.• Bottomline:thereisauniquesolutionforGS andGL
Where:
ΓS =B1 ± B1
2 − 4 C12
2C1
ΓL =B2 ± B2
2 − 4 C22
2C2
B1 =1+ S112− S22
2− Δ
2
B2 =1+ S222− S11
2− Δ
2
C1 = S11 −ΔS22*
C2 = S22 −ΔS11*
Δ = S11S22 − S12S21 (det(S))
MaximumGainDesign,Cont.• So:whattodowiththis?• Find[S]of
amplifyingelement(transistor,usuallyplusbiasnetworks)
• ComputeGS,GL from[S]• Designinputmatching
networktogofromsourcetoGS
• DesignoutputmatchingnetworktogofromloadtoGL
Input&OutputMatching• So:maximumgainamplifierdesignisreallydesigningtwo
matchingnetworks:
Input&OutputMatching• So:maximumgainamplifierdesignisreallydesigningtwo
matchingnetworks:
SpecifiedGainDesign
• Keypoint:alreadyknowhowtodesignanamplifierwithmaximumgain.Whywouldweevergoforless?– Needspecificsignallevel– Morelikely:needmorebandwidththanmax.gaindesigncandeliver;togetbandwidth,needtogiveupsomethingelse
• Approach:lookatGT expression:
• Note:3basicterms(source,S21,andload)
GT =1− ΓS
2
1−ΓinΓS
S212 1− ΓL
2
1− S22ΓL2 =
1− ΓS2
1− S11ΓS
S212 1− ΓL
2
1−ΓoutΓL2
GT =GS ⋅GO ⋅GL
SpecifiedGainDesign,Cont.
• Butalittlecomplicated:GS dependsonload,GLdependsonsource
• Yuck.Solet’smakeasimplifyingassumption—that[S]isunilateral(e.g.S12 =0).ThenGin=S11 andGout=S22
• Netresult:
• Sohowcanweset/changethegain?Introduce(intentionally)mismatchatsourceand/orload
GS =1− ΓS
2
1− S11ΓS2 ; GL =
1− ΓL2
1− S22ΓL2
SpecifiedGainDesign,Cont.• Formaximumgain,conjugatematchatbothinputandoutput:GS=S11*,GL=S22*(remember,we’reassumingunilateral)
• SothemaximumGS,GL become:
• Itturnsout(read:aftermuchalgebra,youcanshowifyouareluckyandfactorthingsjustexactlyright)that:constant|GS|and|GL|plotascirclesintheGS andGL planes
GS,max =1
1− S112 ; GL,max =
11− S22
2
SpecifiedGainDesign,Cont.• Thesearethe“constantgaincircles”• Mathematically: gs =
GS
GS,max
; gL =GL
GL,max
CS =gsS11
*
1− (1− gs ) S112
RS =1− gs (1− S11
2 )1− (1− gs ) S11
2
CL =gLS22
*
1− (1− gL ) S222
RL =1− gL (1− S22
2 )1− (1− gL ) S22
2
Sourceside: Loadside:
C:coordinates(onimaginaryplane)ofcenterofcircleR:radius
SpecifiedGainDesign,Cont.
• So:ideaistofigureouthowmuchmismatchtointroduceatinput,outputtogetdesiredgain
• Totalgain:– DesignerchoosesGS,GL sothatGT comesoutatvaluedesired(butremember,GS≤GS,max;GL≤GL,max)
– Inprinciple,anycombinationisok(resultsinthecorrectgain)
– Butusuallywanttogetsomethinginexchangeforthetrade(e.g.bandwidth)
– Thatadditionaltradeiswheredesigninsightcomesin
GT =GS ⋅GO ⋅GL
Example:SpecifiedGain
• Example12.4inPozar isagoodexample• Summary:designanamplifierat4GHzwith11dBgain;trytomaximizethebandwidth– Given:transistorS-parameters:
• CancomputeGS,max;GL,max
Numerically:GS,max =2.29=3.6dB;GL,max =1.56=1.9dBGo=|S21|2 =6.25=8dB– Maxgain:13.5dB. Wecangiveup2.5dBincombinationofGS,GL
S = 0.75∠−120 02.5∠80 0.6∠− 70
#
$%
&
'(
GS,max =1
1− S112 ; GL,max =
11− S22
2
Example:SpecifiedGain(cont.)
• PickafewchoicesforGS,GL
• Plotthegaincircles:
• OK…• Remember:GS,max =3.6dBGL,max=1.9dB
• Options:– GS=3dB,GL=0dB
– GS=2dBGL=1dB
– Bothofthesesetsare2.5dBlessthanthemaximum,giveus11dBtotal
Example:SpecifiedGain(cont.)
• Howtochoose?• Tradeforsomething
else—likebandwidth
• Recall:forlargestbandwidth,matchingnetworkshouldnot“workhard”
• PickGS,GL nearestcenterofSmithChart—”laziest”matchingnetwork
• Ifpickroughlyequalinput,outputmatchingnetworks,overallBWmaximized(filtersincascade)
Example:SpecifiedGain(cont.)
LowNoiseAmplifierDesign
• Lastcase:lownoiseamplifier• Noiselimitsmanysystems(radio,wireline,fiberreceivers,etc.)
• Performancedominated(usually)byfirstamplifierincascade
• Unfortunatefact:bestnoiseperformancenotobtainedatmaximumgain.Havetomatchforeithernoiseorgain;atradeoffisinevitable
NoiseinTwo-PortNetworks
• Noiseinamplifiers(asrepresentedby2-portnetworks)canbequantifiedbynoisefactor:
– NoisefactorisameasureofhowmuchworsetheSNR(power)isattheoutputcomparedtotheinput,duetonoiseaddedbythenetwork
– Noisefactordependsoninputtermination(GS):
F = SNRinSNRout
F = Fmin +4RN
ZO
ΓS −Γopt2
(1− ΓS2 ) 1+Γopt
2
NoiseinTwo-PortNetworks
• Noisefactordependsoninputtermination(GS):
– Gopt,RN,Fmin are“noiseparameters”ofthedevice
• Canshow(ifyouarepatient)thatconstantFcontoursare(gasp)circlesintheGS plane:
• CF iscenter(complexplane),RF isradius
F = Fmin +4RN
ZO
ΓS −Γopt2
(1− ΓS2 ) 1+Γopt
2
CF =Γopt
N +1
RF =N(N +1− Γopt
2
N +1
N =ΓS −Γopt
2
1− ΓS2 =
F −Fmin4RN / ZO
1+Γopt2
LowNoiseAmplifierDesign
• Example12.5inPozar:– Designanamplifierwith2dBnoisefigureandmaximumgain(consistentwiththisnoiselevel)
– PlotNoisefigurecircles– NotethatnoisefigureisrelatedtoGS;butgainistoo(specifiedgain:GS term)
– Sowelookatbothconstantgainandnoisefigurecirclesonthesameplot:
LowNoiseAmplifierDesign(cont.)• Noisefigure:NF=2dBcircle• SeveralGS circles1.0,1.5,1.7dB
• Needtosatisfyboth:findintersectionbetweenNF,highestgainGScircle
• Whataboutoutput?Conjugately matchonceinputisfinalized
