Design Study on the Switched and Linear Operation of Broadband CMOS Class-E Power Amplifiers

136 Pages·2010·6.32 MB·English

by  Ronghui Zhang

Design Study on the Switched and Linear
Operation of Broadband CMOS Class-E
Power Amplifiers
Athesissubmitted tothe
FacultyofElectricalEngineering,MathematicsandComputerSciences
inpartialfulfillment oftherequirementsforthedegreeof
MasterofScienceinElectricalEngineering
at
elft niversity of echnology
D U T
by
Ronghui Zhang
Thesissupervisors:
Ir. MustafaAcar
Dr.-Ing. LeoC.N.deVreede
Dr.-Ing. MarkP.vanderHeijden
P.D.Eng. MelinaApostolidou
NXPSemiconductorsResearch
Eindhoven,TheNetherlands DelftUniversityofTechnology
Delft,TheNetherlands
August 2010

Abstract
Thisresearchworkaimstogainunderstandingofthepoweramplifier(PA)operatingasalinear
PA under low power drive conditions and as a switch-mode PA in high power drive conditions
both with the same Class-E load. Two approaches were taken here. Firstly, an analytical ap-
proachwasdevelopedtoinvestigatetheswitchingoperationofconventionalClass-Eamplifier.
The model used in the analytical approach takes into account the non-ideal switch resistance,
finite dc-feed inductance, finite loaded quality factor, and arbitrary switch duty-cycle. This ap-
proachpresentsanaccurateclosed-formexpressionformodelingClass-Epoweramplifier. Us-
ingthisapproach,thefrequencyresponseofconventionalClass-Epoweramplifierwasstudied
indetailandtheimpactoftheloadedqualityfactorandfinitedc-feedinductanceonthebroad-
band performance was analyzed. It shows that the Class-E PA with conventional load network
cannotprovidestableoutputpower,efficiency, andreliableoperatingvoltageconditionsacross
abroadfrequencyband(∆B> 40%). Inaddition,studyoftheloadimpedancesoftheamplifier
indicatesthattheClass-EPAissensitivetotheloadphaseangleatfundamentalfrequency.
In the second approach, a purely linear voltage-control current source was constructed numer-
ically as a way to represent the transistor. Based upon that model, the influence of non-ideal
drivesignalontheswitchingoperationwasstudied. Itshowsthatthepoweramplifierwithfinite
dc-feed inductance is tolerant to a non-ideal drive signal. For the rise and fall times of 25%T,
only 5% drop in drain efficiency was found for the optimum finite dc-feed inductance. The
performanceofthatmodelinlinearoperationwasalsoinvestigated. Theresultsagreewiththe
classicaltheoryforlinearpoweramplifiers.
The linearity (intermodulation distortion and 1dB compression point) was analyzed by using
a realistic transistor model (an extended drain NMOS). It shows that the Class-B biased PA
withfinitedc-feedinductancecanprovidenotonlysimilarIMD3featureastheoptimumClass-
AB biased PA with RF choke does, but also high efficiency simultaneously. Based upon this
device,asystematicdesignprocesswasappliedtoimplementabroadbandhighefficiencyClass-
EPA.ThePCBforthisbroadbandhighefficiencyClass-EPAwasfabricated. Goodagreement
was found between the simulation and measurement. The measurements indicated that the PA
achievesadrainefficiency> 67%andaPAE> 52%withaPout> 30dBmfrom560-1050MHz,
where the output power variation is within 1.0dB and efficiency variation is within 13%. The
highestefficiencyisobservedat700MHzfroma5.0Vsupplywithpeakdrainefficiencyof77%
and peak PAE of 65% at 31dBm output power and 17dB power gain. When using dynamic
supplymodulation,thePAachievesaPAEof40%andadrainefficiencyof60%at10dBpower
back-offacrossthefrequencyband500MHzto1100MHz.
Acknowledgements
I would like to take the opportunity to acknowledge to all the people who helped me in my
worksandlife.
MysinceregratitudeisdirectedtomydailysupervisorIr. MustafaAcaratNXPSemiconductors
Research. He actively instructed me through the entire project, shared the valuable knowledge
with me, offered useful support at every stage of the project, and answered all my questions
with great patience. I would like to thank my other two supervisors at NXP Semiconductors
Research: Dr.-Ing. Mark P. van der Heijden and P.D. Eng. Melina Apostolidou for the fruitful
discussions in daily work and the feedback during the monthly meetings. Also thanks Dr.-Ing.
AgneseBargagliforkindhelpinCadencesimulation.
I am deeply grateful to my supervisor Dr.-Ing. Leo C.N. de Vreede at Delft University of
Technology for providing me such a good opportunity to do this interesting research project at
NXP,forvisitingmyprogresspresentationsinEindhoven,andforreviewingmythesisreport. I
alsothankalltheM.Sc. ThesisCommitteemembersforreviewingthisreport.
My thanks are extended to all engineers at NXP Nijmegen, especially Michel de Langen and
Tennyson Nguty, for bonding the dies and assembling the boards. I would also like to express
my appreciation for the support I received from Jan Vromans in doing the measurements with
theLabviewsetup.
I would like to acknowledge my friends and teachers at Delft University of Technology of the
Netherlandswhowerekindlyhelpingmeduringmycourseworkandteachingmewiththebest
oftheirknowledge.
Iowemylovingthankstomyparents,mysistersandfriendsinChina. Theysupportedmevery
much during my study abroad. Without their encouragement and understanding it would have
beenimpossibleformetofinishthiswork.
RonghuiZhang
Eindhoven,TheNetherlands
August15th,2010
iv
Contents
Abstract iii
Acknowledgements iv
ListofFigures vii
ListofTables x
Nomenclature xi
1 Introduction 1
1.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 ThesisResearchGoal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.3 StateoftheArtReview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.4 ThesisOrganization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
2 Background 7
2.1 ParametersofPowerAmplifiers . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.1.1 OutputPower . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.1.2 PowerGain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.1.3 Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.1.4 Power-OutputCapability . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.1.5 Linearity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2 PowerAmplifierClassification . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.2.1 LinearPowerAmplifier . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2.2 SwitchingPowerAmplifier . . . . . . . . . . . . . . . . . . . . . . . . 14
3 Switch-ModeClass-EPowerAmplifierAnalyticalModeling 17
3.1 AnalyticalDerivationofClass-EPowerAmplifierModel . . . . . . . . . . . . 17
3.1.1 CircuitDescriptionandAssumptions . . . . . . . . . . . . . . . . . . 18
3.1.2 DerivationofClass-EAmplifierEquationswithInfiniteLoadedQuality
Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.1.3 DerivationofClass-EAmplifierEquationswithFiniteLoadedQuality
Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.2 AnalysisandDiscussionofClass-EPowerAmplifierModel . . . . . . . . . . 33
3.2.1 AccuracyComparisonbetweenAnalyticalApproachandADSSolution 34
3.2.2 EffectsofDrainLoadImpedancesonClass-EAmplifier . . . . . . . . 35
v
vi
3.2.3 BroadbandCharacteristicsofConventionalClass-EOutputLoadNetwork 45
3.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4 EffectsofDriveSignalandLinearOperationofClass-EPowerAmplifier 53
4.1 NumericalModelingofCMOSTransistor . . . . . . . . . . . . . . . . . . . . 54
4.2 EffectsofDriveSignalonClass-EPowerAmplifier . . . . . . . . . . . . . . . 58
4.3 LinearOperationofClass-EPowerAmplifier . . . . . . . . . . . . . . . . . . 60
4.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
5 BroadbandClass-EPowerAmplifierDesignBasedUponED-NMOSDevice 65
5.1 AnalysisofSwitchingandLinearOperationofED-NMOS . . . . . . . . . . . 65
5.1.1 DCI-VCharacteristicsandNon-LinearCapacitancesofED-NMOS . . 65
5.1.2 BondwiresSimulation . . . . . . . . . . . . . . . . . . . . . . . . . . 70
5.1.3 Switch-ModeOperationofED-NMOS . . . . . . . . . . . . . . . . . 71
5.1.4 LinearOperationofED-NMOS . . . . . . . . . . . . . . . . . . . . . 71
5.2 BroadbandClass-EPowerAmplifierDesign . . . . . . . . . . . . . . . . . . 75
5.2.1 OptimumLoadDesign . . . . . . . . . . . . . . . . . . . . . . . . . . 77
5.2.2 BroadbandOutputLoadNetwork . . . . . . . . . . . . . . . . . . . . 82
5.3 LayoutandPost-LayoutSimulations . . . . . . . . . . . . . . . . . . . . . . . 86
5.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
6 Measurements 97
6.1 TestSetup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
6.2 MeasurementResults . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
6.2.1 ComparisonofSimulatedandMeasuredResults . . . . . . . . . . . . 98
6.2.2 DynamicInverterGateBias . . . . . . . . . . . . . . . . . . . . . . . 101
6.2.3 DynamicSupplyVoltageforED-NMOSandInverter . . . . . . . . . . 102
6.2.4 Third-OrderIntermodulationDistortion . . . . . . . . . . . . . . . . . 103
6.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
7 ConclusionsandFutureWork 109
7.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
7.2 RecommendationsforFutureWork . . . . . . . . . . . . . . . . . . . . . . . . 110
A MapleCodeforAnalyticalAnalysis 111
Bibliography 121
List of Figures
1.1 Mixed-modeoutphasingamplifier . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 TopologiesofoutputloadnetworkforbroadbandClass-Epoweramplifiers . . 5
2.1 Blockdiagramofpoweramplifier . . . . . . . . . . . . . . . . . . . . . . . . 7
2.2 3rd-orderinterceptpointand1dBcompressionpointdefinitions. . . . . . . . . 10
2.3 Linearpoweramplifierschematic. . . . . . . . . . . . . . . . . . . . . . . . . 11
2.4 Waveforms of the gate-to-source voltage V , and drain current I of (a) Class
gs ds
A,(b)ClassB,(c)ClassAB,(d)ClassC. . . . . . . . . . . . . . . . . . . . . 12
2.5 Class-Fpoweramplifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.6 Class-Dpoweramplifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.7 Class-Epoweramplifier. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.1 Class-Eamplifier. (a)Basiccircuit. (b)Equivalentcircuit. . . . . . . . . . . . . 18
3.2 Generaldrainvoltageandcurrentwaveforms . . . . . . . . . . . . . . . . . . 19
3.3 Class-Eamplifierwithfiniteloadedqualityfactor . . . . . . . . . . . . . . . . 26
3.4 AnalyticaldesignflowchartofClass-Epoweramplifieratasinglefrequency. . 32
3.5 RelationsbetweentheelementsofthedesignsetK . . . . . . . . . . . . . . . 33
3.6 Class-Eamplifiercomponentsdesign:(a)foragivendevice,(b)foragivensup-
plyvoltage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.7 Class-EamplifierwaveformsforanalyticalapproachandADSsimulation . . . 34
3.8 Class-EmodelinADS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
3.9 ElementsofthedesignsetK , K ,K ,K asafunctionofq . . . . . . . . . . 36
P C L X
3.10 Drainefficiencyandpower-outputcapabilityasafunctionofq . . . . . . . . . 37
3.11 DrainloadimpedancesofClass-EPAs . . . . . . . . . . . . . . . . . . . . . . 37
3.12 Equivalentdrainloadimpedanceasafunctionofq: (a)fundamentalimpedance
interms of resistanceand reactance, (b)secondand thirdharmonics impedance
intermsofreactance,(c)fundamentalimpedanceintermsofmagnitudeandphase 38
3.13 Effects of load phase angle θ on: (a) drain efficiency and K , (b) maximum
1 P
drain-sourcevoltageandcurrent . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.14 Waveforms as a function of load phase angle θ : (a) drain-source voltage, (b)
1
switchcurrent . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.15 Effects of magnitude Z on: (a) drain efficiency and K , (b) maximum drain-
1 P
| |
sourcevoltageandcurrent . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.16 Waveformsasafunctionof Z : (a)drain-sourcevoltage,(b)switchcurrent . . 40
1
| |
3.17 Effects of load phase angle θ of second harmonic impedance: (a) drain effi-
2
ciencyandK ,(b)maximumdrain-sourcevoltageandcurrent . . . . . . . . . 42
P
3.18 Waveformsasafunctionofθ : (a)drain-sourcevoltage,(b)switchcurrent . . . 42
2
3.19 Effects of magnitude Z of second harmonic impedance: (a) drain efficiency
2
| |
andK ,(b)maximumdrain-sourcevoltageandcurrent . . . . . . . . . . . . . 42
P
vii
viii
3.20 Waveformsasafunctionof Z : (a)drain-sourcevoltage,(b)switchcurrent . . 43
2
| |
3.21 Effectsofloadphaseangleθ ofthirdharmonicimpedance: (a)drainefficiency
3
andK ,(b)maximumdrain-sourcevoltageandcurrent . . . . . . . . . . . . . 43
P
3.22 Waveformsasafunctionofθ : (a)drain-sourcevoltage,(b)switchcurrent . . . 44
3
3.23 Effectsofmagnitude Z ofthirdharmonicimpedance: (a)drainefficiencyand
3
| |
K ,(b)maximumdrain-sourcevoltageandcurrent . . . . . . . . . . . . . . . 44
P
3.24 Waveformsasafunctionof Z : (a)drain-sourcevoltage,(b)switchcurrent . . 44
3
| |
3.25 FundamentalimpedanceasafunctionoffrequencyfordifferentQ . . . . . . . 46
0
3.26 SecondharmonicimpedanceasafunctionoffrequencyfordifferentQ . . . . 46
0
3.27 Effectsoffiniteloadqualityfactoronthewidebandoperation . . . . . . . . . . 47
3.28 FundamentalimpedanceasafunctionoffrequencyfordifferentQ . . . . . . . 48
0
3.29 Effectsoffinitedc-feedinductanceonthewidebandoperation . . . . . . . . . 49
3.30 Effectsofduty-cycleonthewidebandoperation . . . . . . . . . . . . . . . . . 50
4.1 Simplifiedsmall-signalmodelofClass-Epoweramplifier . . . . . . . . . . . . 53
4.2 6th-orderpolynomialfunctionsfittingmeasuredI-Vcurves . . . . . . . . . . . 55
4.3 I-V curves created by Eq. 4.4 for g = 1, V = 0V, I = 1A, V = 0.05V
m TH max k
andλ = 0 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
4.4 NMOSsmall-signalequivalentmodel . . . . . . . . . . . . . . . . . . . . . . 56
4.5 S-parameters measured by Cadence and modeled S-parameters using extracted
modelparameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
4.6 NumericalmodelofClass-Epoweramplifier . . . . . . . . . . . . . . . . . . 57
4.7 Simulationmodel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.8 Testwaveformsofdrivesignaltogateterminal . . . . . . . . . . . . . . . . . 58
4.9 EffectsofdrivesignalontheperformanceofClass-Epoweramplifier . . . . . 59
4.10 Drain-sourcevoltageanddraincurrentwaveformsasafunctionofriseandfall
time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
4.11 Outputpoweranddrainefficiencyasafunctionofinputpowerforlinearoperation 61
4.12 VoltageandcurrentwaveformsofClass-AandBbiasingatq = 1.41 . . . . . . 62
4.13 Effects of dc-feed inductance for Class-E power amplifier at 1dB compression
pointwithdifferentgatebiasvoltages . . . . . . . . . . . . . . . . . . . . . . 63
4.14 Waveformsat1dBcompressionpointforq = 1.41 . . . . . . . . . . . . . . . . 64
5.1 Schematicsofactivedevice . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
5.2 Layoutofactivedevice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
5.3 DCI-Vmeasurementsetup . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
5.4 MeasuredDCI-VcurvesforVBN=VBP=0V . . . . . . . . . . . . . . . . . . 68
5.5 Schematicsofactivedevicewithparasiticcapacitance(red)extractedbyCadence 68
5.6 ED-NMOS device capacitances obtained by Cadence simulation for different
gatebiasvoltageV : (a)C ,(b)C ,(c)C . . . . . . . . . . . . . . . . . . . . 69
gs ds gd gs
5.7 Synthesizedtransistormodel . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
5.8 Bondwiresillustrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
5.9 Bondwiresequivalentcircuit . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
5.10 Switch-modeperformanceofED-NMOSusingsynthesizedmodel . . . . . . . 72
5.11 Largesignalperformanceoverpowersweepat1GHzfordifferentgatebiasandq 73
5.12 Simulateddrainefficiency,power-outputcapability,1dBcompressionpointand
powergainversusqforClass-A,AB,andBbiases. . . . . . . . . . . . . . . . . 75
ix
5.13 3rd-order intermodulation distortion as a function of output power for different
qat f = 1GHzwith∆f = 100kHz. . . . . . . . . . . . . . . . . . . . . . . . 76
0
5.14 Simulatedinverteroutputsignalat1GHz . . . . . . . . . . . . . . . . . . . . . 78
5.15 Calculatedsupplyvoltageandloadresistancefor P =31dBm . . . . . . . . . 79
out
5.16 Simulatedresultsasafunctionofqfordifferentα . . . . . . . . . . . . . . . . 80
5.17 Drain-sourcevoltageanddraincurrentwaveformsfordifferentα . . . . . . . . 81
5.18 Loadimpedanceasafunctionofqfordifferentα . . . . . . . . . . . . . . . . 82
5.19 Class-Epoweramplifierdesignflowchart . . . . . . . . . . . . . . . . . . . . 83
5.20 Effectsofloadphaseangleθ ontheperformanceofpoweramplifier . . . . . . 84
1
5.21 OptimumfundamentalloadimpedancesZ overfrequency . . . . . . . . . 84
L1opt
5.22 Idealoutputpower,drainefficiencyandPAEfortheidealoptimumloadimpedances 84
5.23 BroadbandoutputloadnetworkforthePA . . . . . . . . . . . . . . . . . . . . 85
5.24 Synthesizeddrainloadimpedancesasafunctionoffrequencywithideallumped
elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
5.25 Poweramplifierperformanceforthesynthesizedideallumpedelements . . . . 87
5.26 Drain-source voltage waveforms at different frequencies for the synthesized
ideallumpedelements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
5.27 FinalPCBlayout . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
5.28 DrainloadimpedancesforfinallayoutwithMuratacomponents . . . . . . . . 89
5.29 Post-layout simulation results of switch-mode operation over broad frequency
range. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
5.30 Drive signal waveforms tuning by gate bias voltages of NMOS and PMOS of
inverter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
5.31 Effectsofvariationsofduty-cycleontheperformanceofswitch-mode . . . . . 92
5.32 DCstaticgate-sourcebiasvoltageasafunctionofV andV . . . . . . . . . 93
BN BP
5.33 Post-layoutsimulationresultsoflinear-modeoperationat0.7GHz. . . . . . . . 93
5.34 Post-layoutsimulationresultsoflinear-modeoperationat0.8GHz. . . . . . . . 94
5.35 Post-layoutsimulationresultsoflinear-modeoperationat0.9GHz. . . . . . . . 94
5.36 Post-layoutsimulationresultsoflinear-modeoperationat1.0GHz. . . . . . . . 95
5.37 Post-layoutsimulationresultsoflinear-modeoperationat1dBcompressionpoint 95
6.1 PhotographofimplementedbroadbandClass-Epoweramplifier . . . . . . . . 97
6.2 BlockdiagramofthemeasurementsetupforbroadbandClass-Epoweramplifier 98
6.3 Comparisonofsimulatedandmeasuredperformanceoftheproposedbroadband
Class-E PA as a function of frequency: (a) output power, (b) power gain, (c)
drainefficiency,(d)poweraddedefficiency. . . . . . . . . . . . . . . . . . . . 99
6.4 BroadbandmeasurementofdynamicinvertergatebiasofClass-EPA:(a)output
power,(b)powergain,(c)drainefficiency,(d)poweraddedefficiency. . . . . . 101
6.5 MeasuredRFinputpowersweepat0.9GHzwithinvertergatebiasasaparam-
eter: (a) output power, (b) power gain, (c) drain efficiency, (d) power added
efficiency. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
6.6 Broadband measurement of dynamic supply voltage for ED-NMOS: (a) output
power,(b)drainefficiency,(c)poweraddedefficiency. . . . . . . . . . . . . . 103
6.7 Measured output power as a function of V at 900MHz with V as a pa-
DD2 DD1
rameter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
6.8 EfficiencyagainstoutputpowerforthesupplymodulationshowninFig.6.7: (a)
drainefficiencyvs.Pout,(b)PAEvs. Pout. . . . . . . . . . . . . . . . . . . . . 104
x
6.9 Measured drain efficiency and PAE with optimum supplies of ED-NMOS and
Inverter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
6.10 MeasureddrainefficiencyandPAEversusoutputpowerfortheoptimumsupply
voltagesofED-NMOSandInverterat: (a)0.5GHz,(b)0.6GHz,(c)0.7GHz,(d)
0.8GHz,(e)1.0GHz,and(f)1.1GHz. . . . . . . . . . . . . . . . . . . . . . . 105
6.11 MeasuredIMD3withVBN=VBPasaparameterat0.9GHz . . . . . . . . . . 106
6.12 MeasuredIMD3,drainefficiencyandPAEversusoutputpowerat: (a)0.5GHz,
(b)0.6GHz, (c)0.7GHz, (d)0.8GHz, (e)0.9GHz, (f)1.0GHz, (g)1.1GHz, and
(h)1.2GHz. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107