， Iftheaspectratioofanenhancementn-channelMOSFETis4μm/1μm,(therelativemodelparameterscanbeseeninTable1.1)thevoltagesofdrain,gate,sourceandbulkare3V,2V,0Vand0Vrespectively,calculatethedraincurrentinthisdevice.Thengiventheresultofanotherp-channelMOSFET,whosevoltagesofdrain,gate,source,andbulkare-3V,-2V,0Vand0Vrespectively.(V=0)00VK11050γ00λ0040010050012|Φ00VSoVDS=3V，VGS=2V，VSB=0VVTHNVTH0I1K'W )2(1 N 1*110*

2

N

*(20.7)(10.04*SoVSD=3V，VSG=2V，VSB=0VVTHPVTH0I1K'W )2(1V P 1*50*

2

P

*(20.7)(10.05* Findthesmall-signalmodel(gm,gmb,gds)forann-channeltransistorwiththedrainat4V,gateat4V,sourceat2V,andthebulkat0V.AssumethemodelparametersfromTable1.1,andW/L=10μm/1μm.2FVTVT02FVT0.70.4[0.72.00.7]KI v)2(1v I11010610(21.02)2(10.42)570 2K2KWID211010610211010610570 m2(2

2(0.7

136gdsgds5701060.04 CurrentIdsinatransistoris62.5Awhenitsgate-sourcevoltageis1V.Thecurrentis1mAwhenV=2.5V.Whichtransistoroperatingregion(linearorsaturated)dothesevaluesofVcorrespondCalculateandVTforgivenFigureBothV1andV2arelargerthanVT,1VT2.5VT

)2

)2 ItcanbederivedfromaboveequationsVTN500A/V ShowthattwoMOStransistorsconnectedinparallelwithchannelwidthsofW1andW2andidenticalchannellengthsofLcanbemodeledasoneequivalentMOStransistorwhosewidthisW1+W2andwhoselengthisL,asshowninFig.1.2.Assumethetransistorsareidenticalexceptfortheirchannelwidths.

ForVDSVGS

1V2 OX 2 W2 1V2 OX 2 Wn 1V2 OX 2 W1W2 Wn 1V2 2ForVDSVGSI 1

Thustheequivalentlength=Landtheequivalentwidth=W1+W2+…+1-5.ShowthattwoMOStransistorsconnectedinserieswithchannellengthsofL1andL2andidenticalchannelwidthsofWcanbemodeledasoneequivalentMOStransistorwhosewidthisWandwhoselengthisL1+L2,asshowninFig.1.5.Assumethetransistorsareidenticalexceptfortheirchannellengths.Ignorethebodyeffectandchannel-lengthmodulation.

M

FigureGGS

D SWhenVGS<VTHandVGE<VGS<VTH,theMOSFETsareincutWhileM1operatesintriode(VDE<VGE–VTHN),thatisequivalenttoVDE+VES<VGE+i.e.VDS<VGSThusM2operatesintriode, 1ID1nCOXL[(VGEVTH)VDE2VDE]1W 1V22ID2nCOX 2 2VDSVDEV

ID1ID2 Itcanbederivedfromequations(1),(2),(3),(4)and(5) 1V2L2 V)1 2

1

1V2

2 SowecangetID

2VDS(3)WhileM1operatesinsaturation(VDE>VGE–VTHN).ItmeansVDE+VES>VGE+VES–VTHN,VDS>VGSVEVG–VGEVG–VTHNitmeansVESVGS–VTHN。M2operatesintriode. 1

W

2nOX 1L 1 1L

2 2nVDSVDEV

2

ID1ID2 Itcanbederivedfromequations(1),(2),(3),(4)and(5)I1 1 2nOX1

ThatjustlikeaMOSFEToperatinginsaturation,whichhasalengthofL1+L2andawidthofItcanbedeductedsimilarlythatnMOSFETsinseriesactsasaMOSFETwithanaspectrationofW/(L1+L2+…Ln).1-6.A)Fig.1.3showstherealandidealI-VcharacteristicsoftwoenhancementN-MOSFETsbyreallineandbrokenlinerespectively.ComparethedifferenceofthetwoMOSFETsandexinwhydifferent. FigureB)InTable1.1,whyisγPgreaterthanγNforan-well,CMOSVGS1——longchanneldeviceVGS2——ShortchanneldeviceTheexpressionforγ Becauseγisafunctionofsubstratedo,ahigherdoresultsinalargervalueforγ.Ingeneral,forannwellprocess,thewellhasagreaterdoconcentrationthanthesubstrateandthereforedevicesinthewellwillhavealargerγ.That’swhyγPisgreaterthanγN.，F(xiàn)igure3.1illustratesasource-degeneratedcurrentsource.UsingTable3.1modelCalculatetheoutputatthegivencurrentCalculatetheminimumoutputvoltagerequiredtokeepthedevicein++-VGGr

Figure 2.5106

2KWNL2110A2KWNL2110AV221

10.2Aroutrrds2gm2gmbs2rds2rgm2rds2r 2 2110AV2 21orthemoreaccuratesolutioncanbederivedroutrrds2gm2gmbs2rds221.725106WhileVDS≥VGS–VTHandVGS>VTH,MOSFETworksinsaturationvDSMIN=VGSID1KN'WID1KN'W L10111021Calculatetheoutput andtheminimumoutputvoltage,whilemaintainingalldevicesinsaturation,forthecircuitsshowninFigure3.2.AssumethatiOUTisactually10μA.UseTable3.1fordevicemodelinformation.AA+ -Figurevout(min)VGS3VGS4VT2VGS3 VT4VTVGS3 +-DesignM3andM4ofFigure3.3(a)sothattheoutputcharacteristicsare+-

+-

FigureFor

'ii

InFig.3.5a),Thusto

i3i45Aiout10A33

L

2LW L

1W2L2L

142 InFig.3.5b)i4=i3=1WV42WV121V424V1 V4 1V V 2V1VG4VTVG2VG4VTVMINAndwegetVMINinFig.3.5(a):VMINVG2VG4VT2V1InFig.3.5(a):i4i3

andV41V421WV1L L 2LW 1WV1 L 2L1V4V4 V1 For V1

4 V4 W L

1W8L8L

148 AsthecircuitsshowninFigure3.4,IREF=0.3mAandγ=0.UsingthemodelparametersinTable3.1,CalculatethevoltageVbwhenXY40/0.5IfVbis100mVsmallerthanthevaluein(a),calculatethedeviationXY40/0.5Figure 0.7 (l0.5u)(l1u)

0.0420.08V

1 0.3103 2.229106 10.08，4-1.ThecircuitshowninFigure3.1illustratesasingle-channelMOSresistorwithaW/Lof2μm/2μm.UsingTable3.1modelparameterscalculatethesmall-signalon oftheMOStransistoratvariousvaluesforVSandfillinthetablebelow.(Notethatthetransistorwasinlinearregion)Theequationforthresholdvoltageisrepresentedwithabsolutevaluessothatitcanbeappliedton-channelorp-channeltransistorswithoutconfusion.2FVTVT02FID/ Forn-channelVT00.70.42F0.7KWhenVS0,VGS5andVSB2F2VTVT02F2r

WhenVS1,VGS4andVSB2F2VTVT02F2r

WhenVS2,VGS3andVSB2F2VTVT02F2r

WhenVS3,VGS2andVSB2F2VTVT02F2r

WhenVS4,VGS1andVSB2F2VTVT02F2VGSVTThedeviceiscutoff,soronWhenVS5,VGS0andVSBThedeviceiscutoff,soron4-2.AnactiveresistivevoltagedividerwasshowninFigure3.2.IfVDD=5V,VSS=0V,VOUT=2.5V,I=15μA,usingmodelparametersinTable3.1,determinetheW/LratioofM1andM2.Assumeλ=0.

FigureI

2

(L)1(VGS1-VTN

(L)2(VGS2-VTP(W)

2 L

K -V

100(2.5 W )

2 L

K -V

50(2.5 4-3.Figure4.3illustratesvariouswaystoimplementthelayoutofaresistordivider.Choosethelayoutthatbestachievesthegoalofa2:1ratio.ExinwhytheotherchoicesarenotFigureOptionAsufferstheOrientationofthe2Rresistorispartlyorthogonaltothe1Rresistor.Matchedresistorsshouldhavethesameorientation.Resistorsdonothavetheappropriateetchcompensating(dummy)resistors.Dummystripesshouldsurroundallactiveresistors.OptionBsuffersthe Resistorsdonothavetheappropriateetchcompensating(dummy)resistors.Dummystripesshouldsurroundallactiveresistors.ResistorsdonotshareacommoncentroidastheyOptionCsufferstheResistorsdonotshareacommoncentroidastheyUncertaintyisintroducedwiththeadditionalnotchatthecontactOptionDsuffersthe Resistorsdonothavetheappropriateetchcompensating(dummy)resistors.Dummystripesshouldsurroundallactiveresistors.OptionEsufferstheOptionFsufferstheViolatestheunit-matching Resistorsdonothavetheappropriateetchcompensating(dummy)resistors.Dummystripesshouldsurroundallactiveresistors.ResistorsdonotshareacommoncentroidastheyClearly,option(e)isthebest5-1.DeterminethecurrentIinFigure5.1andcalculateitsTC(TemperatureCoefficient)usingCN20processshowninTable5.1.NeglectoxideencroaentandassumethatM5isoperatinginthesaturationregion.Allunlabeledn-channelsare15/5andallunlabeledp-channelsare70/5.AssumeResistorRispolysiliconandhasatemperaturecoefficientof1500ppm/℃,thresholdvoltageVThasatemperaturecoefficientof2.3103V/CFigure UsingCMOS20NMOSmodel, 1 I2I42I22VT12

Themoreaccuratesolutioncanbederived I2I42I22 1R R 3 1R R 83010 2R2

50AV2100830103

2 I2 1R 2 1 1d

1 1TCF I I

R

R 2 2VT11 12

RdT

2.3103VC1 1 1 FTC T 4271ppm/FVT R

R 5-2.DetermineVref(OutputVoltage)inFigure5.2andtheconditionsunderwhichtheTCofVrefiszero.AssumeallPMOStransistorsareidenticalandallNMOStransistorsare

IVBEVTlnSForthecircuitinFig.2,weVrefLlnKVTVBE(D3)Vrefisdependentontemperatureandwe

Figure

LlnK

VdVT0.085mV

andVBE(D3)

2mVLetVrefhaszerotemperaturecoefficientand

LlnK

VBE(D3)Ll·

0,orTCVref0AssumingK=10，thecorrespondingL＝10.2≈10IfI=10uA，Is=10-15AUndertheseconditionstheVrefthathaszeroTCVrefLlnKVTVBE(D3)，5-1.Judgethetypeofeachsingle-stageamplifiershowninFigure5.3,andcalculatethesmall-signalgainofeachcircuit,assumingγ=0.V V

FigureAg(r/ //1 m1

A gm2(ro1//ro2

/

gr

rm2

m2o1

CommonGateAgm1RDro1A R 5-2.ConsiderthecircuitofFigure5.4with(W/L)1=20/0.5,I1=1mA,andIS=0.75mA.AssumingVDD=3V,andλ=0,calculatetheratioof(W/L)2thatcesM1attheedgeofthetrioderegion.Whatisthesmall-signalgainunderthiscondition?ThedeviceparametersaregiveninTab.5.2.FigureVinVTH1 0.7 M1operatesattheedgeofthetrioderegionVoutVinVTH11.310.7III1 PCox(L)2 TH I 1103()2 5.2 C 1001043.8103(30.612P TH 20/ Am1 10.37V/g 100 gNMOS

GVSB=0GCJ中的冪指6-1.AssumethatW/LratiosofFigure6.1are(W/L)1=2μm/1μmand(W/L)2=(W/L)3==1μm/1μm.FindthedcvalueofvINthatwillgiveadccurrentinM1of110μA.CalculatethesmallsignalvoltagegainandoutputusingtheparametersofTable6.2.Assume 2KN(L)1 1101(110)2 VinID3ID4100ID2ID1ID310Agm1

Figure

11021102

1 g，CalculatethedifferentialtransconductancegmdandthedifferentialvoltagegainAvofann-channelinputdifferentialamplifiershowninFigure6.2,withtheparametersshownintable6.2.ConsiderIss=100μA,andW1/L1=W2/L2=W3/L3=W4/L4=1.Assumingallthechannellengthsareequalto1μm,andVDD=5V.IfW1/L1=W2/L2=10W3/L3=10W4/L4=10,repeatthe Figurea)WWW

WL L L L gmdgm1gm2 Av

Wb)L

W10W10 L L L gmdgm1gm2 Av

73.71V/ Calculatetheum(VIC(max))andtheminimuminputcommon-mode(VIC(min)),andtheinputcommonmodevoltagerange(ICMR)ofann-channelinputdifferentialamplifiershowninFigure6.2,withtheparametersshownintable6.2.AssumeallMOSFETsareinsaturation,allthe(W/L)sareequalto10μm/1μm,ISS=10μA,andVDD=5V.Findthevalueoftheunloadeddifferential-transconductance,gmd,andtheunloadeddifferential-voltagegain,Av,forthep-channelinputdifferentialamplifierofFigure6.4whenISS=10μAandISS=1μA.Whatistheslewrateofthedifferentialamplifierifa100pFcapacitorisattachedtotheoutput?AssumingW1/L1=W2/L2=W3/L3=W4/L4=1,andallthechannellengthsareequalto1μm.UsethetransistorparametersofTable6.2. FigureGivengmdgm1gm2Av

49.69V/Given

gmdgm1gm2Av

ThecircuitshowninFigure6.5calledafolded-currentmirrordifferentialamplifierandisusefulforlowvaluesofpowersupply.AssumethatallW/Lvaluesofeachtransistoris100.Usingtheparametersshownintable6.2,Findtheuminputcommonmodevoltage,VIC(max)andtheminimuminputcommonmodevoltage,VIC(min).Keepalltransistorsinsaturationforthisproblem.Whatistheinputcommonmodevoltagerange,Findthesmallsignalvoltagegain,vout/vin,ifvin=v1-Figurev1(max)VGS3VTN0.7 0.7VICMRv1(max)v1(min)1.4950.9302c.)Avgm1(ro2//ro4//ro7)116.5V/NMOS

VSB=0GCJ中的冪指CJSW，Exercise2-1.AnNMOSwithW=50μmandL=0.5μmoperatesinthesaturatedregionanditslayoutisfoldedshownasFig.2-1.CalculatetheallcapacitancesbyusingtheparametersinTable2-1andCox=3.8×10-3F/m,VR=0.6V.Assumethattheminimumsize(lal)ofS/DregionisCj00.56103F/m2,Cjsw00.351011F/m,mj0.45,mjsw 0.4109F/m,W50m,L0.5m,L0.08m,E1.5106 V0.6V,20.9V, 3.8103F/m2,

11.98.851012F/m,q1.61019Cj

Cj)/2 )

RFRF

L Cd

W

2(W

16.9

2(W

2(W

)33.7 2(WC)20.0 2WL 63.1 eff 2-2.ThereisanN-typecurrentsource,IDis0.5mA,andthedrain-sourcevoltageVDSmustlessthan0.4Vwhenitworksasacurrentsource.Iftheminimumoutput is20KΩ,determinethelengthandwidthofthedevicebyusingtheparametersinTable2.1.r

o o

Fromthetable2.1,LcanbedeterminedasLeffL2LD0.5m20.08mCalculatingI1 W V-V L2 nL2

47 C