Prof. S. Ben-Yaakov , DC-DC Converters [2- 1] …

1 1 Prof. S. Ben-Yaakov , DC-DC Converters [2- 1] Buck Operation Voltage transfer Current modes (CCM, DCM) Capacitor Boost Operation Voltage transfer Buck-Boost Comparison between topologies Simulation of The simulations Basics of average model of Example: Boost average model simulationsBUCK, BOOST, BUCK-BOOST, DCMProf. S. Ben-Yaakov , DC-DC Converters [2- 2]Buck converter Constant Switching FrequencytONONONtONONON controlswitchtontoffTSssT1f=DorDTtonson =D1 DTtoffsoff =Switch frequency:Duty Cycle:SVinDLCR controlProf. S. Ben-Yaakov , DC-DC Converters [2- 3]Operation modesOnOffAt steady state Ia=IbSVinDLCRSVinDLCRVLILtstVin-Vo-VoIaI btSelf commutationVLILtstVin-VoIatCommutation2 Prof. S. Ben-Yaakov , DC-DC Converters [2- 4]In this caseInductor current waveform at steady stateLVVoin tontILtoffLVo I SVinDCRtontoffBuckProf.

2 S. Ben-Yaakov , DC-DC Converters [2- 5]Voltage transfer functionThe I methodLeft triangleonointLVVI = Right triangleoffotLVI = offoonointLVtLVV= onsonoffononinoDTttttVV==+=Independent of L !LVVoin tontILtoffLVo I Prof. S. Ben-Yaakov , DC-DC Converters [2- 6]-VoVLtofftVin-VotonTs+-At steady state, over one switching cycle: ;0VL=oninoDVV0SS= =+ +;t)VV(Sonoin =+;t)V(Soffo = SVinDCRtontoffVoVLVoltage transfer functionThe average voltage method3 Prof. S. Ben-Yaakov , DC-DC Converters [2- 7]Load Change with Fixed D tontILtoffTsHow will ILchange if R is getting smaller?SVinDLCR controlVoProf. S. Ben-Yaakov , DC-DC Converters [2- 8]tontILtoffTsR2R1R3 LVVoin LVo CCM - Continues Conductor Current ModeDCM - Discontinues Conductor Current Mode321 RRR<<Load ChangeProf. S. Ben-Yaakov , DC-DC Converters [2- 9]Discontinuous Inductor Current Mode (DCM)SVinDLCRVxVocontrolzDifferent voltage transfer ratio DonzHigher ripple currenttILTsR4R3t'offtofftonR4>R34 Prof.

3 S. Ben-Yaakov , DC-DC Converters [2- 10]tontILt'offTsIpkVoltage transfer function (DCM)The I methodoffoonoinpktLVtLVVI = =outonoutinoffVD)VV(D = + =)DD(TTLVV21T1 IoffonSonoinSAVRVIoAV=)VVV1(DTLVV21 IooinononoinAV + =2oinS2onoinLV2 VTD)VV(R= +=1 TDRL81L4 TDRVVs2ons2oninoProf. S. Ben-Yaakov , DC-DC Converters [2- 11]Boundary of CCM and DCMtonttoffTsLVo LVVoin ILL2 LminIavzFor CCM L > LminzIn BuckavpkoffminoI2 ItLV==soffsavoffominf2 DRfI2 DVL==Prof. S. Ben-Yaakov , DC-DC Converters [2- 12]ExampleA BUCK converter has a following characteristics: Output voltage: Output current: Input voltage: Frequency: Current mode: CCM Find: V5Vo=A10 IIavout==V10 Vin=kHz100fs= = === = ==5 Prof. S. Ben-Yaakov , DC-DC Converters [2- 13]ILtIavtIavIRICtACDCC apacitor currentCapacitor currentSVinDLCRILICIR controlVoRLCIII =zAssumption: V0has small rippleProf.

4 S. Ben-Yaakov , DC-DC Converters [2- 14]BOOST Step-UpzVo > VinWhy ??SVinDLCRVXVoProf. S. Ben-Yaakov , DC-DC Converters [2- 15]ONVL=VinOFFVL=Vin-VoVinLCRVoVinLCRVoO peration modesVLILtstVinIatVLILtstVinVin-VoIaIbtB oost6 Prof. S. Ben-Yaakov , DC-DC Converters [2- 16]toffTSVoVxtoffinooffoinD1 VVDVV= =SVinDLCRVXVoThe average voltage method;DVTtVV;VV;VV;0VV;0 VoffosoffoxininxinxinL===== =Voltage transfer functionProf. S. Ben-Yaakov , DC-DC Converters [2- 17]Voltage transfer functionThe I methodtonILtoffTstLVVino LVinI offinoonintLVVtLV = offooffonintV)tt(V =+ offinoD1VV=SVinDLCRVXVoProf. S. Ben-Yaakov , DC-DC Converters [2- 18]BUCK-BOOSTStep-Up Step-DownzFind Vo/VinHint: Average of Vx?SVinDLCRVoVX7 Prof. S. Ben-Yaakov , DC-DC Converters [2- 19]Comparison between basic topologies CCMSVinDLCRVoSVinDLCRVoSVinDLCRVoSDLB asic CellLabcSwitched inductorProf.

5 S. Ben-Yaakov , DC-DC Converters [2- 20]IintIintIintIotIotIotSource currentLoad currentBuckBoostBuck BoostContinues current -> Low ripple componentDiscontinues current -> High ripple component Input and Output CurrentsProf. S. Ben-Yaakov , DC-DC Converters [2- 21]ModulatorControleVDinVAssemblySwitche doV+ The simulation problem8 Prof. S. Ben-Yaakov , DC-DC Converters [2- 22] The problematic part : Switched Assembly Rest of the circuit continuous - SPICE compatible Only possible simulation :Time domain (cycle-by-cycle) -Transient The objective : translate the Switched Assembly into an equivalentcircuit which is SPICE compatible ModulatorControleVDinVAssemblySwitchedoV + The simulation problemProf. S. Ben-Yaakov , DC-DC Converters [2- 23]+ + bdcafCLoadRoutVinVLIbICIoutVoutVLoadRLoa dRfCfCLadcbCILIbIinVinVbonTLbILICIdcLBuc kBoostBoostBuck onT+ Average Simulation of PWM ConvertersProf.

6 S. Ben-Yaakov , DC-DC Converters [2- 24]Ton - switch conduction time Toff- diode conduction timeTDCM- no current time (in DCM)LabcbonTDCMToffTLcaThe Switched Inductor Model9 Prof. S. Ben-Yaakov , DC-DC Converters [2- 25]The concept of average signalstttaIbIcIbIaIcIbcaLonToffTaIbIcIT he Switched Inductor Model (SIM) (CCM)Prof. S. Ben-Yaakov , DC-DC Converters [2- 26] bca?aIcIbIbcaLonToffTaIbIcIThe SIM Objective : To replace the switched part by a continuous networkProf. S. Ben-Yaakov , DC-DC Converters [2- 27]IbILIbIONTSTonLSonLbDITTII==SONonTTD= offLSoffLcDITTII==LaII=Similarly :bcaLonToffTaIbIcIAverage current10 Prof. S. Ben-Yaakov , DC-DC Converters [2- 28]bcbIcIaaGbGcGaIbcaLaII=onLbDII =offLcDII = Ga, Gb,Cc - currentdependent sources offLconLbLaDIGDIGIG Toward a continuous modelProf. S. Ben-Yaakov , DC-DC Converters [2- 29]LIDerivingLVtLILIVLVLVLILILVdtIdLVdtd ILLLL= =Average inductor currentProf.

7 S. Ben-Yaakov , DC-DC Converters [2- 30]bcaL)b,a(V)c,a(VLV()b,aV()c,aVonToffT sToffonSoffonLD)c,a(VD)b,a(VTT)c,a(VT)b, a(VV + == + =Average inductor current11 Prof. S. Ben-Yaakov , DC-DC Converters [2- 31]bcaaGbGcGLLrLILELVT opology independent !offonLD)c,a(VD)b,a(VE + =offLcDIG =onLbDIG =LaIG=bcaLonToffTThe Generalized Switched Inductor Model(GSIM)Prof. S. Ben-Yaakov , DC-DC Converters [2- 32]1. The formal approachbcaaGbGcGoRoCinVoVLELIL)b,a(V)c, a(VLroff0onin0LD]V0[D]VV[E + =offconbaD)L(IGD)L(IG)L(IG = ==ExampleImplementation in Buck TopologySVinDLVoRoCobcaProf. S. Ben-Yaakov , DC-DC Converters [2- 33]2. The intuitive approach - by inspection LoCoRinVoVLIinEbGSLoCoRinVDoVPolarity: (voltage and current sources) selected by inspectionLoinVVE onininDVE =onLbDIG =Implementation in Buck Topology12 Prof. S. Ben-Yaakov , DC-DC Converters [2- 34]SLoCoRinVDoVLoCoRinVoVooffVD offLDI Emulate average voltage on inductor sourcescurrentdependentICreateLBoostProf .

8 S. Ben-Yaakov , DC-DC Converters [2- 35]LoCoRinVDoVLoCoRinVoVooffoninVDDV + offLDI onLDI Buck-BoostProf. S. Ben-Yaakov , DC-DC Converters [2- 36]LoCoRinVoVLrcrdsonRbcaSIMP artially accounting for parasitics13 Prof. S. Ben-Yaakov , DC-DC Converters [2- 37]inVdsonRbcaGbGcGoCoRcraLLrLILELV offcaonbaLD)VV(D)VV(E + =offLcDIG =onLbDIG =LaIG=Modified Average ModelProf. S. Ben-Yaakov , DC-DC Converters [2- 38]ILand Donare time dependent variables {IL(t), Don (t) }Donis not an electrical variableonDLIbGLLIM aking the model SPICE compatibleProf. S. Ben-Yaakov , DC-DC Converters [2- 39] Donis coded into voltage+ SourceonD"D":nodeofNameon)L(I)D(Von LGvalueIn SPICE environment14 Prof. S. Ben-Yaakov , DC-DC Converters [2- 40]Running SPICE simulationDC (steady state points) - as isTRAN (time domain) - as isAC ( small signal) - as is* Linearization is done by simulator !

9 SimulationProf. S. Ben-Yaakov , DC-DC Converters [2- 41]LIbcaLonToffTonToffToffTsTtpkLILI onsonsoffD1 TTT'D = =onsoffTT'T =Discontinuous Model (DCM)Prof. S. Ben-Yaakov , DC-DC Converters [2- 42] average inductor current in DCMLV)b,a(V)c,a(VsTonToffToff'TtbcaL)b,a (V)c,a(VonTCCM inasD)c,a(VD)b,a(VVoffonL+=Combining CCM / DCM15 Prof. S. Ben-Yaakov , DC-DC Converters [2- 43]bcaaGbGcGaIbIcItonToffTLSILIsTLIoffon LoffonsLLsDDITTTII+=+=LaIisI LscbIsamplingareIisI offcTduringsampledisI onbTduringsampledisI Combining CCM / DCMProf. S. Ben-Yaakov , DC-DC Converters [2- 44]bcaaGbGcGaIbIcILaIG=offononLbDDDIG+=o ffonoffLcDDDIG+=1)DD(:CCMinoffon=+tonTof fTLSILIsTLIC ombining CCM / DCMProf. S. Ben-Yaakov , DC-DC Converters [2- 45]onToffTLIoff'TLVabtLVacpkILILT)b,a(VI onpk=SoffononLT)TT(LT)b,a(V21I+ =)DD(Lf2D)b,a(VIoffonsonL+=ononsLoffDD)b ,a(VLfI2D =onoffD1D = onoffD1D Doff in DCM16 Prof.

10 S. Ben-Yaakov , DC-DC Converters [2- 46]bcaLbcaaGbGcGLaIG offononLbDDDIG+ offonoffLcDDDIG+ offonLD)c,a(VD)b,a(VE + = =ononsLonoffDD)b,a(VLfI2),D1(minDLLrLILE LVThe combined DCM / CCM mode Prof. S. Ben-Yaakov , DC-DC Converters [2- 47]Example: Boost average model simulationRsw{Rsw}EDoffmin(2*I(Lmain)*Lm ain/(Ts*v(a,b)*V(Don))-V(Don),1-V(Don))e tableOUT+OUT-IN+IN-Resr{Resr}GcV(Doff)*I (Lmain)/(V(Don)+V(Doff))GVALUEOUT+OUT-IN +IN-PARAMETERS:LMAIN = 75uCOUT = 220uRLOAD = 10 DoffGbV(Don)*I(Lmain)/(V(Don)+V(Doff))GV ALUEOUT+OUT-IN+IN-0 Lmain{Lmain}RLoad{RLoad}DbreakDmainVDon{ VDon}+-Rinductor{Rinductor}EL(V(Don)*V(a ,b)+V(Doff)*V(a,c))EVALUEOUT+OUT-IN+IN-1 0 PARAMETERS:FS = 100kTS = {1/fs}bVin_DC{Vin_DC}+-aCout{Cout}PARAME TERS:RESR = = = :VIN_DC = 10vVDON = (Lmain)GVALUEOUT+OUT-IN+IN-DonSLoCoRinVD oVProf. S. Ben-Yaakov , DC-DC Converters [2- 48]Example: Boost average model simulation17 Prof.