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

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.

2 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. 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.

3 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.

4 S. Ben-Yaakov , DC-DC Converters [2- 9]Discontinuous Inductor Current Mode (DCM)SVinDLCRVxVocontrolzDifferent voltage transfer ratio DonzHigher ripple currenttILTsR4R3t'offtofftonR4>R34 Prof. 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.

5 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. S. Ben-Yaakov , DC-DC Converters [2- 14] BOOST Step-UpzVo > VinWhy ?

6 ?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.

7 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. 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.

8 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.

9 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.

10 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. 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 !