Buck Boost

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<p>1Prof. S. Ben-Yaakov , DC-DC Converters [2- 1]2.1 Buck converter2.1.1 Operation modes2.1.2 Voltage transfer function2.1.3 Current modes (CCM, DCM)2.1.4 Capacitor current2.2 Boost converter2.2.1 Operation modes2.2.2 Voltage transfer function2.3 Buck-Boost converter2.4 Comparison between topologies 2.5 Simulation of SMPS2.5.1 The simulations problem2.5.2 Basics of average model of SMPS2.5.3 Example: Boost average model simulationsBUCK, BOOST, BUCK-BOOST, DCMProf. S. Ben-Yaakov , DC-DC Converters [2- 2]Buck Converter Constant Switching FrequencytON ON ONtON ON ONcontrolswitchtontoffTSssT1f =D or DTtonson =D 1 DTtoffsoff =Switch frequency:Duty Cycle:SVin DLCRcontrolProf. S. Ben-Yaakov , DC-DC Converters [2- 3]Operation modesOnOffAt steady state Ia=IbSVin DLCRSVin DLCRVLILtstVin-Vo-VoIaIbtSelf commutationVLILtstVin-VoIatCommutation2Prof. S. Ben-Yaakov , DC-DC Converters [2- 4]In this caseInductor current waveform at steady stateLV Vo in tontILtoffLVoI SVinDCRtontoffBuckProf. S. Ben-Yaakov , DC-DC Converters [2- 5]Voltage transfer functionThe I methodLefttriangleono intLV VI = RighttriangleoffotLVI = offoono intLVtLV V=|.|</p> <p>\| onsonoff ononinoDTtt ttVV= =+= Independent of L !LV Vo in tontILtoffLVoI Prof. S. Ben-Yaakov , DC-DC Converters [2- 6]-VoVLtofftVin-VotonTs+-At steady state, over one switching cycle:; 0 VL =oninoDVV0 S S = = + +; t ) V V ( Son o in =+; t ) V ( Soff o =SVinDCRtontoffVoVLVoltage transfer functionThe average voltage method3Prof. S. Ben-Yaakov , DC-DC Converters [2- 7]Load Change with Fixed D tontILtoffTsHow will ILchange if R is getting smaller?SVin DLCRcontrolVoProf. S. Ben-Yaakov , DC-DC Converters [2- 8]tontILtoffTsR2R1R3LV Vo in LVoCCM - Continues Conductor Current ModeDCM - Discontinues Conductor Current Mode3 2 1R R R &lt; Lminz In Buckav pk offminoI 2 I tLV= =soffs avoff ominf 2D Rf I 2D VL = =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: V 5 Vo = A 10 I Iav out= =V 10 Vin = kHz 100 fs =minLH 2 . 110 10 25 . 0 5f I 2D VL5 . 0 D 1 DCCM5 . 0 DVV5s avoff ominon off onino = = == = = =5Prof. S. Ben-Yaakov , DC-DC Converters [2- 13]ILtIavtIavIRICtACDCCapacitor currentCapacitor currentSVinDLCRILIC IRcontrolVoR L CI I I =z Assumption: V0has small rippleProf. S. Ben-Yaakov , DC-DC Converters [2- 14]BOOST Step-Upz Vo &gt; VinWhy ??S VinDLCRVXVoProf. S. Ben-Yaakov , DC-DC Converters [2- 15]ON VL=VinOFF VL=Vin-VoVinLCRVoVinLCRVoOperation modesVLILtstVinIatVLILtstVinVin-VoIaIbtBoost6Prof. S. Ben-Yaakov , DC-DC Converters [2- 16]toffTSVoVxtoff inooff o inD1VVD V V = =S VinD LCRVXVoThe average voltage method; D VTt VV; V V; V V ; 0 V V ; 0 Voff osoff oxininx in x in L= === = =Voltage transfer functionProf. S. Ben-Yaakov , DC-DC Converters [2- 17]Voltage transfer functionThe I methodtonILtoffTstLV Vin o LVinI offin oonintLV VtLV= off o off on int V ) t t ( V = + off inoD1VV=S VinD LCRVXVoProf. S. Ben-Yaakov , DC-DC Converters [2- 18]BUCK-BOOSTStep-Up Step-Downz Find Vo/VinHint: Average of Vx?SVinDLC RVoVX7Prof. S. Ben-Yaakov , DC-DC Converters [2- 19]Comparison between basic topologies CCMSVinD LCRVoSVinDLCRVoSVinDLCRVoSD LBasic CellLabcSwitched inductorProf. S. Ben-Yaakov , DC-DC Converters [2- 20]IintIintIintIotIotIotSource current Load currentBuckBoostBuck BoostContinues current -&gt; Lowripple componentDiscontinues current -&gt; High ripple component Input and Output CurrentsProf. S. Ben-Yaakov , DC-DC Converters [2- 21]Modulator ControleVDinVAssemblySwitchedoV+The simulation problem8Prof. 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 Modulator ControleV DinVAssemblySwitchedoV+The simulation problemProf. S. Ben-Yaakov , DC-DC Converters [2- 23]++b d cafCLoadRoutVinVLIbICIoutVoutVLoadRLoadRfCfCLa d cbCILIbIinVinVbonTLbILICIdcLBuck BoostBoost Buck onT+Average Simulation of PWM ConvertersProf. S. Ben-Yaakov , DC-DC Converters [2- 24]Ton - switch conduction time Toff- diode conduction timeTDCM- no current time (in DCM)La bcb onTDCMToffTLcaThe Switched Inductor Model9Prof. S. Ben-Yaakov , DC-DC Converters [2- 25]The concept of average signalstttaIbIcIbIaIcIbcaLonToffTaIbIcIThe 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]IbILIbIONTSTon LSon LbD ITT II = =SONonTTD =off LSoff LcD ITT II = =L aI I =Similarly :bcaLonToffTaIbIcIAverage current10Prof. S. Ben-Yaakov , DC-DC Converters [2- 28]bcbIcIaaGbGcGaIbcaL aI I =on L bD I I =off L cD I I =Ga, Gb,Cc - currentdependentsources off L con L bL aD I GD I GI G Toward a continuous modelProf. S. Ben-Yaakov , DC-DC Converters [2- 29]LI DerivingLVtLILIVLVLVLILILVdtI dLVdtdILLL L= =Average inductor currentProf. S. Ben-Yaakov , DC-DC Converters [2- 30]bcaL) b , a ( V) c , a ( VLV( ) b , a V( ) c , a VonToffTsToff onSoff onLD ) c , a ( V D ) b , a ( VTT ) c , a ( V T ) b , a ( VV + == + =Average inductor current11Prof. S. Ben-Yaakov , DC-DC Converters [2- 31]bcaaGbGcGLLrLILE L VTopology independent !off on LD ) c , a ( V D ) b , a ( V E + =off L cD I G =on L bD I G =L aI G=bcaLonToffTThe Generalized Switched Inductor Model(GSIM)Prof. S. Ben-Yaakov , DC-DC Converters [2- 32]1. The formal approachbcaaGbGcGoRoCinVoVLELIL) b , a ( V) c , a ( VLroff 0 on in 0 LD ] V 0 [ D ] V V [ E + =off c on b aD ) L ( I G D ) L ( I G ) L ( I G = = =Example Implementation in Buck TopologySVinDLVoRoCobcaProf. S. Ben-Yaakov , DC-DC Converters [2- 33]2. The intuitive approach - by inspection LoCoR inVoVLIinEbGSLoC oRinVDoVPolarity: (voltage and current sources) selected by inspectionL o inV V E on in inD V E =on L bD I G =Implementation in Buck Topology12Prof. S. Ben-Yaakov , DC-DC Converters [2- 34]SLoC oRinVDoVLoCoRinVoVo offV D off LD I Emulate average voltage on inductor sources current dependent I CreateLBoostProf. S. Ben-Yaakov , DC-DC Converters [2- 35]L oC oRinVDoVLoCoR inVoVo off on inV D D V + off LD I on LD I Buck-BoostProf. S. Ben-Yaakov , DC-DC Converters [2- 36]LoCoRinVoVLrcrdsonRbcaSIMPartially accounting for parasitics13Prof. S. Ben-Yaakov , DC-DC Converters [2- 37]inVdsonRbcaGbGcGoCoRcraLLrLILE L Voff c a on b a LD ) V V ( D ) V V ( E + =off L cD I G =on L bD I G =L aI G=Modified Average ModelProf. S. Ben-Yaakov , DC-DC Converters [2- 38]ILand Donare time dependent variables {IL(t), Don (t) }Donis not an electrical variableonDLIbGL LIMaking the model SPICE compatibleProf. S. Ben-Yaakov , DC-DC Converters [2- 39]Donis coded into voltage+SourceonD" D " : node of Nameon) L ( I ) D ( Von LGvalueIn SPICE environment14Prof. S. Ben-Yaakov , DC-DC Converters [2- 40]RunningSPICEsimulationDC (steady state points) - as isTRAN (time domain) - as isAC ( small signal) - as is* Linearization is done by simulator !SimulationProf. S. Ben-Yaakov , DC-DC Converters [2- 41]LIbcaLonToffTonToffToffTsTtpk LI LIonson soffD 1TT T' D ==on s offT T ' T =Discontinuous Model (DCM)Prof. S. Ben-Yaakov , DC-DC Converters [2- 42]1.The average inductor current in DCMLV) b , a ( V) c , a ( VsTonToffToff' TtbcaL) b , a ( V) c , a ( VonTCCM in as D ) c , a ( V D ) b , a ( V Voff on L+ =CombiningCCM / DCM15Prof. S. Ben-Yaakov , DC-DC Converters [2- 43]bcaaGbGcGaIbIcItonToffTLSILIsTLIoff onLoff ons LLsD DIT TT II+=+=L aI is I Ls c bI sampling are I is I off cT during sampled is I on bT during sampled is I CombiningCCM / DCMProf. S. Ben-Yaakov , DC-DC Converters [2- 44]bcaaGbGcGaIbIcIL aI G=off onon LbD DD IG+=off onoff LcD DD IG+=1 ) D D ( : CCM inoff on= +tonToffTLSILIsTLICombiningCCM / DCMProf. S. Ben-Yaakov , DC-DC Converters [2- 45]onToffTLIoff' TLVabtLVacpkILILT ) b , a ( VIonpk =Soff on onLT) T T (LT ) b , a ( V21I+|.|</p> <p>\|=) D D (Lf 2D ) b , a ( VIoff onsonL+ =onons LoffDD ) b , a ( VLf I 2D =on offD 1 D = on offD 1 D Doff in DCM16Prof. S. Ben-Yaakov , DC-DC Converters [2- 46]bcaLbcaaGbGcGL aI Goff onon LbD DD IG+off onoff LcD DD IG+off on LD ) c , a ( V D ) b , a ( V E + =)`||.|</p> <p>\| =onons Lon offDD ) b , a ( VLf I 2), D 1 ( min DLLrLILE L VThe combined DCM / CCM mode Prof. S. Ben-Yaakov , DC-DC Converters [2- 47]Example: Boost average model simulationRsw{Rsw}EDoffmin(2*I(Lmain)*Lmain/(Ts*v(a,b)*V(Don))-V(Don),1-V(Don))etableOUT+OUT-IN+IN-Resr{Resr}GcV(Doff)*I(Lmain)/(V(Don)+V(Doff))GVALUEOUT+OUT-IN+IN-PARAMETERS:LMAIN = 75uCOUT = 220uRLOAD = 10DoffGbV(Don)*I(Lmain)/(V(Don)+V(Doff))GVALUEOUT+OUT-IN+IN-0Lmain{Lmain}RLoad{RLoad}DbreakDmainVDon{VDon}+-Rinductor{Rinductor}EL(V(Don)*V(a,b)+V(Doff)*V(a,c))EVALUEOUT+OUT-IN+IN-10PARAMETERS:FS = 100kTS = {1/fs}bVin_DC{Vin_DC}+-aCout{Cout}PARAMETERS:RESR = 0.07RINDUCTOR = 0.1RSW = 0.1PARAMETERS:VIN_DC = 10vVDON = 0.5outcGaI(Lmain)GVALUEOUT+OUT-IN+IN-DonSLoC oRinVDoVProf. S. Ben-Yaakov , DC-DC Converters [2- 48]Example: Boost average model simulation17Prof. S. Ben-Yaakov , DC-DC Converters [2- 49]Example: Boost average model simulationSLoC oRinVDoVProf. S. Ben-Yaakov , DC-DC Converters [2- 50]Example: Boost average model simulationSLoC oRinVDoVProf. S. Ben-Yaakov , DC-DC Converters [2- 51]Boost: Response to step of input voltage Ti me30ms 35ms 40ms 45ms 50msV( out )18V19V20V21VSEL&gt;&gt;V( a )9V10V11V12V(average model simulation)VinVout18Prof. S. Ben-Yaakov , DC-DC Converters [2- 52]Boost: Response to step of duty cycle DonVoutTi me30ms 35ms 40ms 45ms 50msV( OUT)25. 0V37. 5V50. 0V10. 0VSEL&gt;&gt;V( Don)400mV600mV800mVProf. S. Ben-Yaakov , DC-DC Converters [2- 53]VDon0V 0. 1V 0. 2 V 0. 3 V 0. 4V 0. 5V 0 . 6V 0 . 7V 0 . 8V 0. 9V 1. 0VV( OUT) / V( a ) V( i de a l )051015Boost transfer function (CCM)on inoD 11VV=DC Sweep simulationideal casereal caseParasitic resistances are taken into account</p>