Topic 6Main contentsLast lecture reviewBuck-Boost Converter
Main contents • Last lecture review • Buck-Boost Converter Topic 6
1.1 Buck Converter at CcMiioidYSteady-state analysisL+++VLVoi本(a)VaV.=VRIc=0V.= 0I。= IL(V-Va)Ia = DIVLAIp = (1-D)IL(b)B(-Va)1(Va -V。)ton =V(T, -ton)iLV.T(l,=l)ton0D(7-3)(c)T,VaidBased on"Volt-seconds(d)over T equal zeroiD4(e)
ID = (1−D)IL C Id = DIL L Io = IL V = 0 I = 0 Steady-state analysis + Vd - + vL - + C vo=Vo R - + voi - (a) L i iL d io t 0 A B Ts ton 0 t 0 t iD (b) (c) (d) (e) iL id vL (Vd-Vo) (-Vo) (IL=Io) t toff 1.1 Buck Converter at CCM = = D (7 − 3) t on Vd Ts d o on o s on Vo （V −V )t = V (T − t ) Based on “Volt-seconds over T equal zero
Pa = P。id10L+1Therefore :Vala =V.IVoi本(a)+ VL-CVo=VVaR1。and :(7 -4)(Va-V)VLADIa1(b)N.Ic= 0Ii = I。(-V)Riic(t) ~i,rpple (t)T(a,=la)(c)it(t) =I +iLripple(t)-(Va-V)DT, :Nit=-(7-22)(1-D)T
4 R V IL = Io = o IC = 0 i (t) C (t) iL,ripple +iL,ripple (t) iL (t) = IL L d o s o s （7 −22） L L i = 1 (V −V )DT = 1 V (1−D)T + Vd - R + C vo=Vo - + voi - (a) L + vL - id io t 0 t A B Ts (b) (c) iL vL (Vd-Vo) o (-V) (IL=Io) = 1 I d D and : Io =Vo Io (7 −4) Pd = Po Therefore :Vd Id
1.2BoundarybetweenCCMandDCMULVa = ConstantILB=IoB(Va - Vo)ILB=1oBiL, peak证+T,Vd+ILB.max8L(-V)Coff1-D0.51.0T(b)(a)Figure 7-6Current at the boundary of continuous--discontinuous conduction: (a) currentwaveform; (b) ILBversus DkeepingVaconstant.DTNitKopeak(7-5)=1-oBLB222L2LT,VaD(1- D)WhenVd(7-6)= cons tan t :LB2LTVWhen1V=constant:(1-D)(7-18)LB52L
5 2 (7 −18) (7 − 6) (7 − 5) 2L When D(1− D) 2L When 2L DT 2 2L I I = TsVo (1−D) o LB = TsVd d LB oB (Vd −Vo ) = I s d o = on iL t = iL, peak LB V = constan t： V = constan t： I = （V −V ) = 1.2 Boundary between CCM and DCM
1.3Buck Converter at DCM: Occurs at light loadsV.D(7-10)iL,peakVaD +△1ULV△,T1V1peakL0D +△peak2VaT,D△,DTAiT2L42TTVT(D + 4)△)Figure 7-7 Discontinuous conduction in step-down converter.2L6: Steady state; inductor current discontinuous
1 1 • Steady state; inductor current discontinuous 6 1 2 = = (7 −10) (D + ) 2L V T D 2L D +1 I = i T L V i = o s = Vd Ts o L, peak 1 s o L, peak Vd D +1 Vo D • Occurs at light loads 1.3 Buck Converter at DCM