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
1.4 Output voltage rippleUL!!AtCCM(Vd-o)-Uoic(t) =iLripple (t)114/, T4QSAV(7-21)0AIC2C2 2POVT(7-22)(1-D)TNLAV。= T?V.(1- D)(7 -23)8CLNote:in practice, capacitorequivalentseriesresistanceFigure 7-10Output voltage ripple in a step-down converter.(esr) further increases △V
1.4 Output voltage ripple = L s o Q 1 1 C C 2 2 2 V = （7 −22) 7 (esr) further increases ΔVo . s o L (1− D)T L V I = (7 −23) 8CL T 2V (1− D) Vo = s o !! At CCM I T iC (t) iL,ripple (t) （7 − 21） Note: in practice, capacitor equivalent series resistance
AV.元(1- D)T(1-D)2(Jc)(7 -24)V.28CLfsUL141(Va-U)T2元/LC-Uo>The voltage ripple can beizlminimizedbyselectingaAcornerfrequency（截止频率中T2I-I。心频率）f.ofthelow-passfilterat the output such that f.The ripple is independentof the output load powerFigure 7-10 Output voltage ripple in a step-down converter
8 T of the output load power. c s s fs 2 LC 1 ( c ) 2 o s Vo 8CL 2 2 2 f = f = 1 (7 −24) ( 1 − D ) f = = V T (1 − D ) ➢The voltage ripple can be minimized by selecting a corner frequency （截止频率、 中 心频率） fc of the low -pass filter at the output such that f c<<fs. ➢The ripple is independent
2.1 Boost converterDip2 Steady-state analysis:平In the dc steady state:R(a)VIc= 0Vi=0VLIp= I。Ia = I(Va)(b)(VaVo)Vaton +(Vin -V.)torfr = 0Tit1V-E(c)(7-26)1- DVatoffFtonOis(d)>V.can be controlled byip9varying the duty ratio D.(e)
9 In the dc steady state: 1 (7 −26) V t 1− D V T −V )t = 0 d off o = s = Vd o off ton +(Vin IC = 0 ID = Io VL =0 Id = IL t 0 t (Vd -Vo ) Ts ton 0 t 0 t iD (b) (c) (e) vL iL is (d) (Vd) IL toff + - L V i L L D iD + o V - C R + - d V i (a) s 2 Steady-state analysis: ➢Vo can be controlled by varying the duty ratio D. 2.1 Boost converter
D,ipAssuming a lossless circuit,立+1Pa= P。R(a)isVdTherefore : Vala = VII。= (1-D)VL Aand :(7-27)Id(Va)(b)(Va-V)1 V.IL=1F-DRiL(c)ic(t) idiode,rpple (t) = idiode - I。tonntis(d)Ai= a(DT,)= V-Va)(1- D)T,1ip10(e)0
10 C diode o i (t) i (t) = i − I diode,ripple 1 1 iL = L Vd (DTs ) = L (Vo −Vd )(1− D)Ts I L = Id = 1− D R 1 Vo t 0 t (Vd-Vo) Ts ton t 0 t (b) (c) D (e) vL iL is (d) 0 i (Vd) IL toff + - L V i L L D iD + V o - C R + - d V i (a) s Assuming a lossless circuit, (7 −27) d d o o Id Io and : =（1−D) Therefore :V I = V I Pd = Po
2.2 Boundary between continuous anddiscontinuous-conductionmode>Fora constantV.VatoniL,peakTV。LD(1- D)1(7-28)LB22L2LTY.D(1- D)2(7 -29)1OB2LV。=ConstantT,V.B.ma8LIL=ILBiL,peak0.074T,VIIoB,maxDILILEIoBID0.751.00.5o0.25()(6)(a)11Figure 7-13 Step-up dc-dc converter at the boundary of continuous-discontinuousogonE-mail:xjhuang@bjtu.edu.cn
E-mail: xjhuang@bjtu.edu.cn 11 2.2 Boundary between continuous and discontinuous-conduction mode (7 −29) (7 −28) 2L 2 2L 2L I I = TsVo D(1− D) 2 oB = = TsVo D(1− D) Vd t = on iL, peak LB ➢For a constant Vo