The maximumvalue of lBoccurs atD=0.5.T,VI LB,max(7-32)ILB = 4ILB,maxD(1- D)8L: The maximum value of IoB occurs at D=1/327 2T,V.1(7-33)D(1- D)2oBoB,maxoB,max427LV。 ConstantT,VoR.m8LIIuBiL,peak0.074T,V(IoB,maxULLIuB0.751.00.500.25（）(b)(a)12Figure 7-13 Step-up dc-dc converter at the boundary of continuous-discontinuousE-mail:xjhuancconduction
E-mail: xjhuang@bjtu.edu.cn 12 8L I ILB = 4I = LB,maxD(1− D) （7 −32） TsVo LB,max • The maximum value of ILB occurs at D=0.5. • The maximum value of IoB occurs at D=1/3 I D(1− D) 2 （7 −33） 27L 4 I oB oB,max = 2TsVo = 27 I oB,max
2.3 Discontinuous-conduction mode:Occurs at light loadsULULiL0+Va-V.(Vd - V.)++42T+41T,+(b)(a)Figure 7-14Step-up converter waveforms: (a) at the boundary of continuous-discontinuous conduction; (b) at discontinuous conduction.△, + DV.(7-34)Va△1Va(7-37)DT.(D+△,)(7-36)ODA2L1321
2.3 Discontinuous-conduction mode • Occurs at light loads 1 (7 −37) 13 (7 −36) (7 −34) 2L 2L I = I I = ( TsVd = DTs(D + 1 ) o )D Vd d L Vo = 1 + D Vd 1
Boost converter:voltagetransfer ratioV1(7 -26)V1-DThevoltageconversionratioofBoostconvertersoperatinginCCMdependsonD.butisindependentoftheoutputload.Iftheoutputloaddecreasestothe extent thati, becomes discontinuous (DCM),the relationship (7-26) is nolongervalid.VAtVV.VT1DittDDaiDaa.DCMLomCCM(b)(a)Which one will have higher output voltage? CCM or DCM?14
Boost converter: voltage transfer ratio The voltage conversion ratio of Boost converters operating in CCM depends on D, but is independent of the output load. If the output load decreases to the extent that iL becomes discontinuous (DCM), the relationship (7-26) is no longer valid. = (7 −26） Vin 1− D Vo 1 Which one will have higher output voltage? CCM or DCM?14
2.4 Output voltage ripple!!Fora continuous-conductionmodeAQIDT0SAVipc0CAQV.DT,ID = I.AQ(7-39)0RCic(t) ~ idiode,ripple(t)= idiode - IAVDT,T.(7-40)V.RC>The ripple isdependent of the+-(1-D)T,DT.outputloadpower.Figure 7-17 Step-up converter output voltage ripple15
15 2.4 Output voltage ripple = RC C (7 −39) Q I DT C V = = VoDTs o s o !! For a continuous-conductionmode (7 −40) Vo = DTs Vo RC ➢The ripple is dependent of the output load power. − I iC (t) idiode,ripple (t)= idiode o
Example 7-B In the following Boost converter, the inductorcurrent has △i,= 2A. It is operating in dc steady state underthe following conditions: Vin=5V, V。=12V,P。=10W, andf,=200kHz.Assuming ideal components, calculate L and draw thewaveformsSolutionP10(a)2ALL5△ii,=2A<2IContinuousconductionmodeg=0(b)(c):Boostconverter:operation andwaveforms
16 Example 7-B In the following Boost converter, the inductor current has ΔiL= 2A. It is operating in dc steady state under the following conditions: Vin =5V , Vo =12V ,Po=10W , and fs=200kHz . Assuming ideal components, calculate L and draw the waveforms. Solution Vin 5 = 10 = = 2A Po IL = Iin iL = 2A 2IL Continuous conduction mode