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.<<fs>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