2.2 Continuous-conduction modeitid1Steady-state analysis++VLVoi本(a)Va-V, = 0Ic=0I。= IL(V-Va)Ia = DIVLIp = (1-D)I(b)(-Va)Based on"Volt-secondsover Tequal zero"(Va -V.)ton = V(T, -ton)iV.(i=l)tonOD(7-3)(c)T.Vaid>V.can be controlled by(d)varying the duty ratio D.i(e)
+ 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 ID = (1−D)IL C Id = DIL L Io = IL V = 0 I = 0 Steady-state analysis 2.2 Continuous-conduction mode = = 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” ➢Vo can be controlled by varying the duty ratio D
Neglecting power losses associatewithall the circuit elementsPa = P。id10L+1Therefore:Vala =V.I。Voi本(a)+VL-Vo=VVaR1。and :(7 -4)(Va-V)VLADIa1(b)N.Ic= 0Ii = I。(-V)Ritic(t) ~ i,rpple (t)(,=la)(c)it(t) =IL +iLripple(t)(Va -V。)DT, :(7-22)Ai=-(1-D)T13
13 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 Neglecting power losses associate with all the circuit elements
SwitchingcomverterExample 01:888+-Ly10AVinRV50V本100VCPPin500Ww=500WPlosr small1. From the figure shown, how is the duty circle D?2. If Vo=24V, how is D again?3. If Vo=24, but Vin fluctuated to 120V, once again tocalculate D.14
14 Example 01: 1. From the figure shown, how is the duty circle D? 2. If Vo=24V, how is D again? 3. If Vo=24, but Vin fluctuated to 120V, once again to calculate D. R in
Example 7-A In the Buck dc-dc converter of following figureL=24uH . It is operating in dc steady state under the followingconditions: Vin= 20V, D=0.6,P。=12W, and f.=200kHz.Assuming ideal components, calculate and draw the waveformslin(Vm-V.)a(-V.)9=(b)一V=O9=0(d)E-maC
E-mail: xjhuang@bjtu.edu.cn 15 Example 7-A In the Buck dc-dc converter of following figure, L=24µH . It is operating in dc steady state under the following conditions: Vin = 20V , D=0.6 , Po =12W , and fs=200kHz. Assuming ideal components, calculate and draw the waveforms