(2) During the toff period:4At t=ton, turning off the transistor:VaV,=-V。→V =-(N (N )V , forcingthe input current to zero. Due toΦ cannot changeinstantaneously,i, suddenlyV.jumps to its peak value.Duringthe toff, Φ declines linearlyton<t<T-(N/N2)VNVΦ(0)(10 -4)N2ip(10 -6)d(T,) =d(O)
(2) During the toff period: At t=ton, turning off the transistor: 2 o 1 1 2 o v =-V →V =-(N /N )V , forcing the input current to zero. Due to Φ cannot change instantaneously, i2 suddenly jumps to its peak value. During the toff, Φ declines linearly. ˆ 2 2 o s on (Ts ) =(0) (Ts −ton ) (10 −4) (10 −6) N V (T ) = − ) ton t Ts N (t) = ˆ − Vo (t −t iD v1 Φ Φ(0) -(N1/N2)Vo Vd off ton t Io t t D t C R T i1 + Vd - + Vo - i2 N1 :N2 + v1 - - v2 +
During the toff period:the output load is entirely suppliedVaby the energy stored in thetransformer.im(t)= l21Lm(ton<t<T)(10-11)iz(t)=ip(t)(tNi(t) =0-(N/N2)VΦTheflybacktransformerisΦ(0)actually a two-winding inductor,whichstoresandtransfersDenergy
1 (10−11) N2 N L N2 N V ( ) i2 (t) =iD (t) = 1 im (t) (ton t Ts ) m o im (t) = I ˆ − (t − t ) m on i D v1 Φ Φ(0) -(N1/N2)Vo Vd toff ton Io t t D energy. t C R T i1 + Vd - + Vo - i2 N1 :N2 + v1 - - v2 + During the toff period: the output load is entirely supplied by the energy stored in the transformer. i1 (t) =0 The flyback transformer is actually a two-winding inductor, which stores and transfers
In the continuous-conduction modeNi + △i,=0VdVDVa1-DN0A1N2DV.N2(10 -7)VdN, 1- D-(N,/N2)V。dEq. 10-7 shows the dependence (0)of the voltage-ratio on the duty-1ratio D is identical to that in theDBuck-Boost converter
(10 −7) Vd N1 1− D ratio D is identical to that in the i v1 Eq. 10-7 shows the dependence Φ(0) of the voltage-ratio on the duty- Φ -(N /N1 2 )Vo Vd off ton t t t D C R T i1 + Vd - + Vo - i2 N1:N2 + v1 - - v2 + In the continuous-conduction mode i1 + ip =0 = Vd 1− D V1 D 2 D Io Buck-Boost converter. t 1 = 0 N N i1 + i2 Vo = N2 D
TVdN2)V+-Nor-toff-(N,/N2)VΦApplication:Φ(0)low powerlevel below50wD
Application: low power level below 50W. iDΦ Φ(0) -(N 1/N 2)Vo v 1 Vdton t off Io ttt D C R T i 1 +Vd - +Voi2 N1 :N2 +v1 - -v 2+ o d d o N V N NN ) V ) V 12 D , peak 21 T , peak = V + ( V = V + (
3WaveformsindifferentoperatingmodesViViLRuLontontoffon大T.T.T.VTVTVTUNNIimaxilImaxilimoi212i2I2maxb)Boundarybetweena) discontinuous-c)continuouscontinuousandconductionmodeconductionmodediscontinuousconduction
0 toff Ts 0 N1Uo N2 U + N1Uo d N2 v1 0 a) discontinuousconduction mode Vd 0 Uo N1 N2 U+ N1U d N2 o L1 Ud t L2 I2max − Uot 0 0 b) Boundary between continuous and discontinuous conduction c) continuousconduction mode 0 t 0 L1 Ud t U L2 I2max − o t Ud Uo + N1 N2 Ud 0 0 v1 v1 vT vT vT i1 i1 i2 i1 i2 i2 I2max I1max I1max I1max I2max I2max Ts Ts ton t t on off Vd N1 N Uo 2 on tm toff Vd 3 Waveforms in different operatingmodes