Page 302 - Rashid, Power Electronics Handbook

292 S. Hui and H. Chung

Step 2: Soft-switching criterion is Lr L

V o RL
Z ð15:8Þ SW
r
I sðmaxÞ
Vin Q D C Vout
p 
where Z ¼ L =C is the impedance of the resonant tank. Cr
r
r
r
For a chosen resonant frequency f , L and C can be
r
r
r
obtained from (a)
p  L D
2pf ¼ 1= L C ð15:9Þ
r r r
RL
Cr Lr
15.11.2.2 Filter Component Design
Vin Q C Vout
The minimum conversion ratio is
SW
1
M ðminÞ ¼ V =V sðmaxÞ ¼ ð15:10Þ
o
1 ÿðF =f þ T =T Þ (b)
e
r
sw
sw
where T sw ¼ 1=f sw and t is the extended period. From Eq. Lr D
e
(5.10), minimum t can be estimated.
e
The turn-on period of the SW1 is RL
SW
Vin L C Vout
T onðsw1Þ ¼ t þ 1=f r ð15:11Þ Q
e
Cr
Inductor value L is obtained from
(c)

T onðsw1Þ
L V sðmaxÞ ð15:12Þ FIGURE 15.40 A family of EP-QR converters: (a) Buck converter;
DI (b) boost converter; and (c) ¯yback converter.
The ®lter capacitor value C can be determined from
!
DV
C ÿ1 ¼ I o ð15:13Þ where T ¼ 1=f is the period of the ac voltage supply
s
s
T =p sin ðI =I sðmaxÞ Þ frequency.
o
s

(a) (b)
FIGURE 15.41 (a) Conducted EMI from hard-switched ¯yback converter; and (b) radiated EMI from hard-switched ¯yback converter.