AN-6094
© 2012 Fairchild Semiconductor Corporation
www.fairchildsemi.com
Rev. 1.0.0 • 9/27/12
8
Once the t
OFF
is determined at operating point B, the
MOSFET conduction time is obtained as:
@
@
min
@
@
1/
(1
)
S
OFF
B
ON
B
DL
B
S
P
O
B
F
f
t
t
V
N
N
V
V
−
=
+
⋅
+
(24)
Then, the transformer primary-side inductance can be
calculated as:
min
2
@
@
. @
(
)
2
DL
B
ON
B
m
S
IN T
B
V
t
L
f
P
⋅
=
⋅
(25)
Once the transformer primary-side inductance is
determined, DCM operation at operating point C should
be checked. To prevent CCM operation, FAN302
decreases the switching frequency as the output voltage
drops, as illustrated in Figure 13. The switching frequency
at the minimum output voltage is obtained as:
@
.
@
@
.
(2.15
)
O
C
F SH
S
S
C
S
SH
A
N
SH
O
F SH
V
V
f
f
f
V
V
V
V
+
Δ
=
−
−
⋅
Δ
+
(26)
where
Δ
f
S
/
Δ
V
SH
is 64 kHz / V for UL version and
38 kHz / V for HL version, and V
F.SH
is the rectifier
diode forward voltage drop at the V
S
sampling instant
(85% of diode conduction time).
Then, the MOSFET conduction time at operating point C
is given as:
. @
@
min
@
@
2
1
IN T
C
m
ON
C
DL
C
S
C
P
L
t
V
f
=
(27)
The non-conduction time at operating point C is given as:
min
@
@
@
@
@
1
(1
)
DL
C
S
OFF
C
ON
C
S
C
P
O
C
F
V
N
t
t
f
N
V
V
=
−
+
⋅
+
(28)
The non-conduction time should be larger than 15% of
switching period, considering the transformer variation
and frequency hopping.
Figure 12. Variation of t
ON
, t
D
, and t
OFF
Figure 13. Frequency Reduction in CC Mode
Once the transformer primary-side inductance is obtained,
the maximum peak drain current can be calculated at the
nominal output condition (operating point A) as:
. @
2
IN T
A
PK
DS
m
S
P
I
L
f
=
⋅
(29)
The minimum number of turns for the transformer
primary side to avoid the core saturation is given by:
min
PK
m
DS
P
sat
e
L I
N
B
A
=
(30)
where AE is the cross-sectional area of the core in m
2
and B
sat
is the saturation flux density in Tesla. Figure 14
shows the typical characteristics of a ferrite core from
TDK (PC40). Since the saturation flux density (B
sat
)
decreases as the temperature rises, the high temperature
characteristics should be considered, especially for
charger application in an enclosed case. If there is no
reference data, use B
sat
=0.25~0.3T. With the turns ratio
obtained in STEP-3, determine the proper integer for
N
s
such that the resulting
N
P
is larger than
N
P
min
obtained
from Equation (30).
Figure 14. Typical B-H Curves of Ferrite Core
(TDK/PC40)
