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AN-6094
Once the t
is determined at operating point B, the
OFF
MOSFET conduction time is obtained as:
−
1/
f
t
@
=
S
OFF
B
t
@
ON
B
min
V
N
@
+
⋅
(1
DL
B
S
+
N
V
V
@
P
O
B
Then, the transformer primary-side inductance can be
calculated as:
min
⋅
2
(
)
V
t
@
@
=
⋅
DL
B
ON
B
L
m
2
P
. @
IN T
B
Once
the
transformer
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:
Δ
f
=
−
−
(2.15
S
f
f
V
@
S
C
S
Δ
V
SH
where Δf
/ ΔV
is 64 kHz / V for UL version and
S
SH
38 kHz / V for HL version, and V
diode forward voltage drop at the V
(85% of diode conduction time).
Then, the MOSFET conduction time at operating point C
is given as:
2
1
P
. @
=
IN T
t
@
min
ON
C
V
f
@
DL
C
S
The non-conduction time at operating point C is given as:
1
=
−
(1
t
t
@
@
OFF
C
ON
C
f
@
S
C
The non-conduction time should be larger than 15% of
switching period, considering the transformer variation
and frequency hopping.
Figure 12. Variation of t
© 2012 Fairchild Semiconductor Corporation
Rev. 1.0.0 • 9/27/12
(24)
)
F
(25)
f
S
primary-side
inductance
+
V
V
@
.
⋅
O
C
F SH
)
@
(26)
SH
A
+
N
V
V
.
O
F SH
is the rectifier
F.SH
sampling instant
S
L
C m
(27)
@
C
min
V
N
@
+
⋅
DL
C
)
S
+
(28)
N
V
V
@
P
O
C
F
, t
, and t
ON
D
OFF
is
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
P
. @
=
IN T
A
PK
I
⋅
DS
L
f
m
S
The minimum number of turns for the transformer
primary side to avoid the core saturation is given by:
PK
L I
min
=
m DS
N
P
B A
sat
e
where AE is the cross-sectional area of the core in m
and B
is the saturation flux density in Tesla. Figure 14
sat
shows the typical characteristics of a ferrite core from
TDK (PC40). Since the saturation flux density (B
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
obtained in STEP-3, determine the proper integer for N
such that the resulting N
from Equation (30).
Figure 14. Typical B-H Curves of Ferrite Core
8
=0.25~0.3T. With the turns ratio
sat
is larger than N
min
obtained
P
P
(TDK/PC40)
www.fairchildsemi.com
(29)
(30)
2
)
sat
s
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