AN-6094
© 2012 Fairchild Semiconductor Corporation
www.fairchildsemi.com
Rev. 1.0.0 • 9/27/12
5
The input power of transformer at operating point A is
given as:
. @
. @
N
N
O
O
IN T
A
FF S
A
I
P
E
V
=
(5)
To reduce the switching frequency as the output voltage
drops in CC Mode for maintaining DCM operation, the
output voltage needs to be sensed. FAN302 senses the
output voltage indirectly by sampling auxiliary winding
voltage just before the diode conduction finishes, as
explained with Figure 4 in Section 2. Since the switching
frequency starts decreasing as V
S
sampling voltage drops
below 2.15 V, as illustrated in Figure 6, the output voltage
at operating point B can be obtained as:
@
.
.
@
2.15
(
)
N
O
B
O
F SH
F SH
SH
A
V
V
V
V
V
=
⋅
+
−
(6)
where V
SH@A
is the V
S
sampling voltage at operating
point A, which is typically designed as 2.5 V and V
F.SH
is the rectifier diode forward voltage drop at the V
S
sampling instant (85% of diode conduction time), which
is typically about 0.1 V. Note that V
F.SH
is less than a
third of V
F
since the Vs voltage sampling occurs when
the diode current is very small.
The overall efficiency at operating point B, where the
frequency reduction starts, can be estimated as:
@
@
@
@
N
O
B
O
F
FF
B
FF
A
N
O
B
F
O
V
V
V
E
E
V
V
V
+
≅
⋅
⋅
+
(7)
Note that the efficiency changes as the output voltage
drops in CC Mode. The efficiency should be also
estimated for each operating point (B and C).
The secondary-side efficiency at operating point B can be
estimated as:
@
. @
. @
@
N
O
B
O
F
FF S
B
FF S
A
N
O
B
F
O
V
V
V
E
E
V
V
V
+
≅
⋅
⋅
+
(8)
Then, the power supply input power and transformer input
power at operating point B are given as:
@
@
@
N
O
B
O
IN
B
FF
B
V
I
P
E
⋅
=
(9)
@
. @
. @
N
O
B
O
IN T
B
FF S
B
V
I
P
E
⋅
=
(10)
The overall efficiency at operating point C can be
approximated as:
@
@
@
N
O
C
O
F
FF
C
FF
N
O
C
F
O
V
V
V
E
E
V
V
V
+
≅
⋅
⋅
+
(11)
where V
O@C
is the minimum output voltage for CC
Mode at operating point C.
The secondary-side efficiency at operating point C can be
estimated as:
@
. @
. @
@
N
O
C
O
F
FF S
C
FF S
A
N
O
C
F
O
V
V
V
E
E
V
V
V
+
≅
⋅
⋅
+
(12)
Then, the power supply input power and transformer input
power at operating point C are given as:
@
@
@
N
O
C
O
IN
C
FF
C
V
I
P
E
⋅
=
(13)
@
. @
. @
N
O
C
O
IN T
C
FF S
C
V
I
P
E
⋅
=
(14)
(Design Example)
To maximize efficiency, a low-voltage-drop Schottky
diode whose forward voltage drop is 0.35 V is selected.
Assuming the overall efficiency is 73% and the
transformer efficiency is 97% at operating point A
(nominal output voltage and current) for low line, the
secondary-side efficiency is obtained as:
. @
.
0.907
N
O
FF S
A
FF TX
N
O
F
V
E
E
V
V
≅
⋅
=
+
Then, the input powers of the power supply and
transformer at operating point A are obtained as:
@
@
6
8.22
0.73
N
N
O
O
IN
A
FF
A
V
P
I
W
E
=
=
=
. @
. @
6
6.62
0.907
N
N
O
O
IN T
A
FF S
A
V
I
P
E
W
=
=
=
The efficiencies at operating point B are:
@
@
@
@
0.722
N
O
B
O
F
FF
B
FF
A
N
O
B
F
O
V
V
V
E
E
V
V
V
+
≅
⋅
⋅
=
+
@
. @
. @
@
0.896
N
O
B
O
F
FF S
B
FF S
A
N
O
B
F
O
V
V
V
E
E
V
V
V
+
≅
⋅
⋅
=
+
Then, the input powers of the power supply and
transformer at operating point B are obtained as:
@
@
@
7.07
N
O
B O
IN
B
FF
B
V
P
I
W
E
=
=
@
. @
. @
5.69
N
O
B O
IN T
B
FF S
B
V
P
I
W
E
=
=
The primary-side and secondary-side efficiencies at the
operating point C are calculated as:
@
@
@
@
0.610
N
O
C
O
F
FF
C
FF
A
N
O
C
F
O
V
V
V
E
E
V
V
V
+
≅
⋅
⋅
=
+
@
. @
. @
@
0.758
N
O
C
O
F
FF S
C
FF S
A
N
O
C
F
O
V
V
V
E
E
V
V
V
+
≅
⋅
⋅
=
+
Then, the input powers of the power supply and
transformer at operating point C are obtained as:
@
@
@
2.46
N
O
C
O
IN
C
FF
C
V
P
I
W
E
=
⋅
=
@
. @
. @
1.98
N
O
C
O
IN T
C
FF S
C
V
P
I
W
E
⋅
=
=
