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2.2.3
Voltage gain
It is for efficiency optimization to operate the LLC converter around the resonant frequency at nominal
input voltage, where the voltage gain
is neglected due to the implementation of individual resonant choke.
The worst case we need to consider for resonant network and transformer design is the full load
operation at minimum input voltage
V
_
=
in
nom
M
M
max
nom
V
_
min
in
2.2.4
Transformer turns ratio
Assuming the drain-source voltage drop of secondary-side MOSFET
ratio will be:
V
_
=
in
nom
n
M
+
nom
( 2
)
V
V
o
f
2.2.5
Effective load resistance
The effective load resistance can be given as:
8
8
V
=
2
=
o
R
n
π
π
2
2
eff
I
o
2.2.6
Resonant network
Defining the normalised frequency to
the voltage gain of the converter can be written as:
=
(
,
)
Mj
F
Q
−
2
(
) 1
F
m
Its magnitude is:
=
(
,
)
Re(
(
G
F
Q
Mj
F
The graph of voltage gain
Application Note
=
M
nom
. The maximum voltage gain at
V
_
min
in
400
=
=
1 *
. 1
19
337
2 .
400
=
=
1 *
16
+
2
( *
12
0
) 1 .
12
2
=
Ω
*
16
5 .
*
106
25
F =
is
f
r
−
2
(
) 1
F
m
+
−
−
2
(
1
)(
) 1
jF
F
m
Q
+
2
,
))
Im(
(
,
))
Q
Mj
F
Q
Vs
for different
F
G
1
, on condition that the secondary-side leakage inductance
5 .
f
, the load factor of the LLC converter is
f
r
2
can be plotted based on [7] with Mathcad:
Q
7
can be calculated as:
V
_
min
in
=
0
1 .
, the transformer turns
V
V
f
[3]
[4]
[5]
L
r
C
,
Q =
r
R
eff
[6]
[7]
2011-07-06
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