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