Design guide IDP2303(A)
LLC design
Application Note
28
Revision 2.0
2017-05-03
4.2.2.4
Selection of resonant factor m
Numerous factors come into play while considering the value of the resonant factor
𝑚
.
r
r
m
r
p
L
L
L
L
L
m
In order to achieve the highest efficiency possible, the magnetizing inductance
𝐿
𝑚
should be set to be large.
Therefore, the magnetizing current
𝐼
𝑚𝑎𝑔
is small for the specified value of bus voltage and switch-on time,
thus allowing for low core and conduction loss in transformer.
𝐼
𝑚𝑎𝑔
=
1
4
𝑉
𝑏𝑢𝑠
𝑡
𝑜𝑛
𝐿
𝑚
On the other hand, the magnetizing current must be large enough to charge and discharge the output
capacitance
𝐶
𝑠𝑤
of the primary side MOSFET during the deadtime
𝑡
𝑑𝑡
, to achieve ZVS and thus ensure safe
switching and reduce switching losses.
𝐼
𝑚𝑎𝑔
≅
𝑉
𝑏𝑢𝑠
𝐶
𝑠𝑤
𝑡
𝑑𝑡
Furthermore, sufficient magnetizing current is required to ensure that the MOSFET body diode can complete
reverse recovery during turn-on at light load [4].
The value of the resonant factor
𝑚
also has an effect on the shape of gain curves and the attainable
maximum gain. Larger values of
𝑚
result in flatter gain curves which leads to a wider operation frequency
range.
In the real world, the selection of
𝑚
is also limited by the structure of the selected transformer, which
determines the value of the leakage inductance
𝐿
𝑟
.Therefore, determining the value of
𝑚
can be an
iterative process involving many factors.
4.2.2.5
Selection of resonant capacitor
The current through the resonant capacitor is the sum of the magnetizing current and the load current
referred to the primary. Its RMS value can be calculated as:
𝐼
𝐶
𝑟
_𝑟𝑚𝑠
=
1
𝜂
√(
𝜋𝐼
𝑜
2𝑛
𝑒
√2
)
2
+ [
𝑛
𝑒
(𝑉
𝑜
+𝑉
𝐹
)
4√2𝑓
𝑛𝑜𝑚
𝑀
𝑛𝑜𝑚
(𝐿
𝑝
−𝐿
𝑟
)
]
2
=
1
0.93
√(
𝜋 ∗ 5
2 ∗ 7.5√2
)
2
+ [
7.5 ∗ (24 + 0.5)
4√2 ∗ 110 ∗ 10
3
∗ 0.94 ∗ 847 ∗ 10
−6
]
2
=
1
0.93
√0.74
2
+ 0.37
2
= 0.89 𝐴
The voltage across the resonant capacitor reaches a peak at the over current trigger point (OCP), which is
estimated to have a 65% margin over the peak current in the primary side during normal operation. The
accurate maximum OCP trigger point, including consideration of the tolerance is calculated in section 4.3.2.
𝐼
𝑜𝑐𝑝
= √2𝐼
𝐶
𝑟
_𝑟𝑚𝑠
(1 + 65%) = 2.1 𝐴
𝑉
𝐶
𝑟
≅
𝑉
𝑏𝑢𝑠
2
+
𝐼
𝑜𝑐𝑝
2𝜋𝑓
𝑚𝑖𝑛
𝐶
𝑟
=
390
2
+
2.1
2𝜋 ∗ 100 ∗ 10
3
∗ 10 ∗ 10
−9
= 529 𝑉
A 630 V rated low-ESR film capacitor is selected as the resonant capacitor.
