Design guide IDP2303(A)
LLC design
Application Note
25
Revision 2.0
2017-05-03
The maximum voltage gain
𝑀
𝑚𝑎𝑥
required is during conditions of full load operation at minimum input
voltage
𝑉
𝑏𝑢𝑠_𝑚𝑖𝑛
, which can be calculated as:
𝑀
𝑚𝑎𝑥
=
𝑉
𝑏𝑢𝑠_𝑛𝑜𝑚
𝑉
𝑏𝑢𝑠_𝑚𝑖𝑛
𝑀
𝑛𝑜𝑚
=
390
338
0.94 = 1.08
4.2.2.2
Equivalent circuit and resonant network
All analysis and calculation in this section is based upon the equivalent circuit in Figure 18 that can be
derived with the First Harmonic Approximation (FHA) modelling methodology.
Figure 18
Equivalent circuit
If the total output load is referred to 24 V, the effective load resistance can be given as:
𝑅
𝑒𝑓𝑓
=
8
𝜋
2
𝑛
𝑒
2 𝑉
𝑜
𝐼
𝑜
=
8
𝜋
2
7.55
2 24
5
= 216
Ω
Defining the normalised frequency
𝑓
𝑟
is
𝐹 =
𝑓
𝑓
𝑟
, the load factor of the LLC converter is
𝑄
𝑒
=
√𝐿
𝑟
𝐶
𝑟
⁄
𝑅
𝑒𝑓𝑓
, the
voltage gain of the converter can be obtained based on the equivalent circuit Figure 19:
𝑀
𝑗
(𝐹, 𝑄) =
𝐹
2
(𝑚 − 1)
(𝐹
2
𝑚 − 1) + 𝑗𝐹(𝐹
2
− 1)(𝑚 − 1)𝑄
𝑒
Its magnitude is:
𝐺(𝐹, 𝑄) = √𝑅𝑒(𝑀
𝑗
(𝐹, 𝑄
𝑒
))
2
+ 𝐼𝑚(𝑀
𝑗
(𝐹, 𝑄
𝑒
))
2
The graph of voltage gain
𝐺
vs
𝐹
for different values of
𝑄
can be plotted as in Figure 19, based on the
equation above:
