The reference [19] shows the LLC design using APR model whereas the reference [1] shows the LLC design using T-type transformer model. Here, for this design example, UCC25640xEVM specifications[3] with T-type transformer model is considered.

LLC Voltage Gain with T-type Transformer Model

Equation 7 gives voltage gain expression for T-type transformer model shown in Figure 1-5.

where

$$\text{Normalized}\text{frequency:}fr=\frac{\omega }{{\omega }_0}$$

$$\begin{array}{l}\text{Angular}\text{resonant}\text{frequency}\text{between}\text{leakge}\text{inductance}\text{(primary-side inductance }\\ \text{when the secondary side is completely short-circuited)}\text{and}\text{Cr:}{\omega }_0=\frac{1}{\sqrt{L_{lk}\cdot C_r}}\end{array}$$

$$\begin{array}{l}\text{Angular}\text{resonant}\text{frequency}\text{between}\text{primary}\text{inductance}\text{(self-inductance of }\\ \text{the primary winding)}\text{and}\text{Cr:}{\omega }_s=\frac{1}{\sqrt{L_p\cdot C_r}}\end{array}$$

$$\text{Characteristic impedance:}{Z}_0=\sqrt{\frac{L_{lk}}{C_r}}$$

$$Q=\frac{R_{ac}}{Z_0}=\frac{8\cdot n^2}{{\pi }^2}\cdot \frac{R_L}{Z_0}$$

$$n\text{ : primary to secondary turns ratio}$$

$$k\text{ : Coupling coefficient between primary and secondary winding of the transformer}$$

Design Example