Choosing “Qe” and “Ln” for Designing an LLC Resonant Converter

This is the link to the video of this post.

The first step in designing an LLC converter is selecting the quality factor (Q_e) and the normalized inductance (L_n) of the resonant tank network. This step is very crucial in the design process of the resonant converter since it will determine the performance of the converter itself. Usually, we need to tune the Q_e and L_n values several times to get an optimal performance.

This time we use Microsoft Excel to calculate the gain of the resonant tank over different values Q_e and L_n then plot it. So, by plotting it we can see whether we have enough gain using the chosen Q_e and L_n values.

The picture above shows how to use Microsoft Excell to plot the voltage gain of the resonant tank network.

f_r is the resonant frequency of the resonant tank that we want.
f_sw is the switching frequency starting from 0 Hz until 200 kHz.
F_x is the normalized value of the switching frequency over the resonant frequency.
Q_e is the quality factor, we can input any value to see its impact on the gain plotting.
L_n is the normalized value of the resonant inductance over the magnetizing inductance, we can input any value and see its impact on the gain plotting.

Now, we can play around with the resonant Q_e and L_n values and choose one that will fit with our LLC resonant converter criteria.

We will see that,

• Higher Q_e will give a lower maximum gain that can be achieved and the curve is more flat but, the controller will need less effort to cover the frequency range.
• Higher L_n will give a lower maximum gain that can be achieved and the curve is more flat but, the converter will be more efficient because the ripple current on the magnetizing inductance will be lower.