TIDUF18A October 2022 – February 2024
While selecting Lrp, the ratio of Lm to Lrp is widely used as a design parameter,

The Ln value is selected such that it ensures the voltage gain in the resonant tank is enough across the operating range of the converter. In this design, as the input voltage comes from a PFC stage and will have a estimated 10% ripple, a gain variation of at least 10% is needed. With this criteria in mind and the fact that Ln should be kept higher to reduce the inductor value, and hence the losses, Ln equal to 14 is selected for this design, based on the plot of the FHA with Ln varying with load (see Figure 2-7).
Figure 2-7 CLLLC Tank Gain Variation With Ln VaryingNow that the selection of Ln is made, Lrp can be calculated using Equation 4. Lrp and Crp determine the series resonant frequency of the converter and they are related by Equation 5.

Equation 5 can then be used to calculate the Crp needed on the design. However, due to component availability, the next closest value of Crp is used on the design. With these component values, the BCM gain is shown in Figure 2-7.
In Figure 2-7, as the load increases (that is, RL_dc goes lower), the gain curve becomes non-monotonic in the region below series resonant frequency. This can lead to the loss of ZVS on the primary FETs and, more critically, the loss of control. Therefore assuming maximum load at nominal Vout, the load is limited or clamped to RL_dc = 30 Ω, for which the gain is monotonic (see Figure 2-7).
Additionally Figure 2-7 shows that in BCM we have enough gain across our operating frequency of 200kHz to 800kHz to cover all operating conditions. Lastly, it is worth noting that if the PFC ripple can be reduced then the totally expected input range will also reduce. This causes the required gain range to reduce, and ultimately helping to reduce the frequency variation needed to support all load conditions.