Planar Transformers in LLC Resonant Converters: High-Frequency Fringing Losses Modeling

Fringing losses play a detrimental role in high-frequency transformers. The tendency toward higher power density and miniaturization of power converters leads to higher switching frequency and enforces the use of low-profile components such as gapped planar transformers. Due to the air gap, lower magnetizing inductance and better regulation of LLC (L
_m
, L
_s
, C
_s
) can be achieved, but fringing fluxes can also be induced, resulting in extra magnetic losses and more hotspots. These losses are highly dependent on the frequency and the core material, so it is critical to model them for gapped planar transformers in LLC resonant converters, which operate at high frequencies and use ferrite material. In this article, fringing losses for gapped ferrite transformers in LLC converters are thoroughly modeled in order to provide a precise prediction regardless of the materials and core geometries. The proposed method provides an accurate and compact formula for predicting the fringing losses of planar transformers. This formula is obtained based on the finite-element method so as to consider and evaluate different design parameters. An LLC resonant converter with different planar transformers is implemented to show the compatibility of the proposed model. Experimental results show the higher accuracy of the proposed model compared to traditional ones and confirm that the proposed loss model can be applied to diverse core shapes. In addition, the gradient descent method is used to calibrate the theoretical and experimental results. Moreover, temperature deviations of the transformer due to the fringing losses are measured and evaluated both experimentally and theoretically to show the accuracy of the proposed loss formula. Due to the proposed model's higher accuracy, an improved design procedure for planar transformers is obtained, adding substantial value for design engineers.