Planar Transformer with Half Turns
Article from an interesting solution for planar magnetics in LLC converters proposed at the National University of Taiwan.
The first author is Yu-Chen Liu. 
Before entering into his publication, I'm going to talk about the State of the art in this topic.
State of the Art
The works related to Matrix Planar Transformers, which showed a very interesting topic a few years ago, when Fred Lee and his students at CPES started the publications about planar transformers for the high turn ratio applications (16:1) and relatively high current. In the first publication, they explain the problem of using a single transformer with several switches in parallel.
They explain the problem of the current sharing in the parallel switches due to different parasitic inductances. Therefore, they divide the transformer (in 4 small transformers) with the primary winding in series and the secondary in parallel.
The voltage applied and the current in the secondaries is divided by 4 -.
New Solution: The proposed solution for the transformer was based on a 4-column structure, where the flux cancellations reduce the core losses and allow to keep high power density. The solution was used in an LLC converter obtaining a power density of 55 W/cm3.
However, in this new paper , the authors (Yu-Chen Liu and others) propose a different approach to the same idea. Yu-Chen Liu proposes to use half turns instead of full turns, in order to reduce conduction losses. After analyzing different physical constructions, he proposes a two-leg option.
In Figure 1 it is shown the concept of using half turns, where the author demonstrates that using them, the same amount of energy can be transferred as using a full turn. As it will be shown in the results, this is the key to reducing the conduction losses on the secondary side.
Transformer construction and results
The construction of the transformer is discussed in the paper, considering one primary winding and 4 center tap secondary windings and the proposed shape is a custom UI.
During the paper, the author explains the calculations of the dimensions for the center leg, in order to keep core losses to the minimum.
Since the switching frequency is around 1 MHz, the selection of the material is critical. The first statement of the author is to limit to 100 mT the peak flux density, in order to avoid performance problems. This is translated into a unit volume loss of 600kW/m3. The material selected by the author is Hitachi ML91S, where the peak flux density at 1 Mhz will be 74 mT for his design.
During the implementation, the author uses Maxwell for the FEM simulations and according to his simulations, the peak flux will exceed his calculations, increasing the losses. Therefore, the author modifies the core dimensions until getting the expected results.
Once the theoretical results are as expected, the author validates the performance in a prototype and provides comparison tables between his solution and the solutions of the state of the art for the converter. The power density achieved is the best registered until now, nevertheless, the peak efficiency result of CPES is higher.
In the table below, the author shows a comparison of the losses in the transformer. The main difference is on the secondary side, where there is an important variety of results.
The works related to Transformers for LLC converters are showing a great power density and this last publication brings the community interesting usability of half turns.
The works are focus on a 1 kW power rate for doing fair comparisons, but, will someone try to replicate this power density at 10 kW?
 Y. -C. Liu et al., "Design and Implementation of a Planar Transformer With Fractional Turns for High Power Density LLC Resonant Converters," in IEEE Transactions on Power Electronics, vol. 36, no. 5, pp. 5191-5203, May 2021, doi: 10.1109/TPEL.2020.3029001.
 D. Huang, S. Ji and F. C. Lee, "LLC resonant converter with matrix transformer", IEEE Trans. Power Electron., vol. 29, no. 8, pp. 4339-4347, Aug. 2014.
 C. Fei, F. C. Lee and Q. Li, "High-efficiency high-power-density LLC converter with an integrated planar matrix transformer for high-output current applications", IEEE Trans. Ind. Electron., vol. 64, no. 11, pp. 9072-9082, Nov. 2017.