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A DC-DC converter based on the Dual Active Bridge topology is designed, having high power density as main design target. To that aim, a simple structure has been proposed for the transformer with embedded inductor, allowing high frequency operation with low losses and requiring only readily available magnetic core shapes. Simple phase-shift control has been used, and the switching frequency is varied in order to minimize the peak transformer current, thus achieving high conversion efficiency. A fully operational prototype has been built and tested, demonstrating a power density figure of 7.1 kW/Liter with forced air cooling, and a peak efficiency at rated 4 kW load equal to 96.6 %.