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Soft switching in dual-active-bridge (DAB) converters enables their efficient operation at high frequencies, where the reduction in the size of magnetic components could result in ultra-high power densities. Nonetheless, losing soft-switching at high frequencies results in severe efficiency degradations along with excessive thermal and electrical stresses on the transistors. In a previous work, we have presented an enhanced-DAB (E-DAB) topology along with an adjustable-tap high-frequency transformer to extend soft switching over wider voltage gains. The E-DAB achieved a peak efficiency of 97.4% without any complex modulation techniques, enabling a power density of 10 kW/l (or 164 W/inch^3 ) at 300 kHz. Here, we compare two different transformer geometries for their leakage inductance, quality factor and compatibility with the E-DAB. A theoretical gain-versus-power soft-switching characteristic for the E-DAB is verified by measurements of switching transients and amplitude spectrum analysis. The magnetic flux density and its distribution in the transformer core is analyzed using a finite-element analysis (FEA) method and the on-load operation of electromagnetic tap changers is presented. E-DAB converters are of great importance to renewable energy harvesting, Li-ion battery chargers, future dc distribution systems and smart grids due to their high efficiency, high power density and superior controllability.