This paper proposes a Dual Active Bridge converter operating at 1.5 MHz switching frequency for an 11kW bidirectional On-Board Charger (OBC) for Electrical Vehicle (EV) application. An air-core transformer is exploited for high-efficiency requirements and for high power density challenge. In addition, a 650 V GaN device was adopted since it is very suitable for this range of voltage and high frequency application. A study on switching frequency application in addition to the voltage range was presented before determining the soft-switching operating area. The required dead time and capacitance are evaluated and presented in this paper. A prototype was implemented, and experiments validate the theoretical results. The converter designed performed at this frequency in soft switching and results exhibits 96% of efficiency with a power density of 6kW/L. These experiments confirm the simulation result and the analytical calculations and further improvements are expected to increase again the power density in the future.