Europe is currently making a great effort in order to improve the sustainability and reduce the environmental impact of its energy and transportation systems. A key role on these initiatives is played by efficient generation systems, like cogeneration, and clean or renewable energies, like wind or solar energy, as well as, by efficient and improved transportation technologies. In the evolution of these energy and transport systems, the development of Power Electronic Converters with greater functionality, higher reliability, higher efficiency, lower cost, and more sophisticated control will be essential. The main goal of future Power Electronic Converters will be to increase power density, reduce cost and improve reliability. This way, volume, weight and material reduction as well as reliability will gain the future market. A great contribution of these goals will be made by new high-power semiconductor devices, which permit the extension of the frequency range of power converters, and consequently the reduction of magnetic components. A good example of one of these systems are medium-frequency power conversion systems, also known as Power Electronic Transformers, which are able to convert electric power as convectional transformers but with increased features: volume and weight reduction, power transfer and quality control etc. The present work introduces a complete characterization of a medium-frequency power transformer, suitable for efficient Power Electronic conversion systems. The motivation of the present work stems out from the need to evaluate the constraints of conventional transformer characterization and design methodologies. The proposed expressions are able to successfully address the problematic related to non-sinusoidal waveforms, typical of medium-frequency power transformers. Moreover, a design methodology for the optimal design of medium-frequency power transformers is introduced. The characterization, as well as the design methodology, are verified by means of finite element simulations and measurement results.