This paper discusses the technical challenges and trade-offs tied to design of medium frequency transformers (MFTs) for medium-voltage (MV) high-power (HP) power electronic applications, namely emerging solid state transformers (SSTs). A detailed analysis of the factors influencing the MFT operation and limiting the design range is performed. A dedicated MFT design optimization algorithm is used to generate the set of all feasible transformer designs for the given electric requirements, taking into account different MFT geometry ratios, materials and operating frequencies. Design sets are generated for various combinations of design criteria thus exposing the general trends and impact of different design requirements on the feasible design space.