The medium-frequency power transformer (MFPT) is one of the key elements of an isolated bi-directional dc-dc converters in applications such as future all-dc offshore wind farms, traction, and solid state transformers. This paper describes a design methodology taking into account loss calculation, isolation requirements, and thermal management. Incorporating this design methodology, an optimization process with a wide range of parameter variations is applied on a design example to find the highest power density while the efficiency, isolation, thermal, and leakage inductance requirements are all met.