Transformer design is critical as the demands on power converter efficiency and power density increase. Initial transformer core shape and size selection can be challenging, in many cases necessitating multiple elaborate design iterations to find a suitable core. A number of core constants have been proposed in the past to assist with initial core selection, however, most of them do not consider high frequency losses in transformer cores which are becoming increasingly important. The Kgfe transformer design method is adapted in this paper to consider high frequency copper losses in transformer designs with bi-directional excitation and two windings. The presented expressions can be used to quickly determine the minimum achievable power losses for a given core size, material and wire diameter.