High frequency transformers (HFT) are needed along with power electronic converters to replace line frequency transformers in high power systems to increase power density. For the design of HFT, it is important to accurately estimate copper losses due to a duty-cycle modulated current waveform. The design also requires determination of the optimal thickness of winding layers, leading to a minimum AC power loss. This paper shows that the Fourier-series method for the loss computation requires the consideration of a large number of harmonics, leading to considerable computational time in the determination of the optimal thickness. A closed form approximate expression for the power loss is presented in this paper that obviates any need for a large series summation, resulting in a relatively simple computation of optimal thickness. Results are validated through numerical computations.