High frequency transformers are widely used in Switched-mode power supplies and now are being proposed to be used with power electronic converters to replace line-frequency transformers. This paper presents a winding design procedure for minimizing the power losses using foils and solid round wires under sinusoidal excitation to limit the temperature rise. This paper derives the range from which the thickness of the layers can be chosen to obtain the minimum power loss. This thickness range is a function of the number of layers and does not include the 'optimum'based on the previous literature. Using this design procedure, it is shown that interleaving is not necessary in foil-wound transformers to obtain the minimum loss. A comparison of winding losses between foil windings and round conductors is also given. The analytical results are verified by designing six different winding configurations for the same specifications using 2-D Ansys Maxwell finite element design package.