Transformer winding losses with round conductors for duty-cycle regulated square waves

One of the limiting factor in the course of reducing the size of high frequency transformer is the temperature rise. The knowledge of transformer power loss is important to make an estimate of the temperature rise. The transformer winding loss due to a duty-cycle regulated square current waveform can be estimated by summing the copper loss due to each harmonic using Dowell´s formula. The paper shows that a large number of harmonics have to be considered for the loss computation. It is shown that for solid-round wire conductors the losses decrease with increasing diameter and there is no optimal diameter for which the losses are minimum. This paper presents a closed form approximate expression for power loss for a particular range of diameters of round wire that does not require a large series summation. Results from this closed form expression are shown to have reasonable accuracy in comparison to the fourier series method and also validated using 2-D finite element method.