Transformer winding losses with round conductors and foil windings for duty-cycle regulated square waveform followed by winding design and comparison for sinusoidal excitation

Abstract

High frequency transformers are used extensively in Switch mode power supplies (SMPS). The transformer size reduces with an increase in frequency leading to a compact design.With the advent of SiC switches the SMPS can be operated at much higher frequencies. But with the increase in frequency, the losses in transformer increase. This poses a threat in the design of high density magnetic components. In order to design the magnetic components with smallest possible volume the estimation of the losses should be accurate. The losses in a transformer occur in the core as well as in the winding.Simplified expressions for winding loss computation for duty cycle modulated current waveform for different conductors like foil and round is derived in this thesis. The thesis shows that the Fourier series method for the loss computation requires the consideration of a large number of harmonics leading to considerable computational difficulty in the determination of optimal thickness. A closed form approximate expression for power loss is presented that obviates any need for a large series summation resulting in a relatively simple computation of optimal thickness. In case of the solid round wire windings there is no optimal diameter for which the losses are minimum. The losses decrease with increasing diameter and there is a range of normalized diameters that should be avoided. A closed form approximate expression for a particular range of diameters of round wire depending on the current and frequency for power loss is presented that obviates any need for a large series summation.The thesis also demonstrates a winding design procedure for minimizing the power losses using foils and solid round wires under sinusoidal excitation. In this thesis the range from which the thickness of the layers can be chosen to obtain the minimum power loss is derived. 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. The analytical results are verified by designing six different winding configurations for the same specifications using 2-D Ansys Maxwell finite element design package.