Marian K. Kazimierczuk, Ph.D., D.Sci. (Advisor); Saiyu Ren, Ph.D. (Committee Member); Michael A. Saville, Ph.D., P.E. (Committee Member); Ray Siferd, Ph.D. (Committee Member); Yan Zhuang, Ph.D. (Committee Member)
Doctor of Philosophy (PhD)
At the frequencies used in switching dc-dc converters, the skin and proximity effects have a significant effect on both the losses and leakage inductance of the transformers used in these circuits. Analytical expressions that have been derived to calculate ac resistance and leakage inductance have primarily used a 1-D approximation. They also have used Cartesian coordinates or approximations that are equivalent to Cartesian coordinates, as well as usually assuming an ideal core of infinite permeability. The classical result in the case of the resistance/losses is Dowell’s equation, and there are analogous results for leakage inductance. This dissertation derives new equations that take the effect of winding curvature into account by using cylindrical coordinates. These equations are also more general in that they permit any interleaving pattern as well as variable layer thicknesses and gaps between layers. Additionally, new equations for the magnetic field coefficients are derived that take the core permeability into account, which requires a full 2-D model and the method of images applied in two dimensions. These coefficients then allow calculations of resistance/losses and leakage inductance that also take the core permeability and winding width into account. The accuracy of all of these equations is assessed by comparing their results with those of finite-element analysis (FEA) simulations. Due to the large number of parameters involved with the fully general equations, a statistical approach is used in which a large number of randomly generated devices are simulated. Finally, for a special class of more specific transformers, the effects of a reduced number of independent parameters on the resistance/losses and leakage inductance is determined empirically. The relative sensitivity of these quantities on these parameters is also determined.
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