High frequency transformer design and modelling using finite element technique

Abstract

The field of high power density power supplies has received much attention in recent years. The area of the most concern is to increase the switching frequency so as to achieve a reduction in the power supply size. Such concern in high frequency power conversion units has led to many resonant structures (quasi, multi, and pseudo). In all resonant types, the power transfer from the source to the load is controlled by varying the ratio of operating to resonant frequencies. Every effort has been made to reduce the switching losses using zero voltage and/or zero current techniques. In contrast, little attention has been given to the area of the design of the magnetic components at high frequency operation. It is usually accepted that the weak point in further high frequency power supply design is in the magnetic devices ( transformer and inductor ). No accurate model of the transformer taking into account the high frequency range has been performed yet. It is well known that as the frequency increasess o the transformerm odel becomesm ore complicated,d ue to the complexity of the transformer element distribution, and the nature of frequency dependence of some of these elements. Indeed, work of this kind can take many directions, and the attempt here is to introduce a number of mathematics, analytical, numerical, and practical directions to model the transformer. The main factors affecting the high frequency performance are the eddy current losses, leakage flux and the effects due to the transformer elements, where the transformer is part of the resonant converter. Two dimensional transformer finite element modelling is used to examine different cases, including open and short circuit conditions. The frequency dependency of the winding resistance and leakage inductance is fully explained. The practical design of the transformer and testing is used to valididate the simulation results. These results are supported by the results obtained from the mathematical formulation. Special attention is given to reducing both copper losses and leakage in the windings. Three dimensional modelling of the high frequency transformer and the solution using a program solving the full set of Maxwell's equations is the original part of the present work. Frequency response characteristics are found and compared to that obtained from the test. Curves of these characteristics are used to predict a simplified transformer equivalent circuit. This circuit is used with the simulation of a full bridge series resonant converter, where all units ( switches, control, isolation, feedback, and transformer ) are represented by an equivalent circuit. The power supply operation and its behaviour in respect to the change with frequency of each of the transformer elements are examined. Two cases are considered through the simulation, when the operating frequency is above and when it is below the resonant tank frequency. The simulated results are validated by building a practical power supply. In addition, the numerical solution of modelling the transformer by an equivalent network is also introduced. The highest possible number of elements (R, L, and Q are used, where all the elements are found using 2D FEM solution of both magnetostatic and electrostatic fields. This network is solved using the trapezoidal rule of integration and electric network theory. The examination of the influences of the distribution capacitances on the internal winding frequency response characteristic is carefully examined. The last work in the present research is focussed on finding a general model of an exact transformer equivalent circuit to cover the wide frequency range. The thesis is completed with a conclusion.