D.Ing. / Transformer design is an art which spans a century. Although the basic transformer has changed little over this period, the challenges that face high frequency power transformer designers today have grown considerably. Increasing frequency and power density and decreasing size and profile are among the most important. Eddy currents, controlling circuit behaviour and minimising losses are important aspects of design, and close attention is paid to heat removal and cooling. Modern transformers are no longer limited to certain shapes and sizes; choosing the topology and optimising the shape is often part of the design process. For each aspect of design, numerous modelling techniques exist for analysing transformer behaviour, with varying degrees of complexity. A common feature of optimisation techniques is the large number of variables and interdependent functions that relate different aspects, from the associated behavioural models, to one another. In this study, this complexity is reduced by integrating the individual analytical models for transformer behaviour. Since a convenient thermal model for high frequency transformers does not exist at present, a new thermal reference model is devised and verified. It is specifically suited to high frequency transformer applications and design, and practical sets of reference data are provided for a few ferrite materials and for copper. Transformer losses are considered next, with special attention given to eddy current analysis techniques. New formulations of eddy current solutions are given, with extensions of the orthogonality principle for skin- and proximity effects and superposition thereof. An investigation of leakage impedance design as a function of frequency scaling follows. The relationship between leakage reactance voltage drop as a function of frequency scaling by dividing a monolithic transformer into distributed elements is considered, and the results are applied to two case studies of a 35kVA transformer for a plasma burner application. A new model, the generic proportionality model, applies the thermal referenCe model to scaling of transformer parameters. A case study is also presented, demonstrating the relationships that exist between design parameters and performance functions. Another generic model, the scant model, is introduced, which integrates the thermal reference model into optimisation of transformer shape. It uses a limited number of functional and form parameters, and is applicable to a wide variety of geometries. Two case studies, demonstrate the effects of varying the shape of a rectangular configuration on derating factors.

In high-frequency power transformers, magnetic material properties cannot be assumed to be constant. These properties vary with frequency, temperature, and magnetic flux density. Heat generation is, in turn, a function of the magnetic permeability, magnetic flux density, and frequency. Current design methods are either empirical or based on linear, uncoupled models. To better understand the relationship between heat transfer, magnetic flux density, material properties, and core geometry in a miniature, high-frequency transformer, a finite-element program has been developed to solve the coupled thermal-magnetic equations for an axisymmetric transformer. The program accounts for nonlinear temperature and magnetic field dependent material properties, geometry, and driving frequency. The program, HT-MAG, is based on a series of derived magnetic field equations. The Ritz method is applied to the magnetic and thermal equations in the development of the program. The program alternately solves the finite element approximations to the thermal and magnetic governing equations until the magnetic properties match within a specified fraction or a maximum number of iterations are performed. In addition, the program can be linked with existing pre- and post-processors or can accept manual pre- and post-processing. Six test cases were run to test the validity of the program. The first two cases tested the uncoupled heat transfer calculations. One of these tested the thermal conduction calculations while the other tested the heat generation calculations. The next two cases tested the uncoupled magnetic equations. The first was a direct current (DC) case, while the second was an alternating current (AC) case. The final two cases tested the thermal magnetic coupling. Solutions to these cases are presented and discussed. / Master of Science

The design of a high-frequency transformer at levels above 1 kVA is limited by the winding and core materials which are available. This res~arch presents methods for the design and modeling of a 10 kVA transformer operating at a frequency of 20 kHz using readily available materials. A special winding technique is employed to increase both energy density and transformation efficiency by reducing leakage inductance and eddy current losses in the windings. The procedures for calculating the equivalent circuit parameters applicable to this design are outlined, and the calculated values compared with the measured quantities. A thermal analysis of the design is also explored using the equivalent circuit model as a basis for the calculation. Some of the calculations are specific to this particular design, whereas others are quite generic, however the overall concepts employed in the design and analysis of this device have widespread application within the area of high-frequency, high-power transformer design. / Master of Science

An impedance-based core loss measurement technique for power ferrites, the modeling and analysis of mechanisms of high-frequency losses, and design methodology for optimization for high-frequency magnetics are presented. The high-frequency losses of ferrite materials are characterized employing a large-signal impedance measurement technique. The impedance analyzer controlled through an IEEE-488 interface, measures the impedance of the inductor under test under large signal excitation via a power amplifier. The core loss is a form of a parallel resistance is derived from measured impedance characteristics. A wideband impedance probe, enables core loss characterization up to 100 MHz. A comprehensive analysis of all major loss mechanisms in ferrites is presented. A new form of residual losses due to a magnetoelectric effect is postulated to account for losses at high frequencies. Two models of losses in ferrites are proposed, one with emphasis on analysis of loss mechanisms, and the other with an emphasis on the design of high-frequency magnetic components. Both models include the important effect of static bias field, which is the case in many power electronics applications. Magnetic losses due to magnetostriction are measured. Dependence of magnetoelastic resonances on the magnetic bias. core material, core shape and size is studied. The influence of diffusion after-effect on core loss under time-varying bias field is investigated. Thermal stability of high-frequency magnetics is studied. A verification of one- and two- dimensional models of winding losses for solid and litz wire is performed. The optimum design method for high-frequency power transformers and inductors is proposed. / PhD