Analysis and design of half-bridge LLC resonant power converters

The thesis focuses on design and analysis techniques (rather than on feedback control techniques) oriented towards LLC resonant power converters with the objective of improving the state-of-the-art and better understanding advantages and limitations. Then, a different design approach based on the exact analysis of the converter evolution and capable of taking into account the effect of parasitic resistances at both the primary and secondary side of the transformer is proposed. In particular, the sequence of on-off states of all switching devices characterising the operation at resonance (in CCM) is extracted; this allows to solve step-wise the differential equations describing circuital evolution of the converter (including lossy elements, not considered in any of the known design approach in the state-of-the-art) in the MATLAB environment. The MATLAB optimiser is then used to find the optimal design of the converter, imposing the operation at resonance, the periodicity of the state variables, the regulated output voltage, the mean output current value (which depends on the output power specification) and the Zero-Voltage Switching (ZVS) condition. The result of this design phase shows that, when considering the system with parasitic resistive losses, the actual resonance frequency (i.e., the optimal working frequency) does not coincide anymore with the that expected according to the ideal model. This implies that, if the value of the resonance frequency is a-priori set, the optimal values of the resonant capacitor and/or the resonant inductor need to be modified. Then, other MATLAB scripts are developed in order to evaluate the voltage conversion ratio of the LLC as a function of the input frequency. This analysis requires to investigate how the sequence of the on-off states of the switching devices is changed according to the operating frequency and to the resistive load. Of course, any other voltage and current of the circuit can be analysed as a function of the frequency/load, following the same approach. As a conclusion, it is important to underline that the proposed design approach leads to an exact design of the lossy converter while the accuracy of the proposed analysis method is independent on the specific frequency at which the convert is working (e.g. below resonance) since the only assumption is to neglect the duration of the dead-time (which is always very low with respect to the input voltage period). Moreover, the presented model could be useful for studying the effect of other non-idealities, thus further refining the converter design.