Resonant Converter: Power Conversion, Optimal Layout and Magnetic Component Design

Abstract

This PhD thesis contributes to the analysis and design of high-frequency resonant converters, with emphasis on the design of the magnetic components. The contributions lie on the modifications of existing equations and the introduction of new ones to for accurately estimating the inductance of rectangle-shaped single-layer and multilayer planar windings, enabling fast design and optimization processes. Furthermore, this thesis provides closed-form solutions of the differential equations that describe all the operation regions of the LC and LLC resonant converters, providing insight to their behavior and setting the criteria for the selection of passive and active components. A comparison between the regions is carried out and the boundary conditions between each operating region are defined. The structure is as follows:

First, good design practices are presented for high-frequency power electronics printed circuit boards (PCBs), whose design difficulty lies in the fact that they include high-power signals, as well as analog and digital control and measurement signals. The difference on the power level and frequency spectrum can lead to crosstalk between signals inside the board, and to electromagnetic interference between the converter and other electronics devices. The design practices appear scattered in the literature (in books and scientific articles), but also in interviews and presentations of experienced designers of high-frequency boards and power electronics.

The topic of planar windings (PWs) is discussed. Their inductance is affected by the geometrical shape of the winding, and several equations for regular-polygons have been proposed in the literature. However, the use of rectangle-shaped windings provides an additional degree of freedom to the designer, while the exact knowledge of the inductance plays a serious role in calculating the characteristic values of the resonant converter. Modifications to three well-established equations, namely Wheeler, Rosa, and the Monomial, are developed to calculate the inductance of single-layer rectangle-shaped planar windings, without affecting the estimation accuracy. The mean absolute error is less than 1% for the first two equations and less than 5% for the third. In addition, an algorithm for estimating the inductance per turn is presented and validated, providing less than 7% error in the worst case.

A new monomial-like equation for calculating the inductance of multilayer rectangle-shaped inductors is proposed, which retains the high estimation accuracy of the equations for single-level windings. The mean error μ = 0%, the standard deviation σ = 1.77%, and the mean absolute error is less than 1.5%. Moreover, a comparative study is carried out on the accuracy of the various equations in single and multi-level windings, highlighting the most accurate equation for each case. For single-layer PWs, modified Rosa and Wheeler provide a mean absolute error of less than 1.1% and the new proposed Monomial equation less than 2.1%. In the case of multilayer PWs, all modified equations provide a mean absolute error greater than 7.5%, while the new proposed monomial equation has an error of less than 1.5%. In addition, a brief analysis is made of the effect the insertion of the ferrite core has on the inductance of a planar winding, calculating the magnetic flux of an EI core with and without an air-gap.

The common denominator of the aforementioned topics is the resonant converters. Analytical models are presented in the time domain for series-resonant and LLC converters, for all operating regions (inductive, resonant, capacitive), and the initial conditions are deduced. Particular emphasis is given to the boundary conditions of the regions, and especially on the operation between continuous and discontinuous current mode. The solutions yield the values of voltage and current for every node of the converter, as well as the conditions necessary to achieve soft-switching under zero-voltage or zero-current.

Furthermore, a comparison between MOSFET and IGBT devices is carried out for the series-resonant converter, highlighting the most efficient region for each device respectively. The conduction and switching losses models are presented, enabling the estimation of the converter’s efficiency under any condition and operation. Based on the analytical solutions and waveforms, a passive and active component selection procedure is proposed, which includes the parasitic components of semiconductor switches.