Inductors: Variable and Controllable

The book is organized in five chapters. Chapter 1 is an introductory chapter where the basic knowledge on magnetic devices is reviewed. The fundamental laws of magnetic fields are presented, and the different types of magnetic materials and their behavior are revised. Next, the spice modeling of magnetic circuits is presented, showing the different elements that can be used to implement spice models of magnetic structures: air gaps, linear and non-linear reluctances, permanent magnets, windings, etc. The spice definitions of these components are provided for direct implementation in LTspice. The chapter finalizes with some examples of implementation of LTspice models for simple magnetic circuits.Chapter 2 deals with self-variable inductors, which are those whose inductance value changes with the current circulating through them. This chapter is also used to introduce several relevant aspects, as the definition of DC and AC inductors, the effective and differential inductance, and the analysis methodology that will be later used in Chapter 3 to study the behavior of controllable inductors. In this chapter, the real inductor is studied as an example of self-variable inductor since, at the end, any physical inductor implemented on a magnetic material will change its value with the current level circulating through it, so that it can be considered as a self-variable inductor. Also, other more sophisticated structures of variable inductors that can be found in the literature are presented and analyzed at the end of this chapter, namely, the self-variable inductor with stepped air gap, and the self-variable inductor with sloped air gap. These structures can allow the designer to have a better control of the change of the inductance against its current, to better adapt them to a particular application.Chapter 3 focuses on controllable inductors. The chapter explains how a structure of controllable inductor can mathematically be analyzed to obtain the most important characteristics, as the main winding inductance versus bias current characteristic, the DC and AC induction levels in the different parts of the structure, the voltage reflected across the bias windings, the bias winding inductance versus the bias current, etc. Three different structures are used as examples: the double-E structure, the quad-U structure, and the triple-E structure. Some ideas about the use of permanent magnets in the design and implementation of controllable inductors are also provided in this chapter. Finally, a design procedure for controllable inductors is presented in the last section of the chapter. Examples of analysis and simulation of all the structures are included. As in the rest of the book, free software is used for both mathematical analysis and simulation, WinPython and LTspice respectively.In Chapter 4 driving and control issues of controllable inductors are presented. The chapter starts with the basic modeling of the bias circuit and its effect on the controllable inductor dynamics. A full dynamic model of the controllable inductor is also presented. In the second part of the chapter, several solutions to implement bias circuits are studied, which are based on linear current sources and switching power converters. The dynamics of each solution is investigated, and examples are provided with analysis in WinPython and simulations in LTspice.Finally, Chapter 5 presents several application examples of controllable inductors, such as those in resonant inverters, DC-DC converters, LED drivers, and high-power-factor AC-DC converters.