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chap13

# chap13 - 13 Basic Magnetics Theory Magnetics are an...

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13 Basic Magnetics Theory Magnetics are an integral part of every switching converter. Often, the design of the magnetic devices cannot be isolated from the converter design. The power electronics engineer must not only model and design the converter, but must model and design the magnetics as well. Modeling and design of magnet- ics for switching converters is the topic of Part III of this book. In this chapter, basic magnetics theory is reviewed, including magnetic circuits, inductor model- ing, and transformer modeling [1-5]. Loss mechanisms in magnetic devices are described. Winding eddy currents and the proximity effect, a significant loss mechanism in high-current high-frequency windings, are explained in detail [6-11]. Inductor design is introduced in Chapter 14, and transformer design is cov- ered in Chapter 15. REVIEW OF BASIC MAGNETICS The basic magnetic quantities are illustrated in Fig. 13.1. Also illustrated are the analogous, and perhaps more familiar, electrical quantities. The magnetomotive force or scalar potential, between two points and is given by the integral of the magnetic field H along a path connecting the points: where is a vector length element pointing in the direction of the path. The dot product yields the com- 13.1.1 Basic Relationships 13.1

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492 Basic Magnetics Theory ponent of H in the direction of the path. If the magnetic field is of uniform strength H passing through an element of length as illustrated, then Eq. (13.1) reduces to This is analogous to the electric field of uniform strength E, which induces a voltage between two points separated by distance Figur e 13.1 also illustrates a total magnetic flux passing through a surface S having area The total flux is equal to the integral of the normal component of the flux density B over the surface where dA is a vector area element having direction normal to the surface. For a uniform flux density of magnitude B as illustrated, the integral reduces to Flux density B is analogous to the electrical current density J , and flux is analogous to the electric cur- rent I . If a uniform current density of magnitude J passes through a surface of area then the total cur- rent is Faraday’s law relates the voltage induced in a winding to the total flux passing through the inte- rior of the winding. Figure 13.2 illustrates flux passing through the interior of a loop of wire. The loop encloses cross-sectional area According to Faraday’s law, the flux induces a voltage v ( t ) in the wire, given by where the polarities of v ( t ) and are defined according to the right-hand rule, as in Fig. 13.2. For a
13.1 Review of Basic Magnetics 49 3 uniform flux distribution, we can express v ( t ) in terms of the flux density B ( t ) by substitution of Eq. (13.4): Thus, the voltage induced in a winding is related to the flux and flux density B passing through the interior of the winding.

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