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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 [15]. Loss mechanisms in magnetic devices are described. Winding eddy
currents and the proximity effect, a significant loss mechanism in highcurrent highfrequency windings,
are explained in detail [611]. 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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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
Figure 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 crosssectional 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 righthand rule, as in Fig. 13.2. For a
13.1 Review of Basic Magnetics
493
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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This note was uploaded on 01/17/2010 for the course EL 5673 taught by Professor Dariuszczarkowski during the Spring '09 term at NYU Poly.
 Spring '09
 DariuszCzarkowski

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