0195136047.pdf

11.1 MAGNETIC MATERIALS 473

H,At/m

2.4

2.0

1.6

1.2

0.8

0.4

0

B,T

Vanadium permendur

Deltamax

Ingot iron

48 NI

M-19

48 NI

Permalloy sheet

AISI 1020

Cold-rolled steel

Soft ferrite

1.0 10 50 100 1000 10,000

Figure 11.1.2Typical magnetic characteristics of certain core materials.

which is a characteristic of a magnetic core material. The area of the loop represents the heat-
energy loss during one cycle in a unit cube of the core material. The hysteresis loss per cyclePhcycle
in a core of volumeV, possessing a uniform flux densityBthroughout its volume, is given by

Phcycle=V(area of hysteresis loop)=V

∮

HdB (11.1.3)

The hysteresis loss per second is approximated empirically by

Phsecond=khVf Bm^1 .5to2·^5 W (11.1.4)

wherekhis a proportionality constant dependent on the characteristics of iron,fis the frequency of
excitation in hertz, andBmis the maximum value of the core flux density. This loss component of
the core loss can be reduced by choosing a core of electrical steel that has a narrow hysteresis loop.
Square-loop magnetic materials(such as ferrites and permalloy) that have a nearly rectangular
hysteresis loop are used in switching circuits, as storage elements in computers, and in special
types of transformers in electronic circuits.
Another feature of an ac-operated magnetic system is the eddy-current loss, which is the
loss due to the eddy currents induced in the core material. The eddy-current loss is empirically
approximated as

Pe=keVf^2 τ^2 Bm^2 W (11.1.5)

wherekeis a constant dependent on the characteristics of iron,Vis the volume of iron,fis the
frequency,τis the lamination thickness (usually a stack of thin laminations makes up the core),
andBmis the maximum core flux density. By choosing very thin laminations (makingτsmaller),
the eddy-current loss can be reduced.
The laminations (or thin sheets), insulated from each other by a thin coat of varnish, are
oriented parallel to the direction of flux, as shown in Figure 11.1.4. Laminating a core generally
results in an increase in the overall volume. The ratio of the volume actually occupied by the