0195136047.pdf

472 MAGNETIC CIRCUITS AND TRANSFORMERS

11.1 MAGNETIC MATERIALS

For magnetic material media, themagnetic flux density B, expressed in tesla (T) or Wb/m^2 , and

thefield intensity H, expressed in A/m or ampere-turns per meter (At/m), are related through the

relationship

B=μH (11.1.1)

whereμstands for thepermeabilityof the material expressed in henrys per meter (H/m). The free-

space permeabilityμ 0 is a constant given by 4π× 10 −^7 H/m in the SI system of units. The same

value holds good for air as well as for any nonmagnetic material. For a linear magnetic material

which exhibits a straight-line relationship betweenBandH, the permeability is a constant given

by the slope of the linearB–Hcharacteristic, and it is related to the free-space permeability as

μ=μrμ 0 (11.1.2)

whereμris the relative permeability, which is a dimensionless constant. If theB–Hcharacteristic

is nonlinear, as with a number of common magnetic materials, then the permeability varies as a

function of the magnetic induction. The variation ofBwithHis depicted by the saturation curve

of Figure 11.1.1, in which the slope of the curve clearly depends upon the operating flux density,

as classified for convenience into regions I, II, and III.

There are several material classifications with their distinguishing characteristics.Ferromag-

neticmaterials, for whichμr1, exhibit a high degree of magnetizability and are generally

subdivided intohardandsoftmaterials. Soft ferromagnetic materials include most of the steels

and iron, whereas hard ferromagnetic materials include thepermanent-magnetmaterials such as

alnicos and alloys of cobalt with a rare-earth element such as samarium.Ferrimagneticmaterials

are ferrites composed of iron oxides, subdivided into hard and soft categories.Ferrofluids(mag-

netic fluids with iron-oxide particles suspended) andamorphousmagnetic (soft ferromagnetic)

materials were also developed later. Typical magnetic characteristics of some core materials are

shown in Figure 11.1.2.

Core (Iron) Losses

Iron-core losses are usually divided into two components:hysteresis lossandeddy-current loss.

The former is proportional to the area enclosed by thehysteresis loop, shown in Figure 11.1.3,

B,T

Region II

(nearly linear)

Region I

Region III (nonlinear)

Saturation

Typical operating point

H,At/m

Figure 11.1.1Typical magnetization charac-

teristic showing three regions.