4.1.5 B-H Curve
The relationship described by equation 4.3 can be expressed by the B-H curve.
For linear materials mentioned before, the B-H curves are straight lines. How-
ever, there are materials whose B-H curves are not linear. In the design and
analysis of electric machines, two types of materials are of concern as they
play important roles in determining the EM performance of electric machines.
These are soft-magnetic materials and hard-magnetic materials, whose B-H
curves are very different from that of linear materials.
126.96.36.199. Soft-magnetic Material (Ferromagnetic Material)
The relative permeability of a soft-magnetic material is much higher than 1.
These materials are made of iron, nickel, cobalt and manganese, or their com-
pounds. These materials are also known as ferromagnetic materials. The
magnetic performances of these materials also depend on the processes used to
produce them such as heat and rolling treatments. Relative permeability of a
soft-magnetic material is not constant - it varies when the magnetic intensity
It will be shown in section 4.1.6 that, for a given EM device, the fi eld
strength H is proportional to the current source that induces magnetic fi eld
in the device, even if the device structure is complicated and ferromagnetic
materials are used. But the relationship between the fl ux density B and current
source can be complex if ferromagnetic materials are used. The relationship
between B and H can be expressed by the B-H curve of the material. Figure 4.2
shows a typical B-H curve of ferromagnetic material in the fi rst quadrant of
Cartesian coordinate system. The full B-H curve is located in the fi rst and
third quadrants, and is symmetrical about the origin. It is evident from the
curve that the fl ux density varies slowly when H is small. Then for a wide
range of H, B increases rapidly with increasing H and their relationship can
be approximated as linear. For H>H t ,the fl ux density B is a non-linear
function of H, but still monotonic. When the fl ux density is increased to a
certain level (B s ), the material is saturated and further increase of the fl ux
density is diﬃcult. For practical purposes, the B-H curve of the the soft-
magnetic materials can be considered linear in the range (−H t , +H t )thatis
their permeability remains constant.
As their relative permeabilities are higher than 1 and their hysteresis loops
(see section 188.8.131.52) are very narrow, the ferromagnetic materials are widely
used in electric motors as stator core and rotor yoke (see section 4.3) to realize
the required magnetic fi eld path (or the magnetic circuit; see section 4.1.6).
Magnetic performances of some ferromagnetic materials are shown in Table 4.1.