Permeability and Saturation
The nonlinearity of material permeability may be graphed
for better understanding. We'll place the quantity of field intensity (H), equal
to field force (mmf) divided by the length of the material, on the horizontal
axis of the graph. On the vertical axis, we'll place the quantity of flux
density (B), equal to total flux divided by the cross-sectional area of the
material. We will use the quantities of field intensity (H) and flux density (B)
instead of field force (mmf) and total flux (Φ) so that the shape of our
graph remains independent of the physical dimensions of our test material. What
we're trying to do here is show a mathematical relationship between field force
and flux for any chunk of a particular substance, in the same spirit as
describing a material's specific resistance in ohm-cmil/ft instead of its
actual resistance in ohms.
This is called the normal magnetization curve, or B-H
curve, for any particular material. Notice how the flux density for any of
the above materials (cast iron, cast steel, and sheet steel) levels off with
increasing amounts of field intensity. This effect is known as saturation.
When there is little applied magnetic force (low H), only a few atoms are in
alignment, and the rest are easily aligned with additional force. However, as
more flux gets crammed into the same cross-sectional area of a ferromagnetic
material, fewer atoms are available within that material to align their
electrons with additional force, and so it takes more and more force (H) to get
less and less "help" from the material in creating more flux density
(B). To put this in economic terms, we're seeing a case of diminishing returns
(B) on our investment (H). Saturation is a phenomenon limited to iron-core
electromagnets. Air-core electromagnets don't saturate, but on the other hand
they don't produce nearly as much magnetic flux as a ferromagnetic core for the
same number of wire turns and current.
Another quirk to confound our analysis of magnetic flux
versus force is the phenomenon of magnetic hysteresis. As a general term,
hysteresis means a lag between input and output in a system upon a change in
direction. Anyone who's ever driven an old automobile with "loose"
steering knows what hysteresis is: to change from turning left to turning right
(or visa-versa), you have to rotate the steering wheel an additional amount to
overcome the built-in "lag" in the mechanical linkage system between
the steering wheel and the front wheels of the car. In a magnetic system,
hysteresis is seen in a ferromagnetic material that tends to stay magnetized
after an applied field force has been removed (see "retentivity" in
the first section of this chapter), if the force is reversed in polarity.
Let's use the same graph again, only extending the axes to
indicate both positive and negative quantities. First we'll apply an increasing
field force (current through the coils of our electromagnet). We should see the
flux density increase (go up and to the right) according to the normal
Next, we'll stop the current going through the coil of the
electromagnet and see what happens to the flux, leaving the first curve still on
Due to the retentivity of the material, we still have a
magnetic flux with no applied force (no current through the coil). Our
electromagnet core is acting as a permanent magnet at this point. Now we will
slowly apply the same amount of magnetic field force in the opposite
direction to our sample:
The flux density has now reached a point equivalent to
what it was with a full positive value of field intensity (H), except in the
negative, or opposite, direction. Let's stop the current going through the coil
again and see how much flux remains:
Once again, due to the natural retentivity of the
material, it will hold a magnetic flux with no power applied to the coil, except
this time it's in a direction opposite to that of the last time we stopped
current through the coil. If we re-apply power in a positive direction again, we
should see the flux density reach its prior peak in the upper-right corner of
the graph again:
The "S"-shaped curve traced by these steps form
what is called the hysteresis curve of a ferromagnetic material for a
given set of field intensity extremes (-H and +H). If this doesn't quite make
sense, consider a hysteresis graph for the automobile steering scenario
described earlier, one graph depicting a "tight" steering system and
one depicting a "loose" system:
Just as in the case of automobile steering systems,
hysteresis can be a problem. If you're designing a system to produce precise
amounts of magnetic field flux for given amounts of current, hysteresis may
hinder this design goal (due to the fact that the amount of flux density would
depend on the current and how strongly it was magnetized before!).
Similarly, a loose steering system is unacceptable in a race car, where precise,
repeatable steering response is a necessity. Also, having to overcome prior
magnetization in an electromagnet can be a waste of energy if the current used
to energize the coil is alternating back and forth (AC). The area within the
hysteresis curve gives a rough estimate of the amount of this wasted energy.
Other times, magnetic hysteresis is a desirable thing.
Such is the case when magnetic materials are used as a means of storing
information (computer disks, audio and video tapes). In these applications, it
is desirable to be able to magnetize a speck of iron oxide (ferrite) and rely on
that material's retentivity to "remember" its last magnetized state.
Another productive application for magnetic hysteresis is in filtering
high-frequency electromagnetic "noise" (rapidly alternating surges of
voltage) from signal wiring by running those wires through the middle of a
ferrite ring. The energy consumed in overcoming the hysteresis of ferrite
attenuates the strength of the "noise" signal. Interestingly enough,
the hysteresis curve of ferrite is quite extreme:
- The permeability of a material changes with the amount
of magnetic flux forced through it.
- The specific relationship of force to flux (field
intensity H to flux density B) is graphed in a form called the normal
- It is possible to apply so much magnetic field force to
a ferromagnetic material that no more flux can be crammed into it. This
condition is known as magnetic saturation.
- When the retentivity of a ferromagnetic
substance interferes with its re-magnetization in the opposite direction, a
condition known as hysteresis occurs.
Lessons In Electric Circuits copyright (C)
2000-2011 Tony R. Kuphaldt, under the terms and conditions of the Design