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 magnetization curve:
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 the graph:
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:
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REVIEW:
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The permeability of a material changes
with the amount of magnetic flux forced through it.
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The specific relationship of force to flux
(field intensity H to flux density B) is graphed in a form
called the normal magnetization curve.
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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.
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When the retentivity of a
ferromagnetic substance interferes with its
re-magnetization in the opposite direction, a condition
known as hysteresis occurs.
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