Inductor quirks
In an ideal case, an inductor acts as a
purely reactive device. That is, its opposition to AC
current is strictly based on inductive reaction to changes
in current, and not electron friction as is the case with
resistive components. However, inductors are not quite so
pure in their reactive behavior. To begin with, they're made
of wire, and we know that all wire possesses some measurable
amount of resistance (unless it's superconducting wire).
This built-in resistance acts as though it were connected in
series with the perfect inductance of the coil, like this:
Consequently, the impedance of any real
inductor will always be a complex combination of resistance
and inductive reactance.
Compounding this problem is something called
the skin effect, which is AC's tendency to flow
through the outer areas of a conductor's cross-section
rather than through the middle. When electrons flow in a
single direction (DC), they use the entire cross-sectional
area of the conductor to move. Electrons switching
directions of flow, on the other hand, tend to avoid travel
through the very middle of a conductor, limiting the
effective cross-sectional area available. The skin effect
becomes more pronounced as frequency increases.
Also, the alternating magnetic field of an
inductor energized with AC may radiate off into space as
part of an electromagnetic wave, especially if the AC is of
high frequency. This radiated energy does not return to the
inductor, and so it manifests itself as resistance (power
dissipation) in the circuit.
Added to the resistive losses of wire and
radiation, there are other effects at work in iron-core
inductors which manifest themselves as additional resistance
between the leads. When an inductor is energized with AC,
the alternating magnetic fields produced tend to induce
circulating currents within the iron core known as eddy
currents. These electric currents in the iron core have
to overcome the electrical resistance offered by the iron,
which is not as good a conductor as copper. Eddy current
losses are primarily counteracted by dividing the iron core
up into many thin sheets (laminations), each one separated
from the other by a thin layer of electrically insulating
varnish. With the cross-section of the core divided up into
many electrically isolated sections, current cannot
circulate within that cross-sectional area and there will be
no (or very little) resistive losses from that effect.
As you might have expected, eddy current
losses in metallic inductor cores manifest themselves in the
form of heat. The effect is more pronounced at higher
frequencies, and can be so extreme that it is sometimes
exploited in manufacturing processes to heat metal objects!
In fact, this process of "inductive heating" is often used
in high-purity metal foundry operations, where metallic
elements and alloys must be heated in a vacuum environment
to avoid contamination by air, and thus where standard
combustion heating technology would be useless. It is a
"non-contact" technology, the heated substance not having to
touch the coil(s) producing the magnetic field.
In high-frequency service, eddy currents can
even develop within the cross-section of the wire itself,
contributing to additional resistive effects. To counteract
this tendency, special wire made of very fine, individually
insulated strands called Litz wire (short for
Litzendraht) can be used. The insulation separating
strands from each other prevent eddy currents from
circulating through the whole wire's cross-sectional area.
Additionally, any magnetic hysteresis that
needs to be overcome with every reversal of the inductor's
magnetic field constitutes an expenditure of energy that
manifests itself as resistance in the circuit. Some core
materials (such as ferrite) are particularly notorious for
their hysteretic effect. Counteracting this effect is best
done by means of proper core material selection and limits
on the peak magnetic field intensity generated with each
cycle.
Altogether, the stray resistive properties
of a real inductor (wire resistance, radiation losses, eddy
currents, and hysteresis losses) are expressed under the
single term of "effective resistance:"
It is worthy to note that the skin effect
and radiation losses apply just as well to straight lengths
of wire in an AC circuit as they do a coiled wire. Usually
their combined effect is too small to notice, but at radio
frequencies they can be quite large. A radio transmitter
antenna, for example, is designed with the express purpose
of dissipating the greatest amount of energy in the form of
electromagnetic radiation.
Effective resistance in an inductor can be a
serious consideration for the AC circuit designer. To help
quantify the relative amount of effective resistance in an
inductor, another value exists called the Q factor,
or "quality factor" which is calculated as follows:
The symbol "Q" has nothing to do with
electric charge (coulombs), which tends to be confusing. For
some reason, the Powers That Be decided to use the same
letter of the alphabet to denote a totally different
quantity.
The higher the value for "Q," the "purer"
the inductor is. Because it's so easy to add additional
resistance if needed, a high-Q inductor is better than a
low-Q inductor for design purposes. An ideal inductor would
have a Q of infinity, with zero effective resistance.
Because inductive reactance (X) varies with
frequency, so will Q. However, since the resistive effects
of inductors (wire skin effect, radiation losses, eddy
current, and hysteresis) also vary with frequency, Q does
not vary proportionally with reactance. In order for a Q
value to have precise meaning, it must be specified at a
particular test frequency.
Stray resistance isn't the only inductor
quirk we need to be aware of. Due to the fact that the
multiple turns of wire comprising inductors are separated
from each other by an insulating gap (air, varnish, or some
other kind of electrical insulation), we have the potential
for capacitance to develop between turns. AC capacitance
will be explored in the next chapter, but it suffices to say
at this point that it behaves very differently from AC
inductance, and therefore further "taints" the reactive
purity of real inductors. |