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.
|
