inductor n : an electrical device that introduces
inductance into a circuit [syn:
inductance]
Translations
passive electrical device
An inductor is a
passive
electrical device employed in
electrical
circuits for its property of
inductance. An inductor can
take many forms.
Physics
Overview
Inductance (L,
measured in
henrys) is
an effect which results from the
magnetic
field that forms around a currentcarrying
conductor.
Electric
current through the conductor creates a
magnetic
flux proportional to the current. A change in this current
creates a change in magnetic flux that, in turn, generates an
electromotive
force (EMF) that acts to oppose this change in current.
Inductance is a measure of the amount of EMF generated for a unit
change in current. For example, an inductor with an inductance of 1
henry produces an EMF of 1 volt when the current through the
inductor changes at the rate of 1 ampere per second. The number of
loops, the size of each loop, and the material it is wrapped around
all affect the inductance. For example, the magnetic flux linking
these turns can be increased by coiling the conductor around a
material with a high
permeability.
Stored energy
The
energy (measured in
joules, in
SI) stored by an
inductor is equal to the amount of work required to establish the
current through the inductor, and therefore the magnetic field.
This is given by:
where L is inductance and I is the current
through the inductor.
Hydraulic model
Electric current can be modeled by the
hydraulic
analogy. The inductor can be modeled by the
flywheel effect of a
turbine rotated by the flow. As
can be demonstrated intuitively and mathematically, this mimics the
behavior of an electrical inductor; voltage is proportional to the
derivative of current with respect to time. Thus a rapid change in
current will cause a big voltage spike. Likewise, in cases of a
sudden interruption of water flow the turbine will generate a high
pressure across the blockage, etc. Magnetic interactions such as in
transformers
are not modeled hydraulically.
Applications
Inductors are used extensively in
analog
circuits and signal processing. Inductors in conjunction with
capacitors and other
components form tuned circuits which can emphasize or
filter
out specific signal frequencies. This can range from the use of
large inductors as chokes in power supplies, which in conjunction
with filter
capacitors
remove residual
hum or other
fluctuations from the direct current output, to such small
inductances as generated by a
ferrite
bead or
torus around a
cable to prevent
radio frequency interference from being transmitted down the
wire. Smaller inductor/capacitor combinations provide
tuned
circuits used in radio reception and broadcasting, for
instance.
Two (or more) inductors which have coupled
magnetic flux form a
transformer, which is a
fundamental component of every electric
utility
power grid. The efficiency of a transformer decreases as the
frequency increases but size can be decreased as well; for this
reason, aircraft use 400 hertz alternating current rather than the
usual 50 or 60 hertz, allowing a great saving in weight from the
use of smaller transformers.
An inductor is used as the energy storage device
in some
switchedmode
power supplies. The inductor is energized for a specific
fraction of the regulator's switching frequency, and deenergized
for the remainder of the cycle. This energy transfer ratio
determines the inputvoltage to outputvoltage ratio. This XL is
used in complement with an active semiconductor device to maintain
very accurate voltage control.
Inductors are also employed in electrical
transmission systems, where they are used to intentionally depress
system voltages or limit
fault
current. In this field, they are more commonly referred to as
reactors.
As inductors tend to be larger and heavier than
other components, their use has been reduced in modern equipment;
solid state switching power supplies eliminate large transformers,
for instance, and circuits are designed to use only small
inductors, if any; larger values are simulated by use of
gyrator circuits.
Inductor construction
An inductor is usually constructed as a
coil of
conducting
material, typically copper wire, wrapped around a
core either
of air or of
ferromagnetic material.
Core materials with a higher
permeability than air confine the magnetic field closely to the
inductor, thereby increasing the inductance. Inductors come in many
shapes. Most are constructed as enamel coated wire wrapped around a
ferrite
bobbin with wire exposed
on the outside, while some enclose the wire completely in ferrite
and are called "shielded". Some inductors have an adjustable core,
which enables changing of the inductance. Inductors used to block
very high frequencies are sometimes made with a wire passing
through a ferrite cylinder or bead.
Small inductors can be etched directly onto a
printed
circuit board by laying out the trace in a
spiral pattern. Some such planar
inductors use a
planar
core.
Small value inductors can also be built on
integrated
circuits using the same processes that are used to make
transistors. In these
cases, aluminium
interconnect is typically
used as the conducting material. However, practical constraints
make it far more common to use a circuit called a "
gyrator" which uses a
capacitor and active
components to behave similarly to an inductor.
In electric circuits
While a
capacitor opposes changes in
voltage, an inductor opposes changes in current. An ideal inductor
would offer no resistance to a constant
direct
current; however, only
superconducting inductors
have truly zero
electrical
resistance.
In general, the relationship between the
timevarying voltage v(t) across an inductor with inductance L and
the timevarying current i(t) passing through it is described by
the
differential
equation:
When there is a
sinusoidal alternating
current (AC) through an inductor, a sinusoidal voltage is
induced. The amplitude of the voltage is proportional to the
product of the amplitude (I_P) of the current and the frequency ( f
) of the current.
 i(t) = I_P \sin(2 \pi f t)\,
 \frac = 2 \pi f I_P \cos(2 \pi f t)
 v(t) = 2 \pi f L I_P \cos(2 \pi f t)\,
In this situation, the
phase of
the current lags that of the voltage by 90 degrees.
Laplace circuit analysis (sdomain)
When using the
Laplace
transform in circuit analysis, the transfer impedance of an
ideal inductor with no initial current is represented in the s
domain by:
 Z(s) = Ls\,


 where

 L is the inductance, and
 s is the complex frequency
If the inductor does have initial current, it can
be represented by:
 adding a voltage source in series with the inductor, having the
value:
 L I_0 \,
(Note that the source should have a polarity that
opposes the initial current)
 or by adding a current source in parallel with the inductor,
having the value:
 \frac


 where

 L is the inductance, and
 ''I_0 is the initial current in the
inductor.
Inductor networks
Inductors in a
parallel configuration each have the same potential difference
(voltage). To find their total equivalent inductance (Leq):
 \frac = \frac + \frac + \cdots + \frac
The current through inductors in
series stays the same, but the voltage across each inductor can
be different. The sum of the potential differences (voltage) is
equal to the total voltage. To find their total inductance:
 L_\mathrm = L_1 + L_2 + \cdots + L_n \,\!
These simple relationships hold true only when
there is no mutual coupling of magnetic fields between individual
inductors.
Q factor
An ideal inductor will be lossless irrespective
of the amount of current through the winding. However, typically
inductors have winding resistance from the metal wire forming the
coils. Since the winding resistance appears as a resistance in
series with the inductor, it is often called the series resistance.
The inductor's series resistance converts electrical current
through the coils into heat, thus causing a loss of inductive
quality. The
quality factor
(or Q) of an inductor is the ratio of its inductive reactance to
its resistance at a given frequency, and is a measure of its
efficiency. The higher the Q factor of the inductor, the closer it
approaches the behavior of an ideal, lossless, inductor.
The Q factor of an inductor can be found through
the following formula, where R is its internal electrical
resistance and \omegaL is Capacitive or Inductive reactance at
resonance:
By using a
ferromagnetic core the
inductance is increased for the same amount of copper, raising the
Q. Cores however also introduce losses that increase with
frequency. A grade of core material is chosen for best results for
the frequency band. At
VHF or higher
frequencies an air core is likely to be used. Inductors wound
around a ferromagnetic core may
saturate
at high currents, causing a dramatic decrease in inductance (and
Q). This phenomenon can be avoided by using a (physically larger)
air core inductor. A well designed air core inductor may have a Q
of several hundred.
An almost ideal inductor (Q approaching infinity)
can be created by immersing a coil made from a
superconducting alloy in
liquid
helium or
liquid
nitrogen. This supercools the wire, causing its winding
resistance to disappear. Because a superconducting inductor is
virtually lossless, it can store a large amount of electrical
energy within the surrounding magnetic field (see
superconducting magnetic energy storage).
Formulae
The table below lists some common formulae for
calculating the theoretical inductance of several inductor
constructions.
See also
Synonyms
inductor in Afrikaans: Induktor
inductor in Arabic: مستحث
inductor in Bosnian: Zavojnica
inductor in Catalan: Inductor
inductor in Czech: Cívka
inductor in Danish: Elektrisk spole
inductor in German: Spule (Elektrotechnik)
inductor in Estonian: Induktor
inductor in Spanish: Inductor
inductor in Esperanto: Induktilo
inductor in French: Bobine (électricité)
inductor in Korean: 코일
inductor in Croatian: Zavojnica
inductor in Indonesian: Induktor
inductor in Icelandic: Spanspóla
inductor in Italian: Induttore
inductor in Hebrew: סליל השראה
inductor in Latvian: Induktivitātes spole
inductor in Hungarian: Tekercs
(elektronika)
inductor in Malay (macrolanguage): Peraruh
inductor in Mongolian: Индукцийн ороомог
inductor in Dutch: Spoel
inductor in Japanese: コイル
inductor in Norwegian: Spole (induktans)
inductor in Norwegian Nynorsk: Spole
inductor in Polish: Cewka
inductor in Portuguese: Indutor
inductor in Romanian: Bobină
inductor in Russian: Катушка индуктивности
inductor in Sicilian: Ruccheddu
inductor in Simple English: Inductor
inductor in Slovak: Cievka (elektrická
súčiastka)
inductor in Slovenian: Dušilka
inductor in Finnish: Kela (komponentti)
inductor in Swedish: Spole
inductor in Tamil: மின்தூண்டி
inductor in Vietnamese: Cuộn cảm
inductor in Turkish: Bobin
inductor in Ukrainian: Котушка
індуктивності
inductor in Chinese: 电感元件