Inductor  

A selection of lowvalue inductors 

Type  Passive 
Working principle  Electromagnetic induction 
First production  Michael Faraday (1831) 
Electronic symbol  
An inductor or a reactor is a passive electrical component that can store energy in a magnetic field created by the electric current passing through it. An inductor's ability to store magnetic energy is measured by its inductance, in units of henries. Typically an inductor is a conducting wire shaped as a coil, the loops helping to create a strong magnetic field inside the coil due to Faraday's Law of Induction. Inductors are one of the basic electronic components used in electronics where current and voltage change with time, due to the ability of inductors to delay and reshape alternating currents.
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Inductance (L) (measured in henries) is an effect resulting from the magnetic field that forms around a currentcarrying conductor which tends to resist changes in the current. Electric current through the conductor creates a magnetic flux proportional to the current, and a change in this current creates a corresponding change in magnetic flux which, in turn, by Faraday's Law generates an electromotive force (EMF) that opposes this change in current. Inductance is a measure of the amount of EMF generated per 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 such as iron. This can increase the inductance by 2000 times, although less so at high frequencies.
Electric current can be modeled by the hydraulic analogy. An inductor can be modeled by the flywheel effect of a heavy turbine rotated by the flow. When water first starts to flow (current), the stationary turbine will cause an obstruction in the flow and high pressure (voltage) opposing the flow until it gets turning. Once it is turning, if there is a sudden interruption of water flow the turbine will continue to turn by inertia, generating a high pressure to keep the flow moving.
An "ideal inductor" has inductance, but no resistance or capacitance, and does not dissipate or radiate energy. A real inductor may be partially modeled by a combination of inductance, resistance (due to the resistivity of the wire and losses in core material), and capacitance. At some frequency, usually higher than the working frequency, some real inductors behave as resonant circuits (due to their self capacitance). At some frequency the capacitive component of impedance becomes dominant. In addition to dissipating energy in the resistance of the wire, magnetic core inductors may dissipate energy in the core due to hysteresis, and at high currents (bias currents) show gradual departure from ideal behavior due to nonlinearity caused by magnetic saturation. At higher frequencies, resistance and resistive losses in inductors grow due to skin effect in the inductor's winding wires. Core losses also contribute to inductor losses at higher frequencies. Additionally, realworld inductors work as antennas, radiating a part of energy processed into surrounding space and circuits, and accepting electromagnetic emissions from other circuits, taking part in electromagnetic interference. Realworld inductor applications deal heavily with "parasitic" parameters, while the "inductance" may be of minor significance.
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. Applications range from the use of large inductors in power supplies, which in conjunction with filter capacitors remove residual hums known as the Mains hum or other fluctuations from the direct current output, to the small inductance of the ferrite bead or torus installed 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 may decrease as the frequency increases due to eddy currents in the core material and skin effect on the windings. Size of the core can be decreased at higher frequencies and, 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^{[1]}.
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 X_{L} 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 depress voltages from lightning strikes and to limit switching currents and fault current. In this field, they are more commonly referred to as reactors.
Larger value inductors may be simulated by use of gyrator circuits.
The term air core coil describes an inductor that does not use a magnetic core made of a ferromagnetic material. The term refers to coils wound on plastic, ceramic, or other nonmagnetic forms, as well as those that actually have air inside the windings. Air core coils have lower inductance than ferromagnetic core coils, but are often used at high frequencies because they are free from energy losses called core losses that occur in ferromagnetic cores, which increase with frequency. One disadvantage of the air core coil is 'microphony': mechanical vibration of the windings can cause variations in the inductance unless it is rigidly supported on a suitable plastic or ceramic form.
To reduce the parasitic capacitance and increased resistance due to skin effect and proximity effect that occur at high frequencies, radio frequency coils use special construction techniques. Often the winding is limited to a single layer, and the turns are spaced apart. Multilayer coils are often wound using a crisscross weave to avoid having adjacent turns of wire lying parallel to each other; this is called a "honeycomb coil". Since the current only flows on the surface of the conductor, to reduce resistance coils are sometimes made of tubing, or silverplated. Sometimes litz wire is used for the windings.
Ferromagneticcore or ironcore inductors use a magnetic core made of a ferromagnetic or ferrimagnetic material such as iron or ferrite to increase the inductance. A magnetic core can increase the inductance of a coil by a factor of several thousand, by increasing the magnetic field due to its higher magnetic permeability. However the magnetic properties of the core material cause several side effects which alter the behavior of the inductor and require special construction:
Low frequency inductors are often made with laminated cores to prevent eddy currents, using construction similar to transformers. The core is made of stacks of thin steel sheets or laminations oriented parallel to the field, with an insulating coating on the surface. The insulation prevents eddy currents from flowing between the sheets, so any remaining currents must flow within the cross sectional area of the individual laminations, reducing the area of the loop and thus the energy loss greatly. The laminations are made of low coercivity silicon steel, to reduce hysteresis losses.
For higher frequencies, inductors are made with cores of ferrite. Ferrite is a ceramic ferrimagnetic material that is nonconductive, so eddy currents cannot flow within it. For inductor cores soft ferrites are used, which have low coercivity and thus low hysteresis losses. Another similar material is powdered iron cemented with a binder.
In an inductor wound on a straight rodshaped core, the magnetic field lines emerging from one end of the core must pass through the air to reenter the core at the other end. This reduces the field, because much of the magnetic field path is in air rather than the higher permeability core material. So higher magnetic fields and inductance can be achieved by winding the coil on a toroidal or doughnut shaped ferrite core. The magnetic field lines form closed loops within the doughnut without leaving the core material. Toroidal inductors also have the advantage that since little of the magnetic flux is outside the core, they radiate less electromagnetic interference than straight coils.
A variable inductor can be constructed by making one of the terminals of the device a sliding spring contact that can move along the surface of the coil, increasing or decreasing the number of turns of the coil included in the circuit. An alternate construction method is to use a moveable magnetic core, which can be slid in or out of the coil. Moving the core farther into the coil increases the permeability, increasing the inductance.
An inductor is usually constructed as a coil of conducting material, typically copper wire, wrapped around a core either of air or of ferromagnetic or ferrimagnetic material. Core materials with a higher permeability than air increase the magnetic field and confine it closely to the inductor, thereby increasing the inductance. Low frequency inductors are constructed like transformers, with cores of electrical steel laminated to prevent eddy currents. 'Soft' ferrites are widely used for cores above audio frequencies, since they don't cause the large energy losses at high frequencies that ordinary iron alloys do. This is because of their narrow hysteresis curves, and their high resistivity prevents eddy currents. 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 by stringing a ferrite cylinder or bead on a wire.
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. Aluminium interconnect is typically used, laid out in a spiral coil pattern. However, the small dimensions limit the inductance, and it is far more common to use a circuit called a "gyrator" which uses a capacitor and active components to behave similarly to an inductor.
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.
In this situation, the phase of the current lags that of the voltage by 90 degrees. #
If an inductor is connected to a DC current source, with value I via a resistance, R, and then the current source short circuited, the differential relationship above shows that the current through the inductor will discharge with an exponential decay:
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:
If the inductor does have initial current, it can be represented by:
(Note that the source should have a polarity that is aligned with the initial current)
Inductors in a parallel configuration each have the same potential difference (voltage). To find their total equivalent inductance (L_{eq}):
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:
These simple relationships hold true only when there is no mutual coupling of magnetic fields between individual inductors.
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(****).
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 ωL is capacitive or inductive reactance at resonance:
By using a ferromagnetic core, the inductance is greatly increased for the same amount of copper, multiplying up 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). Bear in mind that for inductors with cores, core losses still exist.
The table below lists some common formula for calculating the theoretical inductance of several inductor constructions.
Construction  Formula  Dimensions 

Cylindrical coil^{[2]} 


Straight wire conductor ^{[3]} 




Short aircore cylindrical coil 


Multilayer aircore coil 


Flat spiral aircore coil 




Toroidal core (circular crosssection) 

An inductor is an electrical device used in electrical circuits because of magnetic charge.
An inductor is usually made from a coil of conducting material, like copper wire, that is then wrapped around a core made from either air or a magnetic metal. If you use a more magnetic material as the core, you can get the magnetic field around the inductor to be pushed in towards the inductor, giving it better inductance.^{[1]} Small inductors can also be put onto integrated circuits using the same ways that are used to make transistors. Aluminum is usually used as the conducting material in this case.
Contents 
While a capacitor does not like changes in voltage, an inductor does not like changes in current.
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:
Inductors are used often in analog circuits. Two or more inductors that have coupled magnetic flux make a transformer. Transformers are used in every power grid around the world. Inductors are also used in electrical transmission systems, where they are used to lower the amount of voltage an electrical device gives off or lower the fault current. Because inductors are heavier than other electrical components, people have been using them in electrical equipment less often.
