Information about Inductor
An inductor is a passive electrical device employed in electrical circuits for its property of inductance. An inductor can take many forms.
where L is inductance and I is the current flowing through the inductor.
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. 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 general, the relationship between the time-varying voltage v(t) across an inductor with inductance L and the time-varying 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 (
) 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 the inductor does have initial current, it can be represented by:
Inductors in a parallel configuration each have the same potential difference (voltage). To find their total equivalent inductance (Leq):
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 Q factor of an inductor can be found through the following formula, where R is its internal electrical resistance:
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 highter 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).
2. Inductance of a straight wire conductor:
Hence a 10 mm-long conductor having 1 mm diameter will have an inductance of about 5.38 nH but 100 mm of the same will get about 100 nH. The same formula in English units:
3. Inductance of a short air core cylindrical coil in terms of geometric parameters:
4. For a multilayer air core coil:
5. Inductance of a flat spiral air core coil:
Hence a spiral coil with 8 turns at a mean radius of 25 mm and a depth of 10 mm would have an inductance of 5.13 µH.
The same formula in imperial units:
6. Inductance of a winding around a toroidal ring of core material with relative permeability of
with circular cross-section:
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 used 400 hertz alternating current rather than the usual 50 or 60 hertz, allowing a great savings in weight from the use of smaller transformers.
An inductor is used as the energy storage device in some switchmode power supplies. The inductor is energized for a specific fraction of the regulator's switching frequency, and de-energized for the remainder of the cycle. This energy transfer ratio determines the input-voltage to output-voltage 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.
)
Common inductors.
Physics
Overview
Inductance (measured in henries, H) is an effect which results from the magnetic field that forms around a current-carrying conductor. Electrical 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 generated emf for a unit change in current. For example, an inductor with an inductance of 1 henry produces an emf of 1 V when the current through the inductor changes at the rate of 1 ampere per second. The number of turns, the area of each loop/turn, and what it is wrapped around 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 flowing through the inductor.
Hydraulic model
Electrical 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 usefully modeled hydraulically.Inductor construction
)
Inductors. Major scale in centimetres.
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. 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 time-varying voltage v(t) across an inductor with inductance L and the time-varying 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 (
) 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.
Laplace circuit analysis (s-domain)
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:
- :: 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:
- or by adding a current source in parallel with the inductor, having the value:
- :: where
- ::: L is the inductance, and
- ::: ''
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):
-
A diagram of several inductors, side by side, both leads of each connected to the same wires
){kind=spacer}
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:
-
A diagram of several inductors, connected end to end, with the same amount of current going through each
)
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 flowing 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 flowing 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:
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 highter 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
1. Basic inductance formula for a cylindrical coil:- L = Inductance in henries (H)
- μ0 = permeability of free space = 4
× 10-7 H/m
- μr = relative permeability of core material
- N = number of turns
- A = area of cross-section of the coil in square metres (m2)
- l = length of coil in metres (m)
2. Inductance of a straight wire conductor:
- L = inductance in H
- l = length of conductor in metres
- d = diameter of conductor in metres
Hence a 10 mm-long conductor having 1 mm diameter will have an inductance of about 5.38 nH but 100 mm of the same will get about 100 nH. The same formula in English units:
- L = inductance in nanohenries
- l = length of conductor in inches
- d = diameter of conductor in inches
3. Inductance of a short air core cylindrical coil in terms of geometric parameters:
- L = inductance in µH
- r = outer radius of coil in inches
- l = length of coil in inches
- N = number of turns
4. For a multilayer air core coil:
- L = inductance in µH
- r = mean radius of coil in inches
- l = physical length of coil winding in inches
- N = number of turns
- d = depth of coil in inches (i.e., outer radius minus inner radius)
5. Inductance of a flat spiral air core coil:
- L = inductance in H
- r = mean radius of coil in metres
- N = number of turns
- d = depth of coil in metres (i.e., outer radius minus inner radius)
Hence a spiral coil with 8 turns at a mean radius of 25 mm and a depth of 10 mm would have an inductance of 5.13 µH.
The same formula in imperial units:
- L = inductance in µH
- r = mean radius of coil in inches
- N = number of turns
- d = depth of coil in inches (i.e., outer radius minus inner radius)
6. Inductance of a winding around a toroidal ring of core material with relative permeability of
with circular cross-section:
- L = inductance in H
- μ0 = permeability of free space = 4 × 10-7 H/m
- μr = relative permeability of core material
- N = number of turns
- r = radius of coil winding in meters
- D = overall diameter of toroid in meters
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 used 400 hertz alternating current rather than the usual 50 or 60 hertz, allowing a great savings in weight from the use of smaller transformers.
An inductor is used as the energy storage device in some switchmode power supplies. The inductor is energized for a specific fraction of the regulator's switching frequency, and de-energized for the remainder of the cycle. This energy transfer ratio determines the input-voltage to output-voltage 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.
See also
- Electronic Components
- Capacitor
- Resistor
- Electricity
- Electronics
- Gyrator
- Inductance (including mutual inductance)
- induction coil
- Induction cooking
- Induction loop
- Magnetic core
- Saturable reactor
- Transformer
- Reactance
- RL circuit
- RLC circuit
Synonyms
External links
- General
- How stuff works The initial concept, made very simple
- Capacitance and Inductance - A chapter from an online textbook
- Spiral inductor models. Good article on inductor characteristics and modeling.
- Online coil inductance calculator. Online calculator calculates the inductance of conventional and toroidal coils using formulas 3, 4, 5, and 6, above.
- AC circuits
passive component, depending on field, may either refer to a component that consumes (but does not produce) energy, or to a component that is incapable of power gain. A component that is not passive is called an active component.
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electrical network is an interconnection of electrical elements such as resistors, inductors, capacitors, transmission lines, voltage sources, current sources, and switches.
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inductance, or more accurately self-inductance of the circuit. The term was coined by Oliver Heaviside in February 1886. It is customary to use the symbol for inductance, possibly in honour of the physicist Heinrich Lenz.
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inductance, or more accurately self-inductance of the circuit. The term was coined by Oliver Heaviside in February 1886. It is customary to use the symbol for inductance, possibly in honour of the physicist Heinrich Lenz.
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The henry (symbol: H) is the SI unit of inductance. It is named after Joseph Henry (1797-1878), the American scientist who discovered electromagnetic induction independently of and at about the same time as Michael Faraday (1791-1867) in England.
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magnetic field is a field that permeates space and which exerts a magnetic force on moving electric charges and magnetic dipoles. Magnetic fields surround electric currents, magnetic dipoles, and changing electric fields.
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In science and engineering, conductors, such as copper or aluminum, are materials with atoms have loosely held valence electrons. See electrical conduction.
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Conductors in context
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Electric current is the flow (movement) of electric charge. The SI unit of electric current is the ampere (A), which is equal to a flow of one coulomb of charge per second.
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Definition
The amount of electric current (measured in amperes) through some surface, e.g...... Click the link for more information.
Electromotive force (emf, ) is a term used to characterize electrical devices, such as voltaic cells, thermoelectric devices, electrical generators and transformers, and even resistors.
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In electromagnetism, permeability is the degree of magnetization of a material that responds linearly to an applied magnetic field. Magnetic permeability is represented by the Greek letter μ. The term was coined in September, 1885 by Oliver Heaviside.
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energy (from the Greek ενεργός, energos, "active, working")[1] is a scalar physical quantity that is a property of objects and systems of objects which is conserved by nature.
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The joule (IPA: [dʒuːl] or [dʒaʊl]) (symbol: J) is the SI unit of energy.
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Si, si, or SI may refer to (all SI unless otherwise stated):
In language:
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In language:
- One of two Italian words:
- sì (accented) for "yes"
- si
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The electronic Hydraulic analogy (derisively referred to as the Drain-pipe theory by Oliver Heaviside) is the most widely used analogy for "electron fluid" in a metal conductor.
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flywheel is a rotating disk used as a storage device for kinetic energy. Flywheels resist changes in their rotational speed, which helps steady the rotation of the shaft when a fluctuating torque is exerted on it by its power source such as a piston-based (reciprocating) engine, or
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turbine is a rotary engine that extracts energy from a fluid flow. Claude Burdin (1788-1873) coined the term from the Latin turbinis, or vortex during an 1828 engineering competition.
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A coil is a series of s. A coiled coil is a structure where the coil itself is in turn also looping.
A coil is made up of materials, usually rigid, which can be fashioned into a spiral or helical shape.
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General applications
A coil is made up of materials, usually rigid, which can be fashioned into a spiral or helical shape.
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In science and engineering, conductors, such as copper or aluminum, are materials with atoms have loosely held valence electrons. See electrical conduction.
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Conductors in context
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The magnetic core is a key component in electrical devices such as electromagnets, transformers and inductors. Its role is to increase the strength and effect of magnetic fields produced by electric currents.
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Ferromagnetism is the "normal" form of magnetism with which most people are familiar, as exhibited in horseshoe magnets and refrigerator magnets, for instance. It is responsible for most of the magnetic behavior encountered in everyday life.
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In electromagnetism, permeability is the degree of magnetization of a material that responds linearly to an applied magnetic field. Magnetic permeability is represented by the Greek letter μ. The term was coined in September, 1885 by Oliver Heaviside.
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Ferrites are a class of chemical compounds with the formula AB2O4, where A and B represent various metal cations, usually including iron. These ceramic materials are used in applications ranging from magnetic components in microelectronics.
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A bobbin is a spindle or cylinder, with or without flanges, on which wire, yarn, thread or film is wound. Bobbins are typically found in sewing machines, cameras, and within electronic equipment.
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printed circuit boards, or PCBs, are used to mechanically support and electrically connect electronic components using conductive pathways, or traces, etched from copper sheets laminated onto a non-conductive substrate.
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spiral is a curve which emanates from a central point, getting progressively farther away as it revolves around the point.
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Spiral or helix
A "spiral" and a "helix" are two terms that are easily confused, but represent different objects...... Click the link for more information.
integrated circuit (also known as IC, microcircuit, microchip, silicon chip, or chip) is a miniaturized electronic circuit (consisting mainly of semiconductor devices, as well as passive components) that has been manufactured in the surface of a
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A transistor is a semiconductor device, commonly used as an amplifier or an electrically controlled switch. The transistor is the fundamental building block of the circuitry in computers, cellular phones, and all other modern electronic devices.
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Connection, Connected, Connectivity, or Connexion may refer to:
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- Music
- Connected (album) is a 1992 album by the Stereo MC's
- Connected (Foreign Exchange album) is an album by The Foreign Exchange
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The gyrator is an electric circuit which inverts an impedance. In other words, it can make a capacitive circuit behave inductively, a bandpass filter behave like a band-stop filter, and so on. The concept was invented around 1948 by B.D.H.
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capacitor is an electrical/electronic device that can store energy in the electric field between a pair of conductors (called "plates"). The process of storing energy in the capacitor is known as "charging", and involves electric charges of equal magnitude, but opposite polarity,
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