View source for Physics:Magnetic core

{{Short description|Object used to guide and confine magnetic fields}}
A '''magnetic core''' is a piece of [[Physics:Magnetism|magnetic material]] with a high magnetic permeability used to confine and guide [[Physics:Magnetic field|magnetic field]]s in electrical, electromechanical and magnetic devices such as [[Physics:Electromagnet|electromagnet]]s, [[Engineering:Transformer|transformer]]s, [[Physics:Electric motor|electric motor]]s, [[Engineering:Electric generator|generators]], [[Engineering:Inductor|inductor]]s, [[Engineering:Loudspeaker|loudspeaker]]s, magnetic recording heads, and magnetic assemblies.  It is made of [[Physics:Ferromagnetic|ferromagnetic]] metal such as iron, or ferrimagnetic compounds such as [[Physics:Ferrite (magnet)|ferrite]]s.  The high permeability, relative to the surrounding air, causes the magnetic field lines to be concentrated in the core material. The magnetic field is often created by a current-carrying coil of wire around the core.

The use of a magnetic core can increase the strength of [[Physics:Magnetic field|magnetic field]] in an [[Engineering:Electromagnetic coil|electromagnetic coil]] by a factor of several hundred times what it would be without the core.  However, magnetic cores have side effects which must be taken into account.  In [[Physics:Alternating current|alternating current]] (AC) devices they cause energy losses, called [[Engineering:Core losses|core losses]], due to hysteresis and [[Physics:Eddy current|eddy current]]s in applications such as transformers and inductors.  "Soft" magnetic materials with low coercivity and hysteresis, such as silicon steel, or [[Physics:Ferrite (magnet)|ferrite]], are usually used in cores.

[[Image:Electromagnet with gap.svg|thumb|upright=1.7|Magnetic field ''(<span style="color:green;">green</span>)'' created by a current-carrying winding ''(red)'' in a typical magnetic core transformer or inductor, with the iron core ''C'' forming a closed loop, possibly with air gaps ''G'' in it. The purpose of the core is to provide a closed high [[permeability (electromagnetism)|permeability]] path for the magnetic field lines.<br /> 
''B'' – magnetic field in the core will be approximately constant across any cross section<br />
''B<sub>F</sub>'' – "fringing fields".  In the gaps ''G'' the magnetic field lines "bulge" out, so the field strength is less than in the core:  ''B<sub>F</sub>''&nbsp;<&nbsp;''B''<br />
''B<sub>L</sub>''  – leakage flux; magnetic field lines which don't follow complete magnetic circuit<br />
 ]]

== Core materials ==
An electric current through a wire wound into a [[Engineering:Electromagnetic coil|coil]] creates a [[Physics:Magnetic field|magnetic field]] through the center of the coil, due to Ampere's circuital law.  Coils are widely used in electronic components such as [[Physics:Electromagnet|electromagnet]]s, [[Engineering:Inductor|inductor]]s, [[Engineering:Transformer|transformer]]s, [[Physics:Electric motor|electric motor]]s and [[Engineering:Electric generator|generator]]s.  A coil without a magnetic core is called an "air core" coil.  Adding a piece of [[Physics:Ferromagnetic|ferromagnetic]] or ferrimagnetic material in the center of the coil can increase the magnetic field by hundreds or thousands of times; this is called a magnetic core.  The field of the wire penetrates the core material, [[Physics:Magnetization|magnetizing]] it, so that the strong magnetic field of the core adds to the field created by the wire.  The amount that the magnetic field is increased by the core depends on the magnetic permeability of the core material. Because side effects such as [[Physics:Eddy current|eddy current]]s and [[Hysteresis|hysteresis]] can cause frequency-dependent energy losses, different core materials are used for coils used at different [[Physics:Frequency|frequencies]].

In some cases the losses are undesirable and with very strong fields saturation can be a problem, and an 'air core' is used. A former may still be used; a piece of material, such as plastic or a composite, that may not have any significant magnetic permeability but which simply holds the coils of wires in place.

===Solid metals===

==== Soft iron ====

"Soft" ([[Engineering:Annealing (metallurgy)|annealed]]) [[Chemistry:Iron|iron]] is used in magnetic assemblies, [[Physics:Direct current|direct current]] (DC) electromagnets and in some electric motors; and it can create a concentrated field that is as much as 50,000 times more intense than an air core.<ref>{{cite web|url=http://www.physicsforums.com/archive/index.php/t-164613.html|title=Soft iron core}}</ref>

Iron is desirable to make magnetic cores, as it can withstand high levels of [[Physics:Magnetic field|magnetic field]] without [[Physics:Saturation (magnetic)|saturating]] (up to 2.16 [[Tesla (unit)|tesla]]s at ambient temperature.<ref>Daniel Sadarnac, ''Les composants magnétiques de l'électronique de puissance'', cours de Supélec, mars 2001 [in french]</ref><ref>{{Cite journal|last1=Danan|first1=H.|last2=Herr|first2=A.|last3=Meyer|first3=A.J.P.|date=1968-02-01|title=New Determinations of the Saturation Magnetization of Nickel and Iron|journal=Journal of Applied Physics|volume=39|issue=2|pages=669–70|doi=10.1063/1.2163571|issn=0021-8979|bibcode=1968JAP....39..669D|doi-access=free}}</ref>)  Annealed iron is used because, unlike "hard" iron, it has low [[Physics:Coercivity|coercivity]] and so does not remain magnetised when the field is removed, which is often important in applications where the magnetic field is required to be repeatedly switched.

Due to the electrical conductivity of the metal, when a solid one-piece metal core is used in [[Physics:Alternating current|alternating current]] (AC) applications such as transformers and inductors, the changing magnetic field induces large [[Physics:Eddy current|eddy current]]s circulating within it, closed loops of electric current in planes perpendicular to the field.  The current flowing through the resistance of the metal heats it by [[Physics:Joule heating|Joule heating]], causing significant power losses.  Therefore, solid iron cores are not used in transformers or inductors, they are replaced by [[Chemistry:Lamination|laminated]] or powdered iron cores, or nonconductive cores like [[Physics:Ferrite (magnet)|ferrite]].

==== Laminated silicon steel ====
[[File:Laminated core eddy currents 2.svg|thumb|upright=1.4|''(left)'' Eddy currents ''(<span style="color:red;">I, red</span>)'' within a solid iron transformer core. ''(right)'' Making the core out of thin laminations parallel to the field ''(<span style="color:green;">B, green</span>)'' with insulation between them (''C'') reduces the eddy currents.  In this diagram the field and currents are shown in one direction, but they actually reverse direction with the alternating current in the transformer winding.]]

In order to reduce the eddy current losses mentioned above, most low frequency power transformers and inductors use laminated cores, made of stacks of thin sheets of silicon steel:

===== Lamination =====
[[Image:EI Lam.jpg|thumb|right|Typical EI Lamination.]]

[[Chemistry:Lamination|Laminated]] magnetic cores are made of stacks of thin iron sheets coated with an insulating layer, lying as much as possible parallel with the lines of flux.  The layers of insulation serve as a barrier to eddy currents, so eddy currents can only flow in narrow loops within the thickness of each single lamination.  Since the current in an eddy current loop is proportional to the area of the loop, this prevents most of the current from flowing, reducing eddy currents to a very small level.   Since power dissipated is proportional to the square of the current, breaking a large core into narrow laminations reduces the power losses drastically.  From this, it can be seen that the thinner the laminations, the lower the eddy current losses.

===== Silicon alloying =====
A small addition of [[Chemistry:Silicon|silicon]] to iron (around 3%) results in a dramatic increase of the resistivity of the metal, up to four times higher.{{citation needed|date=August 2011}}  The higher resistivity reduces the eddy currents, so silicon steel is used in transformer cores. Further increase in silicon concentration impairs the steel's mechanical properties, causing difficulties for rolling due to brittleness.

Among the two types of silicon steel, grain-oriented (GO) and grain non-oriented (GNO), GO is most desirable for magnetic cores. It is anisotropic, offering better magnetic properties than GNO in one direction. As the magnetic field in inductor and transformer cores is always along the same direction, it is an advantage to use grain oriented steel in the preferred orientation. Rotating machines, where the direction of the magnetic field can change, gain no benefit from grain-oriented steel.

==== Special alloys ====
A family of specialized alloys exists for magnetic core applications. Examples are [[Physics:Mu-metal|mu-metal]], [[Physics:Permalloy|permalloy]], and [[Chemistry:Supermalloy|supermalloy]]. They can be manufactured as stampings or as long ribbons for tape wound cores. Some alloys, e.g. [[Physics:Sendust|Sendust]], are manufactured as powder and [[Earth:Sintering|sintered]] to shape.

Many materials require careful heat treatment to reach their magnetic properties, and lose them when subjected to mechanical or thermal abuse. For example, the permeability of mu-metal increases about 40 times after [[Engineering:Annealing (metallurgy)|annealing]] in hydrogen atmosphere in a magnetic field; subsequent sharper bends disrupt its grain alignment, leading to localized loss of permeability; this can be regained by repeating the annealing step.

==== Vitreous metal ====
[[Chemistry:Amorphous metal|Amorphous metal]] is a variety of alloys (e.g. [[Physics:Metglas|Metglas]]) that are non-crystalline or glassy. These are being used to create high-efficiency transformers.  The materials can be highly responsive to magnetic fields for low hysteresis losses, and they can also have lower conductivity to reduce eddy current losses. Power utilities are currently making widespread use of these transformers for new installations.<ref>{{cite web |title=Metglas® Amorphous Metal Materials – Distribution Transformers |url=https://www.hitachimetals.com/infrastructure-energy/clean-energy-technology/metglas-amorphous-metal-materials-distribution-transformers.php |access-date=25 September 2020}}</ref> High mechanical strength and corrosion resistance are also common properties of metallic glasses which are positive for this application.<ref>{{Cite journal|last1=Inoue|first1=A.|last2=Kong|first2=F. L.|last3=Han|first3=Y.|last4=Zhu|first4=S. L.|last5=Churyumov|first5=A.|last6=Shalaan|first6=E.|last7=Al-Marzouki|first7=F.|date=2018-01-15|title=Development and application of Fe-based soft magnetic bulk metallic glassy inductors|url=http://www.sciencedirect.com/science/article/pii/S092583881732978X|journal=Journal of Alloys and Compounds|language=en|volume=731|pages=1303–1309|doi=10.1016/j.jallcom.2017.08.240|issn=0925-8388}}</ref>

===Powdered metals===
Powder cores consist of metal grains mixed with a suitable organic or inorganic binder, and pressed to desired density. Higher density is achieved with higher pressure and lower amount of binder. Higher density cores have higher permeability, but lower resistance and therefore higher losses due to eddy currents. Finer particles allow operation at higher frequencies, as the eddy currents are mostly restricted to within the individual grains. Coating of the particles with an insulating layer, or their separation with a thin layer of a binder, lowers the eddy current losses. Presence of larger particles can degrade high-frequency performance. Permeability is influenced by the spacing between the grains, which form distributed air gap; the less gap, the higher permeability and the less-soft saturation. Due to large difference of densities, even a small amount of binder, weight-wise, can significantly increase the volume and therefore intergrain spacing.

Lower permeability materials are better suited for higher frequencies, due to balancing of core and winding losses.

The surface of the particles is often oxidized and coated with a phosphate layer, to provide them with mutual electrical insulation.

==== Iron ====
Powdered iron is the cheapest material. It has higher core loss than the more advanced alloys, but this can be compensated for by making the core bigger; it is advantageous where cost is more important than mass and size. Saturation flux of about 1 to 1.5 tesla. Relatively high hysteresis and eddy current loss, operation limited to lower frequencies (approx. below 100&nbsp;kHz). Used in energy storage inductors, DC output chokes, differential mode chokes, triac regulator chokes, chokes for [[Engineering:Power factor|power factor]] correction, resonant inductors, and pulse and flyback transformers.<ref name="coilws"/>

The binder used is usually epoxy or other organic resin, susceptible to thermal aging. At higher temperatures, typically above 125&nbsp;°C, the binder degrades and the core magnetic properties may change. With more heat-resistant binders the cores can be used up to 200&nbsp;°C.<ref name="chalmers">{{cite web|author=Johan Kindmark, Fredrik Rosén |url=http://publications.lib.chalmers.se/records/fulltext/183920/183920.pdf |title=Powder Material for Inductor Cores, Evaluation of MPP, Sendust and High flux core characteristics |publisher=Department of Energy and Environment, Division of Electric Power Engineering, Chalmers University of Technology |location=Göteborg, Sweden |date=2013 |access-date=2017-06-05}}</ref>

Iron powder cores are most commonly available as toroids. Sometimes as E, EI, and rods or blocks, used primarily in high-power and high-current parts.

Carbonyl iron is significantly more expensive than hydrogen-reduced iron.

==== Carbonyl iron ====
{{main article|Chemistry:Carbonyl iron}}

Powdered cores made of [[Chemistry:Carbonyl iron|carbonyl iron]], a highly pure iron, have high stability of parameters across a wide range of [[Physics:Temperature|temperature]]s and [[Physics:Magnetic flux|magnetic flux]] levels, with excellent [[Physics:Q factor|Q factor]]s between 50&nbsp;kHz and 200&nbsp;MHz. Carbonyl iron powders are basically constituted of micrometer-size [[Sphere|sphere]]s of iron coated in a thin layer of electrical insulation. This is equivalent to a microscopic laminated magnetic circuit (see silicon steel, above), hence reducing the eddy currents, particularly at very high frequencies. Carbonyl iron has lower losses than hydrogen-reduced iron, but also lower permeability.

A popular application of carbonyl iron-based magnetic cores is in high-frequency and broadband [[Engineering:Inductor|inductor]]s and [[Engineering:Transformer|transformer]]s, especially higher power ones.

Carbonyl iron cores are often called "RF cores".

The as-prepared particles, "E-type"and have onion-like skin, with concentric shells separated with a gap. They contain significant amount of carbon. They behave as much smaller than what their outer size would suggest. The "C-type" particles can be prepared by heating the E-type ones in hydrogen atmosphere at 400&nbsp;°C for prolonged time, resulting in carbon-free powders.<ref name="handbkferr"/>

==== Hydrogen-reduced iron ====
Powdered cores made of hydrogen reduced iron have higher permeability but lower Q than carbonyl iron. They are used mostly for [[Engineering:Electromagnetic interference|electromagnetic interference]] [[Engineering:Electronic filter|filters]] and low-frequency chokes, mainly in [[Engineering:Switched-mode power supply|switched-mode power supplies]].

Hydrogen-reduced iron cores are often called "power cores".

==== MPP (molypermalloy) ====
An alloy of about 2% [[Chemistry:Molybdenum|molybdenum]], 81% [[Chemistry:Nickel|nickel]], and 17% iron. Very low core loss, low hysteresis and therefore low signal distortion. Very good temperature stability. High cost. Maximum saturation flux of about 0.8 tesla. Used in high-Q filters, resonant circuits, loading coils, transformers, chokes, etc.<ref name="coilws">{{cite web|url=http://www.coilws.com/index.php?main_page=page&id=41|title=How to choose Iron Powder, Sendust, Koolmu, High Flux and MPP Cores as output inductor and chokes : CWS Coil Winding Specialist, manufacturer of transformers, inductors, coils and chokes|first=The Zen Cart™ Team and|last=others|website=www.coilws.com}}</ref>

The material was first introduced in 1940, used in [[Engineering:Loading coil|loading coil]]s to compensate capacitance in long telephone lines. It is usable up to about 200&nbsp;kHz to 1&nbsp;MHz, depending on vendor.<ref name="chalmers"/> It is still used in above-ground telephone lines, due to its temperature stability. Underground lines, where temperature is more stable, tend to use ferrite cores due to their lower cost.<ref name="handbkferr">{{cite book|url=https://books.google.com/books?id=StbgBwAAQBAJ&dq=powder+core+%22carbonyl+iron%22&pg=PA185|title=Handbook of Modern Ferromagnetic Materials|first=Alex|last=Goldman|date=6 December 2012|publisher=Springer Science & Business Media|via=Google Books|isbn=9781461549178}}</ref>

==== High-flux (Ni-Fe) ====
An alloy of about 50–50% of nickel and iron. High energy storage, saturation flux density of about 1.5 tesla. Residual flux density near zero. Used in applications with high DC current bias (line noise filters, or inductors in switching regulators) or where low residual flux density is needed (e.g. pulse and flyback transformers, the high saturation is suitable for unipolar drive), especially where space is constrained. The material is usable up to about 200&nbsp;kHz.<ref name="coilws"/>

==== Sendust, KoolMU ====
An alloy of 6% aluminium, 9% silicon, and 85% iron. Core losses higher than MPP. Very low [[Physics:Magnetostriction|magnetostriction]], makes low audio noise. Loses inductance with increasing temperature, unlike the other materials; can be exploited by combining with other materials as a composite core, for temperature compensation. Saturation flux of about 1 tesla. Good temperature stability. Used in switching power supplies, pulse and flyback transformers, in-line noise filters, swing chokes, and in filters in [[Phase-fired controller|phase-fired controller]]s (e.g. dimmers) where low acoustic noise is important.<ref name="coilws"/>

Absence of nickel results in easier processing of the material and its lower cost than both high-flux and MPP.

The material was invented in Japan in 1936. It is usable up to about 500&nbsp;kHz to 1&nbsp;MHz, depending on vendor.<ref name="chalmers"/>

==== Nanocrystalline ====

A nanocrystalline alloy of a standard iron-boron-silicon alloy, with addition of smaller amounts of [[Chemistry:Copper|copper]] and [[Chemistry:Niobium|niobium]]. The grain size of the powder reaches down to 10–100 nanometers. The material has very good performance at lower frequencies. It is used in chokes for inverters and in high power applications. It is available under names like e.g. Nanoperm, Vitroperm, Hitperm and Finemet.<ref name="chalmers"/>

===Ceramics===

==== Ferrite ====
{{main article|Engineering:Ferrite core}}

[[Physics:Ferrite (magnet)|Ferrite ceramics]] are used for high-frequency applications. The ferrite materials can be engineered with a wide range of parameters. As ceramics, they are essentially insulators, which prevents eddy currents, although losses such as hysteresis losses can still occur.

=== Air ===
<!-- arguably this is not a magnetic core, but the articles need a section to explain the downsides of magnetic cores, and why high permeable cores are not always used, and 'air core' is a well recognized term of art. --->
A coil not containing a magnetic core is called an ''air core''.  This includes coils wound on a plastic or ceramic form in addition to those made of stiff wire that are self-supporting and have air inside them. Air core coils generally have a much lower [[Physics:Inductance|inductance]] than similarly sized ferromagnetic core coils, but are used in [[Engineering:Radio frequency|radio frequency]] circuits to prevent energy losses called core losses that occur in magnetic cores.  The absence of normal core losses permits a higher [[Physics:Q factor|Q factor]], so air core coils are used in high frequency resonant circuits, such as up to a few megahertz. However, losses such as [[Physics:Proximity effect (electromagnetism)|proximity effect]] and dielectric losses are still present. Air cores are also used when field strengths above around 2 Tesla are required as they are not subject to saturation.

== Commonly used structures ==
=== Straight cylindrical rod ===
[[File:Ferrite-R-Core_(7).jpg|thumb|Ferrite rods are simple cylinders of ferrite that can be wound around.]]
Most commonly made of [[Chemistry:Allotropes of iron|ferrite]] or powdered iron, and used in [[Social:Radio|radio]]s especially for tuning an [[Engineering:Inductor|inductor]]. The coil is wound around the rod, or a coil form with the rod inside.  Moving the rod in or out of the coil changes the flux through the coil, and can be used to adjust the [[Physics:Inductance|inductance]]. Often the rod is [[Engineering:Screw thread|thread]]ed to allow adjustment with a screwdriver. In radio circuits, a blob of [[Physics:Wax|wax]] or resin is used once the inductor has been tuned to prevent the core from moving.

The presence of the high permeability core increases the [[Physics:Inductance|inductance]], but the magnetic field lines must still pass through the air from one end of the rod to the other. The air path ensures that the inductor remains linear. In this type of inductor [[Physics:Radiation|radiation]] occurs at the end of the rod and [[Engineering:Electromagnetic interference|electromagnetic interference]] may be a problem in some circumstances.

=== Single "I" core ===

Like a cylindrical rod but is square, rarely used on its own.
This type of core is most likely to be found in car ignition coils.

=== "C" or "U" core ===
''U'' and ''C''-shaped cores are used with ''I'' or another ''C'' or ''U'' core to make a square closed core, the simplest closed core shape.  Windings may be put on one or both legs of the core.
{{multiple image
| align     = center
| direction = horizontal
| width     = 200
<!-- Image 1 -->
| image1    = U_core.png
| caption1  = A U-shaped core, with sharp corners
<!-- Image 2 -->
| image2    = C_core.png
| caption2  = The C-shaped core, with rounded corners
}}

=== "E" core ===
E-shaped core are more symmetric solutions to form a closed magnetic system. Most of the time, the electric circuit is wound around the center leg, whose section area is twice that of each individual outer leg. In 3-phase transformer cores, the legs are of equal size, and all three legs are wound.
{{multiple image
| align     = center
| direction = horizontal
| width     = 200
<!-- Image 1 -->
| image1    = E_core.png
| caption1  = Classical ''E'' core
<!-- Image 2 -->
| image2    = EFD_core.png
| caption2  = The ''EFD''' core allows for construction of inductors or transformers with a lower profile
<!-- Image 3 -->
| image3    = ER_core.png
| caption3  = The ''ETD'' core has a cylindrical central leg.
<!-- Image 4 -->
| image4    = EP_core.png
| caption4  = The ''EP'' core is halfway between a ''E'' and a ''pot'' core
}}

==== "E" and "I" core ====

Sheets of suitable iron stamped out in shapes like the (sans-serif) [[Social:Letter (alphabet)|letters]] "E" and "I", are stacked with the "I" against the open end of the "E" to form a 3-legged structure. Coils can be wound around any leg, but usually the center leg is used. This type of core is frequently used for power transformers, autotransformers, and inductors.

<!-- diagram would be good here-->
{{multiple image
| align     = center
| direction = horizontal
| width     = 200
<!-- Image 1 -->
| image1    = ER core assembly.png
| caption1  = Construction of an inductor using two ''ER'' cores, a plastic bobbin and two clips. The bobbin has pins to be soldered to a [[Engineering:Printed circuit board|printed circuit board]].
<!-- Image 2 -->
| image2    = ER core assembly exploded.png
| caption2  = Exploded view of the previous figure showing the structure
}}

==== Pair of "E" cores ====

Again used for iron cores. Similar to using an "E" and "I" together, a pair of "E" cores will accommodate a larger coil former and can produce a larger [[Engineering:Inductor|inductor]] or [[Engineering:Transformer|transformer]]. If an air gap is required, the centre leg of the "E" is shortened so that the air gap sits in the middle of the coil to minimize fringing and reduce [[Engineering:Electromagnetic interference|electromagnetic interference]].

=== Planar core ===

A planar core consists of two flat pieces of magnetic material, one above and one below the coil. It is typically used with a flat coil that is part of a [[Engineering:Printed circuit board|printed circuit board]]. This design is excellent for [[Finance:Mass production|mass production]] and allows a high [[Physics:Power|power]], small [[Physics:Volume|volume]] [[Engineering:Transformer|transformer]] to be constructed for low cost. It is not as ideal as either a '''pot core''' or '''toroidal core'''{{Citation needed|date=June 2010}} but costs less to produce.
{{multiple image
| align     = center
| direction = horizontal
| width     = 200
<!-- Image 1 -->
| image1    = Planar.png
| caption1  = A planar 'E' core
<!-- Image 2 -->
| image2    = Planar core assembly.png
| caption2  = A planar inductor
<!-- Image 3 -->
| image3    = Planar core assembly exploded.png
| caption3  = Exploded view that shows the spiral track made directly on the printed circuit board
}}

{{clear}}

=== Pot core ===

Usually ferrite or similar. This is used for [[Engineering:Inductor|inductor]]s and [[Engineering:Transformer|transformer]]s. The shape of a pot core is round with an internal hollow that almost completely encloses the coil. Usually a pot core is made in two halves which fit together around a coil former (bobbin). This design of core has a [[Physics:Electromagnetic shielding|shield]]ing effect, preventing [[Physics:Radiation|radiation]] and reducing [[Engineering:Electromagnetic interference|electromagnetic interference]].{{multiple image
| align     = center
| direction = horizontal
| caption_align = center
| image1    = RM core.png
| width1 = 200
| caption1  = A pot core of 'RM' type
| image2    = POT CORE.jpg
| width2 = 320
| caption2  = A Regular Pot Core
}}

=== Toroidal core ===
{{Main article|Engineering:Toroidal inductors and transformers}}

This design is based on a [[Toroid|toroid]] (the same shape as a doughnut).  The coil is wound through the hole in the torus and around the outside.  An ideal coil is distributed evenly all around the circumference of the torus.  The [[Symmetry|symmetry]] of this geometry creates a [[Physics:Magnetic field|magnetic field]] of circular loops inside the core, and the lack of sharp bends will constrain virtually all of the field to the core material.  This not only makes a highly [[Physics:Energy conversion efficiency|efficient]] [[Engineering:Transformer|transformer]], but also reduces the [[Engineering:Electromagnetic interference|electromagnetic interference]] radiated by the coil.

[[Image:Toroid core.png|thumb|150px|A toroidal core]]

It is popular for applications where the desirable features are: high [[Engineering:Power-to-weight ratio|specific power]] per mass and [[Physics:Volume|volume]], low [[Physics:Mains hum|mains hum]], and minimal [[Engineering:Electromagnetic interference|electromagnetic interference]].  One such application is the power supply for a hi-fi audio amplifier.  The main drawback that limits their use for general purpose applications is the inherent difficulty of winding wire through the center of a torus.

Unlike a split core (a core made of two elements, like a pair of ''E'' cores), specialized machinery is required for automated winding of a toroidal core.  Toroids have less audible noise, such as mains hum, because the magnetic forces do not exert [[Physics:Bending moment|bending moment]] on the core.  The core is only in compression or tension, and the circular shape is more stable mechanically.

=== Ring or bead ===
{{Main article|Physics:Ferrite bead}}

[[File:Two inductors (437342545).jpg|thumb|On the left, a non-adjustable ferrite rod with connection wires glued to the ends. On the right, a molded ferrite rod with holes, with a single wire threaded through the holes.]]
[[Image:Ferrite bead no shell.jpg|thumb|right|A ferrite ring on a computer data cable.]]
The ring is essentially identical in shape and performance to the toroid, except that inductors commonly pass only through the center of the core, without wrapping around the core multiple times.

The ring core may also be composed of two separate C-shaped hemispheres secured together within a plastic shell, permitting it to be placed on finished cables with large connectors already installed, that would prevent threading the cable through the small inner diameter of a solid ring.

== A<sub>L</sub> value ==
The A<sub>L</sub> value of a core configuration is frequently specified by manufacturers. The relationship between inductance and A<sub>L</sub> number in the linear portion of the magnetisation curve is defined to be:

:<math>L = n^2 A_L</math>

where n is the number of turns, L is the inductance (e.g. in nH) and A<sub>L</sub> is expressed in inductance per turn squared (e.g. in nH/n<sup>2</sup>).<ref name="AL Value">http://www.jmag-international.com/catalog/101_ChokeCoil_CurrentCharacteristic.html, A<sub>L</sub> Value</ref>

== Core loss ==
When the core is subjected to a ''changing'' magnetic field, as it is in devices that use AC current such as [[Engineering:Transformer|transformer]]s, [[Engineering:Inductor|inductor]]s, and AC motors and [[Physics:Alternator|alternator]]s, some of the power that would ideally be transferred through the device is lost in the core, dissipated as [[Physics:Heat|heat]] and sometimes [[Physics:Noise|noise]].  Core loss is commonly termed ''iron loss'' in contradistinction to [[Engineering:Copper loss|copper loss]], the loss in the windings.<ref>{{cite book|last1=Thyagarajan|first1=T.|last2=Sendur Chelvi|first2=K.P.|last3=Rangaswamy|first3=T.R.|title=Engineering Basics: Electrical, Electronics and Computer Engineering|date=2007|publisher=New Age International|isbn=9788122412741|edition=3rd|pages=184–185|url=https://books.google.com/books?id=oY-pcBq0z48C&pg=PA185}}</ref><ref>{{cite book|last1=Whitfield|first1=John Frederic|title=Electrical Craft Principles|volume=2|date=1995|publisher=IET|isbn=9780852968338|edition=4th|page=195|url=https://books.google.com/books?id=b31Z2x1ZlUEC&pg=PA195}}</ref>  Iron losses are often described as being in three categories:

===Hysteresis losses===
{{main|Physics:Magnetic hysteresis}}
When the magnetic field through the core changes, the [[Physics:Magnetization|magnetization]] of the core material changes by expansion and contraction of the tiny [[Physics:Magnetic domain|magnetic domain]]s it is composed of, due to movement of the [[Physics:Domain wall (magnetism)|domain wall]]s.  This process causes losses, because the domain walls get "snagged" on defects in the crystal structure and then "snap" past them, dissipating energy as heat.  This is called hysteresis loss.  It can be seen in the graph of the ''B'' field versus the ''H'' field for the material, which has the form of a closed loop. 
The net energy that flows into the inductor expressed in relationship to the B-H characteristic of the core is shown by the equation<ref name="Kluwer Academic Publishers">{{cite book|last1=Erickson|first1=Robert|last2=Maksimović|first2=Dragan|title=Fundamentals of Power Electronics, Second Edition|date=2001|publisher=Kluwer Academic Publishers|isbn=9780792372707|page=506}}</ref>
:<math>W=\int{\left(nA_c\frac{dB(t)}{t}\right)\left(\frac{H(t)l_m}{n}\right)dt}=(A_cl_m)\int{HdB}</math>
This equation shows that the amount of energy lost in the material in one cycle of the applied field is proportional to the area inside the hysteresis loop.  Since the energy lost in each cycle is constant, hysteresis power losses increase proportionally with [[Physics:Frequency|frequency]].<ref>{{cite book|last1=Dhogal|first1=P.S.|title=Basic Electrical Engineering, Volume 1|date=1986|publisher=Tata McGraw-Hill Education|isbn=9780074515860|page=128}}</ref> The final equation for the hysteresis power loss is<ref name="Kluwer Academic Publishers"/>
:<math>P_H=(f)(A_cl_m)\int{HdB}</math>

===Eddy-current losses===
If the core is electrically [[Physics:Electrical conductivity|conductive]], the changing magnetic field induces circulating loops of current in it, called [[Physics:Eddy current|eddy current]]s, due to [[Physics:Electromagnetic induction|electromagnetic induction]].<ref>{{cite book|last1=Kazimierczuk|first1=Marian K.|title=High-frequency magnetic components|date=2014|publisher=Wiley|location=Chichester|isbn=978-1-118-71779-0|page=113|edition=Second}}</ref>  The loops flow perpendicular to the magnetic field axis.  The energy of the currents is dissipated as heat in the resistance of the core material.  The power loss is proportional to the area of the loops and inversely proportional to the resistivity of the core material. Eddy current losses can be reduced by making the core out of thin [[Chemistry:Lamination|lamination]]s which have an insulating coating, or alternatively, making the core of a magnetic material with high electrical resistance, like ferrite.<ref>{{cite book|last1=Erickson|first1=Robert|last2=Maksimović|first2=Dragan|title=Fundamentals of Power Electronics, Second Edition|date=2001|publisher=Kluwer Academic Publishers|isbn=9780792372707|page=507}}</ref> Most magnetic cores intended for power converter application use ferrite cores for this reason.

===Anomalous losses===
By definition, this category includes any losses in addition to eddy-current and hysteresis losses.  This can also be described as broadening of the hysteresis loop with frequency.  Physical mechanisms for anomalous loss include localized eddy-current effects near moving domain walls.

=== Legg's equation ===
An equation known as Legg's equation models the [[Physics:Magnetism|magnetic material]] core loss at low [[Physics:Flux|flux]] densities. The equation has three loss components: hysteresis, residual, and eddy current,<ref>{{harvnb|Arnold Engineering Company|n.d.|p=70}}</ref><ref>{{Citation|last=Legg|first=Victor E.|title=Magnetic Measurements at Low Flux Densities Using the Alternating Current Bridge|date=January 1936|url=http://www3.alcatel-lucent.com/bstj/vol15-1936/articles/bstj15-1-39.pdf|journal=[[Engineering:Bell System Technical Journal|Bell System Technical Journal]]|volume=15|issue=1|pages=39–63|publisher=Bell Telephone Laboratories|doi=10.1002/j.1538-7305.1936.tb00718.x}}</ref><ref>{{Cite book|title=Soft ferrites : properties and applications|last=Snelling|first=E.C.|date=1988|publisher=Butterworths|isbn=978-0408027601|edition=2nd|location=London|oclc=17875867}}</ref> and it is given by

:<math>\frac{R_{\text{ac}}}{\mu L} = a B_{\text{max}} f + c f + e f^2</math>

where

* <math>R_{ac}</math> is the effective core loss resistance (ohms),
* <math>\mu</math> is the [[Physics:Permeability (electromagnetism)|material permeability]],
* <math>L</math> is the [[Physics:Inductance|inductance]] (henrys),
* <math>a</math> is the hysteresis loss coefficient,
* <math>B_{\text{max}}</math> is the maximum flux density (gauss),
* <math>c</math> is the residual loss coefficient,
* <math>f</math> is the frequency (hertz), and
* <chem>e</chem> is the eddy loss coefficient.

=== Steinmetz coefficients ===
{{main|Physics:Steinmetz's equation}}
Losses in magnetic materials can be characterized by the Steinmetz coefficients, which however do not take into account temperature variability. Material manufacturers provide data on core losses in tabular and graphical form for practical conditions of use.

== See also ==
* [[Engineering:Balun|Balun]]
*[[Magnetic-core memory]]
* [[Physics:Pole piece|Pole piece]]
* [[Engineering:Toroidal inductors and transformers|Toroidal inductors and transformers]]

== References ==
{{reflist}}
*{{Citation |last=Arnold Engineering Company |date=n.d. |title=MPP Cores |publisher=Arnold Engineering Company |location=Marengo, IL }}

== External links ==
* [http://hyperphysics.phy-astr.gsu.edu/Hbase/magnetic/indtor.html Online calculator for ferrite coil winding calculations]
* [http://computer.howstuffworks.com/question352.htm What are the bumps at the end of computer cables?]
* [https://web.archive.org/web/20070221093730/http://www.murata.com/emc/knowhow/pdfs/te04ea-1/23to25e.pdf How to use ferrites for EMI suppression via Wayback Machine] by Murata Manufacturing


[[Category:Electromagnetic components]]
[[Category:Radio electronics]]
[[Category:Electromagnetic radiation]]

{{Sourceattribution|Magnetic core}}