Solid metals

Laminated silicon steel

Main article: Silicon steel

(left) Eddy currents (I, red) within a solid iron transformer core. (right) Making the core out of thin laminations parallel to the field (B, green) 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

Typical EI 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 silicon to iron (around 3%) results in a dramatic increase of the resistivity of the metal, up to four times higher. 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.

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.

Ceramics

Air

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 inductance than similarly sized ferromagnetic core coils, but are used in radio frequency circuits to prevent energy losses called core losses that occur in magnetic cores. The absence of normal core losses permits a higher Q factor, so air core coils are used in high frequency resonant circuits, such as up to a few megahertz. However, losses such as 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.

Straight cylindrical rod

Ferrite rods are simple cylinders of ferrite that can be wound around.

Most commonly made of ferrite or powdered iron, and used in radios especially for tuning an 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 inductance. Often the rod is threaded to allow adjustment with a screwdriver. In radio circuits, a blob of 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 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 radiation occurs at the end of the rod and 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.

A U-shaped core, with sharp corners

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.

Classical E core

The EFD' core allows for construction of inductors or transformers with a lower profile

The ETD core has a cylindrical central leg.

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) 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.

Construction of an inductor using two ER cores, a plastic bobbin and two clips. The bobbin has pins to be soldered to a printed circuit board.

Exploded view of the previous figure showing the structure

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 printed circuit board. This design is excellent for mass production and allows a high power, small volume transformer to be constructed for low cost. It is not as ideal as either a pot core or toroidal core but costs less to produce.

A planar 'E' core

A planar inductor

Exploded view that shows the spiral track made directly on the printed circuit board

Pot core

Usually ferrite or similar. This is used for inductors and transformers. 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 shielding effect, preventing radiation and reducing electromagnetic interference.

A pot core of 'RM' type

A Regular Pot Core

Toroidal core

This design is based on a 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 of this geometry creates a 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 efficient transformer, but also reduces the electromagnetic interference radiated by the coil.

A toroidal core

It is popular for applications where the desirable features are: high specific power per mass and volume, low mains hum, and minimal 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 bending moment on the core. The core is only in compression or tension, and the circular shape is more stable mechanically.

Ring or bead

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.

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.

Hysteresis losses

When the magnetic field through the core changes, the magnetization of the core material changes by expansion and contraction of the tiny magnetic domains it is composed of, due to movement of the domain walls. 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^[12]

${\displaystyle W=\int {\left(nA_{c}{\frac {dB(t)}{t}}\right)\left({\frac {H(t)l_{m}}{n}}\right)dt}=(A_{c}l_{m})\int {HdB}}$

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 frequency.^[13] The final equation for the hysteresis power loss is^[12]

${\displaystyle P_{H}=(f)(A_{c}l_{m})\int {HdB}}$

Eddy-current losses

If the core is electrically conductive, the changing magnetic field induces circulating loops of current in it, called eddy currents, due to electromagnetic induction.^[14] 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 laminations which have an insulating coating, or alternatively, making the core of a magnetic material with high electrical resistance, like ferrite.^[15] 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 magnetic material core loss at low flux densities. The equation has three loss components: hysteresis, residual, and eddy current,^[16][17][18] and it is given by

${\displaystyle {\frac {R_{\text{ac}}}{\mu L}}=aB_{\text{max}}f+cf+ef^{2}}$

where

• ${\displaystyle R_{ac}}$ is the effective core loss resistance (ohms),
• ${\displaystyle \mu }$ is the material permeability,
• ${\displaystyle L}$ is the inductance (henrys),
• ${\displaystyle a}$ is the hysteresis loss coefficient,
• ${\displaystyle B_{\text{max}}}$ is the maximum flux density (gauss),
• ${\displaystyle c}$ is the residual loss coefficient,
• ${\displaystyle f}$ is the frequency (hertz), and
• ${\displaystyle {\ce {e}}}$ is the eddy loss coefficient.

Steinmetz coefficients

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.