Transformer

A transformer is a device that transfers energy from one electrical circuit to another by magnetic coupling without requiring relative motion between its parts and usually comprises two or more coupled windings, and, in most cases, a magnetic core to concentrate magnetic flux. A voltage applied to one winding creates a time-varying magnetic flux in the core, which induces a voltage in the other windings. Varying the relative number of turns in the windings determines the ratio of their voltages, thus transforming the voltage by stepping it up or down from one circuit to another.

The transformer principle was demonstrated in 1831 by Faraday, though practical designs did not appear until the 1880s. Within less than a decade, the transformer was instrumental during the "War of Currents" in seeing alternating current systems triumph over their direct current counterparts, a position in which they have remained dominant. The transformer has since shaped the electricity supply industry, permitting the economic transmission of power over long distances. All but a fraction of the world's electrical power has passed through a series of transformers by the time it reaches the consumer.

Amongst the simplest of electrical machines, the transformer is also one of the most efficient, with large units attaining performances in excess of 99.75%. Transformers come in a range of sizes from a thumbnail-sized coupling transformer hidden inside a stage microphone to huge giga VA-rated units used to interconnect portions of national power grids. All operate with the same basic principles and with many similarities in their parts, though a variety of transformer designs exist to perform specialized roles throughout home and industry.

History
Michael Faraday built the first transformer in 1831, although he used it only to demonstrate the principle of electromagnetic induction and did not foresee its practical uses. Lucien Gaulard and John Dixon Gibbs, who first exhibited a device called a 'secondary generator' in London in 1882 and then sold the idea to American company Westinghouse. This may have been the first practical power transformer. They also exhibited the invention in Turin in 1884, where it was adopted for an electric lighting system. Their early devices used an open iron core, which was soon abandoned in favour of a more efficient circular core with a closed magnetic path. Russian engineer Pavel Yablochkov in 1876 invented a lighting system based on a set of induction coils, where primary windings were connected to a source of alternating current and secondary windings could be connected to several "electric candles". As the patent said, such a system "allows to provide separate supply to several lighting fixtures with different luminous intensities from a single source of electric power". Evidently, the induction coil in this system operated as a transformer.

William Stanley, an engineer for Westinghouse, built the first practical device in 1885 after George Westinghouse had bought Gaulard and Gibbs' patents. The core was made from interlocking E-shaped iron plates. This design was first used commercially in 1886. Hungarian engineers Károly Zipernowsky, Ottó Bláthy and Miksa Déri at the Ganz company in Budapest in 1885, who created the efficient "ZBD" model based on the design by Gaulard and Gibbs. Russian engineer Mikhail Dolivo-Dobrovolsky in 1889 developed the first three-phase transformer. In 1891 Nikola Tesla invented the Tesla coil, an air-cored, dual-tuned resonant transformer for generating very high voltages at high frequency.

Audio frequency transformers (at the time called repeating coils) were used by the earliest experimenters in the development of the telephone. While new technologies have made transformers in some electronics applications obsolete, transformers are still found in many electronic devices. Transformers are essential for high voltage power transmission, which makes long distance transmission economically practical. This advantage was the principal factor in the selection of alternating current power transmission in the "War of Currents" in the late 1880s. Many others have patents on transformers.

Coupling by mutual induction
The principles of the transformer are illustrated by consideration of a hypothetical ideal transformer consisting of two windings of zero resistance around a core of negligible reluctance. A voltage applied to the primary winding causes a current, which develops a magnetomotive force (MMF) in the core. The current required to create the MMF is termed the magnetising current; in the ideal transformer it is considered to be negligible. The MMF drives flux around the magnetic circuit of the core.

An electromotive force (EMF) is induced across each winding, an effect known as mutual inductance. The windings in the ideal transformer have no resistance and so the EMFs are equal in magnitude to the measured terminal voltages. In accordance with Faraday's law of induction, they are proportional to the rate of change of flux:


 * $${v_P} = {N_P} \frac {d \Phi_P}{dt}$$    and     $${v_S} = {N_S} \frac {d \Phi_S}{dt}$$

where:
 * $$v_P\,\!$$ and $$v_S\,\!$$ are the induced EMFs across primary and secondary windings,
 * $$N_P\,\!$$ and $$N_S\,\!$$ are the numbers of turns in the primary and secondary windings,
 * $$\tfrac{d \Phi_P}{dt}\,\!$$ and $$\tfrac{d \Phi_S}{dt}\,\!$$ are the time derivatives of the flux linking the primary and secondary windings.

In the ideal transformer, all flux produced by the primary winding also links the secondary, and so $$\Phi_P = \Phi_S\, $$, from which the well-known transformer equation follows:


 * $$\frac{v_P}{v_S}=\frac{N_P}{N_S}\,\!$$

The ratio of primary to secondary voltage is therefore the same as the ratio of the number of turns; alternatively, that the volts-per-turn is the same in both windings.

Under load


If a load impedance is connected to the secondary winding, a current will flow in the secondary circuit so created. The current develops an MMF over the secondary winding in opposition to that of the primary winding, so acting to cancel the flux in the core. The now decreased flux reduces the primary EMF, causing current in the primary circuit to increase to exactly offset the effect of the secondary MMF, and returning the flux to its former value. The core flux thus remains the same regardless of the secondary current, provided the primary voltage is sustained. In this way, the electrical energy fed into the primary circuit is delivered to the secondary circuit.

The primary and secondary MMFs differ only to the extent of the negligible magnetising current and may be equated, and so: $${i_P}{N_P}={i_S}{N_S}\!$$, from which the transformer current relationship emerges:
 * $$\frac{i_S}{i_P}=\frac{N_P}{N_S}$$

From consideration of the voltage and current relationships, it may be readily shown that impedance in one circuit is transformed by the square of the turns ratio, a secondary impedance $$Z_S\!$$ thus appearing to the primary circuit to have a value of $$Z_S\!\left(\!\tfrac{N_P}{N_S}\!\right)^2\!\!$$.

Circuit symbols
Standard symbols

Effect of frequency
The time-derivative term in Faraday's Law implies that the flux in the core is the integral of the applied voltage. An ideal transformer would, at least hypothetically, work under direct-current excitation, with the core flux increasing linearly with time. In practice, the flux would rise very rapidly to the point where magnetic saturation of the core occurred and the transformer would cease to function as such. All practical transformers must therefore operate under alternating (or pulsed) current conditions.



Transformer universal EMF equation
If the flux in the core is sinusoidal, the relationship for either winding between its rms EMF E, and the supply frequency f, number of turns N, core cross-sectional area a and peak magnetic flux density B is given by the universal EMF equation:


 * $$ E={\frac {2 \pi f N a B} {\sqrt{2}}} \!=4.44 f N a B$$

The EMF of a transformer at a given flux density increases with frequency, an effect predicated by the universal transformer EMF equation. By operating at higher frequencies, transformers can be physically more compact without reaching saturation, and a given core is able to transfer more power. However efficiency becomes poorer with properties such as core loss and conductor skin effect also increasing with frequency.

In general, operation of a transformer at its designed voltage but at a higher frequency than intended will lead to reduced magnetising current. At a frequency lower than the design value, with the rated voltage applied, the magnetising current may increase to an excessive level. Operation of a transformer at other than its design frequency may require assessment of voltages, losses, and cooling to establish if safe operation is practical. For example, transformers may need to be equipped with "volts per hertz" over-excitation relays to protect the transformer from overvoltage at higher than rated frequency.

Energy losses
An ideal transformer would have no energy losses, and would therefore be 100% efficient. Despite the transformer being amongst the most efficient of electrical machines, with experimental models using superconducting windings achieving efficiencies of 99.85%, energy is dissipated in the windings, core, and surrounding structures. Larger transformers are generally more efficient, and those rated for electricity distribution usually perform better than 95%. A small transformer such as a plug-in "power brick" used for low-power consumer electronics may be less than 85% efficient.

Transformer losses are attributable to several causes and may be differentiated between those originating in the windings, sometimes termed copper loss, and those arising from the magnetic circuit, sometimes termed iron loss. The losses vary with load current, and may furthermore be expressed as "no-load" or "full-load" loss, or at an intermediate loading. Winding resistance dominates load losses, whereas hysteresis and eddy currents losses contribute to over 99% of the no-load loss.

Losses arise from:
 * Winding resistance
 * Current flowing through the windings causes resistive heating of the conductors. At higher frequencies, skin effect and proximity effect create additional winding resistance and losses.


 * Eddy currents
 * Induced eddy currents circulate within the core, causing resistive heating.


 * Hysteresis losses
 * Each time the magnetic field is reversed, a small amount of energy is lost to hysteresis within the magnetic core, the amount being dependant on the particular core material.


 * Magnetostriction
 * Magnetic flux in the core causes it to physically expand and contract slightly with the alternating magnetic field, an effect known as magnetostriction. This produces the familiar buzzing sound, and in turn causes losses due to frictional heating in susceptible ferromagnetic cores.


 * Mechanical losses
 * In addition to magnetostriction, the alternating magnetic field causes fluctuating electromagnetic forces between the primary and secondary windings. These incite vibrations within nearby metalwork, adding to the buzzing noise, and consuming a small amount of power.


 * Stray losses
 * Not all the magnetic field produced by the primary is intercepted by the secondary. A portion of the leakage flux may induce eddy currents within nearby conductive objects, such as the transformer's support structure, and be converted to heat.


 * Cooling system
 * Large power transformers may be equipped with cooling fans, oil pumps or water-cooled heat exchangers designed to remove heat. The power used to operate the cooling system is typically considered part of the losses of the transformer.

Transformer types and uses
A variety of specialised transformer designs has been created to fulfil certain engineering applications. The numerous applications to which transformers are adapted lead them to be classified in many ways:


 * By power level: from a fraction of a volt-ampere (VA) to over a thousand MVA;
 * By frequency range: power-, audio- or radio frequency;
 * By voltage class: from a few volts to hundreds of kilovolts;
 * By cooling type: air cooled, oil filled, fan cooled, or water cooled;
 * By application function: such as power supply, impedance matching or circuit isolation;
 * By end purpose: distribution, rectifier, arc furnace, amplifier output;
 * By winding turns ratio: step-up, step-down, isolating (near equal ratio), variable.

Steel cores
Transformers for use at power or audio frequencies have cores made of many thin laminations of silicon steel. By concentrating the magnetic flux, more of it is usefully linked by both primary and secondary windings. Since the steel core is conductive, it, too, has currents induced in it by the changing magnetic flux. Each layer is insulated from the adjacent layer to reduce the energy lost to eddy current heating of the core. The thin laminations are used to reduce the eddy currents, and the insulation is used to keep the laminations from acting as a solid piece of steel. The thinner the laminations, the lower the eddy currents, and the lower the losses. Very thin laminations are generally used on high frequency transformers. The cost goes up when using thinner laminations mainly over the labor in stacking them.

A typical laminated core is made from E-shaped and I-shaped pieces, leading to the name "EI transformer". In the EI transformer, the laminations are stacked in what is known as an interleaved fashion. Due to this interleaving a second gap in parallel (in an analogy to electronic circuits) to the gap between E and I is formed between the E-pieces. The E-pieces are pressed together to reduce the gap width to that of the insulation. The gap area is very large, so that the effective gap width is very small (in analogy to a capacitor). For this to work the flux has to gradually flow from one E to the other. That means that on one end all flux is only on every second E. That means saturation occurs at half the flux density. Using a longer E and wedging it with two small Is will increase the overlap and additionally make the grains more parallel to the flux (think of a wooden frame for a window). If an air gap is needed (which is unlikely considering the low remanence available for steel), all the E's are stacked on one side, and all the I's on the other creating a gap.

The cut core or C-core is made by winding a silicon steel strip around a rectangular form. After the required thickness is achieved, it is removed from the form and the laminations are bonded together. It is then cut in two forming two C shapes. The faces of the cuts are then ground smooth so they fit very tight with a very small gap to reduce losses. The core is then assembled by placing the two C halves together, and holding them closed by a steel strap. Usually two C-cores are used to shorten the return path for the magnetic flux resulting in a form similar to the EI. More cores would necessitate a triangular cross-section. Like toroidal cores, they have the advantage, that the flux is always in the oriented parallel the grains. Due to the bending of the core, some area is lost for a rectangular winging.

A steel core's remanence means that it retains a static magnetic field when power is removed. When power is then reapplied, the residual field will cause a high inrush current until the effect of the remanent magnetism is reduced, usually after a few cycles of the applied alternating current. Overcurrent protection devices such as fuses must be selected to allow this harmless inrush to pass. On transformers connected to long overhead power transmission lines, induced currents due to geomagnetic disturbances during solar storms can cause saturation of the core, and false operation of transformer protection devices.

Steel cores develop a larger hysteresis loss due to eddy currents as the operating frequency is increased. Ferrite, or thinner steel laminations for the core are typically used for frequencies above 1 kHz. The thinner steel laminations serve to reduce the eddy currents. Some types of very thin steel laminations can operate at up to 10 kHz or higher. Ferrite is used in higher frequency applications, extending to the VHF band and beyond. Aircraft traditionally use 400 Hz power systems since the slight increase in thermal losses is more than offset by the reduction in core and winding weight. Military gear includes 400 Hz (and other frequencies) to supply power for radar or servomechanisms.

Distribution transformers can achieve low off-load losses by using cores made with low loss high permeability silicon steel and amorphous (non-crystalline) steel, so-called "metal glasses" — the high cost of the core material is offset by the lower losses incurred at light load, over the life of the transformer. In order to maintain good voltage regulation, distribution transformers are designed to have very low leakage inductance.

Certain special purpose transformers use long magnetic paths, insert air gaps, or add magnetic shunts (which bypass a portion of magnetic flux that would otherwise link the primary and secondary windings) in order to intentionally add leakage inductance. The additional leakage inductance limits the secondary winding's short circuit current to a safe, or a controlled, level. This technique is used to stabilize the output current for loads that exhibit negative resistance such as electric arcs, mercury vapor lamps, and neon signs, or safely handle loads that may become periodically short-circuited such as electric arc welders. Gaps are also used to keep a transformer from saturating, especially audio transformers that have a DC component added.

Solid cores
Powdered iron cores are used in circuits (such as switch-mode power supplies) that operate above mains frequencies and up to a few tens of kilohertz. These materials combine high magnetic permeability with high bulk electrical resistivity.

At even higher, radio-frequencies (RF), other types of cores made from non-conductive magnetic ceramic materials, called ferrites, are common. Some RF transformers also have moveable cores (sometimes called slugs) which allow adjustment of the coupling coefficient (and bandwidth) of tuned radio-frequency circuits.

Cores are available in a wide variety of shapes, including toroids. Other shapes include so-called E-cores and C-cores.

Air cores
High-frequency transformers may also use air cores. These eliminate the loss due to hysteresis in the core material. Such transformers maintain high coupling efficiency (low stray field loss) by overlapping the primary and secondary windings.

Toroidal cores


Toroidal transformers are built around a ring-shaped core, which is made from a long strip of silicon steel or permalloy wound into a coil, from powdered iron, or ferrite, depending on operating frequency. The strip construction ensures that the grain boundaries are optimally aligned, improving the transformer's efficiency by reducing the core's reluctance. The closed ring shape eliminates air gaps inherent in the construction of an EI core. The cross-section of the ring is usually square or rectangular, but more expensive cores with circular cross-sections are also available. The primary and secondary coils are often wound concentrically to cover the entire surface of the core. This minimises the length of wire needed, and also provides screening to minimize the core's magnetic field from generating electromagnetic interference.

Ferrite toroid cores are used at higher frequencies, typically between a few tens of kilohertz to a megahertz, to reduce losses, physical size, and weight of switch-mode power supplies.

Toroidal transformers are more efficient than the cheaper laminated EI types of similar power level. Other advantages, compared to EI types, include smaller size (about half), lower weight (about half), less mechanical hum (making them superior in audio amplifiers), lower exterior magnetic field (about one tenth), low off-load losses (making them more efficient in standby circuits), single-bolt mounting, and more choice of shapes. This last point means that, for a given power output, either a wide, flat toroid or a tall, narrow one with the same electrical properties can be chosen, depending on the space available. The main disadvantages are higher cost and limited size.

A drawback of toroidal transformer construction is the higher cost of windings. As a consequence, toroidal transformers are uncommon above ratings of a few kVA. Small distribution transformers may achieve some of the benefits of a toroidal core by splitting it and forcing it open, then inserting a bobbin containing primary and secondary windings.

When fitting a toroidal transformer, it is important to avoid making an unintentional short-circuit through the core. This can happen if the steel mounting bolt in the middle of the core is allowed to touch metalwork at both ends, making a loop of conductive material that passes through the hole in the toroid. Such a loop could result in a dangerously large current flowing in the bolt.

Windings
The wire of the adjacent turns in a coil, and in the different windings, must be electrically insulated from each other. The wire used is generally magnet wire. Magnet wire is a copper wire with a coating of varnish or some other synthetic coating. Transformers for years have used Formvar wire, which is a varnished type of magnet wire.

The conducting material used for the winding depends upon the application. Small power and signal transformers are wound with solid copper wire, insulated usually with enamel, and sometimes additional insulation. Larger power transformers may be wound with wire, copper, or aluminium rectangular conductors. Strip conductors are used for very heavy currents. High frequency transformers operating in the tens to hundreds of kilohertz will have windings made of Litz wire to minimize the skin effect losses in the conductors. Large power transformers use multiple-stranded conductors as well, since even at low power frequencies non-uniform distribution of current would otherwise exist in high-current windings. Each strand is insulated from the other, and the strands are arranged so that at certain points in the winding, or throughout the whole winding, each portion occupies different relative positions in the complete conductor. This "transposition" equalizes the current flowing in each strand of the conductor, and reduces eddy current losses in the winding itself. The stranded conductor is also more flexible than a solid conductor of similar size is. (see reference (1) below)

For signal transformers, the windings may be arranged in a way to minimize leakage inductance and stray capacitance to improve high-frequency response. This can be done by splitting up each coil into sections, and those sections placed in layers between the sections of the other winding. This is known as a stacked type or interleaved winding.

Windings on both the primary and secondary of power transformers may have external connections (called taps) to intermediate points on the winding to allow adjustment of the voltage ratio. Taps may be connected to an automatic, on-load tap changer type of switchgear for voltage regulation of distribution circuits. Audio-frequency transformers, used for the distribution of audio to public address loudspeakers, have taps to allow adjustment of impedance to each speaker. A center-tapped transformer is often used in the output stage of an audio power amplifier in a push-pull type circuit. Modulation transformers in AM transmitters are very similar. Tapped transformers are also used as components of amplifiers, oscillators, and for feedback linearization of amplifier circuits.

Winding insulation
The turns of the windings must be insulated from each other to ensure that the current travels through the entire winding. The potential difference between adjacent turns is usually small, so that enamel insulation may suffice for small power transformers. Supplemental sheet or tape insulation is usually employed between winding layers in larger transformers.

The transformer may also be immersed in transformer oil that provides further insulation. Although the oil is primarily used to cool the transformer, it also helps to reduce the formation of corona discharge within high voltage transformers. By cooling the windings, the insulation will not break down as easily due to heat. To ensure that the insulating capability of the transformer oil does not deteriorate, the transformer casing is completely sealed against moisture ingress. Thus the oil serves as both a cooling medium to remove heat from the core and coil, and as part of the insulation system.

Certain power transformers have the windings protected by epoxy resin. By impregnating the transformer with epoxy under a vacuum, air spaces within the windings are replaced with epoxy, thereby sealing the windings and helping to prevent the possible formation of corona and absorption of dirt or water. This produces transformers suitable for damp or dirty environments, but at increased manufacturing cost.

Basic Impulse Insulation Level (BIL)
Outdoor electrical distribution systems are subject to lightning surges. Even if the lightning strikes the line some distance from the transformer, voltage surges can travel down the line and into the transformer. High voltage switches and circuit breakers can also create similar voltage surges when they are opened and closed. Both types of surges have steep wave fronts and can be very damaging to electrical equipment. To minimize the effects of these surges, the electrical system is protected by lighting arresters but they do not completely eliminate the surge from reaching the transformer. The basic impulse level (BIL) of the transformer measures its ability to withstand these surges. All 600 volt and below transformers are rated 10 kV BIL. The 2400 and 4160 volt transformers are rated 25 kV BIL.

Shielding
Where transformers are intended for minimum electrostatic coupling between primary and secondary circuits, an electrostatic shield can be placed between windings to reduce the capacitance between primary and secondary windings. The shield may be a single layer of metal foil, insulated where it overlaps to prevent it acting as a shorted turn, or a single layer winding between primary and secondary. The shield is connected to earth ground.

Transformers may also be enclosed by magnetic shields, electrostatic shields, or both to prevent outside interference from affecting the operation of the transformer, or to prevent the transformer from affecting the operation of nearby devices that may be sensitive to stray fields such as CRTs.

Coolant
Small signal transformers do not generate significant amounts of heat. Power transformers rated up to a few kilowatts rely on natural convective air-cooling. Specific provision must be made for cooling of high-power transformers. Transformers handling higher power, or having a high duty cycle can be fan-cooled.

Some dry transformers are enclosed in pressurized tanks and are cooled by nitrogen or sulphur hexafluoride gas.

The windings of high-power or high-voltage transformers are immersed in transformer oil — a highly refined mineral oil, that is stable at high temperatures. Large transformers to be used indoors must use a non-flammable liquid. Formerly, polychlorinated biphenyl (PCB) was used as it was not a fire hazard in indoor power transformers and it is highly stable. Due to the stability and toxic effects of PCB by-products, and its accumulation in the environment, it is no longer permitted in new equipment. Old transformers that still contain PCB should be examined on a weekly basis for leakage. If found to be leaking, it should be changed out, and professionally decontaminated or scrapped in an environmentally safe manner. Today, non-toxic, stable silicone-based oils, or fluorinated hydrocarbons may be used where the expense of a fire-resistant liquid offsets additional building cost for a transformer vault. Other less-flammable fluids such as canola oil may be used but all fire resistant fluids have some drawbacks in performance, cost, or toxicity compared with mineral oil.

The oil cools the transformer, and provides part of the electrical insulation between internal live parts. It has to be stable at high temperatures so that a small short or arc will not cause a breakdown or fire. The oil-filled tank may have radiators through which the oil circulates by natural convection. Very large or high-power transformers (with capacities of millions of watts) may have cooling fans, oil pumps and even oil to water heat exchangers. Oil-filled transformers undergo prolonged drying processes, using vapor-phase heat transfer, electrical self-heating, the application of a vacuum, or combinations of these, to ensure that the transformer is completely free of water vapor before the cooling oil is introduced. This helps prevent electrical breakdown under load.

Oil-filled power transformers may be equipped with Buchholz relays which are safety devices that sense gas build-up inside the transformer (a side effect of an electric arc inside the windings), and thus switches off the transformer.

Experimental power transformers in the 2 MVA range have been built with superconducting windings which eliminates the copper losses, but not the core steel loss. These are cooled by liquid nitrogen or helium.

Terminals
Very small transformers will have wire leads connected directly to the ends of the coils, and brought out to the base of the unit for circuit connections. Larger transformers may have heavy bolted terminals, bus bars or high-voltage insulated bushings made of polymers or porcelain. A large bushing can be a complex structure since it must provide electrical insulation without letting the transformer leak oil.

Enclosure
Small transformers often have no enclosure. Transformers may have a shield enclosure, as described above. Larger units may be enclosed to prevent contact with live parts, and to contain the cooling medium (oil or pressurized gas).