This article is about electrical and electronic transformers. For other meanings, see Transformers

A transformer is an electrical device that transfers energy from one electrical circuit to another by magnetic coupling without using any moving parts. It is often used to convert between high and low voltages and for impedance transformation. The transformer was an important element in the development of high-voltage electric power transmission and central generating stations.

Basic principles[]

Flux coupling[]

400px-Single-phase transformer.png

A simple single phase transformer consists of two electrical conductors called the primary winding and the secondary winding. The primary is fed with a varying (alternating or pulsed continuous) electric current which creates a varying magnetic field around the conductor. According to the principle of mutual inductance, the secondary, which is placed in this varying magnetic field, will develop an electromotive force or EMF. If the ends of the secondary are connected together to form an electric circuit, this EMF will cause a current to flow in the secondary. Thus, some of the electrical power fed into the primary is delivered to the secondary. In practical transformers, the primary and secondary conductors are coils of conducting wire because a coil creates a denser magnetic field (higher magnetic flux) than a straight conductor.

Transformers alone cannot do the following:

  • Convert DC to AC or vice versa
  • Change the voltage or current of DC
  • Change the AC supply frequency.

However, transformers are components of the systems that perform all these functions.

Electrical laws[]

Consider the following two laws:

  1. According to the law of conservation of energy, the power delivered by a transformer cannot exceed the power fed into it.
  2. The power dissipated in a load at any instant is equal to the product of the voltage across it and the (in phase) current passing through it (see also Ohm's law).

It follows from the above two laws that a transformer is not an amplifier. If the transformer is used to change power from one voltage to another, the magnitudes of the currents in the two windings must also be different, inversely proportional to the voltages. If the voltage were to be stepped down by the transformer, the secondary current available to the load would be greater. For example, suppose a power of 50 watts is supplied to a resistive load from a transformer with a turns ratio of 25:2.

  • P = E·I (power = electromotive force · current)

50 W = 2 V · 25 A in the primary circuit

  • Now with transformer change:

50 W = 25 V · 2 A in the secondary circuit.

The high-current, low-voltage windings have fewer turns of (usually) thicker wire. The high-voltage, low-current windings have more turns of (usually) thinner wire.

The electromotive force (EMF) developed in the secondary is proportional to the ratio of the number of turns in the secondary coil to the number of turns in the primary coil. Neglecting all leakage flux, an ideal transformer follows the equation:

Where is the voltage in the primary coil, is the voltage in the secondary coil, is the number of turns of wire on the primary coil, and is the number of turns of wire on the secondary coil. This leads to the most common use of the transformer: to convert power at one voltage to power at a different voltage.

Neglecting leakage flux, the relationship between voltage, number of turns, magnetic flux intensity and core area is given by the universal emf equation:

Where is the sinusoidal root mean square (RMS) voltage of the winding, is the frequency in hertz, is the number of turns of wire, is the area of the core (square units) and is magnetic flux density in webers per square unit. The value 4.44 collects a number of constants required by the system of units.

In normal operation, a transformer winding should never be energised from a constant DC voltage source, as this would cause a large direct current to flow. In such a situation, in an ideal transformer with an open circuit secondary, the current would rise indefinitely as a linear function of time. In practice, the series resistance of the winding limits the amount of current that can flow, until the transformer either reaches thermal equilibrium or is destroyed. DC is occasionally applied to large power transformers in order to "bake out" water prior to adding the cooling oil and commencing normal operation.


Those credited with the invention of the transformer include:

  • Michael Faraday, who invented an 'induction ring' on August 29, 1831. This was the first transformer, although Faraday used it only to demonstrate the principle of electromagnetic induction and did not foresee the use to which it would eventually be put.
  • Lucien Gaulard and John Dixon Gibbs, who first exhibited a device called a 'secondary generator' in London in 1881 and then sold the idea to American company Westinghouse. This may have been the first practical power transformer, but was not the first transformer of any kind. They also exhibited the invention in Turin in 1884, where it was adopted for an electric lighting system. Their early devices used a linear iron core, which was later abandoned in favour of a more efficient circular core.
  • William Stanley, an engineer for Westinghouse, who built the first practical device in 1885 after George Westinghouse 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 Ottó Bláthy, Miksa Déri and Károly Zipernowsky at the Ganz company in Budapest in 1885, who created the efficient "ZBD" model based on the design by Gaulard and Gibbs.
  • Nikola Tesla in 1891 invented the Tesla coil, which is a high-voltage, air-core, dual-tuned resonant transformer for generating very high voltages at high frequency.

Practical considerations[]

Closeup of an adjustable urban stepdown transformer (one of three mounted to same concrete pole)



Transformers come in a range of sizes from a thumbnail-sized coupling transformer hidden inside a stage microphone to gigawatt units used to interconnect large portions of national power grids, all operating with the same basic principles and with many similarities in their parts.

A rough classification of transformers by the power handled in the circuit, in watts (or, more accurately, VA (volt amperes)):

  • Up to 1 watt: Signal transformers, interstage coupling
  • 1 - 1000 watts: Small power transformers, filament transformers, audio output transformers
  • 1 kilowatt - 1 megawatt: Power transformers; larger units in this range may be oil filled
  • 1 megawatt and over: Large power transformers, used for substations, large electrical consumers, and for power plants and transmission.

Transformers can be classified into various types according to the ratio of the numbers of turns in the coils, as well as whether or not the primary and secondary are isolated:

  • the secondary has more turns than the primary
  • the secondary has fewer turns than the primary
  • intended to transform from one voltage to the same voltage. The two coils have approximately equal numbers of turns, although often there is a slight difference in the number of turns, in order to compensate for losses (otherwise the output voltage would be a little less than, rather than the same as, the input voltage).
  • the primary and secondary have an adjustable number of turns which can be selected without reconnecting the transformer.

In all cases the primary winding, or the secondary winding, or both, may have taps that allow selection of one of several different ratios of primary to secondary turns.


An ideal transformer would have no loss, and would therefore be 100% efficient. However, the coils of a real transformer have resistance. When modeling a real transformer the resistance can be considered as existing in series with the winding of an ideal transformer.

Large power transformers are often more than 98% efficient, in terms of energy supplied to the primary winding of the transformer and coupled to the secondary. The remaining 2% (or less) of the input energy is lost to:

  • Winding resistance
The current flowing through the windings causes resistive heating of the conductors. This is referred to as copper loss (to distinguish this from the rest of the losses below which are primarily attributable to the magnetic core and known as core losses, also called iron losses)
  • Eddy currents
Induced currents circulating in the core causing resistive heating of the core.
  • 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.
  • Hysteresis losses
Each time the magnetic field is reversed, a small amount of energy is lost to hysteresis in the magnetic core. Differing core materials will have different levels of hysteresis loss.
  • Mechanical losses
The alternating magnetic field causes fluctuating electromagnetic forces between the coils of wire, the core and any nearby metalwork, causing vibrations and noise which consume power.
  • Magnetostriction
The flux in the core causes it to physically expand and contract slightly with the alternating magnetic field, an effect known as magnetostriction. This in turn causes losses due to frictional heating in susceptible ferromagnetic cores. The familiar hum or buzzing noise heard near transformers is a result of stray fields causing components of the tank to vibrate, and is also due to magnetostriction vibration of the core itself.
  • Cooling system
Large power transformers may be equipped with cooling fans, oil pumps or water-cooled heat exchangers designed to remove the heat caused by copper losses and core losses. The power used to operate the cooling system is typically considered part of the losses of the transformer. Small transformers, such as a plug-in "wall wart"/"power brick" used to power small consumer electronics, often have high losses and may be less than 85% efficient.

High frequency operation[]

The universal transformer emf equation indicates that at higher frequency, the core flux density will be lower for a given voltage. This implies that a core can have a smaller cross-sectional area and thus be physically more compact without reaching saturation. It is for this reason that the aircraft manufacturers and the military use 400 hertz supplies. They are less concerned with efficiency, which is lower at higher frequencies (mostly due to increased hysteresis losses), but are more concerned with saving weight. Similarly, flyback transformers which supply high voltage to cathode ray tubes operate at the frequency of the horizontal oscillator, many times higher than 50 or 60 hertz, which allows for a more compact component.


A transformer usually has:

  • two or more insulated windings, to carry current
  • a core, in which the mutual magnetic field couples the windings.

In transformers designed to operate at low frequencies, the windings are usually formed around an iron or steel core. This helps to confine the magnetic field within the transformer and increase its efficiency, although the presence of the core causes energy losses. Transformers made to operate at high frequencies may use other lower loss materials, or may use an air core.

Power transformers are further classified by the exact arrangement of the core and windings as "shell type", "core type" and also by the number of "limbs" that carry the flux (3, 4 or 5 for a 3-phase transformer). The differences in the performance of each of these types, while of continuing interest to specialists, is perhaps more detail than is appropriate for a general encyclopedia.


Steel cores[]

Laminated core transformer showing edge of lamination at top of unit

Transformers often have silicon steel cores to channel the magnetic field. This keeps the field more concentrated around the wires, so that the transformer is more compact. The core of a power transformer must be designed so that it does not reach magnetic saturation. Carefully designed gaps are sometimes placed in the magnetic path to help prevent saturation. Practical transformer cores are always made of many stamped pieces of thin steel. The high resistance between layers reduces eddy currents in the cores that waste power by heating the core. These are common in power and audio circuits. A typical laminated core is made from E-shaped and I-shaped pieces, leading to the name "EI transformer". One problem with a steel core is that due to the material's magnetic hysteresis it may retain a static magnetic field when power is removed. When power is then reapplied, the residual field may cause the core to temporarily saturate. This can be a significant problem in transformers of more than a few hundred watts output, since the higher inrush current can cause mains fuses to blow unless current-limiting circuitry is added. More seriously, inrush currents can physically deform and damage the primary windings of large power transformers.

Solid cores[]

In higher frequency circuits such as switch-mode power supplies, powdered iron cores are sometimes used. These materials combine a high magnetic permeability with a high material resistivity. At even higher frequencies (radio frequencies typically) other types of core made of non-conductive magnetic materials, such as various ceramic materials called ferrites are common. Some transformers in radio-frequency circuits have adjustable cores which allow tuning of the coupling circuit.

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, or from ferrite, depending on frequency. This construction ensures that all the grain boundaries are pointing in the optimum direction, making the transformer more efficient by reducing the core's reluctance, and eliminates the 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 wound concentrically to cover the entire surface of the core. This minimises the length of wire needed, and also provides screening to prevent the core's magnetic field from generating electromagnetic interference.

Toroidal cores for use at frequencies up to a few tens of kilohertz may also be made of ferrite material to reduce losses. Such transformers are used in switch-mode power supplies.

Toroidal transformers are more efficient (around 95%) than the cheaper laminated EI types. 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 disadvantage is higher cost.

When fitting a toroidal transformer, it is important to avoid making an unintentional short-circuit through the core (e.g. by carelessly fitting a steel mounting bolt through the middle and fastening it to metalwork at both ends). This would cause a large current to flow through the bolt, converting all of the mains input power into heat, and blowing the input fuse. To avoid this, only one end of the mounting bolt must be fixed to the surrounding metalwork.


The winding material depends on the application. Small power and signal transformers are wound with insulated solid copper wire, often enameled. Larger power transformers may be wound with wire, copper or aluminum rectangular conductors, or strip conductors 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.

Windings on both primary and secondary of a power transformer may have taps to allow adjustment of the voltage ratio; taps may be connected to automatic on-load tap changer switchgear for voltage regulation of distribution circuits.


The conductor material must have insulation to ensure the current travels around the core, and not through a turn-to-turn short-circuit.

In power transformers, the voltage difference between parts of the primary and secondary windings can be quite large. Layers of insulation are inserted between layers of windings to prevent arcing, and the transformer is immersed in transformer oil that provides further insulation and acts as a cooling medium.


Although an ideal transformer is purely magnetic in operation, the close proximity of the primary and secondary windings can create a mutual capacitance between the windings. Where transformers are intended for high electrical isolation between primary and secondary circuits, an electrostatic shield can be placed between windings to minimize this effect.

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 other devices (such as CRTs in close proximity to the transformer). Transformers may also be enclosed for reasons of safety, both to prevent contact with the transformer during normal operation and to contain possible fires that occur as a result of abnormal operation. The enclosure may also be part of the transformer's cooling system.


Small transformers up to a few kilowatts in size usually are adequately cooled by air circulation. Larger "dry" type transformers may have cooling fans.

High-power or high-voltage transformers are bathed 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 of PCB and its environmental accumulation, it is no longer permitted in new equipment. Today, nontoxic, 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. To improve cooling of large power transformers, 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. Large and high-voltage transformers undergo prolonged drying processes, using electrical self-heating, the application of a vacuum, or both 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 transformers tend to be equipped with Buchholz relays - safety devices sensing gas buildup inside the transformer (a side effect of an electric arc inside the windings) and switching 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.


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 both provide electrical insulation, and contain oil within the transformer tank.

Transformer designs[]


A variable autotransformer with a sliding-brush secondary connection and a toroidal core

An autotransformer has only a single winding, which is tapped at some point along the winding. AC or pulsed DC power is applied across a portion of the winding, and a higher (or lower) voltage is produced across another portion of the same winding. Autotransformers are used to compensate for voltage drop in a distribution system or for matching two transmission voltages, for example 115 kV and 138 kV. For voltage ratios not exceeding about 3:1, an autotransformer is less costly, lighter, smaller and more efficient than a two-winding transformer of a similar rating.

Variable autotransformers[]

Variac is a trademark of General Radio (mid-20th century) for a variable autotransformer intended to conveniently vary the output voltage for a steady AC input voltage. The term is often used to describe similar variable autotransformers made by other makers. To provide very small increments of adjustment, the secondary connection is made through a brush that slides across the winding coils. A variable autotransformer is an efficient and quiet method for adjusting the voltage to incandescent lamps. While lightweight and compact semiconductor light dimmers have replaced variacs in many applications such as theatrical lighting, variable autotransformers are still used when an undistorted variable voltage sine wave is required.

Polyphase transformers[]

Wye and delta winding connections

For three-phase power, three separate single-phase transformers can be used, or all three phases can be connected to a single polyphase transformer. The three primary windings are connected together and the three secondary windings are connected together. The most common connections are Y-Δ, Δ-Y, Δ-Δ and Y-Y. If a winding is connected to earth (grounded) the earth connection point is usually the center point of a Y winding. There are many possible configurations that may involve more or fewer than six windings and various tap connections.

Resonant transformers[]

A resonant transformer is one that operates at the resonant frequency of one or more of its coils. The resonant coil, usually the secondary, acts as an inductor, and is connected in series with a capacitor. If the primary coil is driven by a periodic source of alternating current, such as a square or sawtooth wave, each pulse of current helps to build up an oscillation in the secondary coil. Due to resonance, a very high voltage can develop across the secondary, until it is limited by some process such as electrical breakdown. These devices are therefore used to generate high alternating voltages. The current available from this type of coil can be much larger than that from electrostatic machines such as the Van de Graaff generator and Wimshurst machine. They also run at a higher operating temperature than standard units.


  • Tesla coil
  • Oudin coil (or Oudin resonator; named after Paul Marie Oudin, 1851-1923)
  • D'Arsonval apparatus
  • ignition coil or induction coil used in the ignition system of a petrol engine
  • Flyback transformer of a CRT television set or video monitor.

Other applications of resonant transformers are as coupling between stages of a superheterodyne receiver, where a large measure of the selectivity of the receiver is provided by the tuned transformers of the intermediate-frequency amplifiers.

A voltage regulating transformer uses a resonant winding and allows part of the core to go into saturation on each cycle of the alternating current. This effect stabilizes the output of the regulating transformer, which can be used for equipment that is sensitive to variations of the supply voltage. Saturating transformers provide a simple rugged method to stabilize an ac power supply. However, due to the hysteresis losses accompanying this type of operation, efficiency is low.

Instrument transformers[]

Current transformers[]

Current transformers used as part of metering equipment for three-phase 400 ampere electricity supply

A current transformer is designed to provide a current in its secondary which is accurately proportional to the current flowing in its primary.

Current transformers are commonly used in electricity meters to facilitate the measurement of large currents which would be difficult to measure more directly.

Care must be taken that the secondary of a current transformer is not disconnected from its load while current is flowing in the primary as in this circumstance a very high voltage would be produced across the secondary.

Current transformers are often constructed with a single primary turn either as an insulated cable passing through a toroidal core, or else as a bar to which circuit conductors are connected.

Voltage transformers[]

Voltage transformers (also known as potential transformers) are used in the electricity supply industry to measure accurately the voltage being supplied. They are designed to present negligible load to the voltage being measured.

Pulse transformers[]

A pulse transformer is a transformer that is optimised for transmitting rectangular electrical pulses (that is, pulses with fast rise and fall times and a constant amplitude). Small versions called signal types are used in digital logic and telecommunications circuits, often for matching logic drivers to transmission lines. Medium-sized power versions are used in power-control circuits such as camera flash controllers. Larger power versions are used in the electrical power distribution industry to interface low-voltage control circuitry to the high-voltage gates of power semiconductors such as TRIACs, IGBTs, thyristors and MOSFETs. Special high voltage pulse transformers are also used to generate high power pulses for radar, particle accelerators, or other pulsed power applications.

To minimise distortion of the pulse shape, a pulse transformer needs to have low values of leakage inductance and distributed capacitance, and a high open-circuit inductance. In power-type pulse transformers, a low coupling capacitance (between the primary and secondary) is important to protect the circuitry on the primary side from high-powered transients created by the load. For the same reason, high insulation resistance and high breakdown voltage are required. A good transient response is necessary to maintain the rectangular pulse shape at the secondary, because a pulse with slow edges would create switching losses in the power semiconductors.

The product of the peak pulse voltage and the duration of the pulse (or more accurately, the voltage-time integral) is often used to characterise pulse transformers. Generally speaking, the larger this product, the larger and more expensive the transformer.

RF transformers[]

For radio frequency use, transformers are sometimes made from configurations of transmission line wound around ferrite cores. This style of transformer gives an extremely wide bandwidth. The ferrite increases the inductance dramatically while also lowering it's "Q". The windings are sometimes bifilar and sometimes made from coaxial cable. Only a limited number of ratios (such as 1:9,1:4,1:2) can be achieved with this technique. The cores of such transformers help performance at the lower frequency end of the band. This style of transformer is frequently used as an impedance matching balun to convert from 300 ohm balanced to 75 ohm unbalanced in FM receivers.

Uses of transformers[]

  • Electric power transmission over long distances. The simplicity, reliability, and economy of conversion of voltages by stationary transformers was the principal factor in the selection of alternating current power transmission (see War of Currents)
  • High-voltage direct-current HVDC power transmission systems
  • Large, specially constructed power transformers are used for electric arc furnaces used in steelmaking.
  • Rotating transformers are designed so that one winding turns while the other remains stationary. A common use was the video head system as used in VHS and Beta video tape players. These can pass power or radio signals from a stationary mounting to a rotating mechanism, or radar antenna.
  • Sliding transformers can pass power or signals from a stationary mounting to a moving part such as a machine tool head. See linear variable differential transformer,
  • Some rotary transformers are precisely constructed in order to measure distances or angles. Usually they have a single primary and two or more secondaries, and electronic circuits measure the different amplitudes of the currents in the secondaries. See synchro and resolver.
  • Small transformers are often used to isolate and link different parts of radio receivers and audio amplifiers, converting high current low voltage circuits to low current high voltage, or vice versa. See electronics and impedance matching. See also isolation transformer and repeating coil.
  • Balanced-to-unbalanced conversion. A special type of transformer called a balun is used in radio and audio circuits to convert between balanced circuits and unbalanced transmission lines such as antenna downleads. A balanced line is one in which the two conductors (signal and return) have the same impedance to ground: twisted pair and "balanced twin" are examples. Unbalanced lines include coaxial cables and strip-line traces on printed circuit boards. A similar use is for connecting the "single ended" input stages of an amplifier to the high-powered "push-pull" output stage.

See also[]


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