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Pole-mounted distribution transformer with center-tapped secondary winding used to provide "split-phase" power for residential and light commercial service, which in North America is typically rated 120/240 V. Polemount-singlephase-closeup.jpg
Pole-mounted distribution transformer with center-tapped secondary winding used to provide "split-phase" power for residential and light commercial service, which in North America is typically rated 120/240 V.

A transformer is a static electrical device that transfers electrical energy between two or more circuits. A varying current in one coil of the transformer produces a varying magnetic flux, which, in turn, induces a varying electromotive force across a second coil wound around the same core. Electrical energy can be transferred between the two coils, without a metallic connection between the two circuits. Faraday's law of induction discovered in 1831 described the induced voltage effect in any coil due to changing magnetic flux encircled by the coil.

Electrical network interconnection of electrical components or a model of such an interconnection, consisting of electrical elements

An electrical network is an interconnection of electrical components or a model of such an interconnection, consisting of electrical elements. An electrical circuit is a network consisting of a closed loop, giving a return path for the current. Linear electrical networks, a special type consisting only of sources, linear lumped elements, and linear distributed elements, have the property that signals are linearly superimposable. They are thus more easily analyzed, using powerful frequency domain methods such as Laplace transforms, to determine DC response, AC response, and transient response.

Magnetic flux physical quantity

In physics, specifically electromagnetism, the magnetic flux through a surface is the surface integral of the normal component of the magnetic field B passing through that surface. The SI unit of magnetic flux is the weber (Wb), and the CGS unit is the maxwell. Magnetic flux is usually measured with a fluxmeter, which contains measuring coils and electronics, that evaluates the change of voltage in the measuring coils to calculate the magnetic flux.

Electromotive force scalar physical quantity

Electromotive force, abbreviated emf, is the electrical intensity or "pressure" developed by a source of electrical energy such as a battery or generator. A device that converts other forms of energy into electrical energy provides an emf as its output.


Transformers are used for increasing or decreasing the alternating voltages in electric power applications, and for coupling the stages of signal processing circuits.

Since the invention of the first constant-potential transformer in 1885, transformers have become essential for the transmission, distribution, and utilization of alternating current electric power. [3] A wide range of transformer designs is encountered in electronic and electric power applications. Transformers range in size from RF transformers less than a cubic centimeter in volume, to units weighing hundreds of tons used to interconnect the power grid.

Electric power transmission bulk movement of electrical energy from a generating site to an electrical substation

Electric power transmission is the bulk movement of electrical energy from a generating site, such as a power plant, to an electrical substation. The interconnected lines which facilitate this movement are known as a transmission network. This is distinct from the local wiring between high-voltage substations and customers, which is typically referred to as electric power distribution. The combined transmission and distribution network is known as the "power grid" in North America, or just "the grid". In the United Kingdom, India, Myanmar, Malaysia and New Zealand, the network is known as the "National Grid".

Electric power distribution Final stage of electricity delivery to individual consumers in a power grid

Electric power distribution is the final stage in the delivery of electric power; it carries electricity from the transmission system to individual consumers. Distribution substations connect to the transmission system and lower the transmission voltage to medium voltage ranging between 2 kV and 35 kV with the use of transformers. Primary distribution lines carry this medium voltage power to distribution transformers located near the customer's premises. Distribution transformers again lower the voltage to the utilization voltage used by lighting, industrial equipment or household appliances. Often several customers are supplied from one transformer through secondary distribution lines. Commercial and residential customers are connected to the secondary distribution lines through service drops. Customers demanding a much larger amount of power may be connected directly to the primary distribution level or the subtransmission level.


Ideal transformer equations

By Faraday's law of induction:

. . . (eq. 1) [lower-alpha 1] [4]

. . . (eq. 2)

Where is the instantaneous voltage, is the number of turns in a winding, dΦ/dt is the derivative of the magnetic flux Φ through one turn of the winding over time (t), and subscripts P and S denotes primary and secondary.

Derivative operation in calculus

The derivative of a function of a real variable measures the sensitivity to change of the function value with respect to a change in its argument. Derivatives are a fundamental tool of calculus. For example, the derivative of the position of a moving object with respect to time is the object's velocity: this measures how quickly the position of the object changes when time advances.

Voltage difference in the electric potential between two points in space

Voltage, electric potential difference, electric pressure or electric tension is the difference in electric potential between two points. The difference in electric potential between two points in a static electric field is defined as the work needed per unit of charge to move a test charge between the two points. In the International System of Units, the derived unit for voltage is named volt. In SI units, work per unit charge is expressed as joules per coulomb, where 1 volt = 1 joule per 1 coulomb. The official SI definition for volt uses power and current, where 1 volt = 1 watt per 1 ampere. This definition is equivalent to the more commonly used 'joules per coulomb'. Voltage or electric potential difference is denoted symbolically by V, but more often simply as V, for instance in the context of Ohm's or Kirchhoff's circuit laws.

Combining the ratio of eq. 1 & eq. 2:

Turns ratio . . . (eq. 3)

Where for a step-down transformer a > 1, for a step-up transformer a < 1, and for an isolation transformer a = 1.

Isolation transformer transformer used to transfer electrical power from a source of alternating current (AC) power to some equipment or device while isolating the powered device from the power source

An isolation transformer is a transformer used to transfer electrical power from a source of alternating current (AC) power to some equipment or device while isolating the powered device from the power source, usually for safety reasons. Isolation transformers provide galvanic isolation and are used to protect against electric shock, to suppress electrical noise in sensitive devices, or to transfer power between two circuits which must not be connected. A transformer sold for isolation is often built with special insulation between primary and secondary, and is specified to withstand a high voltage between windings.

By law of conservation of energy, apparent, real and reactive power are each conserved in the input and output:

In physics and chemistry, the law of conservation of energy states that the total energy isolated system remains constant; it is said to be conserved over time. This law means that energy can neither be created nor destroyed; rather, it can only be transformed or transferred from one form to another. For instance, chemical energy is converted to kinetic energy when a stick of dynamite explodes. If one adds up all the forms of energy that were released in the explosion, such as the kinetic energy and potential energy of the pieces, as well as heat and sound, one will get the exact decrease of chemical energy in the combustion of the dynamite. Classically, conservation of energy was distinct from conservation of mass; however, special relativity showed that mass is related to energy and vice versa by E = mc2, and science now takes the view that mass–energy is conserved.

. . . . (eq. 4)

Where is conserved power and is current.

Combining eq. 3 & eq. 4 with this endnote [lower-alpha 2] [5] gives the ideal transformer identity:

. (eq. 5)

Where is winding self-inductance.

By Ohm's law and ideal transformer identity:

. . . (eq. 6)

. (eq. 7)

Where is the load impedance of the secondary circuit & is the apparent load or driving point impedance of the primary circuit, the superscript denoting referred to the primary.

Ideal transformer

An ideal transformer is a theoretical linear transformer that is lossless and perfectly coupled. [6] Perfect coupling implies infinitely high core magnetic permeability and winding inductances and zero net magnetomotive force (i.e. ipnp - isns = 0). [7] [lower-alpha 3]

Ideal transformer connected with source VP on primary and load impedance ZL on secondary, where 0 < ZL < [?]. Ideal transformer.svg
Ideal transformer connected with source VP on primary and load impedance ZL on secondary, where 0 < ZL < ∞.
Ideal transformer and induction law Transformer3d col3.svg
Ideal transformer and induction law

A varying current in the transformer's primary winding attempts to create a varying magnetic flux in the transformer core, which is also encircled by the secondary winding. This varying flux at the secondary winding induces a varying electromotive force (EMF, voltage) in the secondary winding due to electromagnetic induction and the secondary current so produced creates a flux equal and opposite to that produced by the primary winding, in accordance with Lenz's law.

The windings are wound around a core of infinitely high magnetic permeability [lower-alpha 5] so that all of the magnetic flux passes through both the primary and secondary windings. With a voltage source connected to the primary winding and load impedance connected to the secondary winding, the transformer currents flow in the indicated directions and the core magnetomotive force cancels to zero. (See also Polarity.)

According to Faraday's law, since the same magnetic flux passes through both the primary and secondary windings in an ideal transformer, [9] a voltage is induced in each winding proportional to its number of windings. Thus, referring to the equations shown in the sidebox at right, according to Faraday's law, we have primary and secondary winding voltages defined by eq. 1 & eq. 2, respectively. [10] The primary EMF is sometimes termed counter EMF. [11] [12] [lower-alpha 6] This is in accordance with Lenz's law, which states that induction of EMF always opposes development of any such change in magnetic field.

The transformer winding voltage ratio is thus shown to be directly proportional to the winding turns ratio according to eq. 3. [13] [14] [lower-alpha 7] However, some sources use the inverse definition. [15] [lower-alpha 8]

According to the law of conservation of energy, any load impedance connected to the ideal transformer's secondary winding results in conservation of apparent, real and reactive power consistent with eq. 4.

The ideal transformer identity shown in eq. 5 is a reasonable approximation for the typical commercial transformer, with voltage ratio and winding turns ratio both being inversely proportional to the corresponding current ratio.

By Ohm's law and the ideal transformer identity:

Real transformer

Leakage flux of a transformer Transformer Flux.svg
Leakage flux of a transformer

Deviations from ideal transformer

The ideal transformer model neglects the following basic linear aspects of real transformers:

(a) Core losses, collectively called magnetizing current losses, consisting of [18]

  • Hysteresis losses due to nonlinear magnetic effects in the transformer core, and
  • Eddy current losses due to joule heating in the core that are proportional to the square of the transformer's applied voltage.

(b) Unlike the ideal model, the windings in a real transformer have non-zero resistances and inductances associated with:

  • Joule losses due to resistance in the primary and secondary windings [18]
  • Leakage flux that escapes from the core and passes through one winding only resulting in primary and secondary reactive impedance.

(c) similar to an inductor, parasitic capacitance and self-resonance phenomenon due to the electric field distribution. Three kinds of parasitic capacitance are usually considered and the closed-loop equations are provided [19]

  • Capacitance between adjacent turns in any one layer;
  • Capacitance between adjacent layers;
  • Capacitance between the core and the layer(s) adjacent to the core;

Inclusion of capacitance into the transformer model is complicated, and is rarely attempted; the ‘real’ transformer model’s equivalent circuit does not include parasitic capacitance. However, the capacitance effect can be measured by comparing open-circuit inductance, i.e. the inductance of a primary winding when the secondary circuit is open, to a short-circuit inductance when the secondary winding is shorted.

Leakage flux

The ideal transformer model assumes that all flux generated by the primary winding links all the turns of every winding, including itself. In practice, some flux traverses paths that take it outside the windings. [20] Such flux is termed leakage flux, and results in leakage inductance in series with the mutually coupled transformer windings. [12] Leakage flux results in energy being alternately stored in and discharged from the magnetic fields with each cycle of the power supply. It is not directly a power loss, but results in inferior voltage regulation, causing the secondary voltage not to be directly proportional to the primary voltage, particularly under heavy load. [20] Transformers are therefore normally designed to have very low leakage inductance.

In some applications increased leakage is desired, and long magnetic paths, air gaps, or magnetic bypass shunts may deliberately be introduced in a transformer design to limit the short-circuit current it will supply. [12] Leaky transformers may be used to supply loads that exhibit negative resistance, such as electric arcs, mercury- and sodium- vapor lamps and neon signs or for safely handling loads that become periodically short-circuited such as electric arc welders. [21]

Air gaps are also used to keep a transformer from saturating, especially audio-frequency transformers in circuits that have a DC component flowing in the windings. [22] A saturable reactor exploits saturation of the core to control alternating current.

Knowledge of leakage inductance is also useful when transformers are operated in parallel. It can be shown that if the percent impedance [lower-alpha 9] and associated winding leakage reactance-to-resistance (X/R) ratio of two transformers were hypothetically exactly the same, the transformers would share power in proportion to their respective volt-ampere ratings (e.g. 500  kVA unit in parallel with 1,000 kVA unit, the larger unit would carry twice the current). However, the impedance tolerances of commercial transformers are significant. Also, the Z impedance and X/R ratio of different capacity transformers tends to vary, corresponding 1,000 kVA and 500 kVA units' values being, to illustrate, respectively, Z ≈ 5.75%, X/R ≈ 3.75 and Z ≈ 5%, X/R ≈ 4.75. [24]

Equivalent circuit

Referring to the diagram, a practical transformer's physical behavior may be represented by an equivalent circuit model, which can incorporate an ideal transformer. [25]

Winding joule losses and leakage reactances are represented by the following series loop impedances of the model:

  • Primary winding: RP, XP
  • Secondary winding: RS, XS.

In normal course of circuit equivalence transformation, RS and XS are in practice usually referred to the primary side by multiplying these impedances by the turns ratio squared, (NP/NS) 2 = a2.

Real transformer equivalent circuit TREQCCT.jpg
Real transformer equivalent circuit

Core loss and reactance is represented by the following shunt leg impedances of the model:

  • Core or iron losses: RC
  • Magnetizing reactance: XM.

RC and XM are collectively termed the magnetizing branch of the model.

Core losses are caused mostly by hysteresis and eddy current effects in the core and are proportional to the square of the core flux for operation at a given frequency. [26] The finite permeability core requires a magnetizing current IM to maintain mutual flux in the core. Magnetizing current is in phase with the flux, the relationship between the two being non-linear due to saturation effects. However, all impedances of the equivalent circuit shown are by definition linear and such non-linearity effects are not typically reflected in transformer equivalent circuits. [26] With sinusoidal supply, core flux lags the induced EMF by 90°. With open-circuited secondary winding, magnetizing branch current I0 equals transformer no-load current. [25]

Instrument transformer, with polarity dot and X1 markings on LV side terminal Instrument Transformer.jpg
Instrument transformer, with polarity dot and X1 markings on LV side terminal

The resulting model, though sometimes termed 'exact' equivalent circuit based on linearity assumptions, retains a number of approximations. [25] Analysis may be simplified by assuming that magnetizing branch impedance is relatively high and relocating the branch to the left of the primary impedances. This introduces error but allows combination of primary and referred secondary resistances and reactances by simple summation as two series impedances.

Transformer equivalent circuit impedance and transformer ratio parameters can be derived from the following tests: open-circuit test, [lower-alpha 10] short-circuit test, winding resistance test, and transformer ratio test.

Transformer EMF equation

If the flux in the core is purely sinusoidal, the relationship for either winding between its rms voltageErms of the winding, and the supply frequency f, number of turns N, core cross-sectional area a in m2 and peak magnetic flux density Bpeak in Wb/m2 or T (tesla) is given by the universal EMF equation: [18] [28]

If the flux does not contain even harmonics the following equation can be used for half-cycle average voltageEavg of any waveshape:

Basic transformer parameters


A dot convention is often used in transformer circuit diagrams, nameplates or terminal markings to define the relative polarity of transformer windings. Positively increasing instantaneous current entering the primary winding's ‘dot’ end induces positive polarity voltage exiting the secondary winding's ‘dot’ end. [29] [30] [31] [lower-alpha 11] </ref> [lower-alpha 12] [lower-alpha 13]

Three-phase transformers used in electric power systems will have a nameplate that indicate the phase relationships between their terminals. This may be in the form of a phasor diagram, or using an alpha-numeric code to show the type of internal connection (wye or delta) for each winding.

Effect of frequency

The EMF of a transformer at a given flux increases with frequency. [18] By operating at higher frequencies, transformers can be physically more compact because a given core is able to transfer more power without reaching saturation and fewer turns are needed to achieve the same impedance. However, properties such as core loss and conductor skin effect also increase with frequency. Aircraft and military equipment employ 400 Hz power supplies which reduce core and winding weight. [34] Conversely, frequencies used for some railway electrification systems were much lower (e.g. 16.7 Hz and 25 Hz) than normal utility frequencies (50–60 Hz) for historical reasons concerned mainly with the limitations of early electric traction motors. Consequently, the transformers used to step-down the high overhead line voltages (e.g. 15 kV) were much larger and heavier for the same power rating than those required for the higher frequencies.

Power transformer over-excitation condition caused by decreased frequency; flux (green), iron core's magnetic characteristics (red) and magnetizing current (blue). Power Transformer Over-Excitation.gif
Power transformer over-excitation condition caused by decreased frequency; flux (green), iron core's magnetic characteristics (red) and magnetizing current (blue).

Operation of a transformer at its designed voltage but at a higher frequency than intended will lead to reduced magnetizing current. At a lower frequency, the magnetizing current will increase. Operation of a large 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, ANSI function 24, relays to protect the transformer from overvoltage at higher than rated frequency.

One example is in traction transformers used for electric multiple unit and high-speed train service operating across regions with different electrical standards. [35] The converter equipment and traction transformers have to accommodate different input frequencies and voltage (ranging from as high as 50 Hz down to 16.7 Hz and rated up to 25 kV) while being suitable for multiple AC asynchronous motor and DC converters and motors with varying harmonics mitigation filtering requirements.

At much higher frequencies the transformer core size required drops dramatically: a physically small transformer can handle power levels that would require a massive iron core at mains frequency. The development of switching power semiconductor devices and complex integrated circuits made switch-mode power supplies viable, to generate a high frequency from a much lower one (or DC), change the voltage level with a small transformer, and, if necessary, rectify the changed voltage.

Large power transformers are vulnerable to insulation failure due to transient voltages with high-frequency components, such as caused in switching or by lightning. [36]

Energy losses

Transformer energy losses are dominated by winding and core losses. Transformers' efficiency tends to improve with increasing transformer capacity. The efficiency of typical distribution transformers is between about 98 and 99 percent. [37] [38] [lower-alpha 14]

As transformer losses vary with load, it is often useful to tabulate no-load loss, full-load loss, half-load loss, and so on. Hysteresis and eddy current losses are constant at all load levels and dominate overwhelmingly without load, while variable winding joule losses dominating increasingly as load increases. The no-load loss can be significant, so that even an idle transformer constitutes a drain on the electrical supply. Designing energy efficient transformers for lower loss requires a larger core, good-quality silicon steel, or even amorphous steel for the core and thicker wire, increasing initial cost. The choice of construction represents a trade-off between initial cost and operating cost. [40]

Transformer losses arise from:

Winding joule losses
Current flowing through a winding's conductor causes joule heating. As frequency increases, skin effect and proximity effect causes the winding's resistance and, hence, losses to increase.
Core losses
Hysteresis losses
Each time the magnetic field is reversed, a small amount of energy is lost due to hysteresis within the core. According to Steinmetz's formula, the heat energy due to hysteresis is given by
, and,
hysteresis loss is thus given by
where, f is the frequency, η is the hysteresis coefficient and βmax is the maximum flux density, the empirical exponent of which varies from about 1.4 to 1.8 but is often given as 1.6 for iron. [40] [41] [42]
Eddy current losses
Eddy currents are produced in the metal transformer core and cause heating of the core. The eddy current loss is a complex function of the square of supply frequency and inverse square of the material thickness. [40] Eddy current losses can be reduced by making the core of a stack of plates electrically insulated from each other, rather than a solid block; all transformers operating at low frequencies use laminated or similar cores.
Magnetostriction related transformer hum
Magnetic flux in a ferromagnetic material, such as the core, causes it to physically expand and contract slightly with each cycle of the magnetic field, an effect known as magnetostriction, the frictional energy of which produces an audible noise known as mains hum or transformer hum. [13] [43] This transformer hum is especially objectionable in transformers supplied at power frequencies [lower-alpha 15] and in high-frequency flyback transformers associated with television CRTs.
Stray losses
Leakage inductance is by itself largely lossless, since energy supplied to its magnetic fields is returned to the supply with the next half-cycle. However, any leakage flux that intercepts nearby conductive materials such as the transformer's support structure will give rise to eddy currents and be converted to heat. [44]
There are also radiative losses due to the oscillating magnetic field but these are usually small.
Mechanical vibration and audible noise transmission
In addition to magnetostriction, the alternating magnetic field causes fluctuating forces between the primary and secondary windings. This energy incites vibration transmission in interconnected metalwork, thus amplifying audible transformer hum. [45]



Core form = core type; shell form = shell type Transformer winding formats.jpg
Core form = core type; shell form = shell type

Closed-core transformers are constructed in 'core form' or 'shell form'. When windings surround the core, the transformer is core form; when windings are surrounded by the core, the transformer is shell form. [46] [47] [48] Shell form design may be more prevalent than core form design for distribution transformer applications due to the relative ease in stacking the core around winding coils. [46] Core form design tends to, as a general rule, be more economical, and therefore more prevalent, than shell form design for high voltage power transformer applications at the lower end of their voltage and power rating ranges (less than or equal to, nominally, 230 kV or 75 MVA). At higher voltage and power ratings, shell form transformers tend to be more prevalent. [46] [49] [50] [51] Shell form design tends to be preferred for extra-high voltage and higher MVA applications because, though more labor-intensive to manufacture, shell form transformers are characterized as having inherently better kVA-to-weight ratio, better short-circuit strength characteristics and higher immunity to transit damage. [51]

Laminated steel cores

Laminated core transformer showing edge of laminations at top of photo Transformer.filament.agr.jpg
Laminated core transformer showing edge of laminations at top of photo

Transformers for use at power or audio frequencies typically have cores made of high permeability silicon steel. [52] The steel has a permeability many times that of free space and the core thus serves to greatly reduce the magnetizing current and confine the flux to a path which closely couples the windings. [53] Early transformer developers soon realized that cores constructed from solid iron resulted in prohibitive eddy current losses, and their designs mitigated this effect with cores consisting of bundles of insulated iron wires. [54] Later designs constructed the core by stacking layers of thin steel laminations, a principle that has remained in use. Each lamination is insulated from its neighbors by a thin non-conducting layer of insulation. [55] The transformer universal EMF equation implies an acceptably large core cross-sectional area to avoid saturation. [18] [28] [lower-alpha 16]

The effect of laminations is to confine eddy currents to highly elliptical paths that enclose little flux, and so reduce their magnitude. Thinner laminations reduce losses, [52] but are more laborious and expensive to construct. [56] Thin laminations are generally used on high-frequency transformers, with some of very thin steel laminations able to operate up to 10 kHz.

Laminating the core greatly reduces eddy-current losses Laminering av karna.svg
Laminating the core greatly reduces eddy-current losses

One common design of laminated core is made from interleaved stacks of E-shaped steel sheets capped with I-shaped pieces, leading to its name of 'E-I transformer'. [56] Such a design tends to exhibit more losses, but is very economical to manufacture. The cut-core or C-core type is made by winding a steel strip around a rectangular form and then bonding the layers together. It is then cut in two, forming two C shapes, and the core assembled by binding the two C halves together with a steel strap. [56] They have the advantage that the flux is always oriented parallel to the metal grains, reducing reluctance.

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 remaining magnetism is reduced, usually after a few cycles of the applied AC waveform. [57] 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 operation of transformer protection devices. [58]

Distribution transformers can achieve low no-load losses by using cores made with low-loss high-permeability silicon steel or amorphous (non-crystalline) metal alloy. The higher initial cost of the core material is offset over the life of the transformer by its lower losses at light load. [59]

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. For frequencies extending beyond the VHF band, cores made from non-conductive magnetic ceramic materials called ferrites are common. [56] Some radio-frequency transformers also have movable cores (sometimes called 'slugs') which allow adjustment of the coupling coefficient (and bandwidth) of tuned radio-frequency circuits.

Toroidal cores

Small toroidal core transformer Small toroidal transformer.jpg
Small toroidal core transformer

Toroidal transformers are built around a ring-shaped core, which, depending on operating frequency, is made from a long strip of silicon steel or permalloy wound into a coil, powdered iron, or ferrite. [60] [61] A 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 E-I core. [21] 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 minimizes the length of wire needed and provides screening to minimize the core's magnetic field from generating electromagnetic interference.

Toroidal transformers are more efficient than the cheaper laminated E-I types for a similar power level. Other advantages compared to E-I 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 greater choice of shapes. The main disadvantages are higher cost and limited power capacity (see Classification parameters below). Because of the lack of a residual gap in the magnetic path, toroidal transformers also tend to exhibit higher inrush current, compared to laminated E-I types.

Ferrite toroidal cores are used at higher frequencies, typically between a few tens of kilohertz to hundreds of megahertz, to reduce losses, physical size, and weight of inductive components. A drawback of toroidal transformer construction is the higher labor cost of winding. This is because it is necessary to pass the entire length of a coil winding through the core aperture each time a single turn is added to the coil. As a consequence, toroidal transformers rated more than a few kVA are uncommon. Relatively few toroids are offered with power ratings above 10 kVA, and practically none above 25 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. [62]

Air cores

A transformer can be produced by placing the windings near each other, an arrangement termed an "air-core" transformer. An air-core transformer eliminates loss due to hysteresis in the core material. [12] The magnetizing inductance is drastically reduced by the lack of a magnetic core, resulting in large magnetizing currents and losses if used at low frequencies. Air-core transformers are unsuitable for use in power distribution, [12] but are frequently employed in radio-frequency applications. [63] Air cores are also used for resonant transformers such as Tesla coils, where they can achieve reasonably low loss despite the low magnetizing inductance.


Windings are usually arranged concentrically to minimize flux leakage. Transformer-hightolow smaller.jpg
Windings are usually arranged concentrically to minimize flux leakage.
Cut view through transformer windings. Legend:
White: Air, liquid or other insulating medium
Green spiral: Grain oriented silicon steel
Black: Primary winding
Red: Secondary winding Transformer min stray field geometry.svg
Cut view through transformer windings. Legend:
White: Air, liquid or other insulating medium
Green spiral: Grain oriented silicon steel
Black: Primary winding
Red: Secondary winding

The electrical conductor used for the windings depends upon the application, but in all cases the individual turns must be electrically insulated from each other to ensure that the current travels throughout every turn. For small transformers, in which currents are low and the potential difference between adjacent turns is small, the coils are often wound from enamelled magnet wire. Larger power transformers may be wound with copper rectangular strip conductors insulated by oil-impregnated paper and blocks of pressboard. [64]

High-frequency transformers operating in the tens to hundreds of kilohertz often have windings made of braided Litz wire to minimize the skin-effect and proximity effect losses. [65] 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. [64] Each strand is individually insulated, 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. The 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, aiding manufacture. [64]

The windings of signal transformers minimize leakage inductance and stray capacitance to improve high-frequency response. Coils are split into sections, and those sections interleaved between the sections of the other winding.

Power-frequency transformers may have taps at intermediate points on the winding, usually on the higher voltage winding side, for voltage adjustment. Taps may be manually reconnected, or a manual or automatic switch may be provided for changing taps. Automatic on-load tap changers are used in electric power transmission or distribution, on equipment such as arc furnace transformers, or for automatic voltage regulators for sensitive loads. 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 circuit. Modulation transformers in AM transmitters are very similar.


Cutaway view of liquid-immersed transformer. The conservator (reservoir) at top provides liquid-to-atmosphere isolation as coolant level and temperature changes. The walls and fins provide required heat dissipation. Drehstromtransformater im Schnitt Hochspannung.jpg
Cutaway view of liquid-immersed transformer. The conservator (reservoir) at top provides liquid-to-atmosphere isolation as coolant level and temperature changes. The walls and fins provide required heat dissipation.

It is a rule of thumb that the life expectancy of electrical insulation is halved for about every 7 °C to 10 °C increase in operating temperature (an instance of the application of the Arrhenius equation). [66] [67] [68] [lower-alpha 17]

Small dry-type and liquid-immersed transformers are often self-cooled by natural convection and radiation heat dissipation. [69] [70] As power ratings increase, transformers are often cooled by forced-air cooling, forced-oil cooling, water-cooling, or combinations of these. [71] Large transformers are filled with transformer oil that both cools and insulates the windings. [72] Transformer oil is a highly refined mineral oil that cools the windings and insulation by circulating within the transformer tank. The mineral oil and paper insulation system has been extensively studied and used for more than 100 years. It is estimated that 50% of power transformers will survive 50 years of use, that the average age of failure of power transformers is about 10 to 15 years, and that about 30% of power transformer failures are due to insulation and overloading failures. [73] [74] Prolonged operation at elevated temperature degrades insulating properties of winding insulation and dielectric coolant, which not only shortens transformer life but can ultimately lead to catastrophic transformer failure. [66] With a great body of empirical study as a guide, transformer oil testing including dissolved gas analysis provides valuable maintenance information. This underlines the need to monitor, model, forecast and manage oil and winding conductor insulation temperature conditions under varying, possibly difficult, power loading conditions. [75] [76]

Building regulations in many jurisdictions require indoor liquid-filled transformers to either use dielectric fluids that are less flammable than oil, or be installed in fire-resistant rooms. [37] Air-cooled dry transformers can be more economical where they eliminate the cost of a fire-resistant transformer room.

The tank of liquid filled transformers often has radiators through which the liquid coolant circulates by natural convection or fins. Some large transformers employ electric fans for forced-air cooling, pumps for forced-liquid cooling, or have heat exchangers for water-cooling. [72] An oil-immersed transformer may be equipped with a Buchholz relay, which, depending on severity of gas accumulation due to internal arcing, is used to either alarm or de-energize the transformer. [57] Oil-immersed transformer installations usually include fire protection measures such as walls, oil containment, and fire-suppression sprinkler systems.

Polychlorinated biphenyls have properties that once favored their use as a dielectric coolant, though concerns over their environmental persistence led to a widespread ban on their use. [77] 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. [37] [78] PCBs for new equipment were banned in 1981 and in 2000 for use in existing equipment in United Kingdom [79] Legislation enacted in Canada between 1977 and 1985 essentially bans PCB use in transformers manufactured in or imported into the country after 1980, the maximum allowable level of PCB contamination in existing mineral oil transformers being 50 ppm. [80]

Some transformers, instead of being liquid-filled, have their windings enclosed in sealed, pressurized tanks and cooled by nitrogen or sulfur hexafluoride gas. [78]

Experimental power transformers in the 500‐to‐1,000 kVA range have been built with liquid nitrogen or helium cooled superconducting windings, which eliminates winding losses without affecting core losses. [81] [82]


Insulation must be provided between the individual turns of the windings, between the windings, between windings and core, and at the terminals of the winding.

Inter-turn insulation of small transformers may be a layer of insulating varnish on the wire. Layer of paper or polymer films may be inserted between layers of windings, and between primary and secondary windings. A transformer may be coated or dipped in a polymer resin to improve the strength of windings and protect them from moisture or corrosion. The resin may be impregnated into the winding insulation using combinations of vacuum and pressure during the coating process, eliminating all air voids in the winding. In the limit, the entire coil may be placed in a mold, and resin cast around it as a solid block, encapsulating the windings. [83]

Large oil-filled power transformers use windings wrapped with insulating paper, which is impregnated with oil during assembly of the transformer. Oil-filled transformers use highly refined mineral oil to insulate and cool the windings and core. Construction of oil-filled transformers requires that the insulation covering the windings be thoroughly dried of residual moisture before the oil is introduced. Drying may be done by circulating hot air around the core, by circulating externally heated transformer oil, or by vapor-phase drying (VPD) where an evaporated solvent transfers heat by condensation on the coil and core. For small transformers, resistance heating by injection of current into the windings is used.


Larger transformers are provided with high-voltage insulated bushings made of polymers or porcelain. A large bushing can be a complex structure since it must provide careful control of the electric field gradient without letting the transformer leak oil. [84]

Classification parameters

Transformers can be classified in many ways, such as the following:


Various specific electrical application designs require a variety of transformer types. Although they all share the basic characteristic transformer principles, they are customized in construction or electrical properties for certain installation requirements or circuit conditions.

An electrical substation in Melbourne, Australia showing three of five 220 kV - 66 kV transformers, each with a capacity of 150 MVA Melbourne Terminal Station.JPG
An electrical substation in Melbourne, Australia showing three of five 220 kV – 66 kV transformers, each with a capacity of 150 MVA


Transformer at the Limestone Generating Station in Manitoba, Canada Transformer-Limestone-Generating-Station.JPG
Transformer at the Limestone Generating Station in Manitoba, Canada

Since the high voltages carried in the wires are significantly greater than what is needed in-home, transformers are also used extensively in electronic products to decrease (or step-down) the supply voltage to a level suitable for the low voltage circuits they contain. [94] The transformer also electrically isolates the end user from contact with the supply voltage. Transformers are used to increase (or step-up) voltage before transmitting electrical energy over long distances through wires. Wires have resistance which loses energy through joule heating at a rate corresponding to square of the current. By transforming power to a higher voltage transformers enable economical transmission of power and distribution. Consequently, transformers have shaped the electricity supply industry, permitting generation to be located remotely from points of demand. [95] All but a tiny fraction of the world's electrical power has passed through a series of transformers by the time it reaches the consumer. [44]

Signal and audio transformers are used to couple stages of amplifiers and to match devices such as microphones and record players to the input of amplifiers. Audio transformers allowed telephone circuits to carry on a two-way conversation over a single pair of wires. A balun transformer converts a signal that is referenced to ground to a signal that has balanced voltages to ground, such as between external cables and internal circuits. Transformers made to medical grade standards isolate the users from the direct current. These are found commonly used in conjunction with hospital beds, dentist chairs, and other medical lab equipment. [90]

Schematic of a large oil filled power transformer - See Note 't' for numbered-balloon item description. Vermogentransformator 1.GIF
Schematic of a large oil filled power transformer - See Note 't' for numbered-balloon item description.


Discovery of induction

Faraday's experiment with induction between coils of wire Induction experiment.png
Faraday's experiment with induction between coils of wire

Electromagnetic induction, the principle of the operation of the transformer, was discovered independently by Michael Faraday in 1831, Joseph Henry in 1832, and others. [97] [98] [99] [100] The relationship between EMF and magnetic flux is an equation now known as Faraday's law of induction:


where is the magnitude of the EMF in Volts and ΦB is the magnetic flux through the circuit in webers. [101]

Faraday performed early experiments on induction between coils of wire, including winding a pair of coils around an iron ring, thus creating the first toroidal closed-core transformer. [100] [102] However he only applied individual pulses of current to his transformer, and never discovered the relation between the turns ratio and EMF in the windings.

Induction coil, 1900, Bremerhaven, Germany Induktionsapparat hg.jpg
Induction coil, 1900, Bremerhaven, Germany

Induction coils

Faraday's ring transformer Faradays transformer.png
Faraday's ring transformer

The first type of transformer to see wide use was the induction coil, invented by Rev. Nicholas Callan of Maynooth College, Ireland in 1836. [100] He was one of the first researchers to realize the more turns the secondary winding has in relation to the primary winding, the larger the induced secondary EMF will be. Induction coils evolved from scientists' and inventors' efforts to get higher voltages from batteries. Since batteries produce direct current (DC) rather than AC, induction coils relied upon vibrating electrical contacts that regularly interrupted the current in the primary to create the flux changes necessary for induction. Between the 1830s and the 1870s, efforts to build better induction coils, mostly by trial and error, slowly revealed the basic principles of transformers.

First alternating current transformers

By the 1870s, efficient generators producing alternating current (AC) were available, and it was found AC could power an induction coil directly, without an interrupter.

In 1876, Russian engineer Pavel Yablochkov invented [103] [104] a lighting system based on a set of induction coils where the primary windings were connected to a source of AC. The secondary windings could be connected to several 'electric candles' (arc lamps) of his own design. [105] [106] The coils Yablochkov employed functioned essentially as transformers. [105]

In 1878, the Ganz factory, Budapest, Hungary, began producing equipment for electric lighting and, by 1883, had installed over fifty systems in Austria-Hungary. Their AC systems used arc and incandescent lamps, generators, and other equipment. [100] [107]

Lucien Gaulard and John Dixon Gibbs first exhibited a device with an open iron core called a 'secondary generator' in London in 1882, then sold the idea to the Westinghouse company in the United States. [54] They also exhibited the invention in Turin, Italy in 1884, where it was adopted for an electric lighting system. [108]

Early series circuit transformer distribution

Induction coils with open magnetic circuits are inefficient at transferring power to loads. Until about 1880, the paradigm for AC power transmission from a high voltage supply to a low voltage load was a series circuit. Open-core transformers with a ratio near 1:1 were connected with their primaries in series to allow use of a high voltage for transmission while presenting a low voltage to the lamps. The inherent flaw in this method was that turning off a single lamp (or other electric device) affected the voltage supplied to all others on the same circuit. Many adjustable transformer designs were introduced to compensate for this problematic characteristic of the series circuit, including those employing methods of adjusting the core or bypassing the magnetic flux around part of a coil. [108] Efficient, practical transformer designs did not appear until the 1880s, but within a decade, the transformer would be instrumental in the War of Currents, and in seeing AC distribution systems triumph over their DC counterparts, a position in which they have remained dominant ever since. [109]

Shell form transformer. Sketch used by Uppenborn to describe ZBD engineers' 1885 patents and earliest articles. Trafo1885.jpg
Shell form transformer. Sketch used by Uppenborn to describe ZBD engineers' 1885 patents and earliest articles.
Core form, front; shell form, back. Earliest specimens of ZBD-designed high-efficiency constant-potential transformers manufactured at the Ganz factory in 1885. DBZ trafo.jpg
Core form, front; shell form, back. Earliest specimens of ZBD-designed high-efficiency constant-potential transformers manufactured at the Ganz factory in 1885.
The ZBD team consisted of Karoly Zipernowsky, Otto Blathy and Miksa Deri ZBD team.jpg
The ZBD team consisted of Károly Zipernowsky, Ottó Bláthy and Miksa Déri
Stanley's 1886 design for adjustable gap open-core induction coils StanleyTransformer.png
Stanley's 1886 design for adjustable gap open-core induction coils

Closed-core transformers and parallel power distribution

In the autumn of 1884, Károly Zipernowsky, Ottó Bláthy and Miksa Déri (ZBD), three engineers associated with the Ganz factory, had determined that open-core devices were impracticable, as they were incapable of reliably regulating voltage. [107] In their joint 1885 patent applications for novel transformers (later called ZBD transformers), they described two designs with closed magnetic circuits where copper windings were either a) wound around iron wire ring core or b) surrounded by iron wire core. [108] The two designs were the first application of the two basic transformer constructions in common use to this day, which can as a class all be termed as either core form or shell form (or alternatively, core type or shell type), as in a) or b), respectively (see images). [46] [49] [100] [111] [112] The Ganz factory had also in the autumn of 1884 made delivery of the world's first five high-efficiency AC transformers, the first of these units having been shipped on September 16, 1884. [113] This first unit had been manufactured to the following specifications: 1,400 W, 40 Hz, 120:72 V, 11.6:19.4 A, ratio 1.67:1, one-phase, shell form. [113]

In both designs, the magnetic flux linking the primary and secondary windings traveled almost entirely within the confines of the iron core, with no intentional path through air (see Toroidal cores below). The new transformers were 3.4 times more efficient than the open-core bipolar devices of Gaulard and Gibbs. [114] The ZBD patents included two other major interrelated innovations: one concerning the use of parallel connected, instead of series connected, utilization loads, the other concerning the ability to have high turns ratio transformers such that the supply network voltage could be much higher (initially 1,400 to 2,000 V) than the voltage of utilization loads (100 V initially preferred). [115] [116] When employed in parallel connected electric distribution systems, closed-core transformers finally made it technically and economically feasible to provide electric power for lighting in homes, businesses and public spaces. [117] [118] Bláthy had suggested the use of closed cores, Zipernowsky had suggested the use of parallel shunt connections, and Déri had performed the experiments; [119]

Transformers today are designed on the principles discovered by the three engineers. They also popularized the word 'transformer' to describe a device for altering the EMF of an electric current, [117] [120] although the term had already been in use by 1882. [121] [122] In 1886, the ZBD engineers designed, and the Ganz factory supplied electrical equipment for, the world's first power station that used AC generators to power a parallel connected common electrical network, the steam-powered Rome-Cerchi power plant. [123]

Although George Westinghouse had bought Gaulard and Gibbs' patents in 1885, the Edison Electric Light Company held an option on the US rights for the ZBD transformers, requiring Westinghouse to pursue alternative designs on the same principles. He assigned to William Stanley the task of developing a device for commercial use in United States. [124] Stanley's first patented design was for induction coils with single cores of soft iron and adjustable gaps to regulate the EMF present in the secondary winding (see image). [110] This design [125] was first used commercially in the US in 1886 [126] but Westinghouse was intent on improving the Stanley design to make it (unlike the ZBD type) easy and cheap to produce. [125]

Westinghouse, Stanley and associates soon developed an easier to manufacture core, consisting of a stack of thin 'E‑shaped' iron plates, insulated by thin sheets of paper or other insulating material. Prewound copper coils could then be slid into place, and straight iron plates laid in to create a closed magnetic circuit. Westinghouse applied for a patent for the new low-cost design in December 1886; it was granted in July 1887. [119] [127]

Other early transformer designs

In 1889, Russian-born engineer Mikhail Dolivo-Dobrovolsky developed the first three-phase transformer at the Allgemeine Elektricitäts-Gesellschaft ('General Electricity Company') in Germany. [128]

In 1891, Nikola Tesla invented the Tesla coil, an air-cored, dual-tuned resonant transformer for producing very high voltages at high frequency. [129] [130]

Audio frequency transformers ('repeating coils') were used by early experimenters in the development of the telephone.[ citation needed ]

See also


  1. With turns of the winding oriented perpendicularly to the magnetic field lines, the flux is the product of the magnetic flux density and the core area, the magnetic field varying with time according to the excitation of the primary. The expression dΦ/dt, defined as the derivative of magnetic flux Φ with time t, provides a measure of rate of magnetic flux in the core and hence of EMF induced in the respective winding. The negative sign in eq. 1 & eq. 2 is consistent with Lenz's law and Faraday's law in that by convention EMF "induced by an increase of magnetic flux linkages is opposite to the direction that would be given by the right-hand rule."
  2. Although ideal transformer's winding inductances are each infinitely high, the square root of winding inductances' ratio is equal to the turns ratio.
  3. This also implies the following: The net core flux is zero, the input impedance is infinite when secondary is open and zero when secondary is shorted; there is zero phase-shift through an ideal transformer; input and output power and reactive volt-ampere are each conserved; these three statements apply for any frequency above zero and periodic waveforms are conserved. [8]
  4. Direction of transformer currents is according to the Right-Hand Rule.
  5. Windings of real transformers are usually wound around very high permeability ferromagnetic cores but can also be air-core wound.
  6. Section Leakage factor and inductance of Leakage inductance derives a transformer equivalent in terms of various measurable inductances (winding, self, leakage, magnetizing and mutual inductances) and turns ratio, which are collectively essential to rigorous counter EMF understanding.
  7. "The turn ratio of a transformer is the ratio of the number of turns in the high-voltage winding to that in the low-voltage winding." (Common usage has evolved over time from 'turn ratio' to 'turns ratio'.)
  8. A step-down transformer converts a high voltage to a lower voltage while a step-up transformer converts a low voltage to a higher voltage, an isolation transformer having 1:1 turns ratio with output voltage the same as input voltage.
  9. Percent impedance is the ratio of the voltage drop in the secondary from no load to full load; and is here represented with the variable Z. [23] In some texts, Z is used for absolute impedance instead.
  10. A standardized open-circuit or unloaded transformer test called the Epstein frame can also be used for the characterization of magnetic properties of soft magnetic materials including especially electrical steels. [27]
  11. ANSI/IEEE Standard C57.13 defines polarity in terms of the relative instantaneous directions of the currents entering the primary terminals and leaving the secondary terminals during most of each half cycle, the word 'instantaneous' differentiating from say phasor current. [32] <ref name='ANSI/IEEE C57.13'> ANSI/IEEE C57.13, ANS Requirements for Instrument Transformers. New York, N.Y.: IEEE. 1978. p. 4 (§3.26). ISBN   978-0-7381-4299-9. (superseded, 1993)
  12. Transformer polarity can also be identified by terminal markings H0,H1,H2... on primary terminals and X1,X2, (and Y1,Y2, Z1,Z2,Z3... if windings are available) on secondary terminals. Each letter prefix designates a different winding and each numeral designates a termination or tap on each winding. The designated terminals H1,X1, (and Y1, Z1 if available) indicate same instantaneous polarities for each winding as in the dot convention. [33]
  13. When a voltage transformer is operated with sinusoidal voltages in its normal frequency range and power level the voltage polarity at the output dot is the same (plus minus a few degrees) as the voltage polarity at the input dot.
  14. Experimental transformers using superconducting windings achieve efficiencies of 99.85%. [39]
  15. Transformer hum's fundamental noise frequency is two times that of the power frequency as there is an extension and a contraction of core laminations for every cycle of the AC wave and a transformer's audible hum noise level is dominated by the fundamental noise frequency and its first triplen harmonic, i.e., by the 100 & 300 Hz, or 120 & 360 Hz, frequencies. [43]
  16. IEC's IEV-121-12-59 defines magnetic saturation as the "state of a ferromagnetic or ferrimagnetic substance in which magnetic polarization or magnetization cannot be significantly increased by increasing the magnetic field strength."
  17. The life expectancy halving rule holds more narrowly when the increase is between about 7 °C to 8 °C in the case of transformer winding cellulose insulation.
  18. For example, the delta-wye transformer, by far the most common commercial three-phase transformer, is known as the Dyn11 vector group configuration, Dyn11 denoting D for delta primary winding, y for wye secondary winding, n for neutral of the wye winding, and 11 for relative phase position on the clock by which the secondary winding leads the primary winding, namely, 30° leading.
  19. While the above formal definition, derived from standards such as IEEE C57.12.80, applies to large transformers, it is not uncommon in colloquial, or even trade, parlance for small general-purpose transformers to be referred to as 'power' transformers, for distribution transformers to be referred to as 'power distribution' transformers, and so on.
  20. 1. Tank 2. Lid 3. Conservator tank 4. The oil level indicator (end of conservator tank) 5. Buchholz relay for detecting gas bubbles after an internal fault 6. Piping to conservator tank and Buchholz relay 7. Tap changer to change output voltage 8. The motor drive of the tap changer (can be controlled by an automatic voltage regulator) 9. Drive shaft for tap changer 10. High voltage (HV) bushing connects the internal HV coil with the external HV grid 11. High voltage bushing current transformers for measurement and protection 12. Low voltage (LV) bushing connects LV coil to LV grid 13. Low voltage current transformers . 14. Bushing voltage-transformer for metering the current through the passing bushing 15. Core 16. Yoke of the core 17. Limbs connect the yokes and hold them up 18. Coils 19. Internal wiring between coils and tapchanger 20. Oil release valve 21. Vacuum valve

Related Research Articles

Electromagnetic coil electrical component

An electromagnetic coil is an electrical conductor such as a wire in the shape of a coil, spiral or helix. Electromagnetic coils are used in electrical engineering, in applications where electric currents interact with magnetic fields, in devices such as electric motors, generators, inductors, electromagnets, transformers, and sensor coils. Either an electric current is passed through the wire of the coil to generate a magnetic field, or conversely an external time-varying magnetic field through the interior of the coil generates an EMF (voltage) in the conductor.

Inductor passive two-terminal electrical component that stores energy in its magnetic field

An inductor, also called a coil, choke, or reactor, is a passive two-terminal electrical component that stores energy in a magnetic field when electric current flows through it. An inductor typically consists of an insulated wire wound into a coil around a core.

Ignition magneto

An ignition magneto, or high tension magneto, is a magneto that provides current for the ignition system of a spark-ignition engine, such as a petrol engine. It produces pulses of high voltage for the spark plugs. The older term tension means voltage.

Tesla coil electrical resonant transformer circuit invented by Nikola Tesla

A Tesla coil is an electrical resonant transformer circuit designed by inventor Nikola Tesla in 1891. It is used to produce high-voltage, low-current, high frequency alternating-current electricity. Tesla experimented with a number of different configurations consisting of two, or sometimes three, coupled resonant electric circuits.

Inductive coupling

In electrical engineering, two conductors are said to be inductively coupled or magnetically coupled when they are configured such that a change in current through one wire induces a voltage across the ends of the other wire through electromagnetic induction. A changing current through the first wire creates a changing magnetic field around it by Ampere's circuital law. The changing magnetic field induces an electromotive force in the second wire by Faraday's law of induction. The amount of inductive coupling between two conductors is measured by their mutual inductance.

Alternating current electric voltage which periodically reverses direction; form in which electric power is delivered to businesses and residences; form of electrical energy that consumers typically use when they plug electric appliances into a wall socket

Alternating current (AC) is an electric current which periodically reverses direction, in contrast to direct current (DC) which flows only in one direction. Alternating current is the form in which electric power is delivered to businesses and residences, and it is the form of electrical energy that consumers typically use when they plug kitchen appliances, televisions, fans and electric lamps into a wall socket. A common source of DC power is a battery cell in a flashlight. The abbreviations AC and DC are often used to mean simply alternating and direct, as when they modify current or voltage.

Inductance electrical property

In electromagnetism and electronics, inductance describes the tendency of an electrical conductor, such as coil, to oppose a change in the electric current through it. The change in current induces a reverse electromotive force (voltage). When an electric current flows through a conductor, it creates a magnetic field around that conductor. A changing current, in turn, creates a changing magnetic field, the surface integral of which is known as magnetic flux. From Faraday's law of induction, any change in magnetic flux through a circuit induces an electromotive force (voltage) across that circuit, a phenomenon known as electromagnetic induction. Inductance is specifically defined as the ratio between this induced voltage and the rate of change of the current in the circuit


A balun is an electrical device that converts between a balanced signal and an unbalanced signal. A balun can take many forms and may include devices that also transform impedances but need not do so. Transformer baluns can also be used to connect lines of differing impedance. Sometimes, in the case of transformer baluns, they use magnetic coupling but need not do so. Common-mode chokes are also used as baluns and work by eliminating, rather than ignoring, common mode signals.

Gyrator analog circuit

A gyrator is a passive, linear, lossless, two-port electrical network element proposed in 1948 by Bernard D. H. Tellegen as a hypothetical fifth linear element after the resistor, capacitor, inductor and ideal transformer. Unlike the four conventional elements, the gyrator is non-reciprocal. Gyrators permit network realizations of two-(or-more)-port devices which cannot be realized with just the conventional four elements. In particular, gyrators make possible network realizations of isolators and circulators. Gyrators do not however change the range of one-port devices that can be realized. Although the gyrator was conceived as a fifth linear element, its adoption makes both the ideal transformer and either the capacitor or inductor redundant. Thus the number of necessary linear elements is in fact reduced to three. Circuits that function as gyrators can be built with transistors and op-amps using feedback.

An autotransformer is an electrical transformer with only one winding. The "auto" prefix refers to the single coil acting alone, not to any kind of automatic mechanism. In an autotransformer, portions of the same winding act as both the primary and secondary sides of the transformer. In contrast, an ordinary transformer has separate primary and secondary windings which are not electrically connected.

Current transformer current transformer

A current transformer (CT) is a type of transformer that is used to measure alternating current (AC). It produces a current in its secondary which is proportional to the current in its primary.

Leakage inductance derives from the electrical property of an imperfectly-coupled transformer whereby each winding behaves as a self-inductance in series with the winding's respective ohmic resistance constant. These four winding constants also interact with the transformer's mutual inductance. The winding leakage inductance is due to leakage flux not linking with all turns of each imperfectly-coupled winding.

Bifilar coil

A bifilar coil is an electromagnetic coil that contains two closely spaced, parallel windings. In engineering, the word bifilar describes wire which is made of two filaments or strands. It is commonly used to denote special types of winding wire for transformers. Wire can be purchased in bifilar form, usually as different colored enameled wire bonded together. For three strands, the term trifilar coil is used.

Blocking oscillator

A blocking oscillator is a simple configuration of discrete electronic components which can produce a free-running signal, requiring only a resistor, a transformer, and one amplifying element. The name is derived from the fact that the transistor is cut-off or "blocked" for most of the duty-cycle, producing periodic pulses. The non-sinusoidal output is not suitable for use as a radio-frequency local oscillator, but it can serve as a timing generator, to power lights, LEDs, Elwire, or small neon indicators. The simple tones are also sufficient for applications such as alarms or a Morse code practice device. Some cameras use a blocking oscillator to strobe the flash prior to a shot to reduce the red-eye effect.

A brushed DC motor is an internally commutated electric motor designed to be run from a direct current power source. Brushed motors were the first commercially important application of electric power to driving mechanical energy, and DC distribution systems were used for more than 100 years to operate motors in commercial and industrial buildings. Brushed DC motors can be varied in speed by changing the operating voltage or the strength of the magnetic field. Depending on the connections of the field to the power supply, the speed and torque characteristics of a brushed motor can be altered to provide steady speed or speed inversely proportional to the mechanical load. Brushed motors continue to be used for electrical propulsion, cranes, paper machines and steel rolling mills. Since the brushes wear down and require replacement, brushless DC motors using power electronic devices have displaced brushed motors from many applications.

Transformer types

A variety of types of electrical transformer are made for different purposes. Despite their design differences, the various types employ the same basic principle as discovered in 1831 by Michael Faraday, and share several key functional parts.

Toroidal inductors and transformers

Toroidal inductors and transformers are inductors and transformers which use magnetic cores with a toroidal shape. They are passive electronic components, consisting of a circular ring or donut shaped magnetic core of ferromagnetic material such as laminated iron, iron powder, or ferrite, around which wire is wound.

Induction regulator

An induction regulator is an alternating current electrical machine, somewhat similar to an induction motor, which can provide a continuously variable output voltage. The induction regulator was an early device used to control the voltage of electric networks. Since the 1930s it has been replaced in distribution network applications by the tap transformer. Its usage is now mostly confined to electrical laboratories, electrochemical processes and arc welding. With minor variations, its setup can be used as a phase-shifting power transformer.

Open-circuit test

The open-circuit test, or "no-load test", is one of the methods used in electrical engineering to determine the no-load impedance in the excitation branch of a transformer. The no load is represented by the open circuit, which is represented on the right side of the figure as the “hole” or incomplete part of the circuit.

Most of the terms listed in Wikipedia glossaries are already defined and explained within Wikipedia itself. However, glossaries like this one are useful for looking up, comparing and reviewing large numbers of terms together. You can help enhance this page by adding new terms or writing definitions for existing ones.


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  2. Mack, James E.; Shoemaker, Thomas (2006). "Chapter 15 - Distribution Transformers" (PDF). The Lineman's and Cableman's Handbook (11th ed.). New York: McGraw-Hill. pp. 15–1 to 15–22. ISBN   0-07-146789-0.
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  5. Brenner & Javid 1959 , §18-1 Symbols and Polarity of Mutual Inductance, pp.=589–590
  6. IEV 131-12-78 , Ideal transformer
  7. Brenner & Javid 1959 , §18-6 The Ideal Transformer, pp.=598–600
  8. Crosby 1958, p. 145
  9. Hameyer 2004 , §2.1.2 Second Maxwell-Equation (Faraday's Law) in Section 2 - Basics, pp. 1112, equations 2-12 to 2-15
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  21. 1 2 Say 1983 , p. 485
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  23. Heathcote 1998, p. 4
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