TheInfoList

A transformer is a
passive component Passivity is a property of engineering systems, most commonly encountered in analog electronics and control systems. Typically, analog designers use ''passivity'' to refer to incrementally passive components and systems, which are incapable of Gai ...
that transfers electrical energy from one electrical circuit to another circuit, or multiple
circuitsCircuit may refer to: Science and technology Electrical engineering * Electrical circuit, a complete electrical network with a closed-loop giving a return path for current ** Analog circuit, uses continuous signal levels ** Balanced circuit, p ...
. A varying current in any one coil of the transformer produces a varying
magnetic flux In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular su ...

in the transformer's core, which induces a varying
electromotive force In electromagnetism Electromagnetism is a branch of physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the ...
across any other coils wound around the same core. Electrical energy can be transferred between separate coils without a metallic (conductive) connection between the two circuits.
Faraday's law of induction Faraday's law of induction (briefly, Faraday's law) is a basic law of electromagnetism Electromagnetism is a branch of physics involving the study of the electromagnetic force, a type of physical interaction that occurs between electric c ...
, discovered in 1831, describes the induced voltage effect in any coil due to a changing magnetic flux encircled by the coil. Transformers are most commonly used for increasing low AC voltages at high current (a step-up transformer) or decreasing high AC voltages at low current (a step-down transformer) in electric power applications, and for coupling the stages of signal-processing circuits. Transformers can also be used for isolation, where the voltage in equals the voltage out, with separate coils not electrically bonded to one another. Since the invention of the first
constant-potential transformer A voltage regulator is a system designed to automatically maintain a constant voltage. A voltage regulator may use a simple feed-forward Feedforward is the provision of context of what one wants to communicate prior to that communication. In purp ...
in 1885, transformers have become essential for the
transmission Transmission may refer to: Science and technology * Power transmissionPower transmission is the movement of energy from its place of generation to a location where it is applied to perform useful Mechanical work, work. Power (physics), Power is d ...

,
distributionDistribution may refer to: Mathematics *Distribution (mathematics) Distributions, also known as Schwartz distributions or generalized functions, are objects that generalize the classical notion of functions in mathematical analysis. Distr ...
, and utilization of alternating current electric power. 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 An electrical grid is an interconnected network for electricity delivery Electricity delivery is the process that starts after generation of electricity in the power station A power station, also referred to as a power plant and someti ...

.

# Principles

Ideal transformer equations By Faraday's law of induction: $V_\text = -N_\text \frac$ . . . (eq. 1) $V_\text = -N_\text \frac$ . . . (eq. 2) Where $V$ is the
voltage Voltage, electric potential difference, electric pressure or electric tension is the difference in electric potential The electric potential (also called the ''electric field potential'', potential drop, the electrostatic potential) is the ...

, $N$ is the number of turns in a winding, dΦ/dt is the
derivative In mathematics Mathematics (from Greek: ) includes the study of such topics as numbers (arithmetic and number theory), formulas and related structures (algebra), shapes and spaces in which they are contained (geometry), and quantities ...

of the magnetic flux Φ through one turn of the winding over time (''t''), and subscripts P and S denotes primary and secondary. Combining the ratio of eq. 1 & eq. 2: Turns ratio $=\frac = \frac=a$ . . . (eq. 3) Where for a step-down transformer ''a'' > 1, for a step-up transformer ''a'' < 1, and for an
isolation transformer An isolation transformer is a transformer A transformer is a passive component that transfers electrical energy from one electrical circuit to another circuit, or multiple Electrical network, circuits. A varying current in any one coil of the ...

''a'' = 1. By law of
conservation of energy In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular s ...
, apparent,
real Real may refer to: * Reality Reality is the sum or aggregate of all that is real or existent within a system, as opposed to that which is only Object of the mind, imaginary. The term is also used to refer to the ontological status of things, ind ...
and
reactive Reactive may refer to: *Generally, capable of having a reaction (disambiguation) *An adjective abbreviation denoting a Bowling ball#Coverstock technology, bowling ball coverstock made of reactive resin *Reactivity (chemistry) *Reactive mind *Reacti ...
power are each conserved in the input and output: $I_\text V_\text = I_\text V_\text$ . . . . (eq. 4) Where $I$ is
current Currents or The Current may refer to: Science and technology * Current (fluid) A current in a fluid In physics, a fluid is a substance that continually Deformation (mechanics), deforms (flows) under an applied shear stress, or external force. ...
. Combining eq. 3 & eq. 4 with this endnote gives the ideal transformer
identity Identity may refer to: Social sciences * Identity (social science), personhood or group affiliation in psychology and sociology Group expression and affiliation * Cultural identity, a person's self-affiliation (or categorization by others ...

: $\frac = \frac=\frac=\sqrt=a$ . (eq. 5) Where $L$ is winding self-inductance. By
Ohm's law Ohm's law states that the current Currents or The Current may refer to: Science and technology * Current (fluid) A current in a fluid In physics, a fluid is a substance that continually Deformation (mechanics), deforms (flows) under an ap ...

and ideal transformer identity: $Z_\text=\frac$ . . . (eq. 6) $Z\text{'}_\text = \frac=\frac=a^2\frac=a^2$ . (eq. 7) Where $Z_\text$ is the load impedance of the secondary circuit & $Z\text{'}_\text$ is the apparent load or driving point impedance of the primary circuit, the superscript $\text{'}$ denoting referred to the primary.

## Ideal transformer

An ideal transformer is a theoretical
linear Linearity is the property of a mathematical relationship (''function Function or functionality may refer to: Computing * Function key A function key is a key on a computer A computer is a machine that can be programmed to carry out se ...

transformer that is lossless and perfectly coupled. Perfect coupling implies infinitely high core
magnetic permeability In electromagnetism Electromagnetism is a branch of physics involving the study of the electromagnetic force, a type of physical interaction that occurs between electric charge, electrically charged particles. The electromagnetic force is ...
and winding inductance and zero net
magnetomotive force In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related entities of energy and force. ...
(i.e. ipnp - isns = 0). 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 In electromagnetism Electromagnetism is a branch of physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the ...
(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 Lenz's law, named after the physicist Emil Lenz Heinrich Friedrich Emil Lenz (; ; also Emil Khristianovich Lenz, russian: Эмилий Христианович Ленц; 12 February 1804 – 10 February 1865), usually cited as Emil Lenz or Hei ...
. The windings are wound around a core of infinitely high magnetic permeability so that all of the magnetic flux passes through both the primary and secondary windings. With a
voltage source A voltage source is a two- terminal device which can maintain a fixed voltage Voltage, electric potential difference, electric pressure or electric tension is the difference in electric potential The electric potential (also called the ' ...

connected to the primary winding and a load connected to the secondary winding, the transformer currents flow in the indicated directions and the core magnetomotive force cancels to zero. According to Faraday's law, since the same magnetic flux passes through both the primary and secondary windings in an ideal transformer, a voltage is induced in each winding proportional to its number of windings. The transformer winding voltage ratio is directly proportional to the winding turns ratio. The ideal transformer
identity Identity may refer to: Social sciences * Identity (social science), personhood or group affiliation in psychology and sociology Group expression and affiliation * Cultural identity, a person's self-affiliation (or categorization by others ...

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. The load impedance ''referred'' to the primary circuit is equal to the turns ratio squared times the secondary circuit load impedance. pp. 2-1, 2-2

## Real 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 *
Hysteresis Hysteresis is the dependence of the state of a system on its history. For example, a magnet may have more than one possible magnetic moment in a given magnetic field, depending on how the field changed in the past. Plots of a single component of t ...

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 * 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 An inductor, also called a coil, choke, or reactor, is a passive Passive may refer to: * Passive voice, a grammatical voice common in many languages, see also Pseudopassive (disambiguation), Pseudopassive * Passive language, a language from whi ...

, 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 * 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 shown below 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. Such flux is termed ''leakage flux'', and results in
leakage inductance Leakage inductance derives from the electrical property of an imperfectly-coupled transformer A transformer is a passive electrical device that transfers electrical energy from one electrical circuit to another, or multiple Electrical network, ci ...
in
series Series may refer to: People with the name * Caroline Series (born 1951), English mathematician, daughter of George Series * George Series (1920–1995), English physicist Arts, entertainment, and media Music * Series, the ordered sets used i ...

with the mutually coupled transformer windings. 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 In electrical engineering, particularly power engineering Power engineering, also called power systems engineering, is a subfield of electrical engineering that deals with the generation, transmission, distribution, and utilization of electric ...
, causing the secondary voltage not to be directly proportional to the primary voltage, particularly under heavy load. 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 A short circuit (sometimes abbreviated to short or s/c) is an electrical circuit An electrical network is an interconnection of electrical component An electronic component is any basic discrete device or physical entity in an electron ...

current it will supply. Leaky transformers may be used to supply loads that exhibit
negative resistance In electronics, negative resistance (NR) is a property of some electrical circuits and devices in which an increase in voltage across the device's terminals results in a decrease in electric current through it. This is in contrast to an ordina ...
, such as
electric arc An electric arc, or arc discharge, is an electrical breakdown of a gas that produces a prolonged electrical discharge. The electric current, current through a normally Electrical conductance, nonconductive medium such as air produces a plasma (ph ...

s, mercury- and sodium- vapor lamps and
neon sign Neon is a chemical element upright=1.0, 500px, The chemical elements ordered by link=Periodic table In chemistry Chemistry is the science, scientific study of the properties and behavior of matter. It is a natural science that co ...

s or for safely handling loads that become periodically short-circuited such as electric arc welders. 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. 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 and associated winding leakage reactance-to-resistance (''X''/''R'') ratio of two transformers were the same, the transformers would share the load power in proportion to their respective ratings. However, the impedance tolerances of commercial transformers are significant. Also, the impedance and X/R ratio of different capacity transformers tends to vary. Nomenclature for Parallel Operation, pp. 585–586

### 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. Winding joule losses and leakage reactances are represented by the following series loop impedances of the model: * Primary winding: ''R''P, ''X''P * Secondary winding: ''R''S, ''X''S. In normal course of circuit equivalence transformation, ''R''S and ''X''S are in practice usually referred to the primary side by multiplying these impedances by the turns ratio squared, (''N''P/''N''S) 2 = a2. Core loss and reactance is represented by the following shunt leg impedances of the model: * Core or iron losses: ''R''C * Magnetizing reactance: ''X''M. ''R''C and ''X''M 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. The finite permeability core requires a magnetizing current ''I''M 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. With
sinusoidal A sine wave or sinusoid is any of certain mathematical curves that describe a smooth periodic oscillation Oscillation is the repetitive variation, typically in time Time is the indefinite continued sequence, progress of existence and ev ...

supply, core flux lags the induced EMF by 90°. With open-circuited secondary winding, magnetizing branch current ''I''0 equals transformer no-load current. The resulting model, though sometimes termed 'exact' equivalent circuit based on
linearity Linearity is the property of a mathematical relationship (''function (mathematics), function'') that can be graph of a function, graphically represented as a straight Line (geometry), line. Linearity is closely related to ''Proportionality (math ...

assumptions, retains a number of approximations. 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, short-circuit test, winding resistance test, and transformer ratio test.

## Transformer EMF equation

If the flux in the core is purely
sinusoidal A sine wave or sinusoid is any of certain mathematical curves that describe a smooth periodic oscillation Oscillation is the repetitive variation, typically in time Time is the indefinite continued sequence, progress of existence and ev ...

, the relationship for either winding between its rms voltage ''E''rms of the winding, and the supply frequency ''f'', number of turns ''N'', core cross-sectional area ''a'' in m2 and peak magnetic flux density ''B''peak in Wb/m2 or T (tesla) is given by the universal EMF equation: : $E_\text = \approx 4.44 f N a B_\text$

## Polarity

A
dot convention Image:Instrument Transformer LV terminals.jpg, 180px, The low voltage side of the instrument transformer, with dot and X1 marking. The X1 and H1 terminals are adjacent. In electrical engineering, dot marking convention, or alphanumeric marking con ...
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. 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 In and , a phasor (a of phase vector), is a representing a whose (''A''), (''ω''), and (''θ'') are . It is related to a more general concept called ,Bracewell, Ron. ''The Fourier Transform and Its Applications''. McGraw-Hill, 1965. p2 ...

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. 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 Skin effect is the tendency of an alternating electric current (AC) to become distributed within a conductor Conductor or conduction may refer to: Music * Conductor (music), a person who leads a musical ensemble like, for example, an or ...

also increase with frequency. Aircraft and military equipment employ 400 Hz power supplies which reduce core and winding weight. Conversely, frequencies used for some
railway electrification system A railway electrification system supplies electric power Electric power is the rate, per unit time, at which electrical energy Electrical energy is energy derived as a result of movement of electrically charged particles. When used loos ...

s 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 were much larger and heavier for the same power rating than those required for the higher frequencies. 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. Transformers may require
protective relay In electrical engineering, a protective relay is a relay device designed to trip a circuit breaker when a fault is detected. The first protective relays were electromagnetic devices, relying on coils operating on moving parts to provide detecti ...

s to protect the transformer from overvoltage at higher than rated frequency. One example is in traction transformers used for
electric multiple unit An electric multiple unit or EMU is a multiple-unit train consisting of self-propelled carriages using electricity as the motive power. An EMU requires no separate locomotive, as electric traction motors are incorporated within one or a numb ...
and
high-speed High Speed or high-speed may refer to: Films * High Speed (1917 film), ''High Speed'' (1917 film), starring Jack Mulhall and Fritzi Ridgeway * High Speed (1920 film), ''High Speed'' (1920 film), an American drama directed by Charles Miller (direct ...
train service operating across regions with different electrical standards. 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). 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 made switch-mode power supplies viable, to generate a high frequency, then change the voltage level with a small transformer. Large power transformers are vulnerable to insulation failure due to transient voltages with high-frequency components, such as caused in switching or by lightning.

## 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. 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 at no load, while winding loss increases 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 upright=1.35, Polycrystalline structure of electrical steel after coating has been removed. Electrical steel (lamination steel, silicon electrical steel, silicon steel, relay steel, transformer steel) is an iron Iron () is a chemical elemen ...
, or even amorphous steel for the core and thicker wire, increasing initial cost. The choice of construction represents a
trade-off A trade-off (or tradeoff) is a situational decision that involves diminishing or losing one quality, quantity, or property of a set or design in return for gains in other aspects. In simple terms, a tradeoff is where one thing increases, and another ...
between initial cost and operating cost. Transformer losses arise from: ; Winding joule losses :Current flowing through a winding's conductor causes
joule heating Joule heating, also known as resistive, resistance, or Ohmic heating, is the process by which the passage of an electric current An electric current is a stream of charged particles, such as electrons or ions, moving through an electrical condu ...
due to the
resistance Resistance may refer to: Arts, entertainment, and media Comics * Either of two similarly named but otherwise unrelated comic book series, both published by Wildstorm: ** ''Resistance'' (comics), based on the video game of the same title ** ''Th ...
of the wire. As frequency increases, skin effect and proximity effect causes the winding's resistance and, hence, losses to increase. ;
Core losses A magnetic core is a piece of magnetic material with a high magnetic permeability used to confine and guide magnetic field A magnetic field is a vector field that describes the magnetic influence on moving electric charges, electric currents, ...
:; Hysteresis losses ::Each time the magnetic field is reversed, a small amount of energy is lost due to
hysteresis Hysteresis is the dependence of the state of a system on its history. For example, a magnet may have more than one possible magnetic moment in a given magnetic field, depending on how the field changed in the past. Plots of a single component of t ...

within the core, caused by motion of the
magnetic domain A magnetic domain is a region within a magnetic material in which the magnetization is in a uniform direction. This means that the individual magnetic moment The magnetic moment is the magnetic strength and orientation of a magnet or other obje ...
s within the steel. According to Steinmetz's formula, the heat energy due to hysteresis is given by :::$W_\text\approx\eta\beta^_,$ and, ::hysteresis loss is thus given by :::$P_\text\approx_\textf\approx\eta\beta^_$ ::where, ''f'' is the frequency, ''η'' is the hysteresis coefficient and ''β''max 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. For more detailed analysis, see
Magnetic core A magnetic core is a piece of magnetic material Magnetic field lines of a solenoid electromagnet, which are similar to a bar magnet as illustrated below with the iron filings">electromagnet.html" ;"title="solenoid electromagnet">solenoid ele ...
and Steinmetz's equation. :; Eddy current losses :: Eddy currents are induced in the conductive metal transformer core by the changing magnetic field, and this current flowing through the resistance of the iron dissipates energy as heat in the core. The eddy current loss is a complex function of the square of supply frequency and inverse square of the material thickness. Eddy current losses can be reduced by making the core of a stack of laminations (thin 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 Magnetostriction (cf. electrostriction) is a property of magnet, magnetic materials that causes them to change their shape or dimensions during the process of magnetization. The variation of materials' magnetization due to the applied magnetic field ...
, the frictional energy of which produces an audible noise known as
mains hum Mains hum, electric hum, cycle hum, or power line hum is a sound associated with alternating current Alternating current (AC) is an electric current An electric current is a stream of charged particles, such as electrons or ions, moving thro ...
or "transformer hum". This transformer hum is especially objectionable in transformers supplied at power frequencies and in
high-frequency High frequency (HF) is the ITU designation for the range of radio frequency Radio frequency (RF) is the oscillation rate of an Alternating_current, alternating electric current or voltage or of a Magnetic_field, magnetic, electric or electro ...
flyback transformers associated with television . ; 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. ; Radiative :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.

# Construction

## Cores

; 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. 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. 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. 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.

### Laminated steel cores

Transformers for use at power or audio frequencies typically have cores made of high permeability
silicon steel upright=1.35, Polycrystalline structure of electrical steel after coating has been removed. Electrical steel (lamination steel, silicon electrical steel, silicon steel, relay steel, transformer steel) is an iron Iron () is a chemical elemen ...
. The steel has a permeability many times that of
free space A vacuum is space devoid of matter. The word stems from the Latin adjective ''vacuus'' for "vacant" or "Void (astronomy), void". An approximation to such vacuum is a region with a gaseous pressure much less than atmospheric pressure. Physicist ...
and the core thus serves to greatly reduce the magnetizing current and confine the flux to a path which closely couples the windings. 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. 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. The transformer universal EMF equation can be used to calculate the core cross-sectional area for a preferred level of magnetic flux. 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, but are more laborious and expensive to construct. Thin laminations are generally used on high-frequency transformers, with some of very thin steel laminations able to operate up to 10 kHz. One common design of laminated core is made from interleaved stacks of
E-shaped Many shapes have metaphorical names, i.e., their names are metaphor A metaphor is a figure of speech that, for rhetorical effect, directly refers to one thing by mentioning another. It may provide (or obscure) clarity or identify hidden similar ...
steel sheets capped with I-shaped pieces, leading to its name of 'E-I transformer'. 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. They have the advantage that the flux is always oriented parallel to the metal grains, reducing reluctance. A steel core's
remanence Remanence or remanent magnetization or residual magnetism is the magnetization left behind in a ferromagnetic material (such as iron) after an external magnetic field is removed. Colloquially, when a magnet is "magnetized" it has remanence. The r ...
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 Inrush current, input surge current, or switch-on surge is the maximal instantaneous input current Currents or The Current may refer to: Science and technology * Current (fluid) A current in a fluid In physics, a fluid is a substance that con ...

until the effect of the remaining magnetism is reduced, usually after a few cycles of the applied AC waveform. 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. 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.

### 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 Electrical resistivity (also called specific electrical resistance or volume resistivity) is a fundamental property of a material that measures how strongly it resists electric current An electric current is a stream of charged particle In p ...
. For frequencies extending beyond the
VHF band Very high frequency (VHF) is the International Telecommunications Union, ITU designation for the range of radio frequency electromagnetic waves (radio waves) from 30 to 300 megahertz (MHz), with corresponding wavelengths of ten meters to one met ...
, cores made from non-conductive magnetic
ceramic A ceramic is any of the various hard, brittle, heat-resistant and corrosion-resistant Corrosion is a Erosion, natural process that converts a refined metal into a more chemically stable form such as oxide, hydroxide, carbonate or sulfide. ...

materials called ferrites are common. Some radio-frequency transformers also have movable cores (sometimes called 'slugs') which allow adjustment of the coupling coefficient (and
bandwidth Bandwidth commonly refers to: * Bandwidth (signal processing) or ''analog bandwidth'', ''frequency bandwidth'', or ''radio bandwidth'', a measure of the width of a frequency range * Bandwidth (computing), the rate of data transfer, bit rate or thr ...

### Toroidal cores

Toroidal transformers are built around a ring-shaped core, which, depending on operating frequency, is made from a long strip of
silicon steel upright=1.35, Polycrystalline structure of electrical steel after coating has been removed. Electrical steel (lamination steel, silicon electrical steel, silicon steel, relay steel, transformer steel) is an iron Iron () is a chemical elemen ...
or
permalloy Permalloy is a nickel Nickel is a chemical element Image:Simple Periodic Table Chart-blocks.svg, 400px, Periodic table, The periodic table of the chemical elements In chemistry, an element is a pure substance consisting only of atoms that ...
wound into a coil, powdered iron, or ferrite. A strip construction ensures that the
grain boundaries A grain boundary is the interface between two grains, or crystallites, in a polycrystalline material. Grain boundaries are 2D crystallographic defect, defects in the crystal structure, and tend to decrease the electrical conductivity, electrical ...
are optimally aligned, improving the transformer's efficiency by reducing the core's
reluctance Magnetic reluctance, or magnetic resistance, is a concept used in the analysis of magnetic circuits. It is defined as the ratio of magnetomotive force (mmf) to magnetic flux. It represents the opposition to magnetic flux, and depends on the geom ...
. The closed ring shape eliminates air gaps inherent in the construction of an E-I core. The cross-section of the ring is usually square or rectangular, but more expensive cores with circular cross-sections are also available. The primary and secondary coils are often wound concentrically to cover the entire surface of the core. This minimizes the length of wire needed and provides screening to minimize the core's magnetic field from generating
electromagnetic interference Electromagnetic interference (EMI), also called radio-frequency interference (RFI) when in the radio frequency Radio frequency (RF) is the oscillation Oscillation is the repetitive variation, typically in time, of some measure about a cent ...
. 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.

### 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. 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, but are frequently employed in radio-frequency applications. 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

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 Pressboard is a class of cellulose Cellulose is an organic compound with the chemical formula, formula , a polysaccharide consisting of a linear chain of several hundred to many thousands of glycosidic bond, β(1→4) linked glucose, D-glucose un ...
. High-frequency transformers operating in the tens to hundreds of kilohertz often have windings made of braided
Litz wire Litz can refer to: * Litz wire Litz wire is a particular type of multistrand wire A wire is a single usually cylindrical, flexible strand or rod of metal. Wires are used to bear mechanical loads or electricity Electricity is the se ...
to minimize the skin-effect and proximity effect losses. Large power transformers use multiple-stranded conductors as well, since even at low power frequencies non-uniform distribution of current would otherwise exist in high-current windings. Each strand is 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. 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 changer A tap changer is a mechanism in transformer A transformer is a passive electrical device that transfers electrical energy from one electrical circuit to another, or multiple Electrical network, circuits. A varying current in any one coil of the t ...
s are used in electric power transmission or distribution, on equipment such as
arc furnace An electric arc furnace (EAF) is a furnace that heats charged material by means of an electric arc. Industrial arc furnaces range in size from small units of approximately one-tonne capacity (used in foundry, foundries for producing cast iron pro ...
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 An amplifier, electronic amplifier or (informally) amp is an electronic device that can increase the power Power typically refers to: * Power (physics) In physics, power is the amount of energy transferred or converted per unit time. In ...

in a push-pull circuit. Modulation transformers in Amplitude modulation, AM transmitters are very similar.

## Insulation

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. 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.

## Bushings

Larger transformers are provided with high-voltage insulated Bushing (electrical), 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.

# Classification parameters

Transformers can be classified in many ways, such as the following: * ''Power rating'': From a fraction of a volt-ampere (VA) to over a thousand MVA. * ''Duty of a transformer'': Continuous, short-time, intermittent, periodic, varying. * ''Frequency range'': Utility frequency, Power-frequency, audio frequency, audio-frequency, or radio frequency, radio-frequency. * ''Voltage class'': From a few volts to hundreds of kilovolts. * ''Cooling type'': Dry or liquid-immersed; self-cooled, forced air-cooled;forced oil-cooled, water-cooled. * ''Application'': power supply, impedance matching, output voltage and current stabilizer, Pulse transformer, pulse, circuit isolation, Electricity distribution, power distribution, rectifier,
arc furnace An electric arc furnace (EAF) is a furnace that heats charged material by means of an electric arc. Industrial arc furnaces range in size from small units of approximately one-tonne capacity (used in foundry, foundries for producing cast iron pro ...
, amplifier output, etc.. * ''Basic magnetic form'': Core form, shell form, concentric, sandwich. * ''Constant-potential transformer descriptor'': Step-up, step-down, Isolation transformer, isolation. * ''General winding configuration'': By Vector group, IEC vector group, two-winding combinations of the phase designations delta, wye or star, and zigzag transformer, zigzag; autotransformer, Scott-T transformer, Scott-T * ''Rectifier phase-shift winding configuration'': 2-winding, 6-pulse; 3-winding, 12-pulse; . . . n-winding, [n-1]*6-pulse; polygon; etc..

# Applications

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. In electric power transmission, transformers allow transmission of electric power at high voltages, which reduces the loss due to heating of the wires. This allows generating plants to be located economically at a distance from electrical consumers. 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. In many electronic devices, a transformer is used to convert voltage from the distribution wiring to convenient values for the circuit requirements, either directly at the power line frequency or through a switch mode power supply. Signal and audio transformers are used to couple stages of
amplifier An amplifier, electronic amplifier or (informally) amp is an electronic device that can increase the power Power typically refers to: * Power (physics) In physics, power is the amount of energy transferred or converted per unit time. In ...

s and to match devices such as microphones and record players to the input of amplifiers. Audio transformers allowed telephone circuits to carry on a Hybrid coil, 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 line, balanced voltages to ground, such as between external cables and internal circuits. Isolation transformers prevent leakage of current into the secondary circuit and are used in medical equipment and at construction sites. Resonant transformers are used for coupling between stages of radio receivers, or in high-voltage Tesla coils.

# History

## Discovery of induction

Electromagnetic induction, the principle of the operation of the transformer, was discovered independently by Michael Faraday in 1831 and Joseph Henry in 1832. Only Faraday furthered his experiments to the point of working out the equation describing the relationship between EMF and magnetic flux now known as
Faraday's law of induction Faraday's law of induction (briefly, Faraday's law) is a basic law of electromagnetism Electromagnetism is a branch of physics involving the study of the electromagnetic force, a type of physical interaction that occurs between electric c ...
: :$, \mathcal, = \left, \,$ where $, \mathcal,$ is the magnitude of the EMF in volts and ΦB is the magnetic flux through the circuit in Weber (unit), webers. Faraday performed early experiments on induction between coils of wire, including winding a pair of coils around an iron ring, thus creating the first Toroid (geometry), toroidal closed-core transformer. 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 coils

The first type of transformer to see wide use was the induction coil, invented by Rev. Nicholas Callan of Maynooth College, Ireland in 1836. 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, 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 Electric generator, generators producing alternating current, 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 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 Yablochkov candle, 'electric candles' (arc lamps) of his own design. The coils Yablochkov employed functioned essentially as transformers. In 1878, the Ganz Works, 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. 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 Electric Corporation, Westinghouse company in the United States. They also exhibited the invention in Turin, Italy in 1884, where it was adopted for an electric lighting system.

### Early series circuit transformer distribution

Induction coils with open magnetic circuits are inefficient at transferring power to Electrical load, 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. Efficient, practical transformer designs did not appear until the 1880s, but within a decade, the transformer would be instrumental in the war of the currents, and in seeing AC distribution systems triumph over their DC counterparts, a position in which they have remained dominant ever since.

## Westinghouse improvements

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, Jr., William Stanley the task of developing a device for commercial use in United States. 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). This design was first used commercially in the US in 1886 but Westinghouse was intent on improving the Stanley design to make it (unlike the ZBD type) easy and cheap to produce. Westinghouse, Stanley and associates soon developed a core that was easier to manufacture, consisting of a stack of thin 'E‑shaped' iron plates insulated by thin sheets of paper or other insulating material. Pre-wound copper coils could then be slid into place, and straight iron plates laid in to create a closed magnetic circuit. Westinghouse obtained a patent for the new low-cost design in 1887.

## Other early transformer designs

In 1889, Russian-born engineer Mikhail Dolivo-Dobrovolsky developed the first Three-phase electric power, three-phase transformer at the Allgemeine Elektricitäts-Gesellschaft ('General Electricity Company') in Germany. In 1891, Nikola Tesla invented the Tesla coil, an air-cored, dual-tuned resonant transformer for producing very high voltages at high frequency. Audio frequency transformers ("repeating coils") were used by early experimenters in the development of the telephone.

* High-voltage transformer fire barriers * Inductive coupling * Load profile * Magnetization * Paraformer * Polyphase system * Power inverter * Rectiformer * Voltage converter

# Bibliography

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