Transformer wikipedia, the free encyclopedia

7/25/13 Transformer - Wikipedia, the free encyclopedia
en.wikipedia.org/wiki/Transformer 1/26
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
volt.[1][2]
Ideal transformer circuit diagram
Transformer
From Wikipedia, the free encyclopedia
A transformer is a static electrical device that transfers energy by
inductive coupling between its winding circuits. A varying current in the
primary winding creates a varying magnetic flux in the transformer's core
and thus a varying magnetic flux through the secondary winding. This
varying magnetic flux induces a varying electromotive force (emf) or
voltage in the secondary winding.
Transformers range in size from thumbnail-sized used in microphones to
units weighing hundreds of tons interconnecting the power grid. A wide
range of transformer designs are used in electronic and electric power
applications. Transformers are essential for the transmission, distribution,
and utilization of electrical energy.
Basic principles
The ideal transformer
Consider the ideal, lossless, perfectly-coupled transformer shown in the
circuit diagram at right having primary and secondary windings with NP
and NS turns, respectively.
The ideal transformer induces secondary voltage ES =VS as a proportion
of the primary voltage VP = EP and respective winding turns as given by
the equation
,
where,
- VP/VS = EP/ES = a is the voltage ratio and NP/NS =
a is the winding turns ratio, the value of these ratios
being respectively higher and lower than unity for step-
down and step-up transformers,[3][4][a][b]
- VP designates source impressed voltage,
- VS designates output voltage, and,
- EP & ES designate respective emf induced voltages.[c]
Any load impedance connected to the ideal transformer's secondary winding causes current to flow without
losses from primary to secondary circuits, the resulting input and output apparent power therefore being equal as
given by the equation

.
Combining the two equations yields the following ideal transformer identity
.
This formula 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 is defined in terms of secondary circuit voltage and current as follows
.
The apparent impedance of this secondary circuit load referred to the primary winding circuit is governed by a
squared turns ratio multiplication factor relationship derived as follows[6][7]
.
Induction law
The transformer is based on two principles: first, that an electric current can produce a magnetic field and second
that a changing magnetic field within a coil of wire induces a voltage across the ends of the coil (electromagnetic
induction). Changing the current in the primary coil changes the magnetic flux that is developed. The changing
magnetic flux induces a voltage in the secondary coil.
Referring to the two figures here, current passing through the primary coil creates a magnetic field. The primary and
secondary coils are wrapped around a core of very high magnetic permeability, usually iron,[d] so that most of the
magnetic flux passes through both the primary and secondary coils. Any secondary winding connected load causes
current and voltage induction from primary to secondary circuits in indicated directions.
The voltage induced across the secondary coil may be calculated from Faraday's law of induction, which states that:
where Vs = Es is the instantaneous voltage, Ns is the number of turns in the secondary coil, and dΦ/dt is the
derivative[e] of the magnetic flux Φ through one turn of the coil. If the turns of the coil are oriented perpendicularly
to the magnetic field lines, the flux is the product of the magnetic flux density B and the area A through which it cuts.
The area is constant, being equal to the cross-sectional area of the transformer core, whereas the magnetic field
varies with time according to the excitation of the primary. Since the same magnetic flux passes through both the

Ideal transformer and induction law
Instrument transformer, with
polarity dot and X1 markings
on LV side terminal
primary and secondary coils in an ideal transformer,[6] the instantaneous voltage across the primary winding equals
Taking the ratio of the above two equations gives the same voltage ratio and turns ratio relationship shown above,
that is,
.
The changing magnetic field induces an emf
across each winding. [8] The primary emf,
acting as it does in opposition to the
primary voltage, is sometimes termed the
counter emf.[9] This is in accordance with
Lenz's law, which states that induction of
emf always opposes development of any
such change in magnetic field.
As still lossless and perfectly-coupled, the
transformer still behaves as described
above in the ideal transformer.
Polarity
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 at the
secondary winding's dot end.[10][11][12][f][g]
The real transformer
Real transformer deviations from ideal
The ideal model neglects the following basic linear aspects in real transformers:
Core losses collectively called magnetizing current losses consisting of:[15]
Hysteresis losses due to nonlinear application of the voltage
applied in the transformer core
Eddy current losses due to joule heating in core proportional to the
square of the transformer's applied voltage.
Whereas the ideal windings have no impedance, the windings in a real transformer have finite non-zero

Leakage flux of a transformer
impedances in the form of:
Joule losses due to resistance in the primary and secondary windings[15]
Leakage flux that escapes from the core and passes through one winding only resulting in primary and
secondary reactive impedance.
Leakage flux
Main article: Leakage inductance
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.[16] Such flux is termed leakage
flux, and results in leakage inductance in series with the
mutually coupled transformer windings.[9] 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 (see Stray losses
below), but results in inferior voltage regulation, causing the
secondary voltage to not be directly proportional to the
primary voltage, particularly under heavy load.[16]
Transformers are therefore normally designed to have very
low leakage inductance. Nevertheless, it is impossible to
eliminate all leakage flux because it plays an essential part in the operation of the transformer. The combined effect
of the leakage flux and the electric field around the windings is what transfers energy from the primary to the
secondary.[17]
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.[9] Leaky
transformers may be used to supply loads that exhibit negative resistance, such as electric arcs, mercury vapor
lamps, and neon signs or for safely handling loads that become periodically short-circuited such as electric arc
welders.[18]
Air gaps are also used to keep a transformer from saturating, especially audio-frequency transformers in circuits
that have a DC component flowing through the windings.[19]
Knowledge of leakage inductance is for example useful when transformers are operated in parallel. It can be shown
that if the percent impedance (Z) 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.[20][21]
Equivalent circuit

Real transformer equivalent circuit
See also: Steinmetz 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.[22]
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.
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.[23] 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.[23] 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.[22]
The resulting model, though sometimes termed 'exact' equivalent circuit based on linearity assumptions, retains a
number of approximations.[22] 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,[h] short-circuit test, winding resistance test, and transformer ratio test.
Basic transformer parameters and construction

Transformer universal emf equation
If the flux in the core is purely sinusoidal, the
relationship for either winding between its rms
voltage Erms 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:[15]
If the flux does not contain even harmonics the
following equation can be used for half-cycle
average voltage Eavg of any waveshape:
Power transformer over-excitation
condition caused by decreased
frequency; flux (green), iron core's
magnetic characteristics (red) and
magnetizing current (blue).
Effect of frequency
The time-derivative term in Faraday's Law shows that
the flux in the core is the integral with respect to time of
the applied voltage.[25] Hypothetically an ideal
transformer would work with direct-current excitation,
with the core flux increasing linearly with time.[26] In
practice, the flux rises to the point where magnetic
saturation of the core occurs, causing a large increase in
the magnetizing current and overheating the transformer.
All practical transformers must therefore operate with
alternating (or pulsed direct) current.[26]
The emf of a transformer at a given flux density increases
with frequency.[15] 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.[27] 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. As such, the transformers used to step-down the high over-head line
voltages (e.g. 15 kV) were much heavier for the same power rating than those designed only 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
transformer at other than its design frequency may require assessment of
voltages, losses, and cooling to establish if safe operation is practical. For
example, transformers may need to be equipped with 'volts per hertz'
over-excitation relays to protect the transformer from overvoltage at
higher than rated frequency.
One example of state-of-the-art design is traction transformers used for
electric multiple unit and high speed train service operating across
the,country border and using different electrical standards, such
transformers' being restricted to be positioned below the passenger
compartment. The power supply to, and converter equipment being
supply by, such 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 & motors with varying
harmonics mitigation filtering requirements.

Large power transformers are vulnerable to insulation failure due to transient voltages with high-frequency
components, such as caused in switching or by lightning.[28]
Energy losses
An ideal transformer would have no energy losses, and would be 100% efficient. In practical transformers, energy
is dissipated in the windings, core, and surrounding structures. Larger transformers are generally more efficient, and
those rated for electricity distribution usually perform better than 98%.[29]
Experimental transformers using superconducting windings achieve efficiencies of 99.85%.[30] The increase in
efficiency can save considerable energy, and hence money, in a large heavily loaded transformer; the trade-off is in
the additional initial and running cost of the superconducting design.
As transformer losses vary with load, it is often useful to express these losses in terms of no-load loss, full-load loss,
half-load loss, and so on. Hysteresis and eddy current losses are constant at all loads and dominate overwhelmingly
at no-load, 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 and a running cost. Designing
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 so that there is a trade-off between initial cost and running cost (also see
energy efficient transformer).[31]
Transformer losses arise from:
Winding joule losses
Current flowing through winding conductors causes joule heating. As frequency increases, skin effect and
proximity effect causes winding 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.[31][32][33]
Eddy current losses
Ferromagnetic materials are also good conductors and a core made from such a material also
constitutes a single short-circuited turn throughout its entire length. Eddy currents therefore circulate
within the core in a plane normal to the flux, and are responsible for resistive heating of the core
material. The eddy current loss is a complex function of the square of supply frequency and inverse
square of the material thickness.[31] 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

Core form = core type; shell form =
shell type
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.[3][34] This transformer hum is
especially objectionable in transformers supplied at power frequencies[i] and in high-frequency flyback
transformers associated with PAL system 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.[35] 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.[36]
Core form and shell form transformers
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.[37] 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.[37][38][39][40] 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.[40]
Construction
Cores
Laminated steel cores
Transformers for use at power or audio frequencies typically have cores made of high permeability silicon steel.[41]

Laminated core transformer showing
edge of laminations at top of photo
Power transformer inrush current
caused by residual flux at switching
instant; flux (green), iron core's
magnetic characteristics (red) and
magnetizing current (blue).
Laminating the core greatly
reduces eddy-current losses
Transformers for use at power or audio frequencies typically have cores made of high permeability silicon steel.[41]
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.[42] 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.[43] 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.[44] The universal
transformer equation indicates a minimum cross-sectional area for the
core to avoid saturation.
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,[45] but are more laborious and expensive to
construct.[46] 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 steel sheets capped with I-
shaped pieces, leading to its name of
'E-I transformer'.[46] 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.[46] 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.[47] 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.[48]
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.[49]

Small toroidal core transformer
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.[46] 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
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.[50] 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.[18] 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 also 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. 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 physical core is not an absolute requisite and a functioning transformer can be produced simply by placing the
windings near each other, an arrangement termed an 'air-core' transformer. The air which comprises the magnetic
circuit is essentially lossless, and so an air-core transformer eliminates loss due to hysteresis in the core material.[9]
The leakage inductance is inevitably high, resulting in very poor regulation, and so such designs are unsuitable for
use in power distribution.[9] They have however very high bandwidth, and are frequently employed in radio-

Windings are usually arranged
concentrically to minimize flux leakage.
frequency applications,[51] for which a satisfactory coupling coefficient is maintained by carefully overlapping the
primary and secondary windings. They're also used for resonant transformers such as Tesla coils where they can
achieve reasonably low loss in spite of the high leakage inductance.
Windings
Main article: Windings
The conducting material 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.[52] For small power and signal transformers,
in which currents are low and the potential difference between
adjacent turns is small, the coils are often wound from enamelled
magnet wire, such as Formvar wire. Larger power transformers
operating at high voltages may be wound with copper rectangular
strip conductors insulated by oil-impregnated paper and blocks of
pressboard.[53]
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.[25] 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.[53] 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.[53]
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.
Dry-type transformer winding insulation systems can be either of standard open-wound 'dip-and-bake' construction
or of higher quality designs that include vacuum pressure impregnation (VPI), vacuum pressure encapsulation
(VPE), and cast coil encapsulation processes.[54] In the VPI process, a combination of heat, vacuum and pressure
is used to thoroughly seal, bind, and eliminate entrained air voids in the winding polyester resin insulation coat layer,
thus increasing resistance to corona. VPE windings are similar to VPI windings but provide more protection against
environmental effects, such as from water, dirt or corrosive ambients, by multiple dips including typically in terms of
final epoxy coat.[55]

Cut view through transformer windings.
White: insulator. Green spiral: Grain
oriented silicon steel. Black: Primary
winding made of oxygen-free copper. Red:
Secondary winding. Top left: Toroidal
transformer. Right: C-core, but E-core
would be similar. The black windings are
made of film. Top: Equally low capacitance
between all ends of both windings. Since
most cores are at least moderately
conductive they also need insulation.
Bottom: Lowest capacitance for one end of
the secondary winding needed for low-
power high-voltage transformers. Bottom
left: Reduction of leakage inductance
would lead to increase of capacitance.
Cutaway view of liquid-
immersed construction
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 balance.
Cooling
See also: Arrhenius equation
To place the cooling problem in
perspective, the accepted rule of
thumb is that the life expectancy
of insulation in all electric
machines including all
transformers is halved for about
every 7°C to 10°C increase in
operating temperature, this life
expectancy halving rule holding
more narrowly when the
increase is between about 7°C
to 8°C in the case of transformer
winding cellulose
insulation.[56][57][58]
Small dry-type and liquid-
immersed transformers are often
self-cooled by natural
convection and radiation heat
dissipation. As power ratings
increase, transformers are often
cooled by forced-air cooling,
forced-oil cooling, water-
cooling, or combinations of
these.[59] Large transformers are
filled with transformer oil that
both cools and insulates the windings.[60] 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.[61][62] 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.[56] With a great body of empirical study
as a guide, transformer oil testing including dissolved gas analysis provides valuable maintenance information. This
can translate in a need to monitor, model, forecast and manage oil and winding conductor insulation temperature
conditions under varying, possibly difficult, power loading conditions.[63][64]
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.[65] 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.[60] 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.[47] 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.[66] 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.[65][67] PCBs for new equipment was banned in 1981 and in 2000 for use in existing
equipment in United Kingdom[68] 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.[69]
Some transformers, instead of being liquid-filled, have their windings enclosed in sealed, pressurized tanks and
cooled by nitrogen or sulfur hexafluoride gas.[67]
Experimental power transformers in the 500-to-1,000 kVA range have been built with liquid nitrogen or helium
cooled superconducting windings, which, compared to usual transformer losses, eliminates winding losses without
affecting core losses.[70][71]
Insulation drying
Construction of oil-filled transformers requires that the insulation covering the windings be thoroughly dried of
residual moisture before the oil is introduced. Drying is carried out at the factory, and may also be required as a
field service. Drying may be done by circulating hot air around the core, 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. The heating can be
controlled very well, and it is energy efficient. The method is called low-frequency heating (LFH) since the current is
injected at a much lower frequency than the nominal of the power grid, which is normally 50 or 60 Hz. A lower
frequency reduces the effect of the inductance in the transformer, so the voltage needed to induce the current can
be reduced.[72] The LFH drying method is also used for service of older transformers.[73]
Bushings
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.[74]
Classification parameters
Transformers can be classified in many ways, such as the following:
Power capacity: 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: Power-frequency, audio-frequency, or radio-frequency.
Voltage class: From a few volts to hundreds of kilovolts.
Cooling type: Dry and liquid-immersed - self-cooled, forced air-cooled; liquid-immersed - forced oil-
cooled, water-cooled.
Circuit application: Such as power supply, impedance matching, output voltage and current stabilizer or
circuit isolation.
Utilization: Pulse, power, distribution, rectifier, arc furnace, amplifier output, etc..
Basic magnetic form: Core form, shell form.
Constant-potential transformer descriptor: Step-up, step-down, isolation.
General winding configuration: By EIC vector group - various possible two-winding combinations of the
phase designations delta, wye or star, and zigzag or interconnected star;[j] other - autotransformer, Scott-T,
zigzag grounding transformer winding.[75][76][77][78]
Rectifier phase-shift winding configuration: 2-winding, 6-pulse; 3-winding, 12-pulse; . . . n-winding, [n-
1]*6-pulse; polygon; etc..
Types
For more details, see Transformer types or specific main articles, as shown.
A wide variety of transformer designs are used for different applications, though they share several common
features. Important common transformer types include:
Autotransformer: Transformer in which part of the winding is common to both primary and secondary
circuits.[79]
Capacitor voltage transformer: Transformer in which capacitor divider is used to reduce high voltage
before application to the primary winding.
Distribution transformer, power transformer: International standards make a distinction in terms of
distribution transformers being used to distribute energy from transmission lines and networks for local
consumption and power transformers being used to transfer electric energy between the generator and
distribution primary circuits.[79][80][k]
Phase angle regulating transformer: A specialised transformer used to control the flow of real power on
three-phase electricity transmission networks.
Scott-T transformer: Transformer used for phase transformation from three-phase to two-phase and vice
versa.[79]
Polyphase transformer: Any transformer with more than one phase.
Grounding transformer: Transformer used for grounding three-phase circuits to create a neutral in a three
wire system, using a wye-delta transformer,[76][81] or more commonly, a zigzag grounding winding.[76][78][79]
Leakage transformer: Transformer that has loosely coupled windings.
Resonant transformer: Transformer that uses resonance to generate a high secondary voltage.
Audio transformer: Transformer used in audio equipment.
Output transformer: Transformer used to match the output of a valve amplifier to its load.
Instrument transformer: Potential or current transformer used to accurately and safely represent voltage,
current or phase position of high voltage or high power circuits.[79]
Applications

An electrical substation in Melbourne, Australia
showing 3 of 5 220kV/66kV transformers, each
with a capacity of 150 MVA.[82]
Transformer at the Limestone
Generating Station in Manitoba,
Canada
Transformers are used to increase 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.[83] 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.[35]
Transformers are also used extensively in electronic products to step-down the supply voltage to a level suitable for
the low voltage circuits they contain. The transformer also electrically isolates the end user from contact with the
supply voltage.
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.
History
Discovery of induction phenomenon
The principle behind the operation of a transformer, electromagnetic induction, was discovered independently by
Michael Faraday and Joseph Henry in 1831. However, Faraday was the first to publish the results of his
experiments and thus receive credit for the discovery.[85] 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.[86]

Faraday's experiment with induction between
coils of wire[84]
Faraday's ring transformer
Induction coil, 1900, Bremerhavn,
Germany
Faraday performed the first 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.[87]
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 (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.
Early devices for use with alternating current
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 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.[88]
[89] The coils Yablochkov employed functioned essentially as
transformers.[88]
In 1878, the Ganz factory, Budapest, Hungary, began manufacturing
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.[90]
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.[43] They also exhibited the invention in Turin, Italy
in 1884, where it was adopted for an electric lighting system.[91] However, the efficiency of their open-core bipolar
apparatus remained very low.[91]
Early series circuit transformer distribution

Shell form transformer. Sketch used
by Uppenborn to describe ZBD
engineers' 1885 patents and earliest
articles.[91]
Core form, front; shell form, back.
Earliest specimens of ZBD-designed
high-efficiency constant-potential
transformers manufactured at the
Ganz factory in 1885.
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.[91] 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.[92]
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.[94] 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.[91] 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).[37][95][96][38] 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.[97] 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.[97]
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.[98] 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).[99][100]
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.[101][102] Bláthy had suggested the use of closed cores, Zipernowsky had
suggested the use of parallel shunt connections, and Déri had performed the experiments;[103]

The ZBD team consisted of Károly
Zipernowsky, Ottó Bláthy and Miksa
Déri
Stanley's 1886 design for adjustable
gap open-core induction coils[93]
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,[101][104] although the term had
already been in use by 1882.[105][106] 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.[107]
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.[108]
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).[93] This design[109] was first used commercially in
the US in 1886[92] but Westinghouse was intent on improving the
Stanley design to make it (unlike the ZBD type) easy and cheap to
produce.[109]
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.[103][110]
Other early transformers
In 1889, Russian-born engineer Mikhail Dolivo-Dobrovolsky developed the first three-phase transformer at the
Allgemeine Elektricitäts-Gesellschaft ('General Electricity Company') in Germany.[111]
In 1891, Nikola Tesla invented the Tesla coil, an air-cored, dual-tuned resonant transformer for generating very
high voltages at high-frequency.[112][113]
See also
Magnetization
Inductor
Polyphase system
Load profile
Magnetic core

Geomagnetic storm
Paraformer
Rectiformer
Switched-mode power supply
Electronic symbol
Notes
a. ^ "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",[5] common usage having evolved over time from 'turn ratio' to 'turns ratio',
b. ^ 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.
c. ^ As each ideal transformer winding's impressed voltage equals its induced voltage, induced voltages are omitted
for clarity in the next four equations.
d. ^ Transformer winding coils are usually wound around ferromagnetic cores but can also be air-core wound.
e. ^ 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.
f. ^ ANSI/IEEE C57.13, ANS Requirements for Instrument Transformers, defines polarity as the 'designation 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.[13]
g. ^ 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.[14]
h. ^ 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.[24]
i. ^ 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.[34]
j. ^ 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.
k. ^ 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.
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Daniels, A.R. (1985). Introduction to Electrical Machines. Macmillan. ISBN 0-333-19627-9.
Flanagan, William M. (1993). Handbook of Transformer Design & Applications (2nd ed.). McGraw-Hill.
ISBN 0-07-021291-0.
Gottlieb, Irving (1998). Practical Transformer Handbook: for Electronics, Radio and Communications
Engineers (http://books.google.ca/books?
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Hammond, John Winthrop (1941). Men and Volts: The Story of General Electric
(http://archive.org/details/menandvoltsstory00hammrich). J.B.Lippincott Company. pp. see esp. 106–107,
178, 238.
Harlow, James (2004). Electric Power Transformer Engineering (http://books.google.ca/books?
id=THO9U9f2m9EC&printsec=frontcover&source=gbs_ge_summary_r&cad=0#v=onepage&q&f=false).
CRC Press. ISBN 0-8493-1704-5.
Heathcote, Martin (1998). J & P Transformer Book (http://books.google.ca/books?
id=paPKsOXn5FMC&printsec=frontcover&source=gbs_ge_summary_r&cad=0#v=onepage&q&f=false)
(12th ed.). Newnes. ISBN 0-7506-1158-8.
Hindmarsh, John (1977). Electrical Machines and Their Applications (4th ed.). Exeter: Pergammon.
ISBN 0-08-030573-3.
Kulkarni, S.V.; Khaparde, S.A. (2004). Transformer Engineering: Design and Practice
id=qy4QT0BlV0MC&printsec=frontcover&source=gbs_ge_summary_r&cad=0#v=onepage&q&f=false).
CRC Press. ISBN 0-8247-5653-3.
McLaren, Peter (1984). Elementary Electric Power and Machines. Ellis Horwood. ISBN 0-470-20057-
X.
McLyman, Colonel William (2004). Transformer and Inductor Design Handbook
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Pansini, Anthony (1999). Electrical Transformers and Power Equipment
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External links
Inside Transformers, composed by J. B. Calvert, from Denver University
(http://www.du.edu/~jcalvert/tech/transfor.htm)
Substation and Transmission
(http://www.dmoz.org/Business/Electronics_and_Electrical/Substation_and_Transmission//) at the Open
Directory Project
Introduction to Current Transformers (http://www.elkor.net/pdfs/AN0305-Current_Transformers.pdf)
Transformer (Interactive Java applet) (http://www.phy.hk/wiki/englishhtm/Transformer.htm), 'Physics is fun'
by Chui-king Ng
HD video tutorial on transformers (http://www.afrotechmods.com/videos/transformer_tutorial.htm)
Three-phase transformer circuits (http://www.allaboutcircuits.com/vol_2/chpt_10/6.html) from All About
Circuits
Bibliography of Transformer Books (http://www.transformerscommittee.org/info/Bibliographybooks.pdf) by
P.M. Balma, from IEEE Transformer Committee
Einschalten des Transformators. German Wikipedia article about transformer inrush current at switch on (in
German).
Retrieved from "http://en.wikipedia.org/w/index.php?title=Transformer&oldid=565548513"
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