Three-phase pole-mounted step-down transformer.

A transformer is a device that transfers electrical energy from one circuit to another through inductively coupled electrical conductors. Electric energy is the potential energy associated with the conservative Coulomb forces between Charged particles contained within a system, where An electrical network is an interconnection of Electrical elements such as Resistors Inductors Capacitors Transmission lines Voltage In Electronics, change in current flow through one device induces current flow in the other device In Science and engineering, a conductor is a material which contains movable Electric charges. A changing current in the first circuit (the primary) creates a changing magnetic field; in turn, this magnetic field induces a changing voltage in the second circuit (the secondary). Electric current is the flow (movement of Electric charge. The SI unit of electric current is the Ampere. Faraday's law of induction describes an important basic law of electromagnetism which is involved in the working of Transformers Inductors and many forms of By adding a load to the secondary circuit, one can make current flow in the transformer, thus transferring energy from one circuit to the other. If an electric circuit has a well-defined output terminal the circuit connected to this terminal (or its Input impedance) is the load.

The secondary induced voltage V_S, of an ideal transformer, is scaled from the primary V_P by a factor equal to the ratio of the number of turns of wire in their respective windings:

By appropriate selection of the numbers of turns, a transformer thus allows an alternating voltage to be stepped up — by making N_S more than N_P — or stepped down, by making it less. An alternating current ( AC) is an Electric current whose direction reverses cyclically as opposed to Direct current, whose direction remains constant

Transformers are some of the most efficient electrical 'machines',^[1] with some large units able to transfer 99. The efficiency of an entity (a device, component, or System) in Electronics and Electrical engineering is defined as useful 75% of their input power to their output. ^[2] Transformers come in a range of sizes from a thumbnail-sized coupling transformer hidden inside a stage microphone to huge units weighing hundreds of tons used to interconnect portions of national power grids. Electric power transmission, a process in the delivery of Electricity to consumers is the bulk transfer of electrical power All operate with the same basic principles, though a variety of designs exist to perform specialized roles throughout home and industry.

Applications

A key application of transformers is to increase voltage before transmitting electrical energy over long distances through wires. Electric power transmission, a process in the delivery of Electricity to consumers is the bulk transfer of electrical power A wire is a single usually cylindrical, elongated string of drawn Metal. Most wires have resistance and so dissipate electrical energy at a rate proportional to the square of the current through the wire. Electrical resistance is a ratio of the degree to which an object opposes an Electric current through it measured in Ohms Its reciprocal quantity is By transforming electrical power to a high-voltage (and therefore low-current) form for transmission and back again afterwards, transformers enable economic transmission of power over long distances. In Physics, power (symbol P) is the rate at which work is performed or energy is transmitted or the amount of energy required or expended for Electric power transmission, a process in the delivery of Electricity to consumers is the bulk transfer of electrical power Consequently, transformers have shaped the electricity supply industry, permitting generation to be located remotely from points of demand. In Electricity generation, an electrical generator is a device that converts Mechanical energy to Electrical energy, generally using Electromagnetic If an electric circuit has a well-defined output terminal the circuit connected to this terminal (or its Input impedance) is the load. ^[3] All but a fraction of the world's electrical power has passed through a series of transformers by the time it reaches the consumer. Electric power is defined as the rate at which Electrical energy is transferred by an Electric circuit. ^[4] Transformers are used extensively in consumer electronic products to step down the supply voltage to a level suitable for the low voltage circuits they contain. In these kind of applications the transformer may also act as a key safety component that electrically isolates the end user from direct contact with the potentially lethal supply voltage.

Signal and audio transformers are used to couple stages of amplifiers and to match devices such as microphones and record player cartridges to the input impedance of amplifiers. Audio transformers allowed telephone circuits to carry on a two-way conversation over a single pair of wires. Transformers are also used when it is necessary to couple a differential-mode signal to a ground-referenced signal, and for isolation between external cables and internal circuits.

Basic principles

The transformer is based on two principles: firstly that an electric current can produce a magnetic field (electromagnetism) and secondly that a changing magnetic field within a coil of wire induces a voltage across the ends of the coil (electromagnetic induction). Electric current is the flow (movement of Electric charge. The SI unit of electric current is the Ampere. In Physics, a magnetic field is a Vector field that permeates space and which can exert a magnetic force on moving Electric charges Electromagnetism is the Physics of the Electromagnetic field: a field which exerts a Force on particles that possess the property of Faraday's law of induction describes an important basic law of electromagnetism which is involved in the working of Transformers Inductors and many forms of By changing the current in the primary coil, it changes the strength of its magnetic field; since the changing magnetic field extends into the secondary coil, a voltage is induced across the secondary.

An ideal step-down transformer showing magnetic flux in the core

A simplified transformer design is shown to the left. A current passing through the primary coil creates a magnetic field. In Physics, a magnetic field is a Vector field that permeates space and which can exert a magnetic force on moving Electric charges The primary and secondary coils are wrapped around a core of very high magnetic permeability, such as iron; this ensures that most of the magnetic field lines produced by the primary current are within the iron and pass through the secondary coil as well as the primary coil. In Electromagnetism, permeability is the degree of Magnetization of a material that responds linearly to an applied Magnetic field. Iron (ˈаɪɚn is a Chemical element with the symbol Fe (ferrum and Atomic number 26

Induction law

The voltage induced across the secondary coil may be calculated from Faraday's law of induction, which states that:

where V_S is the instantaneous voltage, N_S is the number of turns in the secondary coil and Φ equals the magnetic flux through one turn of the coil. Faraday's law of induction describes an important basic law of electromagnetism which is involved in the working of Transformers Inductors and many forms of Electrical tension (or voltage after its SI unit, the Volt) is the difference of electrical potential between two points of an electrical Magnetic flux, represented by the Greek letter Φ ( Phi) is a measure of quantity of Magnetism, taking into account the strength and the extent of a Magnetic If the turns of the coil are oriented perpendicular to the magnetic field lines, the flux is the product of the magnetic field strength B and the area A through which it cuts. In Physics, a magnetic field is a Vector field that permeates space and which can exert a magnetic force on moving Electric charges 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 primary and secondary coils in an ideal transformer,^[1] the instantaneous voltage across the primary winding equals

Taking the ratio of the two equations for V_S and V_P gives the basic equation^[5] for stepping up or stepping down the voltage

Ideal power equation

The ideal transformer as a circuit element

If the secondary coil is attached to a load that allows current to flow, electrical power is transmitted from the primary circuit to the secondary circuit. Ideally, the transformer is perfectly efficient; all the incoming energy is transformed from the primary circuit to the magnetic field and into the secondary circuit. In Physics, a magnetic field is a Vector field that permeates space and which can exert a magnetic force on moving Electric charges If this condition is met, the incoming electric power must equal the outgoing power. Electric power is defined as the rate at which Electrical energy is transferred by an Electric circuit.

P_incoming = I_PV_P = P_outgoing = I_SV_S

giving the ideal transformer equation

If the voltage is increased (stepped up) (V_S > V_P), then the current is decreased (stepped down) (I_S < I_P) by the same factor. Transformers are efficient so this formula is a reasonable approximation.

The impedance in one circuit is transformed by the square of the turns ratio. ^[1] For example, if an impedance Z_S is attached across the terminals of the secondary coil, it appears to the primary circuit to have an impedance of . This relationship is reciprocal, so that the impedance Z_P of the primary circuit appears to the secondary to be .

Detailed operation

The simplified description above neglects several complicating factors, in particular the primary current required to establish a magnetic field in the core, and the contribution to the field due to current in the secondary circuit.

Models of an ideal transformer typically assume a core of negligible reluctance with two windings of zero resistance. Magnetic reluctance or "magnetic resistance" is analogous to resistance in an Electrical Circuit (although it does not dissipate magnetic Electrical resistance is a ratio of the degree to which an object opposes an Electric current through it measured in Ohms Its reciprocal quantity is ^[6] When a voltage is applied to the primary winding, a small current flows, driving flux around the magnetic circuit of the core. Magnetic flux, represented by the Greek letter Φ ( Phi) is a measure of quantity of Magnetism, taking into account the strength and the extent of a Magnetic A magnetic circuit is a closed path containing a Magnetic flux. ^[6]. The current required to create the flux is termed the magnetising current; since the ideal core has been assumed to have near-zero reluctance, the magnetising current is negligible, although still required to create the magnetic field.

The changing magnetic field induces an electromotive force (EMF) across each winding. Electromotive force ( emf, \mathcal{E} is a term used to characterize electrical devices such as Voltaic cells thermoelectric devices electrical ^[7] Since the ideal windings have no impedance, they have no associated voltage drop, and so the voltages V_P and V_S measured at the terminals of the transformer, are equal to the corresponding EMFs. The primary EMF, acting as it does in opposition to the primary voltage, is sometimes termed the "back EMF". The counter-electromotive force (abbreviated counter emf, or CEMF) is the Voltage, or Electromotive force, that pushes against the current ^[8] This is due to Lenz's law which states that the induction of EMF would always be such that it will oppose development of any such change in magnetic field. Lenz's law (ˈlɛntsɨz ˌlɔː gives the direction of the induced Electromotive force (emf and current resulting from Electromagnetic induction.

Practical considerations

Flux leakage in a two-winding transformer

Flux leakage

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. Leakage inductance is that property of an electrical Transformer that causes a winding to appear to have some inductance in series with the mutually-coupled In practice, some flux traverses paths that take it outside the windings. ^[9] Such flux is termed leakage flux, and results in self-inductance in series with the mutually coupled transformer windings. In Electrical circuits, any Electric current i produces a Magnetic field and hence generates a total Magnetic flux \Phi acting If two or more circuit components are connected end to end like a daisy chain it is said they are connected in series. ^[8] Leakage results in energy being alternately stored in and discharged from the magnetic fields with each cycle of the power supply. In Physics, a magnetic field is a Vector field that permeates space and which can exert a magnetic force on moving Electric charges It is not directly a power loss, but results in inferior voltage regulation, causing the secondary voltage to fail to be directly proportional to the primary, particularly under heavy load. In Electrical engineering, particularly Power engineering, voltage regulation is the ability of a system to provide near constant Voltage over a wide range ^[9] Distribution transformers are therefore normally designed to have very low leakage inductance. Leakage inductance is that property of an electrical Transformer that causes a winding to appear to have some inductance in series with the mutually-coupled

However, in some applications, leakage can be a desirable property, and long magnetic paths, air gaps, or magnetic bypass shunts may be deliberately introduced to a transformer's design to limit the short-circuit current it will supply. Short Circuit is a 1986 comedy Science fiction film starring Ally Sheedy and Steve Guttenberg and directed by ^[8] 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. Negative resistance (or negative differential resistance (NDR or differential negative resistance (DNR is a property of Electrical circuit elements composed An electric arc is an Electrical breakdown of a gas which produces an ongoing plasma discharge, resulting from a current flowing through normally nonconductive Neon signs are luminous-tube signs that contain neon or other inert gases at a low pressure Arc welding uses a Welding power supply to create an Electric arc between an electrode and the base material to melt the metals at the welding point ^[10] Air gaps are also used to keep a transformer from saturating, especially audio-frequency transformers in circuits that have a direct current flowing through the windings.

Effect of frequency

The time-derivative term in Faraday's Law shows that the flux in the core is the integral of the applied voltage. Faraday's law of induction describes an important basic law of electromagnetism which is involved in the working of Transformers Inductors and many forms of The European Space Agency 's INTErnational Gamma-Ray Astrophysics Laboratory ( INTEGRAL) is detecting some of the most energetic radiation that comes from space ^[11] Hypothetically an ideal transformer would work with direct-current excitation, with the core flux increasing linearly with time. ^[12] In practice, the flux would rise very rapidly to the point where magnetic saturation of the core occurred, causing a huge increase in the magnetising current and overheating the transformer. Seen in some Magnetic materials saturation is the state reached when an increase in applied external Magnetizing field H cannot increase the All practical transformers must therefore operate under alternating (or pulsed) current conditions. ^[12]

The EMF of a transformer at a given flux density increases with frequency. In Mathematics, the root mean square (abbreviated RMS or rms) also known as the quadratic mean, is a statistical measure of the In Physics, a magnetic field is a Vector field that permeates space and which can exert a magnetic force on moving Electric charges ^[6] 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. The skin effect is the tendency of an alternating electric current (AC to distribute itself within a conductor so that the current density near the surface of the Aircraft and military equipment employ 400 Hz power supplies which reduce core and winding weight. ^[13]

Operation of a transformer at its designed voltage but at a higher frequency than intended will lead to reduced magnetising current. At a frequency lower than the design value, with the rated voltage applied, the magnetising current 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. A relay is an electrical Switch that opens and closes under the control of another Electrical circuit.

Knowledge of natural frequencies of transformer windings is of importance for the determination of the transient response of the windings to impulse and switching surge voltages.

Energy losses

An ideal transformer would have no energy losses, and would therefore 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%. ^[14]

Experimental transformers using superconducting windings achieving efficiencies of 99. Superconductivity is a phenomenon occurring in certain Materials generally at very low Temperatures characterized by exactly zero electrical resistance 85%,^[15] While the increase in efficiency is small, when applied to large heavily-loaded transformers the annual savings in energy losses is significant.

A small transformer, such as a plug-in "wall wart" type used for low-power consumer electronics, may be no more than 85% efficient; although individual power loss is small, the aggregate losses from the very large number of such devices is coming under increased scrutiny. Wall wart is a Slang term for certain types of Power supply - typically those that are embedded in an over-sized AC plug. ^[16]

The losses vary with load current, and may be expressed as "no-load" or "full-load" loss. Winding resistance dominates load losses, whereas hysteresis and eddy currents losses contribute to over 99% of the no-load loss. Electrical resistance is a ratio of the degree to which an object opposes an Electric current through it measured in Ohms Its reciprocal quantity is A system with hysteresis can be summarised as a system that may be in any number of states independent of the inputs to the system An eddy current (also known as Foucault current) is an electrical phenomenon discovered by French physicist Léon Foucault in The no-load loss can be significant, meaning that even an idle transformer constitutes a drain on an electrical supply, which encourages development of low-loss transformers (also see energy efficient transformer). In a typical grid electric Transformer loss typically contributes about 40-50% of the total transmission & distribution loss ^[17]

Transformers are among the most efficient of machines, but all exhibit losses

Transformer losses are divided into losses in the windings, termed copper loss, and those in the magnetic circuit, sometimes termed iron loss. Copper loss is the term often given to Heat produced by Electrical currents in the conductors of Transformer windings or other electrical devices Core loss (or iron loss) is a form of Energy loss that occurs in electrical Transformers and other Inductors The loss is due to a variety of Losses in the transformer arise from:

Winding resistance

Current flowing through the windings causes resistive heating of the conductors. Joule heating is the process by which the passage of an Electric current through a conductor releases Heat. At higher frequencies, skin effect and proximity effect create additional winding resistance and losses. The skin effect is the tendency of an alternating electric current (AC to distribute itself within a conductor so that the current density near the surface of the In a conductor carrying current if currents are flowing through one or more other nearby conductors such as within a closely wound coil of wire the distribution of current within the first

Hysteresis losses

Each time the magnetic field is reversed, a small amount of energy is lost due to hysteresis within the core. A system with hysteresis can be summarised as a system that may be in any number of states independent of the inputs to the system For a given core material, the loss is proportional to the frequency, and is a function of the peak flux density to which it is subjected. ^[17]

Eddy currents

Ferromagnetic materials are also good conductors, and a solid core made from such a material also constitutes a single short-circuited turn throughout its entire length. Ferromagnetism is the basic mechanism by which certain materials (such as Iron) form Permanent magnets and/or exhibit strong interactions with Magnets it In Science and engineering, a conductor is a material which contains movable Electric charges. Eddy currents therefore circulate within the core in a plane normal to the flux, and are responsible for resistive heating of the core material. An eddy current (also known as Foucault current) is an electrical phenomenon discovered by French physicist Léon Foucault in Joule heating is the process by which the passage of an Electric current through a conductor releases Heat. The eddy current loss is a complex function of the square of supply frequency and inverse square of the material thickness. ^[17]

Magnetostriction

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 is a property of Ferromagnetic materials that causes them to change their shape when subjected to a Magnetic field. This produces the buzzing sound commonly associated with transformers,^[5] and in turn causes losses due to frictional heating in susceptible cores.

Mechanical losses

In addition to magnetostriction, the alternating magnetic field causes fluctuating electromagnetic forces between the primary and secondary windings. These incite vibrations within nearby metalwork, adding to the buzzing noise, and consuming a small amount of power. ^[18]

Stray losses

Leakage inductance is by itself 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. ^[4]

Equivalent circuit

Refer to the diagram below

The physical limitations of the practical transformer may be brought together as an equivalent circuit model (shown below) built around an ideal lossless transformer. ^[19] Power loss in the windings is current-dependent and is easily represented as in-series resistances R_P and R_S. Flux leakage results in a fraction of the applied voltage dropped without contributing to the mutual coupling, and thus can be modeled as self-inductances X_P and X_S in series with the perfectly-coupled region. In Electrical circuits, any Electric current i produces a Magnetic field and hence generates a total Magnetic flux \Phi acting

Iron losses are caused mostly by hysteresis and eddy current effects in the core, and tend to be proportional to the square of the core flux for operation at a given frequency. ^[20] Since the core flux is proportional to the applied voltage, the iron loss can be represented by a resistance R_C in parallel with the ideal transformer.

A core with finite permeability requires a magnetizing current I_M to maintain the mutual flux in the core. In Electromagnetism, permeability is the degree of Magnetization of a material that responds linearly to an applied Magnetic field. The magnetizing current is in phase with the flux; saturation effects cause the relationship between the two to be non-linear, but for simplicity this effect tends to be ignored in most circuit equivalents. ^[20] With a sinusoidal supply, the core flux lags the induced EMF by 90° and this effect can be modeled as a magnetising reactance X_M in parallel with the core loss component. If two or more circuit components are connected end to end like a daisy chain it is said they are connected in series. R_C and X_M are sometimes together termed the magnetising branch of the model. If the secondary winding is made open-circuit, the current I₀ taken by the magnetising branch represents the transformer's no-load current. ^[19]

The secondary impedance R_S and X_S is frequently moved (or "referred") to the primary side after multiplying the components by the impedance scaling factor . Electrical impedance, or simply impedance, describes a measure of opposition to a sinusoidal Alternating current (AC

Transformer equivalent circuit, with secondary impedances referred to the primary side

The resulting model is sometimes termed the "exact equivalent circuit", though it retains a number of approximations, such as an assumption of linearity. The word linear comes from the Latin word linearis, which means created by lines. ^[19] Analysis may be simplified by moving the magnetising branch to the left of the primary impedance, an implicit assumption that the magnetising current is low, and then summing primary and referred secondary impedances, resulting in so-called equivalent impedance.

The parameters of equivalent circuit of a transformer can be calculated from the results of two transformer tests: open-circuit test and short-circuit test. Open circuit test, sometimes called no-load test is one of the methods used in Electrical engineering to determine the value of the Impedance in the Excitation

Types

For more details on this topic, see Transformer types. Power transformers Laminated core This is the most

A variety of specialised transformer designs has been created to fulfill certain engineering applications, though they share several commonalities. Several of the more important transformer types include:

Autotransformer

Main article: Autotransformer

An autotransformer with a sliding brush contact

An autotransformer has only a single winding with two end terminals, plus a third at an intermediate tap point. An autotransformer (sometimes called autoformer) is an electrical Transformer with only one winding. An autotransformer (sometimes called autoformer) is an electrical Transformer with only one winding. An autotransformer (sometimes called autoformer) is an electrical Transformer with only one winding. The primary voltage is applied across two of the terminals, and the secondary voltage taken from one of these and the third terminal. The primary and secondary circuits therefore have a number of windings turns in common. ^[21] Since the volts-per-turn is the same in both windings, each develops a voltage in proportion to its number of turns. By exposing part of the winding coils and making the secondary connection through a sliding brush, an autotransformer with a near-continuously variable turns ratio is obtained, allowing for very fine control of voltage. A brush is a device which conducts current between stationary Wires and moving parts most commonly in a rotating Shaft. ^[22]

Polyphase transformers

For more details on this topic, see Three-phase electric power. This article deals with where how and why "three phase" is used

For three-phase supplies, a bank of three individual single-phase transformers can be used, or all three phases can be incorporated as a single three-phase transformer. This article deals with the basic mathematics and principles of three-phase electricity In this case, the magnetic circuits are connected together, the core thus containing a three-phase flow of flux. ^[23] A number of winding configurations are possible, giving rise to different attributes and phase shifts. The phase of an oscillation or wave is the fraction of a complete cycle corresponding to an offset in the displacement from a specified reference point at time t = 0 ^[24] One particular polyphase configuration is the zigzag transformer, used for grounding and in the suppression of harmonic currents. A Zigzag transformer is a special purpose Transformer. It has primary windings but no secondary winding In Electrical engineering, the term ground or earth has several meanings depending on the specific application areas In Acoustics and Telecommunication, the harmonic of a Wave is a component Frequency of the signal that is an Integer ^[25]

Resonant transformers

A resonant transformer uses the inductance of its windings in combination with external capacitors connected in series or parallel with the windings, and/or the capacitance of the windings themselves, to create one or more resonant circuits. Electrical resonance occurs in an electric circuit at a particular resonance frequency when the impedance between the input and output of the An LC circuit is a variety of resonant circuit or tuned circuit and consists of an Inductor, represented by the letter L and a Capacitor, represented For example, it may use the inductance of the primary winding in series with a capacitor. Resonance can aid in achieving a very high voltage across the secondary. Resonant transformers such as the Tesla coil can generate very high voltages, and are able to provide much higher current than electrostatic high-voltage generation machines such as the Van de Graaff generator. A Tesla coil is a type of resonant transformer circuit invented by Serbian-American scientist Nikola Tesla around 1891 A Van de Graaff generator is an electrostatic machine which uses a moving belt to accumulate very high electrostatically stable Voltages on a hollow metal globe ^[26] Another application of the resonant transformer is to couple between stages of a superheterodyne receiver, where the selectivity of the receiver is provided by tuned transformers in the intermediate-frequency amplifiers. In Electronics, the superheterodyne receiver (also known by its full name the supersonic heterodyne receiver, or by the abbreviated form superhet) is a ^[27]

Leakage transformers

A leakage transformer, also called a stray-field transformer, has a significantly higher leakage inductance than other transformers, sometimes increased by a magnetic bypass or shunt in its core between primary and secondary, which is sometimes adjustable with a set screw. Leakage inductance is that property of an electrical Transformer that causes a winding to appear to have some inductance in series with the mutually-coupled This provides a transformer with an inherent current limitation due to the loose coupling between its primary and the secondary windings. The output and input currents are low enough to prevent thermal overload under all load conditions – even if the secondary is shorted.

Leakage transformers are used for arc welding and high voltage discharge lamps (cold cathode fluorescent lamps, which are series-connected up to 7. Arc welding uses a Welding power supply to create an Electric arc between an electrode and the base material to melt the metals at the welding point A cold cathode is an element used within some Nixie tubes Gas discharge lamps Gas filled tubes and Vacuum tubes Cold cathodes do not 5 kV AC). It acts then both as a voltage transformer and as a magnetic ballast. An electrical ballast (sometimes called control gear) is a device intended to limit the amount of current in an electric

Other applications are short-circuit-proof extra-low voltage transformers for toys or doorbell installations. In Electricity supply, using extra-low voltage ( ELV) is one of several means to protect against Electrical shock. A doorbell is a signaling device commonly found near a Door. It commonly emits a ringing sound to alert the occupant of the building to a visitor's presence

Instrument transformers

Current transformers, designed to be looped around conductors

A current transformer is a measurement device designed to provide a current in its secondary coil proportional to the current flowing in its primary. A current transformer ( CT) is a type of instrument Transformer designed to provide a current in its secondary winding proportional to the alternating current Current transformers are commonly used in metering and protective relaying, where they facilitate the safe measurement of large currents. Power system protection is that part of electrical Power engineering that deals with protecting the electrical power system from faults by isolating the faulted part from the The current transformer isolates measurement and control circuitry from the high voltages typically present on the circuit being measured. ^[28]

Voltage transformers (VTs)--also referred to as Potential transformers (PTs)--are used for metering and protection in high-voltage circuits. They are designed to present negligible load to the supply being measured and to have a precise voltage ratio to accurately step down high voltages so that metering and protective relay equipment can be operated at a lower potential. ^[29]

Classification

The many uses to which transformers are put leads them to be classified in a number of different ways:

• By power level: from a fraction of a volt-ampere (VA) to over a thousand MVA;
• By frequency range: power-, audio-, or radio frequency;
• By voltage class: from a few volts to hundreds of kilovolts;
• By cooling type: air cooled, oil filled, fan cooled, or water cooled;
• By application function: such as power supply, impedance matching, output voltage and current stabilizer, or circuit isolation;
• By end purpose: distribution, rectifier, arc furnace, amplifier output;
• By winding turns ratio: step-up, step-down, isolating (near equal ratio), variable. A volt-ampere in electrical terms means the amount of Apparent power in an Alternating current circuit equal to a current of one Ampere at an The utility frequency ( American English) or mains frequency ( British English) is the Frequency at which Alternating current (AC is An audio frequency (abbreviation AF) or audible frequency is characterized as a periodic vibration whose Frequency is audible to the average human Radio frequency ( RF) is a Frequency or rate of Oscillation within the range of about 3 Hz to 300 GHz Electricity distribution is the penultimate stage in the delivery (before retail) of Electricity to end users A rectifier is an electrical device that converts Alternating current (AC to Direct current (DC a process known as rectification. An electric arc furnace (EAF is a Furnace that heats charged material by means of an Electric arc.

Construction

Cores

Laminated core transformer showing edge of laminations at top of unit.

Laminated steel cores

Transformers for use at power or audio frequencies typically have cores made of high permeability silicon steel. In Electromagnetism, permeability is the degree of Magnetization of a material that responds linearly to an applied Magnetic field. Electrical steel, also called lamination steel, silicon electrical steel, silicon steel or transformer steel, is specialty Steel tailored ^[30] The steel has a permeability many times that of free space, and the core thus serves to greatly reduce the magnetising current, and confine the flux to a path which closely couples the windings. In Classical physics, free space is a concept of Electromagnetic theory, corresponding to a theoretically "perfect" Vacuum, and sometimes ^[31] Early transformer developers soon realised 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. ^[32] 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. ^[23] The universal transformer equation indicates a minimum cross-sectional area for the core to avoid saturation. A transformer is a device that transfers Electrical energy from one circuit to another through inductively coupled Electrical conductors

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,^[30] but are more laborious and expensive to construct. ^[33] Thin laminations are generally used on high frequency transformers, with some types of very thin steel laminations able to operate up to 10 kHz.

Laminating the core greatly reduces eddy-current losses

One common design of laminated core is made from interleaved stacks of E-shaped steel sheets capped with I-shaped pieces, leading to its name of "E-I transformer". Many shapes have metaphorical names, ie their names are Metaphors these Shapes are named after a most common object that has it Many shapes have metaphorical names, ie their names are Metaphors these Shapes are named after a most common object that has it ^[33] 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. ^[33] 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. Remanence is the magnetization left behind in a medium after an external Magnetic field is removed When power is then reapplied, the residual field will cause a high inrush current until the effect of the remanent magnetism is reduced, usually after a few cycles of the applied alternating current. Inrush current or input surge current refers to the maximum instantaneous input current drawn by an electrical device when first turned on ^[34] Overcurrent protection devices such as fuses must be selected to allow this harmless inrush to pass. A relay is an electrical Switch that opens and closes under the control of another Electrical circuit. In Electronics and Electrical engineering a fuse (short for fusible link) is a type of Overcurrent protection device 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. Geomagnetically induced currents (GIC affecting the normal operation of long technological conductor systems are a manifestation at ground level of Space weather ^[35]

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. Electrical steel, also called lamination steel, silicon electrical steel, silicon steel or transformer steel, is specialty Steel tailored An amorphous solid is a Solid in which there is no Long-range order of the positions of the Atoms (Solids in which there is long-range atomic order are The higher initial cost of the core material is offset over the life of the transformer by its lower losses at light load. ^[36]

Solid cores

Powdered iron cores are used in circuits (such as switch-mode power supplies) that operate above main frequencies and up to a few tens of kilohertz. Iron (ˈаɪɚn is a Chemical element with the symbol Fe (ferrum and Atomic number 26 These materials combine high magnetic permeability with high bulk electrical resistivity. In Electromagnetism, permeability is the degree of Magnetization of a material that responds linearly to an applied Magnetic field. Electrical resistivity (also known as specific electrical resistance) is a measure of how strongly a material opposes the flow of Electric current. For frequencies extending beyond the VHF band, cores made from non-conductive magnetic ceramic materials called ferrites are common. Very high frequency (VHF is the Radio frequency range from 30 MHz to 300 MHz. The word ceramic is derived from the Greek word κεραμικός ( keramikos) Ferrites are a class of Chemical compounds with the formula AB2O4 where A and B represent various metal Cations usually including ^[33] Some radio-frequency transformers also have moveable cores (sometimes called 'slugs') which allow adjustment of the coupling coefficient (and bandwidth) of tuned radio-frequency circuits. Bandwidth is the difference between the upper and lower Cutoff frequencies of for example a filter, a Communication channel, or a Signal spectrum

Toroidal cores

Small transformer with toroidal core

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. Steel is an Alloy consisting mostly of Iron, with a Carbon content between 0 Permalloy is the term for a Nickel Iron magnetic Alloy. Generically it refers to an alloy with about 20% iron and 80% nickel content Ferrites are a class of Chemical compounds with the formula AB2O4 where A and B represent various metal Cations usually including ^[37] A strip construction ensures that the grain boundaries are optimally aligned, improving the transformer's efficiency by reducing the core's reluctance. A grain boundary is the interface between two grains in a polycrystalline material Magnetic reluctance or "magnetic resistance" is analogous to resistance in an Electrical Circuit (although it does not dissipate magnetic The closed ring shape eliminates air gaps inherent in the construction of an E-I core. ^[38] The cross-section of the ring is usually square or rectangular, but more expensive cores with circular cross-sections are also available. The primary and secondary coils are often wound concentrically to cover the entire surface of the core. This minimises the length of wire needed, and also provides screening to minimize the core's magnetic field from generating electromagnetic interference.

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 rating.

Ferrite toroidal cores are used at higher frequencies, typically between a few tens of kilohertz to a megahertz, to reduce losses, physical size, and weight of switch-mode power supplies. A switched-mode power supply, switching-mode power supply or SMPS, is an electronic Power supply unit (PSU that incorporates a switching regulator A drawback of toroidal transformer construction is the higher cost of windings. As a consequence, toroidal transformers are uncommon above ratings of a few kVA. Small distribution transformers may achieve some of the benefits of a toroidal core by splitting it and forcing it open, then inserting a bobbin containing primary and secondary windings.

Air cores

A physical core is not an absolute requisite and a functioning transformer can be produced simply by placing the windings in close proximity to 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. A system with hysteresis can be summarised as a system that may be in any number of states independent of the inputs to the system ^[8] The leakage inductance is inevitably high, resulting in very poor regulation, and so such designs are unsuitable for use in power distribution. ^[8] They have however very high bandwidth, and are frequently employed in radio-frequency applications,^[39] for which a satisfactory coupling coefficient is maintained by carefully overlapping the primary and secondary windings. Bandwidth is the difference between the upper and lower Cutoff frequencies of for example a filter, a Communication channel, or a Signal spectrum

Windings

Windings are usually arranged concentrically to minimise flux leakage

Cut view through transformer windings. White: insulator. Green spiral: Grain oriented silicon steel. Electrical steel, also called lamination steel, silicon electrical steel, silicon steel or transformer steel, is specialty Steel tailored Black: Primary winding made of oxygen-free copper. Oxygen-free copper (OFC or Oxygen-free high thermal conductivity ( OFHC) copper generally refer to a group of wrought high conductivity Copper alloys that 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 (bad) conductors 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. Leakage inductance is that property of an electrical Transformer that causes a winding to appear to have some inductance in series with the mutually-coupled

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. In Science and engineering, a conductor is a material which contains movable Electric charges. ^[11] 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. Enameled wire is copper Wire coated with a very thin insulating layer Larger power transformers operating at high voltages may be wound with copper rectangular strip conductors insulated by oil-impregnated paper and blocks of pressboard. A Transformerboard is the brand name of a Cellulose insulating layer for Electrical transformers made popular during the early-mid 20th century ^[40]

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. The skin effect is the tendency of an alternating electric current (AC to distribute itself within a conductor so that the current density near the surface of the ^[11] 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. ^[40] 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. ^[40]

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

Both the primary and secondary windings on power transformers may have external connections, called taps, to intermediate points on the winding to allow selection of the voltage ratio. A transformer tap is a connection point along a Transformer winding that allows a certain number of turns to be selected The taps may be connected to an automatic on-load tap changer for voltage regulation of distribution circuits. A transformer tap is a connection point along a Transformer winding that allows a certain number of turns to be selected 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. In electronics a center tap is a connection made to a point half way along a winding of a Transformer or Inductor, or along the element of a Resistor or Generally an amplifier or simply amp, is any device that changes usually increases the amplitude of a signal. Modulation transformers in AM transmitters are very similar. Amplitude modulation ( AM) is a technique used in electronic communication most commonly for transmitting information via a Radio Carrier wave

Certain transformers have the windings protected by epoxy resin. By impregnating the transformer with epoxy under a vacuum, one can replace air spaces within the windings with epoxy, thus sealing the windings and helping to prevent the possible formation of corona and absorption of dirt or water. A resin casting system is a technical installation to process Casting resin for the purpose of filling sealing covering or soaking technical parts especially in the field This vacuum means "absence of matter" or "an empty area or space" for the cleaning appliance see Vacuum cleaner. This produces transformers more suited to damp or dirty environments, but at increased manufacturing cost. ^[41]

Three-phase oil-cooled transformer with cover cut away. The oil reservoir is visible at the top. Radiative fins aid the dissipation of heat.

Coolant

Extended operation at high temperatures is particularly damaging to transformer insulation. ^[42] Small signal transformers do not generate significant heat and need little consideration given to their thermal management. Heat generated by Electronic devices and Circuitry must be dissipated to improve Reliability and prevent premature Failure. Power transformers rated up to a few kVA can be adequately cooled by natural convective air-cooling, sometimes assisted by fans. Convection in the most general terms refers to the movement of molecules within Fluids (i ^[43] Specific provision must be made for cooling high-power transformers, the larger physical size requiring careful design to transport heat from the interior. Some power transformers are immersed in specialized transformer oil that acts both as a cooling medium, thereby extending the lifetime of the insulation, and helps to reduce corona discharge. Transformer oil is usually a highly- refined Mineral oil that is stable at high temperatures and has excellent electrical insulating properties In Electricity, a corona discharge is an Electrical discharge brought on by the Ionization of a Fluid surrounding a conductor, which ^[44] The oil is a highly refined mineral oil that remains stable at high temperatures so that internal arcing will not cause breakdown or fire; transformers to be used indoors must use a non-flammable liquid. Mineral oil or liquid Petroleum is a By-product in the Distillation of Petroleum to produce Gasoline and other petroleum An electric arc is an Electrical breakdown of a gas which produces an ongoing plasma discharge, resulting from a current flowing through normally nonconductive ^[2]

The oil-filled tank often has radiators through which the oil circulates by natural convection; large transformers employ forced circulation of the oil by electric pumps, aided by external fans or water-cooled heat exchangers. A heat exchanger is a device built for efficient Heat transfer from one medium to another whether the media are separated by a solid wall so that they never mix or the media ^[44] Oil-filled transformers undergo prolonged drying processes to ensure that the transformer is completely free of water vapor before the cooling oil is introduced. General properties of water vapor Evaporation/sublimation Whenever a water molecule leaves a surface it is said to have evaporated This helps prevent electrical breakdown under load. Oil-filled transformers may be equipped with Buchholz relays, which detect gas evolved during internal arcing and rapidly de-energize the transformer to avert catastrophic failure. In the field of electric power distribution and transmission a Buchholz relay, also called a gas relay or a sudden pressure relay, is a safety device mounted on ^[34]

Polychlorinated biphenyls have properties that once favored their use as a coolant, though concerns over their toxicity and environmental persistence led to a widespread ban on their use. Polychlorinated biphenyls ( PCB s are a class of Organic compounds with 1 to 10 Chlorine atoms attached to Biphenyl which is a molecule composed Persistent organic pollutants ( POP s are organic compounds that are resistant to environmental degradation through chemical, biological, and photolytic ^[45] 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. Silicones are largely inert compounds with a wide variety of forms and uses Fluorocarbons are chemical compounds that contain Carbon - Fluorine bonds The relatively low reactivity and high polarity of the carbon-fluorine bond imparts ^[42][2] Before 1977, even transformers that were nominally filled only with mineral oils commonly also contained polychlorinated biphenyls as contaminants at 10-20 ppm. "Parts-per" notation is used especially in Science and Engineering, to denote Ratios (relative proportions in measured quantities particularly ^[46]

Some "dry" transformers are enclosed in pressurized tanks and cooled by nitrogen or sulfur hexafluoride gas. Nitrogen (ˈnaɪtɹəʤɪn is a Chemical element that has the symbol N and Atomic number 7 and Atomic weight 14 Sulfur hexafluoride is an Inorganic compound with the formula. ^[42] To ensure that the gas does not leak and its insulating capability deteriorate, the transformer casing is completely sealed. Experimental power transformers in the 2 MVA range have been built with superconducting windings which eliminates the copper losses, but not the core steel loss. Superconductivity is a phenomenon occurring in certain Materials generally at very low Temperatures characterized by exactly zero electrical resistance These are cooled by liquid nitrogen or helium. Liquid nitrogen (liquid density at the Triple point is 0707 g/mL is the liquid produced industrially in large quantities by Fractional distillation of Helium exists in Liquid form only at very low Temperatures The Boiling point and critical point depend on the Isotope ^[47]

Terminals

Very small transformers will have wire leads connected directly to the ends of the coils, and brought out to the base of the unit for circuit connections. Larger transformers may have heavy bolted terminals, bus bars or high-voltage insulated bushings made of polymers or porcelain. A bushing is an Electrical engineering component that insulates a High voltage conductor passing through a metal enclosure 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. Mathematically the electric field gradient (EFG is the Hessian matrix (the matrix of the second derivatives of the Electrical potential V ^[48]

History

The transformer principle was demonstrated in 1831 by Michael Faraday, although he used it only to demonstrate the principle of electromagnetic induction and did not foresee its practical uses. Michael Faraday, FRS ( September 22 1791 – August 25 1867) was an English Faraday's law of induction describes an important basic law of electromagnetism which is involved in the working of Transformers Inductors and many forms of The first widely used transformer was the induction coil, invented by Irish clergyman Nicholas Callan in 1836. An induction coil or "spark coil" ( archaically known as a Ruhmkorff coil) is a type of Disruptive discharge Coil. Father Nicholas Joseph Callan (1799 &ndash 1864 was a priest and scientist from Darver, Co ^[49] He was one of the first to understand the principle that the more turns a transformer winding has, the larger EMF it produces. Induction coils evolved from scientists efforts to get higher voltages from batteries. They were powered not by AC, but DC from batteries which was interrupted by a vibrating 'breaker' mechanism. An alternating current ( AC) is an Electric current whose direction reverses cyclically as opposed to Direct current, whose direction remains constant Direct current ( DC) is the unidirectional flow of Electric charge. Between the 1830s and the 1870s efforts to build better induction coils, mostly by trial and error, slowly revealed the basic principles of transformer operation. Efficient designs would not appear until the 1880s,^[50] but within less than a decade, the transformer was instrumental during the "War of Currents" in seeing alternating current systems triumph over their direct current counterparts, a position in which they have remained dominant. In the "War of Currents" era (sometimes "War of the Currents" or "Battle of Currents") in the late 1880s George Westinghouse An alternating current ( AC) is an Electric current whose direction reverses cyclically as opposed to Direct current, whose direction remains constant Direct current ( DC) is the unidirectional flow of Electric charge. ^[50]

Russian engineer Pavel Yablochkov in 1876 invented a lighting system based on a set of induction coils, where primary windings were connected to a source of alternating current and secondary windings could be connected to several "electric candles". Pavel Nikolayevich Yablochkov ( Павел Николаевич Яблочков in Russian) (( &ndash) was a Russian Electrical engineer, the Inventor An induction coil or "spark coil" ( archaically known as a Ruhmkorff coil) is a type of Disruptive discharge Coil. A Yablochkov candle (sometimes electric candle) is a type of electric carbon Arc lamp, invented in 1876 by Pavel Yablochkov. The patent claimed the system could "provide separate supply to several lighting fixtures with different luminous intensities from a single source of electric power". Evidently, the induction coil in this system operated as a transformer.

A historical Stanley transformer.

Lucien Gaulard and John Dixon Gibbs, who first exhibited a device with an open iron core called a 'secondary generator' in London in 1882 and then sold the idea to American company Westinghouse. Lucien Gaulard ( 1850 - November 26, 1888) invented devices for the transmission of Alternating current Electrical Energy Founded in 1886 as Westinghouse Electric Company and later renamed Westinghouse Electric Corporation by George Westinghouse. ^[32] They also exhibited the invention in Turin in 1884, where it was adopted for an electric lighting system.

Hungarian engineers Zipernowsky, Bláthy and Déri from the Ganz company in Budapest created the efficient "ZBD" closed-core model in 1885 based on the design by Gaulard and Gibbs. Hungary (Magyarország 'mɔɟɔrorsaːg) officially in English the Republic of Hungary ( Magyar Köztársaság, literally Magyar (Hungarian Republic Károly Zipernowsky (1853 Vienna - 1942 Budapest) was a Hungarian Electrical engineer. Ottó Titusz Bláthy ( August 11, 1860 – September 26, 1939) was a Hungarian Electrical engineer. Miksa Déri (1854 - 1938 was a Hungarian Electrical engineer, co-inventor of the closed iron core Transformer and the ZBD model AC The Ganz ( Ganz vállalatok, "Ganz companies") electric works in Budapest is probably best known for the manufacture of Tramcars ^[51] Their patent application made the first use of the word "transformer". ^[32] Russian engineer Mikhail Dolivo-Dobrovolsky developed the first three-phase transformer in 1889. Mikhail Osipovich Dolivo-Dobrovolsky ( Михаил Осипович Доливо-Добровольский; Michail von Dolivo-Dobrowolsky or Michail Ossipowitch This article deals with the basic mathematics and principles of three-phase electricity In 1891 Nikola Tesla invented the Tesla coil, an air-cored, dual-tuned resonant transformer for generating very high voltages at high frequency. There have already been discussions about Tesla's ethnicity on the talk page A Tesla coil is a type of resonant transformer circuit invented by Serbian-American scientist Nikola Tesla around 1891 The term high voltage characterizes electrical circuits in which the voltage used is the cause of particular safety concerns and insulation requirements Audio frequency transformers (at the time called repeating coils) were used by the earliest experimenters in the development of the telephone. An audio frequency (abbreviation AF) or audible frequency is characterized as a periodic vibration whose Frequency is audible to the average human In Telecommunications a repeating coil is a Voice-frequency Transformer characterized by a closed Magnetic core, a pair of identical balanced Basic principle A traditional landline telephone system also known as "plain old telephone service" (POTS, commonly handles both signaling and audio information

While new technologies have made transformers in some electronics applications obsolete, transformers are still found in many electronic devices. Transformers are essential for high voltage power transmission, which makes long distance transmission economically practical. Power transmission is the movement of Energy from its place of generation to a location where it is applied to performing useful work.

See also

• Electromagnetism
• Inductor
• Polyphase system
• Balun
• Load profile
• Transformer types
• Faraday's law of induction

Notes

References

• Central Electricity Generating Board (1982). The Central Electricity Generating Board (CEGB was the cornerstone of the British electricity industry for almost 40 years from 1957 to Privatisation in the Modern Power Station Practice. Pergamon. ISBN 0-08-016436-6.  
• Daniels, A. R. (1985). Introduction to Electrical Machines. Macmillan. ISBN 0-333-19627-9.  
• Flanagan, William (1993). Handbook of Transformer Design and Applications. McGraw-Hill. ISBN 0-0702-1291-0.  
• Gottlieb, Irving (1998). Practical Transformer Handbook. Elsevier. ISBN 0-7506-3992-X.  
• Hammond, John Winthrop. Men and Volts, the Story of General Electric, published 1941 by J. B. Lippincott. Citations: design, early types - 106-107; design, William Stanley, first built - 178; oil-immersed, began use of - 238. William Stanley Jr ( November 28, 1858 &ndash May 14, 1916) was an American physicist born in Brooklyn,
• Harlow, James (2004). Electric Power Transformer Engineering. CRC Press. ISBN 0-8493-1704-5.  
• Heathcote, Martin (1998). J & P Transformer Book, Twelfth edition. Newnes. ISBN 0-7506-1158-8.  
• Hindmarsh, John (1977). Electrical Machines and their Applications, 4th edition. Exeter: Pergammon. ISBN 0-08-030573-3.  
• Kulkarni, S. V. & Khaparde, S. A. (2004). Transformer Engineering: design and practice. CRC Press. ISBN 0-8247-5653-3.  
• McLaren, Peter (1984). Elementary Electric Power and Machines. Ellis Horwood. ISBN 0-4702-0057-X.  
• McLyman, Colonel William (2004). Transformer and Inductor Design Handbook. CRC. ISBN 0-8247-5393-3.  
• Pansini, Anthony (1999). Electrical Transformers and Power Equipment. CRC Press, p23. ISBN 0-8817-3311-3.  
• Ryan, H. M. (2004). High Voltage Engineering and Testing. CRC Press. ISBN 0-8529-6775-6.  
• Say, M. G. (1983). Alternating Current Machines, Fifth Edition. London: Pitman. ISBN 0-273-01969-4.  
• Winders, John (2002). Power Transformer Principles and Applications. CRC. ISBN 0-8247-0766-4.  
• Gururaj, B. I. (June 1963). "Natural Frequencies of 3-Phase Transformer Windings". IEEE Transactions on Power Apparatus and Systems 82 (66): 318–329. doi:10.1109/TPAS.1963.291359. A digital object identifier ( DOI) is a permanent identifier given to an Electronic document. ISSN 0018-9510. An International Standard Serial Number ( ISSN) is a unique eight-digit number used to identify a print or electronic Periodical publication.  

External links

• Transformers - Interactive Java Tutorial National High Magnetic Field Laboratory

• Transformer Learning Centre Learn more about Transformers and how they work
• Inside Transformers from Denver University
• Understanding Transformers: Characteristics and Limitations from Conformity Magazine
• Indian Transformer Manufacturers Association
• 3 Phase Transformer Information and Construction — The 3 Phase Power Resource Site
• Substation and Transmission at the Open Directory Project
• J.Edwards and T.K Saha, Power flow in transformers via the Poynting vectorPDF (264 KB)
• Introduction to Current TransformersPDF (94. The Open Directory Project ( ODP) also known as dmoz (from directory 6 KB)
• A transformer explodes
• Java applet of transformer