# Encyclopedia

.
Pole-mounted single-phase transformer with center-tapped secondary.
^ Center tapped primary with secondary (a).
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ This auto transformer steps voltage down with a single copper-saving tapped winding.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Moving-slide contacts are too impractical to be used in large industrial power transformer designs, but multi-pole switches and winding taps are common for voltage adjustment.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

A grounded conductor is used as one leg of the primary feeder.
.A transformer is a device that transfers electrical energy from one circuit to another through inductively coupled conductors—the transformer's coils.^ REVIEW: By being able to transfer power from one circuit to another without the use of interconnecting conductors between the two circuits, transformers provide the useful feature of electrical isolation .
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Short Circuit Protection: In the event of an electrical short, the transformer will stop functioning.

^ For now, the most important thing to keep in mind is a transformer's basic operating principle: the transfer of power from the primary to the secondary circuit via electromagnetic coupling.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

.A varying current in the first or primary winding creates a varying magnetic flux in the transformer's core, and thus a varying magnetic field through the secondary winding.^ At first, one might expect this secondary coil current to cause additional magnetic flux in the core.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Photograph of multiple-winding transformer with six windings, a primary and five secondaries.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Consequently, the magnetic flux in the core cannot be affected by secondary coil current.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

.This varying magnetic field induces a varying electromotive force (EMF) or "voltage" in the secondary winding.^ That is, its iron core is “stuffed full” of magnetic lines of flux for a large portion of the AC cycle so that variations in supply voltage (primary winding current) have little effect on the core's magnetic flux density, which means the secondary winding outputs a nearly constant voltage despite significant variations in supply (primary winding) voltage.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Induction heating: Primary insulated winding induces current into lossy iron pipe (secondary).
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ The ability of an inductor to generate this opposing voltage is directly connected with the change in magnetic flux inside the inductor resulting from the change in current, and the number of winding turns in the inductor.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

.This effect is called mutual induction.^ This effect is called mutual inductance : the induction of a voltage in one coil in response to a change in current in the other coil.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

.If a load is connected to the secondary, an electric current will flow in the secondary winding and electrical energy will be transferred from the primary circuit through the transformer to the load.^ REVIEW: Power transformers are limited in the amount of power they can transfer from primary to secondary winding(s).
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ The capacitor, in conjunction with the transformer's primary winding, forms a tank circuit.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ A substantial amount of the current through the primary winding merely works to magnetize the core rather than transfer useful energy to the secondary winding and load.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

In an ideal transformer, the induced voltage in the secondary winding (VS) is in proportion to the primary voltage (VP), and is given by the ratio of the number of turns in the secondary (NS) to the number of turns in the primary (NP) as follows:
$\frac{V_{S}}{V_{P}} = \frac{N_{S}}{N_{P}}$
.By appropriate selection of the ratio of turns, a transformer thus allows an alternating current (AC) voltage to be "stepped up" by making NS greater than NP, or "stepped down" by making NS less than NP.^ Potential transformers are designed to provide as accurate a voltage step-down ratio as possible.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Turns ratio of 10:1 yields 10:1 primary:secondary voltage ratio and 1:10 primary:secondary current ratio.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ This allows for multiple step-up and/or step-down ratios in the same device.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

.In the vast majority of transformers, the windings are coils wound around a ferromagnetic core, air-core transformers being a notable exception.^ An air-core transformer is one lacking a ferromagnetic core.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Air core transformers may be wound on cylindrical (a) or toroidal (b) forms.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Air core transformers .
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

.Transformers range in size from a thumbnail-sized coupling transformer hidden inside a stage microphone to huge units weighing hundreds of tons used to interconnect portions of power grids.^ For now, the most important thing to keep in mind is a transformer's basic operating principle: the transfer of power from the primary to the secondary circuit via electromagnetic coupling.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ The following photograph shows a power transformer of the type used in gas-discharge lighting.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Moving-slide contacts are too impractical to be used in large industrial power transformer designs, but multi-pole switches and winding taps are common for voltage adjustment.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

.All operate with the same basic principles, although the range of designs is wide.^ For this reason, transformers of significant size are designed to operate efficiently in a limited range of frequencies.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ For now, the most important thing to keep in mind is a transformer's basic operating principle: the transfer of power from the primary to the secondary circuit via electromagnetic coupling.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Being that this is impossible to achieve, transformers must be designed to operate within certain expected ranges of voltages and loads in order to perform as close to ideal as possible.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

.While new technologies have eliminated the need for transformers in some electronic circuits, transformers are still found in nearly all electronic devices designed for household ("mains") voltage.^ We still don't know many details about the plot of TRANSFORMERS: REVENGE OF THE FALLEN , but if the new set pics over at Just...
• Transformers: JoBlo.com's Upcoming Movies: Posters, Plot, Pictures, Cast, News... 28 January 2010 1:01 UTC www.joblo.com [Source type: General]

^ Semiconductor circuits exist to “condition” AC power as an alternative to ferroresonant devices, but none can compete with this transformer in terms of sheer simplicity.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ If its impossible to build a transformer with perfect coupling, but easy to design coils with low inductance, then why not just build all transformers with low-inductance coils and have excellent efficiency even with poor magnetic coupling?” .
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

.Transformers are essential for high voltage power transmission, which makes long distance transmission economically practical.^ Indeed, the transformer has made long-distance transmission of electric power a practical reality, as AC voltage can be “stepped up” and current “stepped down” for reduced wire resistance power losses along power lines connecting generating stations with loads.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ As our transformers operate at high frequency, the voltage cannot be read with most meters.

^ Another application is in current control for AC arc welders, which are nothing more than step-down transformers supplying low-voltage, high-current power for the welding process.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

## History

### Discovery

Faraday's experiment with induction between coils of wire [1]
.The phenomenon of 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.^ Michael Faraday discovered the mathematical relationship between magnetic flux (Φ) and induced voltage with this equation: .
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

[2] The relationship between electromotive force (EMF) or "voltage" and magnetic flux was formalized in an equation now referred to as "Faraday's law of induction":
$|\mathcal{E}| = \left|{{d\Phi_B} \over dt}\right|$.
where:
$|\mathcal{E}|$ is the magnitude of the EMF in volts
ΦB is the .magnetic flux through the circuit (in webers).^ In our example, the mmf required to produce this changing magnetic flux (Φ) must be supplied by a changing current through the coil.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Because mmf is proportional to current through the magnetizing coil (mmf = NI, where “N” is the number of turns of wire in the coil and “I” is the current through it), the large increases of mmf required to supply the needed increases in flux results in large increases in coil current.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Magnetic flux through a ferromagnetic material is analogous to current through a conductor: it must be motivated by some force in order to occur.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

[3]
.Faraday's experiments included winding a pair of coils around an iron ring, thus creating the first toroidal closed-core transformer.^ As the core is moved toward the top winding, the voltage across this coil increases due to increased coupling, while the voltage on the bottom coil decreases.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Actually, it is not really a transformer at all, but rather a special kind of inductor whose inductance can be varied by the application of a DC current through a second winding wound around the same iron core.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ The secondary winding is wound in close proximity to the primary, usually around the same nonmagnetic form.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

[4]

### 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 that the more turns the secondary winding has in relation to the primary winding, the larger is the increase in EMF. Induction coils evolved from scientists' and inventors' efforts to get higher voltages from batteries. .Since batteries produce direct current (DC) rather than alternating current (AC), induction coils relied upon vibrating electrical contacts that regularly interrupted the current in the primary to create the flux changes necessary for induction.^ When AC current changes, flux Φ changes.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Induction heating: Primary insulated winding induces current into lossy iron pipe (secondary).
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Because mmf is proportional to current through the magnetizing coil (mmf = NI, where “N” is the number of turns of wire in the coil and “I” is the current through it), the large increases of mmf required to supply the needed increases in flux results in large increases in coil current.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

.Between the 1830s and the 1870s, efforts to build better induction coils, mostly by trial and error, slowly revealed the basic principles of transformers.^ For now, the most important thing to keep in mind is a transformer's basic operating principle: the transfer of power from the primary to the secondary circuit via electromagnetic coupling.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ If its impossible to build a transformer with perfect coupling, but easy to design coils with low inductance, then why not just build all transformers with low-inductance coils and have excellent efficiency even with poor magnetic coupling?” .
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ A drawing of a motor/generator set reveals the basic principle involved: (Figure below ) .
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

.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 alternating current and the secondary windings could be connected to several "electric candles" (arc lamps) of his own design.^ Primary and secondary currents are in-phase.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ In this example, we could apply this fundamental law of electricity to describe the respective voltages of the source and of the inductor coil.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ With less inductance in the primary winding, there is less inductive reactance, and consequently a much larger magnetizing current.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

[5][6] The coils Yablochkov employed functioned essentially as transformers.[5]
.Induction coils with open magnetic circuits are inefficient for transfer of power to loads.^ For now, the most important thing to keep in mind is a transformer's basic operating principle: the transfer of power from the primary to the secondary circuit via electromagnetic coupling.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ No current will exist in the secondary coil, since it is open-circuited.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Recall from our study of network analysis the Maximum Power Transfer Theorem , which states that the maximum amount of power will be dissipated by a load resistance when that load resistance is equal to the Thevenin/Norton resistance of the network supplying the power.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

.Until about 1880 the paradigm for AC power transmission from a high voltage supply to a low voltage load was a series circuit.^ The purpose of the high-voltage, low-frequency AC power source is to “charge” the primary tank circuit.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Voltage gets dropped across this series impedance, resulting in a reduced load voltage: voltage across the load “sags” as load current increases.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Semiconductor circuits exist to “condition” AC power as an alternative to ferroresonant devices, but none can compete with this transformer in terms of sheer simplicity.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

.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 primaries of both transformers are connected to the 2-φ voltages.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Special transformers known as peaking transformers exploit this principle to produce brief voltage pulses near the peaks of the source voltage waveform.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Another application is in current control for AC arc welders, which are nothing more than step-down transformers supplying low-voltage, high-current power for the welding process.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

.The inherent flaw in this method was that turning off a single lamp affected the voltage supplied to all others on the same circuit.^ Now the circuit ground within the machine isn't necessarily at the same potential as the case ground, so flipping the switch connected the circuit ground to the case ground, causing a voltage drop/jump which reset the machine.
• CTRL+V THREAD! [part 2] - The Forbidden Garden of DQN @ 4-ch Archives 20 September 2009 21:52 UTC archives.4-ch.net [Source type: General]

^ We show “DC” polarities all over this AC only circuit, to keep track of the Kirchhoff voltage loop polarities.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ It could be AC, even at a different frequency, and the transformer would isolate it from the primary circuit all the same.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

.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.^ Core flux induces a voltage in any coil wrapped around the core.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Transformers are also constrained in their performance by the magnetic flux limitations of the core.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ And in 1996 the Transformers craze was reborn with Beast Wars , a new series of toys and cartoons that introduced another generation to these " Robots in disguise ."
• Transformers@Everything2.com 3 February 2010 18:59 UTC everything2.com [Source type: General]

[7]
In 1878, the Ganz Company in Hungary began manufacturing equipment for electric lighting, and by 1883 had installed over fifty systems in Austria-Hungary. .Their systems used alternating current exclusively, and included those comprising both arc and incandescent lamps, along with generators and other equipment.^ The transformer in Figure above is intended to provide both high and low voltages necessary in an electronic system using vacuum tubes.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ At either end (both the generator and at the loads), voltage levels are reduced by transformers for safer operation and less expensive equipment.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Sole Statement: This document is the sole statement of the Site's Privacy Policy and no summary, restatement or other version thereof, or other privacy statement or policy, in any form, including, but not limited to, machine-generated, is valid.
• Transformers - Trailer | SPIKE 28 January 2010 1:01 UTC www.spike.com [Source type: General]

[8]
.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.^ At first, one might expect this secondary coil current to cause additional magnetic flux in the core.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ As with the first transformer example we looked at, power transfer efficiency is very good from the primary to the secondary sides of the device.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ However, when the secondary is “loaded” (current supplied to a load), the winding generates an mmf, which becomes counteracted by a “reflected” mmf in the primary winding to prevent core flux levels from changing.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

[9] They also exhibited the invention in Turin, Italy in 1884, where it was adopted for an electric lighting system.[10] However, the efficiency of their open-core bipolar apparatus remained low.[11]
.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.^ Transformers can also be used in electrical instrumentation systems.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Thus, in the business of practical transformer design, compromises must be made.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Since this is a practical concern, transformer manufacturers have come up with a sort of polarity marking standard to denote phase relationships.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

[12]

### Closed-core lighting transformers

The prototypes of the world's first high efficiency transformers (the so-called Ganz "ZBD") (Museum of Applied Arts, Budapest, 1884–1885)
.Between 1884 and 1885, Ganz Company engineers Károly Zipernowsky, Ottó Bláthy and Miksa Déri had determined that open-core devices were impracticable, as they were incapable of reliably regulating voltage.^ Moving the iron slug away from the windings reduces the strength of magnetic coupling between the windings, which diminishes no-load secondary voltage and makes for poorer voltage regulation.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

.In their joint patent application for the "Z.B.D." transformers, they described the design of two with no poles: the "closed-core" and the "shell-core" transformers.^ Two new TRANSFORMERS TV spots were just released, and they bode well for the future of the film.
• Transformers: JoBlo.com's Upcoming Movies: Posters, Plot, Pictures, Cast, News... 28 January 2010 1:01 UTC www.joblo.com [Source type: General]

^ I am reading the other write-ups under this heading, and I can not believe that absolutely no one goes into depth describing the Transformer toys.
• Transformers@Everything2.com 3 February 2010 18:59 UTC everything2.com [Source type: General]

^ They had no freakin idea so many people worldwide were going to be in the mood to make ape noises at the screen for two hours over transforming robots.
• Orci & Kurtzman Talk Trek v Transformers & Future Prime Universe + more | TrekMovie.com 3 February 2010 18:59 UTC trekmovie.com [Source type: General]

.In the closed-core type, the primary and secondary windings were wound around a closed iron ring; in the shell type, the windings were passed through the iron core.^ The secondary winding is wound in close proximity to the primary, usually around the same nonmagnetic form.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ That is, its iron core is “stuffed full” of magnetic lines of flux for a large portion of the AC cycle so that variations in supply voltage (primary winding current) have little effect on the core's magnetic flux density, which means the secondary winding outputs a nearly constant voltage despite significant variations in supply (primary winding) voltage.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Actually, it is not really a transformer at all, but rather a special kind of inductor whose inductance can be varied by the application of a DC current through a second winding wound around the same iron core.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

.In both designs, the magnetic flux linking the primary and secondary windings traveled almost entirely within the iron core, with no intentional path through air.^ Leakage inductance is due to magnetic flux not cutting both windings.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ That is, its iron core is “stuffed full” of magnetic lines of flux for a large portion of the AC cycle so that variations in supply voltage (primary winding current) have little effect on the core's magnetic flux density, which means the secondary winding outputs a nearly constant voltage despite significant variations in supply (primary winding) voltage.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ The familiar “hum” heard around large power transformers is the sound of the iron core expanding and contracting at 120 Hz (twice the system frequency, which is 60 Hz in the United States) -- one cycle of core contraction and expansion for every peak of the magnetic flux waveform -- plus noise created by mechanical forces between primary and secondary windings.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

.When employed in electric distribution systems, this revolutionary design concept would finally make it technically and economically feasible to provide electric power for lighting in homes, businesses and public spaces.^ Due to transformers' ability to step up or step down voltage and current, and the electrical isolation they provide, they can serve as a way of connecting electrical instrumentation to high-voltage, high current power systems.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ A Potential Transformer (PT) is a special instrument transformer designed to provide a precise voltage step-down ratio for voltmeters measuring high power system voltages.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ The transformer keeps the instrument voltage at a safe level and electrically isolates it from the power system, so there is no direct connection between the power lines and the instrument or instrument wiring.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

[13][14] Bláthy had suggested the use of closed-cores, Zipernowsky the use of shunt connections, and Déri had performed the experiments.[15] Bláthy also discovered the transformer formula, Vs/Vp = Ns/Np,[citation needed] and electrical and electronic systems the world over continue to rely on the principles of the original Z.B.D. transformers. The inventors also popularized the word "transformer" to describe a device for altering the EMF of an electric current,[13][16] although the term had already been in use by 1882.[17][18]
Stanley's 1886 design for adjustable gap open-core induction coils[19]
George Westinghouse had bought Gaulard and Gibbs' patents in 1885, and had purchased an option on the Z.B.D. design. He entrusted engineer William Stanley with the building of a device for commercial use.[20] .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.^ As the core is moved toward the top winding, the voltage across this coil increases due to increased coupling, while the voltage on the bottom coil decreases.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Induction heating: Primary insulated winding induces current into lossy iron pipe (secondary).
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ While most transformer designs enclose the coils and core in a metal frame for protection, this particular transformer is open for viewing and so serves its illustrative purpose well: (Figure below ) .
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

(See drawing at left.)[19] .This design was first used commercially in 1886.[12] But Westinghouse soon had his team working on a design whose core comprised a stack of thin "E-shaped" iron plates, separated individually or in pairs by thin sheets of paper or other insulating material.^ The use of amorphous core liquid-filled transformers is now being expanded for use in power applications for industrial and commercial installations.
• Guidelines for transformer application designs. 28 January 2010 1:01 UTC ecmweb.com [Source type: Reference]

^ Recall from the photograph of the transformer cut in half that the iron core was composed of many thin sheets rather than one solid piece.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Additionally, the iron core can be seen in this photograph to be made of many thin sheets (laminations) rather than a solid piece.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

.Prewound copper coils could then be slid into place, and straight iron plates laid in to create a closed magnetic circuit.^ What is important to understand is this: when an AC voltage is applied to the primary coil, it creates a magnetic flux in the core, which induces AC voltage in the secondary coil in-phase with the source voltage.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

Westinghouse applied for a patent for the new design in December 1886; it was granted in July 1887.[15][21]
.Russian engineer Mikhail Dolivo-Dobrovolsky developed the first three-phase transformer in 1889.[citation needed] In 1891 Nikola Tesla invented the Tesla coil, an air-cored, dual-tuned resonant transformer for generating very high voltages at high frequency.^ Frequently air core transformers are paralleled with a capacitor to tune it to resonance.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ The Tesla Coil is a resonant, high-frequency step-up transformer used to produce extremely high voltages.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Toroidal air core transformers are rare except for VHF (Very High Frequency) work.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

[22][23] .Audio frequency transformers (at the time called repeating coils) were used by the earliest experimenters in the development of the telephone.^ Audio frequency impedance matching transformer.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ When used in this capacity, the transformer is called a Potential Transformer , or simply PT .
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ A small impedance-matching transformer (about two centimeters in width) for audio-frequency applications is shown in the following photograph: (Figure below ) .
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

[citation needed]

## 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).^ Loops of wire covered by high-temperature insulation encircle the pipe's circumference, inducing eddy currents within the pipe wall by electromagnetic induction.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Because its operation depends on electromagnetic induction between two stationary coils and a magnetic flux of changing magnitude and “polarity,” transformers are necessarily AC devices.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Special transformers known as peaking transformers exploit this principle to produce brief voltage pulses near the peaks of the source voltage waveform.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

.Changing the current in the primary coil changes the magnetic flux that is developed.^ When AC current changes, flux Φ changes.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ With less inductance in the primary winding, there is less inductive reactance, and consequently a much larger magnetizing current.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Because mmf is proportional to current through the magnetizing coil (mmf = NI, where “N” is the number of turns of wire in the coil and “I” is the current through it), the large increases of mmf required to supply the needed increases in flux results in large increases in coil current.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

.The changing magnetic flux induces a voltage in the secondary coil.^ Changing flux induces a counter EMF. .
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Core flux induces a voltage in any coil wrapped around the core.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ At first, one might expect this secondary coil current to cause additional magnetic flux in the core.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

An ideal transformer
.An ideal transformer is shown in the adjacent figure.^ A small impedance-matching transformer (about two centimeters in width) for audio-frequency applications is shown in the following photograph: (Figure below ) .
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ In the next photograph, Figure below , a transformer is shown cut in half, exposing the cross-section of the iron core as well as both windings.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ A benchtop isolation transformer is shown in Figure below .
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

.Current passing through the primary coil creates a magnetic field.^ With less inductance in the primary winding, there is less inductive reactance, and consequently a much larger magnetizing current.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ At first, one might expect this secondary coil current to cause additional magnetic flux in the core.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ As an inductor, we would expect this iron-core coil to oppose the applied voltage with its inductive reactance, limiting current through the coil as predicted by the equations X L = 2πfL and I=E/X (or I=E/Z).
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

.The primary and secondary coils are wrapped around a core of very high magnetic permeability, such as iron, so that most of the magnetic flux passes through both the primary and secondary coils.^ Consequently, the magnetic flux in the core cannot be affected by secondary coil current.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Core flux induces a voltage in any coil wrapped around the core.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Ferromagnetic core with primary coil (AC driven) and secondary coil.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

### Induction law

The voltage induced across the secondary coil may be calculated from Faraday's law of induction, which states that:
$V_{S} = N_{S} \frac{\mathrm{d}\Phi}{\mathrm{d}t}$
where .VS is the instantaneous voltage, NS is the number of turns in the secondary coil and Φ equals the magnetic flux through one turn of the coil.^ The instantaneous voltage (voltage dropped at any instant in time) across a wire coil is equal to the number of turns of that coil around the core (N) multiplied by the instantaneous rate-of-change in magnetic flux (dΦ/dt) linking with the coil.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ If this secondary coil experiences the same magnetic flux change as the primary (which it should, assuming perfect containment of the magnetic flux through the common core), and has the same number of turns around the core, a voltage of equal magnitude and phase to the applied voltage will be induced along its length.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Because mmf is proportional to current through the magnetizing coil (mmf = NI, where “N” is the number of turns of wire in the coil and “I” is the current through it), the large increases of mmf required to supply the needed increases in flux results in large increases in coil current.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

.If the turns of the coil are oriented perpendicular to the magnetic field lines, the flux is the product of the magnetic flux density B and the area A through which it cuts.^ Leakage inductance is due to magnetic flux not cutting both windings.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Because mmf is proportional to current through the magnetizing coil (mmf = NI, where “N” is the number of turns of wire in the coil and “I” is the current through it), the large increases of mmf required to supply the needed increases in flux results in large increases in coil current.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ At first, one might expect this secondary coil current to cause additional magnetic flux in the core.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

.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.^ Transformer cross-section cut shows core and windings.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ That is, its iron core is “stuffed full” of magnetic lines of flux for a large portion of the AC cycle so that variations in supply voltage (primary winding current) have little effect on the core's magnetic flux density, which means the secondary winding outputs a nearly constant voltage despite significant variations in supply (primary winding) voltage.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Flux containment (making sure a transformer's magnetic flux doesn't escape so as to interfere with another device, and making sure other devices' magnetic flux is shielded from the transformer core) is another concern shared both by inductors and transformers.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

Since the same magnetic flux passes through both the primary and secondary coils in an ideal transformer,[24] the instantaneous voltage across the primary winding equals
$V_{P} = N_{P} \frac{\mathrm{d}\Phi}{\mathrm{d}t}$
Taking the ratio of the two equations for VS and VP gives the basic equation[25] for stepping up or stepping down the voltage
$\frac{V_{S}}{V_{P}} = \frac{N_{S}}{N_{P}}$

### 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.^ No current will exist in the secondary coil, since it is open-circuited.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Any current drawn through the secondary coil to power a load induces a corresponding current in the primary coil, drawing current from the source.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Primary and secondary currents are in-phase.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

.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.^ All ferromagnetic materials tend to retain some degree of magnetization after exposure to an external magnetic field.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ For now, the most important thing to keep in mind is a transformer's basic operating principle: the transfer of power from the primary to the secondary circuit via electromagnetic coupling.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ The better these two inductors are magnetically coupled, the more efficient the energy transfer between them should be.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

.If this condition is met, the incoming electric power must equal the outgoing power.^ It is much the same with electric power sources and loads: there must be an impedance match for maximum system efficiency.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

Pincoming = IPVP = Poutgoing = ISVS
giving the ideal transformer equation
$\frac{V_{S}}{V_{P}} = \frac{N_{S}}{N_{P}} = \frac{I_{P}}{I_{S}}$
.Transformers normally have high efficiency, so this formula is a reasonable approximation.^ For this reason, transformers of significant size are designed to operate efficiently in a limited range of frequencies.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

.If the voltage is increased, then the current is decreased by the same factor.^ Voltage gets dropped across this series impedance, resulting in a reduced load voltage: voltage across the load “sags” as load current increases.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ The primary current is very close to being the same, but notice how the secondary voltage has fallen well below the primary voltage (1.95 volts versus 10 volts at the primary).
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ If we decrease the load resistance so as to draw more current with the same amount of voltage, we see that the current through the primary winding increases in response.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

.The impedance in one circuit is transformed by the square of the turns ratio.^ So, it should be apparent that our two inductors in the last SPICE transformer example circuit -- with inductance ratios of 100:1 -- should have coil turn ratios of 10:1, because 10 squared equals 100.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ The transformation ratio of a transformer will be equal to the square root of its primary to secondary inductance (L) ratio.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ So far, we've explored the transformer as a device for converting different levels of voltage, current, and even impedance from one circuit to another.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

[24] .For example, if an impedance ZS is attached across the terminals of the secondary coil, it appears to the primary circuit to have an impedance of $Z_S\!\left(\!^ For example, take a step-down transformer with a primary voltage rating of 120 volts, a secondary voltage rating of 48 volts, and a VA rating of 1 kVA (1000 VA).
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Since transformers are essentially AC devices, we need to be aware of the phase relationships between the primary and secondary circuits.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ As with the first transformer example we looked at, power transfer efficiency is very good from the primary to the secondary sides of the device.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

frac{N_P}{N_S}\!\right)^2\!\!" src="http://images-mediawiki-sites.thefullwiki.org/05/3/1/1/85228411979727553.png" />. .This relationship is reciprocal, so that the impedance ZP of the primary circuit appears to the secondary to be $Z_P\!\left(\!^ For now, the most important thing to keep in mind is a transformer's basic operating principle: the transfer of power from the primary to the secondary circuit via electromagnetic coupling.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Open circuited secondary sees the same flux Φ as the primary.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Since transformers are essentially AC devices, we need to be aware of the phase relationships between the primary and secondary circuits.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

frac{N_S}{N_P}\!\right)^2\!\!" src="http://images-mediawiki-sites.thefullwiki.org/07/2/0/3/3964055867242783.png" />.

### Detailed operation

.The simplified description above neglects several practical 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.^ Primary and secondary currents are in-phase.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ That is, its iron core is “stuffed full” of magnetic lines of flux for a large portion of the AC cycle so that variations in supply voltage (primary winding current) have little effect on the core's magnetic flux density, which means the secondary winding outputs a nearly constant voltage despite significant variations in supply (primary winding) voltage.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Magnetic core losses are also exaggerated with higher frequencies, eddy currents and hysteresis effects becoming more severe.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

.Models of an ideal transformer typically assume a core of negligible reluctance with two windings of zero resistance.^ Sometimes windings will bear current ratings in amps, but this is typically seen on small transformers.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Equivalent circuit models leakage inductance as series inductors independent of the “ideal transformer”.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Schematic symbol for transformer consists of two inductor symbols, separated by lines indicating a ferromagnetic core.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

[26] .When a voltage is applied to the primary winding, a small current flows, driving flux around the magnetic circuit of the core.^ Magnetic flux, like current, lags applied voltage by 90 o .
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Core flux induces a voltage in any coil wrapped around the core.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ That is, its iron core is “stuffed full” of magnetic lines of flux for a large portion of the AC cycle so that variations in supply voltage (primary winding current) have little effect on the core's magnetic flux density, which means the secondary winding outputs a nearly constant voltage despite significant variations in supply (primary winding) voltage.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

[26] .The current required to create the flux is termed the magnetizing current; since the ideal core has been assumed to have near-zero reluctance, the magnetizing current is negligible, although still required to create the magnetic field.^ Magnetic core losses are also exaggerated with higher frequencies, eddy currents and hysteresis effects becoming more severe.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Because mmf is proportional to current through the magnetizing coil (mmf = NI, where “N” is the number of turns of wire in the coil and “I” is the current through it), the large increases of mmf required to supply the needed increases in flux results in large increases in coil current.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Again, maintaining low magnetic flux levels in the core is the key to minimizing this effect, which explains why ferroresonant transformers -- which must operate in saturation for a large portion of the current waveform -- operate both hot and noisy.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

.The changing magnetic field induces an electromotive force (EMF) across each winding.^ Changing flux induces a counter EMF. .
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ If we change the transformer design to have better magnetic coupling between the primary and secondary coils, the figures for voltage between primary and secondary windings will be much closer to equality again: .
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ This tendency to stay magnetized is called “hysteresis,” and it takes a certain investment in energy to overcome this opposition to change every time the magnetic field produced by the primary winding changes polarity (twice per AC cycle).
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

[27] .Since the ideal windings have no impedance, they have no associated voltage drop, and so the voltages VP and VS measured at the terminals of the transformer, are equal to the corresponding EMFs.^ Voltage gets dropped across this series impedance, resulting in a reduced load voltage: voltage across the load “sags” as load current increases.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ This auto transformer steps voltage down with a single copper-saving tapped winding.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ (Figure below ) Since flux (Φ) is proportional to the magnetomotive force (mmf) in the core, and the mmf is proportional to winding current, the current waveform will be in-phase with the flux waveform, and both will be lagging the voltage waveform by 90 o : .
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

.The primary EMF, acting as it does in opposition to the primary voltage, is sometimes termed the "back EMF".[28] 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.^ This cannot happen, because the primary coil's induced voltage must remain at the same magnitude and phase in order to balance with the applied voltage, in accordance with Kirchhoff's voltage law.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ The ability of an inductor to generate this opposing voltage is directly connected with the change in magnetic flux inside the inductor resulting from the change in current, and the number of winding turns in the inductor.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ With a perfect inductor (no resistance in the coil wire), the opposing voltage comes from another mechanism: the reaction to a changing magnetic flux in the iron core.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

## Practical considerations

### Leakage flux

Leakage flux of a transformer
.The ideal transformer model assumes that all flux generated by the primary winding links all the turns of every winding, including itself.^ Equivalent circuit models leakage inductance as series inductors independent of the “ideal transformer”.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ In other words, the overloaded transformer will distort the waveshape from primary to secondary windings, creating harmonics in the secondary winding's output.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ The ability of an inductor to generate this opposing voltage is directly connected with the change in magnetic flux inside the inductor resulting from the change in current, and the number of winding turns in the inductor.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

.In practice, some flux traverses paths that take it outside the windings.^ One way to meet this design criterion is to engineer the transformer with flux leakage paths for magnetic flux to bypass the secondary winding(s).
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

[29] .Such flux is termed leakage flux, and results in leakage inductance in series with the mutually coupled transformer windings.^ Leakage inductance is due to magnetic flux not cutting both windings.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Leakage inductance is caused by magnetic flux not being 100% coupled between windings in a transformer.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Equivalent circuit models leakage inductance as series inductors independent of the “ideal transformer”.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

[28] .Leakage results in energy being alternately stored in and discharged from the magnetic fields with each cycle of the power supply.^ Because iron is a conductor of electricity as well as being an excellent “conductor” of magnetic flux, there will be currents induced in the iron just as there are currents induced in the secondary windings from the alternating magnetic field.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ In other words, some of the magnetic field isn't linking with the secondary coil, and thus cannot couple energy to it: (Figure below ) .
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Leakage inductance is caused by magnetic flux not being 100% coupled between windings in a transformer.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

.It is not directly a power loss (see "Stray losses" below), but results in inferior voltage regulation, causing the secondary voltage to fail to be directly proportional to the primary, particularly under heavy load.^ In Figure below the secondary coil's polarity is oriented so that its voltage directly adds to the primary voltage.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ In Figure below the secondary coil's polarity is oriented so that its voltage directly subtracts from the primary voltage: .
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Any current drawn through the secondary winding by a load will be “reflected” to the primary winding and drawn from the voltage source, as if the source were directly powering a similar load.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

[29] .Transformers are therefore normally designed to have very low leakage inductance.^ Equivalent circuit models leakage inductance as series inductors independent of the “ideal transformer”.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ If its impossible to build a transformer with perfect coupling, but easy to design coils with low inductance, then why not just build all transformers with low-inductance coils and have excellent efficiency even with poor magnetic coupling?” .
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ The reason for this is an imperfection in our transformer design: because the primary and secondary inductances aren't perfectly linked (a k factor of 0.999 instead of 1.000) there is “stray” or “ leakage ” inductance.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

.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.^ There are some applications, however, where poor regulation is actually desired.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ One way to meet this design criterion is to engineer the transformer with flux leakage paths for magnetic flux to bypass the secondary winding(s).
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ If its impossible to build a transformer with perfect coupling, but easy to design coils with low inductance, then why not just build all transformers with low-inductance coils and have excellent efficiency even with poor magnetic coupling?” .
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

[28] .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.^ Transformers can also be used in electrical instrumentation systems.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ As was stated before, discharge lighting circuits require a step-up transformer with “loose” (poor) voltage regulation to ensure reduced voltage after the establishment of an arc through the lamp.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Powering a simple resistive load like this, a good power transformer should exhibit a regulation percentage of less than 3%.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

[30] .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.^ Audio frequency impedance matching transformer.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Sometimes windings will bear current ratings in amps, but this is typically seen on small transformers.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ For now, the most important thing to keep in mind is a transformer's basic operating principle: the transfer of power from the primary to the secondary circuit via electromagnetic coupling.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

[citation needed]
.Leakage inductance is also helpful when transformers are operated in parallel.^ Equivalent circuit models leakage inductance as series inductors independent of the “ideal transformer”.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Leakage inductance tends to worsen a transformer's voltage regulation (secondary voltage “sags” more for a given amount of load current).
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Because leakage inductance is equivalent to an inductance connected in series with the transformer's winding, it manifests itself as a series impedance with the load.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

.It can be shown that if the "per-unit" inductance of two transformers is the same (a typical value is 5%), they will automatically split power "correctly" (e.g.^ Two new TRANSFORMERS TV spots were just released, and they bode well for the future of the film.
• Transformers: JoBlo.com's Upcoming Movies: Posters, Plot, Pictures, Cast, News... 28 January 2010 1:01 UTC www.joblo.com [Source type: General]

^ REVIEW: Power transformers are limited in the amount of power they can transfer from primary to secondary winding(s).
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Typically, such “tap switches” are not engineered to handle full-load current, but must be actuated only when the transformer has been de-energized (no power).
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

500 kVA unit in parallel with 1000 kVA unit, the larger one will carry twice the current).[citation needed]

### 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.^ In this case, the voltage waveform is the derivative of the flux waveform, and the flux waveform is the integral of the voltage waveform.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Or, as stated before, the voltage waveform is the derivative of the flux waveform, and the flux waveform is the integral of the voltage waveform.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ This cannot happen, because the primary coil's induced voltage must remain at the same magnitude and phase in order to balance with the applied voltage, in accordance with Kirchhoff's voltage law.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

[31] .Hypothetically an ideal transformer would work with direct-current excitation, with the core flux increasing linearly with time.^ Because mmf is proportional to current through the magnetizing coil (mmf = NI, where “N” is the number of turns of wire in the coil and “I” is the current through it), the large increases of mmf required to supply the needed increases in flux results in large increases in coil current.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Connecting transformer to line at AC volt peak: Flux increases rapidly from zero, same as steady-state operation.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Again, maintaining low magnetic flux levels in the core is the key to minimizing this effect, which explains why ferroresonant transformers -- which must operate in saturation for a large portion of the current waveform -- operate both hot and noisy.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

[32] .In practice, the flux would rise to the point where magnetic saturation of the core occurs, causing a huge increase in the magnetizing current and overheating the transformer.^ Transformers are also constrained in their performance by the magnetic flux limitations of the core.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Ferroresonance” is a phenomenon associated with the behavior of iron cores while operating near a point of magnetic saturation (where the core is so strongly magnetized that further increases in winding current results in little or no increase in magnetic flux).
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ During saturation, disproportionate amounts of mmf are needed to generate magnetic flux.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

.All practical transformers must therefore operate with alternating (or pulsed) current.^ Again, maintaining low magnetic flux levels in the core is the key to minimizing this effect, which explains why ferroresonant transformers -- which must operate in saturation for a large portion of the current waveform -- operate both hot and noisy.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Being that this is impossible to achieve, transformers must be designed to operate within certain expected ranges of voltages and loads in order to perform as close to ideal as possible.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Some arc welder designs provide arc current adjustment by means of a movable iron core in the transformer, cranked in or out of the winding assembly by the operator.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

[32]
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 and peak magnetic flux density B is given by the universal EMF equation:[26]
$E_{rms} = {\frac {2 \pi f N a B_{peak}} {\sqrt{2}}} \! \approx 4.44 f N a B$
If the flux does not contain even harmonics the following equation can be used for half-cycle average voltage Eavg of any waveshape:
$E_{avg}= 4 f N a B_{peak} \!$
.The EMF of a transformer at a given flux density increases with frequency.^ Connecting transformer to line at AC volt peak: Flux increases rapidly from zero, same as steady-state operation.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Increased frequency results in increased power losses within a power transformer.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ When the magnetic flux increases in response to a rising voltage, it will increase from zero upward, not from a previously negative (magnetized) condition as we would normally have in a transformer that's been powered for awhile.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

[26] .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.^ Audio frequency impedance matching transformer.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ For example, if a power transformer designed to operate at 60 Hz is forced to operate at 50 Hz instead, the flux must reach greater peak levels than before in order to produce the same opposing voltage needed to balance against the source voltage.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Frequently air core transformers are paralleled with a capacitor to tune it to resonance.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

.However properties such as core loss and conductor skin effect also increase with frequency.^ Increased frequency results in increased power losses within a power transformer.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ It is in high-frequency applications that these effects of iron cores are most problematic.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Eddy current losses increase with frequency, so transformers designed to run on higher-frequency power (such as 400 Hz, used in many military and aircraft applications) must use thinner laminations to keep the losses down to a respectable minimum.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

.Aircraft and military equipment employ 400 Hz power supplies which reduce core and winding weight.^ However, when the secondary is “loaded” (current supplied to a load), the winding generates an mmf, which becomes counteracted by a “reflected” mmf in the primary winding to prevent core flux levels from changing.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ The reactor's “power” winding is the one carrying the AC load current, and the “control” winding is one carrying a DC current strong enough to drive the core into saturation: (Figure below ) .
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Eddy current losses increase with frequency, so transformers designed to run on higher-frequency power (such as 400 Hz, used in many military and aircraft applications) must use thinner laminations to keep the losses down to a respectable minimum.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

[33]
.Operation of a transformer at its designed voltage but at a higher frequency than intended will lead to reduced magnetizing current; at lower frequency, the magnetizing current will increase.^ Eddy current losses increase with frequency, so transformers designed to run on higher-frequency power (such as 400 Hz, used in many military and aircraft applications) must use thinner laminations to keep the losses down to a respectable minimum.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Magnetic saturation of a transformer core may be caused by excessive primary voltage, operation at too low of a frequency, and/or by the presence of a DC current in any of the windings.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ For example, if a power transformer designed to operate at 60 Hz is forced to operate at 50 Hz instead, the flux must reach greater peak levels than before in order to produce the same opposing voltage needed to balance against the source voltage.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

.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.^ Because transformers require such long lengths of wire, this loss can be a significant factor.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ For example, if a power transformer designed to operate at 60 Hz is forced to operate at 50 Hz instead, the flux must reach greater peak levels than before in order to produce the same opposing voltage needed to balance against the source voltage.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Depending on the Promotion, we may also collect an Internet email address or other Information and, depending on the Information collected, the user may also be required to confirm his or her agreement to this Privacy Policy and the Terms of Use Agreement.
• Transformers - Trailer | SPIKE 28 January 2010 1:01 UTC www.spike.com [Source type: General]

.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.^ For example, take a step-down transformer with a primary voltage rating of 120 volts, a secondary voltage rating of 48 volts, and a VA rating of 1 kVA (1000 VA).
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ The 250 volt heater would be said to be a higher impedance load than the 125 volt heater.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ The presence of harmonics in a power system is a source of frequencies significantly higher than normal, which may cause overheating in large transformers.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

.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.^ This auto transformer steps voltage down with a single copper-saving tapped winding.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Moving-slide contacts are too impractical to be used in large industrial power transformer designs, but multi-pole switches and winding taps are common for voltage adjustment.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ It would appear that both voltage and current for the two transformer windings are in-phase with each other, at least for our resistive load.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

### Energy losses

.An ideal transformer would have no energy losses, and would be 100% efficient.^ Transformer energy losses tend to worsen with increasing frequency.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Unfortunately, the ideal transformer would have to be infinitely large and heavy to meet these design goals.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ An ideal transformer would have perfect coupling (no leakage inductance), perfect voltage regulation, perfectly sinusoidal exciting current, no hysteresis or eddy current losses, and wire thick enough to handle any amount of current.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

.In practical transformers energy is dissipated in the windings, core, and surrounding structures.^ Resistance in transformer windings contributes to inefficiency, as current will dissipate heat, wasting energy.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Some arc welder designs provide arc current adjustment by means of a movable iron core in the transformer, cranked in or out of the winding assembly by the operator.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ (Figure (b) above ) Toroidal air core transformers also show a higher degree of coupling, particularly for bifilar windings.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

.Larger transformers are generally more efficient, and those rated for electricity distribution usually perform better than 98%.^ The better these two inductors are magnetically coupled, the more efficient the energy transfer between them should be.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Application of 2-φ Niagara generator power produced a 3-φ output for the more efficient 3-φ transmission line.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ A transformer that increases voltage from primary to secondary (more secondary winding turns than primary winding turns) is called a step-up transformer.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

[34]
.Experimental transformers using superconducting windings achieve efficiencies of 99.85%.^ Moving-slide contacts are too impractical to be used in large industrial power transformer designs, but multi-pole switches and winding taps are common for voltage adjustment.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Sometimes dots will be omitted, but when “H” and “X” labels are used to label transformer winding wires, the subscript numbers are supposed to represent winding polarity.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ It is easy to demonstrate simple transformer action using SPICE, setting up the primary and secondary windings of the simulated transformer as a pair of “mutual” inductors.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

[35] .While the increase in efficiency is small, when applied to large heavily loaded transformers the annual savings in energy losses are significant.^ Transformer energy losses tend to worsen with increasing frequency.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ If the load were a resistor (Figure above (b)), the voltage drop originates from electrical energy loss, the “friction” of electrons flowing through the resistance.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Another noise-producing phenomenon in power transformers is the physical reaction force between primary and secondary windings when heavily loaded.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

.A small transformer, such as a plug-in "wall wart" power adapter commonly used for low-power consumer electronics devices, may be as low as 20% efficient, with considerable energy loss even when not supplying any power to the device.^ If its impossible to build a transformer with perfect coupling, but easy to design coils with low inductance, then why not just build all transformers with low-inductance coils and have excellent efficiency even with poor magnetic coupling?” .
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Increased frequency results in increased power losses within a power transformer.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Moving-slide contacts are too impractical to be used in large industrial power transformer designs, but multi-pole switches and winding taps are common for voltage adjustment.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

Though individual losses may be only a few watts, it has been estimated that the cumulative loss from such transformers in the United States alone exceeded 32 billion kilowatt-hours (kWh) in 2002.[36]
.The losses vary with load current, and may be expressed as "no-load" or "full-load" loss.^ Because their “full load” secondary current is 5 amps, CT ratios are usually described in terms of full-load primary amps to 5 amps, like this: .
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Typically, such “tap switches” are not engineered to handle full-load current, but must be actuated only when the transformer has been de-energized (no power).
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Physical forces causing winding vibration may also generate noise under conditions of heavy (high current) secondary winding load.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

.Winding resistance dominates load losses, whereas hysteresis and eddy currents losses contribute to over 99% of the no-load loss.^ Magnetic core losses are also exaggerated with higher frequencies, eddy currents and hysteresis effects becoming more severe.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Resistance in transformer windings contributes to inefficiency, as current will dissipate heat, wasting energy.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ It would appear that both voltage and current for the two transformer windings are in-phase with each other, at least for our resistive load.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

.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).^ Transformer energy losses tend to worsen with increasing frequency.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Because transformers require such long lengths of wire, this loss can be a significant factor.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ If its impossible to build a transformer with perfect coupling, but easy to design coils with low inductance, then why not just build all transformers with low-inductance coils and have excellent efficiency even with poor magnetic coupling?” .
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

[37]
.Transformer losses are divided into losses in the windings, termed copper loss, and those in the magnetic circuit, termed iron loss.^ Induction heating: Primary insulated winding induces current into lossy iron pipe (secondary).
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ This auto transformer steps voltage down with a single copper-saving tapped winding.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Because iron is a conductor of electricity as well as being an excellent “conductor” of magnetic flux, there will be currents induced in the iron just as there are currents induced in the secondary windings from the alternating magnetic field.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

Losses in the transformer arise from:
Winding resistance
Current flowing through the windings causes resistive heating of the conductors. .At higher frequencies, skin effect and proximity effect create additional winding resistance and losses.^ Magnetic core losses are also exaggerated with higher frequencies, eddy currents and hysteresis effects becoming more severe.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Resistive losses aside, the bulk of transformer power loss is due to magnetic effects in the core.
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^ In addition to blocking harmonics created by the saturated core, this resonant circuit also “filters out” harmonic frequencies generated by nonlinear (switching) loads in the secondary winding circuit and any harmonics present in the source voltage, providing “clean” power to the load.
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Hysteresis losses
Each time the magnetic field is reversed, a small amount of energy is lost due to hysteresis within the core. .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.^ Magnetic core losses are also exaggerated with higher frequencies, eddy currents and hysteresis effects becoming more severe.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ (Figure below ) Since flux (Φ) is proportional to the magnetomotive force (mmf) in the core, and the mmf is proportional to winding current, the current waveform will be in-phase with the flux waveform, and both will be lagging the voltage waveform by 90 o : .
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Also, engineering the core for low flux densities provides a safe margin between the normal flux peaks and the core saturation limits to accommodate occasional, abnormal conditions such as frequency variation and DC offset.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

[37]
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.^ While many transformers have ferromagnetic core materials, there are some that do not, their constituent inductors being magnetically linked together through the air.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Magnetic flux through a ferromagnetic material is analogous to current through a conductor: it must be motivated by some force in order to occur.
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^ Additionally, the iron core can be seen in this photograph to be made of many thin sheets (laminations) rather than a solid piece.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

.Eddy currents therefore circulate within the core in a plane normal to the flux, and are responsible for resistive heating of the core material.^ Magnetic core losses are also exaggerated with higher frequencies, eddy currents and hysteresis effects becoming more severe.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Like the lamination sheets, these granules of iron are individually coated in an electrically insulating material, which makes the core nonconductive except for within the width of each granule.
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^ At first, one might expect this secondary coil current to cause additional magnetic flux in the core.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

.The eddy current loss is a complex function of the square of supply frequency and inverse square of the material thickness.^ Magnetic core losses are also exaggerated with higher frequencies, eddy currents and hysteresis effects becoming more severe.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ In order to maximize the eddy current effect, high-frequency alternating current is used rather than power line frequency (60 Hz).
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^ Perhaps the most significant of these “core losses” is eddy-current loss , which is resistive power dissipation due to the passage of induced currents through the iron of the core.
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[37]
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. .This produces the buzzing sound commonly associated with transformers,[25] and in turn causes losses due to frictional heating in susceptible cores.^ Any amount of DC voltage dropped across the primary winding of a transformer will cause additional magnetic flux in the core.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Heat-dissipating “radiator” tubes on the outside of the transformer case provide a convective oil flow path to transfer heat from the transformer's core to ambient air: (Figure below ) .
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Resistive losses aside, the bulk of transformer power loss is due to magnetic effects in the core.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

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.[38]
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..[39] There are also radiative losses due to the oscillating magnetic field, but these are usually small.^ Because iron is a conductor of electricity as well as being an excellent “conductor” of magnetic flux, there will be currents induced in the iron just as there are currents induced in the secondary windings from the alternating magnetic field.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Resistive losses aside, the bulk of transformer power loss is due to magnetic effects in the core.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Perhaps the most significant of these “core losses” is eddy-current loss , which is resistive power dissipation due to the passage of induced currents through the iron of the core.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

### Dot convention

.It is common in transformer schematic symbols for there to be a dot at the end of each coil within a transformer, particularly for transformers with multiple windings on either or both of the primary and secondary sides.^ In phase: primary red to dot, secondary red to dot.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ The primaries of both transformers are connected to the 2-φ voltages.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Photograph of multiple-winding transformer with six windings, a primary and five secondaries.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

.The purpose of the dots is to indicate the direction of each winding relative to the other windings in the transformer.^ In other words, the overloaded transformer will distort the waveshape from primary to secondary windings, creating harmonics in the secondary winding's output.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ It would appear that both voltage and current for the two transformer windings are in-phase with each other, at least for our resistive load.
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^ Sometimes dots will be omitted, but when “H” and “X” labels are used to label transformer winding wires, the subscript numbers are supposed to represent winding polarity.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

.Voltages at the dot end of each winding are in phase, while current flowing into the dot end of a primary coil will result in current flowing out of the dot end of a secondary coil.^ Resistive load on secondary has voltage and current in-phase.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Out of phase: primary red to dot, secondary black to dot.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ (Figure below ) Both current (Figure below ) and voltage (Figure above ) waveforms are in-phase in going from primary to secondary.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

## 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.^ Equivalent circuit models leakage inductance as series inductors independent of the “ideal transformer”.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Consider this transformer circuit: (Figure below ) .
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ A small impedance-matching transformer (about two centimeters in width) for audio-frequency applications is shown in the following photograph: (Figure below ) .
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[40] .Power loss in the windings is current-dependent and is represented as in-series resistances RP and RS.^ Resistance in transformer windings contributes to inefficiency, as current will dissipate heat, wasting energy.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Unless superconducting wires are used, there will always be power dissipated in the form of heat through the resistance of current-carrying conductors.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ It would appear that both voltage and current for the two transformer windings are in-phase with each other, at least for our resistive load.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

Flux leakage results in a fraction of the applied voltage dropped without contributing to the mutual coupling, and thus can be modeled as reactances of each leakage inductance XP and XS in series with the perfectly coupled region.
.Iron 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.^ Magnetic core losses are also exaggerated with higher frequencies, eddy currents and hysteresis effects becoming more severe.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Another “core loss” is that of magnetic hysteresis .
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ That is, its iron core is “stuffed full” of magnetic lines of flux for a large portion of the AC cycle so that variations in supply voltage (primary winding current) have little effect on the core's magnetic flux density, which means the secondary winding outputs a nearly constant voltage despite significant variations in supply (primary winding) voltage.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

[41] .Since the core flux is proportional to the applied voltage, the iron loss can be represented by a resistance RC in parallel with the ideal transformer.^ Voltage and flux waveforms for a peaking transformer.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Frequently air core transformers are paralleled with a capacitor to tune it to resonance.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ The AR transformer has a soft on feature that applies the voltage gradually.

.A core with finite permeability requires a magnetizing current IM to maintain the mutual flux in the core.^ At first, one might expect this secondary coil current to cause additional magnetic flux in the core.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ (Figure below ) Since flux (Φ) is proportional to the magnetomotive force (mmf) in the core, and the mmf is proportional to winding current, the current waveform will be in-phase with the flux waveform, and both will be lagging the voltage waveform by 90 o : .
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ It should be mentioned that the current through an iron-core inductor is not perfectly sinusoidal (sine-wave shaped), due to the nonlinear B/H magnetization curve of iron.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

.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.^ This ensures that the relationship between mmf and Φ is more linear throughout the flux cycle, which is good because it makes for less distortion in the magnetization current waveform.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Because the mathematical relationship between magnetic flux and mmf is directly proportional, and because the mathematical relationship between mmf and current is also directly proportional (no rates-of-change present in either equation), the current through the coil will be in-phase with the flux wave as in (Figure below ) .
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ REVIEW: The phase relationships for voltage and current between primary and secondary circuits of a transformer are direct: ideally, zero phase shift.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

[41] .With a sinusoidal supply, the core flux lags the induced EMF by 90° and this effect can be modeled as a magnetizing reactance (reactance of an effective inductance) XM in parallel with the core loss component.^ Magnetic flux, like current, lags applied voltage by 90 o .
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Magnetic flux in the core (Φ) lags 90 o behind the source voltage waveform.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Another “core loss” is that of magnetic hysteresis .
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

RC and XM are sometimes together termed the magnetizing branch of the model. .If the secondary winding is made open-circuit, the current I0 taken by the magnetizing branch represents the transformer's no-load current.^ No current will exist in the secondary coil, since it is open-circuited.
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^ Because CTs are designed to be powering ammeters, which are low-impedance loads, and they are wound as voltage step-up transformers, they should never, ever be operated with an open-circuited secondary winding.
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^ Sometimes windings will bear current ratings in amps, but this is typically seen on small transformers.
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[40]
.The secondary impedance RS and XS is frequently moved (or "referred") to the primary side after multiplying the components by the impedance scaling factor (NP/NS)2.^ As with the first transformer example we looked at, power transfer efficiency is very good from the primary to the secondary sides of the device.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Equality of voltage and current between the primary and secondary sides of a transformer, however, is not the norm for all transformers.
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^ The transformer isolates the common-mode voltage so that it is not impressed upon the primary circuit at all, but rather isolated to the secondary side.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

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.^ Equivalent circuit models leakage inductance as series inductors independent of the “ideal transformer”.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ However, sometimes such large numbers of files might cause problems hitting user quotas or other runtime limitations.
• components:transformers [CloverETL wiki] 28 January 2010 1:01 UTC wiki.cloveretl.org [Source type: Reference]

[40] .Analysis may be simplified by moving the magnetizing branch to the left of the primary impedance, an implicit assumption that the magnetizing current is low, and then summing primary and referred secondary impedances, resulting in so-called equivalent impedance.^ Primary and secondary currents are in-phase.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Because transformers can step voltage and current to different levels, and because power is transferred equivalently between primary and secondary windings, they can be used to “convert” the impedance of a load to a different level.
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^ Voltage gets dropped across this series impedance, resulting in a reduced load voltage: voltage across the load “sags” as load current increases.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

.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.^ Short Circuit Protection: In the event of an electrical short, the transformer will stop functioning.

^ Equivalent circuit models leakage inductance as series inductors independent of the “ideal transformer”.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Though it may seem strange to intentionally short-circuit a power system component, it is perfectly proper and quite necessary when working with current transformers.
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## Types

.A wide variety of transformer designs are used for different applications, though they share several common features.^ The total load of 8 fixtures is 280W. We offer 4 different transformers - 50W, 75W, 100W and 150W. This application requires two 150W transformers (EN-12PX-AR).

^ Moving-slide contacts are too impractical to be used in large industrial power transformer designs, but multi-pole switches and winding taps are common for voltage adjustment.
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Important common transformer types include:

### 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.^ This auto transformer steps voltage down with a single copper-saving tapped winding.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ If electrical isolation between secondary circuits is not of great importance, a similar effect can be obtained by “tapping” a single secondary winding at multiple points along its length, like Figure below .
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^ Carrying the concept of winding taps further, we end up with a “variable transformer,” where a sliding contact is moved along the length of an exposed secondary winding, able to connect with it at any point along its length.
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.The primary voltage is applied across two of the terminals, and the secondary voltage taken from one of these and the third terminal.^ This cannot happen, because the primary coil's induced voltage must remain at the same magnitude and phase in order to balance with the applied voltage, in accordance with Kirchhoff's voltage law.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Therefore induced secondary voltage e s is the same magnitude and phase as the primary voltage e p.
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^ The primary current is very close to being the same, but notice how the secondary voltage has fallen well below the primary voltage (1.95 volts versus 10 volts at the primary).
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.The primary and secondary circuits therefore have a number of windings turns in common.^ For now, the most important thing to keep in mind is a transformer's basic operating principle: the transfer of power from the primary to the secondary circuit via electromagnetic coupling.
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^ The secondary winding is wound in close proximity to the primary, usually around the same nonmagnetic form.
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^ Therefore induced secondary voltage e s is the same magnitude and phase as the primary voltage e p.
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[42] .Since the volts-per-turn is the same in both windings, each develops a voltage in proportion to its number of turns.^ The primary current is very close to being the same, but notice how the secondary voltage has fallen well below the primary voltage (1.95 volts versus 10 volts at the primary).
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ (Figure below ) Since flux (Φ) is proportional to the magnetomotive force (mmf) in the core, and the mmf is proportional to winding current, the current waveform will be in-phase with the flux waveform, and both will be lagging the voltage waveform by 90 o : .
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ It would appear that both voltage and current for the two transformer windings are in-phase with each other, at least for our resistive load.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

.An adjustable autotransformer is made by exposing part of the winding coils and making the secondary connection through a sliding brush, giving a variable turns ratio.^ Variable transformers can be made by providing a movable arm that sweeps across the length of a winding, making contact with the winding at any point along its length.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ These opposing mmf's generated between primary and secondary windings as a result of secondary (load) current produce a repulsive, physical force between the windings which will tend to make them vibrate.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Tesla Coil: A few heavy primary turns, many secondary turns.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

[43] Such a device is often referred to as a variac.

### Polyphase transformers

Three-phase step-down transformer mounted between two utility poles
.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.^ For example, you may have a total load of 60W (the equivalent of three Button Lights), and you are using a 100W transformer (EN-12PE-AR).

.In this case, the magnetic circuits are connected together, the core thus containing a three-phase flow of flux.^ (Figure below ) Since flux (Φ) is proportional to the magnetomotive force (mmf) in the core, and the mmf is proportional to winding current, the current waveform will be in-phase with the flux waveform, and both will be lagging the voltage waveform by 90 o : .
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Flux containment (making sure a transformer's magnetic flux doesn't escape so as to interfere with another device, and making sure other devices' magnetic flux is shielded from the transformer core) is another concern shared both by inductors and transformers.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ If the transformer happens to have some residual magnetism in its core at the moment of connection to the source, the inrush could be even more severe.
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[44] .A number of winding configurations are possible, giving rise to different attributes and phase shifts.^ On the other hand, if the dots on each winding of the transformer do not match up, the phase shift will be 180 o between primary and secondary, like this: (Figure below ) .
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

[45] .One particular polyphase configuration is the zigzag transformer, used for grounding and in the suppression of harmonic currents.^ REVIEW: Transformers can be used to transform impedance as well as voltage and current.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Since we're going from a high impedance (high voltage, low current) supply to a low impedance (low voltage, high current) load, we'll need to use a step-down transformer: (Figure below ) .
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^ REVIEW: By being able to transfer power from one circuit to another without the use of interconnecting conductors between the two circuits, transformers provide the useful feature of electrical isolation .
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

[46]

### Leakage transformers

Leakage transformer
.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.^ The transformation ratio of a transformer will be equal to the square root of its primary to secondary inductance (L) ratio.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ A transformer that increases voltage from primary to secondary (more secondary winding turns than primary winding turns) is called a step-up transformer.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ A transformer designed to increase voltage from primary to secondary is called a step-up transformer.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

.This provides a transformer with an inherent current limitation due to the loose coupling between its primary and the secondary windings.^ REVIEW: Power transformers are limited in the amount of power they can transfer from primary to secondary winding(s).
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^ The wire gauge can also be seen to differ between primary and secondary windings.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Primary and secondary currents are in-phase.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

.The output and input currents are low enough to prevent thermal overload under all load conditions—even if the secondary is shorted.^ If its impossible to build a transformer with perfect coupling, but easy to design coils with low inductance, then why not just build all transformers with low-inductance coils and have excellent efficiency even with poor magnetic coupling?” .
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Since we're going from a high impedance (high voltage, low current) supply to a low impedance (low voltage, high current) load, we'll need to use a step-down transformer: (Figure below ) .
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ These opposing mmf's generated between primary and secondary windings as a result of secondary (load) current produce a repulsive, physical force between the windings which will tend to make them vibrate.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

.Leakage transformers are used for arc welding and high voltage discharge lamps (neon lamps and cold cathode fluorescent lamps, which are series-connected up to 7.5 kV AC).^ As was stated before, discharge lighting circuits require a step-up transformer with “loose” (poor) voltage regulation to ensure reduced voltage after the establishment of an arc through the lamp.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Equivalent circuit models leakage inductance as series inductors independent of the “ideal transformer”.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ As our transformers operate at high frequency, the voltage cannot be read with most meters.

.It acts then both as a voltage transformer and as a magnetic ballast.^ The primaries of both transformers are connected to the 2-φ voltages.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Flux containment (making sure a transformer's magnetic flux doesn't escape so as to interfere with another device, and making sure other devices' magnetic flux is shielded from the transformer core) is another concern shared both by inductors and transformers.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ It would appear that both voltage and current for the two transformer windings are in-phase with each other, at least for our resistive load.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

.Other applications are short-circuit-proof extra-low voltage transformers for toys or doorbell installations.^ Short Circuit Protection: In the event of an electrical short, the transformer will stop functioning.

^ It would appear that both voltage and current for the two transformer windings are in-phase with each other, at least for our resistive load.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Since we're going from a high impedance (high voltage, low current) supply to a low impedance (low voltage, high current) load, we'll need to use a step-down transformer: (Figure below ) .
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

### Resonant transformers

A resonant transformer is a kind of leakage transformer. .It uses the leakage inductance of its secondary windings in combination with external capacitors, to create one or more resonant circuits.^ To combat this side effect, ferroresonant transformers have an auxiliary secondary winding paralleled with one or more capacitors, forming a resonant circuit tuned to the power supply frequency.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Leakage inductance is due to magnetic flux not cutting both windings.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ In other words, the overloaded transformer will distort the waveshape from primary to secondary windings, creating harmonics in the secondary winding's output.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

.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.^ The Tesla Coil is a resonant, high-frequency step-up transformer used to produce extremely high voltages.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ A Tesla Coil is a resonant, air-core, step-up transformer designed to produce very high AC voltages at high frequency.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ High voltage high frequency discharge from Tesla coil.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

[47] .One of the applications of the resonant transformer is for the CCFL inverter.^ One consumer application of the variable transformer is in speed controls for model train sets, especially the train sets of the 1950's and 1960's.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ This capacitance can be significant enough to give the transformer a natural resonant frequency , which can be problematic in signal applications.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

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.[48]

### Audio transformers

.Audio transformers are those specifically designed for use in audio circuits.^ Moving-slide contacts are too impractical to be used in large industrial power transformer designs, but multi-pole switches and winding taps are common for voltage adjustment.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Aside from power ratings and power losses, transformers often harbor other undesirable limitations which circuit designers must be made aware of.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Printed circuit board mounted audio impedance matching transformer, top right.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

.They can be used to block radio frequency interference or the DC component of an audio signal, to split or combine audio signals, or to provide impedance matching between high and low impedance circuits, such as between a high impedance tube (valve) amplifier output and a low impedance loudspeaker, or between a high impedance instrument output and the low impedance input of a mixing console.^ Audio frequency impedance matching transformer.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ The “RFC” inductors are “Radio Frequency Chokes,” which act as high impedances to prevent the AC source from interfering with the oscillating tank circuit.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Also, engineering the core for low flux densities provides a safe margin between the normal flux peaks and the core saturation limits to accommodate occasional, abnormal conditions such as frequency variation and DC offset.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

.Such transformers were originally designed to connect different telephone systems to one another while keeping their respective power supplies isolated, and are still commonly used to interconnect professional audio systems or system components.^ Transformers can also be used in electrical instrumentation systems.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Isolation transformer isolates power out from the power line.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ The 24V mode allows installation in longer runs, such as around the perimeter of a room (especially when used with our Linear Track System).

.Being magnetic devices, audio transformers are susceptible to external magnetic fields such as those generated by AC current-carrying conductors.^ All ferromagnetic materials tend to retain some degree of magnetization after exposure to an external magnetic field.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ In such a machine, a motor is mechanically coupled to a generator, the generator designed to produce the desired levels of voltage and current at the rotating speed of the motor.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ That is, when the conductor through the center of the torus is carrying 50 amps of current (AC), there will be 5 amps of current induced in the CT's winding.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

."Hum" is a term commonly used to describe unwanted signals originating from the "mains" power supply (typically 50 or 60 Hz).^ The term is commonly used in everyday speech to describe stoic toughness.
• CTRL+V THREAD! [part 2] - The Forbidden Garden of DQN @ 4-ch Archives 20 September 2009 21:52 UTC archives.4-ch.net [Source type: General]

^ Magnetic flux is higher in a transformer core driven by 50 Hz as compared to 60 Hz for the same voltage.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ In order to maximize the eddy current effect, high-frequency alternating current is used rather than power line frequency (60 Hz).
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

.Audio transformers used for low-level signals, such as those from microphones, often include shielding to protect against extraneous magnetically coupled signals.^ Since we're going from a high impedance (high voltage, low current) supply to a low impedance (low voltage, high current) load, we'll need to use a step-down transformer: (Figure below ) .
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ The transformer in Figure above is intended to provide both high and low voltages necessary in an electronic system using vacuum tubes.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ As has already been observed, transformers must be well designed in order to achieve acceptable power coupling, tight voltage regulation, and low exciting current distortion.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

### Instrument transformers

.Instrument transformers are used for measuring voltage and current in electrical power systems, and for power system protection and control.^ REVIEW: Transformers can be used to transform impedance as well as voltage and current.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Transformers can also be used in electrical instrumentation systems.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Due to transformers' ability to step up or step down voltage and current, and the electrical isolation they provide, they can serve as a way of connecting electrical instrumentation to high-voltage, high current power systems.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

where a voltage or current is too large to be conveniently used by an instrument, it can be scaled down to a standardized, low value. .Instrument transformers isolate measurement, protection and control circuitry from the high currents or voltages present on the circuits being measured or controlled.^ In fact, this design of transformer was quite common in vacuum tube power supply circuits, which were required to supply low voltage for the tubes' filaments (typically 6 or 12 volts) and high voltage for the tubes' plates (several hundred volts) from a nominal primary voltage of 110 volts AC. Not only are voltages and currents of completely different magnitudes possible with such a transformer, but all circuits are electrically isolated from one another.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Due to transformers' ability to step up or step down voltage and current, and the electrical isolation they provide, they can serve as a way of connecting electrical instrumentation to high-voltage, high current power systems.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Short Circuit Protection: In the event of an electrical short, the transformer will stop functioning.

Current transformers, designed for placing around conductors
.A current transformer is a transformer designed to provide a current in its secondary coil proportional to the current flowing in its primary coil.^ Primary and secondary currents are in-phase.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Also, transformers must be designed to carry the expected values of primary and secondary winding current without any trouble.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Induction heating: Primary insulated winding induces current into lossy iron pipe (secondary).
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

[49]
.Voltage transformers (VTs), also referred to as "potential transformers" (PTs), are designed to have an accurately known transformation ratio in both magnitude and phase, over a range of measuring circuit impedances.^ The primaries of both transformers are connected to the 2-φ voltages.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Potential transformers are designed to provide as accurate a voltage step-down ratio as possible.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ A Potential Transformer (PT) is a special instrument transformer designed to provide a precise voltage step-down ratio for voltmeters measuring high power system voltages.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

.A voltage transformer is intended to present a negligible load to the supply being measured.^ Being that this is impossible to achieve, transformers must be designed to operate within certain expected ranges of voltages and loads in order to perform as close to ideal as possible.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ It would appear that both voltage and current for the two transformer windings are in-phase with each other, at least for our resistive load.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ A Potential Transformer (PT) is a special instrument transformer designed to provide a precise voltage step-down ratio for voltmeters measuring high power system voltages.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

.The low secondary voltage allows protective relay equipment and measuring instruments to be operated at a lower voltages.^ At either end (both the generator and at the loads), voltage levels are reduced by transformers for safer operation and less expensive equipment.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ The lower the percentage (closer to zero), the more stable the secondary voltage and the better the regulation it will provide.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Failure to heed this warning will result in the CT producing extremely high secondary voltages, dangerous to equipment and personnel alike.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

[50]
.Both current and voltage instrument transformers are designed to have predictable characteristics on overloads.^ The primaries of both transformers are connected to the 2-φ voltages.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ In such a machine, a motor is mechanically coupled to a generator, the generator designed to produce the desired levels of voltage and current at the rotating speed of the motor.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Note that while the PT is a step-down device, the Current Transformer (or CT ) is a step-up device (with respect to voltage), which is what is needed to step down the power line current.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

.Proper operation of over-current protection relays requires that current transformers provide a predictable transformation ratio even during a short-circuit.^ Short Circuit Protection: In the event of an electrical short, the transformer will stop functioning.

^ After the shorted condition is removed and power is re-applied, the transformer will continue normal operation with no adverse effect to its life span.

^ Circuit Overload Protection: The transformer will cease functioning in the event of a circuit overload condition.

## Classification

Transformers can be classified in different ways:
• By power capacity: 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: 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 (equal or near-equal ratio), variable.

## Construction

### Cores

Laminated core transformer showing edge of laminations at top of photo

#### Laminated steel cores

.Transformers for use at power or audio frequencies typically have cores made of high permeability silicon steel.^ Air core transformers are used at radio frequencies when iron core losses are too high.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Audio frequency impedance matching transformer.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Frequently air core transformers are paralleled with a capacitor to tune it to resonance.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

[51] .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.^ That is, its iron core is “stuffed full” of magnetic lines of flux for a large portion of the AC cycle so that variations in supply voltage (primary winding current) have little effect on the core's magnetic flux density, which means the secondary winding outputs a nearly constant voltage despite significant variations in supply (primary winding) voltage.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Leakage inductance is due to magnetic flux not cutting both windings.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ With less inductance in the primary winding, there is less inductive reactance, and consequently a much larger magnetizing current.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

[52] .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.^ Magnetic effects in a transformer's iron core also contribute to inefficiency.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Dividing the iron core into thin insulated laminations minimizes eddy current loss.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ The main strategy in mitigating these wasteful eddy currents in transformer cores is to form the iron core in sheets, each sheet covered with an insulating varnish so that the core is divided up into thin slices.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

[9] .Later designs constructed the core by stacking layers of thin steel laminations, a principle that has remained in use.^ Additionally, the iron core can be seen in this photograph to be made of many thin sheets (laminations) rather than a solid piece.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Dividing the iron core into thin insulated laminations minimizes eddy current loss.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

.Each lamination is insulated from its neighbors by a thin non-conducting layer of insulation.^ Dividing the iron core into thin insulated laminations minimizes eddy current loss.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

[44] .The universal transformer equation indicates a minimum cross-sectional area for the core to avoid saturation.^ Transformer cross-section cut shows core and windings.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Schematic symbol for transformer consists of two inductor symbols, separated by lines indicating a ferromagnetic core.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Normally, core saturation in a transformer results in distortion of the sinewave shape, and the ferroresonant transformer is no exception.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

.The effect of laminations is to confine eddy currents to highly elliptical paths that enclose little flux, and so reduce their magnitude.^ Dividing the iron core into thin insulated laminations minimizes eddy current loss.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ This coil current resulting from the sum total of all magnetic effects in the core (dΦ/dt magnetization plus hysteresis losses, eddy current losses, etc.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Among the effects are eddy currents (circulating induction currents in the iron core) and hysteresis (power lost due to overcoming the tendency of iron to magnetize in a particular direction).
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

Thinner laminations reduce losses,[51] but are more laborious and expensive to construct.[53] .Thin laminations are generally used on high frequency transformers, with some types of very thin steel laminations able to operate up to 10 kHz.^ With a step-up transformer, we could operate the 250 volt heater element on the 125 volt power system like Figure below .
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ You must declare some variables and use two functions: append() and transform().
• components:transformers [CloverETL wiki] 28 January 2010 1:01 UTC wiki.cloveretl.org [Source type: Reference]

^ Some arc welder designs provide arc current adjustment by means of a movable iron core in the transformer, cranked in or out of the winding assembly by the operator.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

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".[53] Such a design tends to exhibit more losses, but is very economical to manufacture.^ Transformer energy losses tend to worsen with increasing frequency.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Because transformers require such long lengths of wire, this loss can be a significant factor.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Magnetic core losses are also exaggerated with higher frequencies, eddy currents and hysteresis effects becoming more severe.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

.The cut-core or C-core type is made by winding a steel strip around a rectangular form and then bonding the layers together.^ (Figure below ) True to its name, an air core transformer has its windings wrapped around a nonmagnetic form, usually a hollow tube of some material.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ The secondary winding is wound in close proximity to the primary, usually around the same nonmagnetic form.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ In the next photograph, Figure below , a transformer is shown cut in half, exposing the cross-section of the iron core as well as both windings.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

.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.^ A linear variable differential transformer (LVDT) has an AC driven primary wound between two secondaries on a cylindrical air core form.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

[53] 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.^ All ferromagnetic materials tend to retain some degree of magnetization after exposure to an external magnetic field.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Resistive losses aside, the bulk of transformer power loss is due to magnetic effects in the core.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ With enough DC current, the magnetic core can be saturated, decreasing the inductance of the power winding in a controlled fashion.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

.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 alternating current.^ Magnetic core losses are also exaggerated with higher frequencies, eddy currents and hysteresis effects becoming more severe.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ At first, one might expect this secondary coil current to cause additional magnetic flux in the core.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Because iron is a conductor of electricity as well as being an excellent “conductor” of magnetic flux, there will be currents induced in the iron just as there are currents induced in the secondary windings from the alternating magnetic field.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

[54] .Overcurrent protection devices such as fuses must be selected to allow this harmless inrush to pass.^ Because of this, transformer overcurrent protection devices are usually of the “slow-acting” variety, so as to tolerate current surges such as this without opening the circuit.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

.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.^ Isolation transformer isolates power out from the power line.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ In 1896, General Electric built a 35.5 km (22 mi) three-phase transmission line operated at 11 kV to transmit power to Buffalo, New York, from the Niagara Falls Project.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Indeed, the transformer has made long-distance transmission of electric power a practical reality, as AC voltage can be “stepped up” and current “stepped down” for reduced wire resistance power losses along power lines connecting generating stations with loads.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

[55]
.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.^ Air core transformers are used at radio frequencies when iron core losses are too high.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Additionally, winding conductor insulation is a concern where high voltages are encountered, as they often are in step-up and step-down power distribution transformers.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Since we're going from a high impedance (high voltage, low current) supply to a low impedance (low voltage, high current) load, we'll need to use a step-down transformer: (Figure below ) .
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

.The higher initial cost of the core material is offset over the life of the transformer by its lower losses at light load.^ Magnetic core losses are also exaggerated with higher frequencies, eddy currents and hysteresis effects becoming more severe.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Magnetic flux is higher in a transformer core driven by 50 Hz as compared to 60 Hz for the same voltage.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ While many transformers have ferromagnetic core materials, there are some that do not, their constituent inductors being magnetically linked together through the air.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

[56]

#### 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.^ If we desired to operate the 250 volt heater element directly on a 125 volt power system, we would end up being disappointed.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ The main strategy in mitigating these wasteful eddy currents in transformer cores is to form the iron core in sheets, each sheet covered with an insulating varnish so that the core is divided up into thin slices.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ For now, the most important thing to keep in mind is a transformer's basic operating principle: the transfer of power from the primary to the secondary circuit via electromagnetic coupling.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

.These materials combine high magnetic permeability with high bulk electrical resistivity.^ Consequently, these “eddy currents” must overcome significant electrical resistance as they circulate through the core.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Like the lamination sheets, these granules of iron are individually coated in an electrically insulating material, which makes the core nonconductive except for within the width of each granule.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Resistive losses aside, the bulk of transformer power loss is due to magnetic effects in the core.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

.For frequencies extending beyond the VHF band, cores made from non-conductive magnetic ceramic materials called ferrites are common.^ Core materials other than air such as powdered iron or ferrite are preferred for lower radio frequencies.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Toroidal air core transformers are rare except for VHF (Very High Frequency) work.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ While many transformers have ferromagnetic core materials, there are some that do not, their constituent inductors being magnetically linked together through the air.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

[53] .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.^ Frequently air core transformers are paralleled with a capacitor to tune it to resonance.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Some arc welder designs provide arc current adjustment by means of a movable iron core in the transformer, cranked in or out of the winding assembly by the operator.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ To combat this side effect, ferroresonant transformers have an auxiliary secondary winding paralleled with one or more capacitors, forming a resonant circuit tuned to the power supply frequency.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

#### Toroidal cores

Small toroidal core transformer
.Toroidal transformers are built around a ring-shaped core, which, depending on operating frequency, is made from a long strip of silicon steel or permalloy wound into a coil, powdered iron, or ferrite.^ Air core transformers may be wound on cylindrical (a) or toroidal (b) forms.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ A ferrite core is suitable at these frequencies.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Powdered iron cores are often found in transformers handling radio-frequency currents.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

[57] 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.[30] .The cross-section of the ring is usually square or rectangular, but more expensive cores with circular cross-sections are also available.^ In the next photograph, Figure below , a transformer is shown cut in half, exposing the cross-section of the iron core as well as both windings.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ These induced currents -- as described by the perpendicularity clause of Faraday's Law -- tend to circulate through the cross-section of the core perpendicularly to the primary winding turns.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Transformer cross-section cut shows core and windings.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

.The primary and secondary coils are often wound concentrically to cover the entire surface of the core.^ Ferromagnetic core with primary coil (AC driven) and secondary coil.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ The secondary winding is wound in close proximity to the primary, usually around the same nonmagnetic form.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ At first, one might expect this secondary coil current to cause additional magnetic flux in the core.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

.This minimizes the length of wire needed, and also provides screening to minimize the core's magnetic field from generating electromagnetic interference.^ During saturation, disproportionate amounts of mmf are needed to generate magnetic flux.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Flux containment (making sure a transformer's magnetic flux doesn't escape so as to interfere with another device, and making sure other devices' magnetic flux is shielded from the transformer core) is another concern shared both by inductors and transformers.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Magnetomotive force generated by an electromagnet coil is equal to the amount of current through that coil (in amps) multiplied by the number of turns of that coil around the core (the SI unit for mmf is the amp-turn ).
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

.Toroidal transformers are more efficient than the cheaper laminated E-I types for a similar power level.^ I guarantee you they are more surprised than anyone at how well Transformers 2 has done.
• Orci & Kurtzman Talk Trek v Transformers & Future Prime Universe + more | TrekMovie.com 3 February 2010 18:59 UTC trekmovie.com [Source type: General]

^ If Trek were more like Star Wars or Transformers would it make similar numbers?
• Orci & Kurtzman Talk Trek v Transformers & Future Prime Universe + more | TrekMovie.com 3 February 2010 18:59 UTC trekmovie.com [Source type: General]

^ If Trek could make similar numbers to SW or Trans, would Paramount opt to change Trek to make more money than it already does?
• Orci & Kurtzman Talk Trek v Transformers & Future Prime Universe + more | TrekMovie.com 3 February 2010 18:59 UTC trekmovie.com [Source type: General]

.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 impressed voltage in this example is often called a common-mode voltage because it is seen at more than one point in the circuit with reference to the common point of ground.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Furthermore, since the DC control current through both reactors produces magnetic fluxes in different directions through the reactor cores, one reactor will saturate more in one cycle of the AC power while the other reactor will saturate more in the other, thus equalizing the control action through each half-cycle so that the AC power is “throttled” symmetrically.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ If you want to split these records into more records (by one for each month of a year), such new records will consist of 4 fields.
• components:transformers [CloverETL wiki] 28 January 2010 1:01 UTC wiki.cloveretl.org [Source type: Reference]

The main disadvantages are higher cost and limited power capacity (see "Classification" above). 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 switch-mode power supplies. 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 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.^ Consequently some messages and transmissions may not be processed in a timely fashion or at all, and some features or functions may be restricted or delayed or become completely inoperable.
• Transformers - Trailer | SPIKE 28 January 2010 1:01 UTC www.spike.com [Source type: General]

^ They are not stupid, and doing what you are talking about for some ethereal Transformers blockbuster status risks not achieving that status and blowing off its core audience, losing everything.
• Orci & Kurtzman Talk Trek v Transformers & Future Prime Universe + more | TrekMovie.com 3 February 2010 18:59 UTC trekmovie.com [Source type: General]

^ Transformers blockbuster status risks not achieving that status and blowing off its core audience, losing everything.
• Orci & Kurtzman Talk Trek v Transformers & Future Prime Universe + more | TrekMovie.com 3 February 2010 18:59 UTC trekmovie.com [Source type: General]

#### 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.[28] The leakage inductance is inevitably high, resulting in very poor regulation, and so such designs are unsuitable for use in power distribution.[28] They have however very high bandwidth, and are frequently employed in radio-frequency applications,[58] 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.^ What they're trying to do is to create a virtual paradigm shift, and using a collaborative effort, they will fundamentally alter the synergy between these two channels.
• CTRL+V THREAD! [part 2] - The Forbidden Garden of DQN @ 4-ch Archives 20 September 2009 21:52 UTC archives.4-ch.net [Source type: General]

### Windings

Windings are usually arranged concentrically to minimize flux leakage.
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.^ If Trek were equal to Transformers, they could have still made INS & NEM and both grossed a billion dollars between them and kept making them.
• Orci & Kurtzman Talk Trek v Transformers & Future Prime Universe + more | TrekMovie.com 3 February 2010 18:59 UTC trekmovie.com [Source type: General]

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.
.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.^ You must not alter, delete or conceal any copyright or other notices contained on the Site, including notices on any Material you download, transmit, display, print or reproduce from the Site.
• Transformers - Trailer | SPIKE 28 January 2010 1:01 UTC www.spike.com [Source type: General]

^ Or maybe FC was actually part of the current timeline, not the prime one, in which case all is right.
• Orci & Kurtzman Talk Trek v Transformers & Future Prime Universe + more | TrekMovie.com 3 February 2010 18:59 UTC trekmovie.com [Source type: General]

^ Your use of the Site is subject to all applicable local, state, national laws and regulations and, in some cases, international treaties.
• Transformers - Trailer | SPIKE 28 January 2010 1:01 UTC www.spike.com [Source type: General]

[31] .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 enameled magnet wire, such as Formvar wire.^ This was probably discovered by someone who found out the hard way that there was a potential difference between the two, and who then wired in the switch as a joke.
• CTRL+V THREAD! [part 2] - The Forbidden Garden of DQN @ 4-ch Archives 20 September 2009 21:52 UTC archives.4-ch.net [Source type: General]

Larger power transformers operating at high voltages may be wound with copper rectangular strip conductors insulated by oil-impregnated paper and blocks of pressboard.[59]
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.[31] .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.^ Setting it too low can be dangerous since pretty big number addresses might get rejected just because of high latency of DNS domainCacheSize the more the better..
• components:transformers [CloverETL wiki] 28 January 2010 1:01 UTC wiki.cloveretl.org [Source type: Reference]

[59] 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.^ If Trek could make similar numbers to SW or Trans, would Paramount opt to change Trek to make more money than it already does?
• Orci & Kurtzman Talk Trek v Transformers & Future Prime Universe + more | TrekMovie.com 3 February 2010 18:59 UTC trekmovie.com [Source type: General]

[59]
.For signal transformers, the windings may be arranged in a way to minimize leakage inductance and stray capacitance to improve high-frequency response.^ Kirk and Khan clashing may be inevitable, there is simply no way Orci and Kurtzman can IMPROVE on the story.
• Orci & Kurtzman Talk Trek v Transformers & Future Prime Universe + more | TrekMovie.com 3 February 2010 18:59 UTC trekmovie.com [Source type: General]

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. .The taps may be connected to an automatic on-load tap changer for voltage regulation of distribution circuits.^ Now the circuit ground within the machine isn't necessarily at the same potential as the case ground, so flipping the switch connected the circuit ground to the case ground, causing a voltage drop/jump which reset the machine.
• CTRL+V THREAD! [part 2] - The Forbidden Garden of DQN @ 4-ch Archives 20 September 2009 21:52 UTC archives.4-ch.net [Source type: General]

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.
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. .This produces transformers more suited to damp or dirty environments, but at increased manufacturing cost.^ One major improvement, and probably the reason I enjoyed this movie more, was the increased role of the transformers themselves–notably Optimus Prime.
• Orci & Kurtzman Talk Trek v Transformers & Future Prime Universe + more | TrekMovie.com 3 February 2010 18:59 UTC trekmovie.com [Source type: General]

[60]

### Coolant

Cut-away view of three-phase oil-cooled transformer. The oil reservoir is visible at the top. Radiative fins aid the dissipation of heat.
High temperatures will damage the winding insulation.[61] Small transformers do not generate significant heat and are cooled by air circulation and radiation of heat. .Power transformers rated up to several hundred kVA can be adequately cooled by natural convective air-cooling, sometimes assisted by fans.^ One thing I thought might be a cool way to address all the fan complaints is to have nature correcting the imbalances caused by Spock by “resetting” the universe.
• Orci & Kurtzman Talk Trek v Transformers & Future Prime Universe + more | TrekMovie.com 3 February 2010 18:59 UTC trekmovie.com [Source type: General]

[62] In larger transformers, part of the design problem is removal of heat. Some power transformers are immersed in transformer oil that both cools and insulates the windings.[63] The oil is a highly refined mineral oil that remains stable at transformer operating temperature. Indoor liquid-filled transformers must use a non-flammable liquid, or must be located in fire resistant rooms.[64] .Air-cooled dry transformers are preferred for indoor applications even at capacity ratings where oil-cooled construction would be more economical, because their cost is offset by the reduced building construction cost.^ If Trek were more like Star Wars or Transformers would it make similar numbers?
• Orci & Kurtzman Talk Trek v Transformers & Future Prime Universe + more | TrekMovie.com 3 February 2010 18:59 UTC trekmovie.com [Source type: General]

.The oil-filled tank often has radiators through which the oil circulates by natural convection; some large transformers employ forced circulation of the oil by electric pumps, aided by external fans or water-cooled heat exchangers.^ One thing I thought might be a cool way to address all the fan complaints is to have nature correcting the imbalances caused by Spock by “resetting” the universe.
• Orci & Kurtzman Talk Trek v Transformers & Future Prime Universe + more | TrekMovie.com 3 February 2010 18:59 UTC trekmovie.com [Source type: General]

[63] Oil-filled transformers undergo prolonged drying processes to ensure that the transformer is completely free of water vapor before the cooling oil is introduced. This helps prevent electrical breakdown under load. Oil-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.[54]
Polychlorinated biphenyls have properties that once favored their use as a coolant, though concerns over their environmental persistence led to a widespread ban on their use.[65] 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.[61][64] .Before 1977, even transformers that were nominally filled only with mineral oils may also have been contaminated with polychlorinated biphenyls at 10-20 ppm.^ For the last 10 years, I only have to get down around #4 Pirates of the Caribbean to find a film the critics panned almost as badly as Transformers 2.
• Orci & Kurtzman Talk Trek v Transformers & Future Prime Universe + more | TrekMovie.com 3 February 2010 18:59 UTC trekmovie.com [Source type: General]

.Since mineral oil and PCB fluid mix, maintenance equipment used for both PCB and oil-filled transformers could carry over small amounts of PCB, contaminating oil-filled transformers.^ If Trek were equal to Transformers, they could have still made INS & NEM and both grossed a billion dollars between them and kept making them.
• Orci & Kurtzman Talk Trek v Transformers & Future Prime Universe + more | TrekMovie.com 3 February 2010 18:59 UTC trekmovie.com [Source type: General]

[66]
Some "dry" transformers (containing no liquid) are enclosed in sealed, pressurized tanks and cooled by nitrogen or sulfur hexafluoride gas.[61]
Experimental power transformers in the 2 MVA range have been built with superconducting windings which eliminates the copper losses, but not the core steel loss. These are cooled by liquid nitrogen or helium.[67]

### 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.^ To prove it to him, I showed him the very switch, still glued to the cabinet frame with only one wire connected to it, still in the ‘more magic’ position.
• CTRL+V THREAD! [part 2] - The Forbidden Garden of DQN @ 4-ch Archives 20 September 2009 21:52 UTC archives.4-ch.net [Source type: General]

^ The other end of the wire did disappear into the maze of wires inside the computer, but it's a basic fact of electricity that a switch can't do anything unless there are two wires connected to it.
• CTRL+V THREAD! [part 2] - The Forbidden Garden of DQN @ 4-ch Archives 20 September 2009 21:52 UTC archives.4-ch.net [Source type: General]

^ We scrutinized the switch and its lone connection, and found that the other end of the wire, though connected to the computer wiring, was connected to a ground pin.
• CTRL+V THREAD! [part 2] - The Forbidden Garden of DQN @ 4-ch Archives 20 September 2009 21:52 UTC archives.4-ch.net [Source type: General]

Larger transformers may have heavy bolted terminals, bus bars or high-voltage insulated bushings made of polymers or porcelain. A large bushing can be a complex structure since it must provide careful control of the electric field gradient without letting the transformer leak oil.[68]

## Applications

.A major application of transformers is to increase voltage before transmitting electrical energy over long distances through wires.^ One major improvement, and probably the reason I enjoyed this movie more, was the increased role of the transformers themselves–notably Optimus Prime.
• Orci & Kurtzman Talk Trek v Transformers & Future Prime Universe + more | TrekMovie.com 3 February 2010 18:59 UTC trekmovie.com [Source type: General]

Wires have resistance and so dissipate electrical energy at a rate proportional to the square of the current through the wire. By transforming electrical power to a high-voltage (and therefore low-current) form for transmission and back again afterward, transformers enable economic transmission of power over long distances. Consequently, transformers have shaped the electricity supply industry, permitting generation to be located remotely from points of demand.[69] 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.[39]
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.^ Now the circuit ground within the machine isn't necessarily at the same potential as the case ground, so flipping the switch connected the circuit ground to the case ground, causing a voltage drop/jump which reset the machine.
• CTRL+V THREAD! [part 2] - The Forbidden Garden of DQN @ 4-ch Archives 20 September 2009 21:52 UTC archives.4-ch.net [Source type: General]

## Notes

1. ^ Poyser, Arthur William (1892), Magnetism and electricity: A manual for students in advanced classes. London and New York; Longmans, Green, & Co., p. 285, fig. 248. Retrieved 2009-08-06.
2. ^ "Joseph Henry". Distinguished Members Gallery, National Academy of Sciences. Retrieved November 30, 2006.
3. ^ Chow, Tai L. (2006), Introduction to electromagnetic theory: a modern perspective. Sudbury, Massachusetts (USA), Jones and Bartlett Publishers, p. 171. ISBN: 0763738271.
4. ^ Faraday, Michael (1834). "Experimental Researches on Electricity, 7th Series". Philosophical Transactions of the Royal Society of London 124: 77–122. doi:10.1098/rstl.1834.0008.
5. ^ a b
6. ^ W. De Fonveille (1880-1-22). "Gas and Electricity in Paris". Nature 21 (534): 283. Retrieved January 9, 2009.
7. ^ Uppenborn, F. J., History of the Transformer, E. & F. N. Spon, London, 1889.
8. ^ Hughes, Thomas P. (1993). Networks of Power: Electrification in Western Society, 1880-1930. Baltimore: The John Hopkins University Press. p. 96. ISBN 0-8018-2873-2. Retrieved September 9, 2009.
9. ^ a b Allan, D.J., "Power transformers – the second century", Power Engineering Journal
10. ^ Uppenborn, F. J., History of the Transformer, E. & F. N. Spon, London, 1889. p. 41.
11. ^ Friedrich Uppenborn: History of the Transformer, page 35.
12. ^ a b Coltman, J. W. (January 1988), "The Transformer", Scientific American: 86–95, OSTI 6851152
13. ^ a b Bláthy, Ottó Titusz (1860 - 1939), Hungarian Patent Office, January 29, 2004.
14. ^ Zipernowsky, K., M. Déri and O. T. Bláthy, Induction Coil, Patent No. 352,105, U.S. Patent Office, November 2, 1886, retrieved July 8, 2009.
15. ^ a b Smil, Vaclav, Creating the Twentieth Century: Technical Innovations of 1867—1914 and Their Lasting Impact, Oxford University Press, 2005, p. 71.
16. ^ Nagy, Árpád Zoltán, "Lecture to Mark the 100th Anniversary of the Discovery of the Electron in 1897" (preliminary text), Budapest October 11, 1996, retrieved July 9, 2009.
17. ^ Oxford English Dictionary (2nd ed.). Oxford University Press. 1989.
18. ^ Hospitalier, Édouard, 1882, The Modern Applications of Electricity, Translated and Enlarged by Julius Maier. New York, D. Appleton & Co., p. 103.
19. ^ a b Stanley, William, Jr., Induction Coil. Patent No. 0349611, United States Patent Office, September 21, 1886. Retrieved July 13, 2009.
20. ^ Skrabec, Quentin R. (2007). George Westinghouse: Gentle Genius. Algora Publishing. p. 102. ISBN 978-0875865089.
21. ^ Westinghouse, G. Jr., Electrical Converter, Patent No. 366362, United States Patent Office, 1887.
22. ^ Uth, Robert (December 12, 2000). "Tesla coil". Tesla: Master of Lightning. PBS.org. Retrieved May 20, 2008.
23. ^ Tesla, Nikola (1891). "System of elecrical lighting". United States Patent and Trademark Office.
24. ^ a b Flanagan, William M. (January 1, 1993). Handbook of Transformer Design and Applications. McGraw-Hill Professional. Chap. 1, p. 1–2. ISBN 0070212910.
25. ^ a b Winders. Power Transformer Principles and Applications. pp. 20–21.
26. ^ a b c d Say, M. G. (February, 1984). Alternating Current Machines, Fifth Edition. Halsted Press. ISBN 0470274514.
27. ^ Heathcote, Martin (November 3, 1998). J & P Transformer Book, Twelfth edition. Newnes. pp. 2–3. ISBN 0750611588.
28. ^ a b c d e Calvert, James (2001). "Inside Transformers". University of Denver. Retrieved May 19, 2007.
29. ^ a b McLaren, P. G. (January 1, 1984). Elementary Electric Power and Machines. pp. 68–74. ISBN 0132576015.
30. ^ a b Say, M. G. (February, 1984). Alternating Current Machines, Fifth Edition. Halsted Press. p. 485. ISBN 0470274514.
31. ^ a b c Dixon, Lloyd, "Magnetics Design Handbook", Texas Instruments
32. ^ a b Billings, Keith (1999). Switchmode Power Supply Handbook. McGraw-Hill. ISBN 0070067198.
33. ^ "400 Hz Electrical Systems". Aerospaceweb.org. Retrieved May 21, 2007.
34. ^ Kubo, T.; Sachs, H.; Nadel, S. (2001) (PDF), Opportunities for new appliance and equipment efficiency standards, American Council for an Energy-Efficient Economy, p. 39, retrieved June 21, 2009
35. ^ Riemersma, H., et al. (1981), "Application of Superconducting Technology to Power Transformers", IEEE Transactions on Power Apparatus and Systems PAS-100 (7): 3398, doi:10.1109/TPAS.1981.316682
36. ^ Calwell, Chris and Travis Reeder (2002), Power Supplies: A Hidden Opportunity for Energy Savings, Natural Resources Defense Council, pp. 4-9. Retrieved 2010-02-19.
37. ^ a b c Heathcote, Martin (November 3, 1998). J & P Transformer Book, Twelfth edition. Newnes. pp. 41–42. ISBN 0750611588.
38. ^ Pansini, Anthony J. (1999). Electrical Transformers and Power Equipment. Fairmont Press. p. 23. ISBN 0881733113.
39. ^ a b Nailen, Richard (May 2005), "Why we must be concerned with transformers", Electrical Apparatus
40. ^ a b c Daniels, A. R.. Introduction to Electrical Machines. pp. 47–49.
41. ^ a b Say, M. G. (February, 1984). Alternating Current Machines, Fifth Edition. Halsted Press. pp. 142–143. ISBN 0470274514.
42. ^ Pansini. Electrical Transformers and Power Equipment. pp. 89–91.
43. ^ Bakshi, M. V. and Bakshi, U. A.. Electrical Machines - I. p. 330. ISBN 8184310099.
44. ^ a b Kulkarni, S. V. and Khaparde, S. A. (May 24, 2004). Transformer Engineering: design and practice. CRC. pp. 36–37. ISBN 0824756533.
45. ^ Say, M. G. (February, 1984). Alternating Current Machines, Fifth Edition. Halsted Press. p. 166. ISBN 0470274514.
46. ^ Hindmarsh. Electrical Machines and their Applications. p. 173.
47. ^ Abdel-Salam, M. et al.. High-Voltage Engineering: Theory and Practice. pp. 523–524. ISBN 0824741528.
48. ^ Carr, Joseph. Secrets of RF Circuit Design. pp. 193–195. ISBN 0071370676.
49. ^ Guile, A. and Paterson, W. (1978). Electrical Power Systems, Volume One. Oxford: Pergamon Press. pp. 330–331. ISBN 008021729X.
50. ^ Institution of Electrical Engineers (1995). Power System Protection. London: Institution of Electrical Engineers. pp. 38–39. ISBN 0852968345.
51. ^ a b Hindmarsh, John (1984). Electrical Machines and their Applications. Pergamon. pp. 29–31. ISBN 0080305733.
52. ^ Gottlieb, Irving (1998). Practical Transformer Handbook. Newnes. p. 4. ISBN 075063992X.
53. ^ a b c d McLyman, Colonel Wm. T. (2004). Transformer and Inductor Design Handbook. CRC. Chap. 3, pp. 9–14. ISBN 0824753933.
54. ^ a b Harlow, James H.. Electric Power Transformer Engineering. Taylor & Francis. Chap. 2, pp. 20–21.
55. ^ Boteler, D. H.; Pirjola, R. J.; Nevanlinna, H. (1998), "The effects of geomagnetic disturbances on electrical systems at the Earth's surface", Advances in Space Research 22: 17–27, doi:10.1016/S0273-1177(97)01096-X
56. ^ Hasegawa, Ryusuke (June 2, 2000). "Present status of amorphous soft magnetic alloys". Journal of Magnetism and Magnetic Materials 215-216: 240–245. doi:10.1016/S0304-8853(00)00126-8.
57. ^ McLyman. Transformer and Inductor Design Handbook. Chap. 3 p1.
58. ^ Lee, Reuben. "Air-Core Transformers". Electronic Transformers and Circuits. Retrieved May 22, 2007.
59. ^ a b c Central Electricity Generating Board (1982). Modern Power Station Practice. Pergamon Press.
60. ^ Heathcote, Martin (November 3, 1998). J & P Transformer Book. Newnes. pp. 720–723. ISBN 0750611588.
61. ^ a b c Kulkarni, S. V. and Khaparde, S. A. (May 24, 2004). Transformer Engineering: design and practice. CRC. pp. 2–3. ISBN 0824756533.
62. ^ Pansini, Anthony J. (1999). Electrical Transformers and Power Equipment. Fairmont Press. p. 32. ISBN 0881733113.
63. ^ a b Willis, H. Lee (2004). Power Distribution Planning Reference Book. CRC Press. p. 403. ISBN 0824748751.
64. ^ a b
65. ^ ASTDR ToxFAQs for Polychlorinated Biphenyls, 2001, retrieved June 10, 2007
66. ^ McDonald, C. J. and Tourangeau, R. E. (1986). PCBs: Question and Answer Guide Concerning Polychlorinated Biphenyls. Government of Canada: Environment Canada Department. p. 9. ISBN 066214595X. Retrieved November 7, 2007.
67. ^ Pansini, Anthony J. (1999). Electrical Transformers and Power Equipment. Fairmont Press. pp. 66–67. ISBN 0881733113.
68. ^ Ryan, Hugh M. (2001). High Voltage Engineering and Testing. Institution Electrical Engineers. pp. 416–417. ISBN 0852967756.
69. ^ Heathcote. J & P Transformer Book. p. 1.

## References

• Central Electricity Generating Board (1982). 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.
• 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. p. 23. 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.

# Study guide

Up to date as of January 14, 2010

### From Wikiversity

.So what actually is "transformation"?
In English,as we know transformation means "conversion".
That's it,conversion of electro-magneto-electro forms among themselves in an isolated system is noting but the Principe of transformer(transformation).
^ The Transformer idea is actually much older than Transformers themselves.
• Transformers@Everything2.com 3 February 2010 18:59 UTC everything2.com [Source type: General]

^ You actually tried to have an intelligent conversation about Transformers over at AICN. (Boy!
• Orci & Kurtzman Talk Trek v Transformers & Future Prime Universe + more | TrekMovie.com 3 February 2010 18:59 UTC trekmovie.com [Source type: General]

^ The transformer keeps the instrument voltage at a safe level and electrically isolates it from the power system, so there is no direct connection between the power lines and the instrument or instrument wiring.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

lets make it a bit more clear:
.File:Trans1.jpg
so as we can see there are two ports over the core
* one clear;y written primary winding and
* secondary winding

So now we move further:
Let us assume there are Np turns on the primary side and Ns on the secondary side.
^ There are two possible solutions to this issue - either increase the limit (quota) or force FastSort to keep the number of temporary files below some limit.
• components:transformers [CloverETL wiki] 28 January 2010 1:01 UTC wiki.cloveretl.org [Source type: Reference]

^ With less inductance in the primary winding, there is less inductive reactance, and consequently a much larger magnetizing current.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Induction heating: Primary insulated winding induces current into lossy iron pipe (secondary).
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

then let us also assume we have connected the generating station side terminals to the primary side. we are connecting the load across the secondary side.
now upon careful analysis we can say that the two windings over the transformer core are nothing but inductive(inductors).Hence we can say that,flux is emitted from the coil which is excited(the primary side).
now that flux is emitted,it has to get a stable state wherein it can operate.So the flux lines travel through the less susceptible(magnetically resistive)iron core and a few lines travel through air(leakage in electrical terms).so the flux lines which travel through the core go and counter excite secondary coil!.Hence giving up the voltage upto the second port following the relation == .V=IR ==
that is the power rating of the transformer remains the same!
^ Power transformers can be engineered to handle certain levels of power system harmonics, and this capability is sometimes denoted with a “K factor” rating.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Aside from power ratings and power losses, transformers often harbor other undesirable limitations which circuit designers must be made aware of.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

^ Impedance transformation is a highly useful ability of transformers, for it allows a load to dissipate its full rated power even if the power system is not at the proper voltage to directly do so.
• Lessons In Electric Circuits -- Volume II (AC) - Chapter 9 28 January 2010 1:01 UTC openbookproject.net [Source type: FILTERED WITH BAYES]

This above principle can be explained from the faradays laws,as you all know!
that's all for today,I will be back and add up tomorrow.Thanks for patience.

# Simple English

A transformer is a device that moves electrical energy from one circuit to another through electromagnetism. They are an important part of electrical systems.[1]

Transformers can come in many different sizes, from a very small coupling transformer inside a stage microphone to big units that weigh hundreds of tons used in power grids.

The main reason to use a transformer is to make power of one voltage into power of another voltage. More voltage is easier to send a long distance, but less voltage is easier to use in the home.[2]

## References

1. Flanagan, William M. (1993-01-01). Handbook of Transformer Design and Applications. McGraw-Hill Professional. pp. Chap. 1, p. 1–2. ISBN 0070212910.
2. Thomas P. Hughes (1993). Networks of Power: Electrification in Western Society, 1880-1930. Baltimore: Johns Hopkins University Press. p. 119-122. ISBN 0801846145.

# Citable sentences

Up to date as of December 14, 2010

Here are sentences from other pages on Transformers, which are similar to those in the above article.