transformer

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Transformer that can be assembled from components for illustrative purposes. Above the U-shaped part of the iron core, in the middle picture with attached coils; in the lower picture with another ferromagnetic (iron) yoke above the "U" core, with which the magnetic circuit is continuously closed.

A transformer (from Latin transformare , 'to transform, to convert'; also transformer , or transformer for short ) is a component of electrical engineering . It usually consists of two or more coils ( windings ), which are usually made of insulated copper wire and are located on a common magnetic core . A transformer converts an AC input voltage that is applied to one of the coils into an AC output voltage that can be tapped at the other coil. The ratio of input and output voltage corresponds to the ratio of the number of turns in the two coils. Thus, for example, a turns ratio of 20 to 1, an input voltage of 240 volts to an output voltage of 12 volts transformed . Depending on the design of the transformer, the output voltage can be lower, higher or equal to the input voltage.

Transformers are often used for voltage conversion in energy supply systems and in technical devices, especially in power supply units for providing low voltages in many types of electrical and electronic devices. They are also required for signal transmission and protective separation.

history

1885: Zipernowsky, Déri and Bláthy transformer

Patent drawing by William Stanley 1886

Although the induction principle had been known since Michael Faraday's discoveries in 1831, the transformer was not developed until 44 years later. In 1875, Pawel Nikolajewitsch Jablotschkow developed an improved form of the carbon arc lamp and used induction coils for its operation , which in principle represent a transformer. However, he did not deal further with these devices. Lucien Gaulard and John Dixon Gibbs exhibited a transformer in London in 1881, and in 1882 they were awarded the English Patent No. 4362 for it. The term transformer was not common at the time; the devices were referred to as the secondary generator. The assignment of transformers to electrical machines , which is still common today, is derived from this. Károly Zipernowsky , Miksa Déri and Ottó Titusz Bláthy (all three Hungarians) received a patent on the transformer in 1885. This was mechanically constructed according to the reverse principle of today's transformers; The conductor coils were wound around a solid core made of non-magnetic material, over which thick layers of iron wire were placed to form a ferromagnetic shell. This transformer was sold worldwide by the Budapest company Ganz & Cie .

The American George Westinghouse played a major role in the spread of the alternating current system and with it the transformer . He recognized the disadvantages of the power distribution using direct current operated and favored by Thomas A. Edison at the time and instead relied on alternating current (cf. Stromkrieg ). In 1885 Westinghouse acquired the patent rights from Gaulard and Gibbs and imported a number of their secondary generators as well as a generator from Siemens. He used it to build a power grid with AC voltage for electrical lighting in Pittsburgh . William Stanley made major improvements to Lucien Gaulard's and John Gibbs' equipment in the same year as chief engineer at Westinghouse in Pittsburgh. In 1886 Westinghouse installed an AC voltage generator in Great Barrington, Massachusetts , whose 500 V AC voltage was stepped up to 3,000 V for distribution and stepped down to 100 V again to operate the electrical lighting at the connection points. The growing use of transformers, combined with the creation of AC grids, led to the advancement of electrification around the world .

At the beginning of the 1890s, Michail Dolivo-Dobrowolski developed the first transformer for three-phase alternating current at AEG in Berlin and introduced the term three-phase current . His three-phase transformer was used in 1891, at the suggestion of Oskar von Miller , for the first long-distance transmission of electrical energy with three-phase alternating current. The line went into operation on August 24, 1891 between Lauffen am Neckar and the International Electrotechnical Exhibition in Frankfurt am Main, 175 km away. The voltage of 50 V generated in a hydroelectric power station was stepped up to 15 kV for transmission.

In 1888, the Munich electrical engineer Friedrich Uppenborn published a book on the history of the transformer. Until 1907, Gisbert Kapp worked out the basics for the calculation and construction of transformers.

Basic principle

Basic sketch of a transformer

Ideally, a transformer consists of a magnetic circuit , which is called the transformer core and has at least two current-carrying windings. The winding facing the electrical energy source is referred to as the primary side. The one on which the electrical load is located is called the secondary side.

The mode of action can be described by the following mechanisms:

1. An alternating voltage on the primary side of the transformer causes an alternating magnetic flux in the core according to the law of induction . The changing magnetic flux in turn induces a voltage on the secondary side of the transformer (voltage transformation).
2. An alternating current in the secondary winding causes an alternating current in the primary winding (current transformation) in accordance with Ampère's law .

When the AC frequency is low, an iron core made of a ferromagnetic material of high permeability is typically used. Compared to transformers without an iron core, this enables high alternating magnetic flux densities and thus a significantly higher winding voltage to be achieved, which ensures that the power that can be transmitted is large compared to the power loss that arises from the ohmic resistance in the windings. Put simply, a transformer with an iron core requires significantly fewer turns on the windings than a transformer without an iron core.

The magnetic flux in sub-item 1 includes a magnetic field which, similar to an electromagnet, causes a current to flow in the primary coil. The current required to build up the magnetic field is called the magnetizing current . The primary current, which comes from the current transformation according to sub-item 2, is called the primary additional current . It flows in addition to the magnetizing current and, as an active current, is usually much larger than this.

functionality

Ideal transformer

An ideal transformer is understood to be a loss-free transformer that cannot be implemented in practice. This model concept is helpful for the functional description. In practice, more or less large deviations occur, the regularities only apply approximately.

3D drawing of a typical network transformer. The inner winding is designed for mains voltage (the supply voltage) - recognizable by the large number of turns made of thin wire. The output voltage is taken from the outer winding. It is usually much less and therefore requires a smaller number of turns - but the current is higher, so the wire thickness is larger. The transformer core consists of thin iron sheets, which are isolated from each other in order to avoid eddy currents.

In the ideal transformer, the voltages on the windings are proportional to the rate of change of the magnetic flux and the number of turns of the winding due to electromagnetic induction . It follows from this that the voltages are related to one another like the number of turns. If N ₁ , N ₂ , U ₁ and U _{2 are} the number of turns or the effective values ​​of the primary and secondary voltages, then the following applies for the ideal transformer

${\displaystyle {\frac {U_{2}}{U_{1}}}={\frac {N_{2}}{N_{1}}}}$   or.    ${\displaystyle U_{2}={\frac {N_{2}}{N_{1}}}\cdot U_{1}}$

With a suitable choice of the number of turns N ₁ and N ₂ , alternating voltages can both be stepped up by selecting N _{2 to be} greater than N ₁ , or stepped down if N _{2 is selected to be} less than N ₁ .

If a consumer is connected to the secondary winding , it draws electrical energy from the secondary coil . A current is generated on the secondary side and the primary current increases. In contrast to the voltages on the windings, the currents in the windings are directed in opposite directions: If the primary current flows through the coil to the right with respect to the core, the secondary current flows to the left and vice versa ( Lenz's rule ). Physically, the opposing current flow can be explained with the flow rate theorem. It is assumed that the flux density B generated by the primary voltage U ₁ in the core only assumes finitely large values ​​and that the permeability number μ _{r of} the core is very large. Under these circumstances the magnetic field strength H in the core becomes so small that it is almost negligible ( H → 0), and the application of the flow rate theorem to an integration path along the core yields:

${\displaystyle I_{2}={\frac {N_{1}}{N_{2}}}\cdot I_{1}}$.

The opposite direction of flow of the current is indicated in the circuit diagram by the current arrow I ₂ pointing out of the transformer .

The combination of the equations for the voltage and current transformation shows that in an ideal transformer the energy supplied on the primary side is equal to the energy withdrawn on the secondary side. The transformer does not store energy temporarily, nor does it generate heat losses. The following applies, for example:

${\displaystyle U_{1}\cdot I_{1}=U_{2}\cdot I_{2}}$

Real transformer

→ Main article : Real transformer

Ideal transformers are practically impossible to implement. A real transformer differs from the ideal transformer in the following ways:

• The windings have resistances and parasitic capacitances ;
• Eddy current losses occur in the iron core ;
• the magnetic reversal of the core requires energy;
• not all of the magnetic flux that flows through the primary windings also passes through the secondary windings, rather leakage fluxes occur;
• the permeability of the core depends on the frequency and strength of the magnetic flux;
• The saturation effects of the core mean that the inductance of the primary windings is not constant, but depends on the primary-side magnetization current, which in turn changes when passing through the magnetization curve during a voltage half-cycle and which can assume high amplitudes when total iron core saturation is reached;
• the core changes its shape to a small extent due to magnetostriction when the magnetic field changes, which e.g. B. with 50 Hz mains transformers acoustically noticeable as typical mains hum (but it can also be caused by loose windings or transformer plates ).
• when the secondary circuit is idle, a magnetizing current always flows in the primary circuit, which depends on the size of the inductive reactance of the primary transformer coil and U. should be taken into account in the primary wire cross-section.

The resistance of the windings, the reversal of magnetization and the eddy currents lead to energy losses. The losses due to the resistance of the windings are called copper losses , the losses due to magnetic reversal are called hysteresis losses , and the losses due to eddy currents are called eddy current losses . Hysteresis losses and eddy current losses are summarized under the term iron losses .

The copper losses depend on the square of the transformer load, i.e. that is, they are proportional to the square of the currents in each winding, I _x . The iron losses are almost independent of the load, but roughly proportional to the square of the magnetic flux density in the core. The hysteresis losses are also proportional to the frequency, the eddy current losses are proportional to the square of the frequency.

Stray fluxes cause the secondary voltage to be slightly lower than that of the ideal transformer.

The saturation magnetization limits the possible operating frequency downwards or, with a given frequency and number of turns, the possible primary voltage upwards. If the limit is exceeded and saturation is reached, very high currents flow on the primary side, while the voltage is very low on the secondary side. However, by increasing the number of primary turns it can be prevented in practice at the expense of the winding space and the increase in copper losses. The number of secondary turns will of course also increase accordingly. The saturation magnetization also plays an important role when the transformer is switched on ; the inrush current can briefly be a multiple of the rated current .

Loaded and unloaded transformer

If no consumer is connected to the secondary winding, there is no load . The transformer is not loaded. A lossless transformer in no-load operation behaves like an ideal coil . If a sinusoidal alternating voltage is connected to the primary side, a current flows which is phase-shifted by 90 degrees, which is referred to as magnetizing current and which is used to build up the magnetic field. In a real transformer, the phase shift of the no-load current compared to the primary voltage is less than 90 degrees due to iron losses. In no-load operation, the iron losses due to the low input current are much greater than the copper losses due to the no-load current in the primary coil.

Because of the mostly non-linear relationship between magnetic field strength and magnetic induction in the core in reality , the magnetizing current is not sinusoidal, unlike with a lossless transformer. ${\displaystyle H}$ ${\displaystyle B}$

If the transformer is loaded on the secondary side, a secondary current flows. This changes the flux in the core and thus the counter voltage induced in the primary winding. In order to maintain the voltage equilibrium on the primary side, this change in flux must be compensated for by an additional current on the primary side in addition to the magnetizing current. A balance must be established between the flow generated by the secondary flow and the flow caused by the additional flow on the primary side. The primary current at nominal load is therefore much greater than at no load. The magnetic flux density drops slightly under load.

If the secondary side is short-circuited and the input current is regulated to the current at nominal load, the primary voltage must be reduced. The primary voltage set in this way is called the short-circuit voltage , which is not given as an absolute but as a percentage ratio to the nominal voltage. For power transformers it is between 5% and 20%, for small transformers it is between 15% and 40%, for welding transformers it is 100%.

Transformers with a high short-circuit voltage are called soft , those with a low short-circuit voltage are called stiff . The short-circuit voltage depends essentially on the construction of the core and the position of the coils in relation to one another: high leakage fluxes lead to high short-circuit voltages. See also stray field transformer .

The short-circuit current is the current that flows with a secondary-side short circuit and rated voltage. It is much higher than the rated current and can destroy the transformer in a short time. The lower the short-circuit voltage, the higher the short-circuit current. Short circuits are therefore dangerous for transformers with a low short-circuit voltage. Transformers that are designed so that they are not destroyed in the event of a short circuit are referred to as short-circuit-proof . As a rule, only small transformers up to a few VA power, such as bell transformers, are designed to be short-circuit-proof. But even large power transformers must be able to withstand at least a brief surge short- circuit current without mechanical damage from the Lorentz forces that occur .

Efficiency

Typical efficiency curve of a transformer over the load using the example of a 100 VA mains transformer

The efficiency of a transformer is the ratio of the electrical power that leaves the transformer on the secondary side to the power that flows into it on the primary side. Because of the iron and copper losses, it is less than 1.Transformers of high rated power have efficiencies of more than 99%, while the efficiency of small transformers (e.g. 100 VA) is around 80%, and miniature transformers (1 VA) hardly ever reaches 50 % Efficiency come. At a higher frequency, e.g. B. in switched-mode power supplies , even small transformers can achieve high efficiency.

Transformers can be severely overloaded for a short time. Short-term operation is used, for example, for soldering guns , but also for electric locomotives . Transformers deliver a maximum of output power with an efficiency of 50% ( power adjustment ). In the diagram opposite, this point is on the far right at the end of the curve - the transformer on which the example is based supplies around 2.5 times its rated power.

Machine transformers are constantly loaded, they are dimensioned for maximum efficiency, i. This means that iron and copper losses are roughly the same at nominal load.

In the case of a local network transformer that is used in the power grid, the average load duration is only around 40% of the duty cycle, which is why higher copper losses can be accepted here, while iron losses are reduced more. Such transformers are optimized for their annual efficiency. This describes the ratio of the total amount of energy converted per year on the primary and secondary sides. The annual efficiency is higher, the greater the ratio between load and duty cycle.

Network modeling

→ Main article : "Coupling factor and leakage inductance" in the article short circuit inductance

Equivalent circuit diagram of a real transformer

The network modeling of a transformer aims to describe the essential non-ideal properties of a transformer with a small number of parameters. The equivalent circuit diagram opposite shows a model that is frequently carried out using linear components. The individual components have the following meaning:

• ${\displaystyle U_{\mathrm {p} }}$: primary-side voltage source
• ${\displaystyle U_{\mathrm {s} }=U_{2}}$: Output voltage
• ${\displaystyle I_{1}}$, : Input current and transformed output current ${\displaystyle I_{2}'}$
• ${\displaystyle R_{\mathrm {q1} }}$: Internal resistance of the primary-side voltage source
• ${\displaystyle L_{\mathrm {\sigma 1} }}$, : Leakage inductance of the primary side and transformed leakage inductance of the secondary side ${\displaystyle L'_{\mathrm {\sigma 2} }}$
• ${\displaystyle R_{1}}$, : Winding resistance of the primary side and transformed winding resistance of the secondary side ${\displaystyle R'_{2}}$
• ${\displaystyle L_{\mathrm {h1} }}$: Main inductance that carries the magnetizing current
• ${\displaystyle R_{\mathrm {Fe} }}$: linear modeling of the mostly non-linear iron losses in the core (Fe: iron)

The modeling of the parasitic capacitances of the windings was omitted in the model shown. Likewise, non-linear properties of the transformer are not shown.

The ideal transformer drawn obeys the transformation equations:

${\displaystyle {\frac {{\underline {U}}_{1}}{{\underline {U}}_{2}}}=\gamma {\text{ und }}{\frac {{\underline {I}}_{1}}{{\underline {I}}_{2}}}={\frac {1}{\gamma }}.}$

The transfer factor describes the ratio of the number of turns on the primary and secondary side. ${\displaystyle \gamma =N_{1}/N_{2}}$

The sizes that are marked with an additional line 'have been transformed from the secondary side to the primary side. When transforming an impedance from the secondary side to an impedance on the primary side, the following transformation equation applies: ${\displaystyle {\underline {Z}}}$ ${\displaystyle Z'}$

${\displaystyle {\underline {Z'}}=\gamma ^{2}{\underline {Z}}}$

Impedance transformation means that the input terminals of a transformer act like a resistor for an electrical circuit when a resistor R is connected to the secondary side . Thus, with the aid of a transformer, resistances can be increased or decreased by changing the turns ratio . ${\displaystyle \gamma ^{2}\cdot R}$ ${\displaystyle \gamma }$

The impedance transformation is often used in electronic circuits to adapt a network to the characteristic impedance of a line or to adapt the power. In contrast to gyratory coupling, the structure of the network is retained with transformer coupling , i.e. series and parallel connections are retained, and inductive and capacitive behavior are not exchanged for one another.

If the galvanic isolation of the transformer is not important, the ideal transformer in the equivalent circuit diagram can be omitted after transforming all secondary-side components to the primary side.

Waveforms and bandwidth

The supply with a sinusoidal input voltage is typical for power transformers such as those used in the public power grid. The network frequency in a power network is predetermined by the speed of rotation of the generators . Typical values ​​for the mains frequency are 50 Hz (public power grid in Europe) and 60 Hz (power grid in the USA). In the traction power supply, there are also networks with network frequencies of 16.7 Hz and 25 Hz.

In PC power supplies , frequency converters and the inverters of the photovoltaic in particular are switching power supplies square wave voltages produced at much higher frequencies and transformed. The transformers used are mainly used for galvanic separation and voltage adjustment, avoiding saturation of the transformer core.

In flyback converters , two magnetically coupled coils with a core with an air gap are used as energy stores. The energy introduced into the magnetic field via the primary side is not drawn off immediately, but only tapped on the secondary side after the input voltage has been switched off. With rectangular input voltages, approximately triangular input currents result.

When transmitting signals with a transformer, it is important that the signal components of all relevant frequencies are transmitted. When using an ohmic load, the transformer exhibits what is known as a bandpass behavior . If the dimensions are unsuitable or the wiring is incorrect, a transformer can also exhibit undesirable oscillation behavior, a so-called resonance increase .

The lower bandwidth is limited by the main inductance . It short-circuits low frequency signals. Upward, the bandwidth in the network model is limited solely by the leakage inductances and . Their impedance increases with frequency and in this way prevents signal transmission. At high frequencies, the capacitive coupling between the individual windings is also relevant. ${\displaystyle L_{h1}}$ ${\displaystyle L_{\sigma 1}}$ ${\displaystyle L_{\sigma 2}}$

In practice, the lower frequency range of transformers is mainly limited by the required size, which increases sharply with decreasing frequency. The typical frequency range of low-frequency transformers extends down to 16.7 Hz, the nominal frequency for railway power supply. At the upper end of the frequency range are high-frequency transformers in which the windings often consist of only a few or even a single turn. The frequency range of commercially available high-frequency transformers covers a range from a few MHz to around 1 GHz.

Way of energy transfer

Contrary to popular belief, the energy transfer in the transformer does not take place via the transformer core itself, but via the electromagnetic field in the surrounding medium. The Poynting vector , which indicates the direction of the energy flow, is perpendicular to the electric field lines that run in a ring around the transformer core and the magnetic field lines of the stray field, which are formed by primary and secondary currents. A visualization of the connections can be found in the article by Herrmann and Schmid. The illustration shows that both in electrical circuits and in magnetic circuits, the energy never moves in the lines themselves, but always along the lines.

Since the energy transfer takes place by means of the transformer stray field, the idea of ​​an ideal transformer without a stray field is, strictly speaking, in contradiction to Maxwell's equations . In the American Journal of Physics , Newcomb formulates this relationship as follows:

“In conclusion, let us note that there is something paradoxical in the notion of a strictly ideal transformer […]. If such a thing existed, we could reverse the foregoing arguments and conclude that both E and H must vanish in the exterior region, thus making it impossible to account for the power flow. Still, it should also be emphasized that the use of ideal-transformer relations is perfectly legitimate as an asymptotic approximation in the low-frequency limit. "

- William A. Newcomb

“In conclusion, we want to state that the idea of ​​a strictly“ ideal ”transformer contains a paradox [...]. Should one exist, we could discard the previous arguments and instead conclude that both E and H would disappear in the outer area, which would make it impossible to assess the power flow. Nevertheless, it must be emphasized that the equations for ideal transformers are valid as an asymptotic approximation in the low-frequency range. "

In the journal Praxis der Naturwissenschaften - Physik in der Schule (PdN-PhiS), Herrmann recommends that the field between the legs of a transformer should not be called a stray field in connection with the transmission of energy in the transformer, as it is important for energy transport. In the case of the transformer, not only should the field of the magn. Flux density, but also the field of magnetic field strength are discussed and the question of the path of energy transfer is asked on as many occasions as possible.

Behavior in the event of mains faults and when switching on

Course of current and voltage in the event of network disturbances on the loaded transformer

Typical behavior of a transformer when switched on. The maximum of the magnetizing current lies after the first voltage half-wave.

→ Main article : Switching on the transformer

Switch-on processes and network disturbances cause particularly large deviations in transformer behavior from ideal behavior. Both of these processes can saturate the transformer core and cause significant overcurrents.

In accordance with the law of induction, the input voltage alone decides whether or not saturation phenomena occur in a transformer. The load condition does not play an essential role; even a short circuit on the secondary side does not lead to saturation.

In the case of a typical network fault in the 230 V network, one or more voltage half-waves or parts of them fail. The transformer reacts to the failure of the mains half-cycle with a large saturation current in the following half-cycle. The main contribution to core saturation is made by the pre-magnetization of the core, which is caused by the disturbance in the input voltage.

When the voltage is switched off or if the voltage fails, the magnetization state of the core remains in the remanence point that is closest to the magnetization at the time of switch-off. Depending on the polarity and phase position of the returning mains voltage, this can mean that, starting from this remanence point, the remaining induction swing up to the beginning of saturation is smaller than the time area of the returning voltage half-wave . The change in flux in the core, which is forced by the time area of ​​the recurring half-wave, drives it into saturation, whereby large magnetizing currents are required.

The worst case for an air core is switching on a full half-wave, which leads to twice the magnetizing current of the nominal value. The worst case for a toroidal core is switching on when the remanence is at and the polarity of the returning voltage is identical to that before switching off. This process is shown in the schematic diagram below. In this case, the magnetizing current is essentially only limited by the residual inductance and the ohmic resistance of the primary coil and the impedance of the mains lead. It can therefore assume extreme values ​​because the transformer core is completely saturated and can no longer absorb any changes in the magnetic flux. The saturation magnetization also plays an important role when the transformer is switched on ; the inrush current can briefly be a multiple of the rated current . ${\displaystyle B=B_{\mathrm {max} }}$

In any case, these switch-on processes subside in the course of a few half-waves, since the two opposite-polar voltage half-waves also have asymmetrical voltage drops due to the asymmetry of the magnetizing currents. As a result, there is always a little less voltage available for magnetization in the saturation half-wave than in the voltage half-wave with opposite polarity, which leads to demagnetization. As a result, the magnetization loop cycle centers itself automatically after a few network periods, whereby the time constant for this can be calculated from the quotient of the inductance divided by the ohmic resistances in the circuit. In the case of very large transformers, this time constant can therefore be a few minutes.

Schlienz gives a numerical value for a 1.6 kVA transformer (230 V), which is then optimized and loaded with 1 kW, a current of 200 A due to saturation. In comparison, less than 10 A flow in normal operation.

Applications and technical implementation

Energy Technology

Vegetable oil-cooled 380kV transformer in Bruchsal

220kV / 110kV transformer in Karlsruhe

110kV / 20kV transformers at the Recklinghausen substation

5kV / 20kV transformers at the Schwabenheim lock

In energy technology , transformers connect the various voltage levels of the power grid with one another. Machine transformers are still part of the power plants and transform the voltage induced in the generator into high voltage (in Western Europe 220 kV or 380 kV) for feeding into the power grid. Substations connect the supraregional high - voltage network with the medium - voltage network of the regional distribution networks. In transformer stations , the electricity of the regional distribution network with the medium voltage of 10 to 36 kV to supply the low-voltage end customers is transformed to the 400 V conductor-conductor voltage used in the local network. Because of the high transmitted powers called the transformers used in power supply power transformers .

Power transformers are mostly three-phase transformers that are either filled with transformer oil or designed as dry-type transformers. For the former, the standard IEC (EN) 60076-1 applies in the EU, for the latter the standard IEC (EN) 60076-11. The IEEE series of standards C57 exists parallel to the EU standards .

In ring-shaped and multiply fed distribution networks in particular, it is common to increase the power that can be transmitted by connecting transformers in parallel. The transformers used for this have the same voltage ratio, an identical vector group , almost the same short-circuit voltage and similar rated outputs. In three-phase transformers, the transformation ratio can also assume a complex value , depending on the vector group . i.e., in addition to the magnitude of the output voltage, its phase position also changes. Step switches are integrated directly into the transformer housing for control.

To control the power flow, it may be necessary to use special phase-shifting transformers in spatially extensive distribution networks with several parallel lines with different transmission capacities (even with cable systems operated in parallel with overhead lines) .

The transformer principle is also used in power engineering in current transformers . These are used to measure high currents by first stepping down the current. Current transformers often consist of a toroidal core with a secondary coil that encloses the conductor whose current is to be measured. Rogowski coils are constructed like current transformers, but do not have a magnetic core.

A tokamak , a candidate for the design of future fusion power plants and the subject of current research , also works on the transformer principle. A gas discharge is brought about in a ring-shaped vacuum vessel by slowly increasing the current in conductors (poloidal field coils) which are arranged around the vessel in the ring direction. The coils form the primary winding, while the gas in the vacuum vessel represents the secondary winding.

Electrical appliances

In electrical devices that do not work directly with mains voltage, transformers convert the mains AC voltage of typically 230 V that is present at the socket to the operating voltage of the electrical device.

Power packs for electrical devices contain either a conventional power transformer, which is operated at the mains frequency and on the primary side (in principle) directly on the power grid , or a switched-mode power pack , which operates the transformer at a higher frequency than the mains frequency. Switching power supplies are widespread these days, conventional power transformers are rarely found. A higher frequency, instead of the line frequency allows a much smaller and thus lighter and smaller for the same power transformer lowpass - screening members for smoothing the required by the corresponding device DC.

Safety transformers supply a low voltage on the secondary side, e.g. B. 6 V, 12 V or 24 V. They must be short-circuit proof and the isolation of the secondary from the primary winding must be ensured by a partition made of insulating material. Safety transformers include toy transformers such as transformers for operating model railways and bell transformers . Isolating transformers are primarily used to achieve galvanic separation between the primary and secondary side. They are therefore usually constructed symmetrically, i. i.e. the primary voltage corresponds to the secondary voltage. If galvanic isolation is not required, mains transformers can in special cases be designed as so-called autotransformers without galvanic isolation .

Older televisions or computer monitors with cathode ray tubes contain a line transformer which, in addition to supplying the line deflection coils, also generates the voltage (20–30 kV) required to accelerate the electrons. Medium-frequency transformers are designed for frequencies from a few hundred hertz to a few kilohertz. They are used, for example, in resistance welding .

In Germany, transformers with primary voltages of up to 1000 V are subject to the first regulation on the Equipment and Product Safety Act , which implements the European Low Voltage Directive. You have the standard EN 61558 fulfill what the CE marking is documented. A transformer with CE marking without further checks and audits within the EU placed on the market are.

A transformer is only rarely used with the aim of generating the largest possible secondary current (in which case the secondary voltage is of secondary importance). This happens, for example, with electric welding .

Signal transmission

Transformer of the type TG110, as used with Ethernet interfaces

Transformers and pulse transformers are transformers which are not optimized for low-loss power transmission, but on genuine possible transformation of signals. However, there are also transformers that z. B. can be used for thyristor ignition, which form short ignition needle pulses from square-wave signals with some additional components, such as RC diode circuits. In the low frequency range, transformers are manufactured with an iron core, up to the megahertz range with ferrite or iron powder cores and, from a few 100 kHz, often also as air transformers. They are used for impedance matching and / or galvanic isolation of the signal circuits.

In measurement technology , transformers are used for impedance conversion . In sound engineering , they play a role in every stage of signal processing, for example in microphones, DI boxes , amplifiers and loudspeakers. In PA systems , the audio signals are usually transmitted almost loss-free over longer cables using 100-volt technology and only adapted to the loudspeaker impedance directly at the loudspeaker using a transformer. The volume (power) can be adjusted in rough steps (often 6 W, 3 W and 1.5 W) via the taps on the primary winding that are often present.

In signal transmission , transformers up to the three-digit MHz frequency range are used for common mode rejection . Typical examples of common-mode signals that are to be filtered are voltages that are applied to both transmission lines with the same sign. Since transformers only register the difference between the voltages applied to the two terminals, common-mode interference is not transmitted via the transformer. In audio technology, this can be used to prevent so-called hum loops . In disturbed measurement environments, transformers block disturbances on the transmission lines caused, for example, by motors or switched-mode power supplies.

Also in the bandpass filters of the intermediate frequency amplifier , e.g. B. for 455 kHz or 10.7 MHz, there are often coil arrangements - often also with taps that are magnetically coupled like small (economy) transformers and have to adapt the different input and output impedances of the transistors .

Symmetrical signal transmission pursues a similar goal , in which an alternating voltage signal to be transmitted is transmitted twice: One line transmits the original signal, while a second line transmits the signal multiplied by (−1). A transformer with a center tap is typically used to generate the signal pair from an unbalanced signal referenced to earth . An electronic circuit based on operational amplifiers or transistors can also be used for conversion or reconversion .

economic aspects

Railway transport of a transformer with Schnabel car

The world market for transformers has an annual volume of around 10 billion euros. It has so far been dominated by European companies, which are increasingly being challenged by Asian companies. The largest sales market is China with around 25% of the world market volume, followed by the USA, Japan and Germany. In mature markets such as Europe or the USA, operating costs and energy efficiency play a major role in the sales opportunities of a product, while in younger markets such as China, sales are increasingly based on price.

China is also the largest transformer producer in the world: 90% of the transformers sold there are built in this country, most of them by foreign companies. The world's leading manufacturers of transformers are ABB and Alstom . Other major European manufacturers are Areva , Siemens and VA Technologie , which Siemens acquired in 2005 . The leading suppliers in the USA are Cooper Industries , General Electric .

Constructive details

Transformers range from the size of a thumbnail for the transmission of less than a thousandth of a volt-ampere (VA) ( e.g. for stage microphones ) to large units weighing several hundred tons that are used to couple national power grids and for outputs in the range of several million volt-amperes are designed. They are used for a number of different purposes. The design of the windings, the transformer core and the assembly and fastening elements are correspondingly diverse. In order to dissipate the heat loss from large power transformers, rib heat sinks with or without fans or coolant tanks with insulating oil can also be used for air cooling.

Main transformer equation

From the law of induction , the relationship known as the main transformer equation follows for sinusoidal voltages :

${\displaystyle U_{\mathrm {eff} }={{\sqrt {2}}\cdot \mathrm {\pi } \cdot B_{\mathrm {max} }\cdot A\cdot f\cdot N}\!\approx 4{,}44\cdot B_{\mathrm {max} }\cdot A\cdot f\cdot N}$

Here, the effective value of the voltage, the maximum magnetic flux density in the core, the cross-sectional area of the transformer core, the frequency and the number of turns. ${\displaystyle U_{\mathrm {eff} }}$ ${\displaystyle B_{\mathrm {max} }}$ ${\displaystyle A}$ ${\displaystyle f}$ ${\displaystyle N}$

In the case of non-sinusoidal alternating voltages, the constant must be replaced by other values; for square wave voltage through and for triangle voltage through . ${\displaystyle {\sqrt {2}}\cdot \mathrm {\pi } }$ ${\displaystyle 4}$ ${\displaystyle 4{,}62}$

Space requirements and construction parameters

The main transformer equation connects basic parameters of a transformer. The maximum magnetic flux density is limited by the saturation magnetization of the core material. For given values ​​of the output voltage , the operating frequency and the maximum magnetic flux density , the product of the cross-sectional area of ​​the core and the number of turns is determined. These two parameters essentially determine the space and material requirements of a transformer. ${\displaystyle B_{\mathrm {max} }}$ ${\displaystyle U_{\mathrm {eff} }}$ ${\displaystyle f}$ ${\displaystyle B_{\mathrm {max} }}$ ${\displaystyle A\cdot N}$

If the operating frequency is increased with the same output voltage, the product is correspondingly reduced . If, for example, a transformer is operated at 5 kHz instead of 50 Hz, the product of the number of turns and core cross-section can be selected to be a factor of 100 smaller, which means a corresponding reduction in the size of the transformer. In practice, this is not fully used, since the higher the frequency, the greater the hysteresis losses according to the Steinmetz formula and therefore a somewhat lower choice is made for higher frequencies . ${\displaystyle B_{\mathrm {max} }\cdot A\cdot N}$ ${\displaystyle B_{\mathrm {max} }}$

Higher operating frequencies therefore lead to a lower space and material requirement and thus also to a lower weight. This is the reason for the smaller size of switching power supplies .

The maximum operating voltage also has a small influence on the space required. Since the copper fill factor decreases as the supply voltage increases due to the insulation, transformers are larger, the higher the voltages to be processed, with the same transmission power. The current density in the winding wires can be higher with small transformers than with large ones, because the heat can escape better with them. Accordingly, smaller transformers (and those for lower transmission capacities) usually have a lower degree of efficiency.

Windings

material

Solid copper wire is usually used as the conductor material for the windings. Large cross-sections are divided into individual conductors ( Roebel bars ), which are isolated from one another and cyclically exchanged . Foil, strip made of soft copper or high-frequency stranded wire are also used. Ribbons, foils from switched-mode power supply transformers and wires from large transformers are often made of aluminum. Films often only have a purely umbrella function.

For insulation, the wire has a synthetic resin coating ( enamelled copper wire ) or - earlier - also a wrapping . The thinner layer of lacquer has a higher insulation capacity and allows a more compact winding than was possible with braided wires. This is put into perspective when the transformer winding is subsequently soaked or when it is operated in insulating oil ( transformer oil ).

In order not to let the tension between adjacent turns become too high, layer insulation is introduced or the wire is laid in several adjacent chambers during winding. Another method to increase the dielectric strength is with foil wraps. They are sometimes used in switched-mode power supply transformers, but also in large transformers.

The constructional goal is a winding that is as compact as possible in order to be able to accommodate as much copper or aluminum as possible in a winding cross-section given by the core. The type of insulation limits the possible operating temperature upwards (see insulation class ). A compact, possibly impregnated winding also improves heat dissipation from the interior.

Manufacturing

A coil former (English coil former or bobbin ) helps to produce the winding in the right shape and offers additional insulation to the core or to neighboring windings (multi-chamber coil former). Bobbins are mostly made of plastic injection molding and often have injected contact pins or guides for incoming and outgoing winding ends. Orderly winding is thus possible on an automatic winding machine .

In some cases a spool is too expensive or it restricts the winding space too much. A self-supporting roll is then made and attached to the core with wedges or other intermediate layers. Windings only rarely take place directly on the legs of the transformer core, since such windings are difficult to manufacture by machine and only have a low dielectric strength compared to the core.

arrangement

A 100 VA transformer. Above the primary winding (230 V), below the two secondary windings (9 V).

In mains transformers with only one winding chamber, the primary winding is usually wound at the bottom - at lower output voltages, the usually thicker wire of the secondary winding protects the thin wire of the primary winding. With a high output voltage, this winding structure facilitates the insulation to the core. The winding of the primary and secondary coil is also known as a jacket winding .

In the case of safety transformers, the primary and secondary windings are housed in separate chambers of the winding body made of insulating material in order to safely isolate them from one another.

Division of primary and secondary winding into several areas:

• Disc winding : arrangement of the partial windings next to one another on one leg of the core
  • unsupported: spaces between the panes often serve as cooling channels
  • Multi-chamber winding body: lowers the layer tension and reduces the self-capacitance of the winding; better insulation even if the wraps are not soaked
• Nested Windings: Audio transformers (transmitters and output transformers ) often have split, interlocking primary and secondary windings to reduce leakage inductance and thus improve high frequency transmission.

Mains and signal transformers have a shield winding if the leakage current is to be prevented, which without a shield passes from the primary side to the secondary side through capacitive coupling of the winding. This screen is connected to ground connected and serves to reduce the capacitive coupling between the primary and secondary winding. The shield consists of a single-layer wire winding or foil that is only connected at one end. The shield winding must not be an electrically closed loop, which is why the overlap of the two film ends must be electrically isolated. In the case of so-called interference protection transformers, this screen can also consist of highly permeable material. This dampens the transition from high-frequency interference to the secondary side.

Instead of a single transformer, a transformer can also have several separate secondary windings for different voltages or for separate circuits.

Fixation

The winding is often fixed with impregnating or casting resin . This improves insulation, heat dissipation and mechanical strength; the hum of the transformer is reduced and the risk of moisture penetrating is reduced. Switching power supplies and small high-voltage transformers, in particular, are soaked in a vacuum or vented when potting. This eliminates air inclusions which would otherwise lead to partial discharges that reduce the service life .

Taps

This transformer comes from an electric locomotive : Numerous taps on the secondary side, which are contacted with switches, enable jerk-free starting.

The primary winding can have several taps; This means that such a transformer is suitable for primary voltages of different levels, while still transforming to the same output voltages. A transformer that should be used for both the American (120 V) and the European market (230 V) can, for. B. be provided with a tap on the primary winding on the power transformer and a changeover switch. Often, however, two windings for 120 V each are applied, which can be connected either in parallel or in series. You can usually accept the small voltage deviation in favor of the lower copper requirement.

The secondary winding can also have taps in order, for example, to adapt the transformer to different load cases or to generate several voltages with the same reference. The taps can be freely selected under load with special load switches depending on the requirements (voltage or power change), for example in the case of electric arc furnaces or rail vehicles. A power interruption is avoided by using small auxiliary variable transformers.

If the winding on the secondary side is cut after half the total number of turns and led to the outside, this is referred to as a center or center tap. There are three voltages available in a ratio of 1: 1: 2. Such transformers are used as driver or output transformers for push-pull output stages and for supplying two-way rectification. Such a center tap can also be created by applying two windings with the same number of turns to the secondary side and connecting them in series with the correct polarity. This results in two equal voltages that add up.

With variable transformers , a movable sliding contact can contact every single turn of the output winding, which enables the output voltage to be continuously adjusted.

Transformer core

material

The transformer core consists of iron or ferrites , depending on the area of ​​application of the transformer . Some transformers have no core at all; these are called air transformers . Ferromagnetic material in the coil core has a much better magnetic conductivity than air and thus allows a stronger magnetic flux, but has the property of saturating above certain magnetic flux densities. When saturated, the magnetic conductivity is reduced, which leads to a non-linear transmission behavior.

Iron alloys and ferromagnetic steels are of greatest economic importance. For transformers (operating frequency 50 Hz or 60 Hz) is used mainly so-called dynamo sheet in accordance with DIN EN 10107, which consists of iron silicon - alloys consists. Nickel-iron alloys are also used in signal transmitters. The maximum flux density for iron is 1.5 to 2 Tesla, depending on the specification.

The core is built up from a stack of individual metal sheets, between which there are electrically insulating intermediate layers, the sheet metal surface being parallel to the direction of the magnetic flux and thus perpendicular to the induced electric field. This reduces the eddy current losses. The higher the frequency, the thinner the sheets must be chosen. In the case of large transformers, damage to the insulation of the individual laminated cores can lead to considerable local heating of the core.

From frequencies in the kilohertz range, the eddy current losses in iron cores would be too great even with very thin sheets. Cores made of amorphous or nanocrystalline strips or ferrite cores are used. Ferrites have a high permeability, but only a low electrical conductivity. To manufacture ferrite cores, the raw material, which is usually powdery, is placed in a mold and sintered (pressed) under pressure. This results in more design options than with the laminated cores, especially when it comes to adapting to the coil body. With ferrites , the maximum flux density is around 400 mT. The limit to the use of ferrite material lies in the manufacturability in the pressing and sintering process. Cores for larger transformers are partly composed of ferrite blocks. The amorphous and nanocrystalline cores, with their natural band thickness of typically 0.02 mm, allow use at higher frequencies and have very low losses. Typical core shapes for these tapes are toroidal cores or, more rarely, cut tape cores .

Designs

For economic reasons in the field of energy technology (16 ... 60 Hz, laminated iron core), the cross-section of the core is usually selected in relation to the number of turns of the primary winding, the operating voltage and the frequency so that the flux density is close to the maximum permissible voltage and in no-load operation comes to the permissible saturation magnetic flux density. This is not possible with ferrite cores and higher frequencies because the losses would then be too high. The modulation here is often only a tenth of the saturation flux density.

Toroidal cores

Core made from wound dynamo sheet and toroidal transformer made from it

With a toroidal transformer , a comparatively high degree of efficiency is possible with a small size. For this, the winding of the coil is more complex. Toroidal cores are made of sheet metal, powder or ferrites. With windings homogeneously distributed over the circumference, toroidal transformers have only a very small leakage field and correspondingly low leakage inductance.

Cut tape cores

In the case of cut tape cores, attempts are made to combine the advantages of easily manufactured wire windings with the advantages of a core wound from tape. To produce a cut strip core, a sheet metal strip (thickness 0.025-0.3 mm) is wound onto a mandrel with a rectangular cross section and glued. Then the coil is cut transversely in the middle and the parting surfaces are polished. Finally, the halves are inserted into the wound bobbins and glued together. Textured sheet metal strips are also used for cut strip cores.

Due to their residual air gaps, cut tape cores have a smaller remanence than toroidal core transformers and thus smaller inrush currents than these. Due to the two remaining air gaps in the core and its rectangular shape, the material utilization is not as high as with the toroidal core transformer. Nonetheless, cut ribbon cores have properties that are just as good as toroidal cores, the manufacture of windings is simpler than that, but the production of cut ribbon cores is somewhat more expensive than other core designs.

Stacked sheet metal cores

Transformer in jacket design

A distinction is made between jacket design and core design. In the single-phase version of a jacket transformer, both windings are located on the center leg, either next to each other or one above the other. In this design, the middle limb is supplemented by two outer limbs, which each have half the cross section of the middle limb and have no turns. The shell design is formed, for example, from alternately layered stacks of E- and I-shaped sheets, from which the designation EI core follows. Another possibility are so-called M-sheets, which form the entire shell shape and have a separating cut at the end of the center leg for assembly.

Core-type transformer

In the case of the core design, the center leg is missing, the core forms the shape of a rectangle in a side view and has a uniform cross-section. As a rule, the turns are located separately on the two outer legs, but can also be attached together on one leg. The core design is formed, for example, by alternately layered stacks of metal sheets in the shape of a U and I, from which the designation UI core follows. Another possibility is LL sheets - here only one sheet metal shape is required for the two-leg design.

Other core designs

Transformer with pot core

In the case of ferrite cores in particular, there are a large number of designs, including particularly flat designs for better heat dissipation and those with a cylindrical center leg for easier winding of the coil body. Shell and pot cores have low stray fields. RM cores and EP cores are a mixed form of EE core and pot core.

Air gap

As a rule, in order to keep the stored energy in the core low, no air gap is desired in the core. Sheets are therefore alternately layered or the interfaces between the core halves are polished. However, some transformer cores are used for intermediate storage of magnetic energy, as in the case of flyback converters . This can be achieved through an air gap in the magnetic circuit, in which a substantial part of the magnetic field energy is stored. The field strength requirement and thus the magnetizing current increase, the characteristic is sheared or linearized. The magnetic energy stored in the air gap increases the reactive power, but is released again with almost no loss. The remanence in the core is close to zero induction because of the shear of the magnetization characteristic.

Air gaps in the core are also required for direct current components in the primary current such as with output transformers . They also fulfill this function in very simple welding power sources, because there the welding arc acts as a rectifier.

Air gaps increase the leakage flux locally in the vicinity of the gap, which may lead to losses and disturbances there (e.g. in the transformer tank). Such transformers also often have an increased leakage flux in the wider area, since a larger proportion of the total field occurs outside the core.

Air gaps are z. B. achieved with ferrite cores and M sheets by different lengths of legs, with E / I sheets by stacking in the same direction and an intermediate layer.

Powder cores and cores made of sintered metal have a so-called distributed air gap, which consists of the insulating layers between the powder grains. These cores therefore naturally tolerate a higher DC bias.

Magnetic shunt

Stray field transformer 400 VA with adjustable magnetic shunt to adjust the output current ( ballast for fluorescent tubes ); below: primary windings (220 V); above: secondary windings (2 × 2.5 kV, 50… 80 mA); Height 215 mm

An additional unwound yoke with an air gap results in a current limitation in arc welding transformers and scatter transformers ( e.g. for fluorescent tubes ). The yoke serves as a magnetic shunt. Such transformers are often short-circuit-proof and in the case of welding transformers and some fluorescent tube transformers, the yoke can be mechanically adjusted so that the current output can be adjusted. The magnetic flux in this yoke increases with the output current and can be used to trigger an overcurrent shutdown. This was the case, for example, with model railway transformers ME002 from the PIKO / GDR brand . There the yoke served this purpose only and consisted of a sheet metal construction similar to a hinged armature relay. Transformers in microwave ovens and some bell transformers also have a magnetic shunt for these reasons.

Mass for money

Mass-performance ratio of various toroidal power transformers from three different manufacturers

Higher operating frequencies allow less material to be used - see the section on space requirements and construction parameters . However, higher operating frequencies often require more complex constructions such as thinner, more expensive metal sheets, windings made of stranded wire or a nested winding structure. Cores made of ferrites only allow a lower modulation than those made of iron. Nevertheless, with higher working frequencies up into the MHz range, it is possible to extremely reduce the size and mass of transformers. A toroidal transformer for 3 kW for 50 Hz weighs 30 kg; a transformer of the same power for 100 kHz weighs only 0.5 kg.

Mains transformers (50 or 60 Hz, 115 or 230 V) have a mass-performance ratio that decreases slightly with the nominal power, which should be worse for smaller transformers due to the higher proportion of insulating material. On the other hand, smaller transformers can be operated with higher current densities in the winding wire (the heat can be dissipated better because of the lower heat conduction path and higher specific surface), which leads to a poorer efficiency. Therefore the mass-performance ratio is almost a straight line.

The mass-performance ratio can be improved by high induction and thus by means of high-quality core material that is textured for sheet metal. Toroidal transformers and ribbon cores are superior to other laminated cores, as the texture of these can always be directed along the field lines.

Noise development

In transformers, induction-dependent changes in length in the core material of the order of a few µm / m occur due to magnetostriction . This is of particular importance for power transformers . The vibrations with twice the mains frequency are transmitted partly through the mechanical connections between the core and the outer wall and partly through the oil to the casing or tank of the transformer, where they are radiated as sound over a large area to the environment. In addition, mechanical forces act on the windings, which grow quadratically with the current and also excite oscillations with twice the mains frequency. For example, in the immediate vicinity of power transformers with 40 MVA, without the noise level of the cooling equipment, a noise level of the order of 70  dB (A) is achieved. In substations with large transformers in or near residential areas, additional sound-absorbing measures are usually taken. Another source of noise from the transformer are any pumps and fans in the cooling system.

literature

• Peter Bastian, Horst Bumiller, Monika Burgmeier, Walter Eichler, Franz Huber, Jürgen Manderla, Jürgen Schwarz, Otto Spielvogel, Klaus Tkotz, Ulrich Winter, Klaus Ziegler: Electrical engineering . 26th, revised and expanded edition. Europa-Lehrmittel , Haan-Gruiten 2008, ISBN 978-3-8085-3160-0 .
• Hans Rudolf Ris: Electrical engineering for practitioners . 5th, completely revised edition. Electrosuisse, Fehraltorf 2011, ISBN 978-3-905214-71-0 (with CD-ROM ).
• Hans-Ulrich Giersch, Hans Harthus, Norbert Vogelsang: Electrical machines . 5th edition. Teubner, Stuttgart 2003, ISBN 3-519-46821-2 .
• Rudolf Janus: Transformers . VDE, Berlin 1993, ISBN 3-8007-1963-0 .
• Helmut Vosen: Cooling and resilience of transformers . VDE, Berlin 1997, ISBN 3-8007-2225-9 .
• Rolf Fischer: Electrical machines . 12th edition. Hanser, Munich 2004, ISBN 3-446-22693-1 .
• Adolf J. Schwab: Electrical energy systems - generation, transport, transmission and distribution of electrical energy . Springer, 2006, ISBN 3-540-29664-6 .

Web links

Commons : Transformers  - collection of images, videos and audio files

Wiktionary: Transformator  - explanations of meanings, word origins, synonyms, translations

Wikibooks: Transformator  - learning and teaching materials

• TU-Ilmenau: Transformer learning program
• National High Magnetic Field Laboratory of Florida State University: Simulation of a Transformer (Java Applet)
• Course "Basics of Electrical Engineering, Transformer" at TU Dortmund from 2003
• Deutsches Kupferinstitut: Selection and calculation of small transformers (PDF; 682 kB)
• Flash animation on the function of the transformer (dwu teaching materials)

Individual evidence

1. ↑ NATIONAL HIGH MAGNETIC FIELD LABORATORY USA - The Stanley Transformer - 1886 (English)
2. ↑ ^{a b} VDE "Chronicle of Electrical Engineering - Transformer"
3. ^ Borns: Lighting by means of secondary generators. In: Elektrotechnische Zeitung. No. 5, 1884, pp. 77-78
4. ^ VDE website - Dolivo-Dobrowolsky
5. ^ Gerhard Neidhöfer: Michael von Dolivo-Dobrowolsky and the three-phase current. Beginnings of modern drive technology and power supply. VDE book series History of Electrical Engineering Volume 9, 2nd edition. VDE VERLAG, Berlin Offenbach, ISBN 978-3-8007-3115-2 .
6. ↑ WEKA Media Lexicon ( Memento from July 23, 2012 in the web archive archive.today )
7. ^ Friedrich Uppenborn: History of Transformers , Munich / Leipzig, 1888. English translation 1889 as History of The Transformer. In: Open Library ( (full text at Open Library) )
8. ↑ Gisbert Kapp: Transformers for alternating current and three-phase current: A presentation of their theory, construction and application. Berlin, 1907 ( (full text at Open Library) ).
9. ↑ Karl Küpfmüller, Wolfgang Mathis, Albrecht Reibiger: Chapter 29.3 The Transformer In: Theoretical Electrical Engineering, An Introduction. 17th edition, ISBN 3-540-29290-X ( excerpt from Google book search).
10. ↑ HR Ris: Electrical engineering for practitioners . 1st edition. Buchverlag Elektrotechnik Aarau (Switzerland), 1990, ISBN 3-905214-11-3 , p. 495 f .
11. ↑ ^{a b} Eckhard Spring: Electrical machines: An introduction . 3. Edition. Springer, Dordrecht / Heidelberg / London / New York 2009, ISBN 978-3-642-00884-9 , 2.2 Realer Transformer, pp. 115–129 ( limited preview in Google Book search).
12. ↑ ^{a b} Wolf-Ewald Büttner: Fundamentals of electrical engineering . 2nd Edition. tape 2 . Oldenbourg, Munich 2009, ISBN 978-3-486-58981-8 , 9.4.2 Consideration of core losses, p. 294 ( limited preview in Google Book Search [accessed December 8, 2012]).
13. ^ Adolf J. Schwab: Electrical energy systems - generation, transport, transmission and distribution of electrical energy. P. 351.
14. ↑ HR Ris: Electrical engineering for practitioners . 1st edition. Buchverlag Elektrotechnik Aarau (Switzerland), 1990, ISBN 3-905214-11-3 , p. 499 .
15. ↑ DIN EN 60076-5; VDE 0532-76-5: 2007-01: 2007-01: Power transformers - Part 5: Short-circuit strength (IEC 60076-5: 2006)
16. ↑ HR Ris: Electrical engineering for practitioners . 1st edition. Buchverlag Elektrotechnik Aarau (Switzerland), 1990, ISBN 3-905214-11-3 , p. 502 .
17. ↑ Ekbert Hering: Figure 16.13. In: Basic knowledge of the engineer. 14th edition, Fachbuchverlag Leipzig, ISBN 978-3-446-22814-6 , p. 780.
18. ^ Joachim Specovius: Basic course in power electronics. Vieweg, 2003, ISBN 3-528-03963-9 (Section 18.8 Forward converter ).
19. ↑ Manfred Michel: Power Electronics. Introduction to circuits and their behavior. 4th edition, Springer, Berlin 2009, ISBN 978-3-540-75610-1 (Section 7.2.2).
20. ^ Ulrich Schlienz: Switching power supplies and their peripherals. Dimensioning, use, EMC. 3rd edition, Vieweg, 2007, ISBN 3-8348-0239-5 (Chapter 6).
21. ↑ E. Böhmer, D. Ehrhardt, W. Oberschelp: Elements of applied electronics. 14th edition, Vieweg-Verlag, 2007, ISBN 3-528-01090-8 (Chapter 6.2).
22. ^ RF Transformers. (No longer available online.) Minicircuits, archived from the original on September 15, 2011 ; accessed on November 29, 2009 (product overview). Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice.  
23. ^ J. Edwards, TK Saha: Power flow in transformers via the poynting vector. Queensland University of Technology, 2001 ( full text ( Memento from December 28, 2013 in the Internet Archive ); PDF; 271 kB).
24. ^ F. Herrmann: The Poynting vector field and the energy flow within a transformer . In: American Journal of Physics . tape 54 , no. 6 , 1986, pp. 528 , doi : 10.1119 / 1.14554 ( full text (PDF; 346 kB)).
25. ^ ^{A b} William A. Newcomb: Where is the Poynting vector in an ideal transformer? In: American Journal of Physics. 52, No. 8, 1984, pp. 723-724, doi: 10.1119 / 1.13563 .
26. ↑ F. Herrmann: Altlasten der Physik (87) - The stray field of the transformer . In: PdN-PhiS . tape 1/55 , 2006 ( full text (PDF; 346 kB)).
27. ↑ Adolf J. Schwab: Conceptual world of field theory. Practical, clear introduction. Electromagnetic fields, Maxwell's equations, gradient, rotation, divergence. 6th edition, Springer, Berlin 2002, ISBN 3-540-42018-5 .
28. ^ Ulrich Schlienz: Switching power supplies and their peripherals. Dimensioning, use, EMC . 3. Edition. Vieweg Verlagsgesellschaft, 2001, ISBN 3-528-03935-3 , Section 13.5.3 Failure of network half-waves .
29. ^ Ulrich Schlienz: Switching power supplies and their peripherals. Dimensioning, use, EMC . 3. Edition. Vieweg Verlagsgesellschaft, 2001, ISBN 3-528-03935-3 , Section 13.5.4 Switching on a transformer in the zero crossing .
30. ↑ IEEE series of standards C57
31. ^ ^{A b} Electronics Industry Market Research and Knowledge Network: Global Electricity Transformers Market is Expected to Exceed $ 36.7 Billion by 2015 . December 3, 2008.
32. ↑ ^{a b} Goulden Reports: The world markets and manufacturers of transformers 2005-2010 . (PDF; 26 kB).
33. ↑ HR Ris: Electrical engineering for practitioners . 1st edition. Buchverlag Elektrotechnik Aarau (Switzerland), 1990, ISBN 3-905214-11-3 , p. 492 .
34. ↑ Gisbert Kapp: Transformers for alternating current and three-phase current: A presentation of their theory, construction and application. Berlin 1907, p. 28 ( full text at Open Library).
35. ↑ General Association of the Aluminum Industry: Aluminum in Electrical Engineering and Electronics, here 3rd section ( Memento of the original from July 10, 2009 in the Internet Archive ) Info: The archive link was automatically inserted and not yet checked. Please check the original and archive link according to the instructions and then remove this notice. 
36. ↑ GEAFOL - Cast Resin Transformers, three-phase distribution transformer. (PDF) Retrieved on June 28, 2009 (information from Siemens AG on the use of aluminum foil windings in large transformers). 
37. ↑ Wolfgang Böge (Hrsg.): Vieweg handbook electrical engineering: Basics and applications for electrical engineers . 4th edition. Vieweg + Teubner Verlag, 2007, ISBN 978-3-8348-0136-4 , p. 809 .
38. ^ Herbert A. Fritz: Manufacturing technology . Ed .: Günter Schulze. Springer , 2010, ISBN 978-3-642-12878-3 . , P. 162ff
39. ↑ http://www.tme.eu/de/Document/af2ca4e3fc2a87d5df3a187c03c9a4f7/TST10+800-4000.PDF .
40. ↑ 2 x EILP50 / 64 low profile core.
41. ^ Rolf Fischer: Electrical machines . 14th edition. Hanser, 2009, ISBN 978-3-446-41754-0 , pp. 124 to 125 .

This version was added to the list of articles worth reading on October 6, 2009 .