Why is an autotransformer used
A transformer (short: transformer) is an electrotechnical device that is primarily used to transfer electrical energy to a different electrical voltage level. The ratio of the currents at the input and output terminals is the opposite of the ratio of the voltage levels measured there (if the losses are neglected).
The level of the alternating voltage with which the electrical energy is transmitted can be increased or decreased with the help of transformers and thus adapted to the requirements. This enables the economical transmission of electrical energy over long distances with high-voltage lines. The power "put in" is not increased by a transformer, since losses always occur in it.
A transformer consists of at least one coil with several taps or two or more separate coils that are inductively, i.e. magnetically coupled. For optimal guidance of the magnetic flux in the so-called transformer core and to maximize the magnetic coupling of the coils to one another, practical versions of transformers usually have their coils placed on a common iron or ferrite core.
In the terminology of electrotechnical devices, the transformer is also referred to as a “static electrical machine”, as there are no mechanically moving parts. Transformers for power transmission are called transformer, Transformers for metrological purposes are called Transducer and transformers for signal transmission in telecommunications, where it is a matter of galvanic separation of input and output signals, are called Transformer designated.
The phenomenon of the generation of a magnetic field from the flow of electrical current and, conversely, the generation of electricity from a variable magnetic field has been known since Michael Faraday's discoveries in 1831. But it was not until the 1980s that the transformer principle was developed.
The Russian inventor Pawel Nikolajewitsch Jablotschkow introduced voltage regulation based on an arrangement of induction coils for the Jablotschkow candles he developed. The turns of one coil were connected to an alternating current source, the other to the carbon electrodes of the electric candles. The patent submitted for it described that the system could supply “different supplies for different lighting fixtures with different light intensities from a single source of electrical energy” . Obviously, these induction coils worked on the transformer principle.
Lucien Gaulard and John Dixon Gibbs exhibited a device with an open iron core in London in 1882, which they called "secondary generator" . At the Turin exhibition in 1884, they operated an 80 km long demonstration ring line to Lanzo with their system, thus demonstrating the low-loss power supply over greater distances. They also sold the idea to the American George Westinghouse.
The technicians Károly Zipernowsky and Miksa Déri, who work for the Hungarian industrial company Ganz & Cie, designed the two-part rotating single-armature converter in 1884. Together with Ottó Titusz Bláthy, they further developed this device into a fixed, one-piece device and had it patented in 1885. The term "transformer" was used for the first time. . This transformer 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 laid to form a ferromagnetic shell. The device was sold worldwide by the company Ganz & Cie in Budapest.
The American George Westinghouse, who became famous above all for the invention of the compressed air brake, played a major role in the spread of the alternating current system and with it the transformer. Westinghouse recognized the weaknesses of the direct current power distribution operated and favored by Edison at the time and primarily relied on alternating current. In 1885 Westinghouse imported a number of Gaulard-Gibbs transformers and a Siemens alternating voltage generator for electrical lighting in Pittsburgh. His technician William Stanley developed the Gaulard-Gibbs devices further and above all introduced a more effective closed iron core. From 1886 these devices came on the market .
In 1886 Westinghouse installed an AC voltage generator in Great Barrington, Massachusetts, whose 500 volt AC voltage was stepped up to 3,000 volts for distribution and then stepped back down to 100 volts to operate the electrical lighting at the connection points.
The then increasing use of transformers, in connection with alternating current, led to the widespread use of electricity as an energy supplier, because only high-voltage lines enable energy to be transported over long distances without excessive energy losses.
Two physical phenomena are essential for the functioning of a transformer:
An alternating voltage applied to the first coil (“primary coil”) in the primary circuit generates a variable magnetic field in the core, following the law of induction. This field penetrates the second coil ("secondary coil") in a second electrical circuit and here again generates a voltage ("secondary voltage") by induction.
A primary voltage can be transformed via magnetic flux into a proportional secondary voltage as a function of the number of turns ratio of the two coils.
A constantly changing voltage is required to operate a transformer. Therefore only AC voltage can be transformed with a transformer.
If a direct voltage is to be converted to a different voltage level by means of transformers, the conversion of the direct current into alternating current by means of an inverter is necessary so that it can then be transformed. These techniques are used, for example, in switched-mode power supplies.
The maximum level of the induced voltage depends not only on the input voltage but also on the number of turns of the secondary coil, the maximum level of the current on its conductor cross-sections and on the cooling conditions.
In the above description no (common) iron core of the coils is mentioned, nevertheless almost all transformers have a core made of iron sheets, iron wires or ferrite. The reason is that at low frequencies (50 Hz) without an iron core, an extremely large number of turns would be required in order to keep the "no-load current" sufficiently small at low loads. Firstly, this would require an uneconomically high copper content, and secondly, enormous ohmic losses (= heating) would be generated in this very long wire at higher currents.
Both can be greatly reduced by increasing the inductance of the primary coil many times over with an iron core. The higher the operating frequency, the smaller the iron core can be; at a few 100 kHz, as in the Tesla transformer, it can be completely omitted.
They should supply a system or devices to protect against contact with live parts with a secondary voltage that is galvanically separated from the voltage on the primary side. A safe galvanic separation of primary and secondary voltage must be guaranteed. The protective effect is that each of the two poles on the secondary side can be touched without an electric shock. (see also: safety transformer)
The nominal voltage on the secondary side of the isolating transformer must not be higher than 400 V, the short-circuit voltage must not exceed 10%. These are single-phase transformers with complete galvanic separation of the primary and secondary windings.
Bell transformers must be short-circuit proof (Uk = 40%), the no-load voltage on the secondary side must not exceed 32 V. The output terminals must be accessible without the input terminals having to be exposed.
Toy transformers usually have a short-circuit voltage of 20%. They are used to supply children's toys, must be short-circuit-proof and may have an open circuit voltage of no more than 32 V on the secondary side (nominal voltage when the secondary side is loaded: 24 V). The specification of a toy transformer is essentially determined by the fact that children's toys are put in the mouth.
Arrangement as coils
The implementation of a transformer with conductors lying stretched out next to one another would have the effect that a large part of the magnetic field is created as an ineffective stray field in the environment. This stray field contains a large part of the power used, which is then not available for the actual transmission process.
Therefore, the conductors are laid out in the form of coils. In order to keep the loss due to stray fields as small as possible, the primary coils and secondary coils are also nested as small and close together as possible. A secondary condition here is that the conductors and the coils as a whole are electrically insulated from one another, for which purpose usually coated wires and the subsequent coating or cast resin impregnation in a vacuum are used. The coil body is a molded part made of non-magnetic material, mostly plastic, which accommodates the windings, gives them mechanical stability and, if necessary, also insulates them from one another.
The coil that is fed by the input current is called the “primary coil”, the coil in which the voltage is induced is called the “secondary coil”. The ratio of the voltages on the two coils corresponds in theory exactly to the ratio of their number of turns (in practice the voltage on the secondary coil is lower than in theory due to losses).
example: A transformer with 1,000 turns on the primary winding, 100 turns on the secondary winding and 230 volts primary voltage generates an open circuit voltage of 23 volts in the secondary winding. These voltages arise when the transformer is idling. However, the actually usable operating or nominal voltage decreases with increasing load from power consumers, because the current in the coils causes an ohmic voltage drop (see section 4.5 Overload operation!).
Air transformer or ironless transformer
The coreless version is called an "air transformer" and is not efficient at low frequencies. The reason is that the primary coil would then have to have an extremely large number of turns in order to generate the required high inductive resistance. However, the very long wire required would have so great resistance that a large part of the power supplied would be converted into heat.
Air transformers have the advantage of supplying a voltage in the secondary coil with an exact replica of the change in the primary current over time, even if the primary alternating current contains relatively high frequencies. This phenomenon is particularly important when the frequency components of the current extend over a large bandwidth. Therefore air transformers are used as transformers for some purposes.
Further examples are the Tesla transformer as well as coupling and matching coils in high frequency technology.
Iron core transformer
The magnetic field generated by a current-carrying conductor is associated with a flux density of relatively low strength in air or in a vacuum, magnetic coupling and inductance of the coils are low and would require very high operating frequencies.
However, it is possible to increase the flux density considerably by changing the magnetic field of the coils in a closed magnetic circuit made of ferromagnetic material, e.g. B. iron - the transformer core - is performed. For Power transformers (Frequencies of 50 or 60 Hz) predominantly iron-silicon alloys, grain-oriented electrical sheet (textured sheet) according to DIN EN 10107. The higher-quality iron-nickel alloys are also used for signal transmitters and soft magnetic ferrite cores are used at high frequencies.
The increase in the flux density in ferromagnetic materials is based on the fact that, with increasing strength of an externally applied magnetic field, the randomly aligned magnetic crystal areas (Weiss areas) rearrange in a common direction. This magnetic polarization M of the material makes a 1,000 to 100,000 times higher contribution to the flux density B than the magnetic field strength H. This ratio is called the magnetic susceptibility χ, it applies
The following applies to the magnetic flux density B.
and from it finally
- is a natural constant, the absolute permeability constant.
The dimensionless number μr = 1 + χ becomes Relative Permeability Constant or Permeability number named and is material-specific.
Transformers used for power transmission in the power grid always have a closed one Iron coreon which the coils are applied. The cross-section of the iron core is chosen so that the flux density is as possible in the entire ironcore is constant and does not come too close to the saturation magnetic flux density. Cores for single-phase transformers made up of three legs with primary and secondary coil on the middle leg (M-cores) therefore have outer legs with half the cross-section of the middle leg.
Typical flux densities for grain-oriented electrical steel (2.03 Tesla saturation flux density) are 1.6 ... 1.75 T.
Some transformers are subject to particularly high demands on the linearity of the current-voltage characteristic, or they are also used to temporarily store magnetic energy (flyback converters). This can be achieved through an air gap in the magnetic circuit (quasi a hybrid form of air transformer and iron core transformer). 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.
Air gaps increase the leakage flux that may be found elsewhere, e.g. B. in the transformer tank, leads to losses and malfunctions.
Power transformers for frequencies below about 1 kHz usually have cores made of iron sheets that are electrically insulated from one another (electrical sheet). The cores must be laminated because under the influence of the magnetic field in the iron as a conductive material as well as in the secondary coil, voltages are induced which lead to eddy currents in the solid material. These eddy currents generate losses which are higher the better the electrical conductivity of the core. The current path is interrupted by the use of thin metal sheets that are insulated from one another. In the case of large transformers, damage to the insulation of the individual laminated cores can lead to considerable local heating of the core.
The iron core also causes magnetic reversal losses, which are caused by the continual polarity reversal of the magnetic domains (Weiss areas) and also occur when the system is idling. Silicon-iron alloys with a special texture have a sheet thickness of about 0.2 to 0.3 mm at 50 Hz losses of about 0.5 to 1 W / kg, depending on the strength of the magnetic field induced by the coils.
The magnetization behavior of iron is largely linear up to the saturation flux density. Due to the linear behavior, the absorbed no-load alternating current remains largely sinusoidal. During the transformation, the curve shape of the input voltage is largely retained - only harmonics are attenuated due to the leakage inductance, which, however, is even desirable with network transformers.
Like other ferromagnetic materials, iron has a limit for the linearity between field strength and magnetic flux, which is achieved when all Weiss areas of its structure are aligned in the same way. With this saturation magnetization, the iron cannot follow any further amplification of the field strength; the primary current then rises steeply. When designing the transformer, the core must therefore be dimensioned as precisely as possible so that the iron is still in the linear range of its hysteresis characteristic even in the event of overvoltages in the power grid.
Whether a transformer core gets into undesired magnetic saturation depends on the level of the primary voltage - if the primary voltage is too high in relation to the core cross-section or core material, number of turns and frequency, the transformer gets into saturation. The power consumption increases steeply. Magnetic saturation begins when the transformer is loaded at a slightly higher voltage, as the magnetic field strength decreases slightly due to the voltage drop across the ohmic resistance of the primary winding.A heavy load or even a short circuit on the secondary side leads to a significantly lower magnetic field strength in the core and, at the same time, to a strong stray field. This can be used to trigger a short-circuit protection (magnetic fuse).
The hysteresis characteristic shows the relationship between the magnetic field strength and the excitation field as it increases and decreases. It can be used to identify both the saturation induction and the magnetic reversal losses.
For transformers for higher frequencies, instead of iron, other soft magnetic materials such as B. ferrites, amorphous metal tape cores or powder cores are used.
Transformers with toroidal cores have a particularly high degree of efficiency, because the closed toroidal core shape results in only low stray field losses and the iron path is a minimum. Toroidal cores also consist of individual sheet metal layers that are formed by a band wound in a ring. Toroidal transformers can work with higher magnetic flux density and lower hysteresis losses if textured sheet metal strips are used. This also makes a significant contribution to reducing the size. In addition, toroidal cores can also be made from ferrites.
Toroidal cores are also used for variable transformers, where a rotatably mounted wiper makes contact with the individual coil windings. To make contact for the wiper, the turns of the coil are exposed on the outside, i. H. the enamel insulation of the enameled wires is sanded off.
Despite their advantages, toroidal transformers are not generally used because, among other things, the winding of a closed toroidal core is more complex. Cut tape cores represent a compromise solution: 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. The halves are then inserted into the wound bobbins and glued together. Textured sheet metal strips are sometimes used for cut strip cores. Cut ribbon cores have similarly good properties as toroidal cores, but winding production is easier. In contrast, core production is somewhat more expensive (SM, SE, SU, SG, S3U series, see also DIN 41309 and IEC 329).
Due to their minimized iron volume, toroidal and sectional band core transformers have higher inrush currents than other mains transformers, as they are more likely to saturate.
When designing the iron core and the number of turns n the following relationships are valid under certain boundary conditions (sinusoidal voltage form, homogeneous air gap-free magnetic circuit):
- n - number of turns
- ΔB. - induction amplitude (Change in flux density) in Tesla
- U - RMS value of the voltage in volts
- A.Fe - magnetic core cross-section in cm2
- f - Frequency in Hz
Depending on the specification, the maximum flux density for iron is 1.5 ... 2 T. For ferrites, it is around 200 mT.
As the frequency increases, the number of transformer windings required and the size decrease, which is why transformers for higher frequencies can be built very compactly or can transmit higher powers (example: switched-mode power supplies). Doubling the frequency makes it possible for a given size - apart from increasing core losses - to double the power that can be transmitted. For the same voltages, the cross-sections of the winding wires have to be doubled, the required number of turns halved.
The photo of an electronic ballast (EVG) of an energy-saving lamp at the top right shows a ferrite toroidal core transformer for controlling the switching transistors with only three or five turns.
Small ferrite transformers are used, among other things. used in switching power supplies and electronic transformers for low-voltage halogen lamps.
Three-phase alternating voltage can be transmitted with three identical single-phase transformers. In practice, however, the three separate iron cores are predominantly combined to form a common core with three legs. For a better understanding one can imagine the three core legs arranged in a star shape. The practical design simplifies this again in that the three legs are arranged one behind the other in a straight line and are connected at the top and bottom with a common sheet iron yoke.
The magnetic fluxes are effective in the leg cores and change according to the respectively assigned alternating current phase. The phase angle between the three individual alternating currents is ± 120 ° each, so that the magnetic fields induced in the legs cancel each other outwards.
Three-phase transformers are built with rated outputs of around 100 VA to 1,100 MVA.
The formula for the transformation ratio ü = n1 / n2 applies to three-phase transformers only with the same connection of the high and low voltage side, such as with vector group Yy0. The three phase conductors of the electrical voltage are usually designated in Europe with the letters "L1", "L2" and "L3" (formerly "R", "S" and "T"), the three winding phases of three-phase motors and transformers with "U", "V" and "W".
In the case of particularly large transformers, three single-phase transformers can be combined to form a “three-phase bank” for better portability. In this case, however, the step switches and many signaling devices must each be present in triplicate, so that this arrangement is rarely carried out.
With the help of the so-called Scott circuit, the three-phase alternating current is converted into a two-phase system. This type of transformer is often used in heating systems in order to achieve a symmetrical load on the network.
Design of the coil windings
As already mentioned above, the output voltage of the transformer secondary coil is theoretically exactly as high as the number of turns ratio between the windings and the primary voltage dictate.
The following applies:
- U1 - primary voltage
- U2 - secondary voltage
- n1 - number of primary turns
- n2 - Number of secondary turns
However, this only applies to idling or the unloaded state. As soon as a current flows to an external consumer in the secondary coil, the no-load voltage is divided between the internal electrical resistances of the transformer and the consumer. The leakage inductance also leads to a reduction in voltage.
So if a certain voltage is to be drawn at a certain power, the number of turns of the secondary coil must be designed for a correspondingly higher open circuit voltage. The voltage that can be drawn from the coil at nominal power is called "nominal voltage". The nominal power is the output power provided for regular continuous operation on the secondary side. Instead, it is also possible to work with the nominal current.
example: For one type of transformer, due to its size and material, a power loss during transmission of 10% is known. At the intended nominal power, the secondary coil should deliver exactly 240 volts. The number of turns is therefore for an open circuit voltage of
At rated power, the secondary coil then delivers a voltage of
Instead of a single transformer, a transformer can also have several separate secondary windings for different voltages or for separate circuits. The secondary windings can be one or more Taps have: so you can get several different high secondary voltages even with a transformer with only one secondary winding.
The primary windings can also have multiple taps; Such a transformer is then suitable for different primary voltages, which are nevertheless transformed to identical output voltages.
A transformer that should be used for both the American (120 volts) and the European market (230 volts) can, for. B. be provided with a tap on the primary winding on the mains transformer and a changeover switch. Often, however, two windings for 120 volts each are applied, which can be connected either in parallel or in series. As a result, you can usually accept the small voltage deviation in favor of the lower copper requirement.
The autotransformer only has a single winding with one or more taps - with this design there is only voltage adjustment, but no galvanic separation between input and output voltage. Its advantage is the lower mass (iron and copper weight) with the same transmission capacity.
In mains transformers with only one winding chamber, the primary winding is usually wound at the bottom - at lower output voltages, the 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.
Audio transformers (transmitters and output transformers) often have interlocking (so-called nested) windings to reduce leakage inductance and thus improve the transmission of high frequencies.
If the winding on the secondary side is separated after half the total number of turns and led to the outside, this is referred to as a center or center tap. So you have three voltages available. A variation of this center tap is obtained by applying two oppositely wound windings with the same number of turns to the secondary side. This results in, among other things, two voltages that are 180 ° out of phase with one another and have the same amplitude and frequency.
Stress transformation is used to transform (transform) stresses to the desired value. Example: 230 volts from the public power grid in 12 volts for a halogen lamp. In the case of low and medium power outputs, the windings are often cast in resin together with the core.
So-called autotransformers with only one common winding are used for pure voltage adjustment (for example from 230 V to 115 V). The changed output voltage is obtained by tapping (if it should be smaller than the input voltage) or an additional winding attachment (for a voltage greater than the input voltage). The transformer only has to transmit part of the required power (in the example 230/115 V half plus the transformer's own power loss) and can be built correspondingly smaller.
Bell transformers z. B. have the task of generating the voltage of 8 volts required for the doorbell from the mains voltage of 230 V. They are usually short-circuit-proof and have particularly low no-load losses.
For low-loss energy transmission in high-voltage lines, voltages are transformed to high values. The machine transformer of the power plant converts the generator voltage, in large power plants around 10 kV to 30 kV, to the high voltage of around 110 kV to 400 kV, which means that the transport losses in the interconnected network are lower and greater powers can be transmitted. The transformation losses are comparatively low with high-voltage transformers and are usually 0.1% of the transmitted power. The lower current on the high-voltage side with constant transmitted power means that less heat is lost at the ohmic resistance of the line. However, the current on high-voltage lines is relatively high in normal operation and in terms of amount even higher than at lower voltage levels such as the medium-voltage network. The current on 400 kV lines is in the range of 1 kA per phase conductor, in comparison to this on 110 kV lines "only" in the order of magnitude of 500 A, in each case in the normal operating range. The reason for operating high-voltage lines is to achieve an increase in the total power to be transmitted and not to reduce the conductor current on high-voltage lines.
If the transmission voltage is correct, inductive and capacitive reactive power cancel each other out (characteristic impedance Z = (240 ... 300) ohms). However, this statement only applies when the so-called natural power P is transmittedn. For the medium-voltage network, the high voltages are transformed back to 10 kV to 36 kV in substations.
To dissipate the heat loss in large power transformers, these are installed as oil transformers in containers that are filled with transformer oil. If necessary, the cooling by the oil is forced with cooling fins and circulation pumps (see picture with power transformers).
Due to the insulating properties of the oil, the lacquer insulation of the copper conductors is sufficient, depending on the voltage, to dispense with the impregnation or potting of the windings with insulating substances. Large transformers, on the other hand, always contain solid cellulose-based insulation components. However, as the oil ages and the cellulose absorbs water, the insulation properties deteriorate as the operating time increases. In the 1970s to the early 1980s, the toxic, but more stable polychlorinated biphenyls (PCB) were therefore often used.
The voltage adjustment in the event of mains load fluctuations and the coordination when large power transformers are connected in parallel is carried out via step switches built into the boiler. For this purpose, the corresponding windings are provided with taps.
In the picture above the transformer, the three cast resin-insulated, cylindrical ripple control feed-in transformers can be seen, which are in series with the low-voltage side winding and apply audio-frequency control pulse sequences from the ripple control system to the downstream network.
Clocked power supplies / switching power supply
Mains transformers working at a mains frequency of 50 or 60 Hz are relatively large and heavy. Since the rate of change of the magnetic field strength determines the voltage induced in the windings, a transformer operated at a higher frequency can also transmit more power.
As the frequency increases, the number of turns and / or the core cross-section (core volume) can decrease without the voltage changing; see formula (2). In switched-mode power supplies, input voltages with frequencies of around 20 kHz to 2 MHz are generated for the transformer using semiconductor switches. This means that considerably lighter power supplies or power supplies can be built.
The transformer cores of switched-mode power supplies are usually made of ferrite (ferromagnetic ceramic) or iron powder to reduce hysteresis and eddy current losses. At higher frequencies, the windings are also often designed as flat copper tape or by means of high-frequency braids (thin wires connected in parallel) because of the skin effect. Despite the lower saturation induction of ferrites compared to iron, the reduction in mass is considerable. For example, a transformer suitable for transmitting 4000 watts weighs:
- at 50 Hz about 25 kg
- at 125 kHz, on the other hand, only 0.47 kg.
The rapid current and voltage changes in the switched-mode power supply units lead to high-frequency interference, which usually has to be reduced with line filters, shields and output filters.
Medium frequency transformers
The formula for the relationship between number of turns, iron cross-section and voltage is as follows
- N: Number of turns
- ΔB. as induction amplitude (Change in flux density) in Tesla
- U: RMS value of the voltage in volts
- A.Fe: magnetic core cross-section in cm2
- f: Frequency in Hz.
Switching to the iron cross-section shows that the iron cross-section can be made smaller with increasing frequency:
For certain applications, a higher than the usual network frequency is used to build smaller transformers.
- In airplanes, the various voltages required in the previously common tube devices (RADAR, radio, etc.) could be generated in a mass-saving manner with small transformers with 400 Hz three-phase current.
- Medium-frequency transformers are often built into spot welding guns in order to avoid thick power supplies (several thousand amperes are required) and to keep the guns light and mobile (e.g. on robot arms in automobile production).
Compared to an operating frequency of 50 Hz, great weight savings can be achieved. At frequencies up to a few kHz ("medium frequency"), power transformers can still be manufactured with sheet metal (iron) cores, but the sheet metal thickness must be less to avoid higher eddy current losses (about 0.1 mm compared to about 0.5 mm for 50 Hz). The hysteresis losses are then still within limits.
For security reasons (e.g.Lightning strike) a connection of the public power supply is related to earth potential. In order to prevent under all circumstances (e.g. interconnected cables) that a freely accessible, conductive point of the device carries mains potential and thus the maximum safety extra-low voltage is exceeded for the user, a galvanic separation with reinforced insulation or a protective grounding more conductive, accessible Parts are made. Transformers with separate, isolated windings provide this galvanic separation. The so-called "safe electrical separation" (protection class II) is defined in standards (IEC, VDE, UL) and requires particularly high electrical insulation strength between the primary and secondary side. Transformers suitable for this often have separate, encapsulated insulating material chambers for the primary or mains voltage winding.
From an earthed network one can use so-called Isolating transformers (Transmission ratio 1: 1) create a network isolated from earth. Such a network separation is required for many devices in hospitals. In the event of a body shock on a device that comes into contact with people, no earth current can flow. Rather, the network is monitored and the error can be corrected. Switching off is not necessary as long as no second error occurs.
Repair work on mains-operated devices (e.g. televisions) must also be carried out on mains voltage isolated by means of an isolating transformer. However, conventional isolating transformers do not offer any protection against touching the picture tube anode voltage of 17 ... 27 kV: even without contact, you can suffer an electric shock when approaching within the striking distance, as the insulation strength of a conventional isolating transformer is only about 4 kV.
For the measurement of high alternating currents and voltages, transducers are used with which the voltage or current is transformed down to low values that are compliant for the measuring device.
Current transformers designed as straight-through transformers consist only of the secondary coil and the core (clamp-on ammeter). The primary winding is formed by a lead through the power circuit. If necessary, the line can be fed through the transducer several times in order to adapt the measuring range according to the following formulas:
- or .
Particularly high requirements are placed on measuring current transformers and voltage transformers for energy meters. They are used to transform the primary current to be measured to the z. B. for 5 A designed current coil of a mechanical meter or you can generate a small measuring voltage for the evaluation electronics of an electronic meter with a load resistor connected to the secondary winding. By using special alloys for the core, good linearity and a low phase error can be achieved.
Often the voltage also has to be stepped down in order to be able to measure it. The voltage transformers used for this are designed for measurements against earth / neutral conductor or for measuring the voltage between the outer conductors.
Common nominal secondary values of current transformers are 5 A, of voltage transformers 100 V.
Resistance transformation is used to adapt loads and sources with regard to their resistance or characteristic impedance, for example a ferrite antenna to the input stage of the radio or a loudspeaker with an impedance of 4 ohms to the output of a tube amplifier with an impedance of 1000 ohms. When transforming to the same value, the maximum possible power is transferred (power adjustment).
Ohm's law applies to the electrical resistance R of a module
Applying this relationship to the primary and secondary windings of a transformer, it follows
For the ratio of primary and secondary resistance, the required ratio of the number of turns is calculated with U ~ N and I ~ 1 / N:
With a turns ratio of 2 to 1, a resistance transformation of 4 to 1 is achieved.
By converting the resistance, both resistances in the series branch of the equivalent circuit can now be viewed from only one side. The impedance on the side that is not of interest has now been converted to the reference voltage level. The sum gives the short-circuit impedance. All power and short-circuit calculations are based on a voltage.
Electrotechnical definition of ideal transformers
An ideal transformer is an electrical quadrupole with the input variables u1(t) and i1(t), the output variables u2(t) and i2(t) as well as the transfer factor , for which applies:
The sizes u1(t) and i1(t) are called primary quantities of the transformer. The sizes u2(t) and i2(t) are called secondary quantities of the transformer. For γ> 0 the transformer is called “wound in the same direction”, for γ < 0="" heißt="" er="" „gegensinnig="">
The primary and secondary sides are galvanically separated. In connection with the formulas, the counting arrows shown on the right apply to the directions of currents and voltages.
Definition equations for complex calculations
The equations are correspondingly in the case of vector calculations
The terms transformer or transmitter can mean, on the one hand, an electrotechnical component or a model of this component. The meaning results from the context.
The transmission factor γ of the model is first of all a real number which, as a parameter of a pure network model, has no direct physical meaning. If real transformers are modeled using the model of the ideal transformer, the factor γ corresponds to the winding ratio the number of windings on the primary and secondary side or (in a more general representation) the root the ratio of the self-inductances of the primary and secondary coil. It is assumed that windings in the same direction are used on the primary and secondary side.
The indexing γ = n1 / n2 (instead of the more intuitive order: γ = n2 / n1) corresponds to the convention in the relevant literature. In German-language literature, the letter used.
Both sides of the transformer are recorded in the consumer counting arrow system. This convention is physically not intuitive, since the primary side of the transformer mostly plays the role of a producer with regard to the following network. The representation was chosen in order to ensure a representation consistent with the general two-port theory (formerly: four-pole theory). To avoid the negative sign in the formulas, in practice the secondary side of the transformer is often marked with arrows in the generator counting arrow system, deviating from the convention chosen here.
The model of the ideal transformer takes into account the essential properties for which transformers are used and neglects edge effects that must also be taken into account in practice. It is also used to model real transformers. In this respect, the model is an effective means of analyzing and synthesizing electrical transformer circuits.
The ideal model also allows the conversion of constant quantities in this form. Of course, this is not possible with a real transformer.
Transformers are generally used for energy conversion and specifically for voltage transformation, current transformation or resistance transformation.
The ideal transformer is a pure energy converter without an energy store. The power fed into the transformer on the primary side is identical at all times to the power drawn from the transformer on the secondary side so that:
The negative sign is necessary because both transformer sides are arrows according to the meanwhile usual convention in the consumer meter arrow system, but the secondary side is seen as a generator.
The power balance equation is the basis for the current, voltage and resistance transformation of a transformer. It is only approximately achieved in a real transformer.
In the phasor calculation, the power balance is:
The asterisk * indicates that the conjugate complex of the specified size is to be used.
There and according to the agreement are in phase with real γ, one can use the power balance equation with multiply so that the following simplification results:
Voltage and current transformation
From the definition equations it follows directly:
The side with the higher current therefore has the lower voltage and vice versa. In the case of a real transformer, the following applies accordingly: On the side with the high number of windings, there is high voltage and low current.
Connect the secondary side of the transformer with an impedance , it defines the ratio of secondary voltage to secondary current, and the following applies:
With the help of the transformation equations, the ratio of primary voltage to primary current results:
The ratio of primary voltage and primary current is the impedance that the transformer has together with the secondary-side impedance Has. The secondary-side impedance is therefore with the factor γ2 transferred to the primary side of the transformer.
Examples of resistance transformation and power adjustment
1. An AC voltage source without internal resistance drives a transformer with a winding ratio of 1: 3 and the resistance on the secondary side .
The turns ratio applies accordingly . According to the component law for the ohmic resistance we get:
According to the winding ratio, the primary current is thus:
During the transformation, the voltage increases by a factor of 3, the current decreases by a factor of 3. The source therefore “sees” U1 only a ninth of the impedance on the secondary side.
2. A voltage source with the internal resistance drives a load via a transformer with a winding ratio of 1: 3 R.. How big is the load to be selected so that maximum power is transmitted?
Weight R. is on the primary side only R./ 9. To ensure performance adjustment, must apply, so .
On the side with the high number of windings, there is therefore not only the high voltage, but also the high resistance.
A real transformer typically consists of two or more coils or conductor loops that are magnetically closely coupled. The right picture shows an arrangement of two coils with the inductances L.1 and L.2that with the coupling factor M. are magnetically coupled to one another.
Ideally, the following conditions apply:
The physical idea
are n1 and n2 the number of turns of the coils on the primary and secondary side and if the same magnetic flux Φ prevails in both coils, the following applies with the aid of the law of induction:
If the magnetic flux Φ is constant, both equations are identically zero. The transformer does not transmit any energy.
If there are changes in sizes, one can for all time t With divide both equations together, and we get:
However, this simple equation only applies to ideally coupled coils without further parasitic effects.
The lossless transformer
The requirement that the magnetic flux density is identical in both sub-coils is only approximately achieved because of the finite magnetic resistance of the magnetic material and the less than ideal design of the windings. The picture opposite shows the counting arrows of the sizes used and the direction of the coil windings. The counting arrow Φ should apply equally to all magnetic fluxes. It is right-handed coupled to the corresponding currents.
If one accepts coils wound in the same direction and is designated with
- Φ11 the flux that the primary coil creates
- Φσ1 the leakage flux of the primary coil, d. H. the primary coil flux that does not get into the secondary coil
- Φ21 the flux that goes from the primary to the secondary
- Φ22 the flux generated by the secondary coil itself
- Φσ2 the leakage flux of the secondary coil, d. H. the secondary coil flux that does not get into the primary coil
- Φ12 the flux that goes from the secondary to the primary
so the flows prevail in the primary and secondary coil
- Φ1 = Φ11 + Φ12 or.
- Φ2 = Φ22 + Φ21
According to the law of induction then applies:
With the help of self-inductance L.1 the primary coil, the self-inductance L.2 the secondary coil and the coupling inductances M.12 or. M.21 can express the magnetic fields via the associated currents on the primary and secondary side. The flow rate is used implicitly. It results:
The coupling inductances M.12 and M.21 are identical, so that one has the common letter M.: = M.12 = M.21 can use.
Through a Laplace transformation with s = jω goes d / dt in jω over, and it results in vector calculation:
These equations form the basis for the equivalent circuit diagram with current-controlled voltage sources.
The equivalent circuit diagram with controlled voltage sources can be converted into an equivalent circuit diagram with an ideal transformer. It is L.σ1 the leakage inductance of the primary side, L.σ2 the leakage inductance of the secondary side and L.H1 the main inductance of the primary side. The main inductance L.H1 acts because of the transmission properties of the ideal transformer on both the primary and the secondary side.
The following applies to the inductances:
It is k the so-called coupling constant. The coupling constant is a measure of how well the field of the primary coil reaches the secondary coil and vice versa. It is given by the equation:
defined, where k is positive with the same winding direction and negative with opposite winding direction.
k = 1 means perfect coupling in the sense that the entire field of the primary coil penetrates the secondary coil.
k = - 1 also means a perfect coupling, but the windings are in opposite directions.
k = 0 means that the primary and secondary coils are not magnetically coupled, that is, the field of the primary coil does not enter the secondary coil and, conversely, the field of the secondary coil does not enter the primary coil.
The equivalent circuit diagram becomes particularly simple if the secondary quantities of the ideal transformer are transformed to the primary side using the formulas for voltage, current and resistance transformation:
Finally, a verbal description of the components used and the consideration of various boundary conditions should be made:
- The leakage inductances take into account that not the entire magnetic flux of the primary coil passes through the secondary coil or vice versa. Stray inductances act like normal ones, i. H. not coupled, coils.
- The main inductance is connected in parallel to the ideal transformer. A reactive current flows through the main inductance, which is created solely due to the inductive effect of the coil arrangement. This so-called “magnetizing current” takes into account the energy of the magnetic field stored in the transformer core. The current through the main inductance can in a certain way be viewed as parasitic, since it does not transmit any power, but, like every reactive element, briefly absorbs power and then emits it again.
- In particular, the main inductance acts in the case of constant quantities (f = 0) as a short circuit that is parallel to the ideal transformer. It short-circuits both the primary and the secondary side, because the main inductance can also be written to the secondary side of the transformer through a resistance transformation. Formally, the model of the ideal transformer takes into account a transfer of constant quantities.
The lossy transformer
A real transformer has transmission losses due to the ohmic resistance of the winding and due to magnetic reversal losses (= eddy current and hysteresis losses) in the core.
The transmission losses in the windings are shown in the equivalent circuit by the winding resistances R.1 and R.2 of the primary and secondary coil, the so-called copper losses, are taken into account.
The magnetic reversal losses, often also called iron losses, are losses that occur in the magnetic conductor (ferrite core, iron core). They are not present in air-coupled transformers. These are the non-linear eddy current losses and the equally non-linear hysteresis losses. In the sense of a simple network calculation, they are called the linear component in this case R.F.e (Fe for Latin "ferrum", iron) modeled.
This model does not take into account the capacitive coupling between the primary and secondary side, which occurs due to the opposing windings on the primary and secondary side.
In the case of large transformers, the power loss may have to be dissipated by suitable cooling. In the event of prolonged overloading, a transformer can overheat and the insulation can burn out.
The variables in the equivalent circuit have the following meaning:
- L.h1 is the winding inductance, it generates the magnetizing current, which corresponds approximately to the no-load current
- R.Fe represents the hysteresis and eddy current losses, RFe is mostly large compared to the load impedance Z
- R.1 and R.2 are the ohmic resistances of the windings, they cause the current heat losses. They are mostly opposite the load Z low resistance.
- L.σ1.2 are the leakage inductances.
Hysteresis losses and eddy current losses are due to iron and are therefore called Iron losses designated. The current heat losses in the windings are called Copper losses, as transformers are often wound with copper conductors. The Wastage result from the magnetic leakage fluxes of the leakage inductances. They have a purely inductive effect and cause a voltage drop, but no heat. The leakage inductances are largely responsible for the low-pass behavior of a transformer.
The deleted values in the equivalent circuit must be converted according to the transformation ratio of the transformer (i.e. the turns ratio of the two coils to each other):
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