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Electric transformer

An electrical transformer is a converter that allows the values of the voltage and the intensity of the current delivered by an alternating electrical energy source to be modified into a voltage and current system of different values but of the same frequency and the same shape. He performs this transformation with excellent efficiency. It is analogous to a gear in mechanics (the torque on each of the toothed wheels being the analog of the voltage and the speed of rotation being the analog of the current).

A distinction is made between static transformers and commutators. In a static transformer, energy is transferred from primary to secondary via the magnetic circuit formed by the transformer casing. These two circuits are then magnetically coupled. This makes it possible to achieve galvanic isolation between the two circuits. In a commutator, energy is transmitted mechanically between a generator and an electric motor.



Lucien Gaulard, a young French electrician, presented to the Société française des Electriciens in 1884 a “secondary generator”, since called the transformer.

In 1883, Lucien Gaulard and John Dixon Gibbs succeeded in transmitting for the first time, over a distance of 40 km, alternating current at a voltage of 2000 volts using transformers with a core in the form of bars.

In 1884 Lucien Gaulard put into service a looped demonstration link (133 Hz) supplied by alternating current at 2000 volts and going from Turin to Lanzo and back (80 km). We then end up admitting the interest of the transformer which makes it possible to increase the voltage delivered by an alternator and thus facilitates the transport of electrical energy by high voltage lines. The recognition of Gaulard will come too late.

In the meantime, patents have also been taken by others. Gaulard’s first patent in 1882 was not even issued in its day, under the pretext that the inventor claimed to be able to do “something from nothing”! Gaulard attacks, loses his cases, is ruined, and ends his days in an insane asylum. The Gaulard transformer of 1886 does not have much to envy the current transformers, its closed magnetic circuit (the prototype of 1884 included an open magnetic circuit, from where a very poor performance) is made up of a multitude of wires of iron announcing the laminated circuit with insulated sheets.

Thus, in 1885, the Hungarians Károly Zipernowsky, Miksá Déry and Otto Titus Bláthy developed a transformer with an annular core marketed throughout the world by the firm Ganz in Budapest. In the USA, W. Stanley develops transformers.


magnetic circuit and windings.

It is made up of two essential parts, the magnetic circuit and the windings.

The magnetic circuit

The magnetic circuit of a transformer is subjected to a variable magnetic field over time. For transformers connected to the distribution sector, this frequency is 50 or 60 Hertz. The magnetic circuit is generally laminated to reduce eddy current losses, which depend on the amplitude of the signal and its frequency. For the most common transformers, the stacked sheets have the shape of E and I, thus making it possible to slide a coil inside the windows of the magnetic circuit thus formed.

The magnetic circuits of “high-end” transformers have the shape of a torus. The toroid winding being more delicate, the price of toroidal transformers is significantly higher.

Single-phase transformer operation

Perfect or ideal transformer

Transformateur monophasé idéal
Perfect or ideal transformer

Ideal single-phase transformer

It is a virtual transformer without any loss. It is used to model real transformers. These are considered to be a combination of a perfect transformer and various impedances.

In the case where all flux losses and leaks are neglected, the ratio of the number of primary, secondary turns totally determines the transformation ratio of the transformer.

  • Example: A transformer whose primary has 230 turns supplied by a sinusoidal voltage of 230 V rms voltage, the secondary which has 12 turns will present at its terminals a sinusoidal voltage whose rms value will be equal to 12 V. (Attention 1 turn n ‘is not equal to 1 V)
\frac{U_2}{U_1} =  \frac{N_2}{N_1}

As losses are neglected, the power is transmitted in full, which is why the intensity of the current in the secondary will be in the inverse ratio, ie nearly 19 times greater than that circulating in the primary.

S_1 =S_2 \,
U_1I_1 =  U_2I_2 \,
\frac{U_2}{U_1} = \frac{I_1}{I_2}

of the equality of the apparent powers:, i.e.: we draw

  • At the risk of overheating very quickly, the secondary conductor must have a section adapted to the intensity of this current.

The power losses of a transformer

Joule effect losses

P_J = \sum_i R_i I_i^2
R_i \,
I_i \,

The losses by Joule effect in the windings are also called “copper losses”, they depend on the resistance of these windings and the intensity of the current which crosses them: with a good approximation they are proportional to the square of the intensity. with resistance of winding i and intensity of the current flowing through it.

Magnetic losses

These losses in the magnetic circuit, also called “iron losses”, depend on the frequency and the supply voltage. At constant frequency they can be considered as proportional to the square of the supply voltage. these losses have two physical origins:

  • Eddy current losses. They are minimized by the use of varnished magnetic sheets, therefore electrically isolated from each other to constitute the magnetic circuit, this in opposition to a solid circuit.
  • Hysteresis losses

Loss measurement

The separate loss method consists of placing the transformer in two states:

  • A state for which the Joule losses are high (high current) and the magnetic losses very low (low voltage). Short-circuiting the transformer (short-circuit test) with a reduced voltage supply enables these two conditions to be achieved. The losses of the transformer are then almost equal to the Joule losses.
  • A state for which the magnetic losses are high (high voltage) and where the joule losses are very low (low current). No-load operation (no-load test), that is to say without a receiver connected to the secondary, corresponds to this case. The losses are then almost equal to the magnetic losses.

We say that we have two states which allow “a separation” of the losses, hence the expression “method of the separated losses”. They also have the advantage of allowing performance measurement with reduced power consumption, without testing in real operation. This is interesting when testing a high power transformer and when there is not enough power in the workshop to supply it at its rated speed. Except for test platforms at manufacturers, this method is therefore not very useful for only knowing the efficiency because, in this context, a direct measurement at nominal (normal) power is often sufficient.

On the other hand, within the framework of theoretical electrical engineering, it is important because it makes it possible to determine the elements making it possible to model the transformer.

The different types of transformers

These distinctions are often linked to the very many possible applications of transformers.


Symbole d'un autotransformateur. 1 indique le primaire; 2 le secondaire

Symbol of an autotransformer.
1 indicates the primary; 2 secondary

This is a transformer without isolation between the primary and the secondary.

In this structure, the secondary is a part of the primary winding. The current supplied to the transformer flows through the entire primary and a bypass at a given point thereof determines the output of the secondary. The ratio of input voltage to output voltage is the same as for isolated type.

For equal efficiency, an autotransformer occupies less space than a transformer; this is due to the fact that there is only one winding, and that the common part of the single winding is traversed by the difference of the primary and secondary currents. The autotransformer is only interesting when the input and output voltages are of the same order of magnitude: for example, 230V / 115V. One of its main applications is to use electronic equipment in a country intended for a country where the mains voltage is different (United States, Japan, etc.). However, it has the drawback of not having galvanic isolation between the primary and the secondary (that is to say that the primary and the secondary are directly connected), which can present risks from the point of view of personal safety.

Variable transformer – variac – alternostat

It is a variety of auto-transformer, since it has only one winding. The secondary output shunt can move thanks to a sliding contact on the turns of the primary.

Isolation transformer

The isolation transformer is only intended to create electrical isolation between several circuits, often for reasons of safety or of solving technical problems. All transformers with primary winding isolated from the secondary (s) should be considered as isolating transformers; however, in practice, this name designates transformers whose output voltage has the same rms value as that of the input. They are, for example, widely used in operating theaters: each room in the operating theater is equipped with its own isolation transformer, to prevent a fault appearing there from causing malfunctions in another room. Another advantage is to change the neutral system (case of use of computer equipment and / or sensitive electronic equipment in an IT installation).

Impedance transformer

The transformer is still an impedance transformer, but electronics engineers give this name to transformers that are not used in power circuits.

The impedance transformer is mainly intended to adapt the output impedance of an amplifier to its load.

  • This kind of transformer was used in particular in sound reproduction, to adapt the output of an audio tube amplifier (high impedance), with loudspeakers intended for sound reproduction and characterized by low impedance.
  • In professional audio electronics, transformers are always used for inputs and outputs of high-end devices, or in the manufacture of “Di-box” or direct box. The transformer is then used, not only to adapt the impedance and the output level of the devices (synthesizers, electric bass, etc.) to the microphone inputs of the mixing console but also to balance the output of the connected devices.
  • In high frequency technology, transformers are also used whose magnetic circuit is in ferrite or without a magnetic circuit (also called coreless transformer) to adapt the output impedances of an amplifier, a transmission line and an antenna. Indeed, for an optimal transfer of power from the amplifier to the antenna, the standing wave ratio (SWR) must be equal to 1.

Such arrangements also have the advantage of making the connected devices much more resistant to electromagnetic disturbances by a significant increase in the CMRR (Common Mode Rejection Ratio) or common mode rejection rate.

Current transformer

This type of transformer, also called current transformer, is dedicated to the adaptation of the currents involved in different but functionally interdependent circuits.

Such a transformer allows the measurement of high alternating currents. It has one turn at the primary, and several secondary turns: the transformation ratio allows the use of a conventional ammeter to measure the intensity at the secondary, image of the intensity at the primary which can reach several kiloamperes (kA).

Voltage transformer

This transformer is one of the means for measuring high alternating voltages. This is a transformer which has the particularity of having a precisely calibrated transformation ratio, but designed to deliver only a very low load to the secondary, corresponding to a voltmeter. The transformation ratio makes it possible to measure primary voltages expressed in kilovolts (kV). It is found in HTA and HTB. Other technologies exist, such as that of the capacitive divider.

High frequency transformer

Magnetic circuit of HF transformers

Eddy current losses within the magnetic circuit are directly proportional to the square of the frequency but inversely proportional to the resistivity of the material which constitutes it. In order to limit these losses, the magnetic circuit of HF transformers is made using insulating ferromagnetic materials:

  • soft ferrites: mixed oxides of iron and copper or zinc;
  • nanocrystalline materials.

Pulse transformer

This type of transformer is used for controlling thyristors, triacs and transistors. Compared to the optocoupler, it has the following advantages: possible operation at high frequency, simplification of assembly, possibility of supplying a large current, good voltage resistance.

Three phase transformer


In three-phase electrical networks, one could perfectly consider using 3 transformers, one per phase. In practice, the use of three-phase transformers (a single device combines the 3 phases) is generalized: this solution allows the design of much less expensive transformers, with in particular savings in the magnetic circuit. Single-phase transformers are in fact hardly used, except for very large apparent powers (typically greater than 500 MVA), where the transport of a large three-phase transformer is problematic and encourages the use of 3 physically independent units.

Coupling index

This is the characteristic of a three-phase transformer indicating the type of coupling carried out at the primary and the secondary as well as the phase shift between the primary voltage system and the secondary voltage system. Three-phase voltage systems are: “triangle” (D or d) and “star” (Y or y). The first letter of the coupling index is always in upper case and indicates the three-phase system with the highest voltage; the second letter is lowercase and indicates the lowest voltage system. In the “star” system, the “neutral” (central point of the star) can be taken out at the transformer terminal block: this is indicated by the presence of the letter N (or n) in the coupling index. There is also the zig-zag (z) coupling, used mainly in secondary education; it has a neutral. This coupling makes it possible, during the loss of a phase at the primary, to have at the secondary a practically identical voltage on the three phases. Finally, the coupling index is completed by a “hourly index” which gives, in 30 ° steps, the hourly phase shift in 12ths of a turn (as on a watch) between the primary and the secondary of the transformer (eg: 11 = 11×30 ° = 330 ° clockwise or 30 ° anti-clockwise).

For example, a “Dyn11” coupling index therefore defines a transformer including:

  • the three-phase high voltage system is in “delta”;
  • the three-phase low voltage system is in “star” with neutral output (indicated by the “n”);
  • the offset between the two systems is 330 ° (= – 30 ° or even 11 * 30 °).


A switch is an electrotechnical system allowing to modify an electrical supply (voltage / current), using two rotating machines mechanically coupled. One is used as a motor, the other as a generator. The different characteristics of the two machines allow a transformation of electrical energy in the direction of voltages and currents.

Despite a low efficiency and a higher wear rate, the main advantage of the switch over the transformer was to be able to directly produce a DC power supply from an AC power supply. Thus, until the beginning of the 20th century, the direct 750V supplying the trains of the Parisian metro was generated in this way, from the public network which delivered only an alternating voltage.

These devices have been replaced by static converters in power electronics.

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