The transformer is a static electric machine, i.e. with no moving parts, whose operation is based on the principle of the electromagnetic induction (Faraday-Neumann's law); eit can therefore operate only at variable speed and it is fundamentally used at sinusoidal speed. 

There are single phase and three-phase transformers; by referring for simplicity to the single phase case, we can state that it is a two gate device able to absorb power at a gate (primary) and to give it back almost integrally to the other one (secondary), by modifying the voltage and current levels.

The transformer has a large use in both electric and electronic applications. 
Among the most significant uses we can mention the following ones, as an example:

	To transport in a cheap way the electric power it is necessary to apply to transmission lines operating at voltages that are much greater both than the ones convenient for generators and than the ones suitable for the user distribution. The interconnection and the power exchange between the parts of the electric system operating at different voltage levels is made possible by transformers able to rise or reduce the voltage amplitudes without significant power losses. For these applications we use high power three-phase transformers.
	The voltage level at which the delivering utilities provide the electric energy to the users is often different from the one required by the devices contained in the electric equipments; in this case too we obtain the suitable voltage by means of transformers.
	In some circuits, especially electronic ones, it may be necessary to obtain the maximum power transfer at a certain load; even at this purpose we can use a transformer having the property of carrying out the impedance matching, it is very used to transfer power between two parts of an electric mains, by keeping them electrically isolated, we can interpose a transformer.

Rated values

A real transformer is characterized by special voltage and current, power and frequency values, called rated values, that make up the quantities for which we have the optimum operation of the machine. 
They are located by the real quantities listed in the Table:

The voltage and current rated values have the meaning of effective values. 
In case of three-phase machines they refer to the linked voltages and to the line currents. They can be only marginally exceeded (of a little bit only for a limited period); as a matter of fact, if we exceed the rated voltages we can cause magnetic saturation and dielectric settlements of the isolations; if we exceed the rated currents we can cause an excessive heating of the windings and of the mechanic settlements due to the electrodynamic stresses.  Between voltage and current rated values there are, for definition, the relationships:

The rated power has the meaning of apparent power and it is therefore measured in VA; it is bound to the rated voltage and currents by the relationships:

single phase transformers:
three-phase transformer:

In the following pages we specifically deal with the transformers having rated frequency equal to the industrial one (50 or 60 Hz) e sand they are widely used in electric equipments and in industrial and civil installations: they are often called power transformers; they have rated powers that can vary in a very wide range, from few VA to several hundreds of MVA.

Tests on the transformers

To determine the characteristics of a transformer it is necessary to carry out two tests:

	no-load test
	short circuit test.

The no-load test has the purpose of determining the no-load current (I₀), the power P₀ and the power factor cosj. 
The power P₀ represents the no-load losses of the transformer, which are the result of the addition of hysteresis losses and parasitic currents in the core, the thermal effect being negligible. This test can be performed by indifferently supplying the primary or secondary winding of the transformer, but by keeping the not used winding open. This choice is as function of the available supply voltage.
For the voltage regulation it is a good idea to use an induction voltage variator. If in the laboratory you are not sure about the right frequency value and about the sinusoidal aspect of the available voltage, it would have been necessary to connect the frequency meter and the voltmeter V too.

The short circuit test is performed by short circuiting one of the two windings, by supplying the other one with a voltage adjustable from zero, until reaching the value of the rated current of the winding itself. The voltage required at this purpose can be of the order from 4 to 10% of the winding Vn on which we perform the power supply; such a voltage is defined short circuit voltage of the transformer. In this test, the whole absorbed power corresponds to the only copper losses of the two windings, since, the low applied voltage given (in the short circuit test of the transformer), the magnetizing current, the flux in the core and the consequent losses are negligible. In these conditions we determine the equivalent resistance of the transformer. 
In turn we will therefore be able to determine the variations of the secondary voltage that take place from no-load to load condition of the transformer itself. Even in this test it is indifferent to supply the primary or secondary winding. In practice it is necessary to consider that it is suitable that the involved currents reach the tayed value of full load both in the side of the supply winding and in the other short circuited one. The first value will be necessary for the instrument choice, while the second one for the choice of the cable section to be used on the short circuit connections.