# Fundamentals of Transformers and Applications

Introduction to Transformers

Two coils that have mutual inductance make up a transformer. The coil connected to the source of energy is called primary coil and the other is called secondary coil. It is useful in that the electrical energy can be transferred from one circuit to another without direct connection.

It can also change the voltage level from one level to another level depending on the windings ratio of the primary and secondary coils. It can only be used with AC voltage because no voltage is induced if there is no change in magnetic field.

The increase of the inductance of coils can be done by windings the coils on magnetic material like iron core.

Turns Ratio, Voltage and Current

In a varying magnetic field, the voltage induced in a coil is proportional to the number of turns in the coil. If the coils are wound in the same field, the induced voltages will be proportional to the number of turns in each coil.

Vs = Vp(Ns/Np)

where Vs = secondary voltage

Vp = primary voltage

Ns = number of turns on secondary

Np = number of turns on primary

If no current is taken from the secondary(open circuit), the current that flows in the primary is called magnetizing current of the transformer. Typically, the trans. is designed in such a way that the power consumed by it is only to overcome the losses in the iron core and in the resistance of the wire with which the primary is wound.

If the secondary is connected to the load, the current on the primary is given in the formula below assuming that the entire primary current is caused by the secondary load.

Ip = Is(Ns/Np)

where Ip = primary current

Is = secondary current

Ns = number of turns on secondary

Np = number of turns on primary

Impedance Matching

Many devices need a specific value of of load resistance for optimum operation. The impedance of an actual load that is to dissipate the power may differ from this value, so a transformer is used to change the actual load into an impedance of the desired value. This is called impedance matching.

Np/Ns = Square root(Zp/Zs) where

Np = number of turns on primary

Ns = number of turns on secondary

Zp = primary impedance required

Zs = impedance load connected to the secondary

Example : A transistor for audio amplifier requires a load of 200 ohms for optimum operation and is to be connected to a loudspeaker with an impedance of 4 ohms. The turn ratio, Np/Ns required will be Square root (200/4) = 7.1 i.e. the primary must have 7.1 times as many turns as the secondary.

Construction

Two common types of construction are SHELL type and CORE type. In the SHELL type both windings are placed on the inner leg, while in the CORE type the primary and secondary windings may be placed on separate legs. They are usually designed so that the magnetic path around the core is as short as possible.

The material used for the core is usually silicon steel, built up by laminations, insulated from each other by a layer of coating. The number of turns required is inversely proportional to the cross sectional area of the core.

Typically, the windings of small power transformers usually have 6-8 turns/volt on a core of 1 square inch cross section and have a magnetic path of 10-12 inches in length. A longer path or smaller cross section requires more turns/volt and vice versa.