#### Transformers

A transformer is a simple device for changing the voltage of an AC signal. A transformer has two coils, each with a different number of loops, linked by a ferromagnetic core so the magnetic flux from one passes through the other. When the flux generated by one coil changes (as it does continually if the coil is connected to an AC power source), the flux passing through the other will change, inducing a voltage in the second coil. With AC power, the voltage induced in the second coil will also be AC.

The coil that provides the flux (i.e., the coil connected to the AC power source) is known as the primary coil, while the coil in which voltage is induced is known as the secondary coil.

Both coils are exposed to the same changing flux, so:
 -DF Dt
=
 DV1 N1
=
 DV2 N2

The relationship between the primary and secondary voltages is:
 DV1 DV2
=
 N1 N2

Energy (or, equivalently, power) has to be conserved, so:

DV1 I1 = DV2 I2, or:
 I2 I1
=
 N1 N2

A step-down transformer has more turns in the primary than the secondary. It takes a high primary voltage and converts it to a low secondary voltage. The current in the secondary will be higher than that in the primary to compensate. In a step-up transformer the secondary has more turns and, therefore, higher voltage and lower current than the primary.

The ferromagnetic core of a transformer is usually made up of thin laminated slices, electrically insulated from one another, rather than being one solid piece. Why is this?

1. This maximizes surface area, decreasing resistance for the current passing through the core from the primary coil to the secondary coil
2. Losses due to eddy currents are minimized
3. It's easier to line up the ferromagnetic domains in two dimensions than three dimensions
4. All of the above

Transformers are designed to minimize energy losses, but they will dissipate some energy, in the form of:

1. flux leakage - not all the magnetic flux from the primary passes through the secondary
2. heating losses in the coils of the transformer
3. eddy currents

In the ferromagnetic core of a transformer, electrons would swirl in cross-sectional planes. This current would heat up the transformer, wasting power as heat. To minimize power losses due to eddy currents the iron core is made up of thin laminated slices. Current is then confined within each laminated piece, significantly reducing the swirling tendency as well as the losses by heating.