Theory and Principles

Harold Moore

Transformers are devices that transfer energy from one circuit to another by means of a common magnetic field. In all cases except autotransformers, there is no direct electrical connection from one circuit to the other.

When an alternating current flows in a conductor, a magnetic field exists around the conductor as illustrated in Fig. 3.1. If another conductor is placed in the field created by the first conductor as shown in Fig. 3.2, such that the flux lines link the second conductor, then a voltage is induced into the second conductor. The use of a magnetic field from one coil to induce a voltage into a second coil is the principle on which transformer theory and application is based.






Air Core Transformer

Some small transformers for low power applications are constructed with air between the two coils. Such transformers are inefficient because the percentage of the flux from the first coil that links the second coil is small. The voltage induced in the second coil is determined as follows.

E = N d0/dt]10]8

where N = number of turns in the coil

d0/dt = time rate of change of flux linking the coil

Since the amount of flux 0 linking the second coil is a small percentage of the flux from coil 1, the

voltage induced into the second coil is small. The number of turns can be increased to increase the voltage

output, but this will increase costs. The need then is to increase the amount of flux from the first coil that links the second coil. Iron or Steel Core Transformer The ability of iron or steel to carry magnetic flux is much greater than air. This ability to carry flux is called permeability. Modern electrical steels have permeabilities on the order of 1500 compared to 1.0  for air. This means that the ability of a steel core to carry magnetic flux is 1500 times that of air. Steel cores were used in power transformers when alternating current circuits for the distribution of electrical energy were first introduced. When two coils are applied on a steel core as illustrated in Fig. 3.3, almost 100% of the flux from coil 1 circulates in the iron core so that the voltage induced into coil 2 is equal to the coil 1 voltage if the number of turns in the two coils are equal.

The equation for the flux in the steel core is as follows:

        


where
0 = core flux in lines
N = number of turns in the coil
u = permeability
I = maximum current in amperes
d = mean length of the core
Since the permeability of the steel is very high compared to air, all of the flux can be considered as
flowing in the steel and is essentially of equal magnitude in all parts of the core. The equation for the
flux in the core can be written as follows: