Transformer Fundamentals

The simple transformer of Fig. 2 has two windings. The left-hand winding is assumed to be connected to a voltage source and is called the primary winding. The right-hand winding is connected to a load and is called the secondary. The transformer merely delivers to the load a voltage similar to that impressed across its primary, except that it may be smaller or greater in amplitude.

Fig. 2. Simple transformer.

In order for a transformer to perform this function, the voltage across it must vary with respect to time. A d-c voltage such as that of a storage battery produces no voltage in the secondary winding or power in the load. If both varying and d-c voltages are impressed across the primary, only the varying part is delivered to the load. This comes about because the voltage e in the secondary is induced in that winding by the core flux Φ according to the law

[1]

This law may be stated in words as follows: The voltage induced in a coil is proportional to the number of turns and to the time rate of change of magnetic flux in the coil. This rate of change of flux may be large or small. For a given voltage, if the rate of change of flux is small, many turns must be used. Conversely, if a small number of turns is used, a large rate of change of flux is necessary to produce a given voltage. The rate of change of flux can be made large in two ways, by increasing the maximum value of flux and by decreasing the period of time over which the flux change takes place. At low frequencies, the flux changes over a relatively large interval of time, and therefore a large number of turns is required for a given voltage, even though moderately large fluxes are used. As the frequency increases, the time interval between voltage changes is decreased, and for a given flux fewer turns are needed to produce a given voltage. And so it is that low-frequency transformers are characterized by the use of a large number of turns, whereas high-frequency transformers have but few turns.

If the flux Φ did not vary with time, the induced voltage would be zero. Equation 1 is thus the fundamental transformer equation. The voltage variation with time may be of any kind: sinusoidal, exponential, sawtooth, or impulse. The essential condition for inducing a voltage in the secondary is that there be a flux variation. Only that part of the flux which links both coils induces a secondary voltage.

In equation 1, if Φ denotes maxwells of flux and t time in seconds, e denotes volts induced. If all the flux links both windings, equation 1 shows that equal volts per turn are induced in the primary and secondary, or

[2]

where

e₁ = primary voltage
e₂ = secondary voltage
N₁ = primary turns
N₂ = secondary turns.