From Electric Machinery and Transformers, Third Edition

4.4 A Nonideal Transformer

In the previous section we placed quite a few restrictions to obtain useful relations for an idealized transformer. In this section, our aim is to lift those restrictions in order to develop an equivalent circuit for a nonideal transformer.

Winding Resistances

However small it may be, each winding has some resistance. Nonetheless, we can replace a nonideal transformer with an idealized transformer by including a lumped resistance equal to the winding resistance of series with each winding. As shown in Figure 4.6, R 1 and R 2 are the winding resistances of the primary and the secondary, respectively. The inclusion of the winding resistances dictates that (a) the power input must be greater than the power output, (b) the terminal voltage is not equal to the induced emf, and (c) the efficiency (the ratio of power output to power input) of a nonideal transformer is less than 100%.

Figure 4.6: An ideal transformer with winding resistances modelled as lumped resistances.

Leakage Fluxes

Not all of the flux created by a winding confines itself to the magnetic core on which the winding is wound. Part of the flux, known as the leakage flux, does complete its path through air. Therefore, when both windings in a transformer carry currents, each creates its own leakage flux, as illustrated in Figure 4.7. The primary leakage flux set up by the primary does not link the secondary. Likewise, the secondary leakage flux restricts itself to the...

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Toroidal transformers typically consist of copper wire wrapped around a cylindrical core. This design prevents the magnetic flux that occurs within the coil from leaking.
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