#### TRANSFORMER OPERATION

A *transformer *is an dectromagnetic device having two or more mutually coupled windings (share a common magnetic circuit). Figure 4 shows a two-winding, *ideal *transformer; the transformer is ideal in the sense that its core is lossless and is infinitely permeable, it has no leakage fluxes, and the windings have no losses.

Figure 4

In Figure 4, the basic components are the core, the *primary winding, *N1, and the *secondary winding, N2. *If *Φ* is ,the mutual (or core) flux threading each turn of N1 and *N2, *then according to *Faraday´s law *of electromagnetic induction, emfs e1 and e2 are induced in N1 and *N2, *given by

* * (Formula 9)

The direction of *e *is such as to produce a current that gives rise to a flux which opposes the flux change *dΦ *

* (Lenz´s law). *From (9),

*e1/e2 *= N1/ *N2**, *or, in terms of rms values,

*(Formula 10)*

where *a *is the *turns ratio.*

The transformer being ideal,** ***e1 *= *v1 *and *e2 *= *V2** *in Fig. 4; hence the flux and voltage are related by

* *(Formula 11)

If the flux varies sinusoidally, *Φ* = *Φm *sin *ωt, *then the corresponding induced voltage, *e, *in an *N-turn *winding is given by

*e *= *ω**N** Φ**m*cos*ω**t *(13.12)

and the rms value of this induced voltage is

* *(Formula.13)

which is known as the *em! equation. *In *(13), *** j ****= ***ω*/2л is the flux frequency in Hz.