Ideal transformer.

Ideal transformer:

The assumptions to characterize the ideal transformer are:

• ·         The windings of the transformer have no resistance. Thus, there is no copper loss in the winding, and hence no voltage drop.
• ·         Flux is confined within the magnetic core. Therefore, it is the same flux that links the input and output windings.
• ·         Permeability of the core is infinitely high which implies that net mmf (amp-turns) must be zero (otherwise there would be infinite flux) hence IP NP - IS NS = 0.
• ·         The transformer core does not suffer magnetic hysteresis or eddy currents, which cause inductive loss.

(Ideal transformer with a source and a load. NP and NS are the number of turns in the primary and secondary windings respectively.)

If the secondary winding of an ideal transformer has no load, no current flows in the primary winding.

The circuit diagram (right) shows the conventions used for an ideal, i.e. lossless and perfectly-coupled transformer having primary and secondary windings with NP and NS turns, respectively.

The ideal transformer induces secondary voltage VS as a proportion of the primary voltage VP and respective winding turns as given by the equation,

Where,

(a) is the winding turns ratio, the value of these ratios being respectively higher and lower than unity for step-down and step-up transformers,

(VP) designates source impressed voltage,

(VS) designates output voltage, and,

According to this formalism, when the number of turns in the primary coil is greater than the number of turns in the secondary coil, the secondary voltage is smaller than the primary voltage. On the other hand, when the number of turns in the primary coil is less than the number of turns in the secondary, the secondary voltage is greater than the primary voltage.

Any load impedance ZL connected to the ideal transformer's secondary winding allows energy to flow without loss from primary to secondary circuits. The resulting input and output apparent power are equal as given by the equation,

Combining the two equations yields the following ideal transformer identity.

This formula is a reasonable approximation for the typical commercial transformer, with voltage ratio and winding turns ratio both being inversely proportional to the corresponding current ratio.

The load impedance ZL and secondary voltage VS determine the secondary current IS as follows

The apparent impedance ZL' of this secondary circuit load referred to the primary winding circuit is governed by a squared turns ratio multiplication factor relationship derived as follows

For an ideal transformer, the power supplied to the primary and the power dissipated by the load are equal. If ZL = RL where RL is a pure resistance then the power is given by:

The primary current is given by the following equation: