Ideal Transformer

The ideal transformer has no losses. There is no magnetic leakage flux, ohmic resistance in its windings and no iron loss in the core.

EMF Equation of Transformer

N₁ – number of turns in primary.

N₂ – number of turns in secondary.

Φ_m – maximum flux in weber (Wb).

T – time period. Time is taken for 1 cycle.

The flux formed is a sinusoidal wave. It rises to a maximum value Φ_m and decreases to negative maximum Φ_m. So, flux reaches a maximum in one-quarter of a cycle. The time taken is equal to T/4.

Average rate of change of flux = Φ_m/(T/4) = 4fΦ_m

Where f = frequency

T = 1/f

Induced emf per turn = rate of change of flux per turn

Form factor = rms value / average value

Rms value = 1.11  (4fΦ_m) = 4.44 fΦ_m [form factor of sine wave is 1.11]

RMS value of emf induced in winding = RMS value of emf per turn  x  no of turns

Primary Winding

Rms value of induced emf = E₁ = 4.44 fΦm * N₁

Secondary winding:

Rms value of induced emf = E₂ = 4.44 fΦm * N₂

This is the emf equation of the transformer.

For an ideal transformer at no load condition,

E₁ = supply voltage on the primary winding.

E₂ = terminal voltage (theoretical or calculated) on the secondary winding.

Voltage Transformation Ratio

K is called the voltage transformation ratio, which is a constant.

Case1: if N_{2 >} N_1, K>1 it is called a step-up transformer.

Case 2: if N₂< N₁, K<1 it is called a step-down transformer.