Ideal Transformer: properties and phasor diagram

An ideal transformer is an imaginary transformer. The proprieties of the practical transformers are different than the ideal transformers. The operation of the practical transformer is close to the ideal transformer.

Properties of an ideal transformers

  • Primary and secondary winding resistance are negligible.
  • The core has infinite permeability (μ). Hence, very small amount of MMF required to establish the flux in the core.
  • Leakage flux and leakage inductance are zero. The entire flux linked with the core and windings.
  • The efficiency of the ideal transformer is 100%. Because we considered that there are no losses produced due to resistance, hysteresis and eddy current.

Make note that above properties assumed for the ideal transformers only. It is not possible to achieve these properties in the practical transformer.

An ideal iron core transformer consists of two coils wound on the common magnetic core. These coils wound in the same direction. The winding which connected with the supply voltage V1, known as the primary winding. The winding which connected with the load, known as the secondary winding.

ideal transformer construction
ideal transformer construction

Phasor diagram

As we have assumed in the properties, the primary and secondary winding has zero impedance. Therefore, the applied voltage V1 is same as the voltage induced in the primary winding E1. Similarly, the secondary voltage V2 is same as the voltage induced in the secondary winding E2. The primary current I1 is sufficient to produce mutual flux ф1. This flux is enough to produce MMF I1T1 to overcome the demagnetizing effect of the secondary MMF I2T2 as a result of load.

According to the Lenz’s law, E1 is equal and opposite to V1. E1 and E2 induced by the same mutual flux. Therefore, E2 is in the same direction of E1 and opposite to the V1.

The magnetizing current Iμ lags V1 by 90 degree. It produces the magnetizing flux фm in phase with Iμ. E1 and E2 produced by the фm and lag фm by 90 degree. V2 is equal in magnitude to E2 and is opposite to V1.

Below figure shows the phasor diagram of ideal transformers in no load condition.

ideal transformer Phasor diagram
ideal transformer Phasor diagram

For an ideal transformer,

a = transformation ratio (turns ratio)

equation ideal transformer
equation ideal transformer

According to the equation (2), the demagnetizing MMF of secondary are equal and opposite to the magnetizing MMF of primary for an ideal transformers.

According to the equation (3), the apparent power drawn from the primary supply is equal to the apparent power transferred to the secondary without any loss in the ideal transformers.

Input Power = Output Power

Therefore, the input kVA is equal to the output kVA for the ideal transformer. Thus, the efficiency of is 100%.

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