What is an Ideal Transformer : Working and Phasor Diagram

Before going to discuss an ideal transformer, let’s discuss the transformer. A transformer is a fixed electrical device, used to transfer the electrical energy in between two circuits while maintaining stable frequency and also increasing/decreasing the current or voltage. The working principle of a transformer is “Faraday’s law of induction”. When the current in the main winding is changed, then the magnetic flux will be changed, so that an induced EMF can occur within the secondary coil. A practical transformer includes some losses like core losses & copper losses. The copper loss can be defined as, transformer windings which include resistance as well as reactance to cause some loss is called a copper loss. The core loss in the transformer occurs when the transformer is energized; the core loss does not change with load. These losses are caused by two factors like eddy & hysteresis. Because of these losses, the transformer’s output power is less than the input power.

What is an Ideal Transformer?

Definition: A transformer that doesn’t have any losses like copper and core is known as an ideal transformer. In this transformer, the output power is equivalent to the input power. The efficiency of this transformer is 100%, which means there is no loss of power within the transformer.

ideal-transformer
ideal-transformer

Working Principle of Ideal Transformer

An ideal transformer works on two principles like when an electric current generates a magnetic field and a changing magnetic field in a coil induces a voltage across the coil ends. When the current is changed within the primary coil, then the magnetic flux is developed. So changing magnetic field can induce a voltage within the secondary coil.

When the current flows through the primary coil then it creates a magnetic field. The two windings are wrapped in the region of a very high magnetic core like iron, so the magnetic flux supplies through the two windings. Once a load is connected to the secondary coil, then the voltage and current will be in the indicated direction.

Properties

The properties of an ideal transformer include the following.

  • The two windings of this transformer have small resistance.
  • Because of the resistance, eddy current and hysteresis there are no losses in the transformer.
  • The efficiency of this transformer is 100%
  • The total flux generated in the transformer has restricted the core & connects with the windings. Therefore, its flux & inductance leakage is zero.

The core has unlimited permeability so a negligible magnetomotive force is necessary to arrange the flux within the core.
An ideal transformer model is shown below. This transformer is ideal in three conditions when it has no leakage flux, no windings resistance and no iron loss within the core. The properties of practical as well as ideal transformers are not similar to each other.

Ideal Transformer Equations

The properties which we have discussed in the above are not applicable to the practical transformer. In an ideal type transformer, the o/p power is equal to the i/p power. Thus, there is no loss of power.

E2*I2*CosΦ = E1*I1*CosΦ otherwise E2*I2 = E1*I1

E2/E1 = I2/I1

Thus, the conversion ratio equation is shown below.

V2/V1= E2/E1 = N2/N1 = I1/I2 =K

The currents of primary & secondary are inversely proportional to their respective twists.

Phasor Diagram of Ideal Transformer

The phasor diagram of this transformer with no load is shown below. When the transformer is on the no-load condition, then the current within the secondary coil can be zero that is I2 = 0

In the above figure,

“V1’ is the main supply voltage

‘E1’ is induced e.m.f

‘I1’ is the main current

‘Ø’ is Mutual flux

V2’ is the secondary o/p voltage.

‘E2’ is the secondary induced e.m.f.

When the transformer windings have zero impedance, then the induced voltage within the main winding ‘E1’ is equivalent to the applied voltage ‘V1’. But Lenz’s law states that the main winding E1 is equivalent & reverse to the primary voltage ‘V1’. The main current that draws the supply can be enough to generate an alternating flux ‘Ø’ within the core. So this current is also known as magnetizing current as it magnetizes the core & arranges the flux within the core.

Therefore, both the main current and alternating flux are in the equal phase. The main current lags behind the voltage supply with 90 degrees. Since e.m.f induced in two windings are induced with the similar mutual flux ‘Ø’. Thus, both the windings are in a similar direction.

When the secondary winding of the transformer has zero impedance, then the induced e.m.f in winding & secondary o/p voltage will be the same in magnitude & direction.

Advantages

The advantages of the ideal transformer include the following.

  • There are no losses like hysteresis, eddy, and copper.
  • Voltage & current ratios are perfectly based on the twists of the coil.
  • There is no flux leakage
  • It doesn’t depend on the frequency
  • Perfect linearity
  • No stray inductance & capacitance

Thus, an ideal transformer is an imaginary transformer, not a practical transformer. This transformer is mainly used for the purpose of education. Here is a question for you, what are the applications of an ideal transformer?

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