# Ideal transformer: Definition, Working, Phasor Diagram

A transformer is considered to be ideal if it has no losses of any kind. It is a hypothetical transformer without core loss, ohmic resistance, or flux leakage. This crucial feature is present in the optimal transformer.

## Definition of Ideal Transformer

Certain idealizing assumptions are made for better understanding and a very easier explanation of a practical transformer. A Transformer having these ideal properties is hypothetical and referred to as the ideal transformer. Ideal transformers possess certain features of a real transformer and some idealizing assumptions are made which will be described below:

1. No winding resistance:The primary as well as secondary have zero resistance.It means that there is no ohmic power loss and no resistive voltage drop in an ideal transformer.
2. No magnetic leakage: There is no leakage flux and all the flux set up is confined to the core and links both primary as well as secondary winding.
3. No iron loss: Hysteresis losses and eddy current losses in transformer is Zero.
4. Zero magnetizing currents: Since the permeability of the core is infinite and has zero reluctance. so that zero magnetizing currents is required for establishing the requisite amount of flux in the core.

## Behavior of ideal transformer

The ideal transformer consists of two pure inductive coils wound on a loss-free core. In an ideal transformer, the voltage V1 is applied across the primary winding of the transformer. The secondary winding of an ideal transformer is kept open. Magnetizing current(Im) flows through the primary winding of the transformer. The magnetizing current produces the flux Φm in the core of the transformer. N1 and N2 are the number of turns in primary and secondary winding.

Since the permeability of core is infinite the flux of the core link with both winding of transformer. The flux link with the primary winding induces the emf E1 due to self induction.And there would be the other emf E2 induces in the secondary winding due to mutual induction.

In an ideal transformer, the losses are negligible, so the volt-ampere input to the primary and volt-ampere output from the secondary can be approximately equated i.e

output VA= Input VA

i.e primary and secondary currents are inversely proportional to their respective turns.

## Phasor Diagram of ideal transformer

The phasor diagram of an ideal transformer is shown above.Magnetizing current (Im) induces in the transformer lags the input voltage V1 by 90º because the coil of the primary winding is purely inductive.

Where E1 and E2 are the induced emf in primary and secondary winding.And the direction of induced emf is inversely proportional to applied voltage as seen form the phasor diagram.

## what is difference between an ideal and practical transformer?

An ideal transformer is an imaginary transformer that has no winding resistance, no magnetic leakage, no iron loss, and zero reluctance while a particular transformer is an actual transformer that operates at a particular frequency and has winding resistance, magnetic leakage, iron loss, copper loss, and magnetic reluctance.

The following are some benefits of the ideal transformer.

• Losses like hysteresis, eddy, and copper do not exist.
• The twists of the coil fully determine the voltage and current ratios.
• There are no leaks of flux.
• It is independent of frequency
• absolute linearity
• No stray capacitance or inductance

## References

### 1 thought on “Ideal transformer: Definition, Working, Phasor Diagram”

1. MEP Engineer