**What is an Ideal Transformer?**

A transformer with no core loss, an ohmic resistance & no leakage flux is called ideal transformer. The ideal transformer is free from all types of losses. The ideal transformer is also called imaginary transformer.

**The Ideal Transformer has following characteristics:**

1. In Ideal transformer, primary and secondary windings have zero ohmic resistance.

2. The Ideal transformer has zero leakage flux. All flux is utilized and linked with the primary and secondary circuit.

3. In Ideal transformer, core of the transformer having infinite permeability. so less magnetizing current required to magnetizing the core of the transformer and also required negligible mmf.

4. The Ideal transformer is free from all types of losses. So efficiency of ideal transformer is 100 percent.

5. The ideal transformer have no eddy current loss, no hysteresis loss, no ohmic resistance.

6. The Ideal transformer has no copper loss due negligible resistance in primary & secondary windings.

7. In Ideal transformer input power is equal to output power.

8. In Ideal transformer, there is no magnetic saturation means transformer core does not saturate. In ideal transformer magnetic flux increased with increasing primary current.

9. The Ideal Transformer has ideal turns ratio. The ration of number of turns in primary winding to number of turns in secondary winding matches with the voltage ratio.

10. In Ideal transformer, the transformer core requires zero excitation. so Primary induced mmf is equal to secondary induced mmf.

11. In Ideal transformer, coupling coefficient between two transformer windings coil are unity.

12. The Ideal transformer does not depend on frequency.

13. In Ideal Transformer, there is no stray capacitance and inductance.

14. In Ideal Transformer, the primary & secondary windings are considered purely inductive because the transformer windings do not have ohmic resistance.

15. In Ideal Transformer, the primary supply voltage & primary current are mutually perpendicular to each other.

**Working of Ideal Transformer:**

**Ideal Transformer on No Load:**

Consider the primary winding is connected to alternating supply voltage & secondary winding is open circuited. A transformer is ideal, so the primary winding coil is purely inductive.

As shown in the figure, when alternating supply voltage V

_{1 is applied to the primary winding coil of the ideal transformer, the primary winding coil draws small amounts of magnetizing current }I_{m to produce the magnetizing flux }Ï• in the transformer core. As per phasor diagram, magnetizing current I

_{m}lag behind the applied supply voltage V_{1 by 90 degrees. } As per figure, the magnetizing current I

_{m produce the magnetizing flux }Ï•_{m in core of the transformer and which is linked with primary winding coil & secondary winding coil. These linked flux }Ï•_{m induces emf in }E_{1 in the Primary winding coil & }E_{2 in the secondary winding coil. }_{}

_{ In an ideal transformer, emf }E

_{1 induced in the primary winding is equal to applied voltage }V

_{1. But as per lenz law, induced emf }E

_{1 in the primary winding coil is phase opposition with the applied voltage }V

_{1.}

_{}

_{ As per the phasor diagram, induced emf }E

_{1 in the primary winding and induced emf }E

_{2 in the secondary winding are lag behind the magnetic flux }Ï•

_{m by 90 degrees. But the magnitude of }E

_{1 and }E

_{2 depends upon the number of turns in the primary windings coil and the number of turns in the secondary windings coil. }

_{}

_{ As per the Phasor diagram, flux }Ï•

_{m is common in primary and secondary windings, so flux }Ï•

_{m is taken as the reference phasor. }

_{}

_{ As per Phasor diagram, emf }E

_{1 is in phase with the emf }E

_{2. Induced emf }E

_{1 in primary winding coil is equal to the applied voltage }V

_{1 but both are 180 degrees out of phase. The magnetizing current }I

_{m is in phase with magnetizing flux }Ï•

_{m.}

**Ideal Transformer at on Load:**

Consider the load Z

_{L is connected to the ideal transformer secondary winding. The ideal transformer is said to be loaded and secondary load current }I_{2}flow through the secondary winding and also from the load. When we applied alternating supply voltage V

_{1}to primary winding coil of ideal transformer. The primary winding of the transformer draws primary magnetizing current.I

_{1 and produces magnetic flux }Ï•1 in the primary winding which is produced due to the self-induction. This current also induces the main flux Ï• in the core of the ideal transformer. Due to flux Ï•1 in primary winding emf E

_{1}is induced in it. Also due to mutual induction flux Ï•_{2}is produced in the secondary winding and due to this flux emf E_{2}is induced in the secondary winding. In secondary winding of ideal transformer inductive load of impedance Z

_{L }is connected. The secondary induced emf E

_{2 }produced a secondary current I_{2}which flow in the secondary winding and also from the load Z_{L}.Which is given by

I

_{2 = }E_{2/}Z_{L}_{}

_{From the phasor Diagram }

_{E2 = }V

_{2}

_{}

_{I2 = }V

_{2/}Z

_{L}

_{}

_{ In ideal transformer, secondary voltage }V

_{2}is equal to the secondary induced emf E

_{2}. In secondary side load is purely inductive so as per phasor diagram, secondary winding current I

_{2}will be lag behind the output voltage

_{E2 = }V

_{2}. The transformer is ideal so no load current I

_{0}is neglected.

The current I

_{2}flowing through the secondary winding and secondary winding have N_{2}number of turns which produces mmf N_{2}I_{2}and this mmf(N_{2}I_{2)}induces flux Ï•_{2}in secondary winding of the transformer. As per the phasor diagram, the secondary flux Ï•

_{2}is opposite direction to the main flux Ï•_{m}. As a result total flux Ï• = Ï•

_{m=}Ï•1 + Ï•_{2}in the core of the ideal transformer is changes from its original value. As per rules main flux in the core of the transformer should not be changes from its original value. To maintain a flux in the transformer core to its original value, the primary current I1 can develop primary mmf N1I1 which can counterbalance the demagnetizing effect of the secondary mmf N

_{2}I_{2}.N1I1=N2I2

The primary induced mmf is equal to the secondary induced mmf.

When the secondary current I

_{2}increases, the primary current I1 also increases in the same manner to keep the mutual flux Ï•_{m}constant. As per phasor diagram, secondary current I

_{2}lag behind the secondary voltage V_{2}by angle of Ï•_{2.}_{}

_{General formulas for Ideal transformer}

_{In ideal transformer, the output power is equal to the input power. }

_{The transformation ratio of transformer is given by }

From the above equation, the primary and secondary currents are inversely proportional to their respective turns.

_{}