Ideal Transformer

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 V1 is applied to the primary winding coil of the ideal transformer, the primary winding coil draws small amounts of magnetizing current Im to produce the magnetizing flux ϕ in the transformer core. 

      As per phasor diagram, magnetizing current Im lag behind the applied supply voltage V1 by 90 degrees. 

      As per figure, the magnetizing current Im produce the magnetizing flux ϕm in core of the transformer and which is linked with primary winding coil & secondary winding coil. These linked flux ϕm induces emf in E1 in the Primary winding coil & E2 in the secondary winding coil. 

      In an ideal transformer, emf E1 induced in the primary winding is equal to applied voltage V1. But as per lenz law, induced emf E1 in the primary winding coil is phase opposition with the applied voltage V1.

      As per the phasor diagram, induced emf E1 in the primary winding and induced emf E2 in the secondary winding are lag behind the magnetic flux ϕm by 90 degrees. But the magnitude of E1 and E2 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 ϕm is common in primary and secondary windings, so flux ϕm is taken as the reference phasor. 

      As per Phasor diagram, emf E1 is in phase with the emf E2. Induced emf E1 in primary winding coil is equal to the applied voltage V1 but both are 180 degrees out of phase. The magnetizing current Im is in phase with magnetizing flux ϕm. 

Ideal Transformer at on Load:
      Consider the load ZL is connected to the ideal transformer secondary winding. The ideal transformer is said to be loaded and secondary load current I2 flow through the secondary winding and also from the load. 


      When we applied alternating supply voltage V1 to primary winding coil of ideal transformer. The primary winding of the transformer draws primary magnetizing current. 
I1 and produces magnetic flux ϕ1 in the primary winding which is produced due to the self-induction. This current also induces the main flux ϕ in the core of the ideal transformer. 

      Due to flux ϕ1 in primary winding emf E1 is induced in it. Also due to mutual induction flux ϕ2 is produced in the secondary winding and due to this flux emf E2 is induced in the secondary winding. 

      In secondary winding of ideal transformer inductive load of impedance Zis connected. 

      The secondary induced emf Eproduced a secondary current I2 which flow in the secondary winding and also from the load ZL.

Which is given by 
I2 = E2/ZL

From the phasor Diagram 
E2 = V2

I2 = V2/ZL

      In ideal transformer, secondary voltage V2 is equal to the secondary induced emf E2. In secondary side load is purely inductive so as per phasor diagram, secondary winding current I2 will be lag behind the output voltage E2 V2. The transformer is ideal so no load current I0 is neglected.

      The current I2 flowing through the secondary winding and secondary winding have N2 number of turns which produces mmf N2I2 and this mmf(N2I2) induces flux ϕ2 in secondary winding of the transformer. 

      As per the phasor diagram, the secondary flux ϕ2 is opposite direction to the main flux ϕm.

      As a result total flux ϕ = ϕm=ϕ1 + ϕ2 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 N2I2

N1I1=N2I2

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

      For keeping the main flux constant in transformer core, primary winding must draw enough current to neutralize the demagnetizing effect of the secondary current. 

      When the secondary current I2 increases, the primary current I1 also increases in the same manner to keep the mutual flux ϕm constant. 

      As per phasor diagram, secondary current I2 lag behind the secondary voltage V2 by angle of ϕ2.

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. 




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