What is Ideal Transformer ?
An ideal transformer is a transformer with the following assumptions:
- Permeability of transformer is infinite.
- Iron loss in the transformer core are zero.
- Resistance of transformer winding is zero.
- No magnetic leakage flux, so coefficient of coupling is 1.
- Magnetization curve of transformer is linear.
Operation of Ideal transformer under No-Load
1-Phase transformer will have two coils, the primary and the secondary. The primary winding is supplied from an AC voltage source, while secondary winding terminals are connected to the load. By electrical load, it is meant the output current and thus no-load means that the output current is zero, i.e., the secondary terminals are open circuited.
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Schematic diagram of an ideal, single-phase transformer operation under no-load |
The output (secondary) current of a 1-Ⲫ transformer is I2 = V2 / ZL
Where, V2 = Secondary terminal voltage
ZL = Load impedance connected across secondary terminals
Thus, at no-load when I2 = 0, it means that ZL → ∞
i.e., the transformer secondary terminal are open circuited.
When the primary winding of a transformer is connected to an AC voltage source, and the secondary winding terminal are kept open circuited, the transformer is said to be operating at no-load.
Such an ideal transformer under no-load is schematically shown in above figure.
For a sinusoidal input, current in the primary winding is: i1 = Im . Sin(ωt)
Flux is also sinusoidal , Ⲫ = Ⲫm . Sin(ωt)
Self-induced EMF in the primary winding: e1 = Em1 . Sin(ωt - 90°)
Thus, the induced EMF E1 in the primary winding lags behind the mutual flux Ⲫ by 90° in phase.
According to Lenz's law, this induced EMF must oppose the supply voltage V1 . For an ideal transformer, since the winding impedance is neglected, this self-induced EMF in the primary winding will be exactly equal and opposite to the supply voltage, i.e., V1 = -E1 , which means they are exactly opposite in phase, i.e., at 180° with respect to each other.
Note that the same flux Ⲫ links with the secondary coil also and induces a mutually induced EMF in the secondary winding. Value of this secondary EMF is: e2 = Em2 . Sin(ωt - 90°)
Thus, E2 also lags behind the flux Ⲫ by 90° and the two EMFs E1 and E2 are in the same phase. with the secondary terminal open circuited, V2 = E2 .
Note that the two EMFs E1 and E2 are related by the turns ratio:
E1 / E2 = N1 / N2 = a
Diagrammatically, some of these quantities are represented in below figure.
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Signals in a 1-phase transformer |
Phasor diagram for the ideal transformer under no load involving the quantities describe above is shown in below figure:-
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Phasor diagram of ideal transformer operation under no-load |
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