Ideal Transformer: Working, Characteristics & Phasor Diagrams Explained

An ideal transformer is a theoretical concept used to understand transformer behavior without the influence of losses. In such a transformer, the input power is equal to the output power, implying zero internal losses. This simplification is helpful for analysis and design purposes. Although an ideal transformer does not exist in practice, the concept is used to study transformer behavior under lossless conditions. Furthermore, it can be compared with a practical transformer, in which losses occur during real-time applications.

1. No Internal Losses: Both copper losses (in primary and secondary windings) and core (iron) losses such as hysteresis and eddy current losses are considered to be zero.
2. complete Magnetic Coupling: All magnetic flux generated by the primary winding completely links to the secondary winding. There is no flux leakage occurred.
3. High Magnetic Permeability: The permeability of core materials assumed as infinity, so only a minimal current is needed to establish magnetic flux.
4. Zero Primary Winding Resistance: Since the primary winding resistance is negligible, there is no voltage drop across the primary winding. Hence
5. V₁=E₁, Where V_1​ is the applied voltage, and E₁​ is the induced EMF in the primary winding.
6. Zero Secondary Winding Resistance: No voltage drop occurs across the secondary winding, so the induced EMF in the secondary equals the output terminal voltage: E₂=V₂
7. 100% Efficiency: With no losses, the input power equals the output power, making the efficiency: (η=100%)
8. Zero Voltage Regulation: The output voltage remains constant regardless of the load, as there are no internal voltage drops.

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When an AC voltage V₁​ is applied to the primary winding and the secondary is open (no load), the load resistance R_L​ is essentially infinite. The only current drawn is a small magnetizing current I_m needed to establish magnetic flux in the core.

As R₁=0 I_m​ lags E₁by 90°.

Magnetic flux ϕ generated by I_m is in phase with I_m​ and sinusoidal.

This flux links both windings and induces causes a self induced EMF E₁ in the primary and mutual induced EMF E₂​ in the secondary.

Since the secondary is open, no current flows through it, and

E₁=−V₁(by Lenz’s Law)

E2​=V2​

The magnitudes of induced EMFs are proportional to the number of turns

E1∝N1

E2∝N2

So,

\[frac {E_2}{E_1} = \frac{N_2}{N_1} = K\]

Here, E₂ 180° out of phase with V₁ but E₁ and E₂ are in phase with each other.

The power drawn by the ideal transformer at no load is

P₀=V₁I_mcos⁡ϕ₀

Where

ϕ₀=90° the phase angle between V_1​ and I_m

Therefore

cos⁡ϕ₀=cos⁡90°=0

P₀=V₁I_m×0=0

This confirms that no real power is consumed at no-load .Because all power is reactive.

When a load is connected to the secondary winding, current I₂ begins to flow. The magnitude of I₂​ depends on the combined resistance of the load R_L​ and secondary winding R₂​ (which is considered negligible in ideal cases).

• The load current I₂ lags the output voltage V₂ by angle ϕ₂.
• According to Lenz’s Law, I₂ produces magnetic flux ϕ₂ opposing the original flux ϕ
• This reduces the net flux and thus the EMF E₁​, which is meant to oppose V₁​.

To restore the original magnetic flux, an additional current I′₂ flows in the primary, calculated as

\[ I’_2 = I_2 x \frac{N_2}{N_1} = KI_2\]

This current is called the load component of the primary current. The total primary current is the phasor sum of

I₁=I′₂+I_m

As load increases

• I₂ increases.
• The secondary MMF (N₂I₂​) increases.
• This further opposes the primary flux ϕ₁​, reducing E₁​.
• To balance this, I′₂​ increases in the primary winding.
• Thus, total primary current I₁ increases with load to maintain energy balance.