Properties of Ideal Transformer & Phasor Diagram
An ideal transformer is a theoretical concept used to simplify transformer analysis. It assumes perfect energy transfer with zero losses — making it the foundation for understanding real transformer behaviour. In this article, we explore the key properties of an ideal transformer, its no-load phasor diagram, and how these concepts apply to practical transformer design.
What is an Ideal Transformer?
An ideal transformer is an imaginary transformer that transfers electrical energy from primary to secondary winding with 100% efficiency. It has no copper losses, no iron losses, and no leakage flux. While no real transformer achieves these conditions, the ideal transformer model helps engineers understand voltage transformation, current transformation, and impedance transfer without the complexity of real-world losses.
Properties of an Ideal Transformer
- Zero Winding Resistance: Primary and secondary windings have negligible resistance (R₁ = R₂ = 0). No copper loss occurs.
- Infinite Core Permeability: The core has infinite permeability (μ → ∞), so negligible magnetomotive force (MMF) is required to establish flux.
- Zero Leakage Flux: All magnetic flux is confined to the core and links both windings completely. Leakage inductance is zero.
- No Core Losses: There are no hysteresis or eddy current losses in the core material.
- 100% Efficiency: Since there are no losses of any kind, input power equals output power exactly.
Key Assumptions & Their Implications
Phasor Diagram of Ideal Transformer at No Load
The phasor diagram shows the phase relationship between voltages, currents, and flux in an ideal transformer operating without any load connected to the secondary.
No-Load Phasor Diagram of Ideal Transformer
The phasor quantities in the diagram are:
Phasor Diagram Explanation
Since the ideal transformer has zero winding impedance, the voltage induced in the primary winding E₁ equals the applied voltage V₁ in magnitude. However, by Lenz's Law, E₁ is equal and opposite to V₁ (180° phase difference).
E₁/E₂ = N₁/N₂ (Turns Ratio)
The primary current I₁ drawn from the supply at no load is purely magnetizing current — it produces the alternating mutual flux Ø in the core. Key phase relationships:
- I₁ and Ø are in phase — current produces the flux directly
- I₁ lags V₁ by 90° — purely inductive (no resistance)
- E₁ and E₂ are in phase — both induced by the same mutual flux Ø
- V₂ = E₂ — no impedance drop in secondary winding
- I₂ = 0 — no load connected to secondary
The 90° lag between V₁ and I₁ means the ideal transformer at no load draws only reactive power (VAR) and consumes zero real power (watts) — consistent with its lossless nature.
Ideal vs Practical Transformer
Why Study Ideal Transformers?
The ideal transformer model serves several important purposes in electrical engineering:
- Simplifies circuit analysis — allows focus on voltage/current transformation without loss calculations
- Foundation for equivalent circuits — practical transformer models add losses to the ideal model
- Impedance matching — ideal transformer ratio directly gives impedance transfer ratio (Z' = Z × (N₁/N₂)²)
- Power system studies — per-unit system assumes ideal transformation between voltage levels
- Design benchmarking — practical designs are compared against ideal performance
Frequently Asked Questions
1. What is an ideal transformer?
An ideal transformer is a theoretical transformer with zero winding resistance, infinite core permeability, zero leakage flux, and no losses — resulting in 100% efficiency and perfect voltage transformation according to the turns ratio.
2. Why does primary current lag supply voltage by 90° in an ideal transformer at no load?
Because the ideal transformer has zero resistance, the primary winding is purely inductive. In a pure inductor, current always lags voltage by 90°. The current drawn is only magnetizing current needed to establish flux in the core.
3. What is the efficiency of an ideal transformer?
The efficiency of an ideal transformer is exactly 100%. Since there are no copper losses (R=0), no core losses (no hysteresis or eddy currents), and no leakage flux, all input power is transferred to the output.
4. Does an ideal transformer exist in practice?
No, an ideal transformer does not exist in reality. Every practical transformer has finite winding resistance, finite core permeability, some leakage flux, and core losses. However, modern power transformers achieve 95–99% efficiency, approaching ideal behaviour.
5. What is the relationship between E₁ and V₁ in an ideal transformer?
In an ideal transformer, E₁ equals V₁ in magnitude but is opposite in direction (180° phase shift). This is because Lenz's Law states that the induced EMF opposes the cause (applied voltage) that produces it. Mathematically: E₁ = -V₁.