What is an ideal transformer, and what assumptions make a transformer ideal?

In one line

An ideal transformer is an imaginary transformer with no losses, no leakage flux and zero magnetising current, so output power equals input power exactly.

Explained simply

Just as physics problems sometimes assume "no friction" to understand the main idea, the ideal transformer removes every imperfection so you can see how voltage and current transform. Real transformers are very close to ideal (often above 95% efficient), so this model is a good first approximation.

Technically, an ideal transformer has (1) zero winding resistance, so no copper loss and no resistive drop; (2) no leakage flux, so all flux links both windings; (3) no core losses (hysteresis and eddy current); (4) infinite core permeability, so negligible current is needed to magnetise the core.

How it works

1. On no-load, the primary draws only the magnetising current \( I_\mu \), which lags \( V_1 \) by 90° and is negligibly small.
2. Flux \( \phi \) is in phase with \( I_\mu \), so it also lags \( V_1 \) by 90°.
3. \( E_1 \) and \( E_2 \) lag \( \phi \) by 90°, so \( E_1 \) is 180° opposite to \( V_1 \) and equal in magnitude.
4. On load, \( V_2 = E_2 \) exactly; \( I_1/I_2 = N_2/N_1 \); efficiency is 100%.

Phasor diagram at no load: \( V_1 \) up, \( I_\mu \) and \( \phi \) horizontal (90° behind \( V_1 \)), \( E_1 \) and \( E_2 \) pointing down.

Key formula

\( \dfrac{V_2}{V_1} = \dfrac{N_2}{N_1} = \dfrac{I_1}{I_2}, \qquad V_1I_1 = V_2I_2 \)

\( V_1, V_2 \) = primary and secondary voltages (V), \( I_1, I_2 \) = currents (A), \( N_1, N_2 \) = turns.

Quick example

Circuit designers often treat a small signal transformer (for example an audio matching transformer) as ideal when estimating voltage and impedance ratios, because its losses are small compared with the quantities of interest.

Common mistakes

• Saying the ideal transformer draws zero current at no load and therefore has no flux; it needs (an infinitesimal) magnetising current, and flux is still present.
• Drawing \( E_1 \) in phase with \( V_1 \); it is in opposition.
• Listing 'no voltage change' as an ideal assumption; voltage does change in the turns ratio.

How MU asks it

MU states numericals are not expected in this module, so questions are theory. Typical: "What is an ideal transformer? State its properties and draw its phasor diagram at no load" (5 marks), or "Differentiate between ideal and practical transformer". For full marks list all four assumptions, draw the no-load phasor diagram with \( V_1, I_\mu, \phi, E_1, E_2 \), and write \( V_1I_1 = V_2I_2 \).