The Ideal Transformer
Voltage up, current down, power unchanged — and impedance transforming by the square, which is the property usually skipped.
Skip to the animationTwo coils sharing one magnetic circuit develop EMFs in proportion to their turns, so voltage scales by the turns ratio, current by its inverse, and impedance by the square — with no electrical connection between the two sides.
Where the ratios come from
Both windings link the same changing flux, so every turn develops the same EMF. Hence V₁/V₂ = N₁/N₂ — the turns ratio, and nothing more subtle.
A steady flux induces nothing, so the device works only on AC. This is why there is no DC transformer, and it is the reason the grid is AC in the first place.
An ideal transformer has no losses and no storage, so power in equals power out. Halving the voltage therefore doubles the current: I₁/I₂ = N₂/N₁, the inverse ratio.
Impedance transformation, the property usually skipped
Since Z = V/I and voltage and current scale oppositely, impedance transforms by the square of the turns ratio: Z′ = (N₁/N₂)²·Z. A 4 Ω load through a 1:2 step-down looks like 16 Ω.
This is why transformers appear in circuits needing no voltage change at all — matching a 4 Ω speaker to a valve amplifier expecting kilohms, or matching an antenna in RF. The voltage change is incidental to the purpose.
It also lets a whole secondary circuit be referred to the primary side, so the two windings can be analysed as one circuit — which is what makes the equivalent circuit of the next topic tractable.
What 'ideal' assumes away
| Assumption | What it becomes when removed |
|---|---|
| No winding resistance | Copper loss, and a series R |
| No leakage flux | Leakage reactance, in series |
| Infinite core permeability | Magnetising current, in a shunt branch |
| No core loss | Iron loss, as a shunt resistance |
A large transformer is 97–99% efficient, so the ideal model is unusually close to the truth — which is why it is worth learning on its own rather than only as a limiting case.
Why it is the machine to learn first
It is electromechanical energy conversion with the mechanics removed: Faraday's law twice, on one shared flux, with no rotation, slip, commutator or back-EMF to complicate matters.
And an induction motor is literally a transformer whose secondary is free to rotate — not a metaphor. Its equivalent circuit is a transformer's with one resistance made slip-dependent, so learning this model properly does most of the work for the induction topics.
The numbers you will be asked for
- Turns ratio
V₁/V₂ = N₁/N₂ = I₂/I₁
Voltage and current scale oppositely.
- EMF equation
E = 4.44·f·N·Φ_max
Which is why flux is set by voltage and frequency, not by load.
- Impedance transformation
Z′ = (N₁/N₂)² · Z
The ratio squared.
- Power
V₁I₁ = V₂I₂
Ideal — no losses, no storage.
Advantages and disadvantages
Advantages
- Changes voltage at over 99% efficiency with no moving parts.
- Provides galvanic isolation as a by-product.
- Transforms impedance, which matching networks depend on.
- Symmetrical — either winding may be the primary.
Disadvantages
- Works only on AC; a steady flux induces nothing.
- Needs a magnetic core, so it is heavy and bulky at low frequencies.
- Inrush current on switch-on can be many times rated.
- Real units deviate through resistance, leakage, magnetising current and core loss.
Watch it work
Check yourself
question 1 / 4
One question at a time. Pick an answer to see why it is right or wrong, then move on — there is no score to keep and nothing is saved.