Module 3.15 Transformers

Knowledge levels

Sub-module	A	B1 / B2 / B2L	B3
3.15 Transformers	—	2	1

Content: construction and operation; losses and how they are reduced; action on load and no load; power transfer, efficiency, polarity marking; line and phase voltages and currents; three-phase power; primary/secondary current, voltage, turns ratio, power and efficiency; auto-transformers.

How a transformer works

• Two (or more) windings on a common laminated iron core. AC in the primary produces an alternating flux in the core, which induces an EMF in the secondary by mutual induction.
• A transformer works only with changing current; DC produces no continuous output (and would overheat the primary, whose only opposition to DC is its low resistance).
• There is no electrical connection between primary and secondary (except in an auto-transformer) - so it also gives isolation.

The transformer equations (ideal transformer)

Vₚ / Vₛ = Nₚ / Nₛ = Iₛ / Iₚ

• Step-up: more secondary turns, higher secondary voltage, lower secondary current.
• Step-down: fewer secondary turns, lower voltage, higher current.
• Ideal transformer: power in = power out (Vₚ Iₚ = Vₛ Iₛ). The frequency is unchanged.

Worked example - step-down

A transformer has 1 150 primary turns and 260 secondary turns; primary 115 V, 400 Hz. The secondary supplies 5 A.

• Vₛ = 115 × 260 / 1 150 = 26 V
• Iₚ = 5 × 260 / 1 150 = 1.13 A (ignoring losses)
• Output frequency: 400 Hz

Trap answers: inverting the turns ratio (508 V) or multiplying current by the voltage ratio the wrong way (22 A).

Worked example - efficiency

Input 1 000 VA at unity PF, output 960 W.

• η = 960 / 1 000 = 96 %; losses = 40 W.