4.3 - Transformer

Structure and Working Principle

A simple transformer has a primary coil and secondary coil linked by a laminated soft iron core. It changes an input voltage to an output voltage of a different value.
$V_{P}$ and $V_{S}$ are the primary/input voltage and secondary/output voltage; $N_{P}$ and $N_{S}$ are the respective numbers of turns.

An alternating current supply produces alternating current in the primary coil.
The current creates a magnetic field that changes in magnitude and direction.
The soft iron core links magnetic flux from the primary coil to the secondary coil.
The changing magnetic field induces an alternating voltage across the secondary coil.

\frac{V _{S}}{V _{P}} = \frac{N _{S}}{N _{P}}

Type	Turns and voltage
Step-up transformer	$N_{S} > N_{P}$ and $V_{S} > V_{P}$ .
Step-down transformer	$N_{S} < N_{P}$ and $V_{S} < V_{P}$ .

Electrical energy transfers from the primary circuit to the secondary circuit, which supplies the connected equipment.
A real transformer loses energy, so its output power is smaller than input power.
Transformer efficiency, $η$ , is:

η = \frac{Output power}{Input power} \times 100%

Real transformers can have efficiencies as high as 99%.
An ideal transformer has no energy loss: $η = 100%$ , and input power equals output power. With primary current $I_{P}$ and secondary current $I_{S}$ :

V_{P} I_{P} = V_{S} I_{S}

Cause and effect	Method of reducing loss
Coil resistance: current heats the long coil wires; heat escapes to the surroundings.	Use thicker copper wire to reduce resistance.
Eddy currents: the changing field induces currents in the iron core, heating it.	Use a laminated iron core made of thin sheets joined with insulating glue.
Hysteresis: repeated magnetisation and demagnetisation do not recover all the supplied energy; the difference heats the core.	Use soft iron, which needs less energy for magnetisation.
Magnetic flux leakage: some flux from the primary coil does not link to the secondary coil.	Wind the secondary coil over the primary coil so the primary flux passes through it.

A coil supplied with high-frequency alternating current creates a magnetic field changing at high frequency.
This field induces eddy currents in the base of the pan, heating the base. Eddy currents provide useful heating here, although they cause energy loss in a transformer.

Step-down transformers	Step-up transformers
Mobile phone and notebook computer chargers, photocopy machines and welding machines.	Microwave ovens, defibrillators and X-ray machines.

An ideal transformer receives $240 V$ and supplies an electronic device with $27 W$ at $18 V$ . Its secondary coil has 60 turns.
Primary turns:

N_{P} = \frac{V _{P} N _{S}}{V _{S}} = \frac{240 \times 60}{18} = 800

I_{S} = \frac{P _{output}}{V _{S}} = \frac{27}{18} = 1.5 A

I_{P} = \frac{V _{S} I _{S}}{V _{P}} = \frac{18 \times 1.5}{240} = 0.1125 A

At the transmission stage, step-up transformers raise the cable voltage and reduce the cable current. This reduces electrical energy loss from the cable.
At the distribution stage, step-down transformers lower the voltage progressively to values suitable for industrial and residential consumers.
The illustrated system shows generation at 20 kV, transmission at 275 kV and subsequent levels of 132 kV, 33 kV and 11 kV. Heavy industry receives 33 kV, light industry 11 kV and residential homes 230 V.