Transformer Working Principle, Construction and EMF Equation

What is a transformer?

A transformer has two or more windings placed on a common magnetic core. The winding connected to the supply is the primary, and the winding connected to the load is the secondary. There is no electrical connection between the two windings in a two-winding transformer. Energy passes from one to the other only through the magnetic flux in the core.

Because it has no moving parts, a transformer is very efficient. Large power transformers commonly reach efficiencies above 99 percent at their rated load, which is why they can be used at every stage of a power system, from the generator to the distribution network.

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Transformer working principle

A transformer works on Faraday’s law of electromagnetic induction: a changing magnetic flux linking a coil induces an EMF in that coil. The operation happens in four steps:

1. An alternating voltage V1 is applied to the primary winding, and a small magnetising current flows in it.
2. This current sets up an alternating magnetic flux in the core. The core is made of a magnetic material, so almost all the flux stays in it.
3. The same alternating flux links the secondary winding and induces an EMF E2 in it. This is mutual induction.
4. The flux also links the primary itself and induces a back EMF E1, which opposes the applied voltage and limits the primary current.

When a load is connected to the secondary, a secondary current flows. Its magnetising effect opposes the core flux, so the primary draws extra current to restore the flux. In this way the power drawn by the load is passed from the primary to the secondary through the core.

EMF equation of a transformer

Assume the core flux is sinusoidal, with peak value Φm and supply frequency f:

$$\phi = \Phi_m \sin(\omega t), \qquad \omega = 2\pi f$$

By Faraday’s law, the EMF induced in a winding of N turns is:

$$e = -N\frac{d\phi}{dt} = -N\,\omega\,\Phi_m \cos(\omega t)$$

The peak EMF is therefore N ω Φm = 2π f N Φm. For a sinusoid, the RMS value is the peak divided by √2:

$$E = \frac{2\pi}{\sqrt{2}}\, f\, N\, \Phi_m = 4.44\, f\, N\, \Phi_m$$

Here E is in volts, f in hertz, N is the number of turns and Φm is the peak flux in webers. Applying this to each winding gives E1 = 4.44 f N1 Φm and E2 = 4.44 f N2 Φm.

Turns ratio, voltage ratio and current ratio

Dividing the two EMF equations removes f and Φm, because both windings share the same flux. For an ideal transformer, with no losses and no leakage flux, the induced EMFs equal the terminal voltages and the input power equals the output power. This gives:

$$\frac{V_1}{V_2} = \frac{N_1}{N_2} = \frac{I_2}{I_1}$$

• If N2 is greater than N1, the transformer is step-up: the voltage rises and the current falls.
• If N2 is less than N1, the transformer is step-down: the voltage falls and the current rises.

Construction of a transformer

There are two basic core arrangements:

• Core type: the windings surround the limbs of the core. This is common for high-voltage power transformers.
• Shell type: the core surrounds the windings, which sit on the central limb. This gives good mechanical support against short-circuit forces.

Losses in a transformer

A real transformer has two main groups of losses:

• Core (iron) losses: hysteresis loss and eddy current loss in the core. They depend on the voltage and frequency and are almost constant at any load.
• Copper losses: I²R loss in the winding resistances. They vary with the square of the load current.

Maximum efficiency occurs at the load where copper loss equals core loss. Both losses are measured by the open-circuit and short-circuit tests. Because distribution transformers are energised all the time but often lightly loaded, low core loss designs, such as those using amorphous metal cores, can save more energy over a year than designs with low copper loss.

Applications

• Power transmission: step-up transformers raise generator voltage so that power can be sent over long lines with lower current and lower I²R loss.
• Distribution: step-down transformers reduce the voltage to levels used by industry and homes, such as 415 V three-phase in many countries.
• Isolation: isolation transformers separate equipment from the supply for safety or noise reduction.
• Electronics: small transformers supply low voltages in power supplies and control circuits.
• Measurement: current and voltage transformers scale large currents and voltages down for meters and protection relays.

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