Leakage inductance

L_e1 and L_e2 are the leakage inductance (academic)

Leakage inductance is that property of an electrical transformer that causes a winding to appear to have some inductance in series with the mutually-coupled transformer windings. This is due to imperfect coupling of the windings and creation of leakage flux which does not link with all the turns of the winding.

The leakage flux alternately stores and discharges magnetic energy with each electrical cycle and thus effectively acts as an inductor in series in each of the primary and secondary circuits.

Leakage inductance is primarily caused by the design of the core and the windings. Voltage is dropped across the leakage reactance, resulting in poorer supply regulation when the transformer is placed under load.

There are two slightly differing definitions of leakage inductance, which can cause confusion in electronic circuit design. The first definition is based on an academic consideration of the electromagnetism. The second definition is the industrial definition using actual measurements.

Leakage inductance (academic)

Magnetic flux of the transformer

The magnetic flux interlinked to both the primary winding and the secondary winding is said to be the main flux, (φ₁₂ or φ₂₁). The magnetic flux which interlinks only with the primary winding, and does not interlink with the secondary winding, is said to be the primary leakage flux, φ_σ1. The magnetic flux which interlinks with the secondary winding, and does not interlink with the primary winding is said to be the secondary leakage flux, φ_σ2. The primary side leakage flux becomes the primary side leakage inductance, and the secondary side leakage flux becomes the secondary side leakage inductance. Defining k to be the coupling coefficient, and denoting the leakage inductances of the primary side and the secondary side as L_e1 and L_e2 respectively, it follows that:

Leakage inductance (industrial)

measuring of the leakage inductance

If one winding of a transformer which has two windings is short-circuited, the inductance measured from the other winding is said to be the industrial leakage inductance. Denoting the leakage inductances of the primary and secondary sides as L_sc1 and L_sc2 respectively, it follows that:

Applications of leakage inductance

Leakage transformer

Leakage inductance can be an undesirable property, as it causes the voltage to change with loading. In many cases it is useful. Leakage inductance has the useful effect of limiting the current flows in a transformer (and load) without itself dissipating power (excepting the usual non-ideal transformer losses). Transformers are generally designed to have a specific value of leakage inductance such that the leakage reactance created by this inductance is a specific value at the desired frequency of operation.

Power distribution transformers are usually designed with a leakage reactance of between 1% and 10% of the full load impedance.^{[citation needed]} If the load is resistive and the leakage reactance is small (<10%) the output voltage will not drop by more than 0.5% at full load, ignoring other resistances and losses.

Leakage reactance is also used for some negative resistance devices, such as neon signs, where a transformer action is required as well as current limiting. In this case the leakage reactance is usually 100% of full load impedance, so even if the transformer is shorted out it will not be damaged. Without the leakage inductance, the negative resistance characteristic of these gas discharge lamps would cause them to conduct excessive current and be destroyed, very similar to the way fluorescent tubes and LEDs operate although they normally do the same job with inductance and resistance respectively.^{[citation needed]} Transformers with variable leakage inductance are used to control the current in arc welding sets. In these cases, the leakage inductance limits the current flow to the desired magnitude.

Further reading

• Texas Instruments Magnetics Design Handbook covers leakage inductance, its causes and effects as well as how to design it out of a transformer.