Definitions

# Leakage inductance

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.

As for leakage inductance, two kind of the definition exists in this field. This problem often causes confusion in the electronic circuit design. One of a definition is the definition defined by an academic electromagnetism. Other definition is the industrial definition of a actual measurement.

The magnetic flux interlinked to both of the primary winding and the secondary winding is said as the main flux (φ12 or φ21). The magnetic flux which only interlink to the primary winding, and don't interlink to the secondary winding is said as the primary leakage flux φσ1 . The magnetic flux which only interlink to the secondary winding, and don't interlink to the primary winding is said as the secondary leakage flux φσ2 . The primary side leakage flux becomes the primary side leakage inductance, and the secondary side leakage flux becomes the secondary side leakage inductance. When coupling coefficient is as k, each leakage inductances of the primary side and the secondary side are as Le1 and Le2, each leakage inductances are shown in the following.

$L_\left\{mathrm\left\{e1\right\}\right\} = \left(1-k\right)cdot L_\left\{mathrm\left\{1\right\}\right\},$

$L_\left\{mathrm\left\{e2\right\}\right\} = \left(1-k\right)cdot L_\left\{mathrm\left\{2\right\}\right\},$

## Leakage inductance (industrial)

One winding of a transformer which have two windings is short-circuited, the inductance which was measured from the other winding is said the industrial leakage inductance. Each leakage inductances of the primary side and the secondary side are as Lsc1 and Lsc2, each leakage inductances are shown in the following.

$L_\left\{mathrm\left\{sc1\right\}\right\} = \left(1-k^2\right)cdot L_\left\{mathrm\left\{1\right\}\right\},$

$L_\left\{mathrm\left\{sc2\right\}\right\} = \left(1-k^2\right)cdot L_\left\{mathrm\left\{2\right\}\right\},$

## Applications of Leakage Inductance

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. 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. 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.