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Leakage inductance derives from the electrical property of an imperfectly-coupled transformer whereby each winding behaves as a self-inductance constant in series with the winding's respective ohmic resistance constant, these four winding constants also interacting with the transformer's mutual inductance constant. The winding self-inductance constant and associated leakage inductance is due to leakage flux not linking with all turns of each imperfectly-coupled winding.
The leakage flux alternately stores and discharges magnetic energy with each electrical cycle acting as an inductor in series with each of the primary and secondary circuits.
Leakage inductance depends on the geometry of the core and the windings. Voltage drop across the leakage reactance results in often undesirable supply regulation with varying transformer load. But it can also be useful for harmonic isolation (attenuating higher frequencies) of some loads.
The magnetic circuit's flux that does not interlink both windings is the leakage flux corresponding to primary leakage inductance LPσ and secondary leakage inductance LSσ. These leakage inductances are defined in terms of transformer winding open-circuit inductances as well as the transformer's coupling coefficient k, the primary open-circuit self-inductance being given by
It therefore follows that the transformer secondary open-circuit self, magnetizing and leakage inductances are given by
The electric validity of the above transformer diagram depends strictly on open circuit conditions for the respective winding inductances considered, more generalized circuit conditions being as developed in the next two sections.
A real linear two-winding transformer can be represented by two mutual inductance coupled circuit loops linking the transformer's five impedance constants as shown in the diagram at right, where,
The two circuit loops can be expressed by the following voltage and flux linkage equations,
These equations can be developed to show that, neglecting associated winding resistances, the ratio of a winding circuit's inductances and currents with the other winding short circuited and at no-load is as follows,
which allows expression as second shown equivalent circuit with winding leakage and magnetizing inductance constants as follows,
The real transformer can be simplified as shown in third shown equivalent circuit, with secondary constants referred to the primary and without ideal transformer isolation, where,
Referring to the flux diagram at right, the winding-specific leakage factor equations can be defined as follows,
The leakage factor σ can thus be expanded in terms of the interrelationship of above winding-specific inductance and leakage factor equations as follows:
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.
Commercial transformers are usually designed with a short-circuit leakage reactance impedance of between 3% and 10%. 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.
High leakage reactance transformers are used for some negative resistance applications, such as neon signs, where a voltage amplification (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.