short-circuit inductance

Image:Leakage mesure.gif

Short-circuit inductance of a real linear two-winding transformer is inductance measured across the primary or secondary winding when the other winding is short-circuited.Japan Industrial Standard [http://kikakurui.com/c5/C5602-1986-01.html#34 C 5602-1986, pp 34, 4305]This value is sometimes imprecisely referred to as leakage inductance　

The method of measuring the short circuit inductance is described in industrial standard. The industrial standard also stipulates a method for obtaining the coupling factor by combining it with the open circuit inductance value.

Image:Transformer eq2.gif

Measured primary and secondary short-circuit inductances may be considered as constituent parts of primary and secondary self-inductances. They are derived by using Ho-Thevenin's theorem from the equivalent inductance of the three-terminal equivalent circuit as follows. Then they are related according to the coupling factor as,

:$L\_\{\backslash mathrm\{sc1\}\}\; =\; (1-k^2)\backslash cdot\; L\_\{\backslash mathrm\{1\}\}\backslash ,$

:$L\_\{\backslash mathrm\{sc2\}\}\; =\; (1-k^2)\backslash cdot\; L\_\{\backslash mathrm\{2\}\}\backslash ,$

Where

:*k is coupling coefficient

:*L₁ is primary self-inductance

:*L₂ is secondary self-inductance

Short-circuit inductance measurement is used in conjunction with open-circuit inductance measurements to obtain various derived quantities like $k$, the inductive coupling factor and $\backslash sigma$, the inductive leakage factor. $k$ is derived according to:the same k value can be obtained measured from the primary side or from the secondary side

:$k\; =\; \backslash sqrt\{1\; -\; \backslash frac\{L\_\backslash text\{sc\}\}\{L\_\backslash text\{oc\}\}\}$

where

:*$L\_\backslash text\{sc\}$ is the short-circuit measurement of primary or secondary inductance

:*$L\_\backslash text\{oc\}$ is the corresponding open-circuit measurement of primary or secondary inductance

Other transformer parameters like leakage inductance and mutual inductance which cannot be directly measured may be defined in terms of k.

Short-circuit inductance is one of the parameters that determines the resonance frequency of the magnetic phase synchronous coupling in a resonant transformer and wireless power transfer. Short-circuit inductance is the main component of the current-limiting parameter in leakage transformer applications.