# Short-circuit inductance

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. [Notes 1]　Short-circuit inductance measurements are an alternative to, or complement of, open-circuit inductance measurements, and yield different approximations for the coupling factor and other derived quantities. Which measurement methodology is most relevant depends on the application.

Measured primary and secondary short-circuit inductances may be considered as constituent parts of primary and secondary self-inductances; they are related according to the coupling factor as,

$L_{\mathrm {sc1} }=(1-k^{2})\cdot L_{\mathrm {1} }\,$ $L_{\mathrm {sc2} }=(1-k^{2})\cdot L_{\mathrm {2} }\,$ 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 $\sigma$ , the inductive leakage factor. $k$ is derived according to [Notes 2]:

$k={\sqrt {1-{\frac {L_{\text{sc}}}{L_{\text{oc}}}}}}$ where

• $L_{\text{sc}}$ is the short-circuit measurement of primary or secondary inductance
• $L_{\text{oc}}$ 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.