# Short-circuit inductance

Measurement of 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.[1] [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.

Equivalent circuit

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,

${\displaystyle L_{\mathrm {sc1} }=(1-k^{2})\cdot L_{\mathrm {1} }\,}$
${\displaystyle L_{\mathrm {sc2} }=(1-k^{2})\cdot L_{\mathrm {2} }\,}$

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 ${\displaystyle k}$, the inductive coupling factor and ${\displaystyle \sigma }$, the inductive leakage factor. ${\displaystyle k}$ is derived according to [Notes 2]:

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

where

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