**Document**

**Name**

# Measuring Leakage Inductance

**Description**

## How is leakage inductance measured?

When an LCR meter is connected to the primary winding of
a transformer with open-circuit secondary terminals (figure 4), the value
of inductance (L) comprises primary inductance (LP) plus leakage
inductance (LL).

Since LL is a function within the transformer, it is
clearly not possible to measure its value directly. A method must
therefore be used to subtract the value of LP from the total measured
inductance. This is achieved by applying a short circuit across the
secondary terminals (figure 5). A perfect short circuit will result in
zero volts on the output terminals (figure 6) and, through transformer
action, zero volts will also appear across the primary inductance. The
measured value of inductance at the primary terminals will therefore be
the true leakage inductance (LL).

Unfortunately, achieving a perfect short circuit on the
secondary of a transformer is difficult in a laboratory and completely
impractical in a production environment. In production, it is common for
the short circuit to be applied manually or via a switchable relay. Under
these conditions, a perfect short circuit cannot be achieved, and it
follows that the secondary voltage will not be truly zero. The voltage
attributable to the imperfect short circuit will then appear across the
primary inductance as a short-circuit error multiplied by the turns ratio
(figure 7).

Ls/c is reflected in the primary as N^{2}Ls/c
because, in any winding, L is proportional to the number of turns squared
(L α N^{2}). Thus, Ls/c is reflected as a function of:

( Np / Ns ) ^ 2 = ( Lp / Ls )

The measured value of the primary inductance can be
considered vectorially as the sum of the leakage impedance plus the
reflected impedance of the short-circuit error. This is shown in figure 8.