# Leakage inductance on 3-winding transformer

I have a toroidal 3-winding transformer. It's a step up, let's say 1:10 ratio, the secondaries are identical.

If I measure the leakage inductance, shorting one secondary at a time, I get about the same leakage for both secondaries. If I short both, I get about 10% less leakage than the individual leakage.

Does anyone know the reason or have an idea of what the equivalent circuit would look like?

• If you are still here, the coil inductance ratios are related to the turns ratio effects on impedance ratio, while mutual inductance is affected by loading of each coil (shorted) . Look up single transformer equiv circuit and add additional coil equiv cct similar to a 2 winding. model. Commented Sep 30, 2018 at 12:06

Well ... this image is not of a toroidal transformer, but I believe it serves to illustrate the phenomenon. You measure a little less than half the leakage inductance because the magnetic field is distributed differently when both windings are shorted.

And about the equivalent circuit... you must solve a linear system, for example: $$$$\begin{vmatrix} 1 & 1 & 0 \\ 1 & 0 & 1 \\ 0 & 1 & 1 \\ \end{vmatrix}\begin{vmatrix} X_1 \\ X_2 \\ X_3 \\ \end{vmatrix}=\begin{vmatrix} X_{12} \\ X_{13} \\ X_{23} \\ \end{vmatrix}$$$$

where the inductances you measure are X12, X13 and X23.

You have two parallel leakage inductance paths so obviously with both other coils shorted , it will be less than just one shorted.

• I thought of this, but wouldn't you expect it to be about 1/2 of the individual leakage then? Commented Apr 15, 2017 at 16:16
• It depends on the coil winding spec and mutual coupling. Commented Apr 15, 2017 at 16:17
• @Gswffye Not if some of the leakage is common to both paths, ie common to the primary, for instance. Commented Apr 15, 2017 at 16:17
• small reductions indicate good characteristics for multiple forward converters for single feedback for load regulation as in ATX supplies from tight coupling of secondaries. Commented Apr 15, 2017 at 16:19

The leakage inductance comes from the fact that less than 100% of the primary flux goes through a secondary coil.

But some of that bypassing part still meets the other secondary coil. => The shorting of both secondaries increases the proportion of the primary flux that meets a shorted secondary coil.

The calculation is complex, because there are 3 coils with their own inductances and 3 different coupling factors.