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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?

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  • \$\begingroup\$ 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. \$\endgroup\$ Commented Sep 30, 2018 at 12:06

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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.

enter image description here

And about the equivalent circuit... you must solve a linear system, for example: \begin{equation} \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} \end{equation}

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

enter image description here

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

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

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