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"The qualification that the coil should be closely wound on the toroid is to minimize the linkage flux around the individual turns of wire."

What does "the linkage flux around the individual turns of wire mean?

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  • \$\begingroup\$ Linkage or leakage? \$\endgroup\$
    – Chu
    Commented Jan 4, 2018 at 12:18

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what does it mean that "the linkage flux around the individual turns of wire"?

Normally in a well designed inductor, the flux from any single turn would ideally couple to every other turn. However, this is not something that occurs 100% on a practical coil because there is always some small amount of magnetism produced by each turn that manages to avoid passing through the common magnetic core of the coil and therefore this flux doesn't couple to other turns.

For an inductor this isn't a big deal; you just have to add a couple of more turns to reach the theoretical value you need. Normally we use the formula: -

Inductance of a coil = \$A_L\times N^2\$

Where \$A_L\$ is the core factor and N is the number of turns but, in a real situation, if pushed the formula becomes: -

Inductance of a coil = \$A_L\times N^{(2-x)}\$

Where \$x\$ reduces the relationship to slightly less than a turns-squared situation.

It is the presence of flux linkages that gives the inductance a near square value based on turns.

For a transformer this is more problematic because you have the situation where all the flux linkages produced by the primary don't 100% couple with the secondary and this leads to what is known as leakage inductance.

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  • \$\begingroup\$ " Normally we use the formula: - Inductance of a coil = AL×N2" It is valid for long thin coils but not for short thick coils. \$\endgroup\$
    – Uwe
    Commented Nov 9, 2020 at 21:19
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    \$\begingroup\$ I think my answer did cover all the relevant bases on this subject but, feel free to add an answer. That's what this site is about. If you can make a better answer please go ahead. \$\endgroup\$
    – Andy aka
    Commented Nov 9, 2020 at 21:42
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The phrase is taken from David Cheng "Field and Wave Electromagnetics".

I agree that "the linkage flux" is a bit unfortunate term here, instead of leakage as already noticed. The meaning of "closely wound" is that every turn can be considered a radial plane (therefore no significant circumferential component of current).

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