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I took apart a small transformer. It is of shell construction type. Beneath the primary windings, I found a strip of (floating) copper foil wrapped around the secondary windings. Of course there is mylar insulation between those three components.

Based on what I read here: Magnetics Design 4 - Power Transformer Design, small transformers have the problem of limited space, taken up by insulation and voids between round wires. A copper foil increases the copper volume that can provide better magnetic coupling.

Am I right in my explanation? Or is it something else?

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It's there to reduce the coupling of high-frequency noise from the AC line, switching regulator harmonics, or other 'unclean' energy into the secondary winding. The shield won't improve the magnetic coupling but it won't hurt it either, and energy at higher frequencies that would have been transmitted via interwinding capacitance will be attenuated.

Part of a defense-in-depth EMI control strategy, basically.

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    \$\begingroup\$ Otherwise known as an electrostatic shield. \$\endgroup\$
    – MikeJ-UK
    Jul 14, 2011 at 7:57
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    \$\begingroup\$ An "electrostatic shield" is effectively a grounded capacitor plate that prevents capacitive coupling between windings. Instead both are coupled to ground capacitively. \$\endgroup\$
    – Russell McMahon
    Jul 14, 2011 at 8:48

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