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I took apart a laptop PSU, and inside the transformer there is a small copper plate electrically connected to a pin of one of the secondary windings which is grounded on the PCB:

enter image description here

The plate is about 1x1 cm and is entirely visible on the picture. It was originally behind a layer of insulation tape. What could be its purpose? I would expect to see a copper shield between the primary and the secondary windings, not on a side. If this plate is used for EMI suppression, then how does it work?

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What could be its purpose?

It's an EMI shield and the off-shield connection will connect to the live-side DC bus on the PCB. I've had to implement one myself. Radiated emissions from the transformer were just enough to cause an EMC compliance failure but, the copper tape solved it.

I used a 90% wrap around the ferrite and maybe, if I'd "played" a bit more, I might find a "tidier" solution. Product volume was circa 3k per annum so it wasn't a big deal with a 90% wrap.

I would expect to see a copper shield between the primary and the secondary windings, not on a side.

That would be a ploy to reduce conducted emissions on the secondary (as well as a Y capacitor from the DC output to the live-side DC bus.

If this plate is used for EMI suppression, then how does it work?

You know, when you are in a test-lab and pulling your hair out and, the day is getting long and time is running out and, after trying this fix or that fix you find a Goldilocks fix, you just run with it (after double checking). It worked.

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    \$\begingroup\$ So the designers were essentially going to put a shield on it, but found out that a small patch was enough to meet the EMI target while also costing less, so they went for that instead? \$\endgroup\$ – Dmitry Grigoryev Jun 24 '20 at 21:01
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    \$\begingroup\$ @DmitryGrigoryev maybe, or maybe it was a number of fixes applied near enough simultaneously of which one or two had genuine benefit but they ran out of time removing each one, in turn so, they never got to definitively discover which of those simultaneous “fixes” was responsible for solving the problem. So, running out of compliance lab time (and not wishing to pay for another day of testing), they did the right thing and opted to implement them all. I was in the same situation and decided, so what(!); the cost isn’t a bid deal compared to several hundred pounds or dollars of retesting. \$\endgroup\$ – Andy aka Jun 24 '20 at 21:35
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    \$\begingroup\$ Why live-side DC bus? \$\endgroup\$ – P2000 Jun 24 '20 at 21:36
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    \$\begingroup\$ @P2000 most power supplies are compliant with EMC without an earth wire and so, the nearest thing to an earth wire is try and return EMI currents to the DC bus on the live side - very common practice. \$\endgroup\$ – Andy aka Jun 24 '20 at 21:38
  • \$\begingroup\$ @P2000 To clarify, there was a protective earth wire available, but connecting the shield to it would require an additional terminal on the transformer. \$\endgroup\$ – Dmitry Grigoryev Jun 25 '20 at 12:00

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