External PSU EU regulations, need help with formula

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Hi all.

I am in the process of designing an external PSU but maths not being my strong point, I need some help with a formula.

This formula is for working out the efficiency with an active on state to see if it would comply with the latest EU regulations.

The page in question is:
Efficiency Standards for External Power Supplies | DigiKey

The formula is as follows (this is based on a 1W to 49W PSU), according the the page above this formula is to calculate the efficiency as a decimal number, what I don't understand & they make no mention of, is what is ln? & what would Pout be?

0.0834 × ln(Pout) - 0.0014 × Pout + 0.609

Sure hope somebody can help with this, its probably obvious but I just can not see it :confused:
It's possible that ln() is natural log ()
But inserting 49 watts for Pout into the formula gives a nonsense value of 0.865 (=86.5%)
even though there is no data for input or losses.
Trying power = 1 watt, gives another nonsense number of 0.6076 (60.76%)
I don't regognise what the formula is trying to give us.

Found your formula further down.

It is under the heading
Minimum Average Efficiency in Active Mode
If your product needs to comply with the standard, then you must determine the efficiency during a varaiety of operation modes and find the average for typical operations. That average efficiency must be greater than whatever number your formula requires.

But first: do you, or your product, need to comply?
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Thanks for your reply!

From my understanding there is already a ban in place since 2010 for all plug in type AC>DC transformers, the type that has a transformer & rectifier inside. Latest regulations seem to imply that all external PSUs must conform to the efficiency ratings in that document, which I cant seem to make head or tail of as the formula is not at all clear!

It would seem to get those ratings that SMPS would be required, but its unclear as to AC>AC adaptors which can't be SMPS?
AC-AC adaptors are not covered, some small equipment ships with one. AC-DC transformer rectifier units are not banned per se, they just cannot meet the off-load consumption requirements.

If you are designing an external PSU have you also covered all the creepage and clearance distances? And the EMC and insulation breakdown testing?
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Thanks again, really appreciate all these replies!

I was under the impression from that document that this applies to AC>DC & AC>AC because there is a section for AC>AC with maximum off load consumption requirements.

Measuring a good quality AC transformer with just the primary connected, nothing connected to the secondaries, the idle consumption still works out more than any of those off load consumption figures, a toroid is much lower but still more than their figures, which seem unobtainable with anything other than SMPS.

What I can't seem to find any clear information on is does this apply to a simple AC>AC type adaptor, basically a transformer in a box affair because I still see new products on the market using the AC>AC plug in type transformers.
It is quite normal for officials to insist on something which is either impossible, or not realistically achievable given the current state of the art. They have huge faith in the ability of scientists and engineers to modify the universe from what it is to what the officials deem it to be. Fortunately, it is also quite normal for officials to never check that their dictats are being followed - if checking requires spending money. This is why EMC and safety rules are routinely ignored.
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