On LED lamps, and powering them

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What on earth do you mean? There is NO SUCH THING as an MR16 holder. MR 16 means multifaceted reflector 16/8" diameter.
It really does not matter if the MR16 lamp is SES, E14, E27, E28, ES, GU10, G5.3 or even BA22d trying to stick probes into the lamp to measure the supply is not easy, in fact often impossible as with many switch mode power supplies they will close down without a load so there is nothing to measure. Industrial premises often have internal rules as to what voltages are used with which lamp holders, often E27 was used for 110 volt supplies and BA22d for 230 volt supplies, with the exception of discharge lighting where you can't get the bulb in BA22d base anyway. In the main we use G5.3 for extra low voltage however
MR16 LED Bulb 5 Watt LED spotlight 350lm warm white 3000K 240V GU 5.3 Socket die-casting housing 38° non-dimmable pack of 6pcs [Energy Class A+]
you can buy 240 volt versions, so in real terms the only way is the look at the bulb being removed. I was unaware that the GU5.3 holder was rated at 230 volt, however clearly it must be?
I don't have the actual scope screen shot but this is very similar to the wave form found on the output of a SMPS 12 volt AC supply
View attachment 116485
Interesting both kHz and 50Hz at same time, the point is the same however if not 50Hz then a capacitor used as a current limiting device will allow a different amount of current through than the designers intended, also if you look at a basic radio
and the components in a LED bulb you realise the latter is very similar, so with any other supply other than the designed 50Hz you could be building a transmitter. You have all the components you need, at random I selected a set of instructions for an electronic transformer "exclusively designed for the use in halogen lamp systems" and "max. 4m long" for cable length "The transformer can only be used with the halogen lamps" and "To avoid RF interfering radiation, the lengths of the supply cables of the lamps must not be more than max. 4m." as I say it was just selected at random not saying all "Electronic transformers" are the same. this one states 1.5 meters max it does not say quartz halogen only with this data sheet, but it does say "The output leads should not be separated by more than 10mm and should be kept to a minimum length to achieve optimum regulation and EMC suppression."
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It's an AM transmitter.

It's sending out a 50Hz signal on the 300000m band.
AM = amplitude modulated since the transmission is not modulated it is hardly a AM transmitter although it could be a transmitter, the second pdf I linked to states 40 kHz as output frequency, Low Frequency is used for things like time signals, and aircraft navigation beacons, so to cause interference on this frequency is serious.

The problem with electronic transformers is they are only able to comply with electromagnet compatibility requirements if the manufacturers instructions are complied with, since these differ even on the two examples I looked at the problem is when they are replaced or modified by non qualified personal, the general public are unlikely to down load the data sheet and find if the model they have states quartz halogen only, or 4 meters max length or 1 meter max length.

Where an error is made, it could be decades before it is found, it states "Electronic Transformers are not recommended for parallel rod or tensioned wire lighting systems" however who reads the data sheets to know that.
The problem with electronic transformers is they are only able to comply with electromagnet compatibility requirements if the manufacturers instructions are complied with,
That is possible with most of the SMPS devices manufactured and marketed by reputable companies which have instructions and information supplied with them. Less reputable companies do not include adequate instructions / information and too many companies give no information. A few even lie and say their SMPS device is a direct replacement for inductive transformers.
Even I get confused with the information given, and I have a degree and took my RAE so not really the man in the street. We have a switched mode power supply (SMPS) and a pulse width modulated power supply, to me they look the same, I am sure there is a difference! and also an Inverter again to me it seems to do same thing. But main thing to remember with a SMPS it it may alter the frequency, but it does not need to. So using a name like Electronic Transformer or Inverter Control really only tells you it has electronic components, it does not tell you what it does.

When I got a new fridge/freezer and freezer with inverter control I read up on it. It seems there are two completely different systems that use inverter control, the industrial method is to never stop the freezer motor they just control its speed, but the domestic version the inverter is no more than a soft start stopping the motor shaking on start and stop and also compensating for volt drop. It still switches on and off to control the temperature. Nothing wrong with either, but it just shows the problem with the name.

Although we use inverters in the main to step up voltage or produce three phase from a single phase supply, the welding inverter steps the voltage down.

So we have a host of names, from Smart to Plug Socket with no real idea what they really mean. Is a "Plug Socket" a plug or a socket? I would assume it is a French type plug or socket?
the earth on the wall unit is the plug and the line and neutral are sockets, but which does a Plug Socket refer to the wall bit or the cable bit?

This link was given to me as a glossary of terms, but I have never heard of ""Clicks" A connection unit usually used in a lighting installation" is a new one on me. Klik do make ceiling roses which slide in place, but I have never called them "Kliks" never mind "Clicks".

Flanders and Swan has a song, "the English the English the English are" and so on, but it does seem English as far as Electrical items go is lacking.
A pulse width modulated power supply is a switched mode power supply :) The difference is that instead of each half of the AC waveform being converted to a 50% square wave (internally), the PWMPS can supply less than a 50% square wave. This allows for tight regulation of the rail voltage under different loads in an effectively lossless way.

Note that from a power supply the final output is not pulsed, whereas other pulse-width modulation devices such as LED dimmers may actually supply a variable duty cycle square wave.

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