Transformer rating when used as autotransformer ?

Not overloading a transformer means in general, not exceeding rated current density in any of its copper.

Neglecting magnetising current and losses, in auto connection with the load at the midpoint you are correct in saying that half the load current comes down the top half of the winding from the supply, and half is transformed and comes up the bottom leg, for a total of I(load) = 2I(supply). If we consider this transformer to be 1:1 and ignore the magnetising current and losses, both the primary and secondary are rated for 102/115 = 890mA, hence 1.78A is available at 115V or 204VA

With the load at the 25% tap, the limiting factor will be the 890mA coming up the bottom leg. This will reflect as a supply current of 890/4 = 220mA also passing through the load, for a total load current of 1.11A or 67VA. A purpose-made autotransformer could deliver greater power at this tap by having the bottom leg wound with larger wire.

Sometimes a slight tradeoff is possible when one winding or part of it is operating at reduced current density. The reduction in I²R losses in that section might be used to compensate increased losses in another. In this case the reduced primary current when using the 60V tap might permit a slight increase above 890mA in the lower leg. However, since the heat dissipation follows I², the current increase is not proportional, and if the windings are not in effective thermal contact (e.g. in a split bobbin transformer) the saving in heating in one winding is not available to the other at all.

For completeness it's worth noting that in the original isolating configuration, the magnetising and iron loss power currents flow only in the primary. In auto with both windings in series, the currents are halved but flow in both windings.

Two final thoughts; tungsten lamp current does not fall in proportion to the voltage when dimmed, due to the positive tempco of the filament. And it's the current that is the limiting factor for the transformer. OTOH light output falls precipitously, and 25% is very dim and orange indeed.

Thanks for that detailed explanation - it certainly confirmed that I'd missed some details. But I'm lost on one bit ...

Lucien Nunes said:

With the load at the 25% tap, the limiting factor will be the 890mA coming up the bottom leg. This will reflect as a supply current of 890/4 = 220mA also passing through the load, for a total load current of 1.11A or 67VA.

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It's a long time since we did transformers at uni, and I'm not clear exactly what you're saying here ? Specifically where does the 890/4 come from, I was thinking it would be 890/3 in the upper leg ?

Lucien Nunes said:

Two final thoughts; tungsten lamp current does not fall in proportion to the voltage when dimmed, due to the positive tempco of the filament. And it's the current that is the limiting factor for the transformer. OTOH light output falls precipitously, and 25% is very dim and orange indeed.

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The lights are LED, 40off, 2W each as festoon lighting in the garden. As you can imagine, 80w of LED lighting, even when most of it is coloured, is "quite a lot" in a moderate sized garden. Although described as non-dimmable, each is just an inductive dropper, bridge rectifier, smoothing cap, and an array of surface mount LEDs - a quick check with the variac showed that they dim very nicely by varying the voltage. What I haven't got round to doing yet is measuring current vs voltage - I expect that to be linear(ish) but with the "effectively off" voltage to be well above zero due to the knee voltage of the LED strings.

At the moment I've got a rather over-sized site transformer that my late father knocked up from some transformer he'll have "rescued" from somewhere (given your knowledge and interest in old electrical "stuff", I imagine you and my late dad would have got on well), and that gives a switchable option of 110V or 55V - and most of the time I use the original set on the 55V setting which gives a nice decorative effect.
As I've now got two sets of lights, I've been knocking up a smaller transformer in a box more suitable to have in the house to control the newer set, and this box will be switched (3 way rocker) to allow full brightness as well for those few occasions when we want the illumination rather than just decoration.

It's a "temporary" setup until I find time (perhaps in a decade when I've retired and got through other stuff I can't find time for ?) to start playing with some home-brew DALI controls ?. That'll give SWMBO something to say - as it is she keeps going on about me not being allowed to pop my clogs before her because of all the "complicated" stuff I keep putting in the house.

I was thinking it would be 890/3 in the upper leg ?

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Oops yes that's correct of course, I had started out equating Lsupply to Ilamp/4 but did a bungled edit and broke it.

I had visualised tungsten specifically, not sure why, habit I suppose. I am surprised your LED lamps still pass current at such a low fraction of rated voltage, some LED products are completely off at 50%. I am not 100% convinced by your mention of an inductive dropper, but curious to know what is on the PCB.

because of all the "complicated" stuff I keep putting in the house.

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Yes, definitely worth keeping domestic systems simple and reliable. No crazy IOT Web 2.0-enabled Arduinoid controls here. I mean, look at the dining room lighting board; could it be any more straightforward?

Lucien Nunes said:

Yes, definitely worth keeping domestic systems simple and reliable. No crazy IOT Web 2.0-enabled Arduinoid controls here. I mean, look at the dining room lighting board; could it be any more straightforward?

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That is awesome,

I need 5 mock-ups of that for when my wife next asks me to put dimmer switches up at home.
that might change her mind!!

Lucien Nunes said:

Yes, definitely worth keeping domestic systems simple and reliable. No crazy IOT Web 2.0-enabled Arduinoid controls here. I mean, look at the dining room lighting board; could it be any more straightforward?

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Ooh, vintage Furse. I remember they had reostat dimmers at secondary school, but I wasn't involved in backstage back then. By 6th form it was a brand new place, with thyristor dimmers (12 channels, 2 units with 6 channels each) and a nice remote control desk that connected with a longish cable and D connectors - quite handy during rehearsals being able to sit in the auditorium seating and work the lights. Two banks of sliders as well, so easy to do crossfades with the two master sliders.
Somehow, I don't think SWMBO would take too kindly to either setup

At 6th form I managed to get a few practical jokes in. The English dept (who notionally had ownership of theatrical equipment) were paranoid about blowing lamps given the cost. A students band got permission to have a gig in the hall - on condition that there was to be no "flashing of the lights" lest we blow any. So I duly refrained from too much of that, and set a low level on the second bank to keep the filaments warm. The next day was 1st April, and as I went into our physics lesson (the physics teacher was notionally in charge of backstage tech) I casually mentioned that "you know those bulbs that cost £30 ... well we blew one last night" - and he fell for it.
It backfired on me though, at break time he did the same thing to the head of English in the staff room, except the tales was we'd blown two lamps and my jokes "wasn't much appreciated".
That was £30 (or something like it) in 1980s money, for a department with "not a lot" of budget for such things.

But today, when it started raining and so no more outdoor jobs, I got some kit out and took some measurements. This is for a string of 40 lamps, various colours, all nominally 2W so 80W total - but as it turns out, a horrendous power factor ?

The lights start to be visible at around 30V, even in overcast daylight. Now I've got my transformer boxed up, it's giving around 62V and 124V on the lower and middle taps, and the lamps take around 220mA and 630mA respectively.

I have a cheap "no idea how accurate it is (or isn't)" plug in energy meter. At 240V it tells me the current is 1.63A (vs 1.44 measured on my DVM), 72W, 392VA, and 0.18 power factor.

Anyway. the measurements say that the load is well within the rating of the transformer, and would be if I ran both sets of lights from one - which is sort of my plan if/when I can get them wired back into the house ('kin T&G chipboard floors with 'kin click together laminate in the way ?)

Ah, I've now opened up another dead lamp, here's the internal schematic :

I'm assuming it's an inductor, it's labelled RX while resistors are labelled Rn, and it looks like a heatshrink wrapped inductor. The resistor across the cap is 470k, so just a bleed resistor. Seems reasonably well engineered to me - if only they'd even tried to avoid water ingress ?

This is an amber one, different colours have different numbers of LEDs in the string.
The two boards, in a sandwich with a sheet of insulating paper, are in the cap, held in place by the polycarbonate bulb. So the electrics are the first thing water finds when it gets in - there's no seal at all between cap and bulb.

The mylar capacitor is the dropper, Rx is probably a resistor, no reason for it to be called R otherwise and some resistance is needed upstream of the smoothing cap to limit the current on voltage spikes. It looks melty.

The reason for the low pf and operation at unusually low voltage is not far to seek. Three LED chips (15V total max) running from 230V mains. You could get ten times the light power from the same current with more chips.