Say someone wanted to do a 9*XP-G or 9*219 light using a multi-XM-L driver from Intl-Outdoor. Since 3P emitter setups are a no-go, due to varying Vf from one LED to the next and thermal runaway, would three parallel sets of three series emitters act more like 3S higher current emitters (on the basis that the combined forward voltages of 3 emitters in series can average out Vf differences between LEDs, so the three parallel branches are more likely to have a similar Vf)? Does that make sense or is it inherently flawed logic?
This is the approx problem you’re trying to solve: Sum of normally distributed random variables - Wikipedia
The answer is that the variance is only increase. For example, given std.dev, σ of 1 on each unit, σ ~=1.7 for 3 in total.
Good old theorycrafting...
Your 3S/3P idea sounds good, but as agenthex suggests, it's possible that it could also swing the other way and allow for a greater vf between the 3 legs. However, I wouldn't worry about it too much. I've been running a half a dozen 14 xml lights (7S/2P) 24/7 for almost a year without issue (fixed lighting, not flashlights :P ). Go go emperical evidence!
Besides, as current increases to any leg, the corresponding vf of each emitter will rise slightly to help balance things out (Cree has good graphs of this on their datasheets). Thermal runaway is more of a worst case/high abuse concern.
As for 3P only, I've had great success running three emitters in parallel that were all mounted on the same pcb.
One can also hedge their bets by matching the vf of the emitters beforehand. I use the diode setting on a fluke for this (quick and easy).
Hope that helped,
-Match
The other way to think about it is that a direct drive light goes through a far greater range of V (and therefore current) than the likely variation of current between emitter in a 3P setup.
However, it’s a matter of math that the likely variance will only increase when you stack them in series. Eg. (assuming normal distrib, and linear v to i relationship) say σ = 0.2A, with 3, σ = 0.35A. Except v to i is not linear, so if you don’t match it’s even worse.
Trying to match up emitters is always a good idea in a parallel configuration, but just for the record, the diode setting on a fluke DMM will show the threshold voltage. Thats the voltage at which current begins to flow - but very little current. The threshold voltage doesn’t have a whole lot of relation to the Vf at operating current.
PPtk
Since I’ve seen parallel LED arrangement questions come up quite a few times, I figured I’d take a minute and run some analysis…
I created a 3x3 array of LED’s in SPICE. Grabbed the actual Cree XM-L Spice model from CREE.COM and then got to playing…
Three of the models I left as provided by CREE (The Ideal/Typical XM-L).
Three of the LED’s I increased the slope of current/voltage
Three of the LED’s I decreased the slope of current/voltage
Essentially, They all have the same threshold voltage now, but three of them are ideal, three will be a little on the ‘low-vf’ side and three will be a little on the ‘high-vf’ side. I made sure that they all still fall within datasheet specifications, so these are all ‘real’ possibilities. You could actually get these three LED’s from cree and they would all be within spec.
I then hooked them up to battery and swept the bat voltage from 8 to 10.5. Here’s what happens…
As you can see, parallel arrangements work pretty well at low drive currents, but the variance of the LED’s gets magnified as you increase current. Admittedly, this is probably worst case scenario, but it IS possible. Parallel arrangements are not ideal…
PPtk
PilotPTK,
Thanks for info on this, and you bring up a very good point. I knew that I was only measuring threshold voltage, but I always assumed it would be close enough under load.
Looking at your graph, I see a ~1amp variation at higher current levels. At lower levels the swing, while noticable, would seem to be acceptable in practical usage.
For clarification, I drive my afformentioned 7S/2P xml arrays ~1.7 amps @emitter, which is rather on the conservative side.
One other variable might be is how each emitter vf would change over its lifetime or due to temperature variations. Another reason I went conservative on the juice.
Wow, thanks everbody for the very informative responses. I learned quite a bit, and that I need to learn more about statistics.