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How would I make a 2000+ lumen white LED circuit?

I'm thinking of using https://www.instructables.com/id/Circuits-for-using-High-Power-LED-s/step8/a-little-micro-makes-all-the-difference/ so I can drive the circuit with a TTL pulse and three of http://www.ledsupply.com/creexpg-w417.php, but I'm not entirely sure on how to wire up the circuit/choose the correct values for the components. Any help would be awesome!

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That circuit stinks. You end up wasting a LOT of energy in the series resistor. What LED are you actually using, and what are its characteristics ?

Steve
That circuit doesn't use a series resistor to drop the voltage, it uses the resistor as a sense resistor so that the regulator regulates...you still need your source voltage very close to your desired output voltage or you have the regulator doing the old resistor's job...

current limited smps is the way to go really.
All right, you waste the energy in the pass device if you want to get picky. ;-)

IF the device characteristics are right, there are some very very simple solutions for this from Linear Technology. I have a tube of the darned chips on my desk for a future 'ible.

Steve
I'm in the process of making some professional grade led spots and gobos, stage grade equipment with dmx controls -- the only hard part is getting extremely efficient high power led drivers - because anything not actively driven up to the requirement as opposed to squelching down to the requirement is brutally ...hot...when you get into the multi-hundred watt led arrays. Yes, they exist already, but I think we can design it better, and china can manufacture it :D
I managed a 95% efficient buck converter based on a simple switcher - 95% on full, I don't know how it behaved modulated.

Steve