On paper the idea of using a buck circuit to drive the boost circuit might work, but in reality, my gut tells me that there is a lot more complexity involved that needs to be taken into consideration.
If you were going to go through the trouble of installing a buck circuit into the design to run the boost circuit of the module, why not just modify the module you have by replacing the boost circuit with a buck circuit and be done with it? Running both circuits would probably eat up 20% of the power alone, but going to a buck-only circuit will improve efficiency to around 95% or so or better.
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I have a question:
is there any evidence out there to suggest that the 2-3 cell module, when running on 2 cells, is not "as bright" as 3+ cell configurations? Do we know for certain that all this work is going to produce a configuration that is brighter by enough to justify all the complexity?
I've made the mistake myself, of doing a ton of work trying to eek out some performance, only to come back to realize, again, that the eyes don't see these little differences.
Eric