all info here is based solely on the specific configuration mentioned, none of this information i put here, applies to less or more voltage of battery.
i donno, how about a fatman?
http://www.taskled.com/fatman.html
BOOST, wants battery to be lower than voltage of led.
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then this
https://www.kaidomain.com/WEBUI/ProductDetail.aspx?TranID=3150
boost
RammerJammer
but ya know for 3XAA alkaline or lithium, almost EVERY one of these drivers listed at being able to handle 4+ volts on the battery side are RammerJammer curcuits.
https://www.candlepowerforums.com/threads/179551
see my dafynition of RammerJammer in this thread scroll to the pics.
http://www.dealextreme.com/details.dx/sku.6190
this same thing with PWM levels, rated to 4.5 probably still a rammerjammer
boost
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then there is
http://www.dealextreme.com/details.dx/sku.1886
which is a hedgetrimmer, if you have enough input voltage
this would never cause an overdrive situation, but you will still end up with a dwindler because it cant BOTH buck and boost.
This would be OK with enough voltage, so need to know what kind of 3AA Lithium???
current trimmer, voltage wacker
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http://www.dealextreme.com/details.dx/sku.7425
this , high voltage curcuit, falls out of regulation at around 4v, wants 4 not 3 cells.
http://www.dealextreme.com/details.dx/sku.3256
this too
almost every one of these type of drivers falls out of regulation when the voltage on your 3X AA battery goes lower
these make good Dwindlers
Buck style
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http://www.dealextreme.com/details.dx/sku.4735
buck boost, that sags more than a battery
ifrom the data the users provide it looks like Boost only
limpey or rammerjammer, depending on who reviewed it, or wired it? or which item was sent
they got it into a hard overdrive with high voltages.
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http://www.taskled.com/d2dim.html
IF all the curcuits are going to be falling out, or direct driving at some point anyways
then for a single led, might as well put control on your DIRECT DRIVE
this would work with 3xAA alkaline or ni-mhy but not lithium and one led
PWM control only max 3amp
would be RammerJammerDwindler untill you add a bit of resistance, then a dwindler
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its gotta be something from Dat2zip, or the sandwitch shop, they probably have something.
http://home.comcast.net/~theledguy/cpf_store/converters/converters.htm
http://theledguy.chainreactionweb.com/product_info.php?&products_id=327
Mad max
boost from 2x AA (not 3)
in your configuration this would be a Mad RammerJammer
the wizzard, if i remember right would bend both ways.
http://theledguy.chainreactionweb.com/product_info.php?cPath=48_49_61&products_id=920
wizzard replacement GD500 Buck/Boost Converter
A fully regulated buck/boost converter. This converter will step up or step down. Ideal candidate for rechargeable Lithium-ion batteries (4.2V) and driving a Luxeon 1W or Luxeon 3W.
the wizz should be a hedgetrimmer a killer or a limpey, Dat2zip knows his stuff, so i suspect a hedgetrimmer
http://theledguy.chainreactionweb.com/product_info.php?cPath=48_49_61&products_id=1004
the SOB
""Will operate in DD mode when Vin is less than Vout (Vf).""
Dwindler, would be ok falls out of regulation
http://theledguy.chainreactionweb.com/product_info.php?cPath=48_49_61&products_id=721
SHARK
boost (or step-up)
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the only reason i am pointing this stuff out, is because your input and output voltage match sorta needs a Boost&Buck curcuit to do its FULL range of voltages, any one of these things would "work" and work ok. but a good Direct drive (resistered) matchup would work and have less loss going into some chip. and it would treat the batteries better.
that is all i am saying, i am not trying to knock anything, just trying to understand it.