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Hi again Jeff,

             Yes i think the "Brinkmann" circuit will
             work for up to maybe 6 LED's wired in
             parallel. The resistor R2 has to be lowered
             in order to supply the extra current.
             The coil L1 has to be a bit bigger though.
             You can probably get away with a hand wound
             toroid with 10 to 20 turns.
             I did a simulation on that circuit with
             1 to 6 white LEDs in parallel, but i put
             one 10 ohm resistor in series with each
             LED. Also, i used a Schottky diode on the
             output with a 5uf output filter capacitor.
             I found full brightness to be easier to
             attain with the diode and output cap.

             The simulation showed that if you can get one
             LED to conduct 20ma ( by adjusting R2 ) then
             you can get 6 LED's to conduct 20ma by
             dividing the value of R2 by 6 and connecting
             5 more LEDs in parallel (with a series 10 ohm
             resistor for each LED).
             The transistors used were 2N4403 PNP and
             2N2222A NPN.
             The only thing i couldnt determine was
             whether or not the 2N2222A transistor
             would get too hot or not. It looked ok
             with 6 LEDs and R2/6, but i would have to
             build the circuit to find out for sure.
             Should work fine for 4 LEDs, with the value
             of R6 for one led divide by 4.
             Replacing the 2N2222A transistor with a
             2N3055 general purpose audio transistor
             and the circuit doesnt work at all.
             I suspect its because the transistor gain
             and switching speed arent enough.
             Because of this, i would think other high
             powered general purpose transistors wont work
             either (because of low gain), unless you
             get a special type that has high gain, fast
             switching speed, and fairly low Vsat.
             Zetex makes some some good transistors, but i
             havent been able to get ahold of any yet.

             Regulation isnt all that good, so brightness
             diminishes as battery voltage falls.

             I ran a simulation on another circuit which is
             very similar but has feedback. The only drawback
             is that it takes 2 more transistors to provide
             the regulation circuitry, and a few more resistors
             and one more capacitor. Im not really sure
             the extra complexity is worth it.
             I'll have to build this circuit up to make sure
             it behaves like the simulation did also.

             Can you get LM339 ic's? These chips can be
             quite useful in these kinds of apps.
             They are dirt cheap too :-)
             The data sheet says they will work down to
             2 volts also.
             Im thinking of making a circuit up using
             one of these too, with super regulation
             and multiple leds etc.
             Zetex has some specialized chips out just for white leds,
             but again i would have to get ahold of some before
             i could use them. The other drawback is the
             best one only comes in surface mount package.

             I did get to try out a MAX756 ic chip, and its
             pretty good for 2 cell apps, but is quite a pain
             in one cell apps even though the data sheet says
             it works down to 0.7 volts. With only one AA cell,
             you can only really drive 1 LED because of the
             very unusual way the chip works. Yeah it 'works'
             down to 0.7 volts or so, but at hardly any
             output current.
             For 2 cell apps though, you could probably drive
             20 leds or something. Once you get about
             2 volts input, the chip runs smoothly.
             Below 1.2 the output current gets very
             skimpy. Unfortunately, there is also no
             apparent way to fool the chip with a
             pre-regulator/booster either, as the same pin
             that is used for the power supply input is
             also the voltage feedback pin! It bootstraps
             the MOSFET drive voltage for 'normal'
             mosfet drive once the output voltage ramps up
             to par. The only trouble is, if you have a
             significant load on the output, it never
             ramps up to par :-) so you never see
             the benefit of the bootstraped drive voltage.
             In any case, for one cell apps i would stay
             away from this chip except for driving only one led.
             Even then, i would go with the MAX757, which allows
             for output voltage adjustment with two resistors.
             (Oh yeah, the MAX756 has two preset output settings:
             either 3.3 volts or 5.0 volts, so you also cant
             fool it into current feedback mode of operation
             either :-( Instead, you have to settle for setting
             it up at 5 volts and use a current limiting resistor.)

             The nice thing about discreet transistors is you can
             use them down to about 1 volt any way you care too :-)

             Summing up:

             If your in a hurry for a simple circuit to drive 4 leds
             then use the brinkmann circuit with resistors and Schottky
             etc as above (two cell app) and home wound coil.

             If you can wait a little and you dont mind using
             4 transistors i'll be working on the regulator version,
             which provides 20ma to 4 LED's (probably 6) from an
             input of 2 to 3 volts or so (probably regulates down
             to 1.5 volts input and can take up to 4.5 volts input).

             Good luck with your LED circuits :-)