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             Jeff:
             I couldnt agree with everything in your post and im not sure
             what you meant by
             some things so i rewrote a few things with the hope that this
             would help clear
             up some issues. Also, keep in mind this
             is in reference to the Brinkmann circuit,
             not the circuit in PeLu's post ok?

             As you probably already know, in these circuits the transistor
             acts more or less
             like a switch. When current flows base to emitter, it causes the
             collector
             emitter resistance to fall to a very low value. This decrease in
             resistance
             makes the collector emitter look like the two connections of a
             simple
             mechanical switch that is controlled by the base current. When
             base current
             flows, the switch is turned on. When base current stops flowing,
             the switch
             is turned off. There is an exception to this however, and that is if
             the
             current through the collector emitter rises high enough when the
             transistor
             is turned "on", the transistor will appear to turn off even though
             base current
             still flows. This action is what starts Q2 turning off.
             The base drive sets the max level of collector emitter current:
             more base drive means the transistor collector emitter current
             will rise to
             a higher value before starting to turn off. This means R2 will
             partly determine
             the operating frequency as well.

             As you probably already also know, when you turn on Q2 you are
             effectively
             putting a dc voltage across the coil, and when this happens
             current starts to
             rise in the coil according to:

             i=v*t/L
             where
             i is current(ramping up)
             v is voltage
             t is the voltage pulse time
             L is inductance

             This of course means the longer the pulse time, the higher the
             current ramps up to.
             The current ramps up untill the Q2 transistor can no longer stay
             turned on,
             and then it starts to turn off. When it turns off, the voltage
             across the
             inductor suddenly rises because it tries to keep the same current
             flowing
             through the transistor. Since the transistor resistance is
             increasing at this
             time, the voltage keeps increasing untill it reaches the level at
             which the
             LED first turns on, and then the LED resistance starts to limit
             the voltage
             that the inductor will rise up to. Feedback though the cap turns
             off the two
             transistors so that the only resistance left that absorbs L's
             energy is now the LED.
             The voltage is thus clamped by the LED.
             The initial current is about the same as that which was flowing
             before the
             transistor just started to turn off, only somewhat lower because
             the transistor
             does absorb some energy while turning off. The current then
             ramps down
             as the energy from the inductor dissipates through the LED.

             The reason the voltage can rise across the inductor is because
             one important
             property of an inductor is that it tries to maintain a constant
             current
             (over very short periods of time) by reversing (and raising) its
             own terminal
             voltage when the resistance (Q2 collector emitter junction) in
             series with
             the inductor increases. This occurs because the quickly colapsing
             field in
             the inductor generates a reverse voltage which tends to keep the
             current at
             the same level and flowing in the same direction as it was before
             the
             resistance increased.

             Here is your post with some modifications and some other notes:

             1. Current flows Q1(eb) to ground through R1, and R1 limits the
             current flow.
             2. This causes current flow through Q1(ec), so current starts to
             flow through Q2(be)
             through R2, and R2 limits the current flow through Q2(be).

             3. This causes Q2(ce) to conduct current, so current starts
             flowing
             through L1 which builds up a field in L1's core. As L1 charges,
             more current
             flows though L1 as time goes by. The more time that passes, the
             more current
             flows through L1. As the current rises, Q2(ce) is eventually
             forced out of
             saturation.

             4. Eventually Q2(ce) reaches a level where the Q2(ce) doesnt look
             like a short anymore.
             This happens when Q2 comes out of saturation. When this
             happens, Q2(ce) voltage
             starts to rise. This happens because Q2(be) receives only a small
             current through
             its base resistor. Q2 starts to come out of sat approximately
             when the current
             in the coil exceeds Q2's base current times its beta ( ib * B ).

             5. This eventually breaks the current flow through Q2(ce), and L1
             being an inductor,
             needs a place to dump its stored energy and so it creates a high
             voltage across
             it in a direction that will try to keep the current flowing in the
             same
             direction that it was before Q2(ce) opened up.

             6. Since the voltage shoots up to several volts, its enough to
             turn on the LED.
             Once the LED turns on, current starts to flow through it from
             the inductor.
             The voltage will rise to any level that will keep the current flowing
             through it
             and thats what turns the LED on. Since the inductor had
             received a certain
             amount of energy during its charge, it now dumps that energy
             into the LED.
             Theoretically without considering the max flux density in the coil,
             the voltage
             would rise to any level meaning you could wire 100 LED's in
             series and when
             that inductor "kicks back" (when Q2(ce) opens up) they would all
             light up, but
             because the series voltage would be over 300 volts the pulse
             would only last
             for a very short time, and there would be other practical
             considerations such
             as the voltage rating of the transistor. Considering the max flux
             density
             in the coil is limited in any practical coil, the maximum level of
             voltage
             attainable will be limited by whatever the coil can sustain without
             saturating.

             7. Once Q2 turns off, its collector voltage rises and that is
             coupled to
             the base to Q1 through the capacitor. This turns Q1 off which
             then turns
             Q2 off completely. The capacitor then discharges to ground
             through R1.

             8. Once the cap discharges, Q1 starts to turn back on and the
             cycle repeats.

             Notes:

             a. The time it takes for C1 to discharge and the time it takes for
             Q2 to come out of
             saturation approximately determines the operating frequency.
             b. R1 helps to bias Q1 as an inverter, as well as sets the
             discharge time of the cap.
             R2 sets the current level that the inductor reaches before forcing
             Q2 out of sat.
             c. The energy to light the led comes primarily from the L1 field
             collapse when the circuit opens.
             (Yes, thats true). Without the inductive kick back, the voltage
             couldnt rise higher
             then the battery voltage. This is the main idea behind the boost
             converter as well
             as many other types of converters. The inductor is charged up
             with a constant voltage,
             and when the circuit is opened the inductor generates a high
             voltage which is
             then used to drive a higher voltage device such as an LED.

             Scale up proposals for consideration:

             1. This is what im looking at next. Im going to try to answer the
             question:
             "if we could change anything about the circuit in order to drive
             any number
             of led's, what would be the best changes to make for 1 led, 2
             led's, 3 led's,
             etc." There are going to be some things that are better to
             change then others
             while keeping efficiency in mind. My guess is that something will
             have to
             change about the circuit in order to accommodate a particular
             number of LED's.
             Two leds instead of one means either twice the current(parallel)
             or twice the voltage(series).

             Some of the constraints are:

             1. Keeping the duty cycle reasonably high (close to 50%)
             because the higher
             the duty cycle the higher the overall efficiency due to the true
             nature
             of the current vs illumination curve of the led. 50% duty cycle
             seems to
             be a good tradeoff between getting good efficiency and building a
             practical
             circuit. If you have to bang the LED's with a 10% duty cycle, you
             have
             to raise the pulse current considerably higher then at 50% duty
             cycle
             to get to full brightness, so that would reduce efficiency too
             much.
             Also, a low duty cycle creates a problem in trying to get full
             brightness
             from an LED without going over the manufacturers
             recommended max pulse
             current rating.
             2. Being able to easily modify the circuit to operate on either one
             or two
             alkaline cells, or one or two NiCd cells.
             3. Low parts count.
             4. Very low cost so that it doesnt contribute significanly to the
             cost of
             any flashlight, especially flashlights with only one or two LED's.

             Future ideas:

             1. Being able to modify the circuit to provide a constant current
             through the
             LED's for the full life of the battery. Some people really want this.
             Im not sure which i like better, constant current or allowing the
             brightness to fall off a little as the batteries wear down. The
             falling
             brightness gives you an indication that the batteries are wearing
             down
             rather then have the light suddenly go dim. Im not sure what i
             like
             better, but i would like to provide the option of adding constant
             current
             control if desired.

             Some undesirables:

             1. Dont add a cap in parallel with the LEDs though, because the
             transistor will have
             to discharge it and that will generate unwanted heat as well as
             waste energy.

             2. Also, for driving LED's it should be unnecessary to require a
             Schottkey diode
             in the output circuit, but i wont rule it out completely when more
             then one
             LED can be wired in series. With only one white LED, the lost
             efficiency that
             comes with adding a Schottkey output diode is about 10 percent.
             With two LED's
             wired in series that drops to about 5 percent. With three in
             series that drops
             even lower to 3.33 percent. Of course you can only wire them in
             series with
             a circuit that can provide both the required voltage and current
             to the LED
             at a decent duty cycle.
 

             Good luck with your LED circuits,
             --Al

             --------------------

             LED's vs Bulb's, the battle is on.
 

             This link gives more specs:
             http://www.nteinc.com/Web_pgs/device_list.html

             From what i see there, it looks like the
             NTE11 transistor is a good transistor
             for this kind of circuit :-)
             From what i saw of the 2N3055 transistor,
             the gain is low and so is the frequency,
             so i would rather use another type, unless
             i didnt have anything else laying around.
             It will oscillate but with a much lower
             value of R2 and only at a lower frequency.
             After all, its original app was linear audio,
             not switching. The NTE11 is about 10 times
             better except of course the collector current
             rating is lower (but still plenty high
             enough for this app).

             Oh by the way, five of the most important
             transistor characteristics:
             HFE=dc current gain
             Vceo=max voltage across collector emitter
             IC=max collector current
             FT=transition frequency
             Vsat=collector emitter saturation voltage

             HFE is the current gain in a dc circuit.
             For example, if you have 2ma going into the
             base and 200ma flowing through the collector,
             you have an HFE of 100 because 2ma times 100
             equals 200ma.

             Vceo is just the breakdown voltage of the
             transistor across collector and emitter.
             If you exceed this voltage, the transistor
             will break down and be permanantly damaged.

             IC is just the maximum current that can
             flow through the collector before the
             transistor breaks down. Sometimes there
             are two ratings for this:
             continuous current and max current.
             The continuous current rating is just that,
             while the max current is the max for a pulse
             of current.

             FT is just the ac frequency at which the transistor gain goes
             down to 1. Since
             the gain goes down as frequency goes up,
             at a high enough frequency the transistor
             isnt useable any more because you cant get
             any gain out of it, and thats what makes the
             transistor useful in the first place:-)

             Vsat is just the voltage drop across the
             collector and emitter when the transistor
             is turned fully 'on'. There is usually a
             collector current spec with this (like
             200ma or something) so you know what current
             is flowing through the collector at the time
             the Vsat is spec'd. If you go above this
             current, the vsat goes up too.
             The Vsat spec is important for high efficiency and for app's that
             have to
             work at very low voltage (like 1.5v).
             The lower this spec, the better the transistor, but keep in mind
             most NPN
             transistors like we are using all have
             Vsat below 0.4 volts for currents around
             150ma or so.

             Oh as far as the parts go, i would say if
             you like building these circuits up then
             you should probably get more parts to
             try out. You can get packs of 50 resistors
             with an assortment of values. Do you order
             on the web too?

             Well good luck with your LED circuits,
             and ill be posting more circuits on my
             home page now and then too, along with
             some waveforms.

             --Al