The large capacitor tends to prefer squegging over single pulses; it has to do with the relative time constants of the inductor, drive current and hFE, and bias resistor and bypass capacitor. When the bypass cap is adequately discharged during a cycle, it will tend to do single pulses. A smaller value then gives shorter pulses, and larger values give burst operation.
I find base resistance tends to impair function; it seems excessively strong base drive isn't a problem after all, meanwhile maintaining drive strength until end of pulse seems more beneficial. This may have a different priority for squegging (burst mode) operation, not sure.
Squegging can be somewhat discouraged by damping the output network. Consider: if the base capacitor doesn't discharge much during a cycle, then when the flyback pulse finishes, the voltage rings down, overshooting somewhat. And if this overshoot turns on the transistor, it latches on and goes for another cycle, and so on until the capacitor is too discharged to start up after that last cycle. Hmm, ah yes, the series limiting resistor should encourage that then -- by limiting base current, at the expense of weaker drive (but if drive strength is adequate, given desired load and pulse width, it should still be fine).
I forget what the transformer ratio on mine was, might've been a bit shy of 1:1. It's a powder core, something like 1uH total, maybe even less, I'm not sure. You certainly need more than a few hundred mV at the base to get solid switching action, and a few volts seems optimal. Over 7Vpp will cause avalanche and runaway operation (avalanche provides bias current independent of the pull-up -- something like a diesel engine ingesting its own oil!).
Looks like you got a powder core as well (yellow-white?) so that will tend to be well damped, and should be free from saturation. (A common mistake is using something like a ferrite bead; the saturation current even for just a few turns, may be too low to be practical even for a 20mA LED.) Downside is the poor efficiency. Ideal is higher Q material, or gapped ferrite. Rewinding a ferrite spool type inductor is a reasonable [amateur] option.
My flashlight BTW does something like 60% efficiency, between 1.5V input, and like 3.6V output -- as measured with a schottky diode and filter cap instead of the LED. Which has more capacitance, so there will be some difference in switching behavior, but likely still representative.
Tim
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