That's assuming you can get the volts up, of course. It only solves the problem of "not enough amps once the voltage is boosted."
uC's run on microamps these days, you use whatever power is left to run the charge pump until you have enough stored energy to run a few milliamps through the LED for a fraction of a second or so.
Make the "snap-action" symmetrical, like a toggle switch, so that both rising and falling tides generate electricity. It may be possible to do it with just one float, and a spring-loaded detent mechanism.
Sadly, output from a PM motor being used as a generator is DC. 300 millivolts DC has low opportunities for doing much of anything with electronics.
If whoever needs to make use of such low voltage DC has access to germanium transistors, then I would advise doing web searching (Google or the like) for boost converters used with solar cells and using germanium transistors. Sadly here, geranium semiconductors are a lot more obsolete than putting solar cells in series for more voltage.
If the PM motor has its DC output unsteady enough, then it could be fed into a neon sign transformer, and the output from the neon sign transformer can go through a bridge rectifier (maybe preferably made of Schottky diodes) to feed an LED that is efficient at low currents - such as many blue, blue-green and non-yellowish-green ones with nominal wavelength 468 to 529 nm and nominal voltage drop 3.1 to 3.6 volts. Also with characterizing current (current used for most datasheet figures) no more than 20 mA!
Beyond that, can any way of periodically mechanically interrupting the current be worked in? If so, then it gets easier for a step-up transformer that this current goes through to produce something that is useful to power a higher-efficiency LED (through a bridge rectifier). Transformers should be smaller here - maybe run backwards a 6.3V 300 mA "filament transformer".
Other than that, how about upscaling the project to put 10 or 16 of these PM motors in series? That may not only provide sufficient voltage after a bridge rectifier with Schottky diodes (such as 30V 1 amp rectifier duty ones) but maybe also so much current as to consider "high power" LEDs with ratings and characterization currents around 350 mA to an amp. Those actually do well at 50 mA! When current is around or under 50 mA, don't worry about heatsinking! If current is near or over 40 mA, use high power LEDs rather than low power ones - my favorite most-efficient non-red non-orange "low power" LEDs have efficiency maximized at 2-6 mA or so!
Has anyone done the math to calculate the actual power available from such a device? You can't get a force greater than the displacement of your float, and the distance of travel is the tide height. Unless your float is just a few cm thin, you'll only get that each twelve hours. Yes, I know that the tide both rises and falls in that time, but you need a very broad flat float if you're going to generate power in both directions.
The tidal flow varies from 0.5m to 1.5m, averaged across the globe. If your tide heights are 3x that, you can generate an average power of (displacement*3m/12 hours) = 0.68 watts per tonne of displacement. Got some spare 50,000 tonne ships to use as floats? You'll get 34KW out of each one. In the meantime, each will probably lose more steel to rust than the energy in the coal used to make that steel.
Not very impressive - I'm not surprised you're having trouble getting enough voltage from your toy. But thanks for playing...
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