Have you tried a large capacity electrolytic ? 10,000 uF@5V should be small
enough and a smaller one yet may be enough. You only need 35mJ of energy or so.
The 10,000 uF cap will contain 45mJ, and you need much less than that, probably
4700uF@5V should be enough (series scheme). A simple 'capacitor voltage
doubling' single pulse scheme should be plenty enough to run your load for its
required 20msec. Even in ones it should be about 80 cents in NA, and much less
elsewhere.

Peter


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