The best bet would be Dickson triplers stacked.
The first one takes it to 36, the next one takes it to about 100, the next one takes it to just about 300. More like 290 I would say depending on the parameters you give the convertors. Can you get by on 290 ? If not then sta ck another one on top but fed from the original 12 or maybe just a doubler off the 36. Caps will not be cheap because they need low ESR and high volta ge rating.
I would not attempt to multiply it all at once but am at a loss to explain exactly why. It just seems the current in the choppers would be too high fo r good efficiency. Though more junctions means more drop, they are not as s ignificant at higher voltages.
For each stage of the convertor, you are talking 4 good power transistors,
4 very good capacitors and 6 low loss diodes, Shottkies in the first stage at least. In the first stage you might try to find something like the 1N609
5, but those do lose at higher currents.
One nice thing about using Dicksons is that the main output filter has very little to do because it is fed with 2 polarities of a square wave, and I m ean a real square wave not some rounded spiked and "rung" out waveform.
However the cost is ridiculous compared to just biting the bullet and using a transformer. Also with a transformer it can have isolated output.
It is so much easier and cheaper just to go to Digikey and find a transform er with a ~1:20 ratio, feed it with a totem pole at its resonant frequency and use a doubler on the output. Use a chopper before the main filter for r egulation, or synchronous rectification if you can handle designing it. (mo re efficient)
At 150 watts that will be a fairly good size transformer and will cost mone y, but still cheaper than the stacked Dicksons. And much less designing, be cause with the Dicksons each stage has to be different. Different outputs, different diodes and different caps, you must choose them all. With this ma ny components you don't want too much overkill. With a transformer you desi gn ONE circuit and call it a a day.
Your call. I like to avoid transformers because they can become unavailable . But sometimes you can't always get what you want.
I just checked Digikey and no suitable transformer is readily available. Wi nd your own. At the right frequency you only need a few turns in the primar y. So 4 turns there and you want 80 turns on the secondary. For a one off i t may be alot of work but handleable. For production forget it, the Chinese probably have something.