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I would like to generate 100V from one LiPo battery at a output current of 100 mA.

There are circuits with transformers but there are a bit bulky and expensive. The MCP1663 can generate 32V from 3.3V with one 10 uH coil and an output diode. Is there a nice way to build a cascade out of three MCP1663 where each output ground is connected with the output voltage of the lower stage to charge one common capacitor to 100V which can then draw 100 mA. Since there is no isolation to the input stage, what could be the problem?

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100V @ 100mA is 10W.

This will be 3 amps drawn from your LiPo.

You could use a boost converter, but these work best when the output/input ratio is not too high. In your case, the ratio is very high, so the efficiency of a boost converter will be rather low, which will compromise battery life.

A transformer-based converter, on the other hand, will have a much better efficiency at this output/input ratio.

You could use a push-pull or flyback converter.

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The MCP1663 has a max working input voltage of 36 volts and, because this is the rating on the internal switching transistor this is also the maximum output voltage that could be produced so no, there is no benefit from cascading even two devices.

Neither can you tee-off a second stage from the first stage by connecting the 2nd stage ground to the first stage output - how would the 2nd stage receive DC power to its input? No, this is a dead-end idea in my opinion.

Look for a step-up flyback converter - it will use a small transformer (well, actually a coupled inductor) to produce the 100 volts. Here's a flyback design that can produce 300 volts from 6 volts so maybe it can be adapted to produce 100 volts from a LiPo: -

enter image description here

But be prepared to have to use an output transistor in order to drive sufficient current into the primary. This will also be true of the next design.

There is also this circuit worthy of investigation/modification: -

enter image description here

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