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Since you haven't had an answer yet (I have been watching!), I have looked for a single phase in, single phase out VFD circuit before and never found one. I take it that is what you want? (Single phase in, three phase out are common).
It is possible to build one without too much effort, the theory is simple, but when I've researched it I've also read that single phase motors really do not like being slowed down. They tend to easily stall, or not start, if not run at nearly their rated voltage/frequency. That is what I read, anyway. So, I never got around to trying to make one because there seemed no point.
If you reduce the 3 phase bridge of a 3-phase inverter to a H-bridge, you have a single phase inverter. That doesn't you safe much effort, so most people will use a regular 3-phase inverter for single phase.
Technically, the applications for single phase inverters are rather limited, for the reasons explained by FoxyRick.
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