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I'm looking for a circuit diagram that uses an input of 60Hz, and produces a variable frequency output. The circuit would have to be disigned for a minimum of .77A and 120V. If anybody can help, I'd sure appreciate it.
Most AC motors are frequency dependent - the rotational speed is locked into the frequency of the supply. There are a few "universal" motors where input voltage can be varied for speed control but I do not recall if "shaded" pole is one of them. Your thinking is probably correct, that you need a variable frequency drive.
Not many people home brew this sort of thing however that doesn't mean it can't be done. The motor characteristics and the motor load significantly impact the design. Commercial drives are fairly inexpensive and depending on your needs, might be the way to go. As a point of reference, I was told by a dealer that I can buy a 3 hp drive from him for $350 but was also reminded that it is bare - no reactors, bypass relays, etc. However expensive this might seem in my own mind it's fairly inexpensive given the complexities and in the end it will work. The parts alone for even the most basic design aren't free.
On a smaller motor one approach might be to use an audio amp module and drive it with a variable low frequency oscillator - paying attention to output voltage, current, etc. The output voltage could be boosted with a transformer. While crude this might be a place to start.
Good luck, let us know more about the application, the motor, etc.