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Is it possible to power an AC motor, using alternating positive and negative DC current? I would assume toggling between each at 60hz would work.

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    $\begingroup$ It depends. There's more than one sort of AC motor. If it's a universal motor, you can just use DC. If it's almost anything else, the best you can hope for is that it'll be less efficient and more nasty-sounding. $\endgroup$ – TimWescott Apr 16 at 17:33
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This is possible! The AC motors are designed to run with AC currents so this is not a very good idea. A very popular way to do it is PWM, it basically mimics a sin wave by switching between two states, you need a filter and proper timing to run a single phase AC motor.

Some spacial applications require to run at desired frequencies, so we design a rectifier to gain a DC signal and then turn the rectified signal to an AC signal with desired frequenties(this is not possible without the presence of an AC grid).

A multiphase AC motor needs a rotating field, three sin waves make a very smooth rotating field, however a modulated DC signal can't generate a rotating field as smooth as sin wave no matter how well it mimics the sin wave (think about the harmonics). The results are extra vibrations, arising of recoils between mechanical parts of the motor and introducing harmonics to the AC grid. The motor won't work efficient at all.

I have seen many researches and papers coming out each day, DC drive is yet in development stage.

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