It uses time-modulated square waves to turn the output FETs on and off to generate a current sine wave in the three windings. The base frequency of the drive pulses will be much higher than those used for square wave controllers.
I can offer a brief, crude explanation, but the real world is much more complex, so please do your own thinking. Here goes:
Current rises with time when a voltage square wave is applied to an inductor.
By making a voltage square wave very narrow, full current cannot be attained during the on time. If we make the pulse duration n even a little longer, a bit more current will flow, and if we leave it on for a longer time, full current can be obtained. Square wave controllers make voltage pulses at least long enough to allow full current to be obtained, and also make the pulses longer, so full current is sent thru the winding for a longer time. The key is that full current is applied with each pulse.
If we make the pulse very narrow, say 1/10th of the time it would take the current to rise to its full value, a smaller current peak will be obtained. If the next pulse is 1/8 , then a bit higher current will be reached. As we keep increases the time the pulse is on, we will eventually reach full current. So imagine generating a series of 100 pulses of differing duration. We can then control the current to vary between none and full scale, and also from full scale back to none. The motor winding will think it is being driven by a sine wave, even tho we are using voltage square waves to turn the FETs on and off.
Having three phases makes it simpler and more difficult at the same time to make such a wave......
I want to say again, that is not quite how it really works but it is close enough. Just don't tell your Electrical Engineering Professor I said he was wrong....
I hope that helps.
TTFN,
Dennis