well, no the signal comming from the stator is different than the signal put into the rotor.
you can pulse the rotor with square waves and the stator will show some form of sine waves depending on the electronics used to pulse the rotor. 98% of the circuits on the internet is single pulses into the rotor, so if you was to hook a timer and fet to the rotor what you would see on the oscilloscope to the rotor would be a half sine wave then it would drop like a discharg wave. it would look like a hill on the left side and a slide on the right. this is the 98% single sided square wave pulse.
this is because the square wave will charge the coil, and coils have resistance,, therfor it takes time to charge a coil to its peak. This is where you see the half sine wave, now when the pulse is removed you will see a discharge wave from the rotor, it looks like a slide, kinda like a hook. On the stators output you will always see full sine waves.
Single phase is single phase, when you use the timer with a fet to pulse a rotor you are pulsing at half phase, not even 1 phase.
what you would see on the oscilloscope when on the rotor is the timer making half phase wich replicates the ("first half of the sine wave"), the ("fet will switch off") and the rotor will create ("back emf"), the ("right hand side of the sine wave"). but its not a sine wave, ("its a dishcarge wave,") from the rotor discharging.
the alternator has a 3 phase output, even if its full wave rectified, so if you was to hook a oscilloscope to the stator then you will see 3 waves. each wave rides ontop of the other, Google 3 phase sine wave to find a picture of what this looks like. There will be a time when you get square waves from the stator with 3 phase DC harmonics on the top. confusing enough?
