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How to identify whether given motor is permanent magnet AC ie sinusoidal back emf or permanent magnet trapezoidal back emf motor. I am confused as motor I am having seems sinusoidal back emf and control strategies in literature for the two are different

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Sinusoidal and trapezoidal back-emf's on brushless motors are idealizations and on real motors you will never find either one. Generally, when a motor with a trapezoidal-like back-emf is driven with rectangular pulse currents, it is referred to as a BLDC. Also, generally, when a motor with a sinusoidal-like back-emf is driven with sinusoidal currents, it is referred to as a BLAC. However, you can drive motors with trapezoidal-like back-emf's with sinusoidal currents and motors with sinusoidal-like back-emf's with rectangular currents. I see the former (sinusoidal back-emf with rectangular currents) quite often. Duane Hanselman's book Brushless Motors: Magnetic Design, Performance, and Control has a good discussion of all this and the back of his book shows what the line-to-line and phase back-emf's should look like for various motor topologies. Hendershot's Design of Brushless Permanent-Magnet Machines also has a useful discussion of this topic.

With those caveats in mind, in order to identify the back-emf shape you will need to back-drive your motor with another motor and then observe the back-emf waveform by measuring it with an oscilloscope across two of the leads. The shape you see is your back-emf.

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