# Why is back emf of bldc trapezoidal?

I am trying to understand why would the back emf in bldc be trapezoidal. Lets consider a simple motor with two stator coils placed opposite to each other. Lets say a bar magnet is kept as a rotor. If i manually crank the bar magnet and rotate it, then the back emf observed seems to be trapezoidal as per my reading. However, i have an alternate thought. If voltage induced in a coil is supposed to be proportional to rate of change of magnetic flux linkage, then when the bar magnet pole sweeps a coil area during its rotation, this should result in a constant voltage in the coil since field in coil due to magnet increases linearly as magnet pole approaches the coil. And when the pole moves away from the coil, as magnetic flux linkage decreases linearly, there would be negative voltage. Once bar magnet pole passes the coil area completely , then there will be no change in magnetic field in the coil hence zero bemf. This results in a positive and negative pulse followed by zero voltage bemf. Why does the bldc emf not behave the way i mentioned?

• I can't explain to you why the physical design of the motor produces a trapezoidal BEMF, but I can tell you that it was specifically designed to do so in order to run efficiently with square drive waveforms (because those are easy to produce since you just switch transistors on/off). If you expected your motor to be driven with a sinusoidal waveform, you would design it to have a sinusoidal BEMF. That's my understanding of things anyways, someone correct me if I'm wrong. – DKNguyen Mar 19 at 19:30
• Well, real rotors have a continuous stream of magnets. So the magnetic field is constantly alternating N, S, N, S, etc. So there is no such thing as "when the pole moves away from the coil." There is always another pole. It so happens that what you call a positive pulse is more or less a half-sine wave. The negative pulse is a negative half sine wave. Taken together, you end up with a continuous sine wave. Personally, the motors whose EMF I have looked at have not been very trapezoidal. They appear sinusoidal. Not sure how subtle the difference is between "trapezoidal" and "sinusoidal". – mkeith Mar 19 at 19:37
• Trapezoidal waveforms are due to slew rate distortion. The 'Q' of the windings comes into play, as the coils DC resistance is a stronger factor during back EMF then when switched ON. Power supply capacitors, clamping diodes and load resistors can affect back EMF. – Sparky256 Mar 19 at 20:07