Trying to understand why InstaSPIN-BLDC works so much better under conditions where the speed is changing. Shown here on this particular slide is an example of one waveform say phase A and the commutation boundaries are actually shown by the vertical dash lines. Next is the zero crossing point, this is where to start integrating and the area to integrate is shown by the blue triangle. This area is integrated over time and the waveform will look like this shown below. Next set the threshold voltage, the negative threshold voltage to exactly the right value; the flux will reach the threshold value at exactly the right time at which point it will commutate. The designer said earlier that if one integrates voltage, it will be flux. That means the voltage must be the derivative of flux. Actually it is the partial change of flux with respect to angle times the change of angle with respect to time. In other words, it has been busted up into two different variables. One variable is machine-dependent and that is equivalent to the back-EMF constant of the machine but d(theta)/dt, this is actually the speed that the motor is going at. In this particular example, the designer wants to slow the motor down by 1/6th, that means that the amplitude will be 1/6th the amplitude of what it was previously. One will also notice that since the motor is running six times slower now, that just one commutation interval is exactly the same as what six commutation intervals were earlier. Now the area to integrate is the red triangle as shown here. What is interesting is that the area under the curve does not change. In other words, this is the same triangle that the designer had before with the faster waveform. What is lost is amplitude and what is gained is time. So, even though the Y axis got smaller, the X axis got larger by exactly the same proportion. So, what that means is it is going to take longer to create that waveform, the designer is still going to hit the threshold at exactly the time when it was supposed to be commutating. Also notice here that if the speed is changing in real time during the time that is integrated, that is affecting the back-EMF waveform and that will be reflected in the flux waveform so that it is still guaranteed to commutate at the right time even if the speed is changing dynamically.