Abstract: A commutation circuit for a brushless D.C. motor which circuit maximizes motor torque and motor efficiency for all ranges of motor load and speed, regardless of the connecting and conducting method of the phase coil, by optimizing the commutation pulses from the commutation encoder of the motor. Optimization is accomplished by advancing the commutation pulses to an angle corresponding to the inverse tangent function of the motor velocity and the load current, and by optimizing the commutation pulse width.