Back EMF

Motor theory states that in every motor, a voltage is applied to the stator in order to create an electromagnetic force to rotate the motor. In the case of brushed motors, the supply voltage from a DC source is given directly through the commutative “brushes”. However, brushless motors are more complicated and rely on current switching through different windings in order to rotate the motors.

Back EMF is the electromotive force which occurs as the brushless motor turns. When the coil of a motor is turned, magnetic flux (defined as the rate of a magnetic field flowing through a conductor’s cross sectional area) changes and an EMF is induced. The motor thus acts as a generator whenever the coil rotates. This will happen whether the shaft is turned by an external input, or by the action of the motor itself. Therefore - when a motor is doing work and the shaft is turning, an EMF is generated. By Lenz’s law, the EMF opposes any change, so that the input EMF that powers the motor will be opposed by the motor’s self generated EMF, called the back EMF of the motor.

Open

Back EMF is the generator output of the motor, and so it is proportional to the motor’s angular velocity. It is zero when the motor is first turned on, meaning that the coil receives the full driving voltage and the motor draws maximum current when it is on but not turning. As the motor turns faster and faster, the back EMF grows, always opposing the driving EMF, and reduces the voltage across the coil and the amount of current it draws.

BLDC Motors

Manufacturers of BLDC motors specify a parameter as the back EMF constant that can be used to estimate the back EMF for a given speed. The potential across a winding can be calculated by subtracting the back EMF value from the supply voltage. Motors are designed such that when they are running at rated speed, the potential difference between the back EMF and supply voltage will cause the motor to draw the rated current and deliver the rated torque.

Driving the motor beyond the rated speed increases the back EMF substantially, decreasing the potential difference across the windings, and in turn reducing current and lowering torque. Pushing the motor faster still would cause back EMF (plus motor losses) to exactly equal the supply voltage - at which point the current and torque would both equal zero.

Back EMF can reduce a motor’s torque, and is thus often considered a disadvantage. However, in the case of BLDC motor’s it can be used to our benefit - knowing the back EMF can be used to measure and control the speed of the motor, thus eliminating the need for any sensors (hall effect) that are needed to switch current across the different windings.