# Back EMF and why its a nightmare for speed controllers.

Back EMF and why we HATE it!

When a motor is running, it generates a voltage called back-EMF, or counter-electromotive force. This voltage is caused by the interaction of the magnetic fields within the motor and the current flowing through the windings. Back-EMF can be a problem in large motors, like a 100A brushed motor, because it can cause the voltage across the motor to exceed the safe operating range, potentially damaging the windings or the controller.

The back-EMF voltage spike can be calculated using the following equation: E = Ldi/dt where E is the back-EMF voltage, L is the inductance of the motor, i is the current, and dt is the rate of change of current. As you can see from the equation, the back-EMF voltage spike is directly proportional to the inductance of the motor and the rate of change of current.

For example, let's say we have a 100A motor with an inductance of 0.1H and the current changes from 0A to 100A in 1 microsecond. The back-EMF voltage spike would be: E = (0.1H)(100A)/(1x10^-6s) = 10,000V. This is a very high voltage spike that can damage the motor or the controller if not properly controlled.

It's worth noting that the back-EMF voltage spike can vary depending on the load conditions and the type of motor, brush or brushless.

In summary, back-EMF voltage spike is a voltage that is generated in an inductive motor when the motor is running. It can cause damage to the motor or the controller if not properly controlled. The back-EMF voltage spike can be calculated using the equation E = Ldi/dt and it is directly proportional to the inductance of the motor and the rate of change of current. High-performance motors like servo or stepper motor have a more complex control system to handle the back-EMF voltage spike.