Chapter 3

Simulating BLDC Motors to Observe Back-EMF Profile

BLDC motors and PMSMs are similarly structured where both have permanent magnets in the rotor and are defined as synchronous motors. In a synchronous motor, the rotor is synchronized with the stator magnetic field, i.e., the rotor turns at the same speed as the stator magnetic field.

Their key difference is the shape of their back EMF (electromotive force). When electrical motors are rotated, they act as generators. In other words, a voltage is induced in the stator that opposes the driving voltage of the motor. Back EMF is an important characteristic of a motor as its shape dictates the kind of algorithm required to optimally control it.

Due to their design, BLDC motors have a trapezoidal back EMF shape and are commonly controlled by trapezoidal commutation.


  • Trapezoidal Back EMF
  • Controlled by trapezoidal commutation
Trapezoidal back EMF shape

PMSMs are controlled by field-oriented control because their back EMF has a sinusoidal shape.


  • Sinusoidal Back EMF
  • Controlled by field-oriented control
Sinusoidal back EMF shape

Sometimes the terms PMSM and BLDC are used interchangeably among the motor control community, which may cause confusion about their back EMF profiles. For this discussion, BLDC motors will strictly be machines with trapezoidal back EMF.

An easy way to observe back-EMF shape of a motor modeled in Simscape Electrical™ is to simulate it.

Model of a brushless DC motor and its simulated trapezoidal back EMF

Here you can see the simulation of a single pole-pair BLDC with open-circuit terminals, meaning no current to the coils. If you apply torque to turn the rotor the motor will act like a generator. You can watch how the shape of its back EMF is determined by measuring the voltage at phase A over time. The voltage scope shows that the back EMF of the BLDC motor has a trapezoidal shape, which includes regions where the voltage remains flat.

Check out the following tutorial to learn how you can model and simulate a BLDC motor with Simscape Electrical as seen in the image above.