## Sunday, March 14, 2010

### Waveform of a Brushless DC Motor

Brushless DC Motor COMMUTATION SEQUENCE

Figure shows an example of Hall sensor signals with
respect to back EMF and the phase current. Figure 8
shows the switching sequence that should be followed
with respect to the Hall sensors. The sequence numbers
on Figure correspond to the numbers given in Figure 8.
Every 60 electrical degrees of rotation, one of the Hall
sensors changes the state. Given this, it takes six steps
to complete an electrical cycle. In synchronous, with
every 60 electrical degrees, the phase current switching
should be updated. However, one electrical cycle
may not correspond to a complete mechanical revolution
of the rotor. The number of electrical cycles to be
repeated to complete a mechanical rotation is determined
by the rotor pole pairs. For each rotor pole pairs,
one electrical cycle is completed. So, the number of
electrical cycles/rotations equals the rotor pole pairs.

BLDC Motor Waveforms
Figure is a graphical representation of the BEMF formulas
computed over one electrical revolution. To
avoid clutter, only the terminal A waveform, as would
be observed on a oscilloscope is displayed and is
denoted as BEMF(drive on). The terminal A waveform
is flattened at the top and bottom because at those
points the terminal is connected to the drive voltage or
ground. The sinusoidal waveforms are the individual
coil BEMFs relative to the coil common connection
point. The 60 degree sinusoidal humps are the BEMFs
of the driven coil pairs relative to ground. The entire
graph has been normalized to the RMS value of the coil
pair BEMFs.

Notice that the BEMF(drive on) waveform is fairly linear
and passes through a voltage that is exactly half of the
applied voltage at precisely 60 degrees which coincides
with the zero crossing of the coil A BEMF waveform.
This implies that we can determine the rotor
electrical position by detecting when the open terminal
voltage equals half the applied voltage.

BEMF waveforms and the zero-crossing points
The fact that one of the windings is not energized during each sector is an important characteristic of six-step control that allows for the use of a sensorless control algorithm. When a BLDC motor rotates, each winding generates BEMF, which opposes the main voltage supplied to the windings according to Lenz’s Law. The polarity of this BEMF is in the opposite direction of the energizing voltage. Figure 2, below, shows ideal BEMF waveforms and the zero-crossing points.

Waveform of a Brushless DC Motor ESC video
E-flite EFLA311, 20 A ESC driving an E-flite 450 motor.