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AN857

Brushless DC Motor Control Made Easy

Microchip Technology 

AN857

The BEMF generated by the B and C coils in tandem,

as shown in Figure 7, can be expressed as shown in

Equation 7.

EQUATION 7:

BEMFBC = BBEMF - CBEMF

The sign reversal of CBEMF is due to moving the refer-

ence point from the common connection to ground.

Recall that there are six drive phases in one electrical

revolution. Each drive phase occurs +/- 30 degrees

around the peak back EMF of the two motor windings

being driven during that phase. At full speed the

applied DC voltage is equivalent to the RMS BEMF

voltage in that 60 degree range. In terms of the peak

BEMF generated by any one winding, the RMS BEMF

voltage across two of the windings can be expressed

as shown in Equation 8.

EQUATION 8:

BEMFRMS =



2

—3

2

sin



()

-

sin







-

—23d 

6

BEMFRMS =

3234







BEMFRMS = 1.6554

We will use this result to normalize the BEMF diagrams

presented later, but first lets consider the expected

BEMF at the undriven motor terminal.

Since the applied voltage is pulse-width modulated, the

drive alternates between on and off throughout the

phase time. The BEMF, relative to ground, seen at the

A terminal when the drive is on, can be expressed as

shown in Equation 9.

EQUATION 9:

BEMFA =

[V - (BBEMF - CBEMF )]R

2R

- C BEMF + ABEMF

BEMFA

=

V

-

BBEMF

+

CBEMF

2

- CBEMF + ABEMF

Notice that the winding resistance cancels out, so

resistive voltage drop, due to motor torque load, is not

a factor when measuring BEMF.

The BEMF, relative to ground, seen at the A terminal

when the drive is off can be expressed as shown in

Equation 10.

EQUATION 10:

BEMFA = ABEMF - CBEMF

DS00857B-page 10

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