AN1627 Freescale Semiconductor / Motorola, AN1627 Datasheet - Page 4

• Manufacturer Part Number: AN1627
• Description: Low Cost High Efficiency Sensorless Drive for Brushless dc Motor Using MC68HC (7)05MC4
• Manufacturer: Freescale Semiconductor / Motorola

2.1.1
The following set of equations is valid for the presented topology:
where:
The equations (EQ 2-2.) can be written taking into account the motor phase resistance and the
inductance. The mutual inductance between the two motor phase windings can be neglected because
it is very small and has no significant effect. In other words, the motor must be designed this way,
otherwise sensing of the back-EMF would be almost impossible.
where:
The internal torque of the motor itself is defined as:
where:
MOTOROLA
4
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are “branch” voltages; the voltages between one power stage output and its virtual zero.
are motor phase winding voltages.
are phase Back-EMF voltages induced in the stator winding.
is the voltage between the central point of the star and the power stage virtual zero
are phase currents
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Mathematical Model
motor phase resistance, inductance
internal motor torque (no mechanical losses)
rotor speed, rotor position
magnetic flux of phase winding x
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Freescale Semiconductor, Inc.
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(EQ 2-1.)
(EQ 2-2.)
(EQ 2-3.)
REV 0.2
AN1627