Motorola M68HC08 manual Stator Winding Equations, Indirect Back EMF Sensing

Freescale Semiconductor, Inc.

Freescale Semiconductor, Inc.

BLDC Motor Control

Brushless DC Motor Control Theory

3.2.4.1 Stator Winding Equations

The BLDC motor is usually very symmetrical. All phase resistances, phase and mutual inductances, flux-linkages can be thought of as equal to, or as a function of the position θ with a 120° displacement.

The electrical BLDC motor model then consists of a set of the following stator voltage equations (EQ 3-1.).

uSa		= RS	iSa		+	d	ΨSa		(EQ 3-1.)
u			i				Ψ
	Sb			Sb		dt		Sb
uSc			iSc				ΨSc

The task of this section is to explain the background of the back-EMF sensing and to demonstrate how the zero crossing events can be detected. Parasitic effects that negatively influence the back-EMF detection are discussed and their nature analyzed.

3.2.4.2 Indirect Back EMF Sensing

Let us assume a usual situation, where the BLDC motor is driven in six-step commutation mode using PWM technique, where both top and bottom switches in the diagonal are controlled using the same signal (so called “hard switching PWM” technique). The motor phases A and B are powered, and phase C is free, having no current. So the phase C can be used to sense the back-EMF voltage. This is described by the following conditions:

			SAb, SBt ← PWM
	u			−1	, u		= ±	1
		VA		= +--u		VB		--u	d
				2 d				2			(EQ 3-2.)
	iSa = –iSb= i, diSa = –diSb= di
				iSc = 0, diSc = 0
	ubackEMF a + ubackEMF b + ubackEMF c = 0
The branch voltage uVc can be calculated using the above conditions,
uVC	1		c						di		(EQ 3-3.)
	= uSc – --		∑ ubackEMF x + (Lac – Lbc)---- – uVC
	3								dt
			x = a
DRM028 — Rev 0									Designer Reference Manual
MOTOROLA	BLDC Motor Control									29
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