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Mutual capacitance model, Bldc motor control, Freescale semiconductor, inc – Motorola M68HC08 User Manual

Page 34

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BLDC Motor Control

Designer Reference Manual

DRM028 — Rev 0

34

BLDC Motor Control

MOTOROLA

Figure 3-9. Mutual Capacitance Model

Let us focus on the situation when the motor phase A is switched from
negative dc-bus rail to positive, and the phase B is switched from
positive to negative. This is described by these conditions

(EQ 3-8.)

:

(EQ 3-8.)

The voltage that disturbs the back-EMF sensing, utilizing the free (not
powered) motor phase C, can be calculated based the equation:

(EQ 3-9.)

The final expression for disturbing voltage can be found as follows:

(EQ 3-10.)

NOTE:

(EQ 3-10.)

expresses the fact that only the unbalance of the mutual

capacitance (not the capacitance itself) disturbs the back-EMF sensing.
When both capacities are equal (they are balanced), the disturbances
disappear. This is demonstrated in

Figure 3-10

and

Figure 3-11

.

u

Ccb

B

C

A

RC

C

C

C

RC

RC

u /2

d

=

+

-

u /2

d

=

+

-

u

Cba

I

d0

S

At

S

Bt

S

Ab

S

Bb

I

Sb

i

C

i

Cab

i

C

u

Cac

u

VC Cap

u

VB

u

VA

S

Ab

S

Bt

,

PWM

u

VA

1
2

---u

d

1
2

---u

d

=

u

VB

1
2

---u

d

1
2

---u

d

=

,

i

Cac

i

Ccb

i

C

=

=

u

VC Cap

1
2

--- u

Ccb

u

Cac

2R

C

+

+

(

)

u

Ccb

R

C

+

(

)

1
2

--- u

Cac

u

Ccb

(

)

=

=

u

VC Cap

1
2

---

1

C

ac

--------

1

C

cb

--------

 i

C

t

d

1
2

---

C

cb

C

ac

C

cb

C

ac

----------------------

 i

C

t

d

=

=

F

re

e

sc

a

le

S

e

m

ic

o

n

d

u

c

to

r,

I

Freescale Semiconductor, Inc.

For More Information On This Product,

Go to: www.freescale.com

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