A new cost effective sensorless commutation

644 IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 22, NO. 2, MARCH 2007
A New Cost Effective Sensorless Commutation
Method for Brushless DC Motors Without
Phase Shift Circuit and Neutral Voltage
Cheng-Hu Chen and Ming-Yang Cheng, Member, IEEE
Abstract—This paper presents the analysis, design, and imple-
mentation of a high performance and cost effective sensorless con-
trol scheme for the extensively used brushless dc motors. In an ef-
fort to decrease cost and increase ease of implementation, the com-
mutation signals are obtained without the motor neutral voltage,
multistage analog filters, A/D converters, or the complex digital
phase shift (delay) circuits which are indispensable in the conven-
tional sensorless control algorithms. In the proposed method, in-
stead of detecting the zero crossing point of the nonexcited motor
back electromagnetic force (EMF) or the average motor terminal
to neutral voltage, the commutation signals are extracted directly
from the specific average line to line voltages with simple RC cir-
cuits and comparators. In contrast to conventional methods, the
neutral voltage is not needed; therefore, the commutation signals
are insensitive to the common mode noise. Moreover, the complex
phase shift circuit can be eliminated. As a result, the proposed con-
trol algorithm can be easily interfaced with the cost effective com-
mercial Hall effect sensor based commutation integrated circuits.
Due to its inherent low cost, the proposed control algorithm is par-
ticularly suitable for cost sensitive products such as air purifiers,
air blowers, cooling fans, and related home appliances. Theoret-
ical analysis and experiments are conducted over a wide operating
speed range and different back EMF waveforms to justify the ef-
fectiveness of the proposed method.
Index Terms—Brushless dc motor (BLDCM), neutral voltage,
phase shift circuit, sensorless control.
I. INTRODUCTION
DURING the last two decades, a lot of research on sensor-
less control techniques for brushless dc motors (BLDCMs)
have been conducted. This research can be divided into four cat-
egories [1]–[3]. 1) Detection of the zero crossing point (ZCP)
of the motor terminal to neutral voltage with a precise phase
shift circuit [4]–[7]. 2) Back electromagnetic force (EMF) in-
tegration method [8]. 3) Sensing of the third harmonic of the
back EMF [9]. 4) Detection of freewheeling diode conduction
and related extended strategies [10]. Among the various tech-
niques, the back EMF zero crossing detection method is the
most popular. In fact, many commercial sensorless integrated
Manuscript received December 13, 2005; revised May 4, 2006. This paper
was presented in part at the IEEE PEDS’05,Kuala Lumpur, Malaysia, Nov.
28–Dec. 1, 2005. This work was supported by the Electric Motor Technology
Center, National Cheng Kung University. Recommended for publication by As-
sociate Editor M. G. Simoes.
The authors are with the Department of Electrical Engineering, National
Cheng Kung University, Tainan 701, Taiwan, R.O.C. (e-mail: mycheng@
mail.ncku.edu.tw).
Color versions of one or more of the figures in this paper are available online
at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TPEL.2006.890006
circuits (ICs) such as Fairchild ML4425, Allegro 8904, etc. [11],
[12] have been designed using this method. Unfortunately, there
are several practical implementation problems when using the
phase to neutral zero crossing detection method. Firstly, the neu-
tral voltage is required for comparison with the non-conducted
back EMF or the average terminal voltage, in which it will in-
troduce a high common-mode noise [6]. The other problem is
the requirement of the phase shift (delay time) circuit. Since the
zero crossing points of the conventional back EMF method are
inherently leading 30 electric degrees of the ideal commutation
points, a precise velocity estimator and a phase shift circuit (al-
gorithm) are needed to process the zero crossing signals so that
accurate commutation points can be determined. The additional
open loop starting process and a complex phase shift circuit ac-
companied with a precise velocity estimator make the sensorless
commutation much more complex than the Hall effect sensor
based commutation. As a result, it is not surprising that the cost
of the commercial sensorless commutation ICs is usually several
times higher than that of the Hall effect sensor based commuta-
tion ICs.
In order to cope with the aforementioned problems, a new
cost effective sensorless commutation method is proposed. In-
stead of detecting the motor terminal to neutral voltage, the
estimated commutation signals are extracted directly from the
specific average line to line voltage of a BLDCM using simple
single-stage low pass filters and low cost comparators [13]. The
output signals of the new detection circuit can be directly ap-
plied to the conventional commutation table, as if they were ob-
tained from the real Hall effect sensors. That is, the estimated
commutation signals are well in phase with the ideal commuta-
tion points. Unlike conventional solutions, the proposed method
does not require additional virtual motor neutral voltage, com-
plex phase shift circuits, or precise speed estimators. Therefore,
in terms of cost and reliability, the proposed approach has ob-
vious advantages over conventional solutions. Theoretical anal-
ysis and several experiments have been conducted to demon-
strate the feasibility of the proposed approach. The results indi-
cate that the proposed method exhibits satisfactory performance
over a wide speed range under varying load conditions and dif-
ferent back EMF waveforms. These characteristics suggest that
the proposed method is very suitable for cost sensitive applica-
tions such as home appliances, computer peripherals, automo-
tive components, etc.
The remainder of the paper is organized as follows. Section II
derives mathematical models for each commutation state of a
BLDCM, where the switching statuses of the power devices
0885-8993/$25.00 © 2007 IEEE

CHEN AND CHENG: NEW COST EFFECTIVE SENSORLESS COMMUTATION METHOD 645
Fig. 1. Inverter topology and equivalent circuit of a BLDCM.
are considered. The principle and the commutation error of the
new sensorless commutation method based on the speciﬁc av-
erage line to line voltage are explained in Sections III and IV.
Section V discusses the practical implementation and the exper-
imental results. Conclusions are given in Section VI.
II. MATHEMATICAL MODELS OF EACH COMMUTATION STATE
Fig. 1 shows the equivalent circuit of a BLDCM and the in-
verter topology. Fig. 2 illustrates the relationship among the
back EMF waveform of an ideal BLDCM, the armature cur-
rent, the commutation signals (H1–H3), and the switching sig-
nals (S1–S6) for the inverter. It can be seen that the fundamental
characteristics of a BLDCM during each commutation state is
similar to that of a dc brush motor. Since the back EMF and the
armature current are not perfectly sinusoidal, the dynamic equa-
tion of a BLDCM is preferably expressed by the per phase vari-
able method rather than the two axes variable method [1]–[3]
(1)
(2)
where is the phase voltage, is the armature resistance,
is the armature inductance, is the armature current, and
is the armature back EMF.
In order to regulate the conduction current so that the motor
will faithfully follow the given velocity or torque command, the
power switches are generally controlled via a high frequency
PWM signal (5–15 KHz for small to mid-sized motors). The
switching signal can be injected on the high side, low side, or
both sides of the inverter legs. However, in order to reduce the
cost of the gate drive circuit, the boost strap circuit is accompa-
nied with switching on the high side (as shown in Fig. 2). This
method is widely used in many home appliances and industrial
applications [6], [13]. In what follows, the terminal voltages are
derived according to the status of the conduction current and the
switching signal. According to the polarity of the armature cur-
rent as illustrated in Fig. 2, the terminal voltage of each phase
can be divided into three sub-sections, i.e., positive, negative,
and nonconducted. Fig. 3 illustrates the equivalent circuits of
each commutation state for phase-“ ” over one electric cycle,
and the same results can be obtained for the other two phases.
States I and II: Armature Current is Positive: Fig. 3(a) and (b)
illustrate the equivalent circuit of the commutation states (I and
II) where the armature current is positive. If the conduction
Fig. 2. Ideal back EMF, conduction current, commutation signals, and
switching signals of a BLDCM.
voltage caused by the power switches and the diodes is negli-
gible, then the terminal voltage can be obtained according to
the switching status of the power switch S1
conducted states
freewheeling states (3)
States IV and V: Armature Current is Negative:
Fig. 3(c) and (d) illustrate the equivalent circuit of the
commutation states (IV and V) where the armature current is
negative. Since the switch S2 is turned on, the motor terminal is
connected to the power ground. Therefore, the terminal voltage
will be kept low despite the switching status of the upper legs
conducted & freewheeling states (4)
States III and VI: Armature is Open (Nonconducted):
Fig. 3(e) and (f) illustrate the equivalent circuit of the commu-
tation states (III and VI) where the armature is open. Since the
armature is disconnected from the voltage source, the terminal
voltage can be expressed as the summation of the armature
back EMF and the neutral voltage
(5)

Fig. 3. Equivalent circuits of each commutation state for phase “a.” (a) Ar-
mature current is “+,” conducted, states I and II. (b) Armature current is “+”,
freewheeling, states I and II. (c) Armature current is “0,” conducted, states IV
and V. (d) Armature current is “0,” freewheeling, states IV and V. (e) Armature
is open, conducted, states III and VI. (f) Armature is open, freewheeling, states
III and VI.
If the switch of the upper leg is conducted (e.g., S3 is on), the
neutral voltage can be expressed as
(6)
(7)
According to (6) and (7), the neutral voltage can be written as
(8)
If the switch of the upper leg is not conducted (e.g., S3 is off),
the neutral voltage can be expressed as
(9)
(10)
(11)
As illustrated in Fig. 2, the amplitudes of the back EMF for the
conduction phases during each commutation state are equal, and
their polarities are opposite, namely 0. Accordingly,
the neutral voltage can be rewritten as
conducted states (12)
If the waveform of the back EMF is perfectly sinusoidal, one
will have
(14)
Fig. 4. Measured instantaneous terminal voltage and corresponding switching
signals (from top to bottom: terminal voltage V , switching signal for S1,
switching signal for S2).
Substituting (14) into (8) and (11), the motor neutral voltage can
be rewritten as
conducted states (15)
Substituting (12) and (13) into (5), the terminal voltage of a
BLDCM which has an ideal trapezoidal back EMF waveform
can be expressed as
conducted states
and
Equation (18) represents the case where the back EMF wave-
form is perfectly sinusoidal
and conducted states
and
Note that each motor terminal is placed between the upper
diodes, which are connected to the dc source, and the lower
diodesoftheinverter,whichareconnectedtotheground.Itcanbe
expected that the maximum and minimum terminal voltages will
be ﬁxed between and 0. Fig. 4 shows the measured terminal
voltage and the corresponding switching signals. It is found that
the waveforms are in accordance with the theoretical analysis.
III. PROPOSED ZCP DETECTION APPROACH BY
AVERAGE LINE TO LINE VOLTAGE
The major problem of the conventional back EMF sensing
techniques is that they require noisy motor neutral voltage and

Fig. 5. Ideal average terminal voltages under different duty ratios.
a fixed phase shift circuit. Since the noisy motor neutral voltage
will introduce the common mode noise into the sensorless cir-
cuit, a low pass filter is indispensable. On the other hand, the
fixed phase shift function over a wide speed range is hard to im-
plement with analog circuits. Although the digital phase shift
algorithm may provide better performance over a wide speed
range application, it is more complex than the analogue solu-
tion and the cost will therefore be increased significantly. In
order to cope with the aforementioned problems, the proposed
method extracts the commutation points directly from the motor
terminal voltages with simple comparators and a single stage
low pass filter. While conventional methods focus on the phase
to motor neutral voltage, namely the phase back EMF voltage,
the key issue for the proposed approach is the specific line to
line voltage.
If the terminal voltages are expressed in the average form (i.e.,
duty ratio), the switching states in (3), (4), (17), and (18) can be
eliminated. The terminal voltages are rewritten as follows.
States I and II: Armature Current is Positive:
(19)
States III and VI: Armature is Open (Nonconducted):
(20)
States IV and V: Armature Current is Negative:
(21)
According to (19)–(21), the ideal average terminal voltages for
all three phases with different duty ratios are illustrated in Fig. 5.
The measured instantaneous (upper trace) and average (lower
trace) terminal voltages as the duty ratio is increased from 10%,
to 50%, to 100% are shown in Fig. 6. It is observed that the av-
erage terminal voltage can be divided into three sub-sections as
abovementioned. Moreover, the amplitude is proportional to the
Fig. 6. Measured instantaneous (first trace) and average (second trace) terminal
voltages under different duty ratios. (a) Duty ratio = 10%. (b) Duty ratio =
50%. (c) Duty ratio = 100%.
duty-ratio as predicted by the theoretical analysis. The voltage
spikes shown in the upper trace of Fig. 6 are caused by the

Fig. 7. Phase relationship among the back EMF, the average terminal voltage,
and the average line to line voltage.
residual current during the commutation transition, in which
their effect will be discussed in Section IV.
According to the average terminal voltage derived in
(19)–(21), the average line to line voltage can be expressed
as
(22)
(23)
Equation (23) reveals that the zero crossing points of the average
line to line voltage will occur at 30 and 210 electric degrees.
According to (22) and (23), Fig. 7 shows the phase relationship
among the ideal back EMF, the average terminal voltage, and the
average line to line voltage of phase “ ” and phase “ .” It is clear
to see that the average line to line voltage lags 30 electric de-
grees compared with the back EMF , namely the zero crossing
points of the line to line voltage are in phase with the ideal com-
mutation signals. Fig. 8(a) illustrates the practical circuit for
Fig. 8. Proposed and conventional sensorless commutation circuits. (a) Pro-
posed cost effective sensorless commutation circuit. (b) Conventional sensor-
less commutation circuit.
TABLE I
INPUT FOR THE PROPOSED SENSORLESS COMMUTATION
CIRCUIT AND THE CORRESPONDING OUTPUT SIGNALS
implementing the proposed approach to obtain the commuta-
tion signals (namely the virtual Hall effect signals ).
Table I summarizes the three speciﬁc line to line voltages for
the proposed sensorless commutation approach. According to
the properties of the average line to line voltage, the ideal com-
mutation points can be obtained directly from the three motor
terminal voltages without the knowledge of the neutral voltage.
Moreover, the obtained zero crossing points are inherently in
phase with the ideal commutation points, that is, the complex
phase shift circuit/algorithm can be eliminated. Consequently,
the circuit needed in the proposed approach is much simpler
compared with that needed in the conventional circuit shown in
Fig. 8(b).

Fig. 9. Illustration of various commutation errors. (a) Low pass filter. (b) Ar-
mature impedance. (c) Effect of the voltage spike.
IV. ANALYSIS OF THE COMMUTATION ERROR
A. Phase Delay by the Low Pass Filter and the Armature
Impedance
The phase delay angles caused by the input low pass filter
and the armature impedance shown in Fig. 9(a) and (b) can be
expressed as
(24)
(25)
Since the 30 (or 90 ) phase shift circuit shown in Fig. 8(b)
is not required in the proposed approach, the corner frequency
of the input low pass filter can be easily determined by the
maximum motor speed and the switching frequency
, in which the value of can be chosen as
(26)
where 120, and is the pole number of
the BLDCM.
The phase delay caused by the armature impedance can be
neglected in most small to mid-sized BLDCMs due to the fact
that the value of the resistance is usually much larger than the
inductance. The current loop compensator can be used to over-
come the delay caused by the armature impedance, however, it
is not needed in most home appliance applications since it is
only required in very high speed applications.
B. Voltage Spikes by the Residual Current
The voltage spikes shown in Figs. 4 and 6 are created by the
residual current when the armature current is blocked by the
power switches. The voltage spike is the main cause for the
commutation error in the conventional back EMF integration
method and the window-captured back EMF method (detecting
back EMF during the silent period) [7]. In these methods, the
back EMF is compared with the motor neutral voltage or a fixed
dc level, therefore the non-continuous voltage spikes will result
in noisy (virtual) ZCPs. In order to deal with these noisy ZCPs,
additional complex digital filters are indispensable, which will
definitely increase the complexity of the algorithm. Fig. 9(c) il-
lustrates a close look at the effect of the voltage spike in the ter-
minal voltage and the line to line voltage when a proper low pass
filter is added. It can be seen that the polarity of the line to line
voltage is not sensitive to the voltage spike, that is the noisy ZCP
will not occur during the switching transition. In other words,
the proposed method is more robust and easier to implement
compared with the conventional solutions.
V. EXPERIMENTAL EVALUATION
Fig. 10 shows the block diagram of the proposed sensorless
control method. The system can be divided into several sub-
blocks, including a velocity command generator, an open loop
starting process, a line to line voltage based virtual Hall effect
signal circuit, an electric commutation table, and a PWM gen-
erator. The reference voltage determines the duty ratio for the
PWM circuit, and the output speed of the motor is proportional
to the duty ratio. The speed command is implemented using
a variable resistor, while a simple RC circuit can be added to
regulate a required acceleration/deceleration rate to achieve a
smooth start. If the reference speed is too low, namely the refer-
ence voltage is not high enough, the preprogrammed Hall effect
signals will be sent to the commutation table sequentially. It is
known as the open loop starting procedure, where the BLDCM
is operated as a synchronous motor during this process. The
open loop starting procedure lasts 1.5 s to assure that the rotor
will align with the rotating magnetic field generated from the
multi-phase stator coils. The open loop starting speed is set to

Fig. 10. Block diagram of the overall system.
Fig. 11. Structure of the employed BLDCMs. (a) Type I (segmented magnet),
trapezoidal back EMF. (b) Type II (ring magnet), sinusoidal back EMF.
150 RPM in this study. When the input voltage is higher than
, that is, if the back EMF is high enough for the detection
circuit, the sensorless commutation signals will be sent to the
Fig. 12. Measured back EMF waveforms of employed BLDCMs. (a) Type I
motor. (b) Type II motor.
commutation table and the motor is changed to the self com-
mutation mode. That is, the synchronous motor is changed to a
brushless dc motor. Unlike conventional solutions, the complex
speed estimation algorithm and the phase shift algorithm are not
required in the proposed method. Therefore, the proposed sen-
sorless commutation circuit can be easily interfaced with the low
cost Hall effect sensor based commutation ICs.
Fig. 11 shows the assembly of the two BLDCMs employed in
this study, Fig. 12 shows their corresponding back EMF wave-
forms, which are trapezoidal and sinusoidal. Fig. 13(a)–(c) show
the experimental results for a wide speed operation range, from
10% 100% full speed with the type I motor. Fig. 13(d) shows
the low speed performance of the proposed algorithm with the
type II motor. It is found that the proposed algorithm is in-
sensitive to the back EMF waveform and the operating speeds.

Fig. 13. Measured commutation signals under different duty ratios and back EMF waveforms (from top to bottom: average terminal voltage V , average terminal
voltage V , average line to line voltage V , estimated commutation signal, signal from Hall effect sensor). (a) Duty ratio = 10%, type I motor. (b) Duty ratio
= 50%, type I motor. (c) Duty ratio = 100%, type I motor. (d) Duty ratio = 10%, type II motor.
Since the required speed ratio for fans and ventilations are usu-
ally around 3 5, the experimental results reveal that the pro-
posed sensorless commutation approach can be applied to most
home appliance applications. Fig. 14 shows the experimental
results when compared with the conventional method shown in
Fig. 8(b). It can be seen that the signal from the conventional
solution strongly depends on the operating speed; the mismatch
angle is leading 21.8 in 10% full-speed, lagging 14.4 in 50%
full-speed, and lagging 22.8 in full speed. The large commu-
tation error is mainly caused by the multistage ﬁlters; therefore
a speed dependent phase compensation algorithm is usually in-
dispensable. Compared with the conventional solution, the pro-
posed method is not only easier to design and implement, but
also exhibits better performance.
VI. CONCLUSION
Unlike conventional back EMF based sensorless commuta-
tion methods which focus on detection of the ZCP of the motor
terminal to neutral voltage, a novel sensorless commutation
method based on the average line to line voltage is proposed in
this study. Both theoretical analysis and experimental results
verify that satisfactory performance can be achieved with the
proposed sensorless commutation method. Compared with
the conventional solutions, the proposed method has several
advantages, including the following.
1) Elimination of the motor neutral voltage: The neutral
voltage is not required in the proposed method, only the
three motor terminal voltages need to be detected.

Fig. 14. Performance evaluation, compared with the conventional circuit (from
top to bottom: instantaneous motor terminal voltage, signal from Hall effect
sensor, signal from the proposed “line voltage method”, signal from the conven-
tional “phase voltage method”). (a) Duty ratio = 10%. (b) Duty ratio = 50%.
(c) Duty ratio = 100%.
2) Elimination of the fixed phase shift circuit: The proposed
specific average line to line voltage inherently lags 30
electric degrees compared with the phase back EMF.
Moreover, experimental results have revealed that the
phase relationship is insensitive to operating speed and
load conditions.
3) Low starting speed: Since the amplitude of the line to line
voltage is significantly larger than the phase voltage, even
a small back EMF can be effectively detected. Namely, a
lower open loop starting speed can be achieved.
4) Insensitive to the back EMF waveform: Compared with
the third-harmonic detection method, the proposed method
can be used for a BLDCM with nonideally trapezoidal or
sinusoidal back EMF waveforms, since most BLDCMs do
not have ideal back EMF waveforms.
5) Cost effective: Because the speed estimation algorithm
and the complex phase shift circuits are not required, the
costly digital signal processor controller is not needed.
Using a simple starting process, the proposed method can
be easily interfaced with the low cost commercial Hall
effect sensor based commutation ICs. Consequently, the
proposed method is particularly suitable for cost sensitive
applications such as home appliances and related com-
puter peripherals.
ACKNOWLEDGMENT
The authors wish to thank B. Liao for his assistance with this
work.
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Cheng-Hu Chen was born in I-Lan, Taiwan, R.O.C.,
in 1974. He received the B.S. degree in mechanical
engineering from the National Taiwan University of
Science and Technology, Taipei, Taiwan, R.O.C., in
1997, and the M.S. and Ph.D. degrees in mechanical
engineering and electrical engineering from National
Cheng Kung University, Tainan, Taiwan, R.O.C., in
1999 and 2006, respectively.
Currently, he is a Post-Doctoral Fellow at the Na-
tional Cheng Kung University. His current research
interests include sensorless BLDC motor/alternator
control, power factor control, hybrid electric vehicles, and automotive power
systems.
Ming-Yang Cheng (M’97) was born in Taiwan,
R.O.C., in 1963. He received the B.S. degree in
control engineering from the National Chiao-Tung
University, Hsinchu, Taiwan, R.O.C., in 1986 and
the M.S. and Ph.D. degrees in electrical engineering
from the University of Missouri, Columbia, in 1991
and 1996, respectively.
From 1997 to 2002, he held several teaching po-
sitions at the Kao Yuan Institute of Technology, the
Dayeh University, and the National Kaohsiung First
University of Science and Technology. In 2002, he
joined the Department of Electrical Engineering, National Cheng Kung Univer-
sity, Tainan, Taiwan, where he is currently an Associate Professor. His research
interests include motion control, motor drives, visual servoing, and biped loco-
motion.

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