SINUSOIDAL PWM OPERATION OF AN AC INDUCTION MOTOR CONTROLLER

SINUSOIDAL PWM OPERATION
OF AN AC INDUCTION MOTOR CONTROLLER
CONTENTS
Abstract

3

I. Introduction.

3

II. Design Overview.

4

A. AC-to-DC Converter.
B. PWM Generator.
C. Gate Driver.
D. DC-to-AC Inverter.
III. Theory of AC Motor Controller Operation.

9

A. Faraday’s Law.
B. Torque-speed characteristics.
C. Inductive reactance.
D. Duty Cycle.
E. Volts per Hertz Ratio.
F. Synchronous PWM.
G. Gate Driver.
H. Fundamental and Harmonics.

J. Switching Edges.
K. Overshoot.
L. Frequency-Speed Relationship.
IV. Efficiency and Reliability Considerations.

19

A. Efficiency Considerations.
1. Zero-voltage switching.
2. DC-to-DC conversion.
3. Deadtime distortion.
B. Reliability Considerations.
1.Snubber circuits.
2. Electrical isolation.
3. Overcurrent protection.

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5. Source conversion.
6. Thermal protection.
7. Layout.
25

V. Results.
A. Converter Module.

B. PWM Module.
1. Variable Width Pulse
Generation.
2. Switcher Pulse.
C. Inverter Module.
1. Analog Switchers.
2. Gate Drivers.
3. AC Synthesis.
VI. Conclusion.

35

References.

36

Appendix.

37

A. Specification.
B. Assembly Test Form
C. Performance Test Form
D. Component Data Sheets

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SINUSOIDAL PWM OPERATION
OF AN AC INDUCTION MOTOR CONTROLLER
Curtis Nelson, Kelly McKeithan, Tom McDonough, Mark Gelazela

ABSTRACT.
A single-phase ac induction motor controller is presented and the PWM (pulsewidth-modulated) frequency control part of the operation is verified experimentally. The
application for this ac motor controller is existing single-phase ac induction motors less
than ½ hp. The ac motor controller is a VFD (variable frequency drive). Control is by a
voltage source PWM inverter that uses IGBTs for power transistors. The IGBTs are
configured in a full H-bridge with unipolar voltage switching. A variable frequency (45
Hz to 75 Hz) output waveform is generated by the inverter to run a motor at variable
speeds that is directly proportional to this range of frequencies. The objective of this
project is to construct an ac motor controller from scratch with as many base components
as possible, and to demonstrate the sinusoidal PWM operation of the inverter part of the
design that runs an ac induction motor at variable speeds.

I. INTRODUCTION.
Numerous motor driven appliances operate in our homes and businesses today
(refrigerators, air-conditioners, washers, dryers, basement water pumps etc.). Most of
these appliances run on single-phase ac induction motors less than ½ horsepower. And
most of those motors lack a proper motor controller in order to run the motor more
efficiently. Motors can run more efficiently by varying the speed of the motor to match
the load. Motors are rated to operate best at full load. A motor controller that can vary the
speed of the motor automatically as the load changes will save energy. Fifty percent of
electrical energy is consumed by motors. An estimated 10% of this is wasted at idle and
an additional 5% to 10% is wasted when the motor operates at less than full load.
Therefore, the purpose of this paper is to describe an ac motor controller that can
be applied to existing single-phase ac induction motor appliances, and to demonstrate

sinusoidal PWM operation of the converter-inverter phase of the design. The prototype of
this design experimentally verifies the key concept of pulse waveform generation to
produce the switching action of an inverter in order to form a synthesized sine wave that
runs an ac induction motor.
The motor controller of this design is a converter-inverter configuration. The
converter supplies dc voltage to the inverter by rectifying the 120V, 60 Hz incoming ac
signal from the wall outlet to a dc voltage. The ac voltage is also stepped down for the
low-voltage control circuits.
The PWM drives the gates of the power transistors in the inverter. The inverter
synthesizes an ac sine wave from the dc voltage by the switching intervals of its power

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transistors. The switching intervals are determined from the duration of the pulse from
the PWM. The ac induction motor then synthesizes this chopped signal from the inverter
into an ac sine wave, because the motor’s inductance smoothes out the “notches” in the
waveform. The motor will then run at a speed proportional to the frequency of this signal.
This design is intended to be an interface between the ac source and the motor in order to
regulate the motor speed of an appliance to match the load efficiently. The load
requirements are determined by feedback from sensors to the PWM waveform
generators.
The prototype demonstrates waveform generation of the switching action of the
inverter to run an ac induction motor. The small-signal waveforms from the PWM shape
the high voltage sinusoidal output waveform that runs the motor. The sine wave
determines the frequency of the output waveform applied to the load. The triangle wave

determines the switching frequency by the power transistors (IGBTs) of the inverter. The
resulting pulses from the comparison of the sine and triangle waves turns on the switches.
The output waveform varies from 45 Hz to 75 Hz. The speed of the motor varies in direct
relationship to the frequency.
II. DESIGN OVERVIEW.
This design overview section will briefly review the relevant issues of motor
controller design. Fig.1 below is a block diagram of the ac motor controller. A section
covering theory of ac motor controller operation, then a section on efficiency and
reliability considerations, and then the results of the experiment with the prototype will
follow this.

Fig.1. Block diagram of the ac motor controller showing the ac-to-dc conversion, the
PWM pulse, and the dc-to-ac inverter.

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The motor controller shown in Fig.1 operates by converting the ac input signal
into a dc signal through the converter. It then converts the dc signal back into a
controllable ac signal through the inverter in order to run the ac induction motor at a
variable speed.
Part of the dc voltage from the converter operates wave generators in the PWM
that then send pulses in the form of square waves through the gate driver and into the
inverter. There the pulses turn on and off transistor switches at a designed rate in order to
synthesize an ac sine wave at a variable frequency.

A. AC-TO-DC CONVERTER.
The converter section of the motor controller converts ac to dc. Both high and low
voltage dc are required. The converter rectifies the incoming ac signal for the high
voltage requirement.
The converter also supplies the low voltage requirements. A transformer steps
down the incoming ac signal and then this low ac voltage is rectified into a dc signal in
order to power the low voltage PWM generators and control circuits.
The purpose of the rectifier is to convert an ac signal into a dc voltage. However,
unlike voltages cannot be directly connected or else KVL problems will result. If the
diode bridge rectifier connects an ac voltage with a dc voltage, the input current can be
extreme. The ratio between the peak input current and the average output current would
be high in this arrangement. The higher the capacitance, the briefer the total on-time, and
the higher the current spike will need to be to transfer the necessary energy. So a
smoothing inductor acting as a current transfer source should be added to the output of
the rectifier in order to improve its performance.
B. PWM GENERATOR.
The purpose of the PWM component of the controller is to generate pulses that
trigger the transistor switches of the inverter. The pulse-width modulated signal is created
by comparing a fundamental sine wave from a sine-wave generator with a carrier triangle
wave from a triangle wave generator as shown in Fig.2 below.
The variable width pulses from the PWM drives the gates of the switching
transistors in the inverter and controls the duration and frequency that these switches turn
on and off. The frequency of the fundamental sine wave of the PWM determines the
frequency of the output voltage of the inverter. The frequency of the carrier triangle wave
of the PWM determines the frequency of the transistor switches and the resulting number
of square notches in the output waveform of the inverter.

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Fig.2. PWM operation. V1 is compared to Vcarrier. For each time period, T, a square
pulse operates the switch of the inverter to output the fundamental waveform Vo1. [3,
p.212].
A figure of the PWM waveforms together with the resulting pulse is shown below
in Fig.3.

Fig.3. PWM operation. The square pulse from the PWM is superimposed on the sine and
triangle waves as shown in this figure. The pulse is high during the interval when the sine
wave is greater than the triangle wave. [2, p.223].
The square pulse waveform that is formed from the sine and triangle waves drives
the gates of the transistor switches in the inverter and controls the duration and frequency
that these switches turn on and off. The dotted line sine wave in Fig.3 represents both the
low voltage PWM generated sine wave, and also the high voltage output waveform from
the inverter that drives the motor.
C. GATE DRIVER.
The gate driver receives the logic-level control signal generated by the PWM and
then conditions this signal to drive the gates of the power transistors of the inverter. The
gate drivers provide a floating ground for the high-side switching of the IGBTs in a full
H-bridge configuration. The gate voltage must be higher than the emitter voltage for
high-side switching. The input components have to be level-shifted from common to the
emitter voltage. This is accomplished by charging a bootstrap capacitor, which is
composed of a capacitor and diode network, that gates the high-side IGBTs. The gate

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driver also provides under-voltage protection to ensure the gate stays on for the duration
of the turn-on period. The gate driver also provides fast switching edges, by minimizing
turn-on and off times, in order to prevent the IGBTs from operating in a high dissipation
mode and overheating.
D. DC-TO-AC INVERTER.
The purpose of the inverter is to convert the dc signal into an ac signal with a
variable frequency. The output waveform from the inverter is a series of square waves
that the motor ‘sees’ as a sine wave because the inductance of the motor smoothes out
this “chopped” waveform. The amplitude of the synthesized sine wave is determined by
the widths of these square waves. The relative widths of these square waves represent the
applied voltage. The wider the widths and the narrower the notches between the widths,
the higher the amplitude of the synthesized sine wave because more voltage is being
applied.
1. H-BRIDGE.
The inverter consists of an H-bridge, which is a configuration of power
transistors. A full H-bridge for single-phase application using IGBTs (in the positions
where switches are shown) for the power transistors is shown in Fig.4 below.

Fig.4. Single-phase full H-bridge inverter. The switches are IGBTs. The topology is for
bipolar voltage switching. [3, p.212].
TA and TB are the IGBT switching transistors. D A and DB are free-wheeling
diodes. Free-wheeling diodes are used to clamp the motor's kickback voltage, as well as
to steer the motor's current during normal PWM operation.
2. SWITCH.
The symbol for the transistor switch in the inverter that the PWM controls is
shown in Fig.5 below:

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Fig.5. Power transistor (IGBT) that does the switching in the inverter. The gate is turned
on by applying 15 Vdc to G. Current then conducts from C to E.
The high-voltage dc signal from the rectifier is applied to the collector (C). When the
pulse from the PWM arrives at the gate (G), the switch is turned on and the transistor
conducts for the duration of the pulse.

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III. THEORY OF AC MOTOR CONTROLLER OPERATION.
Faraday's Law sets the saturation flux for maximum energy conversion. The
torque-speed characteristics of a motor are affected by the applied voltage and frequency.
Inductive reactance can increase current and heat up the motor. The duty cycle is a
measure of the ratio of the applied voltage and frequency to the motor. The volts-perHertz ratio is set by the sine and triangle waves of the PWM and controlled by a PLL.
Synchronous PWM reduces harmonics. The gate driver conditions the pulse that drives
the IGBT gates. Harmonics are a function of the frequency modulation index. Transistor
switching edges dissipate power. Overshoot occurs at switching. The synchronous speed
of the motor is directly related to the applied frequency.

A. FARADAY'S LAW.
The ac induction motor requires a constant volts per Hertz ratio in the sinusoidal
signal that it receives in order to operate at saturation flux as reported in [1, 2, 3].
Saturation flux represents the highest value for a machine to maximize the energy
conversion process, so the motor can supply its rated torque.
The constant volts per Hertz ratio is explained by Faraday’s Law:
d

∫ E • dS = − dt ∫ B • da
c

s

The line integral of the electric field intensity, E, around a closed contour is equal to the
time rate of change of the magnetic flux, B, linking that contour.
In magnetic structures with windings, like a motor, the E field in the wire is
extremely small and can be neglected, so that the first term reduces to the negative of the
induced voltage, e, at the winding terminals. The flux in the second term is dominated by
the core flux φ. Since the winding (and hence the contour C) links the core flux N times,
Faraday’s Law reduces to [1, p.10]:

e=N

dφ
dt

since λ

= Nφ
dλ

e=
dt
and e = V0 cos ωt

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dλ
= V0 cos ωt
dt
integrating :
V
λ = 0 sin ωt
ω
so

Therefore, the saturation flux is :

λmax =

V0
2πf

Where φ is the magnetic flux in Webers, and λ is the flux linkage in Weber-turns.
So in order to achieve maximum flux linkage, a constant volts per Hertz ratio must be
maintained.

B. TORQUE-SPEED CHARACTERISTICS.
The final speed of the motor is determined by the point in which the load torque
equals the generated torque of the motor as shown in Fig.6 below.

Fig.6. Torque-speed characteristics of a motor operating at saturation flux from stall to 0
slip for operation with no change in voltage, frequency, or speed. [4. p.266].
From the figure it can be seen that the final speed of the motor occurs at a low slip of
around 0.1.
1. EFFECTS OF CONSTANT VOLTAGE.
If the motor does not maintain a constant volts per Hertz ratio, the torque speed
curve will not maintain that straight line characteristic around 0 slip shown in Fig.6 that is
required for saturation flux. The following figure (Fig.7) illustrates maintaining constant
voltage while varying the frequency.

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Fig.7. Torque-speed characteristics for constant voltage and variable frequency. The
motor will increase speed but lose saturation flux at higher speeds. [4, p.270].
Notice from Fig.7 that the torque drops off at higher frequencies causing the motor to
stall with an applied load.
2. EFFECTS OF CONSTANT FREQUENCY.
The next figure (Fig.8) illustrates the effects of constant frequency on the torquespeed curve.

Fig.8. This torque-speed curve illustrates the effects of varying the voltage while
maintaining a constant frequency. The motor does not increase speed, but the torque

drops off as the voltage decreases. [4, p.270].
Notice from Fig.8 that the speed of the motor remains constant no matter the voltage; and
the motor loses its torque characteristics with decreasing voltage.
3. VARIABLE VOLTAGE AND FREQUENCY.
The figure below (Fig.9) illustrates the effects of varying the voltage and
frequency proportional to the duty cycle.

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Fig.9. Torque-speed characteristics for a constant volts per Hertz ratio. The motor
maintains saturation flux at all speeds. [4, p.271].
Notice from Fig.9 that the motor can now supply its rated torque and operate at saturation
flux to provide the highest possible force over the full range of frequencies.
C. INDUCTIVE REACTANCE.
If the frequency is varied while the voltage remains constant, the motor will
maintain good torque-speed characteristics at low frequencies (as shown in the preceding
Fig.7). However excessive currents will be generated in the motor and heat it up. This is
due to the inductive reactance of the motor:
X L = 2π fL
The inductive reactance adds to the resistance and increases the current at low
frequencies:
I=

V
V

=
R + X L R + 2π fL

So as the frequency decreases, the current increases. The figure below (Fig.10) shows this
effect:

Fig.10. The Current, I, will increase at low frequencies due to the inductive reactance,
XL, of the motor if a constant volts per Hertz ratio is not maintained. [4, p.126].

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So, in order to prevent motor overheating due to current rise, the constant volts per Hertz
ratio must be maintained.
D. DUTY CYCLE.
The output ac sinusoidal wave that is generated by the switch action of the
transistor switches in the inverter matches the sine wave that is generated by the PWM.
The duty cycle is a measure of the amplitude and frequency of this sine wave in relation
to the amplitude and frequency of the triangle wave. The duty cycle changes based on the
sinusoidal waveform as a reference.
The amplitude modulation index, ma , is the ratio of the amplitude of the
fundamental sine wave, V1 , to the amplitude of the carrier triangle wave, Vc (from Fig.2).
V
ma = 1
Vc
The frequency modulation index, m f , is the ratio of the frequency of the carrier

triangle wave, f c , to the frequency of the fundamental sine wave, f1 .
f
mf = c
f1
The amplitude modulation index, ma , is usually less than or equal to one, which
means that the amplitude of the carrier wave is greater than or equal to the amplitude of
the sine wave as shown in Fig.11 below.

Fig.11. Ratio of the amplitude of the sine wave to the triangle wave and the resulting
pulse intervals (square wave). [2, p.222].
The amplitude of the sine wave increases with ma as shown in Fig.11. The amplitude of
the triangle wave remains constant.
Overmodulation occurs for ma greater than one and could result in the inverter
waveform degenerating into a square wave. Overmodulation is used for high power
levels; in which case the magnitude of the dc input must be adjusted.

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E. VOLTS PER HERTZ RATIO.
The amplitude modulation index, ma , should vary in proportion to the
fundamental frequency. For example (for a 75 Hz, 150 Vrms maximum operation), if the
fundamental frequency reduces to 80% from 75 Hz to 60 Hz, then ma should be .80 in
order to maintain a constant volts per hertz ratio (the output to the motor would then be
60 Hz, 120 Vrms).
Choosing the frequency of the carrier triangle wave and the resulting switch

frequency is a trade-off between high frequency, for ease in filtering harmonics, and low
frequency, for reduced switching losses. Frequencies in the audible range of about 6 kHz
to about 15 kHz are usually avoided to reduce noise.
A constant volts per hertz ratio can be obtained using a phase-lock loop (PLL).
The PLL drives the PWM. The PLL synchronizes the frequencies and regulates the duty
cycle. A block diagram of the PLL is shown in Fig.12 below.

Fig.12. The PLL (Phase Lock Loop) inputs a frequency, ωin, and outputs a proportional
voltage, Vo, and a synchronous frequency, ωout, to drive the waveform generators of the
PWM.
The PLL operates by comparing an input frequency, ωin (as shown in Fig.12), to
the output frequency of the loop, ωout, through a multiplier, , by the phase detector,
PD. The input signal is
Asin(ωt+θi).
The output signal is
Bcos(ωt+θo).
The product is
Asin(ωt+θi) Bcos(ωt+θo).
The trigonometric identity for this expression is
AB/2[sin(θi-θo) +sin(2ωt+θi+θo)].
The second term of this expression is then filtered out by the lowpass filter and amplified
to produce Vo proportional to ωin. The free running frequency, ωref, is initially set to a
midrange frequency (60 Hz for a range of 45 Hz to 75 Hz). Then as Vo changes with
each loop, ωref changes proportionally. As the phase difference decreases (θi-θo), the
phases lock and the outputs are proportional to the input. A multiplier, N, determines ωin,
the input frequency of the carrier triangle wave, which is then divided out by the 1/N
divider in the PLL.

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F. SYNCHRONOUS PWM.
The frequency modulation index, m f , should be chosen as an odd integer amount
(such as 21, 47, or 301) which results in odd symmetry as well as half-wave symmetry so
that the even harmonics disappear from the waveform. If the sine wave and the triangle
wave vary together in proportion to the ratio m f , then the waveform is a synchronous
PWM. Asynchronous PWM results in subharmonics that are undesirable. m f is often
chosen to be greater than 21. For example, if f c = 2100 Hz and f1 = 60 Hz, then m f =
35. A more realistic representation of the sine wave in relation to the generated pulse is
shown in Fig.13 below.

Fig.13. Typical sine wave generation from the switch action of an inverter. There are
usually a high number of switchings for every sine wave generated..[2, p.225].
This sine wave is the output waveform from the inverter that the motor ‘sees’ and
matches the sine wave generated from the PWM. The inductance of the motor smoothes
out this waveform. The square waves are generated by the switch action of the inverter.
They match the frequency of the triangle wave generated from the PWM. Notice from
Fig. 13 that the sine wave is high when the widths of the square waves are wider at the
top, and low when wider at the bottom. This waveform has a m f of about 60 and a ma of
about 0.5.
G. GATE DRIVER.
The gate driver receives the logic-level control signal generated by the PWM and
then conditions this signal to drive the gates of the power transistors of the inverter. The
function of the gate driver for an IGBT or a MOSFET, with their voltage controlled gate
characteristics, is capacitor charging and discharging. The transistor that is controlled by
a gate driver is modeled with capacitors across each of its terminals. The gate driver must

provide enough charge to account for the substantial current generated by the fast switch
action. And the gate driver must perform at the highest speeds possible.
The gate driver performs the following functions:
1. It minimizes turn-on and off times.
2. It provides adequate drive power to keep the power switch on.

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3. It provides reverse bias in order to ensure the switching device remains in the offstate.
4. It amplifies the control signal.
5. It provides electrical isolation where required.
6. It provides deadtime (blanking time).
7. It provides protection from overcurrent (feedback would be required).
8. It provides a large current for initiating turn-on, then large gate voltage at low current
levels for the duration of the turn-on period.
The gate driver is the interface between the control circuit and the power switch.
The gate driver topology is determined by either unipolar or bipolar voltage
switching, electrical isolation, and either a parallel or series (cascode) connection.
Unipolar voltage switching reduces harmonics. Bipolar voltage switching (BVS) is used
to speed up the switching. The power transistors will turn off as fast as they turn on with
BVS. Bipolar voltage switching provides a reverse bias applied to the power switch that
will ensure fast turn-off. Electrical isolation, when required, is specified as an
optocoupler, fiber optics, or a transformer. The drive circuit is usually shunt (parallel)
connected so that the drive circuit conducts only a fraction of the current carried by the
power switch in the on state.

H. FUNDAMENTAL AND HARMONICS.
The fundamental voltage and the harmonics for an example of
ma = .9 and m f = 47 is calculated below for a normalized voltage and a 60 Hz supply.
Since ma = 0.9 , the fundamental frequency is f1 = 0.9(60 Hz ) = 54 Hz. The harmonics
occur at:
m f ( f1 ) = (1)(47)(54) = 2.538kHz
3m f ( f1 ) = (3)(47)(54) = 7.614kHz
5m f ( f1 ) = (5)(47)(54) = 12.69kHz
as shown in Fig.14 below.

54 Hz

2.5 kHz

7.6 kHz

12.7kHz

Fig.14. Fundamental and harmonic components for bipolar voltage switching of a full Hbridge.

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J. SWITCHING EDGES.
Power dissipation in switching occurs at turn-on and turn-off as shown in figure
15 below. There is also some power loss due to the small amount of on voltage while the

switch is on. Referring to the figure, prior to the on pulse to the switch, the voltage is
high and the current is off. After the switch is turned on, there is a delay then the current
ramps on as the voltage ramps off. This overlap of the voltage turning off and the current
turning on is a power loss, P = IV. This occurs at turn-off also when the current ramps off
while the voltage ramps on.

Fig.15. The top graph represents the pulse from the PWM. The bottom graph is the
resulting switch action of the inverter. The triangular areas where Vce and Ic ramp on
and off (as well as the narrow area at the bottom between them, Von) represents power
loss, P=IV. [3, p.21].
The power dissipated due to the switching action is: PS = 1 Vd I O f S (tc ( on ) + tC ( off ) )
2
And the power due to the on voltage while the current is also on is: Pon = Von I oton f s
K. OVERSHOOT.
In addition to the losses due to the switching edges, there are losses due to
overshoot. The ideal I-V trajectory (the current and voltage trajectory from turn-on to
turn-off and back) is shown by the dashed line in Fig.16 below.

Fig.16. Preferred (dashed line) and actual trajectory of switching action and the
resulting overshoot. When the switch is off, voltage is high but no current conducts. When
the switch is on, the voltage across the switch drops to near zero while the current is
high.

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However, during turn-on and turn-off there is an overshoot, shown by the arrows
in Fig.16, resulting in overcurrent and overvoltage. The value of this additional power
loss can be determined by subtracting the calculated values of Pon plus PS from the
measured value of the actual switch loss.
L. FREQUENCY-SPEED RELATIONSHIP.
Variable speed operation of the motor is obtained by varying the frequency of the
PWM pulses with sensory input to the sine wave generator in the PWM. Since the speed
of an AC induction motor is directly proportional to this applied frequency,
Synchronous speed = 120 (frequency) / (number of poles),
the motor speed can be varied by the frequency. The actual speed of the motor shaft is
determined by the load which sets a slip in the motor.

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IV. EFFICIENCY AND RELIABILITY CONSIDERATIONS.
Since the ac motor controller operates with high voltages and currents, there are a
number of efficiency and reliability issues to consider.
A. EFFICIENCY CONSIDERATIONS.
The ac signal can be rectified into dc voltage and then stepped up with a boost
converter to run the motor at voltages and speeds above the base inputs. Resonant filters
can be added to filter out unwanted harmonics. Since deadtime causes distortion
producing torque pulsations on the motor shaft, a correction term synchronized to the
phase current signal with a current sensing device can be applied to the PWM waveform
to counter-modulate the original PWM signal with the characteristics of this distortion
and provide noise cancellation.

Choosing the frequency of the carrier triangle wave and the resulting switch
frequency is a trade-off between high frequency, for ease in filtering harmonics, and low
frequency, for reducing the switching losses. Frequencies in the audible range of about 6
kHz to about 15 kHz are usually avoided to reduce noise. The frequency modulation
index should be chosen as an odd integer. This results in odd symmetry as well as halfwave symmetry so that the even harmonics disappear from the waveform.
1. ZERO-VOLTAGE SWITCHING.
A snubber circuit across the power transistor will improve the shaping of the
switching trajectory of the switch as it turns off. The turn-off snubber provides zero
voltage across the transistor while the current turns off. A configuration for a snubber
circuit around a power transistor is shown below in Fig.17.

Fig.17. The snubber circuit is composed of a diode, DS , a resistor, RS , and a capacitor,
CS . It protects the power transistor from heat stress. [3, p. 682]
The capacitor, CS of Fig.17, delays the voltage turning on long enough for the
current to turn off. The turn-off snubber capacitor value is:
It
CS = o f
2Vd
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The capacitor energy, which is dissipated in the snubber resistor is:
2
CSVD
WR =
2

Some of the advantages of zero-voltage switching using a turn-off snubber circuit
are the following: The capacitor energy is dissipated in the resistor, which can be cooled
easier than the transistor. The transistor requires no additional energy due to the turn-off.
And the transistor's peak current is not increased because of the turn-off snubber. The
turn-off snubber circuit also reduces dv/dt which minimizes EMI problems. A turn-on
snubber circuit is seldom used because the turn-on snubber inductance must carry the
load current, which is expensive to implement.
2. DC-TO-DC CONVERSION.
A technique that could be used to provide more efficient operation of the motor
controller would be to use the stored voltage from the snubber circuit described in the
preceding section to power the PWM generators. The snubber resistor, RS , shown in
Fig.17, could be replaced with a dc-to-dc converter. This dc voltage could then be used
by the PWM instead of being dissipated in the resistor.
3. DEADTIME DISTORTION.
As reported in [4], deadtime distortion is a result of the deadtime added to the
PWM signal by the gate driver. This deadtime is necessary to prevent the top and bottom
switches of the inverter from shorting out, but it causes voltage and current waveform
distortion when the inverter is driving an inductive load like a motor as shown in Fig.18
below. The net result is the production of torque pulsations on the motor shaft. The
problem is more severe at low voltages due to SNR.

Fig.18. The effects of deadtime distortion on the voltage waveform of the inverter [4,
p.308].
A bipolar square wave that is synchronized to the phase current signal can be used
to approximate this distortion of the phase voltage. Then the original PWM signal can be
counter-modulated with the characteristics of this distortion in order to provide noise
cancellation. This correction term is synchronized to the phase current signal with a
current sensing device and applied to the PWM waveform.

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B. RELIABILITY CONSIDERATIONS.
There are also a number of product reliability factors to consider in order
to ensure end user satisfaction. Snubber circuits can be added to reduce stress on power
semiconductor devices by storing overvoltages from the switching action in the capacitor
and then dissipating the power in the resistor instead of the switches. Transient
overvoltage suppressors can be placed across the input of the controller and the inverter
switches for voltage spikes. Optocouplers can be included as part of the gate drivers for
electrical isolation between logic-level control signals and the power stage. Deadtime
prevents the switches from shorting out by spacing the turn-on time of oppositely biased
switches, and can be built into the gate drivers with a few passive components. Protection
against overcurrent from stalled or shorted motor conditions can be provided with a shunt
resistor in the ground path that feeds back to a comparator in the PWM in order to initiate
shutdown of the gate signals. A transfer source in the form of a smoothing inductor can
be provided between the diode bridge rectifier and the rectifier capacitor for source
conversion.
The junction temperature of the power transistor switches can be controlled with a
temperature sensor to shut down the power stage at critical temperatures. The circuit
layout should be planned to minimize loop areas that can pick up noise, cancel
electromagnetic fields with parallel runs, avoid 90° angles that cause discontinuity and
unwanted reflections, connect the control signal ground from the PWM to a single point
on the power stage of the inverter, and eliminate excessive conductor length to minimize
inductive voltage kickback. Insulation breakdown due to the switching action of the
PWM operation may occur. Therefore, lower switching frequencies, a short cable length
between the controller and the motor, or an inverter duty motor should be considered. In

addition to this, transient overvoltage suppressors should be placed across the input and
the switches in order to ensure survival of the controller when voltage spikes occur
during prototyping.
1. SNUBBER CIRCUITS.
Snubber circuits reduce stress on power semiconductor devices by storing
overvoltages from the switching action in the capacitor (shown as CS in Fig.17) and then
dissipating the power in the resistor, RS . Resonant converters may also used to control
switching stresses.
A snubber circuit should also be used for protection on a single-phase diode
bridge rectifier as shown in Fig.19 below. For the case of continuous conduction, the
filter inductor (shown as Lsmoothing ) should be placed on the dc side.

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Fig.19. An RC snubber circuit and a MOV used to protect a diode bridge rectifier. [3, p.
677].
One RC snubber can be used to protect all the diodes. In addition to the RC snubber, a
MOV (metal-oxice varistor) is used for transient overvoltage protection.
2. ELECTRICALLY ISOLATED DRIVE CIRCUITS.
Electrical isolation between logic-level control signals and drive circuits can be
obtained from optocouplers, fiber optics, or transformers. Optocouplers are preferred
over transformers because they are as effective but not as bulky. Optocouplers are used
with electrical shields between the LED and the receiver transistor in order to avoid
retriggering the power transistor at both turn-on and turn-off. The configuration shown in
Fig.20 below can be used for MOSFETs and IGBTs.

Fig.20. Drive circuit with optocoupler for an IBGT or a MOSFET. The optocoupler
isolates the switch from the control circuitry. [3, p.707].
3.OVERCURRENT PROTECTION.
Current limiting should be used to protect against stalled or shorted motor
conditions as reported in [3, 13]. There are three common overcurrent modes. One is a
short caused by the motor leads shorting out. Another is a ground fault from insulation
breakdown. The third is shoot through caused by false turn-on of an IGBT. Fuses do not
act fast enough to protect power devices. Fast detection of overcurrents compared to a
limit are needed in order to turn off the power transistor in the gate driver by means of a
protection network. The short-circuit current can be estimated from the transistor I-V
characteristics as shown in Fig.21 below.

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APRIL 26, 2000


Fig.21. I-V characteristics of a semiconductor device to determine overcurrent
protection. [3, p. 718].
A safe value to detect overcurrent would be about twice the continuous current rating of
the transistor
A shunt resistor in the ground path can detect overcurrent conditions. From the
International Rectifier product document, one of the traditional protection networks is
described: "One can detect the line-to-line short and shoot through currents by inserting a
Hall-effect sensor or a linear opto-isolator across the shunt resistor. The device should be
in series with the negative dc bus line. For ground fault protection, an additional Halleffect leakage current sensor could be placed either on the ac line input or on the dc bus.
The protection circuit is then implemented by using fast comparators. The output of these

comparators is 'Or'd' with the …PWM generator to initiate the shutdown of the gate
signals" [13]. The IR2137 integrated monolithic IC device is available to perform this
same function.
4. SOURCE CONVERSION.
An ac motor controller performs source conversion. The input ac voltage is
converted to a dc voltage through the rectifier. However, this may cause KVL (Kirchoff’s
voltage law) problems since unlike voltages appear to be connected. Therefore, a transfer
source in the form of a smoothing inductor should be placed between the diode bridge
rectifier and the rectifier capacitor as was shown in Fig.19. Since the inductor represents
a current source, the incoming voltage converts to a current and then this current converts
to a voltage for the inverter.
Krein describes the process this way, “The source conversion concept is a
fundamental of power electronics. In a well designed power converter, both the input and
output ought to have the characteristics of an ideal source. If the input is a voltage source,
then the output should resemble a current source. If the input is a current source, then the
output should have properties of a voltage source" [2, p.87].
5. THERMAL PROTECTION.
One of the most critical reliability design criteria for a controller is to reduce the
junction temperature of the power transistor switches, as reported in [2, 4]. This will help
lower the mechanical stress level and prolong the life of the transistor. For each 10°C rise
in the junction temperature, the long-term reliability of the transistor is reduced by 50%.
Thermal resistance, Rθ , is a measure of the temperature change of a semiconductor material per the applied power level. The case-to-heatsink thermal resistance is

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APRIL 26, 2000

the thermal resistance of the interface material times the average material thickness
divided by the area of the device mounted on the heatsink:
t
RθCS = ρ
A
The junction-to-case thermal resistance, RθJC is equal to the change in temperature
divided by the power dissipation:
T toT
RθJC = J C
PD
The power dissipation, PD, is equal to the current, I C , times the on voltage of the IGBT,.
VCE ,ON
PD = I C VCE , ON
The current draw for calculating the thermal resistance occurs at locked rotor condition
and 100% duty cycle. This represents the worst case for IGBT power dissipation.
Silicone grease is used to ensure a contact surface for heat conduction but may
eventually dry out, so thermal conduction interface pads may be used instead. A
temperature sensor may be added to shut down the power stage at critical temperatures. A
natural air-convection heatsink is used to dissipate the unwanted heat from the power
stage.
6. LAYOUT.
As reported in [3, 4], proper circuit layout is critical to the total design of a motor
controller. Valentine suggests the following rules for layout: Minimize loop areas
because loops are antennas that can pick up noise and affect the power stage. Run the
signal and return close together in order to cancel the electromagnetic fields in the wires.
Avoid 90° angles on wires that carry high-speed signals because this discontinuity will
produce unwanted reflections. And connect the control signal ground from the PWM to a
single point on the power stage of the inverter because transient voltage drops can be
substantial along power grounds due to the high values of di/dt that flows through a finite
inductance [4, p.233].

Inductive voltage kickback, VPK , is caused by conductors with excessive length
and is calculated by the following equation,
di
VPK = L
dt
where the change of current with time is determined by the controller’s switching speed.
And
the
inductance
of
the
conductors
is
calculated
by
 4l

L = (.002 × l )(2.3026 × log − .75  ) µH
d

where l is the length of the conductor, and d is the diameter. Therefore, increasing the
diameter of the conductor has a minimum effect on stray inductance compared to
decreasing the length. In general, leads should be kept under an inch if possible.

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APRIL 26, 2000

V. RESULTS.
This results section analyzes the three modules that comprise the ac motor
controller: the converter module, the PWM module, and the inverter module. The
converter module consists of a step-down transformer and two diode bridge rectifiers.
The PWM module consists of a triangle wave generator, a Wien bridge sine wave
generator and a comparator. The inverter module consists of a full H-bridge with 4
IGBTs, two analog switchers, and two gate drivers.
A. CONVERTER MODULE.
The circuit diagram for the converter module is shown in Fig.22 below. The
incoming ac signal is sent to both the high and low-voltage sections of the converter. The
diode bridge rectifier of the high-voltage section uses diodes that are rated for 15 A, 250
V operation. The diodes of the rectifier form a dc voltage across the resistor and
capacitor. The smoothing inductor, L1, is a transfer current source between the ac input
and the dc output to overcome source conversion. The PTCs are positive temperature
coefficient thermistors. They dampen the inrush current at turn-on. When the current and
resulting temperature rises, the resistance increases. When the current and resulting
temperature falls off with motor operation, the resistance falls off with it for normal
operation. The temperature rises within microseconds of the current rise. An 11kΩ power
resistor is required on the output of the high-voltage section due to the high currents.

CONVERTER MODULE
PTC therm

L1
S1
V1

HIGH
VOLTAGE

SECTION

D7
400uH

D9

PTC therm

+

D10
D8

C1

C2

C4

1.2mF

1.2mF

0

C3
1.2mF

1.2mF

R2
11k

170 Vdc

-

Dbreak
D7
R3
D10

+ 15 Vdc

C1

D9
D8
TX1

R4

0

LOW
VOLTAGE
SECTION

- 15 Vdc

Fig.22. This is the converter module of the ac motor controller. The high-voltage section
supplies the 170 V dc signal for the inverter. The low-voltage section supplies the +15
Vdc and –15 Vdc signals to run the op-amps of the PWM module and the control circuits
of the inverter module.

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