This document provides an overview of various pulse width modulation techniques for voltage source inverters, including naturally sampled PWM, regular sampled PWM, delta modulation, delta sigma modulation, space vector modulation, and hysteresis PWM. It describes the basic concepts and operating principles of each technique, and compares them in terms of performance metrics like harmonic distortion and switching losses. Space vector modulation techniques are ranked as providing the best performance in terms of minimizing harmonics, followed by regular sampled PWM and sine-triangle modulation.

1. Pulse Width Modulated Inverter Techniques
Saurabh kumar, M.Tech (Electric Drives & Power Electronics, IIT ROORKEE)
Abstract-This paper presents review of different
modulation techniques for voltage source inverter. A
variety of techniques, different in concept as naturally
sampled PWM, regular sampled PWM, delta modulation
techniques, delta sigma modulation techniques state
vector modulation and Hysteresis PWM are described
with corresponding waveform.
I. Introduction
One of the most widely utilized strategy for controlling the
A.C. output of power electronics converters is the pulse width
modulation (PWM), which varies the duty cycle (or mark
space ratio) of converter switches at a high switching
frequency to achieve target average low frequency output
voltage or current. Modulation theory has been a major
research area in power electronics for over three decades and
continues to attract considerable attention and interest. This is
not surprising since modulation is at the heart of nearly every
modern power electronic converter. There have been clear
trend in the development of PWM concept and strategies since
1970s, addressing the main objective of reduced harmonic
distortion and increased output magnitude for a given
switching frequency and development of modulation strategies
to suit different converter topology. While there have been
wealth of research investigating the modulation of DC/DC
converters the actual PWM process for these converters is
usually a simple comparison between reference waveform and
a sawtooth or triangular carrier waveform.
II. Scope of the Paper
The work presented in this paper primarily relates to medium
and high power level hard switched inverters (i.e. above 1 kW
power level). This paper considers only modulation strategies
which are appropriate for voltage source converter (VSI).
Topics covered in this paper are
1. Naturally Sampled Pulse Width Modulation
2 Regular Sampled Pulse Width Modulation
3 Delta modulation techniques
4. Delta Sigma modulation techniques
5. Space vector modulation
6. Hysteresis Pulse Width Modulation
1. Naturally Sampled Pulse Width Modulation
A. Sine-Sawtooth Modulation
The earliest and most straightforward modulation strategies is
termed as naturally sampled PWM, which compares a low
frequency target reference waveform (normally sinusoid)
against high frequency carrier waveform. In this process the
phase leg switched to upper DC rail when the reference
waveform is greater than the sawtooth carrier wave. To obtain
a sinusoidal output using this modulation strategy, the
reference waveform has the form
Where
M= modulation index with range 0<M<1
= target output frequency
= arbitrary output phase
With this type of sawtooth carrier, only the trailing edge of the
pulse varies as M varies, and hence this type of modulation is
termed trailing edge naturally sampled PWM For natural
charge of capacitors in FCMIs, this method is specially
used. A typical waveform for five level fling capacitor
inverter is shown For using PSCPWM in a flying
capacitor N -level inverter, N -1 carrier waveform is
needed which phase shifted by 2 / (N -I).
B. Sine triangle Modulation
This is more common form of naturally sampled PWM uses a
triangular carrier instead of sawtooth carrier to compare
against refrence waveform. With this type of carrier, both side
of the switched output pulse from the phase leg are modulated,
which considerably improves the harmonic performance of the
pulse train. This type of modulation is termed double-edge
naturally sampled modulation.
2. Regular Sampled Pulse Width Modulation
Regular sampled PWM control technique significantly
reduces the number of calculations required to generate

2. PWM control in real-time. It also greatly simplifies the
microprocessor software implementation, thereby
considerably reducing the on-line computing
requirements, and thus allows significantly higher
switching frequency PWM to be generated using
microprocessor techniques. In these strategies the low
frequency reference waveforms are sampled and then
held constant during each carrier interval. These sampled
values are compared against the triangular carrier
waveform to control the switching process of each phase
leg. The sampled reference waveform must change
values at either the positive or positive/negative peaks of
carrier waveform, depending on the sampling strategies.
A typical practical implementation of regular sampled
PWM is illustrated in Fig. 2. As shown in the Figure, the
sinusoidal modulating wave a is sampled at regular
intervals tl, r2 etc., and stored by a sample-and hold
circuit to produce an amplitude modulated wave b.
Comparison of b with the triangular carrier wave c
produces the points of intersection TI, T2 defining the
switching edges of the PWM pulses d. The
implementation of Fig. 2 is representative of a typical
analogue or discrete digital hardware implementation, as
shown in the diagram in Fig. 3. An important feature of
Fig. 3 is that the modulating frequency , carrier
frequency , and sampling frequency , are in general,
as shown, independent, and therefore any desired
relationship between them can be defined. The simplest
relationship is to set , and therefore to sample the
modulating wave at the carrier frequency, as shown in
Fig. 3. This result in only one sample being taken every
carrier cycle and therefore the sampled modulating wave
is kept constant throughout the carrier period resulting in
each edge of the PWM pulse being modulated equally;
commonly referred to as symmetric modulation, as
illustrated in Figs. 2 and 4. Alternatively, fs = 2fc can be
used such that two samples of the modulating wave are
taken each carrier cycle. The first sample taken at the
start of the carrier cycle is used to modulate the leading
edge of the pulse and the second sample, taken at the
middle of the carrier cycle, used to modulate the trailing
edge, resulting in asymmetric modulation, as shown in
Fig. 4. Since more samples of the modulating wave are
used to produce asymmetric PWM, the harmonic
spectrum is superior to that of symmetric PWM.

3. 2. Delta Modulation (DM) Technique
The delta modulation (DM) technique requires a very
simple circuit implementation, provides a smooth
transition between the PWM and single pulse modes of
operation and offers constant volts per Hertz operation
without the need of additional circuit complexity. Some
of the key voltage waveforms associated with the delta
modulation technique is illustrated in Fig. 5(a), (b). Fig.
5(c) shows their respective circuit implementation. In
particular, Fig. 5(a) illustrates the method by which the
DM switching function (Fig. 5(b)), applicable to the
PWM inverter, is obtained. This method utilizes a sine
reference waveform and a delta-shaped carrier
waveform is allowed to "oscillate" within a
defined "window" extending equally above and below
the reference wave . The minimum "window" width
and the maximum carrier slope determine the maximum
switching frequency of the inverter switchers ,
Therefore, when setting values for these two parameters,
care should be taken so that sufficient time is provided
for the proper turn-on and turn-off of and . Fig.
5(b) shows the DM switching function which
describes the operation of switching elements and
. The subscript of the element that is gated at any
instance is indicated by the sequence of ones and twos
shown in Fig. 5(b). The temporal relation between the
gating sequence of elements and the waveform of
the DM switching function VI yields that the inverter
phase voltage , and have the same waveforms.
Fig. 5(c) depicts a circuit that is capable of producing the
waveforms shown in Figs. 5(a) and 5(b). This circuit
operates in the following manner. Sine reference wave
is supplied to the input of the comparator while
carrier wave VF is generated by the integrator as
follows: whenever the output of exceed the upper or
lower “window” boundaries (which are preset by the
ratio), comparator A 1 reverses the polarity of at
the input of . This action reverses the slope of VF at
the output of , thus forcing to "oscillate" around
the reference waveform at ripple frequency r. This
forced oscillation ensures that the fundamental
component of (i.e. ) and reference wave have
the same amplitudes and that the dominant harmonics of
and waveforms oscillate at frequencies close to
the ripple frequency r.
3. Delta Sigma modulation techniques
The delta-sigma modulator is effectively applied to a
voltage source inverter system with PWM pattern
generating scheme. The major feature of delta-sigma
modulator is the inherent nature of spread spectrum
characteristic in addition to simple configuration
scheme. Besides, delta-sigma modulator can be
considered as a sort of error amplifier. If the inverter
circuit is taken into feedback loop as a quantizer,
external DC voltage disturbances can be reduced in the
output side of inverter.
4. Space vector modulation
Multiphase motor drives are a very promising
technology, especially for medium and high power
ranges. As known, a multiphase motor drive cannot be
analyzed using the space vector representation in a
single d-q plane, but it is necessary to introduce multiple
d-q planes. So far a general space vector modulation for
multiphase inverters is not available due to the inherent

4. difficulty of synthesizing more than one independent
space vector simultaneously in different d-q planes The
basic scheme of a three-phase inverter is shown in Fig.
6. The signals are switch commands of the
three inverter branches, and can assume only the values
0 or 1. The inverter output pole voltages are
Where is the dc-link voltage.
The main problem is to control the load phase voltages
and according to the requirements
imposed by the application, e.g. vector control of ac
machines. An elegant solution to this problem is the
space vector representation of the load voltages, which
describes the inverter pole voltages introducing a space
vector and a zero sequence component as
follows:
(2)
(3)
Where the coefficients k=1,2,3) are defined as follows:
(4)
The space vector and the zero sequence components can
be expressed as functions of s1, s2 and s3 by substituting
(1) in (2) and (3).
(5)
(6)
It is well-known that the load voltages depend only on
the space vector of the pole voltages, whereas the
inverter zero sequence component affects only the
potential of the load neutral point. In other words, to
control the load, it is sufficient to control the
vector .
SVM for Three-Phase Inverters
The modulation problem consists in controlling the
switch states such that the mean values of the inverter
output voltages are equal to the desired values in any
switching period Tp. There are eight (namely )
possible configurations for a three-phase inverter,
depending on the states of the three switch commands
s1, s2 and s3. Six configurations correspond to voltage
vectors with non-null magnitudes. These vectors, usually
referred to as active vectors, are represented in Fig. 2,
where the configurations of each vector are also
expressed in the form ( . Two configurations,
i.e. and
lead to voltage vectors with null magnitudes, usually
referred to as zero vectors. The space vector modulation
selects two activevectors and applies each of them to the
load for a certain fraction of the switching period.
Finally, the switching period is completed by applying
the zero vectors. The active vectors and their duty-cycles
are determined so that the mean value of the output
voltage vector in the switching period is equal to the
desired voltage vector. The best choice is given by the
two vectors delimiting the sector in which the reference
voltage vector lies. Since two consecutive vectors differ
only for the state of one switch, this choice allows
ordering the active and the zero vectors so as to
minimize the number of switch commutations in a
switching period. For example, if the desired voltage
vector lies in sector 1, as shown in Fig. 7, the two
adjacent voltage vectors are and , whose
configurations (0,0,1) and (0,1,1) differ for only one bit.
After the active vectors have been chosen, the requested
voltage can be expressed as a combination of them as
follows:
(7)
where and are the duty-cycles of and in the
switching period.

5. The explicit expressions of and can be easily calculated
evaluating the following dot products:
(8)
(9)
(10)
(11)
Once and have been calculated, the designer can
still choose in which proportion the two zero vectors are
used to fill the switching period. Fig. 8 shows the vector
sequence corresponding to the example of Fig. 7. In the
sequence of Fig. 3, the zero vectors are equally
distributed in the switching period.
6. Hysteresis Pulse Width Modulation
Hysteresis PWM refers to the technique where the
output is allowed to oscillate within a predefined error
band, called "hysteresis band". The switching instants in
this case are generated from the vertices of the triangular
wave shown in Fig. 9. Hysteresis PWM techniques does
not require any information about the inverter load
characteristics. As long as the reference signal is known
and the inverter output voltage is not saturated, the
inverter output will always follow the reference.
However, the switching frequency of power devices is
not fixed for this technique and will vary depending on
the magnitude and frequency of the reference,. Therefore,
switching losses for this techniques can be higher
compared to other techniques.
IV CONCLUSION
In this term paper pulse width modulation inverter
techniques has been presented. Through various
modulation techniques a general hierarchical consensus
appears to have emerged from this work which ranks
space vector modulation techniques, regular sampled
modulation and sine-triangle modulation strategies in
decreasing order of merit based on harmonics
performance
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