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EXPLORING SIMSCAPETM MODELING FOR PIEZOELECTRIC SENSOR BASED
ENERGY HARVESTER
Vandana Dhayal
Thesis Prepared for the Degree of
MASTER OF SCIENCE
UNIVERSITY OF NORTH TEXAS
May 2017
APPROVED:
Saraju P. Mohanty, Major ProfessorElias Kougianos, Co-Major ProfessorCornelia Caragea, Committee MemberBarrett Bryant, Chair of the Department
of Computer Science and EngineeringCostas Tsatsoulis, Dean
of the College of EngineeringVictor Prybutok, Dean of the
Toulouse Graduate School
Dhayal, Vandana. Exploring Simscape™ Modeling for Piezoelectric Sensor Based
Energy Harvester. Master of Science (Computer Science), May 2017, 60 pp., 43 figures,
40 numbered references.
This work presents an investigation of a piezoelectric sensor based energy
harvesting system, which collects energy from the surrounding environment. Increasing
costs and scarcity of fossil fuels is a great concern today for supplying power to
electronic devices. Furthermore, generating electricity by ordinary methods is a
complicated process. Disposal of chemical batteries and cables is polluting the nature
every day. Due to these reasons, research on energy harvesting from renewable resources
has become mandatory in order to achieve improved methods and strategies of
generating and storing electricity. Many low power devices being used in everyday life
can be powered by harvesting energy from natural energy resources. Power overhead
and power energy efficiency is of prime concern in electronic circuits. In this work, an
energy harvester is modeled and simulated in Simscape™ for the functional analysis and
comparison of achieved outcomes with previous work. Results demonstrate that the
harvester produces power in the 0 μW to 100 μW range, which is an adequate amount
to provide supply to low power devices. Power efficiency calculations also demonstrate
that the implemented harvester is capable of generating and storing power for low
power pervasive applications.
Copyright 2017
by
Vandana Dhayal
ii
ACKNOWLEDGMENTS
First of all, I would like to express my sincere gratitude to my adviser, Prof. Saraju
P. Mohanty, for his constant support and guidance. I am very thankful for his unending
motivation, patience, and support during my time in the lab, and for the personal freedom
of work. His professional awareness has been inspirational and encouraging to achieve higher
goals in my career. I would also like to thank Prof. Elias Kougianos for his any time help
while working on my thesis. He has been a constant support to me. I thank Dr. Cornelia
Caragea for her interest in my work and being my committee member.
I am specially thankful to my parents, Sultansingh Dhayal and Parvati Dhayal, for
nourishing me with great love and support, and teaching me to keep positive attitude toward
progressive life. I am thankful to my siblings Suman, Kamalesh, Manisha, and my brother-
in-law, Nilesh Kumar, for their great support, encouragement, and being there for me in
every situation during this journey. My little newborn nephew, Samar Kumar, is a delight
to watch, making me feel so light while working on my thesis in the final days. Finally,
I would like to convey my thanks to my fellow Nanosystem Design Laboratory (NSDL,
http://nsdl.cse.unt.edu) colleagues.
iii
TABLE OF CONTENTS
Page
ACKNOWLEDGMENTS iii
LIST OF FIGURES vii
CHAPTER 1 INTRODUCTION 1
1.1. Piezoelectricity 3
1.2. History of Piezoelectricity 3
1.3. Piezoelectric Materials: Properties and Classification 4
1.4. Types of Piezoelectric Materials 5
1.4.1. Non-Ferroelectric Piezoelectric Materials 5
1.4.2. Ferroelectric Piezoelectric Materials 5
1.5. Novel Contributions of this Thesis 6
1.6. Organization of this Thesis 6
CHAPTER 2 RESEARCH AREAS OF PIEZOELECTRIC SENSORS 7
2.1. Metrology 7
2.2. Energy Harvesting 8
2.3. Structural Health Monitoring 10
2.4. Ultrasound 11
CHAPTER 3 MODELING AND SIMULATION OF PIEZOELECTRIC SENSOR 12
3.1. Properties of Piezoelectric Sensor 12
3.2. Piezoelectric Sensor 13
3.3. Electrical Model of Piezoelectric Sensor 15
3.4. Essential Components for Implementing Electrical Models in SimscapeTM 15
3.5. Piezoelectric Sensor: Implementation in SimscapeTM 16
iv
3.5.1. Inverted Operational Amplifier 18
3.5.2. Piezoelectric Sensor using Inverted Op-Amp 19
3.5.3. Non-Inverted Operational Amplifier 21
3.5.4. Piezoelectric Sensor using Non-Inverting Op-Amp 22
3.6. Piezoelectric Sensor Output Voltage with Inverted versus Non-Inverted
Op-Amp 24
CHAPTER 4 SELF POWERED ENERGY HARVESTER USING PIEZOELECTRIC
SENSOR 27
4.1. Piezoelectric Sensor 27
4.2. Maximum Scavenged Power 27
4.3. Energy Harvester in SimscapeTM 29
4.3.1. Simulation Results of Energy Harvester without Amplifier 29
4.3.2. Energy Harvester with Inverting Op-Amp 31
4.3.3. Energy Harvester with Non-Inverted Op-Amp 33
4.4. Vibration Tracking Unit 36
4.4.1. Working Principle of Vibration Tracking Unit 37
4.4.2. SimscapeTM Implementation of Vibration Tracking Unit with
Non-Inverted Amplifier 40
4.5. Control Unit 42
4.5.1. Control Unit in SimscapeTM 44
4.6. System Initialization 45
4.7. Established Operations of the System 46
4.8. Overall Energy Harvesting System 47
4.9. Overall Energy Harvesting System with Non-Inverted Op-Amp:
SimscapeTM Model 47
4.9.1. Overall Energy Harvesting System with Non-Inverted Op-Amp
using MPPT Method 49
4.9.2. Overall Energy Harvesting System with Non-Inverted Op-Amp
v
(Fixed Band-Band Method) 51
CHAPTER 5 CONCLUSION 55
5.1. Summary and Conclusion 55
5.2. Future Directions 56
BIBLIOGRAPHY 57
vi
LIST OF FIGURES
Page
Figure 1.1. General Process for Energy Harvesting 1
Figure 1.2. Direct and Reverse Piezoelectric Effect 3
Figure 2.1. Piezoelectricity Research Fields 7
Figure 2.2. Types of Energy Harvesting 9
Figure 3.1. Electrical Model of the Piezoelectric Sensor 15
Figure 3.2. Piezoelectric Sensor in SimscapeTM 17
Figure 3.3. Piezoelectric Sensor Output Voltage at 35 µA Iin and 60 Hz Frequency 18
Figure 3.4. Vp (Piezoelectric Sensor Output Voltage) vs. Iin without Amplification 19
Figure 3.5. Piezoelectric Sensor with Inverting Op-Amp 20
Figure 3.6. Inverted Piezoelectric Sensor Output Voltage at 33 µA Iin 21
Figure 3.7. Vp (Piezoelectric Sensor Output Voltage) vs. Iin with Inverted Op-Amp 22
Figure 3.8. Piezoelectric Sensor with Non-Inverting Op-Amp 23
Figure 3.9. Non-Inverted Piezoelectric Sensor Output Voltage at Iin 33 µA and
Frequency 60 Hz 24
Figure 3.10. Vp(Piezoelectric Sensor Output Voltage) vs. Iin without Amplification 25
Figure 3.11. Comparison of Piezoelectric Sensor Voltage at Output with Inverting and
Non-Inverting Op-Amp 25
Figure 4.1. Electrical Model of Piezoelectric Energy Harvester 28
Figure 4.2. SimscapeTM Model of Piezoelectric Energy Harvester 29
Figure 4.3. Voltage Stored in Energy Harvester without Amplifier 30
Figure 4.4. Power Harvested in Energy Harvester without Voltage Amplification 31
Figure 4.5. Voltage Achieved at Piezoelectric Sensor Output in Energy Harvester
with Inverted Amplifier 32
Figure 4.6. Voltage Stored in Energy Harvester with Inverted Amplifier 33
vii
Figure 4.7. Power Achieved in Energy Harvester with Inverted Amplifier 34
Figure 4.8. Voltage at Piezoelectric Sensor in Energy Harvester with Non-Inverted
Operational Amplifier 35
Figure 4.9. Voltage Stored Across Cs in Piezoelectric Energy Harvester with
Non-Inverted Operational Amplifier 36
Figure 4.10. Power Achieved in Energy Harvester with Non-Inverted Op-Amp 37
Figure 4.11. Electrical Model of Vibration Tracking Unit 38
Figure 4.12. Vibration Tracking Unit in SimscapeTM 40
Figure 4.13. Comparison of Reference Voltages in Vibration Tracking Unit with
Non-Inverted Amplifier 41
Figure 4.14. Voltage Stored in the Vibration Tracking Unit with Non-Inverted
Amplifier 42
Figure 4.15. Power Achieved in Vibration Tracking Unit 43
Figure 4.16. Electrical Model of Control Unit 44
Figure 4.17. Control Unit in SimscapeTM 45
Figure 4.18. CON and Enable Signals in Overall Energy Harvesting System 45
Figure 4.19. Illustration of Overall Energy Harvesting System 46
Figure 4.20. Overall Energy Harvesting System 48
Figure 4.21. Overall Energy Harvesting System in SimscapeTM 48
Figure 4.22. Voltage at Piezoelectric Sensor Output in Overall Energy Harvesting
System with MPPT Scheme 49
Figure 4.23. Voltage Stored in Overall Energy Harvesting System with MPPT Scheme 50
Figure 4.24. Power Harvested in Overall Energy Harvesting System with MPPT
Scheme 51
Figure 4.25. Voltage Achieved at Piezoelectric Sensor Output in Overall Energy
Harvesting System with Fixed Band-Band Scheme 52
Figure 4.26. Voltage Stored in Overall Energy Harvesting System with Fixed
Band-Band Scheme 53
viii
Figure 4.27. Power Harvested in Overall Energy Harvesting System with Fixed
Band-Band Scheme 53
Figure 4.28. Power Efficiency of Overall Energy Harvesting System with MPPT and
Fixed Band-Band Methods at 60 Hz 54
ix
CHAPTER 1
INTRODUCTION
The concept of energy harvesting has been used for many years. It can be defined as
a process of conversion of one form of energy into electrical energy and storing it into a long
lasting electrical cell, such as capacitor, super capacitor, or chemical batteries [30, 28, 21, 20].
This method utilizes unconventional sources of energy for power supplies to the circuitry.
An energy harvesting system circuitry design is considered to perform two major functions:
first to manage the power, and second, to protect the storage and other related device. The
block diagram in Fig. 1.1 represents a common process of energy harvesting.
Energy Conversion
Energy Resource
Load Application
Energy Harvesting
DeviceRegulator
Energy Harvesting Process
Figure 1.1. General Process for Energy Harvesting
Energy can be harvested from any of five sources: sun light, environmental vibra-
tions, temperature differentials, radio frequency, and biochemicals [34]. The solar energy is
captured with the help of solar cells or photo-voltaic cells, a piezoelectric element is used to
collect the energy from the environmental vibrations, and thermoelectric generators are be-
ing used to collect the energy from temperature differentials [34]. The harvested energy can
be utilized directly, or it can be stored to be used later. Thus, it is useful when alternative
power sources are required. The amount of energy harvested via these system is measured in
(µW), commonly 10 µW to 100 µW [34], which is adequate to fulfill the necessity for remote
sensing, body implants, RFID, wireless applications, and other applications which consume
1
low power. This is helpful to improve the battery life as well. The main reason that makes
harvested energy a popular source is that it can remove the usage of batteries, which are
bulky, costly, and temporary to use. Moreover, energy harvesting devices have longer life
and no expiration date. Usually, the system circuitry is designed in such a way that it can
be sustained by itself, has low cost, and rarely requires further maintenance. Removal of
long wires reduces the losses during transmission [30]. In addition, if the captured energy
is sufficient to execute the operation of the required application, then power can be directly
transferred to the application. Hence, power storage may not be required for such cases.
Among all the energy resources, environmental vibrations are the most convenient
because they are available everywhere, they are omni-directional and independent of weather
factors; for example, solar energy can be collected only in the presence of sun. Piezo films
are used to capture the energy from the surrounding vibrations.
This thesis explores the modeling and simulation of a vibration based piezoelectric
energy harvesting system using a piezoelectric sensor in SimscapeTM. At present, most of the
portable devices are using chemical batteries to get supplemental power supply for performing
their operations. Batteries make the devices heavy and bulky. In addition to this, they are
required to be charged periodically. In the end, they are being trashed after expiration.
Electricity, either for recharging batteries or direct supply, is difficult and costly to provide.
Another disadvantage of electricity is the use of fossil fuels that releases hazardous chemicals
and heat in tremendous amount, and is complex process to generate. The biggest reasons of
concern is the limitation of energy resources and pollution. Therefore, there is requirement
to find cheaper, pollution-free, and renewable energy resources to generate electrical energy.
At the same time, portability of electrical energy is equally necessary so that batteries can
be eliminated. Advantages of using such systems are cheaper, smaller, and lighter devices.
Additionally, these systems use natural resources of energy, which are available for free in
nature. Many type of research works are already in progress to resolve these problems; for
example, solar panels are available to generate electricity from solar energy. There are many
types of energy harvesting systems available today depending on the use of particular energy
2
resource; such as environmental vibrations, solar, hydraulic, sound, etc.
1.1. Piezoelectricity
Piezoelectricity is the electricity generated by a piezoelectric material when mechan-
ical pressure is applied to it [23]. The indirect piezoelectric effect states that there is a
change in the dimensions of piezoelectric material if an electric voltage is applied [22]. Fig.
1.2 describes the phenomenon of piezoelectricity in a crystal with dimensional variations[22].
Piezoelectric Material Direct Piezoelectric Effect Reverse Piezoelectric Effect
Same Polarity at output voltage
Opposite Polarity at output voltage
Same Polarity at applied voltage
Opposite Polarity at applied voltage
Polarization Axis
Polarization Direction
Figure 1.2. Direct and Reverse Piezoelectric Effect
1.2. History of Piezoelectricity
Piezoelectricity was discovered for the first time by Pierre Curie and Jacques Curie
in the year 1880 [22]. They provided the relationship between crystal structure and piezo-
electricity. While studying to observe the relation between the crystal symmetry and Pyro-
electricity, they found that some materials generate electrical voltage with the application
of pressure in a specific direction. The word piezo is a Greek word, which means ”to press
or apply pressure.” Hence, this effect is known as the piezoelectric effect. The materials that
posses this effect are called as piezoelectric materials. They studied the phenomena in zinc
blende, sodium chlorate, boracite, tourmaline, quartz, calamine, topaz, tartaric acid, cane
sugar, and rochelle salt.
3
The theory of reverse piezoelectric phenomenon was first discovered by Lippman dur-
ing the study of thermodynamic principles, and were further confirmed by the Curie brothers.
In 1894, Woldmer Voigt combined the geometrically symmetrical elements of crystal with
the symmetric elements of electric vectors and elastic tensors in order to classify the piezo-
electric crystal [22]. He came up with 32 classes of crystals showing piezoelectric effect, and
18 coefficients of piezoelectricity having values other than zero [22]. Paul Langevin, French
mathematician and physicist, gave the direction of practical applications to use the piezo-
electric effect for the first time in the year 1917. He recommended to use an ultrasonic echo
ranging device to detect objects residing under the water. Quartz was used in World War
— as a piezoelectric material in the transducer, which was replaced by the Rochelle salt in
World War —— [22]. After this invention, many devices using piezoelectric materials came
into the market, such as microphones, phones, sound pickups, sound recording and vibration
measurement devices, forces and accelerations.
1.3. Piezoelectric Materials: Properties and Classification
Piezoelectric crystals are mainly divided into four classes depending on their polar-
ization and electrical properties [7]: natural, man-made, ferroelectric, and non-ferroelectric.
Piezoelectric materials exist in two forms, natural and man-made. Quartz (SiO2), rochelle
salt, topaz, tourmaline-group minerals and some organic substances as silk, wood, enamel,
dentin, bone, hair, rubber are examples of natural piezoelectric materials. When force is
applied to these materials, the position of atomic ions is rearranged in the crystal structure
[7]. This causes the formation of net dipole moment which generates polarization and an
electric field.
The molecular structure of man-made piezoelectric materials is similar to the quartz,
ceramics, polymers and composites. Thirty two such crystal classes exist which are classified
into seven groups depending on their material properties and characteristics: monoclinic,
orthorhombic, trigonal, cubic, triclinic, tetragonal, and hexagonal [7]. Ten out of 32 classes
do not possess piezoelectric properties because their unit cells are associated with the ma-
terialized electric dipole moment which causes impetuous polarization even in absence of
4
physical stress [7].
Man-made materials are divided on the basis of their crystal structure as perovskite
and other lead-free piezo-ceramics. Barium titanate (BaTiO3; lead titanate (PbTiO3); lead
zirconate titanate (Pb[ZrxTi1−x]O3, 0 < x < 1) PZT; potassium niobate (KNbO3) ; lithium
niobate (LiNbO3); lithium tantalate (LiTaO3) are examples of perovskite ceramics [7]. The
perovskite crystal structure possess an ABO3 general chemical formulae, where A stands for
a larger metal ions, like lead (Pb) or barium (Ba), B stands for a smaller metal ion, such as
titanium (Ti) and orzirconium (Zr).
1.4. Types of Piezoelectric Materials
1.4.1. Non-Ferroelectric Piezoelectric Materials
When mechanical stress is applied to the piezoelectric material, the geometry of the
crystals in the atomic structure is modified at micro-structure level and ions are separated
[7]. This leads to the formation of a dipole moment. In order to develop a net polarization,
the generated dipole is required to be not neutral in a unit cell. Thus, the atomic structure
of a piezoelectric material has to be non-centrosymmetric. When electrical voltage is applied
to such a material, then electrical dipoles are generated to form a dipole moment leading
to deformation of the material. The polarization is generated in the linear manner [7]. The
electrical dipoles disappear when electrical or mechanical load is applied.
1.4.2. Ferroelectric Piezoelectric Materials
These are the material which possess ferroelectric properties, impetuous polarization
and electrical dipoles appear in the atomic structure without the presence of an electrical
field [7]. The atomic structure of the crystal is the basis of the piezoelectric effect in these ma-
terials. Depending on the type of crystal, variations in the stress may attenuate polarization
. For example, the crystal structures of a traditional piezoelectric ceramic at temperatures
above or below the curie point are cubic with no spontaneous polarization and tetragonal
or rhombohedral developing impetuous polarization respectively [7]. Below the Curie point,
materials do show piezoelectric properties in the ceramic phase [7].
5
1.5. Novel Contributions of this Thesis
In this work, a vibration based piezoelectric energy harvester is implemented. This
energy harvester can be one form of solution for the above issues as it uses atmospheric
vibrations for generating electricity and works without a chemical battery. Electronic devices
are being improved with time at every step in order to achieve convenient, efficient, echo-
friendly, and cheaper designs of devices. Many researches are going on to improve the
circuit design of electronic instruments; for example reducing the size of electronic devices,
increasing longevity of eelctronics, lowering power consumption, easy manufacturing process,
and lower prices. Power consumption is one of the biggest challenge for researchers as it is
impossible to overcome.
All the circuits are modeled and simulated in the SimscapeTM environment due to
advantages it provides over traditional electronic design automation (EDA) or computer
aided design (CAD) tools [24, 12, 3]. The piezoelectric sensor is taken to convert the ambient
vibrations into electrical voltage. This voltage is harvested by the energy harvester using
a capacitor of required value. The energy harvester is first simulated and analyzed first
with no amplifier, then with an inverted amplifier, and finally with a non-inverted amplifier.
A maximum power point tracking (MPPT) method is followed and a vibration propelled
energy capturing platform is considered.
1.6. Organization of this Thesis
Chapter 1 is an introduction explaining the concept of piezoelectricity, requirements
for energy harvesting, and use of piezoelectricity in energy storing. Chapter 2 includes
research areas related to the piezoelectricity describing the respective concepts and their
utilization. Chapter 3 provides electrical modeling and simulation of the piezoelectric sensor
with inverted and non-inverted amplifiers for studying its functional behavior. Chapter 4
presents a detailed description of the energy harvesting system with modeling and simulation
of the various subsystems and the complete system. Finally, chapter 5 concludes the work
and includes future directions for research.
6
CHAPTER 2
RESEARCH AREAS OF PIEZOELECTRIC SENSORS
Piezoelectricity is being used in wide areas of research. Due to its special character-
istics, it has become one of the most important areas of interest for scientists in many fields
such as energy harvesting, metrology, ultrasound, and structural health monitoring. Fig. 2.1
shows a block diagram describing research fields in piezoelectricity.
Metrology Structural Health Monitoring Ultrasound
Research Areas of Piezoelectricity
Energy Harvesting
Figure 2.1. Piezoelectricity Research Fields
2.1. Metrology
The study of measurement with scientific means is known as metrology. Both theo-
retical and experimental characteristics have been considered in the metrology sciences. The
International Bureau of Weights and Measures (BIPM) has described that the science of
metrology has both practical as well as theoretical specifications for every area of measure-
ment in science and technology at every level of uncertainty [4]. The subject of metrology
is mainly divided in three parts depending on the type of actions [6, 10]:
• Defining internally accepted units of measurement
• Realizing accepted and defined units for usage
7
• Applying successive traceable linking measurements available in reference standards
All three activities are used for the verification at specific degree levels in the subfields of
metrology as given below [6]:
• Scientific metrology
• Applied, technical or industrial metrology
• Legal metrology
Piezo technology is playing an important role in the science of metrology due to
its special characteristics; for example, nanopositioning and scanning. Positioning devices
are important for surface inspection, scanning probe microscopy, and scanning electron mi-
croscopy. These devices are required to have high resolution, multiaxis movements, higher
stability in positioning, and a compact and simple structure. Use of piezo films in such
devices fulfills many of these requirements and has been proven to be dominant among
older technologies. Scanning microscopes with the use of piezoelectricity have provided bet-
ter experimental results in first, second, and third degrees of freedom [31]. A metrological
nanopositioning device, which is governed with the help of piezo-dependent internal method
in scanning microscopes has shown a resolution of 16 nm and movement at 1 mm/s speed [36].
The nanopositioner may be applicable in the scanning tunneling microscopy. Piezoelectric
force measuring devices with low-drift charge amplifiers have been approved for low-accuracy
classes of load cells as per the OIML recommendation R60 and may provide energy for static
precision measurements with appropriate systems [19]. Integration of piezoelectric drives in
metrological scanning probe microscopes (SPM) provides higher speed for scanning [27].
2.2. Energy Harvesting
Energy harvesting is a procedure in which different sources of energy are used to en-
capsulate the little amount of energy from the atmosphere. As there is a trimming in the size
of sensors, their power consumption, and in the power consumption trend of complementary
metal oxide semiconductor (CMOS) circuits, there is new research for supplying of power to
such a circuitry from easily accessible power resources. Such harvester circuitry can be used
8
as battery recharger in several environments such as industries, houses [38], the military, and
wearable devices [35]. Utilization of harvested energy can have better chances in wireless
networks because it reduces a significant amount of cost. Biomedical systems are another
area of application, where energy is stored with the help of off-the-self components to con-
sume it for the drug delivery system implementation, sensors [35], actuators, telemetry, and
microelectromechanical systems(MEMS) devices. Research has shown that energy can also
be captured from heart beats and from the occlusion contacts at the time of chewing by
using piezoelectric layers [35]. The fig. 2.2 presents the hierarchical model of relative energy
harvesting approaches and their types.
Seeback Photovoltaic Electromagnetic
RF ( )
Energy Harvesting
Electromagnetic
( ) Mechanical
Electrostatic Piezoelectric
Application
Areas
Working
Principle
Solar Thermal Motion Radio - Frequency
Figure 2.2. Types of Energy Harvesting
Areas of applications brings out the source of energy; whereas, the principle of working
consider the procedure to harvest the energy. Technically, the complete energy harvesting
system can be classified depending in two ways: first, based on the application areas, and
second, based on the principle working. The main design of harvester circuitry can be divided
into two parts. First, a frame, which is coupled with the host structure and transducer to
capture inputs. Next, a power conditioning circuit for manipulating electrical signals. This
9
thesis is specifically focused on piezoelectric energy harvesting [35]. The piezoelectric element
captures the energy from environmental vibrations, which are in the form of light, sound,
and motion. These energies are freely available in tremendous amount in the nature, but
are not being used appropriately. Use of such energies is complementary and beneficial for
the global climate and human beings in many ways.
2.3. Structural Health Monitoring
The necessity of detecting damaged composite structures via internet technologies is
increasing everyday as it is the fastest and the most convenient way to resolve any issue.
Currently, composite structures are used to build the structures because they posses high
stiffness and strength, which is the most important requirement for any structure. Piezoelec-
tric sensors are playing a significant role in solving many problems in the area of structural
health monitoring for detecting damages and maintaining health [33, 32]. These processes
work on the basis of finite elemental analysis techniques and practical outcomes. The chang-
ing responses between the defaced and original structures are detected by these technologies
by considering specific factors such as frequency domain, time domain, impedance domain,
and analyzing the model. Methods depending on vibration based models together with finite
analysis give specifications over the health of a structure for both global and local scopes
without any need of human access [40]. These methods are simple to implement, cheaper,
and able to compensate the need of internet applications [40]. Methods that work on the
basis of frequency domain provide the defaced information by detecting the changes in the
natural frequency [40]. The major reason for using piezoelectric sensors and actuators in
such technologies is that the structures can be pulsated at any frequency and part. The
responses can be achieved continuously. Hence, they provide more accuracy in the received
data. Time domain dependent methods consider frequency parallely and can detect damage
by looking at time history and frequency variations [40]. Similarly, impedance dependent
methods use the variations in impedance for damage detection, and are used particularly for
planar structures [40]. Piezoelectric sensors when implemented with the probabilistic defect
detection and localization algorithm can be used in the health monitoring of aircraft wings
10
[39].
2.4. Ultrasound
Ultrasound techniques are very flexible due to their simple, effective, and wide area of
usability in many fields. Ultrasound technologies are playing a vital role in object detection
and distance measurements in many fields at very large scale; for example, in sonar radars
and sonography. Piezoelectric transducers are again maintaining their significance in the
ultrasound technologies due to their special characteristics. Piezoelectric transducers help
in providing ultrasound devices with improved accuracy, low budget, larger range of opera-
tions, increased convenience, and miniaturization of instruments. For example, piezoelectric
vibration needles are used to give anesthetic effect over a specified area of the body [29].
Ultrasound probes with piezoelectric actuators have provided images of the internal organs
with higher clarity. The variations in the piezoelectric material dimensions due to the voltage
signals keep on contracting and expanding, which provides the interconnection between the
acoustic lens and internal fluids of the human body. After this, the transducer communicates
with the coming echoes to provide the voltage variations for the received echoes [37]. The
flexibility of piezoelectric materials makes the device fabrication simpler [37].
11
CHAPTER 3
MODELING AND SIMULATION OF PIEZOELECTRIC SENSOR
The piezoelectric sensor is a vital part of the energy harvester. This chapter contains
a detailed explanation of the piezoelectric sensor theory, electrical model, implementation
in SimscapeTM, and the related outcome results. The non-traditional design and simulation
flow is based on SimscapeTM and offers distinct advantages over conventional electronic
design automation (EDA) tool based simulations [24, 13, 11]. The piezoelectric sensor is
considered as the heart of the energy harvesting system, and generates electrical voltage from
the surrounding vibrations. Elaborative implementation of the sensor has been completed
with both inverted and non-inverted op-amplifier. The simulation results brings the effective
solution for the vibration detection in structures. The piezoelectric sensor is one of the
most effective sensors for the measurement of strain, force, pressure, or other corresponding
physical properties related to the particular structure. There are several sensor designs
available to measure strain, such as the fiber optical sensor which measures the strain either
by measuring wavelength or by the phase of light, and piezoelectric materials where the
change in strain is directly proportional to the change in resistance [8, 17].
3.1. Properties of Piezoelectric Sensor
The piezo film posses very high sensitivity and acts like a dynamic strain gauge
requiring an independent power source. Thus its frequency response has no limit of high gain
and can be extended upto transducer wavelengths [1]. The piezo film posses characteristics
of high flexibility, lightness, strength, and durability. It is available in a vast collections
of thicknesses and areas. To be used as a transducer, the piezoelectric film exhibits the
following properties [1]:
• Large range frequency 0.001 Hz to 109 Hz
• Wide dynamic range 8 µpsi to 106 µpsi
• Low acoustic impedance close to water, human tissue and adhesive systems
• High elastic conformity
12
• High voltage output 10 times higher than piezo ceramics for the same force input
• High dielectric strength withstanding robust areas (75 V/µm), a point of depolar-
ization for piezo ceramics
• High mechanical robustness and significant resistance 109 Pa to 1010 Pa
• High stability resisting moisture
• Possibility to stick with commercial adhesives
The larger sensitivity is due to the piezo film material’s structural design. Due to
small thickness, a small cross-sectional area is made, so comparatively less longitudinal
forces create enormous stresses in the material. Typically, the 1:3::length:thickness directions
provide a 1000:1 sensitivity ratio [1]. The capacitance of a very small area is high. The lower
frequency of operation can be given either by the largest resistive load achievable or by the
biggest capacitance load which permits the signal to be conveniently detected [1]. Operation
at lower fractions can be performed with the help of either conventional charge amplifiers
or high impedance field-effect transistor(FET) buffer circuits, as signals are comparatively
higher [1].
3.2. Piezoelectric Sensor
The piezoelectric sensor is an electronic device which works on the principle of direct
piezoelectric effect [23]. It is widely used in measuring variations in temperature, strain,
acceleration, and force by transferring their input signals into electrical charge. With the
application of mechanical stress to a piezoelectric film, it generates electrical voltage [23].
The process of generating electrical voltage is completed by using the direct piezoelectric
effect. They have higher high-frequency noise rejection capacity as well as greater signal to
noise ratio [26]. These properties makes piezoelectric sensors more useful in low strain level
measurement applications. Additionally, they have compact structure, simple embedding
process, and average requirements for signal conditioning circuit. If Vp is the output voltage
of the piezoelectric sensor, Cp is its piezoelectric capacitance, and Q is the charge applied,
13
then [26]:
(1) Vp = Q/(Cp)
From the perspective of sensing strain, it is reasonable to make the sensor’s size
as small as possible because it helps in preserving structural dynamics and exploring local
strain. This is an important scenario in vibration detection [15, 14] at a given point [5]. The
concept of local strain is similar to the structure nodes, and may vary in exhibiting strain
at different resonance frequencies. (MEMS) technology is very well proven to be effective
for vibration sensing; also, it gives compact designs of systems. Additionally, it allows batch
fabrication method and decreases the cost of manufacturing. Piezoelectric sensors with
MEMS technology might get affected in sensitivity measurements, because they are very
compact as compared to bulky devices. The strength of the signal is proportional to the
thickness of the sensor therefore this reduction leads to the loss in appropriate vibration
measurement. On the other hand, piezoelectric sensors give improved signal-to-noise ratio
and can detect strain omni directionally simultaneously. Therefore, the characteristics of
a piezoelectric sensor make it a preferable option over the earlier laser-doppler-vibrometer
(LDV) for the measurement of dynamic signals [16]. Vibration is a common problem in
mechanical structures, that is necessary to be controlled in practical implementations to
achieve control over noise immunity, component positioning, and stability in the structure.
The dynamic behavior of a piezoelectric sensor towards the changing input strain
could be proven useful for a broad range of applications. For example, it is already being
used in aerospace engineering machines and as alarms for smoke, temperature, and pressure
detection:
• Quality assurance in health structure monitoring by detecting impairments and
damages occurred in engineering structures, like bridges and buildings
• For vibration detections in machines, to predict earthquakes, tornadoes etc
• Useful in electronic devices to detect real time status of machines in industrial as
well as medical sector
14
• Energy harvesting devices
3.3. Electrical Model of Piezoelectric Sensor
The circuit design of the piezoelectric sensor consists of a capacitor in parallel with
the charge source and a resistor. The resistor typically has very high value. The capacitor
makes the impedance very large at the output of the sensor compared to the operating
frequencies of the data acquisition systems. An interface circuit is included which modifies
the larger output impedance of sensor into the smaller one. The interface circuit removes the
unwanted signals and amplifies the sensing signals. The electrical model of the piezoelectric
sensor is shown in Fig. 3.1. For the amplification of the signals of the piezoelectric sensor,
a single stage topology is used. Conventionally, it contains two kinds of amplifiers:
• Inverting amplifier
• Non-inverting amplifier
CpIp
Figure 3.1. Electrical Model of the Piezoelectric Sensor
3.4. Essential Components for Implementing Electrical Models in SimscapeTM
The piezoelectric sensor model is designed in SimscapeTM using basic electrical el-
ements and an AC source to provide the input current to the circuit. The alternating
current(AC) charge source is set in parallel with the capacitor. Additionally, a resistor in
series with a DC voltage source is connected in parallel to the sensor in order to model the
15
charge leakage due to the circuit parasitics and for removing unwanted noise. Hence, it works
as a noise reduction component for the circuit.
Some other blocks that are required for execution of the model in the software are
added to the circuitry in order to get the desired results. The following blocks are included
in the model:
The Solver Configuration [2]:
It is used to provide the specification of solver parameters for the start-up of the simulation,
i.e. prior to the beginning of the actual simulation. All network blocks in SimscapeTM
required to have a single separate solver configuration connected to that block.
The PS-Simulink Converter [2]:
This block is used to change a physical signal into a Simulink output signal. It also provides
the related units of the signals that are traced at the output.
The Electrical Reference block [2]:
The Electrical Reference block is used to provide an electrical ground. A model having
electrical elements must include at least one Electrical Reference block.
OP-AMP (Operational Amplifier) block [2]:
An operational amplifier is used for the voltage amplification. It shows significant variations
in the amplification of output voltage when the inverting and non-inverting inputs are given
the signal.
Voltage Sensor block [2]: This is to measure the voltage at the output.
3.5. Piezoelectric Sensor: Implementation in SimscapeTM
The output of the piezoelectric sensor depends directly on the vibration input and in-
versely on the input frequency and the piezoelectric capacitance. The resulting voltage is an
AC signal because the magnitude of input vibrations is varying and considered as an AC cur-
rent source. The piezoelectric sensor is implemented in SimscapeTM as shown in the following
Fig. 3.2. In order to plot the graphs for output voltage, To Workspace, Simulink block
is added to transfer the simulation data from SimscapeTM model to workspace environment.
Scope block is used for the simulation statistical study.
16
Figure 3.2. Piezoelectric Sensor in SimscapeTM
The voltage achieved in the simulation of piezoelectric sensor is calculated as per the
following equation:
(2) Vp = Q/(Cp)
For t =1 s, the voltage at the output terminal is found to be 0.32 V at the positive
end and −0.32 V at the negative end. The output voltage is also influenced directly by
variations of the resistive load. The Cp and load resistance values are taken 11.12 nF and
10 Ω respectively in the simulations. Fig. 3.3 presents a plot of the response.
This graph demonstrates that the output voltage of the piezoelectric sensor increases
linearly with the input charge as per equation 1. It is indirectly proportional to the fre-
quency of the input vibration magnitude; thus, the voltage is decreasing with the increase in
frequency. Fig. 3.4 presents a plot of the piezoelectric sensor voltage at the output without
amplification.
17
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1
Time(S)
-0.4
-0.3
-0.2
-0.1
0
0.1
0.2
0.3
0.4
Vpi
ezo
Figure 3.3. Piezoelectric Sensor Output Voltage at 35 µA Iin and 60 Hz Frequency
3.5.1. Inverted Operational Amplifier
Depending on the feedback resistor Rf , the inverted amplifier transfers the sensor’s
current into the output voltage as follows [23]:
(3) Vout = Iin ∗Rf .
The trans-impedance amplifier is susceptible to oscillations in case of improper compensation
states [23] and therefore a feedback capacitor (Cf ) is used to compensate for those unwanted
oscillations. The Rf and Cf elements must be given optimal values in order to achieve the
desirable voltage at output without the injection of additional environmental noise in the
required range of bandwidth.
The same configuration can also be implemented using a charge amplifier, i.e. re-
moving Rf and using only Cf in the feedback loop. This gives normal outputs, especially in
macro-piezoelectric sensors, but is not desirable for practical use. Simulation results provide
18
10 20 30 40 50 60 70 80 90 100
Iin
0
1
2
3
4
5
6V
pes(V
)
Figure 3.4. Vp (Piezoelectric Sensor Output Voltage) vs. Iin without Amplification
proper values for the elements before the implementation of the circuit. The amplification
gain for an inverting amplifier is given as [23]:
(4) A =VinVout
= − Rf
Rin
,
where Rin is the input resistance of the circuit.
3.5.2. Piezoelectric Sensor using Inverted Op-Amp
The output voltage of the piezoelectric sensor with an inverting amplifier shows a
similar pattern as that of the simple piezoelectric sensor, except that it is influenced by the
gain of the inverting operational amplifier, as described in the above equation. The resulting
voltage is given by:
(5) Vout = −(Rf/Rin) ∗ Vp,
19
where Vp is the piezoelectric voltage generated by the sensor. The electrical model of the
piezoelectric sensor with inverted amplifier is shown in Fig. 3.5.
CpIp
Rf
GND1
Cf
Vp
Figure 3.5. Piezoelectric Sensor with Inverting Op-Amp
The resistances Rf and Rin are taken as 10 Ω and 1 Ω respectively. The effect of both
resistances can be seen clearly in that as Rf changes, the resulting voltage varies in direct
proportion. Therefore, the voltage at the output is achieved as 2.6 V at the positive end and
−2.6 V at the negative end. Fig. 3.6 presents the illustrative simulation results.
The output voltage of the piezoelectric sensor increases linearly with input charge as
per equation 1. It is indirectly proportional to the frequency of input vibration magnitude;
thus, the voltage is decreasing with the increase in frequency and is influenced by the inverted
amplifier gain. Fig. 3.7 presents a plot of the piezoelectric sensor voltage at the output with
inverted amplifier.
20
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1
Time (S)
-3
-2
-1
0
1
2
3V
pIA
Figure 3.6. Inverted Piezoelectric Sensor Output Voltage at 33 µA Iin
and 60 Hz Frequency
3.5.3. Non-Inverted Operational Amplifier
This amplifier is useful for the formation of differential input stage signals. This
amplifier is more useful in devices where the amplifying current is very small as it has larger
input impedance [23]. The interface circuit for this amplifier consists of three stages: a
differential input stage for the removal of normally unwanted signals, a high pass filter for
blocking signals at lower frequencies, and a double-to-single end converter at the end for
receiving the amplifying gain. The first stage prevents saturation by removing common
noise signals while the second stage only allows signals for a particular frequency range.
This ensures that the last gain does not allow the circuit to saturate [23]. To remove the
parasitic capacitance, an additional shunt capacitor having smaller value than that of the
sensor’s is placed in parallel to Cs. The amplification gain for the non-inverting amplifier is
21
10 20 30 40 50 60 70 80 90 100
Iin
0
0.5
1
1.5
2
2.5
3V
pIA
(V
)
Figure 3.7. Vp (Piezoelectric Sensor Output Voltage) vs. Iin with Inverted
Op-Amp
given as: [23]:
(6) A = Vin/Vout = 1 +Rf/Rr.
3.5.4. Piezoelectric Sensor using Non-Inverting Op-Amp
The electrical model of the piezoelectric sensor with non-inverted amplifier is shown
in Fig. 3.8. The resulting voltage shows a similar pattern as that of the simple piezoelectric
sensor, but it is changing by the gain of non-inverted operational amplifier as described
22
below. The resulting voltage is:
(7) Vout = (1 +Rf
Rin
) ∗ Vp.
The resistances Rf and Rin are taken 10 Ω and 1 Ω respectively. The effect of both resis-
tances can be seen clearly in that as Rf changes the resulting voltage varies proportionally.
Therefore, the voltage at the output is achieved around 2.2 V at the positive end and −2.2 V
at the negative end. This result is presented in Fig. 3.9.
CpIp Rin
Rf
GND1
Figure 3.8. Piezoelectric Sensor with Non-Inverting Op-Amp
The output voltage of the piezoelectric sensor with non-inverted amplifier increases
linearly with the input charge as per equation 1. It is indirectly proportional to the frequency
of input vibration magnitude, therefore the voltage is decreasing with increasing frequency. It
23
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1
Time(S)
-2.5
-2
-1.5
-1
-0.5
0
0.5
1
1.5
2
2.5V
p(V
)
Figure 3.9. Non-Inverted Piezoelectric Sensor Output Voltage at Iin 33 µA
and Frequency 60 Hz
is influenced by the non-inverted amplifier gain. Fig. 3.10 presents a plot of the piezoelectric
sensor voltage at the output with non-inverted amplifier.
3.6. Piezoelectric Sensor Output Voltage with Inverted versus Non-Inverted Op-Amp
The output voltage of both the inverted and non-inverted amplifier based piezoelectric
sensors is shown in Fig. 3.11. The figure shows that the amplification of voltage in the non-
inverting op-amp based sensor is higher compared to that of the inverting op-amp based
sensor. This is because the larger input impedance of the non-inverting opp-amp provides a
better amplification factor.
24
10 20 30 40 50 60 70 80 90 100
Iin
0
0.5
1
1.5
2
2.5V
p-NIA
(V)
Figure 3.10. Vp(Piezoelectric Sensor Output Voltage) vs. Iin without Amplification
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1
Time (S)
-3
-2
-1
0
1
2
3
VpIA
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1
Time (S)
-3
-2
-1
0
1
2
3
VpN
IA
Figure 3.11. Comparison of Piezoelectric Sensor Voltage at Output with
Inverting and Non-Inverting Op-Amp
The use of operational amplifiers provides the flexibility of increment as well as decre-
25
ment of the voltage at the output of the piezoelectric sensor.
26
CHAPTER 4
SELF POWERED ENERGY HARVESTER USING PIEZOELECTRIC SENSOR
This chapter presents a complete study of the overall energy harvesting system and its
subsystems. The study involves modeling and simulation of each subblock in SimscapeTM as
motivated by prior research on this area [24, 13, 9]. Every system has been implemented and
analyzed thoroughly to obtain the precise details of its functional behavior. The functioning
of all the circuits has been provided to ensure correct operation. The energy storing element
is powered by the surrounding vibrations for collecting energy. The maximum power point
tracking (MPPT) scheme presented in this chapter seizes ambient vibrations for fulfilling
the requirements of the power supply. This method does not utilize any battery. It gets
the capability to start and power the system operations by itself. The power harvested and
the energy efficiency has been calculated in the end in order to present the benefits of this
method. The MPPT system consists of the piezoelectric sensor, energy harvester, vibration
tracking unit, and control unit as explained in the following sections.
4.1. Piezoelectric Sensor
The piezoelectric sensor is modeled and simulated in SimscapeTM in order to precisely
study its elemental behavior for various vibration strengths and ranges. Depending on the
passive elements’ resistance, capacitance, and frequency of vibration, the voltage of the sensor
varies at output. The behavioral study shows that Cp, the capacitance of the piezoelectric
sensor, remains static for a large range of vibration frequency. Rp is very large and can be
ignored.
4.2. Maximum Scavenged Power
An energy storing capacitor caches DC voltage. The voltage obtained at the output
of piezoelectric sensor is AC. Therefore, an AC-DC rectifier is included to convert the AC
voltage into DC voltage. The voltage generated by the piezoelectric sensor at a given time is
very low for running an application. Therefore a capacitor Cp is included in parallel with the
27
AC-DC rectifier to store this collected power. The electrical model of the energy harvester
is shown in Fig. 4.1.
CpIp
GND1
RpCs Rload
D1
D4
D2
D3
Figure 4.1. Electrical Model of Piezoelectric Energy Harvester
The harvested current for the average period of time at the rectifier output is given
as follows [18]:
(8) io(t) =2Ipπ
− 4(Vs + 2δV )πfCp
π,
where Ip is the polarization current of the piezoelectric material, and its value relies on the
magnitude of surrounding vibrations, Vcs is the optimal voltage at output, δV is the forward
voltage drop of the diode, f is the frequency, and Cp is the capacitance of the piezoelectric
sensor. Multiplying by the sensor voltage Vs the output power is obtained:
(9) P (t) >=2IpVsπ
− 4V 2s πfCp
π− 8VsδV πfCp
π
28
To collect the maximum power, the optimal voltage value should be [18]:
(10) Vs,peak =Ip
(4πf ∗R ∗ Cp)− δV,
where R is the load resistance. The maximum value of collected power depends on the
magnitude of energy vibrations Ip and the frequency. Both components are varying in
behavior. Ip depends on the surrounding vibrations and frequency depends on the time.
Hence, the maximum value of harvested power also varies.
4.3. Energy Harvester in SimscapeTM
Energy harvester is primarily implemented without operational amplifier. Its simula-
tion results are observed and taken for studying the behavioral and functional analysis. Fig.
4.2 shows the implementation of piezoelectric energy harvester in SimscapeTM.
Figure 4.2. SimscapeTM Model of Piezoelectric Energy Harvester
4.3.1. Simulation Results of Energy Harvester without Amplifier
The voltage collected across the storage capacitor is directly proportional to the
input vibration magnitude Ip and inversely proportional to the frequency of vibration and
piezoelectric capacitance, which is constant. Therefore voltage is stored in a linear relation
29
with respect to the input vibration magnitude. The voltage stored across the capacitor Cs,
shown in Fig. 4.3, ranges from 0 V to 0.7 V for the vibrational input Ip ranging from 10 µA
to 100 µA.
10 20 30 40 50 60 70 80 90 1000
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Vs (
V)
at f=30 Hzat f=60 Hzat f=90 Hz
Figure 4.3. Voltage Stored in Energy Harvester without Amplifier
The power harvested in the simple energy harvester, with no operational amplifier, is
directly proportional to the input vibrations, stored voltage, and piezoelectric capacitance.
Therefore, the amount of harvested power increases with increase in vibration magnitude.
Simulations are performed at the frequencies of 30 Hz, 60 Hz, and 90 Hz. The piezoelectric
capacitance is kept constant because the frequencies are low. The instantaneous harvested
power has been calculated. A power of 0 µW to 45 µW has been achieved with this energy
harvester. As the frequency increases, the power harvested decreases. This is because the
inverse of frequency is directly proportional to the stored voltage, which automatically causes
it to decrease with the decrease in frequency. This result is presented in Fig. 4.4.
30
10 20 30 40 50 60 70 80 90 100
Iin(μA)
0
5
10
15
20
25
30
35
40
45
Pow
er H
arve
sted
(μw
att)
at f=30 Hzat f=60 Hzat f=90 Hz
Figure 4.4. Power Harvested in Energy Harvester without Voltage Amplification
4.3.2. Energy Harvester with Inverting Op-Amp
An implementation of the energy harvester in SimscapeTM using an inverted opera-
tional amplifier was done in order to achieve increased voltage across the storage capacitor
and hence the harvested power. The circuit has been simulated for frequencies of 30 Hz,
60 Hz, and 90 Hz. As compared to the energy harvester without any amplifier, the en-
ergy harvester with inverted op-amp can provide improved results. The voltages across the
piezoelectric sensor, storage capacitor, the output current through load resistance, and the
harvested power are measured. The voltage stored at the storage capacitor is used for cal-
culating the instantaneous harvested power. At the output of sensor, given in Fig. 4.5, the
voltage measured varies in the range of 0 V to 3 V.
The voltage stored across the storage capacitor is linearly related to the input vi-
bration magnitude Ip and inversely related to the frequency of vibration and piezoelectric
capacitance, which is kept constant. Thus, the voltage harvested varies linearly with respect
31
10 20 30 40 50 60 70 80 90 1000
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
Vp (
V)
at f=30 Hzat f=60 Hzat f=90 Hz
Figure 4.5. Voltage Achieved at Piezoelectric Sensor Output in Energy Har-
vester with Inverted Amplifier
to the input vibration magnitude. The voltage stored across the capacitor Cs, shown in Fig.
4.6, ranges from 0.11 V to 1.1 V for the vibrational input Ip ranging from 10 µA to 100 µA.
The power harvested by the harvester can be calculated from the instantaneous power
equation. The pattern achieved between the vibration magnitude and harvested power is
showing moderate increase with respective to each other. The harvested power gained is
relatively showing gradual increase with the input vibration magnitude Ip and stored voltage,
and gradual decrease with the decrease in frequency of vibration. 0 µW to 70 µW has been
achieved with this energy harvester. The power stored by the harvester increases with the
increase in input vibrational amplitude and decrease in the given frequency. Fig. 4.7 presents
the harvested power versus vibration input at the input.
32
10 20 30 40 50 60 70 80 90 1000.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1V
s (V
)
at f=30 Hzat f=60 Hzat f=90 Hz
Figure 4.6. Voltage Stored in Energy Harvester with Inverted Amplifier
4.3.3. Energy Harvester with Non-Inverted Op-Amp
Finally, a non-inverted operational amplifier was used in the implementation of the
energy harvester for improved results and to compare the performance matrices with inverted
as well as energy harvester with no amplifier. The increase in the stored voltage depends
on the voltage gain of the non-inverted operational amplifier. In a comparison of energy
harvester with non-inverted op-amp to the energy harvester without any amplifier, it is
observed that usage of the non-inverted op-amp enhances the results. This circuit has also
been simulated for the frequencies of 30 Hz, 60 Hz, and 90 Hz. The voltage is measured across
the piezoelectric sensor, the storage capacitor, output current through load resistance, and
33
10 20 30 40 50 60 70 80 90 1000
10
20
30
40
50
60
70at f=30 Hzat f=60 Hzat f=90 Hz
Figure 4.7. Power Achieved in Energy Harvester with Inverted Amplifier
harvested power. The voltage measured at the storage capacitor is utilized to calculate the
instantaneous power harvested by the harvester.
The output voltage of the piezoelectric sensor is directly proportional to the vibration
magnitude and inversely proportional to the piezoelectric capacitance. The piezoelectric ca-
pacitance is kept constant. Therefore, the voltage at piezoelectric sensor output shows linear
relation with the vibration magnitude Ip. Higher voltage is achieved at higher frequency
because they have direct proportionality. At the output of piezoelectric sensor, the voltage
measured varies in the range of 0 V to 1.8 V, as illustrated in Fig. 4.8.
The voltage measured at the storage capacitor has linear relation with the input
vibration magnitude Ip and inverse relation with the frequency of vibration and piezoelectric
capacitance. Cp is constant. Hence, the voltage is captured in a linear manner with respect
to the input vibration magnitude. The increase in the stored voltage depends on the voltage
gain of the amplifier. The voltage stored across the storage capacitor Cs varies from 0 V to
4.5 V for the vibrational input Ip from 10 µA to 100 µA. This is shown in the graph in Fig.
4.9.
34
10 20 30 40 50 60 70 80 90 1000
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
Vp (
V)
at f=30 Hzat f=60 Hzat f=90 Hz
(
Figure 4.8. Voltage at Piezoelectric Sensor in Energy Harvester with Non-
Inverted Operational Amplifier
The harvested power is simply calculated with the help of the equation of instanta-
neous power. The magnitude of the power is varying in a gradual increasing fashion. The
power is varied in magnitude in comparison to both previous circuits due to the variation
in the amplification factor, while the pattern is similar because it is following the same
method for storing the voltage. 0 µW to 250 µW has been achieved with this energy har-
vester. The graph in Fig. 4.10 shows that power harvested is increased with the increase in
input vibrational amplitude and decrease in the given frequency.
35
10 20 30 40 50 60 70 80 90 1000
0.5
1
1.5
2
2.5
3
3.5
4
4.5
Vs (
V)
at f=30 Hzat f=60 Hzat f=90 Hz
Figure 4.9. Voltage Stored Across Cs in Piezoelectric Energy Harvester with
Non-Inverted Operational Amplifier
4.4. Vibration Tracking Unit
Vibration tracking unit is used to keep track of the optimal voltage, i.e., the maximum
power generated by the piezoelectric sensor. The process of tracking optimal power is done
by using a time multiplexing mechanism, in which the vibration tracking unit is connected
to the piezoelectric film in a periodic manner. The block diagram in Fig. 4.11 shows the
circuitry of the vibration tracking unit [18].
36
10 20 30 40 50 60 70 80 90 1000
50
100
150
200
250
at f=30 Hzat f=60 Hzat f=90 Hz
Figure 4.10. Power Achieved in Energy Harvester with Non-Inverted Op-Amp
4.4.1. Working Principle of Vibration Tracking Unit
When the resistive load R is connected to the output of the piezoelectric sensor, the
instantaneous voltage Vo and peak voltage Vo,peak are calculated as shown in the following
equations [18]. The instantaneous voltage at output is the following:
(11) Vo = IpR√
1 + (2πfRCp)2sin(2fπt+ θ).
37
CpIp
R2
D2
R1
R3
D1 R4C1
GND2
R4C2
GND2
Figure 4.11. Electrical Model of Vibration Tracking Unit
The maximum voltage is:
(12) Vo,peak =Ip
(2πfRCp)If (2πfRCp >> 1).
Using the above two equations, the following can be deduced:
(13) Vs =Vo,peak
(2 − δV )
38
Therefore, Vs can be calculated using the maximum power of the piezoelectric sensor. With
the help of the Vs track record, vibrations can be tracked. The Voltage Tracking Unit (VTU)
simply consists of passive elements capacitor and resistor without using a battery.
The optimal voltage Vs is taken as the supply voltage for control unit. Vref1 and Vref2 are
used as input signals for the control unit. In order to perform the right operation, the
reference voltages are needed to be lower than Vs. The values of the input reference voltages
are reduced by including one more capacitor Cd and three resistors in series and in parallel
to the output of piezoelectric sensor. Cd = Cp and the equivalent resistance R of series
resistances R1, R2, and R3 fulfill the condition as per the equation 14:
(14) 2π ∗ f ∗R ∗ (Cp + Cd) >> 1
The equation 15 gives the output voltage in vibration tracking unit [18]:
(15) Vo =Ip
4 ∗ π ∗ f ∗ Cp
.
In order to achieve the appropriate values, a voltage divider and a low pass filters are
used. The resulting reference voltages are calculated as per the following equations [18]:
(16) Vref1 =Ip
(8πf ∗R ∗ Cp)− δV + σ, and
39
(17) Vref2 =Ip
(8πf ∗R ∗ Cp)− δV − σ,
where δV is the forward voltage drop of the diode, and
(18) σ =R2
R1 +R2 +R3
.
Both reference voltages are used for the control unit input signals to continue power tracking
for maximal point of the system.
4.4.2. SimscapeTM Implementation of Vibration Tracking Unit with Non-Inverted Amplifier
Following Fig. 4.12 shows the implementation of vibration tracking unit in SimscapeTM
tool.
Figure 4.12. Vibration Tracking Unit in SimscapeTM
The reference voltages are plotted at a particular frequency, as shown in Fig. 4.13.
Both reference voltages vary with each other by twice the magnitude of σ, as given in the
40
above equation. Both curves show linearly increasing relation with the vibration magnitude.
This is because they are directly proportional to the vibration magnitude Ip and as Ip
increases, Vref2 and Vref2 increase.
10 20 30 40 50 60 70 80 90 100
Iin(Microampere)
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
Vre
fs(V
olt)
Vref1 at f=60 HzVref2 at f=60 Hz
Figure 4.13. Comparison of Reference Voltages in Vibration Tracking Unit
with Non-Inverted Amplifier
The stored voltage can be obtained from the instantaneous output voltage in the vi-
bration tracking unit. Therefore, the instantaneous voltage Vo is plotted against the vibration
magnitude. The Vo vs. Ip curve is linearly increasing because of the direct proportionality
between the instantaneous voltage and vibration magnitude. The instantaneous voltage also
varies directly with the piezoelectric resistance R. It poses an inverse relationship with the
frequency; therefore, it will decreases with increase in the frequency. This is illustrated in
Fig. 4.14.
The power achieved using the instantaneous voltage from the vibration tracking unit
is calculated using the instantaneous power formula. The power is directly proportional to
41
10 20 30 40 50 60 70 80 90 1000
0.2
0.4
0.6
0.8
1
1.2
1.4
Vs(V
)at f=30 Hzat f=60 Hzat f=90 Hz
Figure 4.14. Voltage Stored in the Vibration Tracking Unit with Non-
Inverted Amplifier
Ip and Vo. Vo is inversely proportional to the vibration frequency, so the instantaneous power
achieved is decreases with decrease in the frequency. The power achieved ranges from 0 µW
to 90 µW, as shown in Fig. 4.15. This is less than the energy harvester with both amplifiers,
but still a considerable amount.
4.5. Control Unit
The control unit electrical model is presented in Fig. 4.16. It is required to sustain
the maximum value of resulting voltage for increased efficiency. The control unit is designed
to complete the operation of perpetuating maximal voltage at output. The control unit is so
named because it is governing the optimal voltage at the output of energy harvester. There
are two major components of the circuit, a Schmitt trigger and a comparator. The output
of the Schmitt trigger is used as a signal to operate switch S1. This signal is named as CON
42
10 20 30 40 50 60 70 80 90 1000
10
20
30
40
50
60
70
80
90
at f=30 Hzat f=60 Hzat f=90 Hz
Figure 4.15. Power Achieved in Vibration Tracking Unit
signal because it is connecting the application to the control unit. Similarly, the output of
the comparator is used to set up the functioning of application. This signal is named as
enable signal as it is enabling the operation of the system.
When the CON signal is low, it turns ON switch S1; when it is high, it turns off the
switch. It is low if the capacitor Cs is charged more than twice of reference voltage one,
i.e. 2Vref1. Therefore, S1 is turned ON. Once S1 is high, the application starts its atomic
function, i.e. the application is going to complete its operation. With the utilization of
power, Vs starts decreasing and, when it becomes 2Vref2(1 + R1/R2) [18], the enable signal
is turned low so that the application gets detached and goes to sleep mode. It is required
to store the status of the application for the successive operation before it goes into sleep
mode. Buck converter is used to supply the limited amount of power to the application
43
R2
R1
GND4
Enable
CON
Vref1
0.5Vs
Vref2
Figure 4.16. Electrical Model of Control Unit
for continuing its expected working. When Vs becomes less than 2Vref2, then CON goes
high and puts OFF switch S1 [18]. One cycle of operation is completed over this step. The
capacitor Cs is charged up again and when Vs becomes greater than 2Vref1, the whole cycle
is repeated again [18]. Power loss is the most important parameter for low power overhead.
The comparator design is meant to operate in the subthreshold region.
4.5.1. Control Unit in SimscapeTM
Implementation of the control unit is shown in Fig. 4.17. The Fig. 4.18 shows the
CON and Enable signals in the overall system.
44
Figure 4.17. Control Unit in SimscapeTM
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1
t(S)
-0.8
-0.6
-0.4
-0.2
0
0.2
CO
N (
V)
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1
t(S)
-1
0
1
2
3
4
Ena
ble(
V)
Figure 4.18. CON and Enable Signals in Overall Energy Harvesting System
4.6. System Initialization
In the initial stage, the optimal voltage stored across Cs remains zero even though
there is presence of small amount environmental vibration in the surroundings. As a result,
Vs cannot activate the operation of the pulse generator. This leads to the switch N1 to be low
and P1 to be high. At this time, the piezoelectric film is only responsible for regulating the
system operation. The piezoelectric film current reaches Cs; that is how the storage capacitor
gets charged. Thus, the voltage Vs goes on increasing and reaches to a point, where it can
provide voltage to the pulse generator. The pulse generator provides pulses to the switches
45
due to which, reference voltages 2Vref1 and 2Vref2 are generated by the vibration tracking
unit. Thereafter, the system starts its regular operation.
4.7. Established Operations of the System
The operating procedure of the complete system must be executed regularly with the
proper maintenance of the complete circuitry. The energy given to the buck converter and
application is calculated by the following expression [18]:
(19) E = 2Cs(V2ref1 − V 2
ref2).
The voltage storing capacitor Vcs is taken in such a size that it can harvest sufficient amount
of voltage to complete at least one atomic operation. The operation cycle must be performed
successfully even in the worst case condition or even at the lowest Vcs at the energy harvester.
Fig. 4.19 show illustrative simulation results of the overall system start up and further
execution for Vout - voltage at load resistance, Vin - supply voltage to the buck converter and
load resistance, Vs - voltage stored across storage capacitance, Vref1, and Vref2 signals.
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1-2
0
2
Vs(
V)
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1-1
0
1
Vre
f1(V
)
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1-0.5
0
0.5
Vre
f2(V
)
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1-2
0
2
Vin
(V)
0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1
Time (S)
-5
0
5
Vou
t(V)
Figure 4.19. Illustration of Overall Energy Harvesting System
46
4.8. Overall Energy Harvesting System
Fig. 4.20 contains the block diagram of the complete system of energy harvester,
which works on the basis of vibrations. The harvesting system is functioning on the principle
of time-multiplexing based maximum power point tracking. MOS switches N1 and P1 are
used for the implementation of this MPPT. N1 is used for the periodic connection of the
harvester to the vibration tracking unit and it is connected periodically because the vibrations
vary very slowly. The duty cycle is kept as small as possible so that the power overhead
can be reduced. 1% duty cycle is considered as the most appropriate. The optimal voltage
Vs is not constant therefore a voltage control component is required to maintain the supply
of limited amount of power as per the requirements of the application being used. The
buck converter circuit is included in the system to provide the regulated power Vout for the
application. Vs is also supplied to the pulse generator. The component power consumption
amount should be lower than the amount of Vs to make the system working without using
battery, i.e. to be self-powered.
4.9. Overall Energy Harvesting System with Non-Inverted Op-Amp: SimscapeTM Model
Fig. 4.21 shows the SimscapeTM model of complete energy harvesting system imple-
mentation.
The complete energy harvesting system is simulated in order to ensure whether each
sub-circuit performs its function properly while placed in its specific place in the actual
system. It is also observed and verified if the complete system is operating correctly with
the expected results. While simulating the whole system, it has been taken care that all the
subparts of the system function correctly and give right results, so that no subpart produces
false inputs. All sub-circuits are connected to each other as shown in Fig. 4.20. The
vibration tracking unit is disconnected periodically from the piezoelectric film with the help
of an N-channel MOSFET. The pulse generator provides the voltage pulses to the P-channel
MOSFET. The non-inverted op-amp is more practical to consider for the overall system
implementation due to its operating characteristics. The complete system is simulated to
implement the two methods MPPT method and fixed band-band method.
47
Enable
CON
Vref1
0.5Vs
Vref2
Vibration
Tracking Unit
LoadBuck
Converter
Pulse
Generator
AC-DC
Rectifier
Control Unit
Piezo
Film
Control Pulse
C5
GND5
N1
P1
R2
R1
GND4
S1
Voltage
Divider
Vout
Energy Harvesting System
Figure 4.20. Overall Energy Harvesting System
Figure 4.21. Overall Energy Harvesting System in SimscapeTM
48
4.9.1. Overall Energy Harvesting System with Non-Inverted Op-Amp using MPPT Method
In this method, the vibration tracking unit is connected periodically with the piezo-
electric film to track the optimal voltage. This done by the N-channel MOSFET operation.
Voltages are measured across the piezoelectric sensor and storage capacitor. The complete
system circuit is simulated for three 30 Hz, 60 Hz, and 90 Hz.
The voltage achieved at the output of the piezoelectric sensor in the overall system is mea-
sured as Vpz and varies in the range of 1 V to 6 V. It is directly proportional to Ip and
inversely proportional to the frequency. Therefore, it is increasing linearly with the increase
in vibration magnitude. This voltage must be positive in order to run the system simulation
appropriately. Hence, the achieved voltage does fulfill the necessity of required voltage. This
is illustrated in Fig. 4.22.
10 20 30 40 50 60 70 80 90 1001
1.5
2
2.5
3
3.5
4
4.5
5
5.5
6
Vp(V
)
at f=30 Hzat f=60 Hzat f=90 Hz
Figure 4.22. Voltage at Piezoelectric Sensor Output in Overall Energy Har-
vesting System with MPPT Scheme
The voltage measured at the storage capacitor in this method shows an approximate
49
linear relation with the input vibration magnitude Ip and inverse relation with the frequency
of vibration and piezoelectric capacitance. Cp is constant. So, the voltage is stored in a
direct fashion with respect to the input vibration magnitude. The increase in the stored
voltage influences with the voltage gain of the amplifier. The voltage stored across the
storage capacitor Cs varies from 0 V to 0.9 V. Fig. 4.23 presents this result.
10 20 30 40 50 60 70 80 90 1000
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Vs(V
)
at f=30 Hzat f=60 Hzat f=90 Hz
Figure 4.23. Voltage Stored in Overall Energy Harvesting System with
MPPT Scheme
Here the harvested power is calculated by using the equation of instantaneous power.
The amount of harvested power is increasing gradually. The graph in Fig. 4.24 shows that
the power harvested increases with increase in input vibrational amplitude and decreases in
the given frequency. This is obvious because the instantaneous power is directly proportional
to the vibration magnitude and stored voltage. The power of 0 µW to 60 µW is harvested in
this method of energy harvesting system.
50
10 20 30 40 50 60 70 80 90 1000
10
20
30
40
50
60
at f=30 Hzat f=60 Hzat f=90 Hz
Figure 4.24. Power Harvested in Overall Energy Harvesting System with
MPPT Scheme
4.9.2. Overall Energy Harvesting System with Non-Inverted Op-Amp (Fixed Band-Band
Method)
The second method considered for the implementation of the overall system is fixed
band-band. In this method, the reference voltages Vref1 and Vref2 of the tracking unit are
maintained at an approximate value of difference to get the optimal voltage obtained at the
storage capacitor in a fixed range. The N-channel and P-channel MOSFET play the role of
switches in the system to interconnect the sub-circuits in the required manner. It is con-
firmed that the switches provide correct and applicable inputs and outputs to the referenced
parts. This leads to the proper execution of the system to maintain the harmony. In this
implementation, reference voltages Vref1 and Vref2 are fixed at 1.4 V and 2 V, respectively.
Three sets of frequencies, i.e. 30 Hz, 60 Hz, and 90 Hz are taken into account in this method
as well for the simulation of the system circuit. The voltage at sensor in the harvesting
51
system with this method is shown in Fig. 4.25.
10 20 30 40 50 60 70 80 90 1000
1
2
3
4
5
6
Vp(V
)
at f=30 Hzat f=60 Hzat f=90 Hz
Figure 4.25. Voltage Achieved at Piezoelectric Sensor Output in Overall
Energy Harvesting System with Fixed Band-Band Scheme
The optimal voltage stored in this method must be within the range of 4 times multiple
of Vref2 to maintain the band-band operation in the complete system [18]. As shown in the
graph of Fig. 4.26, the harvested voltage is fulfilling the condition as the max of it is within
the range of 4 times multiple of Vref2. The voltage stored across the storage capacitor Cs is
varying from 0 V to 0.55 V. It is linearly increasing with the increase in vibration magnitude
because they are directly proportional to each other. Although the frequency response should
be in inverse proportion, it is slightly varying on the graph due to the input values of circuit
elements.
The harvested power is calculated with the instantaneous power formula. It is directly
proportional to Ip, while inversely proportional to the input frequency. Therefore, at the
lower frequency, less power is achieved. The power achieved in this method is varying from
0 µW to 30 µW as shown in graph in Fig. 4.27.
52
10 20 30 40 50 60 70 80 90 1000.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
0.55
Vs(V
)
at f=30 Hzat f=60 Hzat f=90 Hz
Figure 4.26. Voltage Stored in Overall Energy Harvesting System with Fixed
Band-Band Scheme
10 20 30 40 50 60 70 80 90 1000
5
10
15
20
25
30
35
at f=30 Hzat f=60 Hzat f=90 Hz
Figure 4.27. Power Harvested in Overall Energy Harvesting System with
Fixed Band-Band Scheme
The power efficiency of the system is calculated as the ratio of power achieved in the
53
system simulation to the maximum power extracted in theory [18].
(20) PowerEfficiency =Powersimulation
Powertheoritical
When vibration Ip is very low in the starting, the energy efficiency is low because the voltage
at the storage capacitor is not sufficient to execute the operation. It increases as the storage
capacitor Cs gets charged. The energy efficiency of the system in the MPPT method and
fixed band-band method is shown in Fig. 4.28 for the 60(Hz) frequency values. The highest
energy efficiency is achieved at the highest frequency. Thus, power efficiency of the system
increases with the increase in frequency of the input vibrations.
10 20 30 40 50 60 70 80 90 1000.06
0.08
0.1
0.12
0.14
0.16
0.18
0.2
0.22
0.24
Pow
er E
ffici
ency
(%
)
In MPPT methodIn Fixed Band-Band method
Figure 4.28. Power Efficiency of Overall Energy Harvesting System with
MPPT and Fixed Band-Band Methods at 60 Hz
54
CHAPTER 5
CONCLUSION
5.1. Summary and Conclusion
Energy harvesting is becoming a necessity as electricity generating resources are lim-
ited. The generation of electricity using conventional methods is very costly and causes
pollution in the surrounding. The waste of electronic devices and cables is not decompos-
able. Additionally, recycling of these wastes is very costly and releases polluting chemicals
in the atmosphere. Every year, tremendous amounts of such trace elements is disposed into
the surrounding. These concerns are indicating requirements to utilize natural resources of
energy for proving electrical power.
This thesis has presented the modeling and simulation of a piezoelectric sensor based battery-
free energy harvesting system in SimscapeTM. The energy harvesting system harvests power
from the ambient energy contained in environmental vibrations. The voltage is stored in
a capacitor. The system shows the ability to operate very well between the frequencies of
20 Hz to 100 Hz with the input vibration magnitude of 0 µA to 100 µA. The system is ca-
pable of harvesting 0 µW to 100 µW power. The energy harvester subcircuitry is modeled
and simulated without amplifier, with inverted, and with non-inverted amplifier to observe
the benefit of using amplifiers. The voltage is stored from 0 V to 100 Hz in all three types of
energy harvester. The complete system is modeled using a non-inverted amplifier because
it provides better results for the small vibration magnitude as current at the input and has
higher input impedance. The overall system is implemented with two methods to observe the
amount of power harvested: maximum power point tracking, and fixed band-band method.
Results show that more power is harvested in the maximum power point tracking method
and hence this system has greater energy efficiency. The outcomes of this work indicate
that the power efficiency is mostly from 0.5% to 30%, which makes the system applicable in
practical applications.
55
5.2. Future Directions
Future work can concentrate on increasing the power efficiency and decreasing power
overhead of the system. Work can be done in achieving more voltage at the storage capac-
itor, which eventually leads to increased power. A sophisticated voltage storage element is
required to improve the storage capacity, but also it is necessary to be applicable in real time
implementation. The vibration tracking unit can be considered to miniaturize the circuitry.
Improved methods for harvesting energy can be expected in the future. Research can be tar-
geted to harvest the energy from other natural energy resources such as tidal, temperature
variant, and RF. Energy harvesting from natural resources is very important requirement
for today’s world as conventional resources are available in limited quantity. Efforts could
be made to provide supply with this method for high power devices. Integration of a piezo-
electric sensor in the battery chargers or smart batteries is an interesting idea for future
research [28, 21, 20]. Higher level integration in wireless sensor networks for diverse applica-
tions in smart cities can be practically beneficial and hence is worthy of further investigation
[32, 33, 25].
56
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