piezo-electric power scavenging for mining applications
TRANSCRIPT
Piezo-electric Power Scavengingfor Mining Applications
Upendra K. Singh
A thesis submitted in partial fulfilmentof the requirements for the degree of
Master of Philosophy
School of Electrical Engineeringand Computer Science
in partnership withCRC Mining
The University of NewcastleCallaghan, NSW 2308
Australia
February, 2007
I hereby certify that the work embodied in this thesis is the re-
sult of original research and has not been submitted for a higher
degree to any other University or Institution.
Upendra K. Singh
ACKNOWLEDGEMENT
I have been very privileged to have undoubtedly the most intuitive, smart and supportive supervisor
anyone could ask for, namely Richard H Middleton. Ever since I met him during my undergraduate
degree supervision, I have been stimulated, encouraged and excited by his constant flow of excellent
ideas. Rick has an ability to cut through reams of ideas with a great visual and meaningful explanation
that I will always admire, and I have learned a great many engineering interpretational skills from
him. He has fostered certainly the most open, friendly, collaborative and competitive research group
in control and power engineering in the school of Electrical Engineering and Computer Science at
the University of Newcastle. He has also known when (and how) to give me a little encouraging and
motivating push in the forward direction when I needed it.
I thank Dianne Piefke for spending her time on helping me to arrange administrative work for schol-
arship and studentship matters. I thank the head of School of Electrical Engineering and Computer
Science, the research co-ordinator, advisor and the relevent academics, dignitaries and executives
from the University of Newcastle for providing me help, resources and a great supervisor to accom-
plish my master of philosophy degree.
Throughout my two years, I was supported financially by CRC Mining. I thank CRC Mining for the
big support. I thank the CRC Mining group for sending me off to student’s retreat programs to learn
and participate in some extra-curricular activities. I thank the CRC mining staff who have been able
to supply me resources when needed. I thank Galina Mirzaeva for keeping both CRC Mining and
myself up-to-date on my progress and I thank Nicholas Hawryluk, our laboratory technical officer
(Research), for making my printed circuit board and Peter Turner for helping me carry out health and
safety induction. I would also like to thank my friends from my church and my housemates for being
with me in hard times and good times encouraging me to keep going to finish the project.
CONTENTS
Acknowledgement iii
Abstract 1
1 Introduction & Background 3
1.1 Energy Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.2 General Power Scavenging . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.2.1 Piezoelectric . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.2.2 Electromagnetic/Inductive . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.2.3 Thermoelectric . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.2.4 Capacitive . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.2.5 Light to Electricity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.2.6 Wind to Electricity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
1.2.7 Suitable source and scavenging of energy in the mining environment . . . . . 16
2 Vibration & Piezoelectric Modeling 17
2.1 Introduction to piezoelectric modeling . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.1.1 Mechanical and Electrical . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.1.2 Piezoelectric Constants and Terminologies . . . . . . . . . . . . . . . . . . 19
2.1.3 Piezo Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.2 Vibration Specifications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.3 Typical RLC . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.3.1 Resonance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
Contents v
2.4 Resonant Peaks Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.5 Vibration Spectrum Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.6 Piezoelectric Element Selection and Specifications . . . . . . . . . . . . . . . . . . 32
3 Idealised Simulations 36
3.1 R load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.1.1 Maximum Power Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.2 RL load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.2.1 Results for L = 55mH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
3.2.2 Results for L = 100mH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.2.3 Results for L = 300mH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.2.4 Results for L = 500mH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.2.5 Results for L = 700mH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.2.6 Results for L = 900mH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
3.3 Summary of results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4 Detailed Simulation 49
4.1 Rectifier and Vdc Load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
4.2 Rectifier, Capacitor, L and DC/DC converter . . . . . . . . . . . . . . . . . . . . . . 53
4.2.1 OPAMP analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
5 Detailed Experimental Results 63
5.1 Rectifier & Vdc load . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
5.2 Rectifier, DC/DC converter & Vdc load . . . . . . . . . . . . . . . . . . . . . . . . 66
5.2.1 Measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
Contents vi
5.2.2 PCB and Breadboard . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
6 Conclusion 77
6.1 Suggestions for further research . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
Glossary 79
Bibliography 81
ABSTRACT
The growing need of creating a network of sensors in critical environment to monitor, sense and alert
an operator about the environment gives rise to the research work carried out in the area of power
supply to these sensors. Wireless sensors are usually designed to run on batteries. However, as
the number of sensors increases and the devices decrease in size, there is clearly a need to explore
alternatives to battery power for wireless sensors. Reliable, efficient and environmentally friendly
energy harvesting methods could be adopted to design and build a new electronic device that could
be used to replace or supplement batteries in wireless sensors.
This thesis focuses on potential ambient sources of power that can be "harvested" to run low power
wireless sensors in mining environments. It discusses several techniques for converting energy from
such sources into useful electrical power. In particular, piezoelectric power conversion technique is
described in detail.
Wireless sensor or sensor networks hold significant potential in the mining environment. The need
for deployment of such sensor networks is increasing daily as mining companies are looking to adopt
the system developed in the "Intelligent Mine - Technology Program (IMTP)" (Särkkä et al. 2000).
The objectives of the IMTP are to increase the mine’s productivity, decrease the total costs and to
improve the working conditions. To complement these objectives, there have to be improved methods
for powering sensor devices to deploy them in large numbers.
Drilling is a crucial component in both underground and surface mining. Water jet assisted drilling
is an example of a new drilling technology employing wireless sensors. There are various forms
of energy that could potentially be used to power wireless electronic sensors provided the waste
energy can be tapped in an intrinsically safe way. In this particular project, the required power to
run sensors could be generated by converting mechanical vibration produced from water jet assisted
drilling into electrical energy with an intrinsically safe circuit. Various power scavenging methods
were researched, but vibration-to-electricity conversion using piezo-ceramic material was selected as
the most promising method for this project.
Piezo-based energy conversion is not normally good for mining applications because of intrinsic
safety issues. In the case of water jet assisted drilling, however, the environment is much more
suitable for piezo-electric conversion. A detailed computer model for this type of power conversion
has been developed. The mechanical model of the vibration spectrum is based on test data from the
Contents 2
CRC-Mining group. A power conversion circuit has been built, detailed circuit simulations studied
and the experimental results are demonstrated.
An example vibration scenario consisting of (20×10−6)rms strain is considered. Based on this, and
a detailed model of a 70mm× 25mm PZT piezoelectric patch with 0.2mm thickness, our computer
simulation studies and experiments demonstrate the ability to harvest up to 210mW of power.
CHAPTER 1
INTRODUCTION & BACKGROUND
Advances in technology enable innovative approaches to long standing engineering problems. Suc-
cessful outcome of such innovative approaches can dramatically benefit society in terms of new prod-
ucts, increased outputs, reduced costs and general modernizations.
Australia possesses abundant natural resources and hence the mining industry has become the largest
source of income for this country. Mining is the extraction of minerals from earth. There are mainly
two types of mining: (1) underground mining and (2) surface mining. Due to the high profits gen-
erated from the export of natural resources (e.g. coal, copper, gold, aluminium, iron and uranium),
both government and private sectors have funded a wide range of research and discovery programs
that could further improve the technologies used in mining. As a result, the birth of this project work
has taken place at CRC Mining group which is a research organisation funded by its members most
of whom are the mining companies and the government.
In most cases technology progresses via a smooth path of continuous improvements. There are some
technologies that change much more rapidly than others. However, innovations in mining technology
typically occur very slowly. Water is used in various ground drilling processes for mining and other
applications. The growth of the technology in waterjet mining has opened up opportunities for some
technology that can be a better alternative to the existing one. For example short-life battery powered
sensors can be powered by a long lasting power supply that can be built to harvest power from avail-
able local source of energy such as vibration in the case of waterjet mining. Recent innovations, such
as waterjet coal mining and longwall mining despite being based on very old technologies have de-
veloped into their modern forms due to new ideas, innovations and advancing inftrastructure. Various
equipments and the technologies that drive them have become more sophisticated and have changed
the way mining is done today from how it used to be done a couple of decades ago. The evolution
of these technologies has brought with it some challenges in modern mining environments where the
need for a reduction in the number of human operators in underground mining is becoming a major
and demanding topic of research. The automation of most mining operations increases productivity,
reduces operating costs and provides better health and safety standard by taking people away from
potentially hazardous areas. Such automation can be achieved by remotely controlled operations,
4
auto-controlled and auto-powered devices and sensors. Sensors are crucial devices for various forms
of automation.
Sensors are used for detecting and monitoring a range of physical conditions in various environments.
The information collected by the sensors can be used for research, maintenance, safety and control.
For example, sensors are used to detect and monitor gas, air flow, temperature, vibration, pressure,
humidity, motion, position and various other useful physical conditions.
An above ground operator could remotely supervise different physical phenomena in the mine from
his computer and thus provide safety precautions and warnings for the miners working underground.
The level of harmful gases such as methane can be monitored and various other physical conditions
like pressure, humidity, temperature, can be monitored. Thus the monitoring applications in mining
industry has become one of various critical operations to maintain safety. These applications can be
seen as a first step towards the concept of the "intelligent mine". However, several difficulties must be
overcome before we can use the immense potential of mobile ad-hoc networks (Särkkä, Liimatainen,
and Pukkila 2000).
The sensors used in water jet mining detect, monitor and convey the position and orientation of water
jet assisted drill to another communication device, a computer in this case. One of the difficulties iden-
tified is supplying power to run these sensors. Replacing alkaline batteries in those sensors becomes a
very tedious, time-consuming and labour intensive job. This difficulty challenges researchers to come
up with alternative sources of power that could replace conventional batteries with more efficient, less
costly and longer life power supplies.
The project specifications highlight the need for more durable, cost effective, efficient and wireless
electrical supply to power electronic sensors. Wireless power supply in this case means that power
can be locally generated from the available sources of energy in the vicinity of a device that requires
power, thus replacing the need of a cable that would otherwise obtain power from a main supply. Ad-
vanced technology in producing electricity from various forms of energy encourage and support us to
explore the sources of energy present in the vicinity of an electronic device. Potential ambient energy
sources available might be light, wind, heat, sound, vibration, pressure and temperature differential.
Given a potential energy source it is also crucial that we examine conversion techniques to generate
electrical power for a small wireless sensor.
(Roundy, Wright, and Rabaey 2003a)"The process of acquiring energy surrounding a system ("am-
bient energy") and converting it into usable electrical energy is termed power harvesting". It is also
5
known as energy scavenging. In the history of humankind, we have always scavenged power for our
various needs. For example, one of the most essential conversion has been burning firewood thus con-
verting it into heat energy to cook food. As the needs of energy consumptions on a safer, cheaper and
more sustainable level are identified, scientists and researchers are challenged to innovate, postulate
and invent new forms of power harvesting methods. Later in this chapter, we will discuss some of
them.
Many ambient energy sources e.g. energy sources available in the forms of vibration in bridges,
buildings, aeroplanes, automobiles are identified as a small source of energy because power extracted
from them are fairly small. However, power extracted from such sources could power up some elec-
tronic devices that use small electrical power such as calculator, mp3/FM players, remote controls,
sensors etc. As the energy requirement of these small devices become smaller, it enables us to tap
these sources and design an alternative power supply. For example, solar powered calculators have
been in use for a while now. This demonstrates the fact that such power sources can be cheaper and
sustainable.
Mostly we rely on main supply for most electrical and electronic devices in small to large scale home
or industrial environments. However, due to lightning and storms, it is highly likely that main power
supply can be lost for a period of time. This kind of situation requires a backup power supply to avoid
or minimise loss or damage or more importantly to keep the devices operational at all times, thus
creating a need of an autonomous power supply designed to make the devices self-powered. For some
devices that rely on electrical power to perform some very critical operations, for example sensors that
are used to monitor some particular area for safety and regulation, a back up power supply preferably
in the form of an autonomous power supply is a must. While UPS and fuel-run generators can be used
as a backup power supplies, they are more expensive, and may not be environmental friendly and are
surely not long lasting. For devices that require small power (for example many modern sensors),
power scavenging from the locally identified sources of energy is a better alternative power source.
Power extracted from such power source is more sustainable.
The use of piezoelectric material to convert vibrational energy into electrical energy is becoming more
popular. Piezoelectric materials have the ability to transform mechanical strain into electrical charge.
For example, as we walk or jog, our walking energy can be converted to electrical energy by using
piezoelectric or a proper power converting mechanism.
Nowadays, miniaturized systems with micro sensors can provide a large amount of information for
monitoring and controlling plants, mining environment, resources and infrastructures. The focus now
1.1 Energy Sources 6
is on how to supply power to these devices in order to enable fully-wireless operation. For example,
"bridge monitoring can be realized by placing smart sensors at a large number of positions on the
bridge" (Faravelli and Rossi 2003). Communication between the sensors and the main data centre will
become more reliable if the sensors have regular power supply at all times. To meet this requirement,
autonomous power supply scavenged from the local source of energy, e.g. vibration in the structure,
can be designed and implemented.
1.1 Energy Sources
Energy is one of the most fundamental needs of our life. In our daily life, we end up using some
sort of energy sources to meet our energy demand. Sources of energy can be found in different forms
and in different quantities. Food is a source of energy for humans and living animals. Our bodies
convert by digestion food into nutrients that we need to maintain our energy level. In the modern
industrialised world, we use energy in different applications, for example electrical energy is used
to drive electrical and electronic devices. Petroleum products are used to drive automobiles and fly
aeroplanes. Chemical energy stored in various forms of batteries is used to run static memory devices,
torch lights and various other electronic equipments. Solar energy is used in various solar powered
applications and in natural photosynthesis process. Heat energy is used to drive steam engines.
As the consumption of small power electronics are becoming more popular, it challenges the science
of power electronics to advance and bring more sophisticated means of power conversion methods
to build new power supplies to run these electronics. To achieve this, one has to identify various
alternative sources of energy. Some of the energy sources are discussed in this section.
We first discuss fundamental sources of energy that may be available before turning to discuss a
variety of energy conversion techniques. Some energy sources are abundant in nature and effectively
may last for an unlimited time. In general, this means they are continually replenished by a natural
processes working from solar energy, or in some cases, arising due to large terrestrial energy stores.
For study and research purpose, we classify such sources as sustainable energy sources. These energy
sources will essentially never run out. Table (1.1) lists some forms of this type of energy.
Energy sources that will eventually run out are known as non-renewable energy source in scientific
community. Among these, some energy sources will last longer than others. Energy source like
nuclear may take either a billion years or a billions of years to run out and hence there is some
argument over whether this should be classified as renewable or non-renewable. Table (1.2) lists
some forms of this category of energy.
1.1 Energy Sources 7
Renewable Energy sources
1 Solar
2 Wind
3 Water: Hydro, tidal, wave
4 Geothermal
5 Biofuel: Liquid, Solid biomass, Biogass
Table 1.1: Renewable Energy Sources
Non-Renewable Energy sources
1 Nuclear
2 Fossil fuels: Coal, Petroleum, Natural gas
3 Chemical: Batteries
Table 1.2: Non-Renewable Energy Sources
There are some energy sources found in an infrastructure, an object, operating machinery or a system.
We classify these as ambient energy sources. Scavenging power from such energy source is becoming
more popular in the modern world. Table (1.3) lists some forms of this type of energy.
Ambient Energy sources
1 Vibration
2 Motion
3 Sound
3 Thermal gradients
3 Light
Table 1.3: Ambient Energy Sources
1.2 General Power Scavenging 8
1.2 General Power Scavenging
This section examines the potential of a range of energy scavenging methods. Six different sources
have been investigated.
• Vibrations (piezoelectric)
• Motion (magnetic transducers)
• Thermal gradients (thermoelectric energy)
• Capacitive
• Light (photo voltaic cells)
• Wind
A block diagram representing a power harvesting technique from some of these sources is shown in
Figure (1.1). MPTT stands for Maximum Power Transfer Theorem which states that if the source and
PiezoTransducer
MagneticTransducer
MPTT
MPTT
MPTT
Rectifier
Rectifier
rechargerDC−DC Rechargeable
BatteriesPowereddevice
Current sensor
PhotovoltaicCell
Figure 1.1: Energy from various sources to recharge batteries (Casciati et al.
2003)
load impedance of a system are equal, maximum power will be transfered from the source to the load.
This is also known as Jacobi’s law after Moritz von Jacobi who discovered it. In the Figure (1.1),
MPTT represents electronic circuitry that uses this theorem.
1.2.1 Piezoelectric
Piezoelectricity is electricity due to piezoelectric effect. Piezoelectric effect is an effect due to strain
caused by a stress on a piezoelectric material, thus causing polarisation of electric charges on the
surface of the piezo material. A mechanical stress or strain on a pieoelectric material cause electric
potential to develop between two points on the surface of a piezo-electric material. The electric charge
is proportional to the force, and hence when under compression, the charge moves into a particular
direction and under tension, the charge moves in opposite direction. The stress or strain can come
1.2 General Power Scavenging 9
from many different sources such as human motion, automobiles, operating equipments, drilling,
earth-quakes, tidal waves, wind power etc.
As shown in the Figure (1.2), the voltage across a capacitor is produced due to strain in the piezoelec-
tric material(Amirtharajah and Chandrakasan 2004).
Figure 1.2: stress/strain on piezoelectric material(Amirtharajah and Chan-
drakasan 2004)
The values Cs and Rs are the source capacitance and resistance as given in Figure (1.3) and Vs is the
source voltage. Figure (1.3) shows a typical piezo generator.
Piezo Generator
Load
Vs
Cs Rs
Figure 1.3: A typical piezo generator with a load(Amirtharajah and Chan-
drakasan 2004)
The details of the piezoelectric power conversion mechanism are discussed in subsequent chapters.
1.2 General Power Scavenging 10
1.2.2 Electromagnetic/Inductive
Electricity can be produced by changing magnetic flux density using Faraday’s law of electromagnetic
induction, the water jet presents a huge force that can turn small turbines that drive small alternators
or generators thus producing electricity. All hydro, tidal, wave, steam and wind power stations use
this technology to produce electricity.
In this case, a coil moves through a magnetic field causing current in wire as given in Figure (1.4a).
In Figure (1.4b), the magnet moves into the coil and causes current to be induced in one direction, the
current is induced in other direction as the magnet moves out of the coil. This is based on Faraday’s
law of electromagnetic induction.
Michael Faraday in 1831 discovered that "a current was induced in a conducting loop when the
magnetic flux linking the loop changed. The quantitative relationship between the induced emf and
the rate of change of the flux linkage is known as Faraday’s law".(Chenge 1993)
e =−Ndφdt
(1.1)
(a) (b)
Figure 1.4: The Figures labeled (a) and (b) shows the induced current in the
coil (Amirtharajah and Chandrakasan 2004)
Electromagnetic induction is based on the following fundamental postulate:
∇×E =−δBδ t
(1.2)
Where E is electric field intensity, B is magnetic flux density and t represents time. Applying the
1.2 General Power Scavenging 11
surface integral of both sides of Equation (1.2) over an open surface and then Stoke’s theorem (Young
and Freedman 1996), we get: ∮
CE.dl =− d
dt
∫
SB.dA (1.3)
where l represents length and A represents Area. Equation (1.3) is valid for any surface S with a
bounding contour C.
The left hand of Equation (1.3) is induced emf. The right hand side of Equation (1.3), magnetic flux
can be written as:
φ =∫
SB.dA
If e be the induced emf, the Equation (1.3) can be reduced to
e =−δφδ t
If we have N number of coils, then
e =−Nδφδ t
which is also one of the Maxwell’s equations.
However, for the particular case of interest, using this technique is not viable due to the presence of
high fidelity magnetic sensors. Sensors used in mining environment have to record more accurate
information about the location and orientation of a drill. Such sensors could suffer from significant
interference from either permanent or electromagnets near the sensor.
1.2 General Power Scavenging 12
1.2.3 Thermoelectric
Thermal source of energy exists whenever there is a temperature difference between two physical lo-
cations. The thermoelectric effect allows the conversion from temperature differentials to electricity.
As shown in Figure (1.5), two junctions T1 and T2 are connected by two different conductors A and
B such that it forms an open loop circuit with a gap in conductor B. Figure (1.5), If T is the temper-
T1
V+
-
B
B
A
T2
Figure 1.5: Thermoelectricity: Seedbeck effect(MacDonald 1962)
ature at junction T1, then let T + δT be the temperature at junction T2. A potential difference, δV is
produced across the gap. δV is directly proportional to δT . The thermoelectric potential is known as
Seebeck potential as it was discovered by Thomas Johann Seebeck (1770-1831)(MacDonald 1962).
The thermoelectric power can be given as the derivative of VAB with respect to temperature T . "If the
thermoelectric potential difference, δV has the polarity as shown in Figure (1.5), then absolute ther-
moelectric power (SA) of conductor A is positive with respect to that (SA) of conductor B"(MacDonald
1962). It can be mathematically expressed as:
dVdT
= SA−SB
or,dV = (SA−SB)dT
Thus,
V =∫ T+δT
T(SA−SB)dT (1.4)
Thus the voltage produced, V due to the thermoelectric effect can be calculated by using the formula
given in Equation (1.4)
Converting heat energy into electricity this way requires thermocouples to be installed. Hence it will
1.2 General Power Scavenging 13
require extra maintenance and cost. The temperature differential needs to be maintained to provide
constant electricity. This may require other sources of energy like propene or natural gas to keep
the temperature differential. Use of such gases in mining environment can lower the intrinsic safety.
Thermo-controllers may be required to control the supply of heat to maintain the temperature differ-
ential. Therefore, in the mining environment, this type of power scavenging would be very complex
to implement.
1.2.4 Capacitive
Vibration energy can be converted to electrical energy by using electrostatic (capacitive coupling).
Ahmed Nounou & Hani F. Ragaie discuss this process in (Nounou and Ragaie 2000). As discussed
in the paper, power generation using this process is feasible using a laterally driven comb structure
based on MEMS technology. "It is shown that the generation of about 10µW is possible using
the SOIMUMPs technology based structure operating at 120 Hz"(Nounou and Ragaie 2000). As
Figure 1.6: Combo Drive for changing capacitance(Nounou and Ragaie 2000)
capacitance is varied, the voltage or charge increases. The concept of this power conversion is based
on changing the capacitance C by keeping either charge, Q or voltage, V constant in the relation C=
Q/V. In either case, the energy stored on the capacitor given by Eq. (1.5) increases.
E =12
CV 2 (1.5)
1.2 General Power Scavenging 14
1.2.5 Light to Electricity
Sunlight is the source of solar energy. It contains photons which may be considered as energy par-
ticles. When a photon strikes a metal surface, it excites the electron to a higher energy state within
the metal, and soon after this, the excited electrons return to their ground state. However in some
devices such as photovoltaic device, the excited electrons are pulled away and are unable to come
back to their ground state. As a result a potential difference is produced. The potential difference is
also known as electromotive force which drives the electrons through an electrical load connected to
it as shown in the Figure (1.7).
e
LOAD
p n
PV Cell
Light
Figure 1.7: Photovoltaic effect (Nelson 2003)
As explained in (Nelson 2003) "solar photovoltaic energy conversion is a one-step conversion process
which generates electrical energy from light energy". A solar cell is a basic building block of all
LoadPV generator
(AC grid)(DC battery)Storage
Powermonitoring andconditioning
Figure 1.8: A typical photovoltaic process and application(Nelson 2003)
photovoltaics. The cell is also known as photovoltaic cell or PV cell. Solar cells are usually made of
silicon crystals. It can be made from either a single crystal of silicon or multiple silicon crystals. It
can also be made from non-crystalline silicon or from other materials. Each PV cell when exposed to
solar light produces direct current of tens of milliamps per cm2 and generates a voltage in the range
or 0.5 to 1V(Nelson 2003). A typical photovoltaic process and application is given in the Figure (1.8)
1.2 General Power Scavenging 15
In an underground mining environment, there is no sunlight, hence it can not be used. Even in the
surface mining environment, while this technique can be considered, the requirement of constant
power supply may not be achieved due to unpredictable weather pattern.
1.2.6 Wind to Electricity
Electricity can be produced by turning turbines using wind energy. Air in motion is wind. Wind has
mass with a low density. When any mass has a velocity, it produces kinetic energy which is
Kinetic Energy =12×Mass×Velocity2
Suppose, A = Area through which the wind would pass normally, M = Mass of the air that would pass
through this area, ρ = the mass per unit air volume = air density, v = wind velocity, V = Volume of
the air, then mass of air per unit time is:
Mt
=ρVt
=ρAL
t= ρAv
where L is a length and Lt is v, velocity of the air. Thus, power, the total kinetic energy of the wind per
unit time is 12 ρAv× v2 = 1
2 ρAv3. Wind power can be directed at the wings of a windmill, as a result
the wings rotate. The rotation produces torque on a rotor used in the windmill.
As explained in the book (Golding 1955), A. Betz of the institue of Gottingen proved in 1927 that the
maximum fraction of the power in the wind that could be extracted by an ideal aeromotor was 0.597
of the available kinetic energy. Thus,the total power converted in an ideal windmill would be:
P = 0.593× 12
ρAv3 (1.6)
Thus, we can say that the amount of power transferred from the available power of the wind to a load
via this process is directly proportional to the area swept out by the rotor, air density, and the cube of
the wind speed.
Again, due to the same drawbacks as found in the solar energy use in the mining environments, this
energy is not suitable either for power scavenging.
1.2 General Power Scavenging 16
1.2.7 Suitable source and scavenging of energy in the mining environment
After the detailed investigation and analysis of available energy sources and their conversion into
electricity in mining environments, one promising source of energy is mechanical vibration which
can be harvested using piezoelectric power conversion technique. Power can be harvested from this
source to supply enough power to the wireless sensors. The research, design, simulation and results
presented in this thesis justify this analysis.
In this project, I have carried out research and have designed and built an electronic circuit that
uses mechanical vibration (from 100HZ to 10KHz) as the source of energy and converts them into
electrical energy which is then stored into 2× 1.2V rechargeable batteries. The conversion method
is piezo-electric; this means, a piezo-ceramic is excited by the vibration of the frequency mentioned
above. The ambient vibrations present in the water jet drilling have been measured by accelerometers
and the measured data is used as the source signal for the design of an electronic circuit. This circuit
takes the piezo generated AC, then convert it to DC using a full wave rectifier and then maximum
power is transferred and regulated to the storage using DC-DC converter method.
CHAPTER 2
VIBRATION & PIEZOELECTRIC
MODELING
2.1 Introduction to piezoelectric modeling
Vibration and piezoelectric modeling requires specification of materials and knowledge about their
electrical and mechanical properties. Because the thesis concentrates on converting mechanical en-
ergy into electrical energy, the mechanical and electrical properties of the materials involved in this
project need to be studied. This chapter describes research on properties of piezoelectric material
used in this project.
Because piezo-electric phenomenon combines mechanical and electrical properties of a piezo-electric
material, knowledge of electrical properties like permittivity and capacitance and the mechanical
properties like Youngs Modulus, Yield’s strength etc are crucial.
2.1.1 Mechanical and Electrical
Before we discuss the direct electrical effect of a force onto a piezoelectric material, let us discuss
some mechanical effects. When an external force is applied to a material, the body of the material
expands and when the force is removed, the material returns to its original shape. "The ability of the
body to return to its original shape is called elasticity"(Weidner and Sells 1975). When a spring is
stretched with a force, F , causing a displacement, x, the relationship between force and displacement
can be given as:
F =−kx (2.1)
(Weidner and Sells 1975) where k is spring constant which is a measure of spring’s stiffness. Stiffer
springs will have a larger value of k. This relationship is also known as Hooke’s law after the 17th
century physicist Robert Hooke who formulated this relation. The Equation (2.1) can also be written
as:
S = sT (2.2)
2.1 Introduction to piezoelectric modeling 18
where S is strain, s is compliance factor and T is stress. This relation is known as Hooke’s law of elas-
ticity. It represents the observation that in many cases the strain in a material is directly proportional
to the stress on the material.
Permittivity and Dielectric Constant
Permittivity of a material is defined as its ability to permit an electric field through itself. Higher
permittivity of a material means easier transmission of electric field through its medium. "The ratio
of capacitance with and without the insulator is called the dielectric constant K of the insulator"(Arya
1979). If Cmed and Cvac are the capacitances of an insulator and vacuum respectively, then
K =Cmed
Cvac
For a parallel plate capacitor with air between the plates, the capacitance can be given as:
C = ε0Ad
If we use a dielectric between the two plates, the capacitance is given as:
C = Kε0Ad
= εAd
(2.3)
where ε is called permittivity of the dielectric and given by
ε = Kε0
or
K =εε0
where ε0 is permittivity constant of free space or vacuum whose value is 8.85418×109Nm2/C2. Thus
we find out, relative dielectric constant of a material can also be defined as the ratio of permittivity of
a material to the permittivity of free space.
Dielectric material has another electrical property called susceptibility denoted by χe. susceptibil-
ity is directly proportional to polarisation of charged particles under an applied electric field. High
susceptibility means the material allows the polarisation to take place quite easily under an applied
electric field. Electric permittivity is determined by this. Various phenomena like electric permittivity,
capacitance and speed of light in the medium are determined by it.
The susceptibility of a medium is related to its relative permittivity εr by
χe = εr−1
2.1 Introduction to piezoelectric modeling 19
In a vacuum, εr = 1 and hence χe=0. The electric displacement D is related to the polarization density
P by
D = ε0E +P = ε0(1+ χe)E
Or, it can be written as
D = εE (2.4)
This is a fundamental relation that says that electric displacement is directly proportional to the ap-
plied electric field.
2.1.2 Piezoelectric Constants and Terminologies
Piezoelectricity and "g","d" constants
Creation of an electric charge by an applied stress is called direct piezoelectric effect. The charge
produced is directly proportional to the applied force. Direction of charge under compression is
opposite to that in tension. It can be expressed mathematically as below:
If D is the dielectric displacement, Q is charge, A is area and T is stress, then we can write
D =QA
= dT
where d is piezoelectric constant expressed in Columbs/Newton
An effect where a material is strained due to an applied electric field is called converse piezoelectric
effect. If E is electric field and S is strain, then
S = dE (2.5)
where d is piezoelectric constant expressed in meters/volt. As we find out in both piezoelectric effects,
the piezoelectric constants "d" is numerically identical. However the most frequently used constant in
direct piezoelectric conversion is "g" which is related to constant "d" by the permittivity ε as below:
g =dε
=d
Kε0
"g" is a measure of the electric field produced by an applied stress. And therefore, material with high
"g" constant is chosen for piezoelectric power conversion application. "g" can be mathematically
expresses as:
g =Electric Field
Applied Mechanical Stress
where the unit for the electric field is Volts/meter and the unit of the applied mechanical stress is
Newton/m2. Thus the unit for the "g" constant is MeterVolts/Newton.
2.1 Introduction to piezoelectric modeling 20
There are two more piezoelectric constants known as "e" and "h" which relates Stress T, Strain S and
electric field E as given below(William and Jaffe 1971):
T =−eE
E =−hS
According to Jaffe and Berlincourt in the book (William and Jaffe 1971), the piezoelectric constants
are the partial derivatives taken at "constant stress (subscript T), constant field (Subscript E), constant
displacement (Subscript D) or constant strain (subscript S)". These can be mathematically written
as:
d = (δSδE
)T = (δDδT
)E
g = (−δEδT
)D = (δSδD
)T
e = (−δTδE
)S = (δDδS
)E
h = (−δTδD
)S = (−δEδS
)D
(William and Jaffe 1971)
Coupling Factor
The coupling factor usually denoted by k is possibly the best indicator of the strength of a piezoelectric
effect. When stress is applied to the piezoelectric material, part of the input mechanical energy applied
is converted into electrical energy and the coupling factor can be defined as follows:
k2 =mechanical energy converted to electrical energy
input mechanical energy
For the converse piezoelectric effect, when an electric field is applied, part of the input electrical
energy is converted into mechanical energy and the coupling factor for this effect is defined as:
k2 =electrical energy converted to mechanical energy
input electrical energy
There is never a 100% conversion of input energy to the output energy, and hence in either effects of
the piezoelectricity, k2<1 and hence k < 1.
2.1 Introduction to piezoelectric modeling 21
The mechanical variables stress and strain are related to the electrical variables field and displacement
with following equations of state of the piezoelectric effect.
D= [d]T+[ε t]E (2.6)
S=[sE]T+[dt ]E (2.7)
where d represents a matrix of the piezoelectric constants. The superscript t stands for matrix-
transpose. The equation (2.6) describes the direct piezoelectric effect. The equation (2.7) describes
the converse piezoelectric effect. These relations are also known as coupling relations of piezoelectric
effect. The mechanical and electrical constants are affected by mechanical and electrical boundary
conditions respectively. These properties are orientation-dependent in all peizoelectric materials.
The above general equation (2.6) and equation (2.7) representing strain-charge relationship for a
material of the 6mm PZT crystal class can also be written as (William and Jaffe 1971):
S1
S2
S3
S4
S5
S6
=
SE11 SE
12 SE13 0 0 0
SE12 SE
11 SE13 0 0 0
SE13 SE
13 SE33 0 0 0
0 0 0 SE44 0 0
0 0 0 0 SE44 0
0 0 0 0 0 SE44
T1
T2
T3
T4
T5
T6
+
0 0 d31
0 0 d31
0 0 d33
0 d15 0
d15 0 0
0 0 0
E1
E2
E3
where SE44 = 2(SE
11−SE12).
D1
D2
D3
=
0 0 0 0 d15 0
0 0 0 d15 0 0
d31 d31 d33 0 0 0
T1
T2
T3
T4
T5
T6
+
ε11 0 0
0 ε11 0
0 0 ε33
E1
E2
E3
As given in the following figure (2.1), the subscript 3 refers to the poling axis, Axes 1 and 2 refer to
arbitrarily chosen orthogonal axes in the plane normal to axes 3. Subscripts 4,5 and 6 represent shear
stress and strain in planes normal to the axes 1,2 and 3 respectively. Conventionally, the first subscript
of "d" constants gives the "electrical" field and the second gives the component of mechanical strain.
2.1 Introduction to piezoelectric modeling 22
X
Y
Z
1
2
3
4
5
6
Poling Axis
Figure 2.1: Piezo Material Poling Direction
Axis numbers and their meaning
Number Axis
1 X
2 Y
3 Z(poled)
4 Shear around X
5 Shear around Y
6 Shear around Z
P Radial vibration
Table 2.1: Axis Definition
Equation (2.7) can be further extended as given below in Equation (2.8). If J represents current
2.1 Introduction to piezoelectric modeling 23
density, then
J =−δDδ t
J3 =δδ t
(D3)
J3 =δδ t
(d31T1 +d32T2 +d33T3)+ εδE3
δ t
I = AJ3
E3 =Vd3
I = Aδδ t
(d31T1 +d32T2 +d33T3)+ εAd3
δVδ t
I = Aδδ t
(d31T1 +d32T2 +d33T3)+ εAd3
δVδ t
I = Cδδ t
(d3
ε33(d31T1 +d32T2 +d33T3)+V )
Or,
I = Cδδ t
(Vx +V ) (2.8)
where Vx = d3ε33
(d31T1 +d32T2 +d33T3)
Vx = Function of stress
XC
Vx
Piezo
Figure 2.2: A typical piezo generator source
2.1 Introduction to piezoelectric modeling 24
Electrical - Mechanical Analogies
Electrical Mechanical
Descriptoin Unit Descriptoin Unit
Voltage, e (V) Force, f (N)
Current, i (A) Velocity, v (m/s)
Charge, Q (C) Displacement, s (m)
Capacitance, C (F) Compliance, CM (m/N)
Inductance, L (H) Mass, M (Kg)
Impedance, Z (Ω) Mechanical Impedance ZM
i = dQdt v = ds
dt
e = L didt = L d2Q
dt2 f = M dvdt = M d2s
dt2
Table 2.2: Electrical and Mechanical Analogies
2.1.3 Piezo Symbols
Piezo Symbol Definitions
Symbol Object Type Size Units Meaning
T vector 6×1 Nm2 stress components (e.g.σ1)
S vector 6×1 mm strain components
E vector 3×1 NC electric field components
D vector 3×1 Cm2 electric charge density displacement components
s matrix 6×6 m2
N compliance coefficients
c matrix 6×6 Nm2 stiffness coefficients
ε matrix 3×3 Fm electric permittivity
d matrix 3×6 CN piezoelectric coupling coefficients for Strain-Charge form
e matrix 3×6 Cm2 piezoelectric coupling coefficients for Stress-Charge form
g matrix 3×6 m2
C piezoelectric coupling coefficients for Strain-Voltage form
q matrix 3×6 NC piezoelectric coupling coefficients for Stress-Voltage form
Table 2.3: Piezo Symbols
2.2 Vibration Specifications 25
Other forms
State variables representing stress T, Strain S, displacement D and electric field E can be rearranged
to give other forms of piezoelectric constitutive equation as given in the Table (2.4)
4 forms of piezoelectric constitutive equation
Strain-Charge Form: Strain-Voltage Form:
S=[sE
]T+[dt ]E S=[sD
]T+[gt ]DD= [d]T+
[εT
]E E= [−g]T+[εT−1
]DStress-Charge Form: Stress-Voltage Form:
T=[cE
]S− [ε t ]E T= [cD]S− [qt ]DD= [e]S+
[εS
]E E= [−q]S+[εS−1
]D
Table 2.4: Four forms of piezoelectric equations(William and Jaffe 1971)
2.2 Vibration Specifications
Water jet assisted drilling gives rise to large mechanical vibrations. Vibration from this source has
been measured with an accelerometer. The acceleration magnitude of the vibrations is plotted against
frequency over the log scale. As shown in Figure (2.3), there are two main resonant peaks to consider
and those peaks at about 400Hz and 1600Hz are chosen. Here is a graph of recorded spectral data
that was supplied by CRC-Mining.
The data presented in Figure (2.3) and (2.4) was supplied by Eddie Prochon from CRC Mining group
in mid 2004. As clearly seen in the graph, there are many peaks. Most of them are small and some
of them are big. We are interested to choose the bigger peaks so that maximum possible voltage can
be generated on the piezo-material during mechanical-to-electrical coupling. Also we need to pick
a finite number of resonances to design a circuit that can approximately represent source data. Such
a model then can be used as a source for the rest of the power harvesting circuits. This is a source
model for the power harvesting circuit, and is used for various stages of the simulation.
In order to achieve a model of the provided spectrum, an electrical circuit with the desired resonances
at 400Hz and 1600Hz is researched and designed in the next section.
2.2 Vibration Specifications 26
Figure 2.3: Spectrum of vibration as supplied by CRC Mining
Figure 2.4: Time response data as supplied by CRC Mining
2.3 Typical RLC 27
2.3 Typical RLC
An understanding of an RLC circuit is required to achieve resonances at desired frequencies. The
cicrcuit displayed in Figure (2.5) is a typical RLC circuit with an AC soure.
v_sin
CR L
Figure 2.5: Typical RLC Circuit
Let the source, E = V0sin(ωt) be an AC emf. The current through the circuit in Figure (2.5) can be
given as follows:
I(t) =V0
Zsin(ωt−φ) (2.9)
where Z is the total impedance of the circuit and its unit is Ohms.
Z =√
R2 +(XL−XC)2
where XL = ωL, XC = 1ωC , ω = 2π f , f is the frequency of the AC. and where
φ = tan−1(XL−XC
R)
2.3.1 Resonance
From the Equation (2.9), we can say that the maximum current is obtained by making Z as small as
possible. If we have a fixed R value, then we can achieve the minimum Z by letting L cancel C. In
mathematical terms, it can be expressed as:
XL = XC
i.e.
ωL =1
ωC
f =1
2π√
LC(2.10)
This simply says that to achieve resonance at the natural frequency of the circuit, values of capacitor
and inductor can be adjusted, and thus the resulted current in the circuit will be maximum.
2.4 Resonant Peaks Design 28
Power can be given as:
Average Power, Pavg = I2rmsR =
E2rmsRZ2
where Average power will be maximum only if Z is minimum which requires again XL = XC.
2.4 Resonant Peaks Design
40nc2
1Kr1v
0 ref:v1
ns:(nv=1,nf=0.1)
10kr2
4l2
5nc5 2l5
.1kr3
2Kr4
50n c4
Figure 2.6: Multiple Series Resonants
In the Figure (2.6), the values of L2 and C2 are chosen such that the lower resonance at lower fre-
quency 400Hz is obtained. Using the Equation (2.10), by choosing C2 = 40nF , the value of L2 must
be 3.96H ≈ 4H to obtain resonance at 400Hz. Similarly to get resonance at a higher frequency of
1600Hz the values of capacitor 5nF requires to have the value of inductor to be 1.98H ≈ 2nH. These
resonances were calculated to approximately match the graph of the source signal sent by the CRC
Mining group. The frequency response of the circuit in Figure (2.6) is given below which approxi-
mately matches the original signal source.
2.5 Vibration Spectrum Modeling
To get an approximate time response of the circuit shown in Figure (2.6), the flat source, V 1 in
Figure (2.6) needs to be replaced by a white noise source in Saber. Saber is an electronic design
and simulation software tool from Syopsis (Synopsis 2007). Thus the new source model shown
in Figure (2.8) was designed that gives a reasonable approximation of the original time response
shown in Figure (2.3) supplied by the CRC Mining group. However, on the original data, the vertical
2.5 Vibration Spectrum Modeling 29
Graph0
Am
plit
ud
e (
(1/r
t(H
z))
)
0.03
0.1
0.3
1.0
3.0
10.0
30.0
f(Hz)
100.0 150.0 200.0 300.0 500.0 700.0 1.0k 1.5k 2.0k 3.0k 5.0k 7.0k 10.0k 15.0k 20.0k
Amplitude ((1/rt(Hz))) : f(Hz)
v.v1
Figure 2.7: Frequency Response of Circuit in Figure (2.6)
scale of the supplied vibration is unknown since the required gains and calibration constants were
not available. Even if they were, since this is acceleration data, very detailed mechanical modelling
would be required to generate the appropriate stress or strain data. Therefore, the model is designed
to be adjustable to match the specifications or requirements.
2.5 Vibration Spectrum Modeling 30
WhiteNoise
NoiseVar
Vr
40n
1K10k
4
5n 2
.1k
2K
50n
c_w
_noi
se
Controlto
Voltage
+
−
var2v
1 2 3
A A
1 2 3
Figure 2.8: Approximate Source vibration model Circuit
The aim of the simulation model is to allow testing various circuit designs for efficiencies and power
extraction ability. The time response of thus designed source model Figure (2.8) is given below in
Figure (2.9).
Graph0
(V
)
−15.0
−10.0
−5.0
0.0
5.0
10.0
15.0
t(s)
0.0 50.0m 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1.0
(V) : t(s)
vr
Figure 2.9: Vr of Figure (2.8) in Time Domain
The spectrum of the signal is given in Figure (2.10).
2.5 Vibration Spectrum Modeling 31
Graph0
(d
Bv/
Hz)
−80.0
−70.0
−60.0
−50.0
−40.0
−30.0
−20.0
−10.0
0.0
10.0
f(Hz)
1.0k 10.0k
(dBv/Hz) : f(Hz)
dB(vr)
Figure 2.10: Source(Vr) Signal Spectrum
2.6 Piezoelectric Element Selection and Specifications 32
2.6 Piezoelectric Element Selection and Specifications
The main purpose of doing research and study on this particular topic is to find out the most suitable
piezo-ceramics for this project. Different piezo ceramics have different properties listed as:
• physical and dielectric
• electromechanical, acousto-mechanical
• temperature
• aging stability
The material that produces maximum charge under applied vibration is targeted. While doing mathe-
matical analysis of the various properties’ factors of these materials, a compromise was made among
various conditions that suit the operating environment. The "g" and "d" factors as mentioned earlier
in this section play important role in determining the type of the material because these factors are
indicative of how much charge the material is going to produce under applied stress or strain. Consid-
ering costs, availibility and quality of different piezoceramic materials from various manufacturers,
the following PZTs from PI Ceramic (Physikinstrumente 2006) were considered for selection.
PIC 151 PIC 255 PIC 155 PIC 152 PIC 181 PIC 141 PIC 241 PIC 300 PIC 110
Table 2.5: PZTs (Physikinstrumente 2006)
The comparison study of different piezo-material from the data sheet from Piceramic (Physikinstru-
mente 2006) wad done. A brief of the main properties relevant to this project is listed below in the
Table (2.6). The details of the datasheet is available on public website as speciefied by the URL given
in the (Physikinstrumente 2006).
As per the properties of the different piezo-material displayed in Table (2.6), we can see that PIC151
has comparatively bigger permittivity, coupling factor and the piezoelectric charge constants than
other piezo-materials. Though the piezoelectric voltage constant for PIC151 is slightly smaller than
the others, the former properties make this material superior to the others in selecting PIC151 for this
project. Also, the availibility of PIC151 in our lab was another factor to select this material.
Thus after comparison studies about various properties of these PZTs, PIC 151 was selected for this
project. Next, the size of the piezo patch was determined according to the available space in the
2.6 Piezoelectric Element Selection and Specifications 33
Properties PIC151 PIC255 PIC155 Unit
Permittivity in polarized direction 2400 1750 1450
Permittivity perpendicular to the polarity 1980 1650 1400
Coupling factors
0.62 0.62 0.62 kp
0.53 0.47 0.48 kt
0.38 0.35 0.35 k31
0.69 0.69 0.69 k33
Piezoelectric charge constant(d)-210 -180 -165 d31 10−12C/N
500 400 360 d33
Piezoelectric voltage constant(g)-11.5 -11.3 -12.9 g31 10−3V m/N
22 25 27 g33
Table 2.6: PZT properties comparison (Physikinstrumente 2006)
mounting device in mining environment. Piezo patches are availabe in different sizes. Comparing
the available space in the mounting device to the different available sizes of the piezo-materials,
PIC151 of 75mm× 25mm area and 0.2mm thickness was selected to be the suitable piezo patch for
this project. Knowing the area, the thickness and the permittivity for this material from Table (2.7),
we can calculate its capacitance using Equation (2.3). The resultant capacitance ≈ 180nF.
The data sheet (Physikinstrumente 2006) for PIC 151 is given below.
2.6 Piezoelectric Element Selection and Specifications 34
Material Type: PIC 151
Physical and Dielectric Properties
Unit
Density ρ( gcm3 7.80
Curie Temperature Tc(C) 250
PermittivityIn the polarization direction ε33T /ε0
2400
Perpendicular to the polarity ε11T /ε01980
Dielectric loss factor tanδ (10−3) 20
Electromechanical Properties
Coupling factors
kp 0.62
kt 0.53
k31 0.38
k33 0.69
Piezoelectric charge constantsd31 10−12C/N -210
d33 10−12C/N 500
Piezoelectric voltage constantsg31 10−3V m/N -11.5
g33 10−3V m/N 22
Acousto-mechanical Properties
Frequency constants
Np (Hzm) 1950
N1 (Hzm) 1500
N3 (Hzm) 1750
Nt (Hzm) 1950
Elastic constants (compliance)S11E 10−12m2/N 15.0
SE33 (10−12m2/N) 19.0
Table 2.7: PZT PIC151 properties (Physikinstrumente 2006)
2.6 Piezoelectric Element Selection and Specifications 35
Material Type: PIC 151
Physical and Mechanical Properties
Unit
Elastic constants (stiffness) CD33 (1010N/m2) 10
Mechanical quality factor Qm 100
Temperature stability
Temperature coefficient of ε33(−20Cto+125C) T K ε33(×10−3/K) 6
Specific Heat Capacity J/Kg K 350
Specific Thermal Conductivity W/m K 1.1
Poisson’s ratio σ 0.34
Static Compressive Strength MPa larger than 600
Coefficient of thermal expansion J/Kg K 350
Thermal expansion coefficientIn the polarization direction /K −4 to −6×10−6
Perpendicular to the polarity /K 4 to 8×10−6
Table 2.8: PZT PIC151 properties: (Physikinstrumente 2006)continued...
Thus the mechanical and electrical properties of materials in general were studied. Then these prop-
erties critical to the requirement of the design of a power scavenging circuit suitable for this project
were studied in detail. After a consideration of various piezoelectric materials, two key properties:
(1) permittivity and (2) high "g" factor were the major players in deciding the type of PZTs. In this
case PIC151 PZT was chosen for the piezoelectric power conversion as the key properties favour this
material for the application.
CHAPTER 3
IDEALISED SIMULATIONS
The main objective of this section is to design a circuit where a load absorbs maximum power from
the driving network. The load model is simplified substantially to examine limits to the performance
achievable with realistic electronic load circuits.
3.1 R load
3.1.1 Maximum Power Transfer
(Cunningham and Stuller 1991) In Figure (3.1), if we know the open circuit rms voltage of the driving
network and its source impedance, the power absorbed by a purely resistive load can be maximized by
selecting the load resistance as follows. In Figure (3.1), XC is the reactance of the capacitor present in
i = Imaxcos(ωt)
RL
XCSource Load
Vs
Figure 3.1: Source and Load Match for Maximum Power Transfer
the source. Just as the current through a resistor is a function of the voltage across the resistor and the
resistance offered by the resistor, the AC current through a capacitor is a function of the AC voltage
across it, and the reactance offered by the capacitor. The impedance of the capacitor can be expressed
as 1ωC and its unit is Ohms(Ω), where C is the capacitance of the capacitor. Let RL represent the load
resistance. Given the open circuit rms voltage Vs, the average power at the load PL is:
PL = irms2RL
where
irms =Imax√
2=
|Vs||Xc +RL|
3.1 R load 37
Thus
PL =|Vs|2
| − jωC +RL|2
RL =RL
R2L + 1
ω2C2
|Vs|2 (3.1)
The power PL absorbed by the load is a function of load RL. Therefore by setting the derivative of PL
with respect to RL to zero, the maximum value of PL can be calculated:
dPL
dRL= 0
Thus, we get
− |Vs|22(RL)2
(R2L + 1
ω2C2 )2+
|Vs|2R2
L + 1ω2C2
= 0
which reduces to
R2L =
1ω2C2
Since Xc = − jωC , we have
RL = |XC| (3.2)
This is a variant of the maximum power transfer theorem which states that when the source impedance
is fixed and the load impedance can be selected, maximum power is absorbed by the load when the
source and load impedances are equal.
In this particular project, the driving network as given in Figure (3.2) is a piezo patch which is under a
random stress and strain from a particular vibration as an energy source generated in waterjet mining.
The source impedance of the piezo is:
|XC|= | 12π fC
|
where C = C6 = 180nF . This value of C is taken from the PIC151 piezo ceramic manufacturer
datasheet for the piezo area 25mm×70mm with 0.2mm thickness with relative permittivity of 2400.
Thus the load resistance RL is calculated, given the frequency, f in Hz as
RL =1
2π fC≈ 885
fKΩ (3.3)
From Equation (3.3), the load resistance depends on frequency of the source signal. For example,
at 500Hz, the load resistance of 1.7KΩ will absorb the maximum power and at 1600Hz, the load
resistance of 552Ω will absorb the maximum power. However, the vibration signal has frequency
components from 1Hz to 10Khz, and it is very difficult to design the load that will adapt to the
varying frequency to match the source impedance.
3.1 R load 38
The aim here is to study how an input impedance matches with a load and to examine the suitable load
to give maximum power transfer to the load. The circuit in Figure (3.2) was designed and simulated
to find the best matching output load resistance to the input impedance. The true rms value of the
WhiteNoise
Vrm
s
NoiseVar
Vr
40n
1K10k
4
5n 2
.1k
2K
50n
c_w
_noi
se
Controlto
Voltage
+
−
var2v
vcvs
5.6vm
vp
180n
c6
2k
r5
1 2 3
A A
1 2 3
Figure 3.2: Circuit with R Load
source signal at the input is (≈ 19V ). The source rms voltage of this value is limited in the current
laboratory setup. This is achieved by combining two broadband power amplifier, each of which gives
about (9.5V )rms at the maximum gain. Therefore, to simulate the circuit in Saber at more realistic
input rms voltage, the gain 5.6 is selected as shown in the Figure (3.2). This value of the VCVS gain
amplifies the real source rms voltage, Vr ≈ 3.43V to be ≈ 19V . At this gain, we see from the graph
in Figure (3.3), the maximum power is 0.34W when the load resistance is ≈ 117.21Ω. Therefore,
we can conclude for this section that that ideal value of a matching load will be ≈ 120Ω for an ideal
"R Load" circuit for the given source signal in this project. 120Ω is the equivalent resistance of a
capacitor with the 180nF at approximately 7372Hz. Though the target frequencies for this project
are 400Hz and 1600Hz, the smaller value of resistance for the maximum power transfer in this case
justifies that high frequency signals reduces the resistance of a capacitor. Therefore matching load
resistance decreases as the frequency increase without having any inductor in the load.
3.1 R load 39
Graph0
Po
we
r(W
)
0.0
50.0m
0.1
0.15
0.2
0.25
0.3
0.35
/r.r5(−) Ohm
1.0 10.0 100.0 1.0k 10.0k
Power(W) : /r.r5(−) Ohm
Ave(power(r.r5))
X_Max: (117.21, 0.33929)
Figure 3.3: Average Power Vs R with different Vrms
3.2 RL load 40
3.2 RL load
In this section, we study the nature of the load resistance changing to match the input impedance at
different values of inductance connected in series with the load resistance. At different frequencies,
the capacitor and inductor offer different response. For example, at low frequency, the capacitor
offers high impedance and inductor offers low impedance. At high frequency, a capacitor offers low
impedance and an inductor offers high impedance. Therefore to match a load resistance to an input
impedance of a piezo, a different value of inductor will be required at different frequencies. We know
the value of the piezo capacitance which is 180nF. The values of inductance that will give resonance at
400Hz and 1600Hz are 900mH and 55mH respectively. Thus the circuit in Figure (3.4) was designed
selecting a value of inductor in between this range of inductor values. The circuit was simulated at
five different values of inductance with the input rms voltage fixed at Vrms ≈ 3.43V ×5.6≈ 19Vrms.
WhiteNoise
Vrm
s
NoiseVar
Vr
40n
1K10k
4
5n 2
.1k
2K
50n
c_w
_noi
se
Controlto
Voltage
+
−
var2v
vcvs
5.6vm
vp
180n
c6
2k
r5
55m
l3
1 2 3
A A
1 2 3
Figure 3.4: Circuit with L &R Load
3.2.1 Results for L = 55mH
The value of inductor l3 connected to the load in the circuit in Figure (3.4) was selected to be 55mH
which gives resonance with the piezo capacitor at 1600Hz. The circuit was simulated in Saber using
parametric sweep of load resistance between 1Ω and 10KΩ with 30 log steps at the input voltage,
Vrms ≈ 19V . The result of the simulation is given in the Figure (3.5). As we can see, the maximum
power transfer to the load occurs when the value of the load resistance is ≈ 30Ω.
3.2 RL load 41
Graph0
Po
we
r(W
)
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
/r.r5(−) Ohm
1.0 10.0 100.0 1.0k
X_Max: (28.072, 0.90373)
Power(W) : /r.r5(−) Ohm
Ave(power(r.r5))
Figure 3.5: Average Vs R at L = 55mH with varying gain
3.2 RL load 42
3.2.2 Results for L = 100mH
The value of inductor l3 connected to the load in the circuit in Figure (3.4) was selected to be 100mH
which is closer towards the value of inductor that gives resonance at 1600Hz. The circuit was simu-
lated in Saber using parametric sweep of load resistance between 1Ω and 10KΩ with 30 log steps at
the input voltage, Vrms ≈ 19V . The result of the simulation is given in the Figure (3.6). As we can see,
the maximum power transfer to the load occurs when the values of the load resistance is ≈ 450Ω.
Graph0
Po
we
r(W
)
20.0m
40.0m
60.0m
80.0m
0.1
0.12
0.14
0.16
0.18
/r.r5(−) Ohm
10.0 100.0 1.0k 10.0k
Power(W) : /r.r5(−) Ohm
Ave(power(r.r5))
X_Max: (452.04, 0.16572)
Figure 3.6: Average Vs R at L = 100mH with varying gain
3.2.3 Results for L = 300mH
The value of inductor l3 connected to the load in the circuit in Figure (3.4) was selected to be 300mH
which is closer towards the value of inductor that gives resonance at 1600Hz. The circuit was simu-
lated in Saber using parametric sweep of load resistance between 1Ω and 10KΩ with 30 log steps at
the input voltage, Vrms ≈ 19V . The result of the simulation is given in the Figure (3.7). As we can see,
the maximum power transfer to the load occurs when the values of the load resistance is ≈ 1500Ω.
3.2 RL load 43
Graph0
Po
we
r(W
)
30.0m
35.0m
40.0m
45.0m
50.0m
55.0m
60.0m
65.0m
70.0m
75.0m
80.0m
85.0m
/r.r5(−) Ohm
100.0 1.0k 10.0k
Power(W) : /r.r5(−) Ohm
Ave(power(r.r5))
X_Max: (1487.4, 0.081434)
Figure 3.7: Average Power Vs R at L = 300mH with varying gain
3.2 RL load 44
3.2.4 Results for L = 500mH
The value of inductor l3 connected to the load in the circuit in Figure (3.4) was selected to be 500mH
which is in between the two values of inductance, 55mH and 900mH where the resonance occurs. The
circuit was simulated in Saber using parametric sweep of load resistance between 1Ω and 10KΩ with
30 log steps at the input voltage, Vrms ≈ 19V . The result of the simulation is given in the Figure (3.8).
As we can see, the maximum power transfer to the load occurs when the values of the load resistance
is ≈ 730Ω.
Graph0
Po
we
r(W
)
20.0m
30.0m
40.0m
50.0m
60.0m
70.0m
80.0m
90.0m
0.1
/r.r5(−) Ohm
10.0 100.0 1.0k 10.0k
X_Max: (727.9, 0.090112)
Power(W) : /r.r5(−) Ohm
Ave(power(r.r5))
Figure 3.8: Average Vs R at L = 500mH with varying gain
3.2.5 Results for L = 700mH
The value of inductor l3 connected to the load in the circuit in Figure (3.4) was selected to be 700mH
which is closer towards the value of inductor that gives resonance at 900mH. The circuit was simu-
lated in Saber using parametric sweep of load resistance between 1Ω and 10KΩ with 30 log steps at
the input voltage, Vrms ≈ 19V . The result of the simulation is given in the Figure (3.9). As we can see,
the maximum power transfer to the load occurs when the values of the load resistance is ≈ 280Ω.
3.2 RL load 45
Graph0
Po
we
r(W
)
20.0m
40.0m
60.0m
80.0m
0.1
0.12
0.14
0.16
0.18
/r.r5(−) Ohm
10.0 100.0 1.0k 10.0k
X_Max: (280.72, 0.1678)
Power(W) : /r.r5(−) Ohm
Ave(power(r.r5))
Figure 3.9: Average Vs R at L = 700mH with varying gain
3.2.6 Results for L = 900mH
The value of inductor l3 connected to the load in the circuit in Figure (3.4) was selected to be 900mH
which gives resonance with the piezo capacitor at 400Hz. The circuit was simulated in Saber using
parametric sweep of load resistance between 1Ω and 10KΩ with 30 log steps. The result of the
simulation is given in the Figure (3.10). As we can see, the maximum power transfer to the load
occurs when the values of the load resistance is ≈ 63Ω.
3.2 RL load 46
Graph0
Po
we
r(W
)
0.0
50.0m
0.1
0.15
0.2
0.25
0.3
0.35
0.4
/r.r5(−) Ohm
1.0 10.0 100.0 1.0k 10.0k
X_Max: (62.102, 0.38143)
Power(W) : /r.r5(−) Ohm
Ave(power(r.r5))
Figure 3.10: Average Vs R at L = 900mH with varying gain
3.3 Summary of results 47
3.3 Summary of results
Simulation ID L(mH) P(mW) R(Ohm)
1 55 900 28
2 100 165 452
3 300 82 1487
4 500 90 727
5 700 168 280
6 900 381 62
Table 3.1: Summary results at all values of L
Figure 3.11: Summary of Power versus load at all L
In Figure (3.11), the horizontal axix represents simulation IDs. Simulation 1 with 55mH inductor
and load resistance 28Ω; and simulation 6 with 900mH and load resistance 62Ω gives more power
than other simulations. Thus, from Table (3.1) and Figure (3.11), it is clear that the power transfer
3.3 Summary of results 48
to the load increases and load resistance decreases around resonant frequencies which are 400Hz and
1600Hz. At these frequencies, we obtain values of L to be 900mH and 55mH respectively to provide
resonance with 180nF capacitor.
CHAPTER 4
DETAILED SIMULATION
The objective of this chapter is to design more realistic circuits for power scavenging. The goal to
achieve maximum power at the battery remains the primary focus of all simulations completed in this
chapter. The current produced due to piezoelectricity is AC in nature. However the battery requires a
DC current to charge itself. Therefore, a full wave rectifier is used. Various electronic circuits where
a load absorbs maximum power from the driving network were studied. There are two different
electronic circuits that were selected for a detail comparison study in both theoretical and practical
simulations. The first circuit uses a full wave rectifier directly connected to a 3V battery as shown in
Section 4.1. Then as shown in Section 4.2, the second circuit has a full wave rectifier feeding rectified
signal to a PWM IC which passes the pulse width modulated signal to the load via a small 220uH
inductor.
4.1 Rectifier and Vdc Load
The circuit in Figure (4.1) is the simplest form of a real power harvesting circuit. The left hand side
VrNoiseVar
Vr
WhiteNoise
40n
c2
r11K
gnd
10k
r2
l2
4
5n
c5
2
l5
.1k
r3
2K
r4
50n
c4
c_w_noiseControl
toVoltage
+
−
var2v
vcvs 5.6vm
vp
180n
c6
gnd
2.7
Battery
1 r5
D1
D2
D3
D4
1 2 3 4 5 6
A
B
C
D
A
B
C
D
1 2 3 4 5 6
Vrm
s =
19.7
3V
Figure 4.1: Rectifier & Vdc Load circuit
of the VCVS amplifier represents the source signal. The source signal, Vr can be measured from
4.1 Rectifier and Vdc Load 50
Figure (4.2).
Graph0
Vr
(V)
−15.0
−10.0
−5.0
0.0
5.0
10.0
15.0
Time(s)
0.0 50.0m 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5
RMS: 3.4124
Vr (V) : Time(s)
vr
Vr (RMS) = 3.4124V
Figure 4.2: Transient analysis: Vr Vs Time
The rms input voltage Vr is ≈3.5V in this case. As per the experiment carried out in the final chapter,
the maximum rms voltage of a combined two broadband amplifier does not exceed 19.3V. Thus
dividing 19.3 by 3.5, we achieve the setting for the gain of the VCVS to be 5.6. C6 is 180nF capacitor
that represents a 25mm×70mm PIC 151 (Physikinstrumente 2006) piezo patch with 0.2mm thickness.
The input signal represents vibration that excites the piezo patch which produces AC that becomes
rectified by the full wave rectifier. Most of the resultant charge is then stored into the battery.
4.1 Rectifier and Vdc Load 51
Graph0
Avera
ge P
ow
er
(W)
0.0
50.0m
0.1
0.15
0.2
0.25
0.3
/v_dc.battery(V)
0.0 2.5 5.0 7.5 10.0 12.5 15.0 17.5 20.0 22.5 25.0 27.5 30.0 32.5 35.0 37.5 40.0
X_Max: (12.308, 0.25876)
Average Power (W) : /v_dc.battery(V)
Ave(power(v_dc.battery))
Figure 4.3: Average Power Vs V-Load
Figure (4.3) displays the average power available at varying battery voltages for input voltage, V =
(19.73V )rms for the circuit shown in Figure (4.1). From Figure (4.3), we see that under the conditions
studied, the maximum power ≈ 0.259W will be achieved when the load voltage is equal to 12.3V.
To find out an equivalent DC load impedance at these values:
Power,P = 0.259W
Voltage,V = 12.3V
Therefore, Current =PV
= 21mA
And, Impedance =VI
= 584Ω
Based on the idealised analysis of Section 3.1, 180nF capacitor at 1500Hz frequency also gives an
impedance of approximately 589Ω. Thus the input impedance of the circuit matches the output
impedance at 1500Hz causing the maximum power transfer from the source to the load.
However, 12.3V can not be achieved in this circuit since we wish to use a battery voltage of 2.7V.
Therefore, maximum power can not be transfered with this very simple circuit and it requires us to
design a more complex circuit that will cause the supply rail voltage to rise closer to the voltage where
maximum power transfer can occur. This leads to the intuition and design of the circuit in Section
4.2.
The graph in Figure (4.3) display approximately 163mW of power at 2.7V battery. This matches the
4.1 Rectifier and Vdc Load 52
average power obtained in Saber by direct transient analysis of the circuit in Figure (4.1) at the fixed
load of 2.7V as also proved in Figure (4.4).
Graph0
t(s)
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Avera
ge P
ow
er
(W)
−2.0
−1.0
0.0
1.0
2.0
3.0
4.0
Ave: 0.16249
Average Power (W) : t(s)
power(v_dc.battery)
Average Battery Power = 162mW
Figure 4.4: Battery Power at Fixed Battery Voltage=2.7V
The Saber(Synopsis 2007) simulation of the circuit in Figure (4.1) with fixed load at 2.7V display the
average current through the battery. The resultant average current is shown in Figure (4.5). Later in
the real experiment, we will find out that the battery current value approximately matches the current
value in the experiments carried out on a breadboard and a circuit built on a PCB.
Graph0
Battery
Curr
ent (A
)
0.0
0.2
0.4
0.6
0.8
1.0
t(s)
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Ave: 0.060183
Battery Current (A) : t(s)
i(v_dc.battery)
Average Battery Current = 60.1mA
Figure 4.5: Battery Current at Fixed Battery Voltage=2.7V
4.2 Rectifier, Capacitor, L and DC/DC converter 53
4.2 Rectifier, Capacitor, L and DC/DC converter
We have now studied various power levels available from Section (4.1). The maximum power at the
battery can be achieved if the output impedance can be matched to input impedance or approximately
brought near the input impedance. One way to achieve such impedance matching is to store charges
on a 10uF capacitor and then use switching technique (PWM) in combination with an OPAMP to
charge the battery as shown in Figure (4.6). The circuit in Figure (4.6) is a power harvesting circuit.
Vr
Vs
PW
M O
utp
ut
Vrm
s40n
1K
4
5n 2
.1k
2K
50n
180n
vcvs
5.6vm
vp
Controlto
Voltage
+
−
var2v10.
1u
4 r6
pwm_ideal
eai
ramp
cmpin
eani out
gnd
eaout
2.7
Battery
220u
Switch
10u
33p
Vdc
v_dc
1.22
vee
vcc
lmc6482
Vdc
33u
D3
D4
D2
D1
Z1
D5
c_w_noise
1u10k
Vcc
22kr12 2MEGr14
2MEGr15
500k r18
1
0 1 2 3 4
A
B
C
D
E
A
B
C
D
E
0 1 2 3 4
Figure 4.6: Rectifier & DC/DC converter
Based on various ideal simulations, this circuit has been fine tuned in Saber(Synopsis 2007). The left
hand side of the circuit including the VCVS is an ideal source that represents the characteristics of
the vibration source and the piezoelectric patch. The details of this source and its spectrum are given
in chapter 2. The source is connected to a full wave bridge rectifier, thus converting AC into DC. A
filter capacitor with the value of 10uF is used to smooth out DC pulses.
The zener diode immediately after the full bridge rectifier is used as an overvoltage protection device.
The Zener voltage of the diode used in the prototype electronic circuit for this project is 33V , since
the rectifier diodes have a maximum blocking voltage rating of 40V .
An ideal Pulse Width Modulation (PWM) circuit and switch are used as a simplified model of the
real PWM IC used. The particular component selected for the electronic circuit, MAX5033D was not
found in the Saber library, and hence this simplification was adopted.
4.2 Rectifier, Capacitor, L and DC/DC converter 54
The motivation behind using PWM is to have a high efficiency interface between the rectified source
(which is variable voltage) and the almost constant voltage rechargeable batteries. In this circuit using
PWM causes the rectified supply Vcc to rise to a range of desired values otherwise not obtained with-
out using PWM. This rise in the values of Vcc helps achieve a better impedance matching between
the source and the load for maximum power transfer, and thereby implements a form of ’maximum
power point tracking’(Casciati et al. 2003).
D5 and the 220uH inductor are added to give a simple forward (or buck) converter. It converts the
high DC voltages to low DC voltages and hence it is also known as step-down DC to DC converter.
A voltage divider circuit, or series regulator could also be used to lower the voltage however these are
much less efficient than the buck converter.
Resistor, r6 in parallel with the 33uF capacitor give a means of sensing the approximate average DC
current flowing from the rectified signal. Because quiescent current of the pwm chip is very small
which is 270uA, essentially all the DC current from the rectified signal has to flow through to ground
via r6.
The 1Ω resistor in series with the voltage source is there to permit simple measurement of the current
through the battery for testing purposes. Once testing and debugging is completed and the circuit is
finalised, this component could be omitted and replaced by a short circuit.
The LMC OP Amp, and associated circuits allows for comparison of the average current and the DC
voltage from the rectifier, which is used in feedback to the PWM chip. This allows the PWM chip to
adjust its duty cycle in an appropriate range for the impedance matching between the source and the
load.
4.2 Rectifier, Capacitor, L and DC/DC converter 55
4.2.1 OPAMP analysis
In Figure (4.7), we know the open circuit voltage and the short-circuit current, hence dividing the
voltage by the current gives an equivalent resistance. From the circuit in Figure (4.7), the equivalent
Icc
gnd
D1
D2
D3
D4
c7
10u
Vcc
Input Signal
Rx (Load)
1 2 3 4 5 6
A
B
C
D
A
B
C
D
1 2 3 4 5 6
Figure 4.7: Equivalent Resistance Rx = VccIcc
impedance of the circuit can be given as Rx = VccIcc
. Therefore if we can deduce an equation that relates
Vcc to Icc, then we can design the circuit by tuning the circuit elements’ parameter values related to this
equation in Saber(Synopsis 2007) simulation. The following OPAMP analysis can help us achieve the
relation. In an ideal OPAMP operation, V−= V+. Therefore, in the circuit in Figure (4.7), Vs = V−,
Vdc
VsVcc 1.22V
vee
vcc
lmc6482
22k
r12
2MEG
r14
2MEG
r15
0 1 2 3 4
A
B
C
D
E
A
B
C
D
E
0 1 2 3 4
Figure 4.8: OmAmp Analysis
Or,
Vs =(r12||r15)1.22V(r12||r15)+ r14
+(r12||r14)Vcc
(r12||r14)+ r15
4.2 Rectifier, Capacitor, L and DC/DC converter 56
Because r12 is much smaller than r15 and r14, r12||r15 ≈ r12 and r12||r14 ≈ r12.
Vs =r121.22Vr12 + r14
+r12Vcc
r12 + r15
For the reasons explained above, r12 + r14 ≈ r14 and similarly r12 + r15 ≈ r15
Thus,
Vs ≈ r12
[1.22V
r14+
Vcc
r15
]
In this case, fine tuning of the circuit in Saber for maximum power transfer gives r14 = r15 = 2MΩ and
r12 = 22KΩ. 1.22V is the required voltage for pin number 4 on a Maxim 5033D PWM IC (Maxim
2006). This pin is connected to the output pin of the OPAMP, TS942 (STMicroelectronics 2006).
Therefore,
Vs =22K2M
[1.22V +Vcc] (4.1)
When the switch is on, almost all of the supply current has to flow through 4Ω resister as there would
be negligible amount of current flowing through any other grounded circuit element, therefore,
Vs ≈ 4× Icc (4.2)
Combining Equation (4.1) and Equation (4.2), we get,
1.22V +Vcc
Icc=
4Ω×2M22K
(4.3)
If Vcc >> 1.22V , thenVcc
Icc=
4Ω×2M22K
= 363Ω
The mathematical analysis of OPAMP as given above suggests that there are some differences be-
tween the input impedance (584Ω) and the effective DC resistance which actually gives best power
transfer. The mismatch is due to some inefficiencies in the circuit that depend on the DC voltage Vcc.
In particular, for larger Vcc, the PWM duty cycle will be lower, and this will increase the power loss
in the free-wheeling diode, D5 in Figure (4.6). This, combined with the fact that the average power
versus V-Load (see Figure (4.3)) is very flat near the optimal point, means that the optimal Vcc for
maximum battery power is significantly less than 12V.
4.2 Rectifier, Capacitor, L and DC/DC converter 57
Battery Power at Varying Input RMS Signal
Graph0
Po
we
r(W
)
0.0
25.0m
50.0m
75.0m
0.1
0.125
0.15
0.175
0.2
0.225
0.25
0.275
0.3
time(s)
0.0 50.0m 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1.0
Ave: 0.016275
Power(W) : time(s)
power(v_dc.battery)
Battery Average Power = 16.275mW
Graph0
Po
we
r (W
)
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
time(s)
0.0 50.0m 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1.0
Ave: 0.045556
Power (W) : time(s)
power(v_dc.battery)
Battery Average Power = 45.556mW
Battery Power at Vrms = 5.27V Battery Power at Vrms = 8.55VGraph0
Po
we
r(W
)
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
time(s)
0.0 50.0m 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1.0
Ave: 0.084788
Power(W) : time(s)
power(v_dc.battery)
Battery Average Power = 85mW
Graph0
Po
we
r(W
)
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
time(s)
0.0 50.0m 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1.0
Ave: 0.14228
Power(W) : time(s)
power(v_dc.battery)
Average Battery Power = 142.28mW
Battery Power at Vrms = 11.765V Battery Power at Vrms = 15.60V
Figure 4.9: Average Battery Power at varying input signal, Vrms
We see in Figure (4.9) that the average battery power rises as the input voltage, Vrms increases. In
Figure (4.12), we also see that Vcc rises as the Vrms rises, and hence it clearly indicates that the supply
voltage, Vcc has to rise closer to 12V to give maximum power at the battery. Later in the section, we
will find that RT hevenin changes as we vary the input signal, Vrms.
In Saber, the average battery power was plotted versus varying input voltage, Vrms as shown in Fig-
ure (4.11).
4.2 Rectifier, Capacitor, L and DC/DC converter 58
Graph0
Po
we
r (W
)
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
Time(s)
0.0 50.0m 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1.0
Ave: 0.21061
Power (W) : Time(s)
power(v_dc.battery)
Battery Average Power = 210mW
Battery Power at Vrms = 18.71V
Figure 4.10: Average Battery Power at varying input signal..continued..., Vrms
Graph0
Po
we
r(W
)
0.0
20.0m
40.0m
60.0m
80.0m
0.1
0.12
0.14
0.16
0.18
0.2
/vcvs.vcvs2(−)
1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.8 4.0 4.2 4.4 4.6 4.8 5.0
Power(W) : /vcvs.vcvs2(−)
Ave(power(v_dc.battery))
Figure 4.11: Battery Average Power at 3.42V ≤Vrms ≤ 18.71V
4.2 Rectifier, Capacitor, L and DC/DC converter 59
Graph1
t(s)
0.0 50.0m 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1.0
Vcc(
V)
2.5
2.75
3.0
3.25
3.5
3.75
4.0
4.25
Ave: 3.1807
Vcc(V) : t(s)
vc
Average Vcc = 3.1807V
Graph0
Vcc(
V)
3.0
3.5
4.0
4.5
5.0
5.5
6.0
6.5
7.0
7.5
8.0
t(s)
0.0 50.0m 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1.0
Ave: 5.5303
Vcc(V) : t(s)
vc
Average Vcc = 5.5V
Vcc at Vrms = 5.27V Vcc at Vrms = 8.55VGraph0
t(s)
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Vcc
(V
)
0.0
5.0
10.0
15.0
Ave: 7.7692
Vcc (V) : t(s)
vc
Vrms = 11.765V
Average Vcc = 7.7692V
Graph0
t(s)
0.0 50.0m 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1.0
Vcc
(V)
7.0
8.0
9.0
10.0
11.0
12.0
13.0
14.0
15.0
Ave: 10.159
Vcc(V) : t(s)
vc
Average Vcc = 10.159V
Vcc at Vrms = 11.765V Vcc at Vrms = 15.60V
Figure 4.12: Vcc at varying input signal, Vrms
4.2 Rectifier, Capacitor, L and DC/DC converter 60
Graph0
Vcc
(V)
7.5
10.0
12.5
15.0
17.5
20.0
t(s)
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Ave: 12.538
Vcc(V) : t(s)
vc
Average Vcc = 12.538
Vcc at Vrms = 18.71V
Figure 4.13: Vcc at varying input signal..continued.., Vrms
4.2 Rectifier, Capacitor, L and DC/DC converter 61
Graph0
Cu
rre
nt(
A)
0.0
20.0m
40.0m
60.0m
80.0m
0.1
0.12
t(s)
0.0 50.0m 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1.0
Ave: 0.0060278
Current(A) : t(s)
i(v_dc.battery)
Battery Average Current = 6mA
Graph0
Cu
rre
nt(
A)
0.0
25.0m
50.0m
75.0m
0.1
0.125
0.15
0.175
0.2
0.225
0.25
0.275
0.3
t(s)
0.0 50.0m 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1.0
Ave: 0.016873
Current(A) : t(s)
i(v_dc.battery)
Battery Average Current = 16.873mA
Icc at Vrms = 5.27V Icc at Vrms = 8.55VGraph0
(A
)
0.0
50.0m
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
t(s)
0.0 50.0m 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1.0
(A) : t(s)
i(v_dc.battery)
Battery Average Current = 32mA
Ave: 0.031958
Graph0 C
urr
en
t(A
)
0.0
50.0m
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
0.55
t(s)
0.0 50.0m 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1.0
Ave: 0.052698
Current(A) : t(s)
i(v_dc.battery)
Battery Average Current = 52.7mA
Icc at Vrms = 11.765V Icc at Vrms = 15.60VGraph0
Cu
rre
nt
(A)
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
t(s)
0.0 50.0m 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95 1.0
Ave: 0.078005
Current (A) : t(s)
i(v_dc.battery)
Battery Average Current = 78mA
Icc at Vrms = 18.71V
Figure 4.14: Icc at varying input signal, Vrms
4.2 Rectifier, Capacitor, L and DC/DC converter 62
3 4 5 6 7 8 9 10 11 12 130
10
20
30
40
50
60
70
80
Vcc (V)
Icc
(mA
)
3 4 5 6 7 8 9 10 11 12 13150
200
250
300
350
400
450
500
550
Vcc (V)
Rth
(O
hm)
Icc versus Vcc Rth versus Vcc
Figure 4.15: Icc and Vcc at varying input signal, Vrms
From the Figure (4.12) and Figure (4.14), Vcc and Icc were recorded, and then RT hevenin was calculated
by dividing Vcc by Icc as shown in the Table (4.1). The graph of Vcc versus Icc; and RT hevenin versus
Vcc were plotted in Matlab as shown in Figure (4.15). The result presented in the Table (4.1) also
validates the reason of impedance mismatch discussed in the OPAMP Analysis earlier in this section.
At the Thevenin impedance, 160Ω, the battery recieves the maximum power. As discussed earlier
in the OPAMP analysis, there is clearly a mismatch between the input impedance and effective DC
resistance due to inefficiencies in the circuit as Vcc increases.
Vrms Vcc(V ) Icc(mA) Rth(Ω)
5.27 3.181 6 530
8.55 5.5 16.8 327.4
11.76 7.77 32 242.5
15.6 10.16 52.7 192.6
18.71 12.54 78 160.6
Table 4.1: RT hevenin for Various Vrms
CHAPTER 5
DETAILED EXPERIMENTAL RESULTS
The source data as shown in Figure (5.5) and equipments shown in Figure (5.1) were used to examine
the real circuit:
1. Source noise model from Saber
2. Function Generator
3. Power Amplifier
4. Oscilloscope/Earth isolated transformer
5. True RMS and Normal multimeter
6. Power Scavenging Electronic Circuit on PCB
7. Power Scavenging Electronic Circuit on Breadboard
8. Decade Resistor and decade capacitor
64
Function Generator Oscilloscope
Broadband Power Amplifier Multimeters
Printed Circuit Board Breadboard
Decade Capacitor and Resistor
Figure 5.1: Laboratory Equipments
5.1 Rectifier & Vdc load 65
Source noise data was exported in CSV format from Saber. The source was imported into Func-
tion generator software on a computer running Microsoft Windows XP. Using the function generator
software, the source noise was downloaded via serial cable to the function generator. The function
generator was connected to the input of Power Amplifier. The output of Power Amplifier was con-
nected to the input of the electronic circuit. The results were measured as given in following sections.
5.1 Rectifier & Vdc load
Figure 5.2: Breadboard: Power Scavenging
The breadboard as displayed in Figure (5.2) was used to simulate the circuit in Figure (4.1) from
Section 4.1. The input source with rms 19.73V signal source was introduced to the input of the circuit.
The circuit contains equivalent piezo capacitance, full wave rectifier and a pair of 1.2V rechargeable
batteries as a load. A 1 Ohm resister was used to measure the current flow through the batteries.
After connecting the source to the input of the circuit, the output current through the battery was
5.2 Rectifier, DC/DC converter & Vdc load 66
measured to be 61mA. The total battery voltage measured was 2.8V. Therefore the power transfered
to the battery from the source in this case is:
Prect_to_battery = 2.8V ×0.061A = 0.17W
The result matches the one that is produced by Saber simulation program running on the computer.
Saber simulation of the same circuit gives 0.171W of power at the battery.
5.2 Rectifier, DC/DC converter & Vdc load
The circuit in Figure (4.6) from Section (4.2) was exported to Protel for printed circuit board manufac-
turing purpose. Maxim 5033D PWM IC replaces the ideal PWM IC that was designed and simulated
in Saber. Because Saber does not have Maxim5033 part in its library, the circuit in Figure (4.6) uses
ideal PWM IC that is available in Saber parts library. Max5033D PWM IC from Maxim Inc. was
chosen due to its low power loss while operating. Other electronic parts for the circuit were also
chosen so that their power losses are minimum. TS941 OPAMP from STElectronics, Phillips zener
diode (BZX79C36), diodes (D1N5819) from Semiconductor Components Industries were chosen for
the circuit. The datasheets for these parts are provided on a CDROM disk. The Protel schematic for
this circuit is given in Figure (5.3).
5.2 Rectifier, DC/DC converter & Vdc load 67
Figure 5.3: Circuit Schematic from Protel
5.2 Rectifier, DC/DC converter & Vdc load 68
Based on the schematic in Figure (5.3), PCB in Figure (5.4) was manufactured. Its size is 10cm×
Figure 5.4: PCB: Power Scavenging
6.3cm. It accommodates two AA size batteries. However the size is scalable, for example, using
surface mount electronic components, the size can be made as small as 5cm×5cm if we use a pair of
AAA size batteries. And furthermore, if coin battery is used, the size could be further minimized.
5.2 Rectifier, DC/DC converter & Vdc load 69
5.2.1 Measurements
Waveform of the source signal, Vr given in the circuit from Figure (4.6) was saved in CSV format
in Saber program. The CSV file was exported from computer to the function generator given in
Figure (5.1) using a serial cable. This CSV file is supplied on a CDROM Disk. The source signal was
displayed on Oscilloscope as given in Figure (5.5). The time-domain signal given in Figure (5.5) is the
input signal to the power scavenging circuit. This was recorded from Tektronix TDS220 Oscilloscope
by a digital camera. In Figure (5.5), time scale is 2.5msec per division, and voltage scale is 1V per
Figure 5.5: Real-time Input Signal (zoomed)
division.
5.2 Rectifier, DC/DC converter & Vdc load 70
The spectrum of the signal is given in Figure (5.6). The spectrum was calculated using Saber calcu-
lator.
Graph0
(d
Bv/
Hz)
−80.0
−70.0
−60.0
−50.0
−40.0
−30.0
−20.0
−10.0
0.0
10.0
f(Hz)
1.0k 10.0k
(dBv/Hz) : f(Hz)
dB(vr)
Figure 5.6: Real-time Input Signal Spectrum
5.2 Rectifier, DC/DC converter & Vdc load 71
The PWM signal at the output pin of PWM chip displayed in Figure (5.7) by a Tektronix TDS220
Oscilloscope was recorded by a digital camera. Along with the PWM signal, source signal was also
recorded as displayed in the Figure (5.7). In Figure (5.7), time scale is 25uSec per division, and
Figure 5.7: PWM signal: Power Scavenging
voltage scale is 5V per division for both channels 1 and 2.
5.2.2 PCB and Breadboard
The output signal source was connected to a broadband power amplifier. The clipping of the voltage
was noted at approximately 315mV. Therefore 300mV peak-to-peak amplitude for the signal was
selected. 50Hz frequency is a very good representation of a real time repetition frequency of the
vibration source in drilling environment. Repetition frequency is the rate of the whole noise sample
per time. Therefore function generator was programmed to output 300mV peak-to-peak amplitude
at 50Hz repetition frequency. The signal is then sent to a power amplifier to amplify the source rms
input signal for the PCB or a breadboard circuit.
Measurements at the load were taken feeding the source signal to the input of the circuit in both PCB
and Breadboard cases. Because the PCB has only one input, we are able to connect only one amplifier
output to the input of PCB.
5.2 Rectifier, DC/DC converter & Vdc load 72
Figure 5.8: PCB: Power Scavenging
5.2 Rectifier, DC/DC converter & Vdc load 73
However, the breadboard given in Figure (5.9) has multiple inputs. As a result higher rms voltages
can be sent to the input of the circuit to study various results at the load. When the input rms voltage
Figure 5.9: Breadboard: Power Scavenging
is (9.7V )rms, the battery current is 18.4mA in both PCB and breadboard cases. However, since we
can supply a rms input upto 19V in breadboard case, when the input rms voltage is ≈ (19V )rms, the
battery current is measured to be 76mA. Current through the battery was measured by measuring
voltage drop across 1Ω resister connected in series with the battery using a multimeter.
Current through the 2.77V Battery was measured to be ≈ 76mA. Thus, average Power at the battery
Ppwm_to_battery = 2.77V ×0.076A = 0.21W
This proves 25% improvement in the power increase at the load by using dc-dc converter.
5.2 Rectifier, DC/DC converter & Vdc load 74
Battery Power at Varying Input Signal
The limit of Vrms was extended from (9.7V )rms from a single broadband amplifier to (19.73V )rms by
adding a second broadband power amplifier. If the inverting output of the first amplifier is V1 and the
non-inverting output of the second amplifier is V2, the the difference between the two is V1− (−V2).
That means the resultant is the addition of the two outputs. The reason, we needed to increase the
RMS voltage, is obviously known from Section 4.1 that the Vcc needs to rise above 9V so that we
can track the voltage at which maximum transfer of power occurs from the source to the battery. The
Vrms Vcc(V ) Icc(mA) Rth(Ω) Battery Power (mW )
3.731 5.08 4 1270 10.0
5.44 5.09 5.2 980 14.04
5.71 5.09 6 850 16.2
8.84 5.17 16.8 310 45.36
10 5.21 20.5 250 55.35
12.24 5.44 33.6 160 90.72
15.64 7.28 48.6 150 131.22
17 7.61 58.6 130 158.22
19.04 8.5 76 112 205.2
Table 5.1: Real-time Battery Power for Various Vrms
experiment was carried out to observe how battery power varies as we vary the Vrms. The Table (5.1)
displays all the experimental results recorded and the graphs in Figure (5.10) were plotted in Matlab
over the observed set of data. As we see from the Figure (5.10), the battery power rises as we increase
the Vrms. In all occurances in this chapter, Icc is a symbol meaning the current that flows through
the 4Ω resistor when the switch is on. Effectively, this current has to be approximately equal to
the supply current as there is almost no other elements that allow current flow into the ground as
mentioned earlier due to extremely low leakage current of the other the grounded circuit elements.
Vcc was also recorded as shown in the Table (5.1). Thus by dividing Vcc by Icc, we get the Thevenin
resistance of the circuit. The graphs in Figure (5.10) display the relationship between Vcc versus Icc,
Vrms versus Rth, Rth versus Icc and Vrms versus battery power.
The Icc versus Vcc and Thevenin Resistance results differ between experiment and simulation. This
is because the diodes used in simulation were ideal diodes. The practical diodes have more losses
as opposed to ideal diodes. And also there is small amount quiescent current of the PWM chip that
5.2 Rectifier, DC/DC converter & Vdc load 75
2 4 6 8 10 12 14 16 18 200
50
100
150
200
250
Vrms (V)
Bat
tery
Pow
er (
W)
5 5.5 6 6.5 7 7.5 8 8.50
10
20
30
40
50
60
70
80
Vcc (V)
Icc
(mA
)
Battery Power at varying Vrms Icc versus Vcc
2 4 6 8 10 12 14 16 18 200
200
400
600
800
1000
1200
1400
Vrms (V)
RT
heve
nin
(Ohm
)
2 4 6 8 10 12 14 16 18 200
10
20
30
40
50
60
70
80
Vrms(V)
Icc
(mA
)
Thevenin Resistance at varying Vrms Icc versus varying Vrms
Figure 5.10: Results obtained at varying Vrms
accounts for some of the difference.
5.2 Rectifier, DC/DC converter & Vdc load 76
The results as shown in the graph match those obtained from Saber. In both Saber and real PCB or
Breadboard case, the average battery power rises as the Vrms increases. The results obtained from
Figure (5.10) validates that the results obtained from both Saber and real-time simulation have a good
match in their behaviour.
CHAPTER 6
CONCLUSION
A source vibration model was first designed and simulated to match the supplied spectrum from
CRC Mining. Then various loads were tested to achieve the desired power. At the end, two ideal
simulations with R and RL load were considered to be included to be informative and relevant parts
for this project. The AC current was then rectified using full wave rectifier, and combination of highly
efficient and low power rated PWM and rail-to-rail dual OPAMP were used to regulate the power at
the maximum level as expected. The power extracted from the given source to the battery is 210mW.
This meets the power requirement of many wireless sensors. Thus this device can be used as power
source for such low power electronics working in a suitable condition. Use of this device is scalable
and viable in many other applications where vibration can be found as a source of energy.
The research has opened the door to explore a few more techniques that can improve the regulation
of maximum power to the load. For example one of the techniques to be explored is Active Front End
(HBridge) load. Also to completely get rid of the use of any inductor on the electronic board, the idea
of synthetic impedance can be researched and the real inductance can be replaced by the synthetic
impedance which will provide the same results with a lower risk of interferences in the environments
where magnetism becomes a serious concern.
Thus this project encourages research in the area of power scavenging. As we face a challange to
meet our energy demand by consuming the conventional energy sources, this research work brings
a new approach to meet some of energy demands by deploying an alternative source of energy that
would otherwise not be used.
6.1 Suggestions for further research
• Small inductor in resonance with the piezo-capacitance can be used to further boost the power
flow. There were some preliminary experiments done as a part of this research and very promis-
ing results were seen, but are yet to be analyzed in detail.
• H bridge and Active front end technique can be employed to allow reverse power transfer to
Piezo, so we can possibly achieve simulated source inductance.
6.1 Suggestions for further research 78
• Intrinsic safety procedures may need to be considered depending on the physical conditions of
the surroundings where the device may be used.
• Voltage regulation techniques can be used to set and regulate a specified voltage at all times at
the output.
• To extract more power from a source, a low power microcontroller can be used to control the
impedance matching between the source and the load at all discrete frequencies defined within
a range of frequencies.
APPENDIX
GLOSSARY
Terms Meaning
CMOS Complementary Metal Oxide Semiconductor
PWM Pulse Width Modulation
PZT Lead Zirconate Titanate
OPAMP Operational Amplifier
IC Integrated Circuit
Thevenin’s Impedance In this thesis, most occurrences of the words ’Thevenin’s Impedance’ refer to
the equivalent resistance with the ratio of open circuit voltage divided by short
circuit current
RMS Root Mean Square
VCVS Voltage Controlled Voltage Source
DC Direct Current
AC Alternating Current
Saber Electronic Design and Simulation Program. Saber Sketch Version 4.0. Copy-
right ©1985-2006, Synopsis Inc. All Rights Reserved. Saber Sketch is a
schematic capture package by Saber®
Duty cycle Duty cycle is the proportion of time during which a component, device, or
system is operated.
CSV Comma Separated Value.
PCB Printed Circuit Board.
Breadboard A breadboard is used to make temporary circuits for testing an electronic cir-
cuit. No soldering is required. Therefore it is easy to change connections and
replace components.
Table 1: Glossary
80
Contents of CDROM Disk submitted
1 Signal source waveform generated by Saber and saved in CSV file format
2 Datasheets
3 OPAMP (TS941/TS942)
4 PWM Chip (Max5033D)
5 Phillips Zener Diode (BZX79C36)
6 Semiconductor Component Industry Diodes (D1N5819)
Table 2: CDROM Contents
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