piezo-electric power scavenging for mining applications

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

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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.

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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

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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.


1.2.3 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

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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)

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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)

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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.


1.2.7 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


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.


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.


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.


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


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


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.

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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.


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).


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


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.

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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)

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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.

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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)


Ave(power(r.r5))

Figure 3.5: Average Vs R at L = 55mH with varying gain

3.2 RL load 42



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


Ave(power(r.r5))

X_Max: (452.04, 0.16572)




which is closer towards the value of inductor that gives resonance at 1600Hz. The circuit was simu-




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


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



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)


Ave(power(r.r5))




which is closer towards the value of inductor that gives resonance at 900mH. The circuit was simu-




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)


Ave(power(r.r5))




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)


Ave(power(r.r5))


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.


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


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.


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.


4.2.1 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


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.


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).


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


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


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


Vcc at Vrms = 11.765V Vcc at Vrms = 15.60V

Figure 4.12: Vcc at varying input signal, Vrms


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


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)


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)


Icc at Vrms = 18.71V

Figure 4.14: Icc at varying input signal, Vrms


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).


Figure 5.3: Circuit Schematic from Protel


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.


5.2.1 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.


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


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.


Figure 5.8: PCB: Power Scavenging


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.


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


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.


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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