Chapter 1

INTRODUCTION

Energy is the fuel of the global economy. Without sufficient energy to light houses, run

businesses, power manufacturing plants, and stoke our cars and planes, our world would come

to a standstill. With the increasing demand for energy, decreasing conventional energy sources

and environmental concerns, the use of renewable and alternative energy has become a solution

for these issues. Many technologies in energy harvesting in the form of solar, wind, and

geothermal have been established. Energy harvesting is the process of capturing minute

amount of energy from one or more of these naturally-occurring energy sources, accumulating

and storing them for later use. The energy coming from natural sources that are constantly

replenished is termed as renewable energy. There are several sources of renewable energy

among which are solar, wind, ocean, hydro, electromagnetic, electrostatic, thermal, vibration,

and human body motions. Energy harvesting devices have been intensively considered not

only to cope with the global energy crises but also to improve the efficiency of systems, by

reusing some of the waste energy to power new technologies. Mechanical energy is one of the

largest sources of wasted energy in the modern advancement. Hence, various methods have

been developed to convert the mechanical energy into the electrical energy using different

mechanisms such as electrowetting, electromagnetics, magnetostriction, piezoelectricity, and

triboelectricity.

Piezoelectric and triboelectric energy harvesting devices which convert mechanical

energy into electrical energy have been making a development recently. Triboelectric

nanogenerator (TENG) based on the triboelectrification effect has been demonstrated to be a

reliable source of energy since it was firstly reported in 2012, and its unique properties, such
as high-output performance, clean, sustainability, etc., result in the explosive growth of TENG

research. TENGs have been incorporated as micro and macro-scale power source, and self-

powered sensors. Since its initial discovery, the researchers have greatly increased the power

output density by a factor of over 100,000. However, TENG has a likely lower durability. The

output characteristics of TENGs are high voltage but low current, but general electronics

require a regulated power of a few volts. Approaches have to be developed to lower the output

voltage without sacrificing the output power [1]. On the other hand, the development on the

production technique of the piezoelectric nanomaterials has promoted the miniaturization of

the piezoelectric generators in the last decade. This nanogenerator has attracted great interest

of researchers due to the great potential in the application of micro and nano-scaled power

supply system [2]. Despite its minor drawbacks, great efforts have been done to improve the

device performance, including the employing of several kinds of piezoelectric materials with

higher piezoelectric properties, the design of device structures and the hybrid of

nanogenerators with other types of energy harvesters.

Although nanostructures enhances triboelectric output, its low energy efficiency and

complex manufacturing procedure are not favorable in terms of the massive production and

long- term durability of the device. Furthermore, today’s highly developed energy harvesting

devices when operated under small mechanical force, such as body movements, deliver low

output power and thereby, imposing a constraint on the range of their applications. Thus, an

improved energy harvesting device that addresses these concerns is needed.

The study aims to utilize mechanical energy due to human motions, such as walking

and running, and convert it to electrical energy using a hybrid generator that demonstrates both

piezoelectric and triboelectric mechanisms. This hybrid generator which will be implemented
as shoe insoles combines the high output current of the piezoelectric and the high output

voltage of the triboelectric. The specific objectives of this study are: (1) To design a 5V DC

power supply using a shoe insole-embedded piezo-triboelectric hybrid generator (2) To

develop a system that will maximize the power generated and increase the overall efficiency

to provide and achieve a fix output from the characterized input (3) To support mobility,

provide a clean source of energy and deliver sufficient power to charge a power bank that will

be used for self-powered electronics such as mobile electronics.

The proposed study provides an alternative source of energy that converts mechanical

energy to electrical energy using a hybridized piezoelectric and triboelectric generator realized

in shoe insoles. Due to the cooperative operation of piezoelectric and triboelectric, the hybrid

generator can produce high output power by small mechanical force applied. Since human

motion like walking is utilized, this study proposes a convenient and clean source of energy,

as it produces electricity free of carbon emissions. As a wearable charging device, it shows a

convenient technique in charging mobile electronics without any restriction on time and

location unlike the conventional power supplies. This study presents an initial working

prototype in applying energy-harvesting technology for self-powered electronics which is

envisioned for use in future research in this field and to further provide information or data to

future researchers in the development of this renewable technology.

The proposed study will cover the energy conversion of mechanical vibrations and

rubbing of materials and converting the obtained energy into electricity using the hybrid

generator. The study will also contain the design and operation for each system- piezoelectric

generator and triboelectric generator. The proponents will use characterized data as input and

focus only on prototyping and implementation of the hybrid generator on the shoe insoles. The
types of footwear were not taken into considerations. The specific properties and detailed

construction of the piezoelectric and triboelectric materials used in the prototype, as well as

the economical aspect of the construction of the prototype are not covered in the study. The

gathered electricity will be stored in a small-size power bank which then be able to apply solely

for small-load consumer electronics devices.

 Chapter 2

REVIEW OF RELATED LITERATURE AND STUDIES

2.1 Piezoelectric Materials

The term piezoelectricity originated from a Greek word used to describe a gain of

electrical energy due to the application of a mechanical stress, such as pressure and vibration,

on dielectric materials [3]. Piezoelectricity represents pressure electricity and is a property of

certain crystalline materials such as barium titanate, quartz, Rochelle salt and tourmaline that

develop electricity when pressure is applied. This is called the direct piezoelectric effect. On

the other hand, a piezoelectric material will undergo deformation - a change in dimension when

it is exposed in an electric field. This inverse mechanism is called as the converse piezoelectric

effect or electrostriction [4]. The direct piezo electric effect is responsible for the materials

ability to function as a sensor and the converse piezo electric effect is accountable for its ability

to function as an actuator [5]. Harvesting wasted energy from ambient environment is

renewable and environmentally friendly compared with the use of traditional batteries.

Hereinto, piezoelectric materials have huge potential to become an ideal source of energy

harvesting because of their nature of directly converting mechanical energy into electric energy

and the ease at which they can more readily be integrated into a system, than other similar or

different types of materials [6]. The piezoelectric energy harvesting method, among other

mechanical energy harvesting methods, has been regarded by many researchers for future

innovations due to its low complexity configurations – direct mechanical energy to electricity

conversion and its readiness for any integration for desired applications [7]. With the recent

surge of microscale devices, piezoelectric power generation can provide a convenient

alternative to traditional power sources used to operate certain types of sensors/actuators,

telemetry, and MEMS devices. The advances have allowed numerous doors to open for power

harvesting systems in practical real-world applications [8].

The application of the piezoelectric power was not given much attention in the past

because the electromechanical conversion efficiency was relatively low and the quantity of

generating electricity of piezoelectric was very small. But with the development of physics,

material science and micro process technology, the new piezoelectric materials with high

piezoelectricity performance are being developed continuously, electromechanical conversion

efficiency of the piezoelectric materials was improved by a large margin [9]. Over the past few

years, vibration-based piezoelectric energy harvesting has been investigated by several

researchers [10]. In 2005, a study reported on a piezoelectric cymbal transducer for energy

harvesting. At 100Hz, the output power can reach 52 m W when connected with a load of 400

kN under an cyclic force of 70 N with a pre-stress load of 67 N [11]. In 2007, a study reported

on a piezoelectric drum transducer for energy harvesting. Under a pre-stress of 0.15 N and a

cyclic stress of 0.7 N, a power of 11 mW was generated at 590 Hz with an 18 ill resistor [12].

2.2 Piezoelectric Effect

A piezoelectric substance is one that produces an electric charge when a mechanical

stress is applied (the substance is squeezed or stretched). Conversely, a mechanical

deformation (the substance shrinks or expands) is produced when an electric field is applied.

This effect is formed in crystals that have no center of symmetry. To explain this, we have to

look at the individual molecules that make up the crystal. Each molecule has a polarization,

one end is more negatively charged and the other end is positively charged, and is called a

dipole. This is a result of the atoms that make up the molecule and the way the molecules are

shaped. The polar axis is an imaginary line that runs through the center of both charges on the
molecule. In a monocrystal the polar axes of all of the dipoles lie in one direction. The crystal

is said to be symmetrical because if you were to cut the crystal at any point, the resultant polar

axes of the two pieces would lie in the same direction as the original. In a polycrystal, there

are different regions within the material that have a different polar axis. It is asymmetrical

because there is no point at which the crystal could be cut that would leave the two remaining

pieces with the same resultant polar axis. Figure 1 illustrates this concept.

Figure 2. 1: Mono vs. Poly Crystals

In order to produce the piezoelectric effect, the polycrystal is heated under the application of a

strong electric field. The heat allows the molecules to move more freely and the electric field

forces all of the dipoles in the crystal to line up and face in nearly the same direction (Figure

2).

Figure 2. 2: Polarization of Ceramic Material to Generate Piezoelectric Effect

The piezoelectric effect can now be observed in the crystal. Figure 3 illustrates the piezoelectric

effect. Figure 3a shows the piezoelectric material without a stress or charge. If the material is
compressed, then a voltage of the same polarity as the poling voltage will appear between the

electrodes (b). If stretched, a voltage of opposite polarity will appear (c). Conversely, if a

voltage is applied the material will deform. A voltage with the opposite polarity as the poling

voltage will cause the material to expand, (d), and a voltage with the same polarity will cause

the material to compress (e). If an AC signal is applied then the material will vibrate at the

same frequency as the signal (f) [13].

Figure 2. 3: Example of Piezoelectric Effect

2.2.1 Field and stress direction specifications

To designate the directions of a piezoelectric crystal, a conventional 3-D orthogonal

modal space has been defined with reference to the piezoelectric structure.
 Figure 2 1 Three- dimensional orthogonal modal space with reference the piezoelectric structure

Let 'I' be the direction of axis of mechanical stress and 'J' be the direction of electric

field intensity. Most important piezoelectric strain coefficients while designing harvesting

elements are 𝜆31 and 𝜆33. In the ‘31’ mode, imposed transverse mechanical strain in ‘1’

direction is perpendicular to the induced electric field in ‘3’ direction, while in ‘33’ mode,

strain and electric field directions are parallel to each other.

Figure 2. 4: (a) Compression along 3 axis. (b) Expansion strain on upper

Here it is worth mentioning that the electro-mechanical coupling of 3-3 mode is greater than

that of 3-1 mode. But still the 3-1 mode is far more popular because of its simplicity and ease

of integration. It is much more compliant also, that is larger strain is produced with smaller

input forces [14].

 2.3 Triboelectric Effect

The term triboelectric effect originated from the Greek word “tribos” meaning “the

action of rubbing together”. The triboelectric effect occurs as an electron transfer between two

bodies which are rubbed together. An example of the effect is the well-known discharge that

occurs when walking across a rug, especially in the winter, and a jolt is generated by a spark

from the fingertips to a metal doorknob [15].

Figure 2. 5: Schematic illustration of the structure and working principle of the triboelectric generator. (a) The structure of an
integrated generator in bending and releasing process and related electrical measurement tests. Photographic images of a flexible
TEG and mechanical bending equipment. (b) Proposed mechanism of a TEG (see text for details): charges are generated by
fractioning two polymer films, which results in the creation of a triboelectric potential layer at the interfacial region (indicated by
dashed lines); a mechanical compression results in a change in the distance between the two electrodes (from D to d), thus, under
the driving of the triboelectric potential, a change in system capacitance leads to the flow of current in the external load which
drives the flow of the free electrons across the electrodes to minimize the total energy of the system.
 A TEG device and power generation mechanism is illustrated in Fig. 1 a and b. As the

external force is applied to the device during the deformation process, two insulating polymeric

materials are touched and rubbed with each other. Although the surfaces of the two polymer

films appear bright and smooth under light, they are in fact non-uniform with a different

roughness of hundreds of nanometers. Mechanical compression between the two layers of

polymers leads to a relative sliding. As a result of small degree of friction, electrostatic charges

with opposite signs are generated and distributed on the two surfaces of the polymer films due

to the presence of the nanometer scale roughness, with the PET film positively charged and

Kapton film negatively charged, and forming an interface dipole layer, which is called a

triboelectric potential layer. Such a dipole layer forms an inner potential layer between the

planar metal electrodes. The induced charges will not be quickly conducted away or

neutralized owing to the insulative nature of the polymer films. To minimize the energy created

by the triboelectric potential, electrostatically induced free-charges will flow across the

external load between the two electrodes. Simultaneously, mechanical compression between

the two layers of polymers leads to a small reduction in the interplanar distance (from D to d)

[16].

2.3.1 Vertical Contact-separation Mode

The vertical contact-separation mode was the first invented operation mode for TENGs.

A physical contact between the two dielectric films with distinct electron affinity creates

oppositely charged surfaces. Once the two surfaces are separated by a gap, a potential drop is

created between the electrodes deposited on the top and bottom surfaces of two dielectric films.

If the two electrodes are electrically connected by a load, free electrons in one electrode would

flow to the other electrode in order to balance the electrostatic field.

 Figure 2. 6: Theoretical
models for (a) dielectric-to-dielectric contact mode TENG
and (b) conductor-to-dielectric contact mode TENG

Once the gap is closed, the potential drop created by triboelectric charges disappears, the

induced electrons will flow back. A periodic contact and separation between the two materials

drives the induced electrons to flow back and forth between the two electrodes, resulting in an

AC output in the external circuit. In this mode, the electricity generation process depends on a

periodic switching between the contact and separation states of the two contact surfaces, and

the output is AC. To realize this type of mechanical motion, various structural designs were

developed, including arch-shaped, spring-supported, zig-zag, cantilever based, and so on. This

mode was featured as a simple structural design, great device robustness, and high

instantaneous power density. However, an indispensable design of the vertical contact

separation mode is a cavity with constantly changing volume which renders a challenge for the

packaging of the TENG.

The vertical contact-separation mode has been widely used to harvest energy from finger

typing, engine vibration, human walking, and biomedical systems. And it was also developed

to build self-powered sensor systems, including magnetic sensors, pressure sensors, vibration

sensors, mercury ion sensors, catechin detection sensors, and acoustic sensors [17].
2.4 Triboelectric Series

Static electricity is a form of the triboelectric effect. It occurs when some materials are

rubbed together and the friction generates static electricity. Walking over a rug on a dry day

and touching a metal doorknob is shocking, but not too useful [18]. When two different

materials are pressed or rubbed together, the surface of one material will generally steal some

electrons from the surface of the other material. The material that steals electrons has the

stronger affinity for negative charge of the two materials, and that surface will be negatively

charged after the materials are separated. (Of course the other material will have an equal

amount of positive charge.) If various insulating materials are pressed or rubbed together and

then the amount and polarity of the charge on each surface is separately measured, a very

reproducible pattern emerges [19].

The triboelectric series in Table 1 is an attempt to classify materials in a systematic

way to describe their position relative to their ability to interchange electrons. Some materials

give up electrons easily and become positively charge. Other materials accept electrons easily

and become negatively charged. The triboelectric series shows only the positive or negative

influence of one material on another. The level of electrostatic voltage generated depends

upon:

1. Friction or lubricity (degree of surface smoothness)

2. Capacitance (electrical) of the object

3. Rubbing area

4. Humidity

5. Temperature

6. Contact pressure
Table 1: Table 2. 1 The Triboelectric Series: TRIBOELECTRIC MATERIAL CHARGE ORDER

Negative Charge (-)

Air Amber Formatted Table

Human hands Sealing wax

Asbestos Hard rubber

Rabbit fur Nickel, copper

Positive Charge (+)

Acrylic Brass, silver

Phenolic Gold, platinum

Cellulose acetate Sulfur

Glass Synthetic rubber

Mica Acetate rayon

Human hair Polyester

Nylon Celluloid

Wood Orlon

Wool Saran

Fur Polyurethane

Lead Polyehtylene

Silk PVC (vinyl)

Aluminum KEL-F (CTFE)

Paper Silicon

Cotton (almost neutral level) Teflon

Steel Silicon rubber

Wood

The judicious use of the triboelectric series provides some measure of defense against

electrostatic discharge (ESD). Since the greatest number of charges is generated when

materials from widely spaced positions in the series are rubbed together, it is better to keep

those materials away from each other. If possible, for example glass should be kept away from

polyethylene; while synthetic rubber and acetate rayon might make relatively compatible

neighbors [20].
2.5 Harvesting Energy From People

Mechanical energy is one of the largest sources of the wasted energy in the modern

civilization. With the abundant amount of mechanical energy found in our surroundings such

as human walking or even running, harvesting electricity from human activity makes sense.

Numerous emerging technologies have been developed to convert mechanical energy to

electricity for driving practical and functional devices. The technology that makes it possible

is the piezoelectric effect, in 1880, the brothers Jacques and Pierre Curie discovered that

placing crystals under pressure produced an electric charge [21]. Today, manufacturing

technology has made it possible to place piezoelectric devices in the pavements, school

corridors, gadgets such as laptops or computers and even shoes. In the Netherlands,

Rotterdam's new Club WATT has a floor that harnesses the energy created by the dancers'

steps. The floor is based on the piezoelectric effect. As the club goers dance, the floor is

compressed by less than half an inch. It makes contact with the piezoelectric material under it

and generates anywhere from two to 20 watts of electricity, depending on the impact of the

patrons' feet. For now, it's just enough to power LED lights in the floor, but in the future, more

output is expected from newer technology [22].

2.6 Hybrid Generators

Harvesting energy, such as light, heat and vibration, from our ambient environment,

has been an active subject due to the severe needs of energy. Nowadays, different mechanisms

have been used to convert the mechanical energy into electrical energy such as electrowetting,

electromagnetics, magnetostriction, piezoelectricity, and triboelectricity. However, there are

several issues to be overcome for the application in the self-powered electronics. First, the

output power of the energy harvesters is still quite low. Second, the energy harvester has to be
strong enough to withstand the vibrational motions. Third, the fabrication process has to be

favorable in terms of the massive production. Finally, portable devices for harvesting energy.

Here, demonstrating an ideal, piezoelectric/triboelectric hybrid generator that can produce high

output power due to the cooperative operation of piezoelectric and triboelectric mechanisms

in a single press-and-release cycle. This hybrid generator has several advantages over the

previously reported energy harvesters [23]. First, it produces a high output power even at a

mechanical force of as small as 0.2 N, which is capable of lighting 600 LEDs. Second, it can

be fabricated at nominal cost and in large scale because it does not need nanostructures that

still require a complicated process to fabricate. Third, as it consists of organic materials without

any nanostructures, it will be more resistant to the mechanical failure. Fourth, it exhibits high

current density owing to the use of both triboelectric and piezoelectric outputs. Compared with

the piezoelectric nanogenerators, the proposed hybrid generator is superior in terms of not only

the output voltage but also the output current [24].

2.7 Vibration Energy

Energy harvesting devices have been intensively investigated not only to cope with the

global energy crises, but also to realize the self-powered electronics such as implanted medical

devices and mobile electronics. Mechanical energy is one of the largest sources of the wasted

energy in the modern civilization. Therefore, a variety of approaches have been demonstrated

to convert the mechanical energy into the electric energy using different mechanisms: for

example, electro wetting, electromagnetics, magnetostriction, piezoelectricity, and

triboelectricity [25]. In harvesting vibration energy, it uses piezoelectric effect to convert

mechanical vibration or the strain variation with time into electric energy and store it in energy

storage devices such as super-capacitors and rechargeable batteries. A significant amount of

research has been done on piezoelectric generators [26] and on the electronic circuits

processing and storing electrical energy [27]. In piezoelectric generators, investigated

configurations include the piezoelectric unimorph and bimorph cantilever beams, stacked

piezoelectric actuators piezoelectric membranes thin elastic plates or their combination with

piezoelectric components and others deriving from the above-listed structures [28]. To

increase the vibration energy-harvesting capability of the piezoelectric generator based

on a cantilever beam, we have proposed a piezoelectric generator that not only uses the strain

change of piezoelectric components bonded on a cantilever beam, but also employs the weights

at the tip of the cantilever beam to hit piezoelectric components located on the 2 sides of

weights [29].

2.8 Energy Harvesting for Wearables

One of the most important trends in the electronic equipment technology from its

origins has been the reduction in size and the increase in functionality. Nowadays small,

handheld, though very powerful devices are commercially available that allow the user to play

music, to wirelessly communicate or to compute practically everywhere or, in other words,

ubiquitously. In the next years there will be new products available providing vision and other

extended functions to the wearer. The size of such devices is becoming so small that instead

of portable devices they are becoming wearable devices that can be integrated in everyday use

objects like watches, glasses, clothes, etc. [30].

The term energy harvesting summarizes several different approaches which might lead

us a step closer to such an ideal world. Instead of charging wearables with some sort of cable,

new wearables could produce the energy they need from the light, heat or vibration in their

surroundings [31]. The electrical energy to power the wearable devices is generated from either
kinetic, electromagnetic or thermal energy. The obtained energy can then be used to recharge

a secondary battery or, in some cases, to power directly the wearable devices [32].

Piezoelectric harvesting converts mechanical energy from vibrations or shocks into

electrical energy. In piezoelectric elements, the piezo effect generates a small electrical current

whenever the element is manipulated by mechanical forces. For energy harvesting in

wearables, the piezoelectric elements are often designed to produce energy with the vibrations

that occur when walking, breathing or moving your hands. Piezoelectric harvesting generates

comparably small amounts of energy, which limits the technology to applications with low

power demands and to body areas continuously in motion. Scientists are also working on

polymeric piezoelectric fibers which are flexible, strong, and breathable and could be

integrated into textiles, allowing for a whole new range of health monitoring and other

applications [33].

2.9 Power Banks

Smartphones and handheld computers work continuously [34]. Often battery

discharges when you are away or on some important assignment. This is when Power Banks

are much needed. This could be particularly useful for hikers and mountain climbers, who

spend much of their time away from power sources. This product is universal, portable and a

rechargeable power source designed for mobile phones and other rechargeable electronic

devices. The Power Bank fits in your pocket, purse, or briefcase, and is ideal for traveling [35].

2.10 Piezoelectric Nanogenerators Latest Developments

In the last few years, there has been an increasing demand for low-power and portable-

energy sources due to the development and mass consumption of portable electronic devices.
Furthermore, the portable-energy sources must be associated with environmental issues and

imposed regulations. These demands support research in the areas of portable-energy

generation methods. [36]

In a 2010 research by J. G. Rocha, et al., it describes the use of piezoelectric polymers

in order to harvest energy from people walking and the fabrication of a shoe capable of

generating and accumulating the energy. In this scope, electroactive β-polyvinylidene fluoride

used as energy harvesting element was introduced into a bicolor sole prepared by injection,

together with the electronics needed to increase energy transfer and storage efficiency. An

electrostatic generator was also included in order to increase energy harvesting. [37]

In 2012, energy harvesting from floor using organic piezoelectric modules was

designed by E. Bischur and N. Schwesinger. Generator modules have been developed, which

are able to generate electrical energy from mechanical loading, which occur in the shape of

compressive forces in the ground. Compressive forces, for example, can be caused by the

weight of people or vehicles moving across the ground. The conversion principle of the

generator modules bases on the piezoelectric longitudinal effect of PVDF. [38]

It was found that the polarization process of the PVDF film had a decisive influence:

The higher the remnant polarization, the better the energy conversion. Due to production lags

of the foil it was not possible to polarize PVDF with optimal parameters. Dielectric

breakdowns of the foil allowed only very poor polarization parameters. [39]

In 2013, researchers constructed a friendly approach to increasing the frequency. A

wide bandwidth piezoelectric generator (PZG) was constructed and tested experimentally. The

PZG was characterized using chirp and wideband random excitations. The experimental results
showed that by proper shaping of an attached cantilever beam it is possible to increase the

number of vibration modes of the PZG and, hence, to improve the effectiveness of the energy

harvesting as compared with a conventional cantilever PZG configuration. The proposed

structure was designed to produce 3 vibration modes, which extend the operation around the

frequencies 35Hz, 57Hz and 76Hz. As a result, the bandwidth was widened by a factor of 2.81

as compared with a conventional harvester. [40]

In a 2014 research paper by Nilotopa Manna, some investigation has been made how

energy can be extracted from piezo-electric generators and efficiency can be improved. As a

result, the piezoelectric elements can deliver a good amount of power that may be useful for

low power electronic devices or portable instruments. Piezoelectric elements offer a unique set

of capabilities of temperature stability and long life. This experimental study was made on

commercially available piezo-elements. However there is lot of researches to improve the

performance of piezoelectric elements and manufacturers offer wide range piezoelectric

elements of higher performance. Using proper mechanism piezoelectric elements can be used

in continuous vibrating environment to generate electricity and these may be used as the

replacement of battery. Thus the lost energy can be revived and utilized. [41]

Another research was presented later that year. R. Sahul, together with his two

colleagues, have presented a study on the optimization of piezoelectric transducer design by

modeling and simulation. Comparison between experimental and modeling data for the

transducers with analysis of their effectiveness and efficiency demonstrate significant

performance advantage of single crystal versus other conventional piezoelectric materials.

Modeling and simulation for proof of technical solutions, prototyping, and production stages
of transducer gives opportunity to accelerate all these stages during engineering processes and

find the best solutions for optimization of the transducer design. [42]

In a 2015 research by Zhaoyang Yu, et al., a piezoelectric transducer using first bending

vibration modes was proposed; it can be used as a stator for an ultrasonic motor. The transducer

has a symmetrical structure, in which a conical horn is located at one end. On the tip of the

horn, a cylindrical driving foot is machined. Bending vibrations are superimposed in the

transducer to generate elliptical trajectory movement at the driving foot. The working principle

of the proposed transducer is analyzed. The resonant frequencies and the electromechanical

coupling factor of the bending modes are analyzed under different structural parameters. An

improved structure for the initial model is proposed. The motion trajectory of the driving foot

is obtained by transient analysis. The results can be a theoretical guidance for the design of

piezoelectric actuator using bending transducer. [43]

In a recent study by Jiˇr´ı Erhart. He proposed a study of transformation and load

parameters of the disk piezoelectric transformer. The disk design of ceramic transformers was

studied theoretically and experimentally for the set of samples. The transformer design rules

were theoretically developed for the disk PTs including mechanical losses. There are similar

trends in calculated transformation ratio results like for the experimental data, but the

approximation accuracy is limited by 5% due to the poling nonhomogeneity and therefore

nonhomogeneous values of the electromechanical parameters. The efficiency for the

fundamental resonance is much smaller than for the first overtone, where it reaches up to 92%.

The presented disk transformer is studied analytically and realized experimentally for the first

time. It shows excellently high transformation ratio and efficiency similar to the conventional

rectangular Rosen-type transformer. The disk design of the PT with very high transformation
ratio allows, e.g., for its application in plasma generators (plasma generated at the outer edge

electrode). [44]

2.11 Triboelectric Nanogenerators Latest Developments

The trend in the development of portable electronics is toward low power consumption,

which makes it possible to use the energy harvested from the working environment of the

device to power directly the device, forming a trend of self-powered systems for application in

ultrasensitive chemical and bimolecular sensors, nanorobotics, micro-electromechanical

systems, remote and mobile environmental sensors, homeland security and even

portable/wearable personal electronics. New technologies that can harvest energy from the

environment as sustainable self-sufficient micro/nano-power sources are the newly emerging

field of nanoenergy, which is concerned with the application of nanomaterials and

nanotechnology for harvesting energy to power micro/nano-systems.

In 2012, Wang, et al. firstly demonstrated an innovative energy harvester named the

triboelectric nanogenerator (TENG) that converts environmental mechanical energy into

electric energy. Mechanical energy scavenging based on triboelectric effect has been proven

to be simple, cost-effective, and robust. The researchers designed an arch-shaped triboelectric

nanogenerator (TENG) by utilizing the contact electrification between a polymer thin film and

a metal thin foil. The working mechanism of the TENG was studied by finite element

simulation. The output voltage, current density, and energy volume density reached 230 V,

15.5 μA/cm2, and 128 mW/cm3, respectively, and an energy conversion efficiency as high as

10–39% has been demonstrated. The TENG was systematically studied and demonstrated as a

sustainable power source that can not only drive instantaneous operation of light-emitting

diodes (LEDs) but also charge a lithium ion battery as a regulated power module for powering
a wireless sensor system and a commercial cell phone, which is the first demonstration of the

nanogenerator for driving personal mobile electronics, opening the chapter of impacting

general people’s life by nanogenerators. [45]

Since then, various TENGs based on the triboelectric effect and electrostatic

induction have been developed as an energy source for applications including an

electrochromic device, water splitting, portable electronics and self-powered sensors

without reliance on traditional power supplies. Over the recent years, triboelectric

nanogenerator (TENG) has shown progressive development as a new energy technology and

in self-powered portable electronics.

In a 2013 study by Hou, et al., a simple fabrication, great performance and cost-

effective triboelectric nanogenerator (TENG) was presented. It is based on the cycled contact-

separation between a polydimethylsiloxane (PDMS) film and a polyethylene terephthalate

(PET) film, for effectively harvesting footfall energy. The elastic sponge is first used as the

spacer in the TENG, where the size and the thickness of the spacers have a significant effect

on the output performance of the TENG. By using the optimized device, a TENG-based shoe

insole is used to harvest human walking energy, where the maximum output voltage and

current density reached up to 220 V and 40 µA, respectively. It also demonstrates that the

fabricated shoe insole using a single layer of TENG can be directly used to light up 30 white

light-emitting diodes (LEDs) in serial connection. By taking the merits of this simple

fabrication, outstanding performance, robust characteristic and low-cost technology, we

believe that TENG can open up great opportunities not only for powering small electronics,

but also can contribute to large-scale energy harvesting through engineering design. [46]
 In the same year, the use of triboelectric nanogenerator for harvesting vibration energy

in full space and as self-powered acceleration sensor was researched by Zhang, et al. A

spherical three-dimensional triboelectric nanogenerator (3D-TENG) with a single electrode is

designed, consisting of an outer transparent shell and an inner polyfluoroalkoxy (PFA) ball.

Based on the coupling of triboelectric effect and electrostatic effect, the rationally developed

3D-TENG can effectively scavenge ambient vibration energy in full space by working at a

hybridization of both the contact-separation mode and the sliding mode, resulting in the

electron transfer between the Al electrode and the ground. By systematically investigating the

output performance of the device vibrating under different frequencies and along different

directions, the TENG can deliver a maximal output voltage of 57 V, a maximal output current

of 2.3 μA, and a corresponding output power of 128 μW on a load of 100 MΩ, which can be

used to directly drive tens of green light-emitting diodes. Moreover, the TENG is utilized to

design the self-powered acceleration sensor with detection sensitivity of 15.56 V g-1. This work

opens up many potential applications of single-electrode based TENGs for ambient vibration

energy harvesting techniques in full space and the self-powered vibration sensor systems. [47]

In 2014, researchers proposed the use of case-encapsulated triboelectric nanogenerator

for harvesting energy from reciprocating sliding motion. Reciprocating motion is a widely

existing form of mechanical motion in natural environment. A case-encapsulated triboelectric

nanogenerator (cTENG) based on sliding electrification to convert reciprocating motion into

electric energy is presented. Patterned with multiple sets of grating electrodes and lubricated

with polytetrafluoroethylene (PTFE) nanoparticles, the cTENG exported an average effective

output power of 12.2 mW over 140 kΩ external load at a sliding velocity of 1 m/s, in

corresponding to a power density of 1.36 W/m2. The sliding motion can be induced by direct-
applied forces as well as inertia forces, enabling the applicability of the cTENG in addressing

ambient vibration motions that feature large amplitude and low frequency. The cTENG was

demonstrated to effectively harvest energy from human body motions and wavy water surface,

indicating promising prospects of the cTENG in applications such as portable and stand-alone

self-powered electronics. [48]

Important progress in TENGs has been achieved in increasing the output power and

efficiency while new structures have emerged. While their robustness and endurance have

increased, some critical concerns still remain about the degradation and lifetime of TENGs. In

2015, Lee, et al. addressed this issue and proposed the use of shape memory polymers (SMPs)

to extend TENGs’ lifetimes and guarantee their performance. For this purpose, a new smart

SMP-based self-healing TENG, which has the capacity to be healed and to recover good

performance after degradation of its triboelectric layer, was introduced. As the degradation and

healing process of the SMP–TENG, and the improvement in its endurance and lifetime are

being studied, the huge potential of self-healing SMP–TENGs can be demonstrated. [49]

In a recent study, Quan, et al. proposed a hybridized nanogenerator including a

triboelectric nanogenerator (TENG) and six electromagnetic generators (EMGs) that can

effectively scavenge biomechanical energy for sustainably powering an electronic watch.

Triggered by the natural motions of the wearer’s wrist, a magnetic ball at the center in an

acrylic box with coils on each side will collide with the walls, resulting in outputs from both

the EMGs and the TENG. By using the hybridized nanogenerator to harvest the biomechanical

energy, the electronic watch can be continuously powered under different motion types of the

wearer’s wrist, where the best approach is to charge a 100 μF capacitor in 39 s to maintain the

continuous operation of the watch for 456 s. To increase the working time of the watch further,
a homemade Li-ion battery has been utilized as the energy storage unit for realizing the

continuous working of the watch for about 218 min by using the hybridized nanogenerator to

charge the battery within 32 min. This research will provide the opportunities for developing

a nanogenerator-based built-in power source for self-powered wearable electronics such as an

electronic watch. [50]

 Chapter 3

DESIGN OF A 5V DC POWER SUPPLY USING A SHOE INSOLE- EMBEDDED

PIEZO- TRIBOELECTRIC HYBRID GENERATOR

Introduction

Energy is the fuel of the global economy. Without sufficient energy to light houses, run

businesses, power manufacturing plants, and stoke our cars and planes, our world would come

to a standstill. With the increasing demand for energy, decreasing conventional energy sources

and environmental concerns, the use of renewable and alternative energy has become a solution

for these issues. Many technologies in energy harvesting in the form of solar, wind, and

geothermal have been established. Energy harvesting is the process of capturing minute

amounts of energy from one or more of these naturally-occurring energy sources, accumulating

and storing them for later use. The energy coming from natural sources that are constantly

replenished is termed as renewable energy. There are several sources of renewable energy

among which are solar, wind, ocean, hydro, electromagnetic, electrostatic, thermal, vibration,

and human body motions. Energy harvesting devices have been intensively considered not

only to cope with the global energy crises but also to improve the efficiency of systems, by

reusing some of the waste energy to power new technologies. Mechanical energy is one of the
largest sources of wasted energy in the modern advancement. Hence, various methods have

been developed to convert the mechanical energy into the electrical energy using different

mechanisms such as electrowetting, electromagnetics, magnetostriction, piezoelectricity, and

triboelectricity.

Piezoelectric and triboelectric energy harvesting devices which convert mechanical

energy into electrical energy have been making a development recently. Triboelectric

nanogenerator (TENG) based on the triboelectrification effect has been demonstrated to be a

reliable source of energy since it was firstly reported in 2012, and its unique properties, such

as high-output performance, clean, sustainability, etc., result in the explosive growth of TENG

research. TENGs have been incorporated as micro and macro-scale power source, and self-

powered sensors. Since its initial discovery, the researchers have greatly increased the power

output density by a factor of over 100,000. However, TENG has a likely lower durability. The

output characteristics of TENGs are high voltage but low current, but general electronics

require a regulated power of a few volts. Approaches have to be developed to lower the output

voltage without sacrificing the output power [1]. On the other hand, the development on the

production technique of the piezoelectric nanomaterials has promoted the miniaturization of

the piezoelectric generators in the last decade. This nanogenerator has attracted great interest

of researchers due to the great potential in the application of micro and nano-scaled power

supply systems [2]. Despite its minor drawbacks, great efforts have been done to improve the

device performance, including the employing of several kinds of piezoelectric materials with

higher piezoelectric properties, the design of device structures and the hybrid of

nanogenerators with other types of energy harvesters.

 Although nanostructures enhances triboelectric output, its low energy efficiency and

complex manufacturing procedure are not favorable in terms of the massive production and

long- term durability of the device. Furthermore, today’s highly developed energy harvesting

devices when operated under small mechanical force, such as body movements, deliver low

output power and thereby, imposing a constraint on the range of their applications. Thus, an

improved energy harvesting device that addresses these concerns is needed.

The study aims to utilize mechanical energy due to human motions, such as walking

and running, and convert it to electrical energy using a hybrid generator that demonstrates both

piezoelectric and triboelectric mechanisms. This hybrid generator which will be implemented

as shoe insoles combines the high output current of the piezoelectric and the high output

voltage of the triboelectric. The specific objectives of this study are: (1) To design a 5V DC

power supply using a shoe insole-embedded piezo-triboelectric hybrid generator (2) To

develop a system that will maximize the power generated and increase the overall efficiency

to provide and achieve a fix output from the characterized input (3) To support mobility,

provide a clean source of energy and deliver sufficient power to charge a power bank that will

be used for self-powered electronics such as mobile electronics.

The proposed study provides an alternative source of energy that converts mechanical

energy to electrical energy using a hybridized piezoelectric and triboelectric generator realized

in shoe insoles. Due to the cooperative operation of piezoelectric and triboelectric, the hybrid

generator can produce high output power by small mechanical force applied. Since human

motion like walking is utilized, this study proposes a convenient and clean source of energy,

as it produces electricity free of carbon emissions. As a wearable charging device, it shows a

convenient technique in charging mobile electronics without any restriction on time and
location unlike the conventional power supplies. This study presents an initial working

prototype in applying energy-harvesting technology for self-powered electronics which is

envisioned for use in future research in this field and to further provide information or data to

future researchers in the development of this renewable technology.

The proposed study will cover the energy conversion of mechanical vibrations and

rubbing of materials and converting the obtained energy into electricity using the hybrid

generator. The study will also contain the design and operation for each system- piezoelectric

generator and triboelectric generator. The proponents will use characterized data as input and

focus only on prototyping and implementation of the hybrid generator on the shoe insoles. The

types of footwear were not taken into considerations. The specific properties and detailed

construction of the piezoelectric and triboelectric materials used in the prototype, as well as

the economical aspect of the construction of the prototype are not covered in the study. The

gathered electricity will be stored in a small-size power bank which then be able to apply solely

for small-load consumer electronics devices

Methodology
Figure 3. 1 Conceptual Framework
Data Gathering

- Gather all the data that will be needed in the design process. These data will be analyzed

by the researchers in order to choose the appropriate materials for the prototype so that

the system will run properly.

Design of the Prototype

- The next step is to design the prototype that will match the gathered data. In this case,

the design will be piezo/triboelectric hybrid generator because it can harvest high

amount of energy than piezoelectric and triboelectric alone.

Figure 3. 2:System Flow

Canvassing of the Materials

- In this part, the researchers can estimate their overall expenditures throughout the

study. Also, they will know the availability of the materials that they’re going to use

and if some are not available in the market, there will be a revision of the design.

Construction of the Design

- Now that the materials are all set, the researchers will start the implementation of the

design. It is possible to have many changes of the design in this process because while

working personally on the prototype, the researchers could find a new approach that

will speed up the construction and will make the system better.
Testing of the Prototype

- Upon completion of the prototype, it will now be tested if the system works as it is

supposed to be. It must be able to fully charge a power bank within the couple of hours

just like charging it on a 220 AC voltage. If the prototype does not work, the researcher

will create a new design to resolve all these errors.

Data Acquisition

- This is the process of gathering and measuring information on variable of interest. In

an established systematic fashion that enables one to answer stated research question

hypotheses, and evaluate outcomes.

Analyzation and Interpretation of Results

- The result from the testing of prototype will be presented into graphs, tables, statistics

and figures. These representations will make the analyzation and interpretation of

results much easier.

Conclusion and Recommendation

- This part contains the most important statements because the researchers will now

make a conclusion about their study based on the results and observations; then, they

will propose their recommendation for possible future improvements if other people

want to continue the study.

Figure 3. 3: Hybrid Generator Flowchart
 Figure 3. 4: Hybrid Generator Block Diagram

V1
1 D1

4 3

R1
2
R2

C1 D3

D4 R3

1 D2
V2
4 3

Figure 3. 5: Hybrid Generator Circuit Diagram

1 Vpk 1 Vpk 10µF 5V

1kHz 1kHz 1B4B42 1B4B42 10Ω
10Ω
0° 0°

1MΩ
1N4001

Figure 3. 6: (a) Charging Circuit of piezo/triboelectric hybrid generator. (b) Actual Charging
Circuit of piezo/triboelectric hybrid generator.
Design Prototype

This study will design a prototype as shown in Figure 14, a model of what it will look

like. It will be the final design for a 5V DC Power Supply using a shoe insole- embedded Piezo-

Triboelectric Hybrid Generator as an alternative source of energy.

Figure 3. 7: (a) Schematic view of piezo/triboelectric hybrid generator.

Table 3. 1: Design Considerations of the Hybrid Generator

DESIGN CONSIDERATIONS OF THE HYBRID GENERATOR

MATERIALS/PARAMETER DESCRIPTIONS
Crystal Transducer 0.3 mm of thickness
FEP (Fluorinated Ethylene Propylene ) 0.025 mm of thickness

Al (Aluminum) 0.2 mm of thickness

Size of Hybrid Generator Insole
Output Specifications 5V, 1A
Gantt Chart
Budget Proposal

Materials Price (Peso)

Lithium Ion Rechargeable Battery 100

Connecting Wires 100

Electronic Components(Resistor, Capacitor and Diode) 75

Terminal Block 30

PCB 90

Shoe Insole 120

Shoes 300

Kapton Tape 250

Aluminum Foil 60

FEP Sheet 3740

Crystal Transducer 75

Aluminum Tape 50

Teflon Plastic 260

Cardboard 20

TOTAL P 5270
Mathematical Model

Piezoelectricity

The interactions between mechanical and electrical properties of the piezoelectric material can

be explained by the static linear relations in strain charge form (IEEE 1988) in the following

equations. Linear piezoelectricity is the combined effect of:

 The linear electrical behavior of the material:

𝐷 = 𝜀𝐸 ⟹ 𝐷𝑖 = 𝜀𝑖𝑗 𝐸𝑖𝑗 (Eq. 1)

∇ ∙ 𝐷=0

∇×𝐸 =0

Where: D is the electric charge density displacement (electric displacement), ε

is permittivity (free-body dielectric constant), E is electric field strength

 Hooke's Law for linear elastic materials:

𝑺 = 𝑠𝑻 ⟹ 𝑆𝑖𝑗 = 𝑠𝑖𝑗𝑘𝑙 𝑇𝑘𝑙 (Eq. 2)

∇ ∙ 𝑇=0

(∇𝑢 + 𝑢∇)
S=
2
 Where: S is strain, s is compliance under short-circuit conditions, T is stress

These may be combined into so-called coupled equations, of which the strain-charge form is:

𝑺 = 𝑠𝑻 + 𝑑𝑡 𝑬 ⟹ 𝑆𝑖𝑗 = 𝑠𝑖𝑗𝑘𝑙 𝑇𝑘𝑙 + 𝑑𝑘𝑖𝑗 𝐸𝑘 (Eq. 3)

𝑫 = 𝑑𝑻 + 𝜀𝑬 ⟹ 𝐷𝑖 = 𝑑𝑖𝑗𝑘 𝑇𝑗𝑘 + 𝜀𝑖𝑗 𝐸𝑖𝑗 (Eq. 4)

In matrix form,

{𝑆} = [𝑠 𝐸 ]{𝑇} + [𝑑 𝑡 ]{𝐸} (Eq. 5)

{𝐷} = [𝑑]{𝑇} + [𝜀 𝑡 ]{𝐸} (Eq. 6)

Where:

[d] is the matrix for the direct piezoelectric effect

[𝑑 𝑡 ] is the matrix for the converse piezoelectric effect

Superscript E indicates a zero, or constant, electric field

Superscript T indicates a zero, or constant, stress field; and the

Superscript t stands for transposition of a matrix.

Notice that the third order tensor d maps vectors into symmetric matrices. There are no non-

trivial rotation-invariant tensors that have this property. That is why there are no isotropic

piezoelectric materials.

For output voltage estimation and further analysis, the open circuit voltage is given by:

𝑉𝑜𝑐 = 𝑃 × 𝑆𝑣 × 𝐷 (Eq. 7)

Where: V is the output peak voltage, P is the pressure applied, 𝑆𝑣 is the voltage sensitivity

of the piezoelectric material and D is the thickness of the piezoelectric stack.

The available electrical energy from piezoelectric transducer can be determined in two ways –

either by calculating the theoretical energy stored on a capacitor for the peak voltage induced

on the device or by acquiring signal data through a known load. In the first case, knowing that

the energy stored in a capacitor is given by

1
𝐸𝑐 = 𝐶𝑣 𝑉 2 𝑜𝑐 (Eq. 8)
2

Where: Cp is the source capacitance and Voc is the voltage at full compression.

Table 3. 2 Fundamental Equations and Piezoelectric Coefficients

FUNDAMENTAL EQUATIONS AND PIEZOELECTRIC COEFFICIENTS

FORMULA PARAMETERS DESCRIPTIONS
electric flux density, or
D
dielectric displacement
T mechanical stress
E electric field
S mechanical strain
D = dT + εTE
E piezoelectric charge
S = s T + dE D
coefficient
dielectric permittivity
εT
(for T = constant)
elastic coefficient
sE
(for E = constant)
permittivity value in the
polarization direction when an
electric field is applied
Permittivity ε ε33T
parallel to the direction of the
(ε0= 8.85 x 10-12 F/m),
polarity, under conditions of
constant mechanical stress (T
= 0:“free“permittivity).
permittivity if the electric field
and dielectric displacement
ε11 S
are in direction 1 at constant
deformation (S =
0:“clamped“permittivity).
mechanical strain induced per
unit of electric field applied in
Piezoelectric Charge or Strain
V/m or charge density in C/m2
Coefficient, d33
per unit pressure in
Piezo Modulus dij N/m2, both in polarization
direction.
 describes the electric field
induced in direction 3 per unit of
Piezoelectric Voltage mechanical stress acting in
g31
Coefficient gij direction 1. Stress = force per
unit area, not necessarily
orthogonal.

FUNDAMENTAL EQUATIONS AND PIEZOELECTRIC COEFFICIENTS

FORMULA PARAMETERS DESCRIPTIONS
the ratio of the mechanical
strain in direction 3 to the
s33E mechanical stress in the
direction 3, at constant electric
field (for E = 0: short circuit).
Elastic Compliance sij
the ratio of a shear strain to the
effective shear stress at
s55D constant dielectric
displacement (for D = 0: open
electrodes).
describes the frequency
coefficient for the longitudinal
N3 oscillation of a slim rod
polarized in the longitudinal
direction.
is the frequency coefficient for
the transverse oscillation of a
N1
slim rod polarized in the 3-
direction.
Frequency Coefficient Ni
is the frequency coefficient of
N = fsA.
N5 the thickness shear oscillation
of a thin disk.
is the frequency coefficient of
NP the planar oscillation of a
round disk.
is the frequency coefficient of
the thickness oscillation of a
NT
thin disk polarized in the
thickness direction.
corresponds in a first
approximation to the
Elasticity or Young’s
reciprocal value of the
modulus Yij
corresponding elasticity
coefficient.
 The mechanical quality factor Qm
characterizes the “sharpness of
the resonance“ of a piezoelectric
body or resonator and is
Mechanical Quality Factor Qm primarily determined from the 3
dB bandwidth of the series
resonance of the system which is
able to oscillate.

FUNDAMENTAL EQUATIONS AND PIEZOELECTRIC COEFFICIENTS

FORMULA PARAMETERS DESCRIPTIONS
the coupling factor for the
k33
longitudinal oscillation.
the coupling factor for the
k31
transverse oscillation.
the coupling factor for the
kP planar radial oscillation of a
Coupling Factors k round disk.
the coupling factor for the
kt thickness oscillation of a
plate.
the coupling factor for the
k15 thickness shear oscillation of a
plate.

Triboelectricity

We analyze the operation of the energy harvester in two modes by investigating both short

circuit current and open circuit voltage. These give us upper bounds for the current and voltage

that can be supplied by the Triboelectric Generators as a power source.

Short Circuit Current

When the two electrodes are connected to each other through a small resistance, they are at the

same potential at the steady state. The charge density in equilibrium on the bottom sheet, 𝜎1 , the
𝐶
top sheet, 𝜎2 , and the FEP, 𝜎𝑇 (133.24μ ), are related to each other as:
𝑚2

𝜎1 + 𝜎𝑇 + 𝜎2 = 0 (Eq. 9)

The potential difference, V, between the electrodes can be found by the line integration of the

electric field between them. It will be zero because the electrodes are shorted:

𝑑 +𝑑 𝜎1 𝑑𝑇 𝜎2 𝑑𝑇 𝜎𝑇 𝑑𝑇
V = ∫0 𝑇 𝐸. 𝑑𝑙 = ( + 𝑑) − ( + 𝑑) + ( + 𝑑) = 0 (Eq. 10)
2𝜀0 𝜀𝑇 2𝜀0 𝜀𝑇 2𝜀0 𝜀𝑇

where εT is the relative dielectric permittivity of FEP (≈2.1), dT is the thickness of the FEP

sheet, d is the distance between the FEP and the top electrode, and ε0 is the dielectric
𝐹
permittivity of free space (≈ 8.9 x 10−12 𝑚).

𝑑𝑇
Defining the electrical thickness of FEO as 𝑑𝑇𝐸 = 𝜀𝑇
and combining (9) and (10) we get:

1 1
𝜎1 = − 𝜎𝑇 𝑑 , and 𝜎2 = − 𝜎𝑇 𝑑 (Eq. 11)
1+ 𝑇𝐸 1+
𝑑𝑇𝐸
𝑑

The charge on the top and bottom electrodes is dictated by the distance, d; and by changing it

mechanically, induced charges can be moved between the sheets.

The initial and final distances between the electrodes are 𝑑𝑖 and 𝑑𝑓 their surface areas are A,

and they move for 𝛥𝑡 seconds. The average harvested current, 𝐼𝐻 flowing from the top

electrode to the bottom electrode can be calculated as:

 𝑓 𝑓
𝛥𝑄 𝐴(𝜎𝑖 − 𝜎𝑖 ) 𝐴𝜎𝑇 𝑑 𝑑𝑓
𝐼𝐻 = 𝛥𝑡
= 𝛥𝑡
= 𝛥𝑡
(𝑑 + 𝑑𝑖 − 𝑑𝑓 + 𝑑𝑇𝐸
) (Eq.12)
𝑖 𝑇𝐸

Equations (11) and (12) suggest that when the top electrode is brought closer to the

FEP (𝑑𝑓 < 𝑑𝑖 ), the current is negative; flowing from the bottom electrode to the top. When

the top electrode is moved further away, (𝑑𝑓 < 𝑑𝑖 ), the current is positive and flows in the

opposite direction. When the top electrode is brought into contact with FEP, (𝑑𝑓 = 0), the

total charge flowing out of the top electrode increases with the FEP surface charge density, the

electrode surface area, and the initial distance. The average current also depends on the speed

of the electrode movement.

Open Circuit Voltage

When the electrodes are not connected to a load, their potential difference is free to change

with distance d. Assuming that the initial and final distances between the sheets are 𝑑𝑖 and 𝑑𝑓

respectively, and the initial potential difference is zero, the potential difference at the final state

is:
𝑑 +𝑑 𝜎2 −𝜎1 𝜎𝑇
𝑉𝑓 = ∫0 𝑇 𝐸. 𝑑𝑙 = (𝑑 𝑇𝐸 + 𝑑𝑓 ) − (𝑑𝑇𝐸 − 𝑑𝑓 ) (Eq. 13)
2𝜀0 2𝜀0

Combining (5) and (3) we get:

𝜎𝑇 𝑑𝑇𝐸 (𝑑𝑖 − 𝑑𝑓 )
𝑉𝑓 = . (Eq. 14)
𝜀0 𝑑𝑖 + 𝑑𝑇𝐸

Therefore, for the case where df= 0

𝜎𝑇 𝑑𝑇𝐸 (𝑑𝑖 )
𝑉𝑓 = . (Eq. 15)
𝜀0 𝑑𝑖 + 𝑑𝑇𝐸
Energy and Efficiency

Further, using an average 3/5 Hz stepping frequency and assuming that the developed charge

is fully poled two times during each cycle (compression and relaxation), the anticipated

average electric power available from cyclic excitation of the transducer is

3
𝑃𝑖𝑛𝑝𝑢𝑡 = 2𝐸𝑐 ( ) (Eq. 16)
5

Or, using the average walking frequency of the test subject, providing for better comparison of

theoretical and actual data

𝑃𝑜𝑢𝑡𝑝𝑢𝑡 = 2𝐸𝑐 (𝑓) (Eq. 17)

Where: f is the average walking frequency of the test subject

Therefore, the mechanical work performed on the transducer and the input power are

𝑊𝑖𝑛𝑝𝑢𝑡 = 𝐹𝑑 (Eq. 18)

𝑃𝑖𝑛𝑝𝑢𝑡 = 𝑊𝑖𝑛𝑝𝑢𝑡 × 𝑡 (Eq. 19)

1
Where: t =
𝑓

∆𝐸
𝑃 = 𝐼𝑉 = (Eq. 20)
∆𝑡

Where: P is the average power, I is the average current, V is the average voltage.

∆𝐸
𝑡𝑐 = (Eq. 21)
𝐼𝑉

Where: tc is the charging time

And, the efficiency of the Hybrid Generator is

𝑃𝑜𝑢𝑡𝑝𝑢𝑡
𝜂= 𝑃𝑖𝑛𝑝𝑢𝑡
× 100 (Eq. 22)

Piezoelectric Generator at Press and Release Cycle

1. First, when the force is to be applied at the upper layer, it will suffer from tensile stress.

The voltage starts to increase at positive alternation.

2. At full-contact state, the voltage reaches its peak value at positive alternation.

3. At separation state, voltage slowly decreases to zero at positive alternation then the

voltage starts to increase at negative alternation.

4. Lastly, at full-separation state, the upper layer suffers from compression stress. The

voltage reaches its peak value at negative alternation.

Triboelectric Generator at Press and Release Cycle

1. First at full contact state, the voltage spike to its peak value at positive alternation.

2. At separation state, the voltage suddenly decreases to zero then the voltage at positive

alternation spikes to its peak value.

3. Lastly, at full separation state, the voltage at negative alternation suddenly decreases to

zero.
Result and Discussion

Mechanism Testing

A. Piezoelectric Generator

Table 3. 3: Piezoelectric Rating with Variable Force Input

Force 10 N 20 N 30 N
Voltage Current Voltage Current Voltage Current
Trial
(V) (uA) (V) (uA) (V) (uA)
1 11.4 71 18.7 110 19.7 119
2 11.9 72 21.3 110 20.2 122
3 5.6 58 16.1 94 24.4 133
4 7.2 58 16.1 99 25.3 140
5 5.4 57 22 114 29.3 153
6 5.5 58 23 117 32.1 164
7 11.9 75 12.1 82 15.8 104
8 12.5 75 12.4 82 16.7 108
9 15.1 81 27.3 147 26.7 145
10 15.7 83 28.2 147 19.5 116
11 8.1 59 10.1 62 33.6 166
12 8.3 60 10.8 80 36.1 183
13 4.3 49 24 135 16.8 109
14 4.9 50 25.2 138 17.7 112
15 17.3 89 17.3 103 20.4 124
16 18.8 97 18.6 105 21.7 125
17 8.8 61 13.6 87 27.4 146
18 10 68 14.1 87 27.4 146
19 2.5 41 14.3 88 22.6 130
20 3.2 45 15.6 88 23.4 131

Average 9.42 65.35 18.04 103.75 23.84 133.8

 Piezoelectric Voltage Rating Comparison
40
35
30
Voltage (V)

25
20
15
10
5
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Trial

10 N 20 N 30 N

Figure 3. 8: Piezoelectric Voltage Rating Comparison with Variable Force Input

As indicated in the above figure, it shows the comparison of the piezoelectric output

voltage rating when force values of 10N, 20N and 30N are applied with 20 trials each. The

average output voltage for the respective force values are 9.42V, 18.04V and 23.84V. It can

clearly be seen that the output voltage of the piezoelectric generator increases as the amount

of the force applied is increased.

Piezoelectric Current Rating Comparison

200

150
Current (uA)

100

50

0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Trial

10 N 20 N 30 N

Figure 3. 9: Piezoelectric Current Rating Comparison with Variable Force Input

 As indicated in the above figure, it shows the comparison of the piezoelectric output

current rating when force values of 10N, 20N and 30N are applied with 20 trials each. The

average output current for the respective force values are 65.35μA, 103.75μA and 133.8μA. It

can clearly be seen that the output current of the piezoelectric generator increases as the amount

of the force applied is increased.

B. Triboelectric Generator

Table 3. 4: Triboelectric Rating with Variable Force Input

Force 10 N 20 N 30 N
Voltage Current Voltage Current Voltage Current
Trial
(V) (uA) (V) (uA) (V) (uA)
1 1.93 1 3.06 1 4.48 1
2 2.31 1 3.1 1 4.61 1
3 2.36 1 2.93 <1 4.91 1
4 2.66 1 2.77 <1 5.05 1
5 1.27 <1 3.24 1 4.35 1
6 1.4 <1 2.9 <1 4.42 1
7 1.69 1 3.74 1 3.97 <1
8 1.73 1 3.85 1 4 <1
9 2.66 1 3.35 1 4.46 1
10 1.45 <1 3.45 1 5.72 1
11 1.5 <1 2.98 <1 3.95 <1
12 1.5 <1 3.06 <1 4.07 <1
13 1.52 <1 3.22 1 4.1 1
14 2.94 1 3.13 1 4.81 1
15 3.64 1 3.27 1 5.21 1
16 1.62 <1 2.5 <1 4.03 <1
17 1.75 1 3.97 1 5.14 1
18 2.92 1 3.12 1 5.19 1
19 1.57 <1 2.78 <1 4.06 <1
20 1.61 <1 2.83 <1 4.07 <1

Average 2.0015 0.55 3.1625 0.6 4.53 0.65

 Triboelectric Voltage Rating Comparison
7
6
5
Voltage (V)

4
3
2
1
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Trial

10 N 20 N 30 N

Figure 3. 10: Triboelectric Voltage Rating Comparison with Variable Force Input

As indicated in the above figure, it shows the comparison of the triboelectric output

voltage rating when force values of 10N, 20N and 30N are applied with 20 trials each. The

average output voltage for the respective force values are 2.0015V, 3.1625V and 4.53V. It can

clearly be seen that the output voltage of the triboelectric generator didn’t make any significant

change as the amount of force applied is increased.

Triboelectric Current Rating comparison

1.2
1
Current (uA)

0.8
0.6
0.4
0.2
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Trial

10 N 20 N 30 N

Figure 3. 11: Triboelectric Current Rating Comparison with Variable Force Input
 As indicated in the above figure, it shows the comparison of the triboelectric output

current rating when force values of 10N, 20N and 30N are applied with 20 trials each. The

average triboelectric current for the respective force values are 0.55μA, 0.6μA and 0.65μA. It

can clearly be seen that there is a slight occurrence of current flow within the triboelectric

generator when force is applied. Indications of values 0 and <1 are valid for the reason of the

current produced by the triboelectric is small that the multimeter is unable to read the exact

value. Taking note that the multimeter used during testing can read up to 2000μA.

C. Hybrid Generator

Table 3. 5: Hybrid Rating with Variable Force Input

Force 10 N 20 N 30 N
Voltage Current Voltage Current Voltage Current
Trial
(V) (uA) (V) (uA) (V) (uA)
1 14.3 67 22.4 106 29.5 149
2 15.1 62 23.4 108 31.9 152
3 13.6 62 16.9 91 22.7 120
4 16.7 65 17.1 92 23.1 124
5 18.3 87 25.8 134 19.6 110
6 20.7 44 27.5 145 27.3 141
7 13.8 75 14.1 89 24.1 125
8 13.9 85 15.8 89 19.8 111
9 10.4 72 16.2 90 21.3 115
10 11.6 50 18.7 98 24.7 127
11 15.8 50 21.6 101 25.4 132
12 16 63 22.2 105 36 184
13 22.4 77 24.6 125 22.4 118
14 11.9 64 25.1 126 19.2 109
15 19.1 55 19.3 99 33.4 167
16 13.2 81 20.3 101 34.2 169
17 11.7 98 23.6 108 27.8 146
18 22.6 42 16.4 91 29.3 147
19 13.1 76 24 109 26.2 134
20 19.2 72 24.2 115 27 135

Average 15.67 67.35 20.96 106.1 26.245 135.75

 Hybrid Voltage Rating Comparison
40

30
Voltage (V)

20

10

0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Trial

10 N 20 N 30 N

Figure 3. 12: Hybrid Voltage Rating Comparison with Variable Force Input

As indicated in the above figure, it shows the comparison of the hybrid output voltage

rating when force values of 10N, 20N and 30N are applied with 20 trials each. The average

output voltage for the respective force values are 15.67V, 20.96V and 26.245V. It can clearly

be seen the output voltage of the hybrid generator increases as the amount of the force applied

is increased. There is a slight variance of values compared to output voltage of the individual

generators as for the reason of low performance of triboelectric generator.

Hybrid Voltage Rating Comparison

40
Voltage (V)

30
20
10
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Trial

10 N 20 N 30 N

Figure 3. 13: Hybrid Current Rating Comparison with Variable Force Input
 As indicated in the above figure, it shows the comparison of the hybrid output current

rating when force values of 10N, 20N and 30N are applied with 20 trials each. The average

output current for the respective force values are 67.35μA, 106.1μA and 135.75μA. It can

clearly be seen the output current of the hybrid generator increases as the amount of the force

applied is increased. There is a slight variance of values compared to output current of the

individual generators as for the reason of low performance of triboelectric generator.

Walk Testing

Table 3. 6: Generator Rating while Walking

Piezoelectric Triboelectric Hybrid

Trial Voltage Current Voltage Current Voltage Current
(V) (uA) (V) (uA) (V) (uA)
1 19 30 5.3 1 39 94
2 21 32 6.2 1 44 99
3 39 56 4.2 <1 30 66
4 41 62 4.3 <1 31 74
5 29 39 5.3 1 53 118
6 30 39 5.3 1 18 32
7 47 85 2.2 1 20 34
8 51 88 3 <1 36 85
9 45 74 4.5 1 38 87
10 23 32 4.7 1 24 57
11 29 38 3 <1 25 63
12 35 50 3.3 <1 18 27
13 19 30 3.7 <1 31 74
14 35 52 4.1 <1 23 55
15 39 55 6.8 1 31 78
16 33 42 7.8 1 35 80
17 33 43 4.8 1 38 92
18 34 45 5.2 1 39 93
19 15 25 3.3 <1 20 35
20 19 26 3.6 <1 21 41

Average 31.8 47.15 4.53 0.55 30.7 69.2

 A. Piezoelectric Generator

Piezoelectric Voltage Rating (Walking)

60

50

40
Voltage (V)

30

20

10

0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Trial

Figure 3. 14: Piezoelectric Voltage Rating (Walking)

As indicated in the above figure, it shows the piezoelectric output voltage rating when

put under a walking phase with 20 steps. The average output voltage for the piezoelectric

generator is 31.8V.

Piezoelectric Current Rating (Walking)

100
90
80
70
Current (uA)

60
50
40
30
20
10
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Trial

Figure 3. 15: Piezoelectric Current Rating (Walking)

 As indicated in the above figure, it shows the piezoelectric output current rating when

put under a walking phase with 20 steps. The average output current for the piezoelectric

generator is 47.15μA.

B. Triboelectric Generator

Triboelectric Voltage Rating (Walking)

9
8
7
6
Voltage (V)

5
4
3
2
1
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Trial

Figure 3. 16: Triboelectric Voltage Rating (Walking)

As indicated in the above figure, it shows the triboelectric output voltage rating when

put under a walking phase with 20 steps. The average output voltage for the triboelectric

generator is 4.53V.

Triboelectric Current Rating (Walking)

1.2
1
Current (uA)

0.8
0.6
0.4
0.2
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Trial

Figure 3. 17: Triboelectric Current Rating (Walking)

 As indicated in the above figure, it shows the triboelectric output current rating when

put under a walking phase with 20 steps. The average output current for the triboelectric

generator is 2.6μA.

C. Hybrid Generator

Hybrid Voltage Rating (Walking)

60

50

40
Voltage (V)

30

20

10

0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Trial

Figure 3. 18: Hybrid Voltage Rating (Walking)

As indicated in the above figure, it shows the hybrid output voltage rating when put

under a walking phase with 20 steps. The average output current for the hybrid generator is

30.7V.

Hybrid Current Rating (Walking)

150
Current (uA)

100

50

0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Trial

Figure 3. 19: Hybrid Current Rating (Walking)

 As indicated in the above figure, it shows the hybrid output current rating when put

under a walking phase with 20 steps. The average output current for the hybrid generator is

69.2μA.

Run Testing

Table 3. 7: Generator Rating while Running

Piezoelectric Triboelectric Hybrid

Trial Voltage Current Voltage Current Voltage Current
(V) (uA) (V) (uA) (V) (uA)
1 67.7 105 5.2 <1 69.4 122
2 71 106 5.7 <1 78.1 127
3 58.6 95 6.8 1 56.8 108
4 59 99 6.6 1 60.2 113
5 56.8 93 5.8 1 45.9 63
6 57.8 94 6.1 1 48.3 69
7 64 102 7.4 1 63.8 120
8 65.7 103 7.8 1 64.9 121
9 54.7 85 5.2 <1 56.4 102
10 55.5 87 5.7 <1 43.1 55
11 41.3 77 4.1 <1 61.5 115
12 43.4 79 4.3 <1 49.5 83
13 77.2 107 6.9 1 56.3 102
14 81.1 114 7.2 1 78.2 146
15 55.8 90 6.3 1 43.2 60
16 44.4 80 6.4 1 45.7 62
17 53.3 85 5.1 <1 49.8 85
18 61.4 101 5.2 <1 50.2 91
19 44.4 80 3.1 <1 50.6 94
20 45.7 83 6.7 1 55.4 102

Average 57.94 93.25 5.88 0.55 56.365 97

 A. Piezoelectric Generator

Piezoelectric Voltage Rating (Running)

90
80
70
60
Voltage (V)

50
40
30
20
10
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Trial

Figure 3. 20: Piezoelectric Voltage Rating (Running)

As indicated in the above figure, it shows the piezoelectric output voltage rating when

put under a running phase with 20 steps. The average output voltage for the piezoelectric

generator is 57.94V.

Piezoelectric Current Rating (Running)

120

100

80
Current (uA)

60

40

20

0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Trial

Figure 3. 21: Piezoelectric Current Rating (Running)

 As indicated in the above figure, it shows the piezoelectric output current rating when

put under a running phase with 20 steps. The average output current for the piezoelectric

generator is 93.25μA.

B. Triboelectric Generator

Triboelectric Voltage Rating ( Running)

10
8
Voltage (V)

6
4
2
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Trial

Figure 3. 22: Triboelectric Voltage Rating (Running)

As indicated in the above figure, it shows the triboelectric output voltage rating when put

under a running phase with 20 steps. The average output voltage for the triboelectric generator

is 5.88V.

Triboelectric Current Rating (Running)

1.2
1
0.8
Current

0.6
0.4
0.2
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Trial

Figure 3. 23: Triboelectric Current Rating (Running)

 As indicated in the above figure, it shows the triboelectric output current rating when

put under a running phase with 20 steps. The average output current for the triboelectric

generator is 0.55μA.

C. Hybrid Generator

Hybrid Voltage Rating (Running)

100

80
Voltage (V)

60

40

20

0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Trial

Figure 3. 24: Hybrid Voltage Rating (Running)

As indicated in the above figure, it shows the hybrid output voltage rating when put

under a running phase with 20 steps. The average output current for the hybrid generator is

56.365V.

Hybrid Current Rating (Running)

200
Current (uA)

150

100

50

0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Trial

Figure 3. 25: Hybrid Current Rating (Running)

 As indicated in the above figure, it shows the hybrid output current rating when put

under a running phase with 20 steps. The average output current for the hybrid generator is

97μA.

Prototype Testing

Table 3. 8: Rating of the Prototype

Trial Voltage (V) Current (uA)

1 1.64 22
2 2.87 24
3 4.25 25
4 5.23 31
5 5.35 32
6 5.41 33
7 5.42 33
8 5.44 35
9 5.45 36
10 5.47 36
11 5.49 37
12 5.51 38
13 5.54 38
14 5.58 39
15 5.63 40
16 5.63 44
17 5.65 59
18 5.68 59
19 5.71 61
20 5.79 65
Average 5.137 39.35
 Prototype Voltage Rating
7
6
5
Voltage (V)

4
3
2
1
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Trial

Figure 3. 26: Voltage Rating of the Prototype

As indicated in the above figure, it shows the voltage rating of the prototype when put

under a walking phase with 20 steps. At this point, this is where the hybrid generator is

connected to the energy harvesting circuit with its voltage already rectified, filtered, regulated

and is now ready for charging. The voltage from the generator was already rectified, filtered

and regulated. As you can see, the voltage harvested from the generator starts to warm up until

it is completely regulated through the use of a zener diode. The regulated voltage of the piezo-

triboelectric hybrid generator is 5.137V.

Prototype Current Rating

80
Current (uA)

60

40

20

0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
Trial

Figure 3. 27: Current Rating of the Prototype

 As indicated in the above figure, it shows the current rating of the prototype when put

under a walking phase with 20 steps. At this point, this is where the hybrid generator is

connected to the energy harvesting circuit with its voltage already rectified, filtered, regulated

and is now ready for charging. The voltage from the generator was already rectified, filtered

and regulated. As you can see, the voltage harvested from the generator starts to warm up until

it is completely regulated through the use of a zener diode. The current rating of the piezo-

triboelectric hybrid generator is 40.2µA.

Piezoelectric Generator with 10 N Force input

 STATISTICAL MEASURES

Table 3. 9: Statistical Measures for Piezoelectric Generator with 10 N Force input

Statistical
Voltage Current
Measures
Mean 9.42000 65.35000
Median 8.55000 60.50000
Mode 11.90000 58.00000
Standard
4.78744 14.89710
Deviation
Variance 22.91958 221.92368
Coefficient of
0.50822 0.22796
Variation
  REGRESSION AND CORRELATION

Table 3. 10: Linear Model for Piezoelectric Generator with 10 N Force input

Linear
Voltage (V) Current (µA)
Trial x^2 y^2 xy
(x) (y)
1 11.4 71 129.96000 5041.00000 809.40000
2 11.9 72 141.61000 5184.00000 856.80000
3 5.6 58 31.36000 3364.00000 324.80000
4 7.2 58 51.84000 3364.00000 417.60000
5 5.4 57 29.16000 3249.00000 307.80000
6 5.5 58 30.25000 3364.00000 319.00000
7 11.9 75 141.61000 5625.00000 892.50000
8 12.5 75 156.25000 5625.00000 937.50000
9 15.1 81 228.01000 6561.00000 1223.10000
10 15.7 83 246.49000 6889.00000 1303.10000
11 8.1 59 65.61000 3481.00000 477.90000
12 8.3 60 68.89000 3600.00000 498.00000
13 4.3 49 18.49000 2401.00000 210.70000
14 4.9 50 24.01000 2500.00000 245.00000
15 17.3 89 299.29000 7921.00000 1539.70000
16 18.8 97 353.44000 9409.00000 1823.60000
17 8.8 61 77.44000 3721.00000 536.80000
18 10 68 100.00000 4624.00000 680.00000
19 2.5 41 6.25000 1681.00000 102.50000
20 3.2 45 10.24000 2025.00000 144.00000
188.40000 1307.00000 2210.20000 89629.00000 13649.80000

Regression Coefficients
B = 3.07221
A = 36.40981

Regression Equation

ŷ = 36.40981 + 3.07221x

Coefficient of Correlation
r = 0.98731
 Table 3. 11: Exponential Model for Piezoelectric Generator with 10 N Force input

Exponential
Voltage (V) Current (µA)
Trial x^2 (ln y)^2 xlny
(x) (ln y)
1 11.4 4.26268 129.96000 18.17044 48.59455
2 11.9 4.27667 141.61000 18.28991 50.89237
3 5.6 4.06044 31.36000 16.48717 22.73846
4 7.2 4.06044 51.84000 16.48717 29.23517
5 5.4 4.04305 29.16000 16.34625 21.83247
6 5.5 4.06044 30.25000 16.48717 22.33242
7 11.9 4.31749 141.61000 18.64072 51.37813
8 12.5 4.31749 156.25000 18.64072 53.96863
9 15.1 4.39445 228.01000 19.31119 66.35620
10 15.7 4.41884 246.49000 19.52615 69.37579
11 8.1 4.07754 65.61000 16.62633 33.02807
12 8.3 4.09434 68.89000 16.76362 33.98302
13 4.3 3.89182 18.49000 15.14626 16.73483
14 4.9 3.91202 24.01000 15.30390 19.16890
15 17.3 4.48864 299.29000 20.14789 77.65347
16 18.8 4.57471 353.44000 20.92797 86.00455
17 8.8 4.11087 77.44000 16.89925 36.17566
18 10 4.21951 100.00000 17.80426 42.19510
19 2.5 3.71357 6.25000 13.79060 9.28393
20 3.2 3.80666 10.24000 14.49066 12.18131
188.40000 83.10167 2210.20000 346.28765 803.11302

Regression Coefficients
B = 0.04661
A = 3.71606

Regression Equation

ŷ = 41.10221e0.04661x

Coefficient of Correlation
r = 0.97584
 Table 3. 12: Power Model for Piezoelectric Generator with 10 N Force input

Power
Voltage (V) Current (µA)
Trial (log x)^2 (log y)^2 logxlogy
(log x) (log y)
1 1.0569 1.85126 1.11704 3.42716 1.95660
2 1.07555 1.85733 1.15681 3.44967 1.99765
3 0.74819 1.76343 0.55979 3.10969 1.31938
4 0.85733 1.76343 0.73501 3.10969 1.51184
5 0.73239 1.75587 0.53640 3.08308 1.28598
6 0.74036 1.76343 0.54813 3.10969 1.30557
7 1.07555 1.87506 1.15681 3.51585 2.01672
8 1.09691 1.87506 1.20321 3.51585 2.05677
9 1.17898 1.90849 1.38999 3.64233 2.25007
10 1.1959 1.91908 1.43018 3.68287 2.29503
11 0.90849 1.77085 0.82535 3.13591 1.60880
12 0.91908 1.77815 0.84471 3.16182 1.63426
13 0.63347 1.6902 0.40128 2.85678 1.07069
14 0.6902 1.69897 0.47638 2.88650 1.17263
15 1.23805 1.94939 1.53277 3.80012 2.41344
16 1.27416 1.98677 1.62348 3.94726 2.53146
17 0.94448 1.78533 0.89204 3.18740 1.68621
18 1 1.83251 1.00000 3.35809 1.83251
19 0.39794 1.61278 0.15836 2.60106 0.64179
20 0.50515 1.65321 0.25518 2.73310 0.83512
18.26908 36.09060 17.84292 65.31391 33.42253

Regression Coefficients
B = 0.39433
A = 1.44433

Regression Equation

ŷ = 27.81831x0.39433

Coefficient of Correlation
r = 0.97908
 Table 3. 13: Hyperbolic Model for Piezoelectric Generator with 10 N Force input
Hyperbolic
Voltage (V) Current (µA)
Trial (1/x)^2 (1/y)^2 (1/x)(1/y)
(1/x) (1/y)
1 0.08772 0.01408 0.00769 0.00020 0.00124
2 0.08403 0.01389 0.00706 0.00019 0.00117
3 0.17857 0.01724 0.03189 0.00030 0.00308
4 0.13889 0.01724 0.01929 0.00030 0.00239
5 0.18519 0.01754 0.03430 0.00031 0.00325
6 0.18182 0.01724 0.03306 0.00030 0.00313
7 0.08403 0.01333 0.00706 0.00018 0.00112
8 0.08 0.01333 0.00640 0.00018 0.00107
9 0.06623 0.01235 0.00439 0.00015 0.00082
10 0.06369 0.01205 0.00406 0.00015 0.00077
11 0.12346 0.01695 0.01524 0.00029 0.00209
12 0.12048 0.01667 0.01452 0.00028 0.00201
13 0.23256 0.02041 0.05408 0.00042 0.00475
14 0.20408 0.02 0.04165 0.00040 0.00408
15 0.0578 0.01124 0.00334 0.00013 0.00065
16 0.05319 0.01031 0.00283 0.00011 0.00055
17 0.11364 0.01639 0.01291 0.00027 0.00186
18 0.1 0.01471 0.01000 0.00022 0.00147
19 0.4 0.02439 0.16000 0.00059 0.00976
20 0.3125 0.02222 0.09766 0.00049 0.00694
2.86788 0.32158 0.56742 0.00543 0.05219

Regression Coefficients
B = 0.03891
A = 0.01050

Regression Equation

𝒙
ŷ = 95.24871
𝟑.𝟕𝟎𝟔𝟔𝟎+𝒙

Coefficient of Correlation
r = 0.95212
 Table 3. 14: Summary of Mathematical Models for Piezoelectric Generator with 10 N Force

input

Mathematical Models
Regression and
Correlation Linear Exponential Power Hyperbolic
Parameters
B 3.07221 0.04661 0.39433 0.03891
A 36.40981 3.71606 1.44433 0.01050
Regression
ŷ = 36.40981 + 3.07221x ŷ = 41.10221e 0.04661x
ŷ = 27.81831x0.39433 ŷ = 95.24871
Equation
r 0.98731 0.97584 0.97908 0.95212

Since the coefficient of correlation of the linear model (r = 0.98731) is the nearest

absolute value to 1 among the other mathematical models, then it is considered to be the best-

fit curve for the system of data.

Best Fit Curve:

120

100

80
Current (µA)

60

40

20

0
0 5 10 15 20
Voltage (V)

Figure 3. 28: Best Fit Curve Piezoelectric Generator with 10 N Force input
Piezoelectric Generator with 20 N Force input

 STATISTICAL MEASURES

Table 3. 15: Statistical Measures for Piezoelectric Generator with 20 N Force input

Statistical
Voltage Current
Measures
Mean 18.04000 103.75000
Median 16.70000 101.00000
Mode 16.10000 110.00000
Standard
5.49271 23.70848
Deviation
Variance 30.16989 562.09211
Coefficient of
0.30447 0.22852
Variation
  REGRESSION AND CORRELATION

Table 3. 16: Linear Model for Piezoelectric Generator with 20 N Force input

Linear
Voltage (V) Current (µA)
Trial x^2 y^2 xy
(x) (y)
1 18.7 110 349.69000 12100.00000 2057.00000
2 21.3 110 453.69000 12100.00000 2343.00000
3 16.1 94 259.21000 8836.00000 1513.40000
4 16.1 99 259.21000 9801.00000 1593.90000
5 22 114 484.00000 12996.00000 2508.00000
6 23 117 529.00000 13689.00000 2691.00000
7 12.1 82 146.41000 6724.00000 992.20000
8 12.4 82 153.76000 6724.00000 1016.80000
9 27.3 147 745.29000 21609.00000 4013.10000
10 28.2 147 795.24000 21609.00000 4145.40000
11 10.1 62 102.01000 3844.00000 626.20000
12 10.8 80 116.64000 6400.00000 864.00000
13 24 135 576.00000 18225.00000 3240.00000
14 25.2 138 635.04000 19044.00000 3477.60000
15 17.3 103 299.29000 10609.00000 1781.90000
16 18.6 105 345.96000 11025.00000 1953.00000
17 13.6 87 184.96000 7569.00000 1183.20000
18 14.1 87 198.81000 7569.00000 1226.70000
19 14.3 88 204.49000 7744.00000 1258.40000
20 15.6 88 243.36000 7744.00000 1372.80000
360.80000 2075.00000 7082.06000 225961.00000 39857.60000

Regression Coefficients
B = 4.22973
A = 27.44566

Regression Equation

ŷ = 27.44566 + 4.22973x

Coefficient of Correlation
r = 0.97993
 Table 3. 17: Exponential Model for Piezoelectric Generator with 20 N Force input

Exponential
Voltage (V) Current (µA)
Trial x^2 (ln y)^2 xlny
(x) (ln y)
1 18.7 4.70048 349.69000 22.09451 87.89898
2 21.3 4.70048 453.69000 22.09451 100.12022
3 16.1 4.54329 259.21000 20.64148 73.14697
4 16.1 4.59512 259.21000 21.11513 73.98143
5 22 4.7362 484.00000 22.43159 104.19640
6 23 4.76217 529.00000 22.67826 109.52991
7 12.1 4.40672 146.41000 19.41918 53.32131
8 12.4 4.40672 153.76000 19.41918 54.64333
9 27.3 4.99043 745.29000 24.90439 136.23874
10 28.2 4.99043 795.24000 24.90439 140.73013
11 10.1 4.12713 102.01000 17.03320 41.68401
12 10.8 4.38203 116.64000 19.20219 47.32592
13 24 4.90527 576.00000 24.06167 117.72648
14 25.2 4.92725 635.04000 24.27779 124.16670
15 17.3 4.63473 299.29000 21.48072 80.18083
16 18.6 4.65396 345.96000 21.65934 86.56366
17 13.6 4.46591 184.96000 19.94435 60.73638
18 14.1 4.46591 198.81000 19.94435 62.96933
19 14.3 4.47734 204.49000 20.04657 64.02596
20 15.6 4.47734 243.36000 20.04657 69.84650
360.80000 92.34891 7082.06000 427.39941 1689.03319

Regression Coefficients
B = 0.04023
A = 3.89176

Regression Equation

ŷ = 48.99717e0.04023x

Coefficient of Correlation
r = 0.97123
 Table 3. 18: Power Model for Piezoelectric Generator with 20 N Force input

Power
Voltage (V) Current (µA)
Trial (log x)^2 (log y)^2 logxlogy
(log x) (log y)
1 1.27184 2.04139 1.61758 4.16727 2.59632
2 1.32838 2.04139 1.76459 4.16727 2.71174
3 1.20683 1.97313 1.45644 3.89324 2.38123
4 1.20683 1.99564 1.45644 3.98258 2.40840
5 1.34242 2.0569 1.80209 4.23084 2.76122
6 1.36173 2.06819 1.85431 4.27741 2.81632
7 1.08279 1.91381 1.17243 3.66267 2.07225
8 1.09342 1.91381 1.19557 3.66267 2.09260
9 1.43616 2.16732 2.06256 4.69728 3.11262
10 1.45025 2.16732 2.10323 4.69728 3.14316
11 1.00432 1.79239 1.00866 3.21266 1.80013
12 1.03342 1.90309 1.06796 3.62175 1.96669
13 1.38021 2.13033 1.90498 4.53831 2.94030
14 1.4014 2.13988 1.96392 4.57909 2.99883
15 1.23805 2.01284 1.53277 4.05152 2.49200
16 1.26951 2.02119 1.61166 4.08521 2.56592
17 1.13354 1.93952 1.28491 3.76174 2.19852
18 1.14922 1.93952 1.32071 3.76174 2.22894
19 1.15534 1.94448 1.33481 3.78100 2.24654
20 1.19312 1.94448 1.42354 3.78100 2.32000
24.73878 40.10662 30.93914 80.61252 49.85373

Regression Coefficients
B = 0.72108
A = 1.11340

Regression Equation

ŷ = 12.98377x0.72108

Coefficient of Correlation
r = 0.97453
 Table 3. 19: Hyperbolic Model for Piezoelectric Generator with 20 N Force input

Hyperbolic
Voltage (V) Current (µA)
Trial (1/x)^2 (1/y)^2 (1/x)(1/y)
(1/x) (1/y)
1 0.05348 0.00909 0.00286 0.00008 0.00049
2 0.04695 0.00909 0.00220 0.00008 0.00043
3 0.06211 0.01064 0.00386 0.00011 0.00066
4 0.06211 0.0101 0.00386 0.00010 0.00063
5 0.04545 0.00877 0.00207 0.00008 0.00040
6 0.04348 0.00855 0.00189 0.00007 0.00037
7 0.08264 0.0122 0.00683 0.00015 0.00101
8 0.08065 0.0122 0.00650 0.00015 0.00098
9 0.03663 0.0068 0.00134 0.00005 0.00025
10 0.03546 0.0068 0.00126 0.00005 0.00024
11 0.09901 0.01613 0.00980 0.00026 0.00160
12 0.09259 0.0125 0.00857 0.00016 0.00116
13 0.04167 0.00741 0.00174 0.00005 0.00031
14 0.03968 0.00725 0.00157 0.00005 0.00029
15 0.0578 0.00971 0.00334 0.00009 0.00056
16 0.05376 0.00952 0.00289 0.00009 0.00051
17 0.07353 0.01149 0.00541 0.00013 0.00084
18 0.07092 0.01149 0.00503 0.00013 0.00081
19 0.06993 0.01136 0.00489 0.00013 0.00079
20 0.0641 0.01136 0.00411 0.00013 0.00073
1.21195 0.20246 0.08002 0.00215 0.01306

Regression Coefficients
B = 0.12026
A = 0.00284

Regression Equation

𝒙
ŷ = 352.66096𝟒𝟐.𝟒𝟏𝟎𝟕𝟖+𝒙

Coefficient of Correlation
r = 0.96459
Table 3. 20: Summary of Mathematical Models for Piezoelectric Generator with 20 N Force input

Mathematical Models
Regression and
Correlation Linear Exponential Power Hyperbolic
Parameters
B 4.22973 0.04023 0.72108 0.12026
A 27.44566 3.89176 1.11340 0.00284
Regression
ŷ = 27.44566 + 4.22973x ŷ = 48.99717e 0.04023x
ŷ = 12.98377x 0.72108
ŷ = 352.66096
Equation
r 0.97993 0.97123 0.97453 0.96549

Since the coefficient of correlation of the linear model (r = 0.97993) is the nearest

absolute value to 1 among the other mathematical models, then it is considered to be the best-

fit curve for the system of data.

Best Fit Curve:

160

140

120

100
Current (µA)

80

60

40

20

0
0 5 10 15 20 25 30
Voltage (V)

Figure 3. 29: Best Fit Curve Piezoelectric Generator with 20 N Force input
Piezoelectric Generator with 30 N Force input

 STATISTICAL MEASURES

Table 3. 21: Statistical Measures for Piezoelectric Generator with 30 N Force input

Statistical
Voltage Current
Measures
Mean 23.84000 133.80000
Median 23.00000 130.50000
Mode 27.40000 146.00000
Standard
5.84820 21.41716
Deviation
Variance 34.20147 458.69474
Coefficient of
0.24531 0.16007
Variation
  REGRESSION AND CORRELATION

Table 3. 22: Linear Model for Piezoelectric Generator with 30 N Force input

Linear
Voltage (V) Current (µA)
Trial x^2 y^2 xy
(x) (y)
1 19.7 119 388.09000 14161.00000 2344.30000
2 20.2 122 408.04000 14884.00000 2464.40000
3 24.4 133 595.36000 17689.00000 3245.20000
4 25.3 140 640.09000 19600.00000 3542.00000
5 29.3 153 858.49000 23409.00000 4482.90000
6 32.1 164 1030.41000 26896.00000 5264.40000
7 15.8 104 249.64000 10816.00000 1643.20000
8 16.7 108 278.89000 11664.00000 1803.60000
9 26.7 145 712.89000 21025.00000 3871.50000
10 19.5 116 380.25000 13456.00000 2262.00000
11 33.6 166 1128.96000 27556.00000 5577.60000
12 36.1 183 1303.21000 33489.00000 6606.30000
13 16.8 109 282.24000 11881.00000 1831.20000
14 17.7 112 313.29000 12544.00000 1982.40000
15 20.4 124 416.16000 15376.00000 2529.60000
16 21.7 125 470.89000 15625.00000 2712.50000
17 27.4 146 750.76000 21316.00000 4000.40000
18 27.4 146 750.76000 21316.00000 4000.40000
19 22.6 130 510.76000 16900.00000 2938.00000
20 23.4 131 547.56000 17161.00000 3065.40000
476.80000 2676.00000 12016.74000 366764.00000 66167.30000

Regression Coefficients
B = 3.64937
A = 46.79912

Regression Equation

ŷ = 46.79912 + 3.64937x

Coefficient of Correlation
r = 0.99650
 Table 3. 23: Exponential Model for Piezoelectric Generator with 30 N Force input

Exponential
Voltage (V) Current (µA)
Trial x^2 (ln y)^2 xlny
(x) (ln y)
1 19.7 4.77912 388.09000 22.83999 94.14866
2 20.2 4.80402 408.04000 23.07861 97.04120
3 24.4 4.89035 595.36000 23.91552 119.32454
4 25.3 4.94164 640.09000 24.41981 125.02349
5 29.3 5.03044 858.49000 25.30533 147.39189
6 32.1 5.09987 1030.41000 26.00867 163.70583
7 15.8 4.64439 249.64000 21.57036 73.38136
8 16.7 4.68213 278.89000 21.92234 78.19157
9 26.7 4.97673 712.89000 24.76784 132.87869
10 19.5 4.75359 380.25000 22.59662 92.69501
11 33.6 5.11199 1128.96000 26.13244 171.76286
12 36.1 5.20949 1303.21000 27.13879 188.06259
13 16.8 4.69135 282.24000 22.00876 78.81468
14 17.7 4.7185 313.29000 22.26424 83.51745
15 20.4 4.82028 416.16000 23.23510 98.33371
16 21.7 4.82831 470.89000 23.31258 104.77433
17 27.4 4.98361 750.76000 24.83637 136.55091
18 27.4 4.98361 750.76000 24.83637 136.55091
19 22.6 4.86753 510.76000 23.69285 110.00618
20 23.4 4.8752 547.56000 23.76758 114.07968
476.80000 97.69215 12016.74000 477.65016 2346.23556

Regression Coefficients
B = 0.02655
A = 4.25159

Regression Equation

ŷ = 70.21702e0.02655x

Coefficient of Correlation
r = 0.99546
 Table 3. 24: Power Model for Piezoelectric Generator with 30 N Force input

Power
Voltage (V) Current (µA)
Trial (log x)^2 (log y)^2 logxlogy
(log x) (log y)
1 1.29447 2.07555 1.67565 4.30791 2.68674
2 1.30535 2.08636 1.70394 4.35290 2.72343
3 1.38739 2.12385 1.92485 4.51074 2.94661
4 1.40312 2.14613 1.96875 4.60587 3.01128
5 1.46687 2.18469 2.15171 4.77287 3.20466
6 1.50651 2.21484 2.26957 4.90552 3.33668
7 1.19866 2.01703 1.43679 4.06841 2.41773
8 1.22272 2.03342 1.49504 4.13480 2.48630
9 1.42651 2.16137 2.03493 4.67152 3.08322
10 1.29003 2.06446 1.66418 4.26200 2.66322
11 1.52634 2.22011 2.32971 4.92889 3.38864
12 1.55751 2.26245 2.42584 5.11868 3.52379
13 1.22531 2.03743 1.50138 4.15112 2.49648
14 1.24797 2.04922 1.55743 4.19930 2.55737
15 1.30963 2.09342 1.71513 4.38241 2.74161
16 1.33646 2.09691 1.78613 4.39703 2.80244
17 1.43775 2.16435 2.06713 4.68441 3.11179
18 1.43775 2.16435 2.06713 4.68441 3.11179
19 1.35411 2.11394 1.83361 4.46874 2.86251
20 1.36922 2.11727 1.87476 4.48283 2.89901
27.30368 42.42715 37.48365 90.09035 58.05528

Regression Coefficients
B = 0.64281
A = 1.24381

Regression Equation

ŷ = 17.53113x0.64281

Coefficient of Correlation
r = 0.99541
 Table 3. 25: Hyperbolic Model for Piezoelectric Generator with 30 N Force input

Hyperbolic
Voltage (V) Current (µA)
Trial (1/x)^2 (1/y)^2 (1/x)(1/y)
(1/x) (1/y)
1 0.05076 0.0084 0.00258 0.00007 0.00043
2 0.0495 0.0082 0.00245 0.00007 0.00041
3 0.04098 0.00752 0.00168 0.00006 0.00031
4 0.03953 0.00714 0.00156 0.00005 0.00028
5 0.03413 0.00654 0.00116 0.00004 0.00022
6 0.03115 0.0061 0.00097 0.00004 0.00019
7 0.06329 0.00962 0.00401 0.00009 0.00061
8 0.05988 0.00926 0.00359 0.00009 0.00055
9 0.03745 0.0069 0.00140 0.00005 0.00026
10 0.05128 0.00862 0.00263 0.00007 0.00044
11 0.02976 0.00602 0.00089 0.00004 0.00018
12 0.0277 0.00546 0.00077 0.00003 0.00015
13 0.05952 0.00917 0.00354 0.00008 0.00055
14 0.0565 0.00893 0.00319 0.00008 0.00050
15 0.04902 0.00806 0.00240 0.00006 0.00040
16 0.04608 0.008 0.00212 0.00006 0.00037
17 0.0365 0.00685 0.00133 0.00005 0.00025
18 0.0365 0.00685 0.00133 0.00005 0.00025
19 0.04425 0.00769 0.00196 0.00006 0.00034
20 0.04274 0.00763 0.00183 0.00006 0.00033
0.88652 0.15296 0.04139 0.00120 0.00701

Regression Coefficients
B = 0.11004
A = 0.00277

Regression Equation

𝒙
ŷ = 360.94141 𝟑𝟗.𝟕𝟏𝟔𝟔𝟒+𝒙

Coefficient of Correlation
r = 0.99292
 Table 3. 26: Summary of Mathematical Models for Piezoelectric Generator with 30 N

Force input

Mathematical Models
Regression and
Correlation Linear Exponential Power Hyperbolic
Parameters
B 3.64937 0.02655 0.64281 0.11004
A 46.79912 4.25159 1.24381 0.00277
Regression
ŷ = 46.79912 + 3.64937x ŷ = 70.21702e 0.02655x ŷ = 17.53113x0.64281 ŷ = 360.94141
Equation
r 0.99650 0.99546 0.99541 0.99294

The linear model has a correlation coefficient of 0.99650 which is the nearest

absolute value to 1 among the other mathematical models, thus, it is considered to be the

best-fit curve for the system of data.

Best Fit Curve:

200
180
160
140
Current (µA)

120
100
80
60
40
20
0
0 5 10 15 20 25 30 35 40
Voltage (V)

Figure 3. 30: Best fit Curve Piezoelectric Generator with 30 N Force input
Piezoelectric Generator (Walking)

 STATISTICAL MEASURES

Table 3. 27: Statistical Measures for Piezoelectric Generator (Walking)

Statistical
Voltage Current
Measures
Mean 31.80000 47.15000
Median 33.00000 42.50000
Mode 19.00000 30.00000
Standard
10.20114 18.44558
Deviation
Variance 104.06316 340.23947
Coefficient of
0.32079 0.39121
Variation
  REGRESSION AND CORRELATION

Table 3. 28: Linear Model for Piezoelectric Generator (Walking)

Linear
Voltage (V) Current (µA)
Trial x^2 y^2 xy
(x) (y)
1 19 30 361.00000 900.00000 570.00000
2 21 32 441.00000 1024.00000 672.00000
3 39 56 1521.00000 3136.00000 2184.00000
4 41 62 1681.00000 3844.00000 2542.00000
5 29 39 841.00000 1521.00000 1131.00000
6 30 39 900.00000 1521.00000 1170.00000
7 47 85 2209.00000 7225.00000 3995.00000
8 51 88 2601.00000 7744.00000 4488.00000
9 45 74 2025.00000 5476.00000 3330.00000
10 23 32 529.00000 1024.00000 736.00000
11 29 38 841.00000 1444.00000 1102.00000
12 35 50 1225.00000 2500.00000 1750.00000
13 19 30 361.00000 900.00000 570.00000
14 35 52 1225.00000 2704.00000 1820.00000
15 39 55 1521.00000 3025.00000 2145.00000
16 33 42 1089.00000 1764.00000 1386.00000
17 33 43 1089.00000 1849.00000 1419.00000
18 34 45 1156.00000 2025.00000 1530.00000
19 15 25 225.00000 625.00000 375.00000
20 19 26 361.00000 676.00000 494.00000
636.00000 943.00000 22202.00000 50927.00000 33409.00000

Regression Coefficients
B = 1.73053
A = -7.88079

Regression Equation

ŷ = -7.88079 + 1.73053x

Coefficient of Correlation
r = 0.95705
 Table 3. 29: Exponential Model for Piezoelectric Generator (Walking)

Exponential
Voltage (V) Current (µA)
Trial x^2 (ln y)^2 xlny
(x) (ln y)
1 19 3.4012 361.00000 11.56816 64.62280
2 21 3.46574 441.00000 12.01135 72.78054
3 39 4.02535 1521.00000 16.20344 156.98865
4 41 4.12713 1681.00000 17.03320 169.21233
5 29 3.66356 841.00000 13.42167 106.24324
6 30 3.66356 900.00000 13.42167 109.90680
7 47 4.44265 2209.00000 19.73714 208.80455
8 51 4.47734 2601.00000 20.04657 228.34434
9 45 4.30407 2025.00000 18.52502 193.68315
10 23 3.46574 529.00000 12.01135 79.71202
11 29 3.63759 841.00000 13.23206 105.49011
12 35 3.91202 1225.00000 15.30390 136.92070
13 19 3.4012 361.00000 11.56816 64.62280
14 35 3.95124 1225.00000 15.61230 138.29340
15 39 4.00733 1521.00000 16.05869 156.28587
16 33 3.73767 1089.00000 13.97018 123.34311
17 33 3.7612 1089.00000 14.14663 124.11960
18 34 3.80666 1156.00000 14.49066 129.42644
19 15 3.21888 225.00000 10.36119 48.28320
20 19 3.2581 361.00000 10.61522 61.90390
636.00000 75.72823 22202.00000 289.33857 2478.98755

Regression Coefficients
B = 0.03582
A = 2.64723

Regression Equation

ŷ = 14.11489e0.03582x

Coefficient of Correlation
r = 0.98782
 Table 3. 30: Power Model for Piezoelectric Generator (Walking)

Power
Voltage (V) Current (µA)
Trial (log x)^2 (log y)^2 logxlogy
(log x) (log y)
1 1.27875 1.47712 1.63520 2.18188 1.88887
2 1.32222 1.50515 1.74827 2.26548 1.99014
3 1.59106 1.74819 2.53147 3.05617 2.78148
4 1.61278 1.79239 2.60106 3.21266 2.89073
5 1.4624 1.59106 2.13861 2.53147 2.32677
6 1.47712 1.59106 2.18188 2.53147 2.35019
7 1.6721 1.92942 2.79592 3.72266 3.22618
8 1.70757 1.94448 2.91580 3.78100 3.32034
9 1.65321 1.86923 2.73310 3.49402 3.09023
10 1.36173 1.50515 1.85431 2.26548 2.04961
11 1.4624 1.57978 2.13861 2.49570 2.31027
12 1.54407 1.69897 2.38415 2.88650 2.62333
13 1.27875 1.47712 1.63520 2.18188 1.88887
14 1.54407 1.716 2.38415 2.94466 2.64962
15 1.59106 1.74036 2.53147 3.02885 2.76902
16 1.51851 1.62325 2.30587 2.63494 2.46492
17 1.51851 1.63347 2.30587 2.66822 2.48044
18 1.53148 1.65321 2.34543 2.73310 2.53186
19 1.17609 1.39794 1.38319 1.95424 1.64410
20 1.27875 1.41497 1.63520 2.00214 1.80939
29.58263 32.88832 44.18478 54.57254 49.08635

Regression Coefficients
B = 1.02806
A = 0.12377

Regression Equation

ŷ = 1.32976x1.02806

Coefficient of Correlation
r = 0.96058
 Table 3. 31: Hyperbolic Model for Piezoelectric Generator (Walking)

Hyperbolic
Voltage (V) Current (µA)
Trial (1/x)^2 (1/y)^2 (1/x)(1/y)
(1/x) (1/y)
1 0.05263 0.03333 0.00277 0.00111 0.00175
2 0.04762 0.03125 0.00227 0.00098 0.00149
3 0.02564 0.01786 0.00066 0.00032 0.00046
4 0.02439 0.01613 0.00059 0.00026 0.00039
5 0.03448 0.02564 0.00119 0.00066 0.00088
6 0.03333 0.02564 0.00111 0.00066 0.00085
7 0.02128 0.01176 0.00045 0.00014 0.00025
8 0.01961 0.01136 0.00038 0.00013 0.00022
9 0.02222 0.01351 0.00049 0.00018 0.00030
10 0.04348 0.03125 0.00189 0.00098 0.00136
11 0.03448 0.02632 0.00119 0.00069 0.00091
12 0.02857 0.02 0.00082 0.00040 0.00057
13 0.05263 0.03333 0.00277 0.00111 0.00175
14 0.02857 0.01923 0.00082 0.00037 0.00055
15 0.02564 0.01818 0.00066 0.00033 0.00047
16 0.0303 0.02381 0.00092 0.00057 0.00072
17 0.0303 0.02326 0.00092 0.00054 0.00070
18 0.02941 0.02222 0.00086 0.00049 0.00065
19 0.06667 0.04 0.00444 0.00160 0.00267
20 0.05263 0.03846 0.00277 0.00148 0.00202
0.70388 0.48254 0.02798 0.01299 0.01898

Regression Coefficients
B = 0.62462
A = 0.00214

Regression Equation

𝒙
ŷ = 466.41657
𝟐𝟗𝟏.𝟑𝟑𝟒𝟔𝟖+𝒙

Coefficient of Correlation
r = 0.96206
 Table 3. 32: Summary of Mathematical Models for Piezoelectric Generator (Walking )

Mathematical Models
Regression and
Correlation Linear Exponential Power Hyperbolic
Parameters
B 1.73053 0.03582 1.02806 0.62462
A -7.88079 2.64723 0.12377 0.00214
Regression
ŷ = -7.88079 + 1.73053x ŷ = 14.11489e 0.03582x ŷ = 1.32976x1.02806 ŷ = 466.41657
Equation
r 0.95705 0.98782 0.96058 0.96206

The exponential model has a correlation coefficient of 0.98782 which is the nearest

absolute value to 1 among the other mathematical models, then it is considered to be the best-

fit curve for the system of data.

Best Fit Curve:

5
4.5
4
3.5
Current (µA)

3
2.5
2
1.5
1
0.5
0
0 10 20 30 40 50 60
Voltage (V)

Figure 3. 31: Best Fit Curve for Piezoelectric Generator (Walking)

Piezoelectric Generator (Running)

 STATISTICAL MEASURES

Table 3. 33: Statistical Measures for Piezoelectric Generator (Running)

Statistical
Voltage Current
Measures
Mean 57.94000 93.25000
Median 57.30000 93.50000
Mode 44.40000 85.00000
Standard
11.07935 10.99701
Deviation
Variance 122.75200 120.93421
Coefficient of
0.19122 0.11793
Variation
  REGRESSION AND CORRELATION

Table 3. 34: Linear Model for Piezoelectric Generator (Running)

Linear
Voltage (V) Current (µA)
Trial x^2 y^2 xy
(x) (y)
1 67.7 105 4583.29000 11025.00000 7108.50000
2 71 106 5041.00000 11236.00000 7526.00000
3 58.6 95 3433.96000 9025.00000 5567.00000
4 59 99 3481.00000 9801.00000 5841.00000
5 56.8 93 3226.24000 8649.00000 5282.40000
6 57.8 94 3340.84000 8836.00000 5433.20000
7 64 102 4096.00000 10404.00000 6528.00000
8 65.7 103 4316.49000 10609.00000 6767.10000
9 54.7 85 2992.09000 7225.00000 4649.50000
10 55.5 87 3080.25000 7569.00000 4828.50000
11 41.3 77 1705.69000 5929.00000 3180.10000
12 43.4 79 1883.56000 6241.00000 3428.60000
13 77.2 107 5959.84000 11449.00000 8260.40000
14 81.1 114 6577.21000 12996.00000 9245.40000
15 55.8 90 3113.64000 8100.00000 5022.00000
16 44.4 80 1971.36000 6400.00000 3552.00000
17 53.3 85 2840.89000 7225.00000 4530.50000
18 61.4 101 3769.96000 10201.00000 6201.40000
19 44.4 80 1971.36000 6400.00000 3552.00000
20 45.7 83 2088.49000 6889.00000 3793.10000
1158.80000 1865.00000 69473.16000 176209.00000 110296.70000

Regression Coefficients
B = 0.95983
A = 37.63745

Regression Equation

ŷ = 37.63745 + 0.95983x

Coefficient of Correlation
r = 0.96702
 Table 3. 35: Exponential Model for Piezoelectric Generator (Running)

Exponential
Voltage (V) Current (µA)
Trial x^2 (ln y)^2 xlny
(x) (ln y)
1 67.7 4.65396 4583.29000 21.65934 315.07309
2 71 4.66344 5041.00000 21.74767 331.10424
3 58.6 4.55388 3433.96000 20.73782 266.85737
4 59 4.59512 3481.00000 21.11513 271.11208
5 56.8 4.5326 3226.24000 20.54446 257.45168
6 57.8 4.54329 3340.84000 20.64148 262.60216
7 64 4.62497 4096.00000 21.39035 295.99808
8 65.7 4.63473 4316.49000 21.48072 304.50176
9 54.7 4.44265 2992.09000 19.73714 243.01296
10 55.5 4.46591 3080.25000 19.94435 247.85801
11 41.3 4.34381 1705.69000 18.86869 179.39935
12 43.4 4.36945 1883.56000 19.09209 189.63413
13 77.2 4.67283 5959.84000 21.83534 360.74248
14 81.1 4.7362 6577.21000 22.43159 384.10582
15 55.8 4.49981 3113.64000 20.24829 251.08940
16 44.4 4.38203 1971.36000 19.20219 194.56213
17 53.3 4.44265 2840.89000 19.73714 236.79325
18 61.4 4.61512 3769.96000 21.29933 283.36837
19 44.4 4.38203 1971.36000 19.20219 194.56213
20 45.7 4.41884 2088.49000 19.52615 201.94099
1158.80000 90.57332 69473.16000 410.44147 5271.76947

Regression Coefficients
B = 0.01027
A = 3.93365

Regression Equation

ŷ = 51.09335e0.01027x

Coefficient of Correlation
r = 0.96314
 Table 3. 36: Power Model for Piezoelectric Generator (Running)

Power
Voltage (V) Current (µA)
Trial (log x)^2 (log y)^2 logxlogy
(log x) (log y)
1 1.83059 2.02119 3.35106 4.08521 3.69997
2 1.85126 2.02531 3.42716 4.10188 3.74938
3 1.7679 1.97772 3.12547 3.91138 3.49641
4 1.77085 1.99564 3.13591 3.98258 3.53398
5 1.75435 1.96848 3.07774 3.87491 3.45340
6 1.76193 1.97313 3.10440 3.89324 3.47652
7 1.80618 2.0086 3.26229 4.03447 3.62789
8 1.81757 2.01284 3.30356 4.05152 3.65848
9 1.73799 1.92942 3.02061 3.72266 3.35331
10 1.74429 1.93952 3.04255 3.76174 3.38309
11 1.61595 1.88649 2.61129 3.55884 3.04847
12 1.63749 1.89763 2.68137 3.60100 3.10735
13 1.88762 2.02938 3.56311 4.11838 3.83070
14 1.90902 2.0569 3.64436 4.23084 3.92666
15 1.74663 1.95424 3.05072 3.81905 3.41333
16 1.64738 1.90309 2.71386 3.62175 3.13511
17 1.72673 1.92942 2.98160 3.72266 3.33159
18 1.78817 2.00432 3.19755 4.01730 3.58406
19 1.64738 1.90309 2.71386 3.62175 3.13511
20 1.65992 1.91908 2.75533 3.68287 3.18552
35.10920 39.33549 61.76380 77.41405 69.13034

Regression Coefficients
B = 0.59890
A = 0.91542

Regression Equation

ŷ = 8.23045x0.59890

Coefficient of Correlation
r = 0.96934
 Table 3. 37: Hyperbolic Model for Piezoelectric Generator (Running)

Hyperbolic
Voltage (V) Current (µA)
Trial (1/x)^2 (1/y)^2 (1/x)(1/y)
(1/x) (1/y)
1 0.01477 0.00952 0.00022 0.00009 0.00014
2 0.01408 0.00943 0.00020 0.00009 0.00013
3 0.01706 0.01053 0.00029 0.00011 0.00018
4 0.01695 0.0101 0.00029 0.00010 0.00017
5 0.01761 0.01075 0.00031 0.00012 0.00019
6 0.0173 0.01064 0.00030 0.00011 0.00018
7 0.01563 0.0098 0.00024 0.00010 0.00015
8 0.01522 0.00971 0.00023 0.00009 0.00015
9 0.01828 0.01176 0.00033 0.00014 0.00021
10 0.01802 0.01149 0.00032 0.00013 0.00021
11 0.02421 0.01299 0.00059 0.00017 0.00031
12 0.02304 0.01266 0.00053 0.00016 0.00029
13 0.01295 0.00935 0.00017 0.00009 0.00012
14 0.01233 0.00877 0.00015 0.00008 0.00011
15 0.01792 0.01111 0.00032 0.00012 0.00020
16 0.02252 0.0125 0.00051 0.00016 0.00028
17 0.01876 0.01176 0.00035 0.00014 0.00022
18 0.01629 0.0099 0.00027 0.00010 0.00016
19 0.02252 0.0125 0.00051 0.00016 0.00028
20 0.02188 0.01205 0.00048 0.00015 0.00026
0.35734 0.21732 0.00661 0.00239 0.00396

Regression Coefficients
B = 0.36287
A = 0.00438

Regression Equation

𝒙
ŷ = 228.17378𝟖𝟐.𝟕𝟗𝟕𝟏𝟑+𝒙

Coefficient of Correlation
r = 0.96827
 Table 3. 38: Summary of Mathematical Models for Piezoelectric Generator (Running)

Mathematical Models
Regression and
Correlation Linear Exponential Power Hyperbolic
Parameters
B 0.95983 0.01027 0.59890 0.36287
A 37.63745 3.93365 0.91542 0.00438
Regression
ŷ = 37.63745 + 0.95983x ŷ = 51.09335e 0.01027x ŷ = 8.23045x0.59890 ŷ = 228.17378
Equation
r 0.96702 0.96314 0.96934 0.96827

Since the correlation coefficient of the power mathematical model is 0.96934 which

is the nearest absolute value to 1 among the other mathematical models, thus, it is considered

to be the best-fit curve for the system of data.

Best Fit Curve:

2.08
2.06
2.04
2.02
2
Current (µA)

1.98
1.96
1.94
1.92
1.9
1.88
1.86
1.6 1.65 1.7 1.75 1.8 1.85 1.9 1.95
Voltage (V)

Figure 3. 32: Best Fit Curve for Piezoelectric Generator (Running)

Hybrid Generator with 10 N Force input

 STATISTICAL MEASURES

Table 3. 39: Statistical Measures for Hybrid Generator with 10 N Force input

Statistical
Voltage Current
Measures
Mean 15.67000 67.35000
Median 14.70000 66.00000
Mode - 62.00000
Standard
3.63522 14.74083
Deviation
Variance 13.21484 217.29211
Coefficient of
0.23199 0.21887
Variation
  REGRESSION AND CORRELATION

Table 3. 40: Linear Model for Hybrid Generator with 10 N Force input

Linear
Voltage (V) Current (µA)
Trial x^2 y^2 xy
(x) (y)
1 14.3 67 204.49000 4489.00000 958.10000
2 15.1 62 228.01000 3844.00000 936.20000
3 13.6 62 184.96000 3844.00000 843.20000
4 16.7 65 278.89000 4225.00000 1085.50000
5 18.3 87 334.89000 7569.00000 1592.10000
6 20.7 44 428.49000 1936.00000 910.80000
7 13.8 75 190.44000 5625.00000 1035.00000
8 13.9 85 193.21000 7225.00000 1181.50000
9 10.4 72 108.16000 5184.00000 748.80000
10 11.6 50 134.56000 2500.00000 580.00000
11 15.8 50 249.64000 2500.00000 790.00000
12 16 63 256.00000 3969.00000 1008.00000
13 22.4 77 501.76000 5929.00000 1724.80000
14 11.9 64 141.61000 4096.00000 761.60000
15 19.1 55 364.81000 3025.00000 1050.50000
16 13.2 81 174.24000 6561.00000 1069.20000
17 11.7 98 136.89000 9604.00000 1146.60000
18 22.6 42 510.76000 1764.00000 949.20000
19 13.1 76 171.61000 5776.00000 995.60000
20 19.2 72 368.64000 5184.00000 1382.40000
313.40000 1347.00000 5162.06000 94849.00000 20749.10000

Regression Coefficients
B = -1.42738
A = 89.71708

Regression Equation

ŷ = 89.71708 – 1.42738x

Coefficient of Correlation
r = -0.35201
 Table 3. 41: Exponential Model for Hybrid Generator with 10 N Force input

Exponential
Voltage (V) Current (µA)
Trial x^2 (ln y)^2 xlny
(x) (ln y)
1 14.3 4.20469 204.49000 17.67942 60.12707
2 15.1 4.12713 228.01000 17.03320 62.31966
3 13.6 4.12713 184.96000 17.03320 56.12897
4 16.7 4.17439 278.89000 17.42553 69.71231
5 18.3 4.46591 334.89000 19.94435 81.72615
6 20.7 3.78419 428.49000 14.32009 78.33273
7 13.8 4.31749 190.44000 18.64072 59.58136
8 13.9 4.44265 193.21000 19.73714 61.75284
9 10.4 4.27667 108.16000 18.28991 44.47737
10 11.6 3.91202 134.56000 15.30390 45.37943
11 15.8 3.91202 249.64000 15.30390 61.80992
12 16 4.14313 256.00000 17.16553 66.29008
13 22.4 4.34381 501.76000 18.86869 97.30134
14 11.9 4.15888 141.61000 17.29628 49.49067
15 19.1 4.00733 364.81000 16.05869 76.54000
16 13.2 4.39445 174.24000 19.31119 58.00674
17 11.7 4.58497 136.89000 21.02195 53.64415
18 22.6 3.73767 510.76000 13.97018 84.47134
19 13.1 4.33073 171.61000 18.75522 56.73256
20 19.2 4.27667 368.64000 18.28991 82.11206
313.40000 83.72193 5162.06000 351.44900 1305.93677

Regression Coefficients
B = -0.02384
A = 4.55967

Regression Equation

ŷ = 95.55236e-0.02384x

Coefficient of Correlation
r = -0.38142
 Table 3. 42: Power Model for Hybrid Generator with 10 N Force input

Power
Voltage (V) Current (µA)
Trial (log x)^2 (log y)^2 logxlogy
(log x) (log y)
1 1.15534 1.82607 1.33481 3.33453 2.10973
2 1.17898 1.79239 1.38999 3.21266 2.11319
3 1.13354 1.79239 1.28491 3.21266 2.03175
4 1.22272 1.81291 1.49504 3.28664 2.21668
5 1.26245 1.93952 1.59378 3.76174 2.44855
6 1.31597 1.64345 1.73178 2.70093 2.16273
7 1.13988 1.87506 1.29933 3.51585 2.13734
8 1.14301 1.92942 1.30647 3.72266 2.20535
9 1.01703 1.85733 1.03435 3.44967 1.88896
10 1.06446 1.69897 1.13308 2.88650 1.80849
11 1.19866 1.69897 1.43679 2.88650 2.03649
12 1.20412 1.79934 1.44990 3.23762 2.16662
13 1.35025 1.88649 1.82318 3.55884 2.54723
14 1.07555 1.80618 1.15681 3.26229 1.94264
15 1.28103 1.74036 1.64104 3.02885 2.22945
16 1.12057 1.90849 1.25568 3.64233 2.13860
17 1.06819 1.99123 1.14103 3.96500 2.12701
18 1.35411 1.62325 1.83361 2.63494 2.19806
19 1.11727 1.88081 1.24829 3.53745 2.10137
20 1.2833 1.85733 1.64686 3.44967 2.38351
23.68643 36.35996 28.23673 66.28735 42.99375

Regression Coefficients
B = -0.36954
A = 2.25565

Regression Equation

ŷ = 180.15578x-0.36954

Coefficient of Correlation
r = -0.36890
 Table 3. 43: Hyperbolic Model for Hybrid Generator with 10 N Force input

Hyperbolic
Voltage (V) Current (µA)
Trial (1/x)^2 (1/y)^2 (1/x)(1/y)
(1/x) (1/y)
1 0.06993 0.01493 0.00489 0.00022 0.00104
2 0.06623 0.01613 0.00439 0.00026 0.00107
3 0.07353 0.01613 0.00541 0.00026 0.00119
4 0.05988 0.01538 0.00359 0.00024 0.00092
5 0.05464 0.01149 0.00299 0.00013 0.00063
6 0.04831 0.02273 0.00233 0.00052 0.00110
7 0.07246 0.01333 0.00525 0.00018 0.00097
8 0.07194 0.01176 0.00518 0.00014 0.00085
9 0.09615 0.01389 0.00924 0.00019 0.00134
10 0.08621 0.02 0.00743 0.00040 0.00172
11 0.06329 0.02 0.00401 0.00040 0.00127
12 0.0625 0.01587 0.00391 0.00025 0.00099
13 0.04464 0.01299 0.00199 0.00017 0.00058
14 0.08403 0.01563 0.00706 0.00024 0.00131
15 0.05236 0.01818 0.00274 0.00033 0.00095
16 0.07576 0.01235 0.00574 0.00015 0.00094
17 0.08547 0.0102 0.00731 0.00010 0.00087
18 0.04425 0.02381 0.00196 0.00057 0.00105
19 0.07634 0.01316 0.00583 0.00017 0.00100
20 0.05208 0.01389 0.00271 0.00019 0.00072
1.34000 0.31185 0.09394 0.00512 0.02051

Regression Coefficients
B = -0.09257
A = 0.02179

Regression Equation

𝒙
ŷ = 45.88302 𝒙−𝟒.𝟐𝟒𝟕𝟑𝟎

Coefficient of Correlation
r = -0.37041
 Table 3. 44: Summary of Mathematical Models for Hybrid Generator with 10 N Force input

Mathematical Models
Regression and
Correlation Linear Exponential Power Hyperbolic
Parameters
B -1.42738 -0.02384 -0.36954 -0.09257
A 89.71708 4.55967 2.25565 0.02179
Regression
ŷ = 46.79912 + 3.64937x ŷ = 95.55236e -0.02384x ŷ = 180.15578x-0.36954 ŷ = 45.88302
Equation
r -0.35201 -0.38142 -0.36890 -0.37041

Since the correlation coefficient of the exponential model (r = -0.38142) is the nearest

absolute value to 1 among the other mathematical models, thus, it is considered to be the

best-fit curve for the system of data.

Best Fit Curve:

5
4.5
4
3.5
Current (µA)

3
2.5
2
1.5
1
0.5
0
0 5 10 15 20 25
Voltage (V)

Figure 3. 33: Best Fit Curve for Hybrid Generator with 10 N Force input
Hybrid Generator with 20 N Force input

 STATISTICAL MEASURES

Table 3. 45: Statistical Measures for Hybrid Generator with 20 N Force input

Statistical
Voltage Current
Measures
Mean 20.96000 106.10000
Median 21.90000 103.00000
Mode - 108.00000
Standard
3.90740 15.90730
Deviation
Variance 15.26779 253.04211
Coefficient of
0.18642 0.14993
Variation
  REGRESSION AND CORRELATION

Table 3. 46: Linear Model for Hybrid Generator with 20 N Force input

Linear
Voltage (V) Current (µA)
Trial x^2 y^2 xy
(x) (y)
1 22.4 106 501.76000 11236.00000 2374.40000
2 23.4 108 547.56000 11664.00000 2527.20000
3 16.9 91 285.61000 8281.00000 1537.90000
4 17.1 92 292.41000 8464.00000 1573.20000
5 25.8 134 665.64000 17956.00000 3457.20000
6 27.5 145 756.25000 21025.00000 3987.50000
7 14.1 89 198.81000 7921.00000 1254.90000
8 15.8 89 249.64000 7921.00000 1406.20000
9 16.2 90 262.44000 8100.00000 1458.00000
10 18.7 98 349.69000 9604.00000 1832.60000
11 21.6 101 466.56000 10201.00000 2181.60000
12 22.2 105 492.84000 11025.00000 2331.00000
13 24.6 125 605.16000 15625.00000 3075.00000
14 25.1 126 630.01000 15876.00000 3162.60000
15 19.3 99 372.49000 9801.00000 1910.70000
16 20.3 101 412.09000 10201.00000 2050.30000
17 23.6 108 556.96000 11664.00000 2548.80000
18 16.4 91 268.96000 8281.00000 1492.40000
19 24 109 576.00000 11881.00000 2616.00000
20 24.2 115 585.64000 13225.00000 2783.00000
419.20000 2122.00000 9076.52000 229952.00000 45560.50000

Regression Coefficients
B = 3.73466
A = 27.82153

Regression Equation

ŷ = 27.82153 + 3.73466x

Coefficient of Correlation
0.91737
r=
 Table 3. 47: Exponential Model for Hybrid Generator with 20 N Force input

Exponential
Voltage (V) Current (µA)
Trial x^2 (ln y)^2 xlny
(x) (ln y)
1 22.4 4.66344 501.76000 21.74767 104.46106
2 23.4 4.68213 547.56000 21.92234 109.56184
3 16.9 4.51086 285.61000 20.34786 76.23353
4 17.1 4.52179 292.41000 20.44658 77.32261
5 25.8 4.89784 665.64000 23.98884 126.36427
6 27.5 4.97673 756.25000 24.76784 136.86008
7 14.1 4.48864 198.81000 20.14789 63.28982
8 15.8 4.48864 249.64000 20.14789 70.92051
9 16.2 4.49981 262.44000 20.24829 72.89692
10 18.7 4.58497 349.69000 21.02195 85.73894
11 21.6 4.61512 466.56000 21.29933 99.68659
12 22.2 4.65396 492.84000 21.65934 103.31791
13 24.6 4.82831 605.16000 23.31258 118.77643
14 25.1 4.83628 630.01000 23.38960 121.39063
15 19.3 4.59512 372.49000 21.11513 88.68582
16 20.3 4.61512 412.09000 21.29933 93.68694
17 23.6 4.68213 556.96000 21.92234 110.49827
18 16.4 4.51086 268.96000 20.34786 73.97810
19 24 4.69135 576.00000 22.00876 112.59240
20 24.2 4.74493 585.64000 22.51436 114.82731
419.20000 93.08803 9076.52000 433.65580 1961.08997

Regression Coefficients
B = 0.03435
A = 3.93440

Regression Equation

ŷ = 51.13150e0.03435x

Coefficient of Correlation
r = 0.94081
 Table 3. 48: Power Model for Hybrid Generator with 20 N Force input

Power
Voltage (V) Current (µA)
Trial (log x)^2 (log y)^2 logxlogy
(log x) (log y)
1 1.35025 2.02531 1.82318 4.10188 2.73467
2 1.36922 2.03342 1.87476 4.13480 2.78420
3 1.22789 1.95904 1.50771 3.83784 2.40549
4 1.233 1.96379 1.52029 3.85647 2.42135
5 1.41162 2.1271 1.99267 4.52455 3.00266
6 1.43933 2.16137 2.07167 4.67152 3.11092
7 1.14922 1.94939 1.32071 3.80012 2.24028
8 1.19866 1.94939 1.43679 3.80012 2.33666
9 1.20952 1.95424 1.46294 3.81905 2.36369
10 1.27184 1.99123 1.61758 3.96500 2.53253
11 1.33445 2.00432 1.78076 4.01730 2.67466
12 1.34635 2.02119 1.81266 4.08521 2.72123
13 1.39094 2.09691 1.93471 4.39703 2.91668
14 1.39967 2.10037 1.95908 4.41155 2.93982
15 1.28556 1.99564 1.65266 3.98258 2.56551
16 1.3075 2.00432 1.70956 4.01730 2.62065
17 1.37291 2.03342 1.88488 4.13480 2.79170
18 1.21484 1.95904 1.47584 3.83784 2.37992
19 1.38021 2.03743 1.90498 4.15112 2.81208
20 1.38382 2.0607 1.91496 4.24648 2.85164
26.27680 40.42762 34.65837 81.79257 53.20635

Regression Coefficients
B = 0.67419
A = 1.13560

Regression Equation

ŷ = 13.66483x0.67419

Coefficient of Correlation
r = 0.91672
 Table 3. 49: Hyperbolic Model for Hybrid Generator with 20 N Force input

Hyperbolic
Voltage (V) Current (µA)
Trial (1/x)^2 (1/y)^2 (1/x)(1/y)
(1/x) (1/y)
1 0.04464 0.00943 0.00199 0.00009 0.00042
2 0.04274 0.00926 0.00183 0.00009 0.00040
3 0.05917 0.01099 0.00350 0.00012 0.00065
4 0.05848 0.01087 0.00342 0.00012 0.00064
5 0.03876 0.00746 0.00150 0.00006 0.00029
6 0.03636 0.0069 0.00132 0.00005 0.00025
7 0.07092 0.01124 0.00503 0.00013 0.00080
8 0.06329 0.01124 0.00401 0.00013 0.00071
9 0.06173 0.01111 0.00381 0.00012 0.00069
10 0.05348 0.0102 0.00286 0.00010 0.00055
11 0.0463 0.0099 0.00214 0.00010 0.00046
12 0.04505 0.00952 0.00203 0.00009 0.00043
13 0.04065 0.008 0.00165 0.00006 0.00033
14 0.03984 0.00794 0.00159 0.00006 0.00032
15 0.05181 0.0101 0.00268 0.00010 0.00052
16 0.04926 0.0099 0.00243 0.00010 0.00049
17 0.04237 0.00926 0.00180 0.00009 0.00039
18 0.06098 0.01099 0.00372 0.00012 0.00067
19 0.04167 0.00917 0.00174 0.00008 0.00038
20 0.04132 0.0087 0.00171 0.00008 0.00036
0.98882 0.19218 0.05075 0.00188 0.00973

Regression Coefficients
B = 0.12063
A = 0.00364

Regression Equation

𝒙
ŷ = 274.36687 𝟑𝟑.𝟎𝟗𝟕𝟖𝟔+𝒙

Coefficient of Correlation
r = 0.91533
 Table 3. 50: Summary of Mathematical Models for Hybrid Generator with 20 N Force input

Mathematical Models
Regression and
Correlation Linear Exponential Power Hyperbolic
Parameters
B 3.73466 0.03435 0.67419 0.12063
A 27.82153 3.93440 1.13560 0.00364
Regression
ŷ = 27.82153 + 3.73466x ŷ = 51.13150e 0.03435x ŷ = 13.66483x0.67419 ŷ = 274.36687
Equation
r 0.91737 0.94081 0.91672 0.91533

The exponential model has a correlation coefficient of 0.94081which is the nearest

absolute value to 1 among the other mathematical models, thus, it is considered to be the

best-fit curve for the system of data.

Best Fit Curve:

5.1

4.9

4.8
Current (µA)

4.7

4.6

4.5

4.4

4.3
0 5 10 15 20 25 30
Voltage (V)

Figure 3. 34: Best Fit Curve for Hybrid Generator with 20 N Force input
Hybrid Generator with 30 N Force input

 STATISTICAL MEASURES

Table 3. 51: Statistical Measures for Hybrid Generator with 30 N Force input

Statistical
Voltage Current
Measures
Mean 26.24500 135.75000
Median 25.80000 133.00000
Mode - -
Standard
4.97557 21.07849
Deviation
Variance 24.75629 444.30263
Coefficient of
0.18958 0.15527
Variation
  REGRESSION AND CORRELATION

Table 3. 52: Linear Model for Hybrid Generator with 30 N Force input

Linear
Voltage (V) Current (µA)
Trial x^2 y^2 xy
(x) (y)
1 29.5 149 870.25000 22201.00000 4395.50000
2 31.9 152 1017.61000 23104.00000 4848.80000
3 22.7 120 515.29000 14400.00000 2724.00000
4 23.1 124 533.61000 15376.00000 2864.40000
5 19.6 110 384.16000 12100.00000 2156.00000
6 27.3 141 745.29000 19881.00000 3849.30000
7 24.1 125 580.81000 15625.00000 3012.50000
8 19.8 111 392.04000 12321.00000 2197.80000
9 21.3 115 453.69000 13225.00000 2449.50000
10 24.7 127 610.09000 16129.00000 3136.90000
11 25.4 132 645.16000 17424.00000 3352.80000
12 36 184 1296.00000 33856.00000 6624.00000
13 22.4 118 501.76000 13924.00000 2643.20000
14 19.2 109 368.64000 11881.00000 2092.80000
15 33.4 167 1115.56000 27889.00000 5577.80000
16 34.2 169 1169.64000 28561.00000 5779.80000
17 27.8 146 772.84000 21316.00000 4058.80000
18 29.3 147 858.49000 21609.00000 4307.10000
19 26.2 134 686.44000 17956.00000 3510.80000
20 27 135 729.00000 18225.00000 3645.00000
524.90000 2715.00000 14246.37000 377003.00000 73226.80000

Regression Coefficients
B = 4.19165
A = 25.74011

Regression Equation

ŷ = 25.74011 + 4.19165x

Coefficient of Correlation
r = 0.98944
 Table 3. 53: Exponential Model for Hybrid Generator with 30 N Force input

Exponential
Voltage (V) Current (µA)
Trial x^2 (ln y)^2 xlny
(x) (ln y)
1 29.5 5.00395 870.25000 25.03952 147.61653
2 31.9 5.02388 1017.61000 25.23937 160.26177
3 22.7 4.78749 515.29000 22.92006 108.67602
4 23.1 4.82028 533.61000 23.23510 111.34847
5 19.6 4.70048 384.16000 22.09451 92.12941
6 27.3 4.94876 745.29000 24.49023 135.10115
7 24.1 4.82831 580.81000 23.31258 116.36227
8 19.8 4.70953 392.04000 22.17967 93.24869
9 21.3 4.74493 453.69000 22.51436 101.06701
10 24.7 4.84419 610.09000 23.46618 119.65149
11 25.4 4.8828 645.16000 23.84174 124.02312
12 36 5.21494 1296.00000 27.19560 187.73784
13 22.4 4.77068 501.76000 22.75939 106.86323
14 19.2 4.69135 368.64000 22.00876 90.07392
15 33.4 5.11799 1115.56000 26.19382 170.94087
16 34.2 5.1299 1169.64000 26.31587 175.44258
17 27.8 4.98361 772.84000 24.83637 138.54436
18 29.3 4.99043 858.49000 24.90439 146.21960
19 26.2 4.89784 686.44000 23.98884 128.32341
20 27 4.90527 729.00000 24.06167 132.44229
524.90000 97.99661 14246.37000 480.59802 2586.07402

Regression Coefficients
B = 0.03009
A = 4.11014

Regression Equation

ŷ = 60.95538e0.03009x

Coefficient of Correlation
r = 0.99372
 Table 3. 54: Power Model for Hybrid Generator with 30 N Force input

Power
Voltage (V) Current (µA)
Trial (log x)^2 (log y)^2 logxlogy
(log x) (log y)
1 1.46982 2.17319 2.16037 4.72275 3.19420
2 1.50379 2.18184 2.26138 4.76043 3.28103
3 1.35603 2.07918 1.83882 4.32299 2.81943
4 1.36361 2.09342 1.85943 4.38241 2.85461
5 1.29226 2.04139 1.66994 4.16727 2.63801
6 1.43616 2.14922 2.06256 4.61915 3.08662
7 1.38202 2.09691 1.90998 4.39703 2.89797
8 1.29667 2.04532 1.68135 4.18333 2.65211
9 1.32838 2.0607 1.76459 4.24648 2.73739
10 1.3927 2.1038 1.93961 4.42597 2.92996
11 1.40483 2.12057 1.97355 4.49682 2.97904
12 1.5563 2.26482 2.42207 5.12941 3.52474
13 1.35025 2.07188 1.82318 4.29269 2.79756
14 1.2833 2.03743 1.64686 4.15112 2.61463
15 1.52375 2.22272 2.32181 4.94048 3.38687
16 1.53403 2.22789 2.35325 4.96349 3.41765
17 1.44404 2.16435 2.08525 4.68441 3.12541
18 1.46687 2.16732 2.15171 4.69728 3.17918
19 1.4183 2.1271 2.01157 4.52455 3.01687
20 1.43136 2.13033 2.04879 4.53831 3.04927
28.23447 42.55938 39.98607 90.64638 60.18254

Regression Coefficients
B = 0.79222
A = 1.00958

Regression Equation

ŷ = 10.22296x0.79222

Coefficient of Correlation
r = 0.98196
 Table 3. 55: Hyperbolic Model for Hybrid Generator with 30 N Force input

Hyperbolic
Voltage (V) Current (µA)
Trial (1/x)^2 (1/y)^2 (1/x)(1/y)
(1/x) (1/y)
1 0.0339 0.00671 0.00115 0.00005 0.00023
2 0.03135 0.00658 0.00098 0.00004 0.00021
3 0.04405 0.00833 0.00194 0.00007 0.00037
4 0.04329 0.00806 0.00187 0.00006 0.00035
5 0.05102 0.00909 0.00260 0.00008 0.00046
6 0.03663 0.00709 0.00134 0.00005 0.00026
7 0.04149 0.008 0.00172 0.00006 0.00033
8 0.05051 0.00901 0.00255 0.00008 0.00046
9 0.04695 0.0087 0.00220 0.00008 0.00041
10 0.04049 0.00787 0.00164 0.00006 0.00032
11 0.03937 0.00758 0.00155 0.00006 0.00030
12 0.02778 0.00543 0.00077 0.00003 0.00015
13 0.04464 0.00847 0.00199 0.00007 0.00038
14 0.05208 0.00917 0.00271 0.00008 0.00048
15 0.02994 0.00599 0.00090 0.00004 0.00018
16 0.02924 0.00592 0.00085 0.00004 0.00017
17 0.03597 0.00685 0.00129 0.00005 0.00025
18 0.03413 0.0068 0.00116 0.00005 0.00023
19 0.03817 0.00746 0.00146 0.00006 0.00028
20 0.03704 0.00741 0.00137 0.00005 0.00027
0.78804 0.15052 0.03207 0.00116 0.00608

Regression Coefficients
B = 0.14809
A = 0.00169

Regression Equation

𝒙
ŷ = 591.38201 𝟖𝟕.𝟓𝟕𝟕𝟖𝟏+𝒙

Coefficient of Correlation
r = 0.98807
 Table 3. 56: Summary of Mathematical Models for Hybrid Generator with 30 N Force input

Mathematical Models
Regression and
Correlation Linear Exponential Power Hyperbolic
Parameters
B 4.19165 0.03009 0.79222 0.14809
A 25.74011 4.11014 1.00958 0.00169
Regression
ŷ = 25.74011 + 4.19165x ŷ = 60.95538e 0.03009x ŷ = 10.22296x0.79222 ŷ = 591.38201
Equation
r 0.98944 0.99372 0.98916 0.98807

Since the coefficient of correlation of the exponential model (r = 0.99372) is the

nearest absolute value to 1 among the other mathematical models, then it is considered to be

the best-fit curve for the system of data.

Best Fit Curve:

5.3

5.2

5.1
Current (µA)

4.9

4.8

4.7

4.6
0 5 10 15 20 25 30 35 40
Voltage (V)

Figure 3. 35: Best Fit Curve for Hybrid Generator with 30 N Force input
Hybrid Generator (Walking)
 STATISTICAL MEASURES

Table 3. 57: Statistical Measures for Hybrid Generator (Walking)

Statistical
X y
Measures
Mean 30.70000 69.20000
Median 31.00000 74.00000
Mode 31.00000 74.00000
Standard
9.59221 25.69579
Deviation
Variance 92.01053 660.27368
Coefficient of
0.31245 0.37133
Variation
  REGRESSION AND CORRELATION

Table 3. 58: Linear Model for Hybrid Generator (Walking)

Linear
Voltage (V) Current (µA)
Trial x^2 y^2 xy
(x) (y)
1 39 94 1521.00000 8836.00000 3666.00000
2 44 99 1936.00000 9801.00000 4356.00000
3 30 66 900.00000 4356.00000 1980.00000
4 31 74 961.00000 5476.00000 2294.00000
5 53 118 2809.00000 13924.00000 6254.00000
6 18 32 324.00000 1024.00000 576.00000
7 20 34 400.00000 1156.00000 680.00000
8 36 85 1296.00000 7225.00000 3060.00000
9 38 87 1444.00000 7569.00000 3306.00000
10 24 57 576.00000 3249.00000 1368.00000
11 25 63 625.00000 3969.00000 1575.00000
12 18 27 324.00000 729.00000 486.00000
13 31 74 961.00000 5476.00000 2294.00000
14 23 55 529.00000 3025.00000 1265.00000
15 31 78 961.00000 6084.00000 2418.00000
16 35 80 1225.00000 6400.00000 2800.00000
17 38 92 1444.00000 8464.00000 3496.00000
18 39 93 1521.00000 8649.00000 3627.00000
19 20 35 400.00000 1225.00000 700.00000
20 21 41 441.00000 1681.00000 861.00000
614.00000 1384.00000 20598.00000 108318.00000 47062.00000

Regression Coefficients
B = 2.61595
A = -11.10960

Regression Equation

ŷ = -11.10960 + 2.61595x

Coefficient of Correlation
r = 0.97653
 Table 3. 59: Exponential Model for Hybrid Generator (Walking)

Exponential
Voltage (V) Current (µA)
Trial x^2 (ln y)^2 xlny
(x) (ln y)
1 39 4.54329 1521.00000 20.64148 177.18831
2 44 4.59512 1936.00000 21.11513 202.18528
3 30 4.18965 900.00000 17.55317 125.68950
4 31 4.30407 961.00000 18.52502 133.42617
5 53 4.77068 2809.00000 22.75939 252.84604
6 18 3.46574 324.00000 12.01135 62.38332
7 20 3.52636 400.00000 12.43521 70.52720
8 36 4.44265 1296.00000 19.73714 159.93540
9 38 4.46591 1444.00000 19.94435 169.70458
10 24 4.04305 576.00000 16.34625 97.03320
11 25 4.14313 625.00000 17.16553 103.57825
12 18 3.29584 324.00000 10.86256 59.32512
13 31 4.30407 961.00000 18.52502 133.42617
14 23 4.00733 529.00000 16.05869 92.16859
15 31 4.35671 961.00000 18.98092 135.05801
16 35 4.38203 1225.00000 19.20219 153.37105
17 38 4.52179 1444.00000 20.44658 171.82802
18 39 4.5326 1521.00000 20.54446 176.77140
19 20 3.55535 400.00000 12.64051 71.10700
20 21 3.71357 441.00000 13.79060 77.98497
614.00000 83.15894 20598.00000 349.28557 2625.53758

Regression Coefficients
B = 0.04150
A = 2.88376

Regression Equation

ŷ = 17.88137e0.04150x

Coefficient of Correlation
r = 0.92560
 Table 3. 60: Power Model for Hybrid Generator (Walking)

Power
Voltage (V) Current (µA)
Trial (log x)^2 (log y)^2 logxlogy
(log x) (log y)
1 1.59106 1.97313 2.53147 3.89324 3.13937
2 1.64345 1.99564 2.70093 3.98258 3.27973
3 1.47712 1.81954 2.18188 3.31073 2.68768
4 1.49136 1.86923 2.22415 3.49402 2.78769
5 1.72428 2.07188 2.97314 4.29269 3.57250
6 1.25527 1.50515 1.57570 2.26548 1.88937
7 1.30103 1.53148 1.69268 2.34543 1.99250
8 1.5563 1.92942 2.42207 3.72266 3.00276
9 1.57978 1.93952 2.49570 3.76174 3.06401
10 1.38021 1.75587 1.90498 3.08308 2.42347
11 1.39794 1.79934 1.95424 3.23762 2.51537
12 1.25527 1.43136 1.57570 2.04879 1.79674
13 1.49136 1.86923 2.22415 3.49402 2.78769
14 1.36173 1.74036 1.85431 3.02885 2.36990
15 1.49136 1.89209 2.22415 3.58000 2.82179
16 1.54407 1.90309 2.38415 3.62175 2.93850
17 1.57978 1.96379 2.49570 3.85647 3.10236
18 1.59106 1.96848 2.53147 3.87491 3.13197
19 1.30103 1.54407 1.69268 2.38415 2.00888
20 1.32222 1.61278 1.74827 2.60106 2.13245
29.33568 36.11545 43.38755 65.87928 53.44475

Regression Coefficients
B = 1.31453
A = -0.12237

Regression Equation

ŷ = 0.75446x1.31453

Coefficient of Correlation
r = 0.96655
 Table 3. 61: Hyperbolic Model for Hybrid Generator (Walking)

Hyperbolic
Voltage (V) Current (µA)
Trial (1/x)^2 (1/y)^2 (1/x)(1/y)
(1/x) (1/y)
1 0.02564 0.01064 0.00066 0.00011 0.00027
2 0.02273 0.0101 0.00052 0.00010 0.00023
3 0.03333 0.01515 0.00111 0.00023 0.00050
4 0.03226 0.01351 0.00104 0.00018 0.00044
5 0.01887 0.00847 0.00036 0.00007 0.00016
6 0.05556 0.03125 0.00309 0.00098 0.00174
7 0.05 0.02941 0.00250 0.00086 0.00147
8 0.02778 0.01176 0.00077 0.00014 0.00033
9 0.02632 0.01149 0.00069 0.00013 0.00030
10 0.04167 0.01754 0.00174 0.00031 0.00073
11 0.04 0.01587 0.00160 0.00025 0.00063
12 0.05556 0.03704 0.00309 0.00137 0.00206
13 0.03226 0.01351 0.00104 0.00018 0.00044
14 0.04348 0.01818 0.00189 0.00033 0.00079
15 0.03226 0.01282 0.00104 0.00016 0.00041
16 0.02857 0.0125 0.00082 0.00016 0.00036
17 0.02632 0.01087 0.00069 0.00012 0.00029
18 0.02564 0.01075 0.00066 0.00012 0.00028
19 0.05 0.02857 0.00250 0.00082 0.00143
20 0.04762 0.02439 0.00227 0.00059 0.00116
0.71587 0.34382 0.02806 0.00722 0.01401

Regression Coefficients
B = 0.69893
A = -0.00783

Regression Equation

𝒙
ŷ = -127.77938𝒙−𝟖𝟗.𝟑𝟎𝟓𝟔𝟕

Coefficient of Correlation
r = 0.95361
 Table 3. 62: Summary of Mathematical Models for Hybrid (Walking)

Mathematical Models
Regression and
Correlation Linear Exponential Power Hyperbolic
Parameters
B 2.61595 0.04150 1.31453 0.69893
A -11.10960 2.88376 -0.12237 -0.00783
Regression
ŷ = -11.10960 + 2.61595x ŷ = 17.88137e 0.04150x ŷ = 0.75446x1.31453 ŷ = -127.77938
Equation
r 0.97653 0.92560 0.96655 0.95361

Since the correlation coefficient of the linear model is 0.97653 which is the nearest

absolute value to 1 among the other mathematical models, then it is considered to be the best-

fit curve for the system of data.

Best Fit Curve:

140

120

100
Current (µA)

80

60

40

20

0
0 10 20 30 40 50 60
Voltage (V)

Figure 3. 36: Best Fit Curve for Hybrid Generator (Walking)

Hybrid Generator (Running)

 STATISTICAL MEASURES

Table 3. 63: Statistical Measures for Hybrid Generator (Running)

Statistical
X y
Measures
Mean 56.36500 97.00000
Median 55.85000 102.00000
Mode - 102.00000
Standard
10.48424 25.63920
Deviation
Variance 109.91924 657.36842
Coefficient of
0.18601 0.26432
Variation
  REGRESSION AND CORRELATION

Table 3. 64: Linear Model for Hybrid Generator (Running)

Linear
Voltage (V) Current (µA)
Trial x^2 y^2 xy
(x) (y)
1 69.4 122 4816.36000 14884.00000 8466.80000
2 78.1 127 6099.61000 16129.00000 9918.70000
3 56.8 108 3226.24000 11664.00000 6134.40000
4 60.2 113 3624.04000 12769.00000 6802.60000
5 45.9 63 2106.81000 3969.00000 2891.70000
6 48.3 69 2332.89000 4761.00000 3332.70000
7 63.8 120 4070.44000 14400.00000 7656.00000
8 64.9 121 4212.01000 14641.00000 7852.90000
9 56.4 102 3180.96000 10404.00000 5752.80000
10 43.1 55 1857.61000 3025.00000 2370.50000
11 61.5 115 3782.25000 13225.00000 7072.50000
12 49.5 83 2450.25000 6889.00000 4108.50000
13 56.3 102 3169.69000 10404.00000 5742.60000
14 78.2 146 6115.24000 21316.00000 11417.20000
15 43.2 60 1866.24000 3600.00000 2592.00000
16 45.7 62 2088.49000 3844.00000 2833.40000
17 49.8 85 2480.04000 7225.00000 4233.00000
18 50.2 91 2520.04000 8281.00000 4568.20000
19 50.6 94 2560.36000 8836.00000 4756.40000
20 55.4 102 3069.16000 10404.00000 5650.80000
1127.30000 1940.00000 65628.73000 200670.00000 114153.70000

Regression Coefficients
B = 2.30102
A = -32.69697

Regression Equation

ŷ = -32.69697 + 2.30102x

Coefficient of Correlation
r = 0.94092
 Table 3. 65: Exponential Model for Hybrid Generator (Running)

Exponential
Voltage (V) Current (µA)
Trial x^2 (ln y)^2 xlny
(x) (ln y)
1 69.4 4.80402 4816.36000 23.07861 333.39899
2 78.1 4.84419 6099.61000 23.46618 378.33124
3 56.8 4.68213 3226.24000 21.92234 265.94498
4 60.2 4.72739 3624.04000 22.34822 284.58888
5 45.9 4.14313 2106.81000 17.16553 190.16967
6 48.3 4.23411 2332.89000 17.92769 204.50751
7 63.8 4.78749 4070.44000 22.92006 305.44186
8 64.9 4.79579 4212.01000 22.99960 311.24677
9 56.4 4.62497 3180.96000 21.39035 260.84831
10 43.1 4.00733 1857.61000 16.05869 172.71592
11 61.5 4.74493 3782.25000 22.51436 291.81320
12 49.5 4.41884 2450.25000 19.52615 218.73258
13 56.3 4.62497 3169.69000 21.39035 260.38581
14 78.2 4.98361 6115.24000 24.83637 389.71830
15 43.2 4.09434 1866.24000 16.76362 176.87549
16 45.7 4.12713 2088.49000 17.03320 188.60984
17 49.8 4.44265 2480.04000 19.73714 221.24397
18 50.2 4.51086 2520.04000 20.34786 226.44517
19 50.6 4.54329 2560.36000 20.64148 229.89047
20 55.4 4.62497 3069.16000 21.39035 256.22334
1127.30000 90.76614 65628.73000 413.45813 5167.13230

Regression Coefficients
B = 0.02447
A = 3.15922

Regression Equation

ŷ = 23.55211e0.02447x

Coefficient of Correlation
r = 0.90293
 Table 3. 66: Power Model for Hybrid Generator (Running)

Power
Voltage (V) Current (µA)
Trial (log x)^2 (log y)^2 logxlogy
(log x) (log y)
1 1.84136 2.08636 3.39061 4.35290 3.84174
2 1.89265 2.1038 3.58212 4.42597 3.98176
3 1.75435 2.03342 3.07774 4.13480 3.56733
4 1.7796 2.05308 3.16698 4.21514 3.65366
5 1.66181 1.79934 2.76161 3.23762 2.99016
6 1.68395 1.83885 2.83569 3.38137 3.09653
7 1.80482 2.07918 3.25738 4.32299 3.75255
8 1.81224 2.08279 3.28421 4.33801 3.77452
9 1.75128 2.0086 3.06698 4.03447 3.51762
10 1.63448 1.74036 2.67152 3.02885 2.84458
11 1.78888 2.0607 3.20009 4.24648 3.68635
12 1.69461 1.91908 2.87170 3.68287 3.25209
13 1.75051 2.0086 3.06429 4.03447 3.51607
14 1.89321 2.16435 3.58424 4.68441 4.09757
15 1.63548 1.77815 2.67479 3.16182 2.90813
16 1.65992 1.79239 2.75533 3.21266 2.97522
17 1.69723 1.92942 2.88059 3.72266 3.27467
18 1.7007 1.95904 2.89238 3.83784 3.33174
19 1.70415 1.97313 2.90413 3.89324 3.36251
20 1.74351 2.0086 3.03983 4.03447 3.50201
34.88474 39.41924 60.96222 77.98306 68.92681

Regression Coefficients
B = 1.48139
A = -0.61294

Regression Equation

ŷ = 0.24382x1.48139

Coefficient of Correlation
r = 0.93397
 Table 3. 67: Hyperbolic Model for Hybrid Generator (Running)

Hyperbolic
Voltage (V) Current (µA)
Trial (1/x)^2 (1/y)^2 (1/x)(1/y)
(1/x) (1/y)
1 0.01441 0.0082 0.00021 0.00007 0.00012
2 0.0128 0.00787 0.00016 0.00006 0.00010
3 0.01761 0.00926 0.00031 0.00009 0.00016
4 0.01661 0.00885 0.00028 0.00008 0.00015
5 0.02179 0.01587 0.00047 0.00025 0.00035
6 0.0207 0.01449 0.00043 0.00021 0.00030
7 0.01567 0.00833 0.00025 0.00007 0.00013
8 0.01541 0.00826 0.00024 0.00007 0.00013
9 0.01773 0.0098 0.00031 0.00010 0.00017
10 0.0232 0.01818 0.00054 0.00033 0.00042
11 0.01626 0.0087 0.00026 0.00008 0.00014
12 0.0202 0.01205 0.00041 0.00015 0.00024
13 0.01776 0.0098 0.00032 0.00010 0.00017
14 0.01279 0.00685 0.00016 0.00005 0.00009
15 0.02315 0.01667 0.00054 0.00028 0.00039
16 0.02188 0.01613 0.00048 0.00026 0.00035
17 0.02008 0.01176 0.00040 0.00014 0.00024
18 0.01992 0.01099 0.00040 0.00012 0.00022
19 0.01976 0.01064 0.00039 0.00011 0.00021
20 0.01805 0.0098 0.00033 0.00010 0.00018
0.36578 0.22250 0.00688 0.00269 0.00426

Regression Coefficients
B = 0.98582
A = -0.00690

Regression Equation

𝒙
ŷ = -144.82946𝒙−𝟏𝟒𝟐.𝟕𝟕𝟓𝟖𝟔

Coefficient of Correlation
r = 0.92610
 Table 3. 68: Summary of Mathematical Models for Hybrid (Running)

Mathematical Models
Regression and
Correlation Linear Exponential Power Hyperbolic
Parameters
B 2.30102 0.02447 1.48139 0.98582
A -32.69697 3.15922 -0.61294 -0.00690
Regression
ŷ = -32.69697 + 2.30102x ŷ = 23.55211e 0.02447x ŷ = 0.24382x1.48139 ŷ = -144.82946
Equation
r 0.94092 0.90293 0.93397 0.92610

The linear model has a correlation coefficient of 0.94092 which is the nearest

absolute value to 1 among the other mathematical models, then it is considered to be the best-

fit curve for the system of data.

Best Fit Curve:

160

140

120

100
Current (µA)

80

60

40

20

0
0 10 20 30 40 50 60 70 80 90
Voltage (V)

Figure 3. 37: Best Fit Curve for Hybrid Generator (Running)

 The proponents computed the variance in order to measure how far a set of numbers

(voltage and current rating) are spread out. Based on the table provided, the computed value

of the variance of piezoelectric, triboelectric and hybrid generator is not that high, therefore, it

indicates that the data points tend to be very close to the mean (expected value) and hence to

each other.

Construction of Prototype

The pictures shown are the important part of the prototype. Below is the charging

circuit that regulates at 5V, piezoelectric generator, triboelectric generator and the design

prototype which is the hybrid generator.

Figure 3. 38: Charging Circuit

Figure 3. 39: Triboelectric Generator

Figure 3. 40: Piezoelectric Generator

Figure 3. 41: Actual Prototype

 The picture shown below is the mechanism that the proponents used to test the voltage

and the current reading of the piezo-triboelectric generator using characterized inputs.

Figure 3. 42: Testing Piezoelectric Generator using 10N Force as input

Figure 3. 43: Testing Set-up for the Piezo-Triboelectric Generator using characterized inputs
 The illustrations shown are the actual testing of the design prototype. Walking and

running are the activity in this test.

Figure 3. 44: Actual Testing Set-up for the Piezo-Triboelectric Generator

The figures below are the simulation on the oscilloscope. The waveform of the
output AC voltage of each generator is shown.

Figure 3. 45: Waveform of the output AC voltage of Piezo-Triboelectric Generator

Computation:
 Computation for Triboelectric Generator

Short Circuit Current

𝐶
𝜎𝑇 =133.24 μ (Charge Density of FEP)
𝑚2

𝑑 𝑇 = 0.025 𝑚𝑚 (Thickness of FEP)

𝑑 = 5 mm (Spacing of FEP and the Upper electrode)

𝜀0 = 8.9 x 10−12 F/m (Permittivity of Free Space)

𝜀𝑟 = 2.1 (permittivity of FEP)

A = 200 mm x 40 mm (Surface Area)

t = 1.67 s (Time)

𝑑𝑇
𝑑 𝑇𝐸 =
𝜀𝑇

0.025 𝑚𝑚
𝑑 𝑇𝐸 = 2.1

𝑑 𝑇𝐸 = 0.0119047619 𝑚𝑚
1
𝜎1 = − 𝜎𝑇 𝑑
1+ 𝑇𝐸
𝑑

𝐶 1
𝜎1 = − 133.24 𝜇 ( 0.0119047619 𝑚𝑚 )
𝑚2 1+
5 𝑚𝑚

𝐶
𝜎1 = −132.9235154 𝜇 𝑚2

1
𝜎2 = − 𝜎𝑇 𝑑
1+
𝑑𝑇𝐸

𝐶 1
𝜎2 = − 133.24 𝜇 ( 5 𝑚𝑚 )
𝑚2 1+
0.0119047619 𝑚𝑚

𝐶
𝜎2 = − 0.3164845604 𝜇
𝑚2
 𝑓 𝑓
𝛥𝑄 𝐴(𝜎𝑖 − 𝜎𝑖 ) 𝐴𝜎𝑇 𝑑 𝑑𝑓
𝐼𝐻 = 𝛥𝑡
= 𝛥𝑡
= 𝛥𝑡
(𝑑 + 𝑑𝑖 − 𝑑𝑓 + 𝑑𝑇𝐸
)
𝑖 𝑇𝐸

𝐶
8000 𝑥 10−3 𝑚2 (133.24 𝜇 ) 5 𝑚𝑚
𝑚2
𝐼𝐻 = 1.67𝑠
(5𝑚𝑚+0.119047619 𝑚𝑚 − 0)

𝐼𝐻 = 0.623431834 𝜇𝐴

Open Circuit Voltage

𝜎𝑇 𝑑𝑇𝐸 (𝑑𝑖 )
𝑉𝑓 = .
𝜀0 𝑑𝑖 + 𝑑𝑇𝐸

𝐶
133.24 𝜇 0.0119047619 𝑚𝑚(5 𝑚𝑚𝑖 )
𝑚2
𝑉𝑓 = .
8.9 x 10−12 F/m 5 𝑚𝑚+0.0119047619 𝑚𝑚

𝑉𝑓 = 177.8003149 V

 Computation for power

Energy in the Lithium Ion battery with the capacity of 2600mAh with a voltage of 3.7V:
∆𝐸
𝑃 = 𝐼𝑉 =
∆𝑡
∆𝐸 = 𝐼𝑉∆𝑡 = (2.6𝐴)(3.7𝑉)(3600𝑠) = 34.632 𝑘𝐽

Ideal Charging Time: V = 5 V; I = 1A

∆𝐸
𝑡𝑐 =
𝐼𝑉
34632000 𝐽
𝑡𝑐 =
(1𝐴)(5𝑉)
𝑡𝑐 = 6926.4 𝑠
𝑡𝑐 = 1.924 ℎ𝑜𝑢𝑟𝑠

Prototype Charging time: V = 5.137 V; I = 42.45 × 10−6 A

∆𝐸
𝑡𝑐 =
𝐼𝑉
34632000 𝐽
𝑡𝑐 =
(42.45 × 10−6 𝐴)(5.137𝑉)
 𝑡𝑐 = 158.81 × 106 𝑠
𝑡𝑐 = 44115.16 ℎ𝑜𝑢𝑟𝑠

 Computation for Efficiency

𝑜𝑢𝑡𝑝𝑢𝑡 𝑝𝑜𝑤𝑒𝑟
EFF = 𝑖𝑛𝑝𝑢𝑡 𝑝𝑜𝑤𝑒𝑟
x 100 %

5.137 𝑉 (39.35 𝜇𝐴)

EFF = x 100 %
30.7 𝑉 (69.2 𝜇𝐴)

EFF = 9.52 %
 Chapter 4

CONCLUSION

Based on the data gathered through the testing, the design of the circuit did not work well as

we did not consider the low current generated by both piezoelectric and triboelectric material.

Each component used in the circuit has its own resistance which lead to drop of current.

Therefore, the circuit is inefficient because it was not able to maximize the input power.

The piezo-triboelectric generator provides a clean source of energy but delivers

insufficient power to charge a power bank that will be used for self-powered electronics. It is

because the output power of the hybrid generator is much smaller compared to the power rating

required to charge the power bank.

One of the factors that affect the maximum output generation capabilities of the hybrid

generator is the nature of the materials used. The performance of piezoelectric material is

influenced by its mechanical quality factor. The electro-conductivity of the triboelectric

material is poor that there is no strong electrode existing between the two triboelecric material

sheet/film to support the proper flow of the electrons.

The behavior of the piezoelectric material when excited also affects the output of the

generator. When excited, the piezoelectric material generates a voltage spike with a very short

duration of time. But, the interval between that first and next voltage spike is very large causing

it to lose the momentum of operation of the circuit.

The proponents, therefore, conclude that piezo-triboelectric generator is a good source

of renewable energy when connected to a low-loss energy harvesting circuit and when efficient

materials are used.

 Chapter 5

RECOMMENDATION

The design of the piezo-triboelectric generator embedded in a shoe-insole can be

further developed. The proponents would like to recommend more techniques for future

attempts in improving the said generator to those who want to continue the study.

For piezoelectric material, the use of sheet/film rather than crystal transducer would be

more helpful in increasing the output of the generator. Also, Sheet/film is more durable than

crystal transducer, subjecting the transducer to too much pressure can cause a crack to the

crystal.

For triboelectric material, understand the Triboelectric Series before choosing. It is a

handy tool to determine which combination of material can create the most static electricity.

The generator should undergo to some process like thermal spraying and ionization. Thermal

spraying can increase the conductivity of the generator by coating it with a melted conductive

material (preferably gold, silver, copper and aluminum). The thickness of the coating should

range from micrometers to several millimeters. Ionization, on the other side, can increase the

positive or negative charge of the material by gaining or losing electrons to form ions, often in

conjunction with other chemical changes.

Find another application where the continuous force is applied to the generator to

maintain the desired output. These recommendations are intended to solve to problems that the

proponents have encountered and for the betterment of the design.

 Using the output parameters gathered in the piezo-triboelectric generator embedded in

a shoe-insole, the proponents would like to recommend the following application for future

works.

Micropower miniature Digital Motion Detector module operates on 3 to 5 volts at only

40 microamperes is ideal for OEM (original equipment manufacturer) applications. The DP-

002A is designed to detect infrared radiation (IR) from a moving human or animal both in

daylight and at night. It will only respond to a moving source of infrared radiation. It will not

detect a static IR source.

The S1D14F00 series is a two-level grayscale EPD passive panel driver IC. The device

integrates drivers that are necessary for display updates of the EPD passive panel (segment,

top plane and back plane) and a control circuit for driver waveforms to one chip. The device

also includes a Flash memory that stores output drive waveform data for the EPD passive panel

drivers and a power supply circuit. The S1D14F00 series can compose a two-level grayscale

EPD passive panel display controller that operates on 3.75V to 5.2V at 100nA when deep

standby and 50uA when standby.

The 8045ABM is the successor of the 8044. It is an integrated circuit designed

specifically to perform the function of an electronic Morse keyer. It included debouncing

circuitry for the key paddles, logic to produce dots and dashes, iambic mode (alternating dots

and dashes when both paddles are closed), a sidetone generator, positive (added) and negative

(reduced) weighting circuitry, output stage capable of driving an NPN keying transistor, and

finally, a built-in 85character volatile message memory that can be expanded to over 500

characters using external nonvolatile memory. The 8045ABM operates on 4 Vdc min., 6 Vdc

max. (5 Vdc recommended) at quiescent current less than 50µΑ at 5Vdc.

 BIBLIOGRAPHY

[1] Wang, Z. (2014). Triboelectric Nanogenerators as New Energy Technology and Self-

Powered Sensors – Principles, Problems and Perspectives. Faraday Discussions, Vol. 176,

pp. 447-458

[2] Wang, Z., et al. (2014). Piezoelectric Nanowires in Energy Harvesting Applications.

Advances in Materials Science Engineering. Article ID 165631, doi:10.1155/2015/165631

[3] Ramadan, K. S., Sameoto, D., and Evoy S. (2014). A review of piezoelectric polymers

as functional materials for electromechanical transducers. Smart Materials and

Structures, Vol. 23, pp. 1-26

[4] Kim, H.S, Kim J.-H., and Kim J. (2011). A review of piezoelectric energy harvesting

based on vibration. International Journal of Precision Engineering and Manufacturing,

Vol 12, No 6, pp. 1129-1141

[5-6] Sodano, H. A., Inman, D. J., and Park, G. (2004). A review of power harvesting from

vibration using piezoelectric materials. The Shock and Vibration Digest, Vol. 36, No. 3 pp.

197-205

[7] Dhingra, P., Biswas, J., Prasad, A., and Meher, S. S. (2012). Energy Harvesting using

Piezoelectric Materials. Special Issue of International Journal of Computer Applications

[8] Xiao, H. and Wang X. (2014). A review of piezoelectric vibration energy harvesting

techniques. International Review of Mechanical Engineering

[9] Sodano, H. A., Inman, D. J., and Park, G. (2004). A review of power harvesting from

vibration using piezoelectric materials. The Shock and Vibration Digest, Vol. 36, No. 3 pp.

197-205

[10] Beeby, S. P., Tudor, M. J., and White, N. M. (2006). Energy harvesting vibration

sources for microsystems applications. Meas. Sci. Technology, Vol. 17, pp. 175-195

[11] Kim, H. W., Priya, S., Uchino, K., and Newnham, R. E. (2005). Piezoelectric energy

harvesting under high pre-stressed cyclic vibrations. J.Electroceram.. Vol. 15, pp. 27-34

[12] Wang, S., Lam, K. H., Sun, C. L., Kwok, K. W., Chan, H. L. W., Guo, M. S., et aI.,

(2007). Energy harvest with piezoelectric drum transducer. Appl. Phys. Lett., Vol. 90, pp.

113-506

[13] Paradiso, J. and Starner, T. (2005). Energy scavenging for mobile and wireless

electronics. IEEE Pervasive Computing, Vol. 4, No. 1, pp. 18–27

[14] Saha, P., Goswami, S., Chakrabarty, S. and Sarkar, S. (2014). Simulation and model

verification of shoe embedded piezoelectric energy harvester. Power India International

Conference (PIICON). Vol., no., pp.1-6

[15] Arabia, J. (1989) Computer Integrated Electronics Manufacturing and Testing. Boca

Raton, FL: CRC Press

[16] Fan, F.-R., et al. (2012). Flexible triboelectric generator, Nano Energy

doi:10.1016/j.nanoen.2012.01.004
[17] Wang, Z.L., Chen, J. and Lin, L. (2015). Progress in triboelectric nanogenerators as

a new energy technology and self-powered sensors. Energy Environ. Sci.Vol 8, No. 2250.,

pp. 1-33

[18] Wong, W. (2014, January 31). Harvesting Power Using Triboelectric Generators.

Retrieved from http://electronicdesign.com/

[19] The TriboElectric Series. Retrieved from https://www.trifield.com/

[20] Arabia, J. (1989) Computer Integrated Electronics Manufacturing and Testing.

Boca Raton, FL: CRC Press

[21] Staff, S. (2009). Harvesting Energy from Humans. Retrieved from

http://www.popsci.com/environment/article/2009-01/harvesting-energy-humans Formatted: Font: (Default) Times New Roman, 12 pt, Bold,

Font color: Auto
Formatted: Font: Bold, Underline
[22] Shadbolt, P. (2015). Future cities may harvest energy from human footsteps.

Tomorrow Transformed. Retrieved from

http://edition.cnn.com/2014/12/30/tech/innovation/tomorrow-transformed-energy- Formatted: Font: (Default) Times New Roman, 12 pt, Bold,

Font color: Auto

harvesting/ Formatted: Font: Bold, Underline

[23-24] Jung, W.-S. et al., (2015). High Output Piezo/Triboelectric Hybrid Generator. Sci.

Rep. 5, 9309; DOI:10.1038/srep09309

[25-26] Kymissis, J., Kendall, C., Paradiso, J., and Gershenfeld, N. (1998). Parasitic

power harvesting in shoes. in Proc. 2nd IEEE Int. Conf. Wearable Computing, pp. 132–

139
[27] Guyomar, D., Badel, A,. Lefeuvre, E., and Richard, C. (2005). Toward energy

harvesting using active materials and conversion improvement by nonlinear processing.

IEEE Trans. Ultrason. Ferroelectr. Freq. Control, vol. 52, no. 4, pp. 584–595

[28-29] Paradiso, J. and Starner, T. (2005). Energy scavenging for mobile and wireless

electronics. IEEE Pervasive Computing, Vol. 4, No. 1, pp. 18–27

[30] Mateu, L. and Moll, F. (2005). Review of Energy Harvesting Techniques and

Application for Microelectronics. SPIE Microtechnologies for the New Millenium

[31] Schumacher, F. (2014, July 2). Energy Harvesting for Wearables. Retrieved from

https://www.wearable-technologies.com/

[32] Mateu, L. and Moll, F. (2005). Review of Energy Harvesting Techniques and

Application for Microelectronics. SPIE Microtechnologies for the New Millenium

[33] Schumacher, F. (2014, July 2). Energy Harvesting for Wearables. Retrieved from

https://www.wearable-technologies.com/

[34] Power Banks. Retrieved from http://www.techulator.com/

[35] Power Bank Instructions. Retrieved from http://www.markfeldstein.com/ Formatted: Font: Bold, Font color: Auto
Formatted: Font: (Default) Times New Roman, 12 pt, Bold,
Font color: Auto
[36] A. Bachtold et al., “Logic Circuits with Carbon Nanotube Transistors,” Science, vol. Formatted: Font: Bold, Underline

294, no. 5545, 2001, pp. 1317–1320.

[36-37] Rocha, J.G., Goncalves, L.M., Rocha, P.F., Silva, M.P., and Lanceros-Mendez, S.

(2010). Energy Harvesting From Piezoelectric Materials Fully Integrated in Footwear.

IEEE Transactions On Industrial Electronics, Vol. 57, No. 3

[38-39] Bischur, E. and Schwesinger, N. (2012). Energy harvesting from floor using

organic piezoelectric modules. Power Engineering and Automation Conference (PEAM),

2012 IEEE.

[40] Ben-Yaakov, S., Hadar, G., Shainkopf, A. and Krihely, N. (2013). A Friendly

Approach to Increasing the Frequency Response of Piezoelectric Generators. 2013 IEEE

XXXIII International Scientific Conference Electronics and Nanotechnology (ELNANO)

pp. 349-353

[41] Nilotpal Manna (2014). Study on Piezoelectric Elements for Energy Harvesting.

Proceedings of 2014 1st International Conference on Non Conventional Energy (ICONCE

2014) pp. 334 – 338

[42] Sahul, R. Nesvijski, E., and Hackenberger, W. (2014). Optimization of Piezoelectric

Transducer Design by Modeling and Simulation. Applications of Ferroelectrics,

International Workshop on Acoustic Transduction Materials and Devices & Workshop on

Piezoresponse Force Microscopy (ISAF/IWATMD/PFM), 2014 Joint IEEE International

pp. 1-3

[43] Zhaoyang Yu, Yingxiang Liu, Dongmei Xu, Junkao Liu and Weishan Chen (2015).

Vibration Characteristic Analysis of a Piezoelectric Transducer Using First Bending

Vibration Modes. Applications of Ferroelectric, International Symposium on Integrated

Functionalities and Piezoelectric Force Microscopy Workshop (ISAF/ISIF/PFM), 2015

Joint IEEE International Symposium pp. 32-35

[44] Erhart, J. (2016). Transformation and Load Parameters of the Disk Piezoelectric

Transformer. IEEE Transactions on Power Electronics, Vol. 31, No. 3

[45] Sihong Wang, Long Lin, and Zhong Lin Wang (2012). Nanoscale Triboelectric-

Effect-Enabled Energy Conversion for Sustainably Powering Portable Electronics. Nano

Letters 2012, 12 (12), pp. 6339-6346. DOI: 10.1021/nl303573d

[46] Te-Chien Hou, Ya Yanga, Hulin Zhanga, Jun Chena, Lih-Juann Chen and Zhong

Lin Wang (2013). Triboelectric nanogenerator built inside shoe insole for harvesting

walking energy. Nano Energy. http://dx.doi.org/10.1016/j.nanoen.2013.03.001

[47] Hulin Zhang, Ya Yang, Te-Chien Hou, Jun Chen, Lih-Juann Chen and Zhong Lin Formatted: Font: Bold, Font color: Auto
Formatted: Font: (Default) Times New Roman, 12 pt, Bold,
Wang (2013). Triboelectric Nanogenerator for Harvesting Vibration Energy in Full Font color: Auto
Formatted: Font: Bold, Font color: Auto

Space and as Self-Powered Acceleration Sensor. DOI: 10.1002/adfm.201302453 Formatted: Font: (Default) Times New Roman, 12 pt, Bold,
Font color: Auto
Formatted: Font: Bold, Font color: Auto
Formatted: Font: (Default) Times New Roman, 12 pt, Bold,
Font color: Auto
Formatted: Font: Bold, Font color: Auto
[48] Qingshen Jing, Guang Zhu, Peng Bai, Yannan Xie, Jun Chen, Ray P. S. Han,
Formatted: Font: (Default) Times New Roman, 12 pt, Bold,
Font color: Auto
and Zhong Lin Wang (2014). Case-Encapsulated Triboelectric Nanogenerator for Formatted: Font: Bold, Font color: Auto
Formatted: Font: Bold, Underline
Harvesting Energy from Reciprocating Sliding Motion. ACS Nano, 2014, 8 (4), pp 3836–
Formatted: Normal, Space After: 0 pt, Pattern: Clear
Formatted: Font: Bold, Underline
3842. DOI: 10.1021/nn500694y
Formatted: Font: (Default) Times New Roman, 12 pt, Bold,
Font color: Auto

[49] Jeong Hwan Lee, Ronan Hinchet, Sung Kyun Kim, Sanghyun Kim and Sang-Woo Formatted: Font: Bold, Underline
Formatted: Default Paragraph Font, Font: (Default) +Body
(Calibri), 11 pt, Bold, Underline
Kim (2015). A Shape memory polymer-based self-healing triboelectric nanogenerator.
Formatted: Font: Bold, Underline

Energy Environ. Sci., 2015, Advance Article. DOI: 10.1039/C5EE02711J Formatted: Font: (Default) Times New Roman, 12 pt, Bold,
Font color: Auto
Formatted: Font: Bold, Underline
[50] Ting Quan, Xue Wang, Zhong Lin Wang, and Ya Yang (2015). Hybridized Formatted: Default Paragraph Font, Font: (Default) +Body
(Calibri), 11 pt, Bold, Underline
Electromagnetic–Triboelectric Nanogenerator for a Self-Powered Electronic Watch. Formatted: Font: Bold, Underline
Formatted: Font: (Default) Times New Roman, 12 pt, Bold,
ACS Nano, Article ASAP. DOI: 10.1021/acsnano.5b05598 Font color: Auto
Formatted: Font: Bold, Underline
Formatted: Font: (Default) Times New Roman, 12 pt, Bold,
Font color: Auto
Formatted: Font: Bold, Underline
 APPENDICES

APPENDIX A- Data Sheet of Piezoelectric Element

APPENDIX B- Data Sheet of Triboelectric Element

 LIST OF FIGURES

Figure 2. 1: Mono vs. Poly Crystals ................................................................................................... 7

Figure 2. 2: Polarization of Ceramic Material to Generate Piezoelectric Effect ................................... 7
Figure 2. 3: Example of Piezoelectric Effect ...................................................................................... 8
Figure 2 1 Three- dimensional orthogonal modal space with reference the piezoelectric structure ....... 9
Figure 2. 4: (a) Compression along 3 axis. (b) Expansion strain on upper ........................................... 9
Figure 2. 5: Schematic illustration of the structure and working principle of the triboelectric generator.
(a) The structure of an integrated generator in bending and releasing process and related electrical
measurement tests. Photographic images of a flexible TEG and mechanical bending equipment. (b)
Proposed mechanism of a TEG (see text for details): charges are generated by fractioning two
polymer films, which results in the creation of a triboelectric potential layer at the interfacial region
(indicated by dashed lines); a mechanical compression results in a change in the distance between the
two electrodes (from D to d), thus, under the driving of the triboelectric potential, a change in system
capacitance leads to the flow of current in the external load which drives the flow of the free electrons
across the electrodes to minimize the total energy of the system. ..................................................... 10
Figure 2. 6: Theoretical models for (a) dielectric-to-dielectric contact mode TENG and (b) conductor-
to-dielectric contact mode TENG .................................................................................................... 12
Figure 3. 1Conceptual Framework ................................................................................................... 32
Figure 3. 2:System Flow .................................................................................................................. 33
Figure 3. 3: Hybrid Generator Flowchart .......................................................................................... 35
Figure 3. 4: Hybrid Generator Block Diagram .................................................................................. 36
Figure 3. 5: Hybrid Generator Circuit Diagram ................................................................................ 36
Figure 3. 6: (a) Charging Circuit of piezo/triboelectric hybrid generator. (b) Actual Charging Circuit
of piezo/triboelectric hybrid generator. ............................................................................................ 36
Figure 3. 7: (a) Schematic view of piezo/triboelectric hybrid generator. ........................................... 37
Table 3: Fundamental Equations and Piezoelectric Coefficients ....................................................... 42
Figure 3. 8: Piezoelectric Voltage Rating (F = 10 N) ............................ Error! Bookmark not defined.
Figure 3. 9: Piezoelectric Current Rating (F = 10 N) ............................. Error! Bookmark not defined.
Figure 3. 10: Piezoelectric Voltage Rating (F = 20 N) ........................... Error! Bookmark not defined.
Figure 3. 11: Piezoelectric Current Rating (F = 20 N) ........................... Error! Bookmark not defined.
Figure 3. 12: Piezoelectric Voltage Rating (F = 30 N) ........................... Error! Bookmark not defined.
Figure 3. 13: Piezoelectric Current Rating (F = 30 N) ........................... Error! Bookmark not defined.
Figure 3. 14: Piezoelectric Voltage Rating Comparison ........................ Error! Bookmark not defined.
Figure 3. 15Piezoelectric Current Rating Comparison ........................... Error! Bookmark not defined.
Figure 3. 16: Triboelectric Voltage Rating (F = 10 N) ........................... Error! Bookmark not defined.
Figure 3. 17: Triboelectric Current Rating (F = 10 N) ........................... Error! Bookmark not defined.
Figure 3. 18: Triboelectric Voltage Rating (F = 20 N) ........................... Error! Bookmark not defined.
Figure 3. 19: Triboelectric Current Rating (F = 20 N) ........................... Error! Bookmark not defined.
Figure 3. 20: Triboelectric Voltage Rating (F = 30 N) ........................... Error! Bookmark not defined.
Figure 3. 21: Triboelectric Current Rating (F = 30 N) ........................... Error! Bookmark not defined.
Figure 3. 22: Triboelectric Voltage Rating Comparison ......................... Error! Bookmark not defined.
Figure 3. 23:Triboelectric Current Rating Comparison .......................... Error! Bookmark not defined.
Figure 3. 24Hybrid VoltageRating (F = 10 N) ....................................... Error! Bookmark not defined.
Figure 3. 25: Hybrid Current Rating (F = 10 N) .................................... Error! Bookmark not defined.
Figure 3. 26: Hybrid Voltage Rating (F = 20 N) ................................... Error! Bookmark not defined.
Figure 3. 27: Hybrid Current Rating (F = 20 N) .................................... Error! Bookmark not defined.
Figure 3. 28: Hybrid Voltage Rating (F = 30 N) .................................... Error! Bookmark not defined.
Figure 3. 29: Hybrid Current Rating (F = 30 N) .................................... Error! Bookmark not defined.
Figure 3. 30: Hybrid Voltage Rating Comparison .................................. Error! Bookmark not defined.
Figure 3. 31: Hybrid Current Rating Comparison ................................. Error! Bookmark not defined.
Figure 3. 32Piezoelectric Voltage Rating (Walking).............................. Error! Bookmark not defined.
Figure 3. 33: Piezoelectric Current Rating (Walking) ........................... Error! Bookmark not defined.
Figure 3. 34: Triboelectric Voltage Rating (Walking) ............................ Error! Bookmark not defined.
Figure 3. 35: Triboelectric Current Rating (Walking) ............................ Error! Bookmark not defined.
Figure 3. 36: Hybrid Voltage Rating (Walking) ..................................... Error! Bookmark not defined.
Figure 3. 37:Hybrid Current Rating (Walking) ...................................... Error! Bookmark not defined.
Figure 3. 38: Piezoelectric Voltage Rating (Running) ............................ Error! Bookmark not defined.
Figure 3. 39: Piezoelectric Current Rating (Running) ............................ Error! Bookmark not defined.
Figure 3. 40: Triboelectric Voltage Rating (Running) ............................ Error! Bookmark not defined.
Figure 3. 41: Triboelectric Current Rating (Running) ............................ Error! Bookmark not defined.
Figure 3. 42: Hybrid Voltage Rating (Running)..................................... Error! Bookmark not defined.
Figure 3. 43: Hybrid Current Rating (Running) .................................... Error! Bookmark not defined.
Figure 3. 44: Voltage Rating of Regulated Output of the Generator ....... Error! Bookmark not defined.
Figure 3. 45: Current Rating of Regulated Output of the Generator ....... Error! Bookmark not defined.
Figure 3. 46: Charging Circuit ....................................................................................................... 125
Figure 3. 47: Triboelectric Generator ............................................................................................. 125
Figure 3. 48:Piezoelectric Generator .............................................................................................. 126
Figure 3. 49: Actual Prototype ....................................................................................................... 126
Figure 3. 50: Testing Piezoelectric Generator using 10N Force as input ......................................... 127
Figure 3. 51: Testing Set-up for the Piezo-Triboelectric Generator using characterized inputs ........ 127
Figure 3. 52: Actual Testing Set-up for the Piezo-Triboelectric Generator ...................................... 128
Figure 3. 53: Waveform of the output AC voltage of Piezo-Triboelectric Generator ....................... 129
 LIST OF TABLES

Table 2. 1 The Triboelectric Series: TRIBOELECTRIC MATERIAL CHARGE ORDER................ 14

Table 3. 1: Design Considerations of the Hybrid Generator .............................................................. 37
Table 3. 2 Fundamental Equations and Piezoelectric Coefficients .................................................... 42
Table 3. 3: Piezoelectric Rating ( F = 10 N) .......................................... Error! Bookmark not defined.
Table 3. 4: Piezoelectric Rating (F = 20 N) ........................................... Error! Bookmark not defined.
Table 3. 5: Piezoelectric Rating (F = 30 N) ........................................... Error! Bookmark not defined.
Table 3. 6: Piezoelectric Voltage Rating Comparison ............................ Error! Bookmark not defined.
Table 3. 7: Piezoelectric Current Rating Comparison ............................ Error! Bookmark not defined.
Table 3. 8: Triboelectric Rating (F = 10 N) .......................................... Error! Bookmark not defined.
Table 3. 9:Triboelectric Rating (F = 20 N) ............................................ Error! Bookmark not defined.
Table 3. 10: Triboelectric Rating (F = 30 N) ......................................... Error! Bookmark not defined.
Table 3. 11Triboelectric Voltage Rating Comparison ........................... Error! Bookmark not defined.
Table 3. 12: Triboelectric Current Rating Comparison .......................... Error! Bookmark not defined.
Table 3. 13: Hybrid Rating (F = 10 N) .................................................. Error! Bookmark not defined.
Table 3. 14: Hybrid Rating (F = 20 N) .................................................. Error! Bookmark not defined.
Table 3. 15: Hybrid Rating (F = 30 N) .................................................. Error! Bookmark not defined.
Table 3. 16: Hybrid Voltage Rating Comparison ................................... Error! Bookmark not defined.
Table 3. 17: Hybrid Current Rating Comparison ................................... Error! Bookmark not defined.
Table 3. 18: Piezoelectric Rating (Walking) .......................................... Error! Bookmark not defined.
Table 3. 19: Triboelectric Rating (Walking) .......................................... Error! Bookmark not defined.
Table 3. 20: Hybrid Rating (Walking) .................................................. Error! Bookmark not defined.
Table 3. 21: Piezoelectric Rating (Running) .......................................... Error! Bookmark not defined.
Table 3. 22: Triboelectric Rating (Running) .......................................... Error! Bookmark not defined.
Table 3. 23: Hybrid Rating (Running) ................................................... Error! Bookmark not defined.
Table 3. 24: Rating of Regulated Output of the Generator ..................... Error! Bookmark not defined.
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