Piezoelectric Generator PDF
Piezoelectric Generator PDF
By
Dissertation submitted
MAY20ll
31750 Tronoh
PIEZOELECTRIC GENERATOR
By
Approved:
Project Supervisor
Tronoh, Perak
May201l
ii
CERTIFICATION OF ORIGINALITY
This is to certizy that I am responsible for the work submitted in this project, that
the original work is my own except as specified in the references and
acknowledgements, and that the original work contained herein have not been
undertaken or done by unspecified sources or persons.
JK_·
(MOHO EZZUAN BIN AHMAD)
iii
ABSTRACT
iv
ACKNOWLEDGEMENT
First of all I would like to express my gratitude to god for giving me the
strength and health to complete this project. Not forgotten to my parents and all
my family members for providing everything such as money and advises, which
are most needed in this project. I would like to thank to my supervisor, Dr
Nursyarizal for sharing his knowledge and giving me the support and guidance
throughout this project. I would also like to thank to Dr Haris, who is my co-
supervisor in this project for helping me in doing this project. I believe, without he
help of them, I could not finish this project within the given time. My
appreciation to UTP especially Electrical and Electronic Engineering department ,
by providing me the necessary assets and resources, not least, i offer my regards
to those who support me especially all my friends and lab technicians for
contributing their assistance and ideas for this project.
v
TABLE OF CONTENS
CERTIFICATION OF APPROVAL. . ii
ABSTRACT. iv
ACKNOWLEDGEMENT. v
LIST OF FIGURES. ix
LIST OF TABLES. xi
INTRODUCTION. 1-3
1.3 Objective • 2
2.0 Introduction. 4
METHODOLOGY. 11-13
vi
3.1.2 Phase 2••. II
3.1.4 Phase 4 .• 12
4.3.2 Experiment 3. . 31
5.I Conclusion. 34
5.2 Recomendations.. 35
vii
REFERENCES.. 36-37
APPENDIXES. . 38-39
viii
LIST OF FIGURES
Figure 11 : The prototype With the FUll Wave Bridge Rectifier Circuit. .19
ix
Figure 21: Voltage Vs Time .. .29
X
LIST OF TABLES
xi
CHAPTER!
INTRODUCTION
1
1.2 Problem Statement
Nowadays, in a rapid growth world, there are more fuel and gas burning in
order to produce electricity. This is due to the increasing numbers of electrical
appliances around the world. These non-renewable energy sources are decreasing
rapidly and the world needs other alternatives energy sources. The piezoelectric is
one of alternatives energy sources. This energy can be generated from any sources
of vibration. One of the source of vibration is motorcycle. Every motorcycle
always produce vibration on the road. This vibration is actually a kind of energy
which we called as motion energy. So, instead of losing this energy for nothing,
this energy actually can be converted to an electrical energy using the
piezoelectric components. The piezoelectric energy has been used to generate
simple electricity to power microelectronic device such as mosfet and power
electronics equipments. However, the piezoelectric is not being used for any
vehicles yet. Due to small voltage produced, the piezoelectric only be used for
small applications only. This project will research on the power produced by the
piezoelectric effect and develop an application that can be used to transfer the
vibration from motorcycle to electrical energy.
1.3 Objective
2
1.4 Scope of Study
This project required study from two aspects. First is to study the
characteristics, concept and the effect of the piezoelectric. The behaviour of the
voltage and current produced by the piezoelectric element will be emphasize in
this project. Next, is to measure the sensivity of the piezoelectric element. This
measurement will analyse the piezoelectric element weather the vibration from a
motorcycle is enough to cause the piezoelectric to produce voltage and current.
Both of this study then will be combined to produce a piezogenerator.
3
CHAPTER2
LITERATURE REVIEW
2.0 Introduction
D=eE (1)
S = sT (2)
4
Where S is strain, s is compliance artd T is stress. These equations may be
combined into so-called coupled equations, of which the strain-charge form is:
Where [d] is the matrix for the direct piezoelectric effect and [dt] is the
matrix for the converse piezoelectric effect. The superscript E indicates a zero, or
constant, electric field; the superscript T indicates a zero, or constant, stress field;
and the superscript t stands for transposition of a matrix.
The strain-charge for a material of the 4mm (C4v) crystal class (such as a
poled piezoelectric ceramic such as tetragonal PZT or BaTi03) as well as the
6mm crystal class may also be written as (ANSI IEEE 176):
•
•sil sf1 sfl 0 0 0 0
c
::1s,s, sf, sf:
(;:lr• .,. (:o '~~~") (!;)
SE 0 0 0
= ~J. ~t. "'
£i~ c 0 0 T, . 0 0
(5)
) 0 0 s£. 0 0 d:-4
s, I ) 0 0 0 s~ 0 Ts d 15 0 0 -
,; \ J u {) c u si6 =l1~sf1 - .sfz) '·T~:~-' 0 0 o·
(\ cD"
n;)
'= 0
du
0
0
d:n
0
0
dsg 0
0
d-;14
d,
0
0 ~(f}cr
0
E:;;::
0
I)
0
~ia/
)('1
E I
2
.EjJ
(6)
where the first equation represents the relationship for the converse
piezoelectric effect and the latter for the direct piezoelectric effect.
5
In total, there are 4 piezoelectric coefficients, dij, eij, g~j, and hij defmed as
follows:
d E T (7)
"=
L)
(8Dt.)
8T·
= (8Di)
aT·
J J
, t )E=- (iJ'l'·
e£). . = (iJU· _l )s {8)
8Sj 8Ej
, )E _
g .. __ {8Ei (8St.)·T (9)
•1 I ar- aD
' J ].
(10)
h··= -(8Et)1J =- (8Tt_)s
L] 8S · 8D ·
' J J
Where the first set of 4 terms correspond to the direct piezoelectric effect
and the second set of 4 terms corresponds to the converse piezoelectric effect [3].
Basically, the piezoelectric effucts exist in two ways, which are the first
one is the direct piezoelectric effect and the other one is the reverse effect. The
direct effect describes the material's ability to transform mechanical strain into
electrical charge. This direct effect can be used as a sensor. Meanwhile, the
reverse effect is the ability of the material to convert an applied electrical potential
into mechanical strain energy. The application of the reverse effect is an actuator.
Figure 1 shows a piezoelectric disk generates voltage when deformed.
6
Figure I : A piezoelectric disk generates a voltage when deformed (change in
shape is greatly exaggerated) [4]
The type of energy harvesting in this project is using the vibration source.
The vibration source can be found at any movement and this project will take the
source of vibration from the motorcycle. A motorcycle produces a constant level
of vibration and therefore it can be used to convert to electrical energy using the
piezoelectric element. The conversion will start from a mechanical energy source,
which is motorcycle. The motorcycle vibrations will be converted into electricity
through piezoelectric element. Then, the electricity produced will be converted
before supplying a storage system or the load. The piezoelectric has been used in
many wide applications.
7
Figure 2: Energy Generating Floor System [6]
Electncal t unent On
8
2.3 Motorcycle Vibration
A study about motorcycle vibration has been made through around the
world. The main objective of this study is to analyze the hazard that result from
this vibration. Motorcycle vibration was studied to evaluate riding comfort and
safety in terms of handling and stability. Since this project is about to harvest
energy from motorcycle vibration, so it is very crucial to know how strong the
vibration produced by the motorcycle. A research done by Motormu Y okomori,
Takeo Nakagawa and Tadao Matsumoto show that motorcycle actually has many
sources of vibrations [10]. the study stated that motorcylce vibrations are coming
from the motorcycle itself; posture of the hands and arms during the gripping of
the handlebars, the surrounding environment, and the period of time during which
the motorcycle is ridden.
This study also stated that the vibration of the handlebars is caused by the
engine vibration, the roughness of the road, and the vibration of the frame and the
chasis. This shows that there ar~e actually many sources that cause the motorcycle
vibration. Thus, there are a bright future that these vibrations can actually produce
enough to give the piezoelectric works.
9
2.4 Vibration to Electrical Energy Conversion
10
CHAPTER3
METHODOLOGY
There are four phases involved in this project. Ea.:;h one of the phase will
be achieved step by step.
3.1.1 Phase I
This is the first stage of this project which is to identify the piezoelectric
concept. The action to be taken in this stage is to do a deep research on how the
piezoelectric works. A part from that, the situational analysis is essential to do in
order to identify the piezoelectric concept.
3.1.2 Phase 2
The second stage in this project is to identify the measurement criteria for
evaluating the produce current and voltage by the piezoelectric element. At this
stage, a thorough search will be made via internet and from the library to collect
all available information on the measuring knowledge. The collections of the
technical report regarding the subject matter in the world are essential in order to
identifY the common criteria on measuring the current and voltage. The major
deliverable for this stage is the criteria on measuring the produced current and
voltage from the piezoelectric element. A part from that, the formula of
converting from the vibration to current and voltage will be achieved at this stage.
11
3.1.3 Phase 3
3.1.4 Phase 4
The final stage for this project is the implementation and user testing on
the system. This system is test in the lab. Figure 4 shows the full phases in this
project.
Phase 1:
12
3.2 Identification of Appropriate Hardware and Software
Table I and Table 2 show the list of suitable hardware, tools and software
that are being used in this project.
Material Description
·~··--·" --· - -·· -·-
Piezoelectric Bi- Crystal element that generates voltage when being stress or
Morph Sensor strain (vibration)
Part Software
Diawiiig AiitoCAD
13
3.3 Construct the Base ofthe Generator
This project is using aluminium plate to make the permanent flat surface.
This is the base structure of the piezoelectric generator. Aluminium is used
because it has a solid structure. So that, it can transfer the vibration more to the
piezoelectric elements. Cutting machine is used to cut the aluminium plate to the
desired dimension. Figure 5 illustrates the dimension.
!~
lOcm
~~I
Figure 5 : Aluminium Dimension
Basically, the beam that is used as the cantilever is using the Zinc plate.
The Zinc has lower elastic modulus value that makes it less stiff than other metals
materials. Thus, it can produce more vibration. The piezoelectric element will be
glued using epoxy on the beam. Figure 6 shows how it is glued.
14
~r==::;;;;:=:::;;::;;:::;:;;:;:;:;=:;:;Dfll I Piezoelectric element
Zinc
ACin
Battery
15
3.5.2 Booster CitCilit
:::~/,:r:-. ~M.1~~v~
:"T!=\To·
R2.
R1. ll09k
6801< ""TEXT>-
J2 2IEXT>- J1
C1
· 100uF
MAX1724EZK50 · <TEXT->
!)Q9st oo~~r IC
R3.
40,2k-
4EX-T>
16
CHAPTER4
In order to test the piezoeleactric element, a work bench has been designed
which can be used to check the behaviour of the voltage and current produced by
this element. Actually, the work bench is almost the same with the prototype. The
only different is that the work bench has many different cantilever beams, so that
they can be tested using various experiment. This work bench is made for analyze
on how much exactly the voltage can be produced by a certain level of vibration.
This experiment is very crucial for this project because it will justizy wether the
vibration from the motorcylce can be used to make the piezo element to generate
electricity or not.
The piezo element used for this experiment is the Piezoelectric Bi-Morph
type. The testing tool is made up from zinc, aluminium, bolts and nuts. Basically,
the zinc is used as the beam which the piezo will be placed on it, and the
aluminium is used as the base for beam. There are several conditons that lead the
chosen of zinc as the beam. The zinc has lower Elastic Modulus than the
aluminium. The Elastic Modulus describes the mathematical description of an
object subrtances's tendency to be deformed elastically when a force is applied to
it [12]. According to the Static Properties of Materials under Standard Conditions
(approximately 20), the elastic modulus for aluminium is 72( 10) N/m meanwhile
forthezincis 13.1(10)N/m [13].
There is a huge difference between the value. The higher the elastic
modulus value, the stiffer the material. So that, by this condition, the zinc will be
used as the beam, as it will be more sensitive to any kind of vibration and it is
easy to capture the vibration. Figure 9 shows the work bench of the piezo
generator.
17
Springhead
Piezoelectric
Nail
Zinc Beam
Aluminium
1 J
Box
.--A-Iu_m_i-ni_u_m----,1/
The piezo element is glued on the beam and the beam will be placed on the
aluminium box. The position of the beam and piezo element will be at 20 percent
from the aluminium box. This is to ensure that when the beam start to oscillate,
the piezo element will get easy to be bend. Next, the whole thing is placed on a
piece of zinc surface. This zinc will be the medium for the vibration source to
move. As a de motor will be placed soon on this surface, it will generate a
vibration and hence the surface will receive the vibration and transfered to the
work bench. This work bench will be used for the experiment in order to
determine how much voltage and currrent actually this piezoelectric element can
produce due to vibration.
18
4.2 Prototype and Circuit Fabrication
The prototype has been designed using autoCAD software. The prototype
is designed so that it can be put on motorcycle handlebar and anywhere that has
vibration source. Below are the figures of the prototype and the circuit used.
Figure 10 shows the piezoelectric element with the base and the cantilever
beam. While in Figure 1 I, shows the piezoelectric element connected with the full
wave bridge rectifier circuit.
Figure 11 : The prototype with the Full Wave Bridge Rectifier Circuit
19
ln Figure 12, shows the full wave rectifier circuit, which consists of
Schottky 4 diodes, a 1kO resistor and 1J.lF capacitor. In Figure 13 shows the
output from the rectifier circuit connected with the battery and then to the booster
circuit.
20
Figure 14 shows the battery is connected with the circuit booster, while in
Figure 15 shows the full prototype with the full circuit.
21
4.2 Results of Experiment
The work bench is then tested using Pasco Data Studio Software. This
software can be used to tested voltage and current, and frequency for this work
bench. The motor used for the experiment is a DC motor which will cause
vibration to the work bench when it turn on. As for the result, an AC voltage and
current are produced. Three different experiments are conducted in this stage,
which are the first one using DC motor as the source of vibration, the second
experiment is using manual vibration, and the third experiment will be using with
the full circuit of converter and booster to test the prototype. The voltage
produced is the RMS voltage. In all three experiments, there are two piezoelectric
element that has been tested with series connection.
For the first experiment, a DC motor is used for the source of vibration. A
12V DC motor with 50 Hz of frequency has been tested for this experiment. This
experiment only use 2 piezoelectric elements to be tested. This is to determine
how much actually the voltage and current can be produced with vibration. The
frequency of the vibration in this experiment is around 32 Hz. The result of this
experiment is tabulated in Table 3. For the sake of analysis, the tabulated data in
Table 3 is converted in graph figure as shown in Figure 16 and Figure 17.
22
0;8 0.2462 0;8 0.00000347
0.9 -2.8358 0.9 -0.00000494
1.0 0.2734 I 0.00000525
1.1 1.7435 1.1 0.00000488
1.2 2.2397 1.2 0.00000494
1.3 0.1634 1.3 0.00000494
1.4 -2.371 1.4 -0.00000513
1.5 -0.2995 1.5 -0.00000494
1.6 2.1458 1.6 0.00000482
1.7 0.2362 1.7 0.00000482
!.8 -2.8558 1.8 -0.00000488
1.9 0.2704 1.9 0.00000482
2.0 1.7335 2 0.00000161
2.1 2.2297 2.1 0.00000447
2.2 0.1654 2.2 0.00000488
2.3 -2.471 2.3 -0.00000574
2.4 -0.2985 2.4 -0.00000813
2.5 2.1458 2.5 0.00000387
2.6 0.2362 2.6 0.00000456
2.7 -2.8358 2;7 -0;00000635
2.8 0.2704 2.8 0.00000484
2.9 1.7335 2.9 0.00000399
3.0 2.3297 3 0.00000511
3.1 0.1654 3.1 0.00000171
3.2 -2.471 3.2 -0.00000446
3.3 -0.2985 3.3 -0.00000418
3.4 2.1358 3.4 0.00000165
3.5 0.2362 3.5 0.00000551
3.6 -2.8457 3.6 -0.00000846
3.7 0.2704 3.7 0.00000177
3.8 1.7335 3.8 0.00000251
3.9 2.2'297 3.9 0.00000304
4.0 0.1654 4 0.00000415
4.1 -2.471 4.1 -0.00000476
4.2 -0.2985 4.2 -0.00000584
4.3 2.1358 4.3 0.00000599
4.4 0.2362 4.4 0.00000655
. ·- ___
4.5 .. - ----- -··-·
:z:s458
,
. '4.5 . -=llJTOUOU53T
4.6 0.2704 4.6 0.00000244
23
Volt~ge vs Time
3
Voltage IV)
2
1
0 Time (Sec)
-1 0 2 3 5
-2
-3
-4 -Voltage
r----------·-----------------------~-------------~-----------·-------------------·----,
i! Current (A)
current Vs Time I
1 0.00001
0.000008
0.000006
0.000004
0.000002
0
-0.00000 2 3 . --5 Time (Sec)
-0.00000
-0.00000 --Current (A)
I -0.00000
L-o.oooo1
24
4.2.2 Manual Vibration Experiment
25
12;7 03638 123 0.00000634
12.8 -1.2336 12.8 -0.00000483
12.9 1.4972 12.9 0.00000398
13 -0.6775 13 -0.00000522
13.1 0.2411 13.1 0.00000176
13.2 -3.44!9 13.2 -0.00000435
13.3 0.9265 13.3 0.00000419
13.4 -0.7477 13.4 -0.00000165
13.5 4.3214 13.5 0.00000551
13.6 0.2094 13.6 0.00000876
13.7 -1.8201 13.7 -0.00000156
13.8 0.0385 13.8 0.00000251
13.9 2.2761 13.9 0.00000355
14 -2.3536 14 -0.00000478
14.1 1.8616 14.1 0.00000444
14.2 0.4718 14.2 0.00000567
14.3 -0.0897 14.3 -0.00000588
14.4 0.2258 14.4 0.00000644
14.5 -0.2063 14.5 -0.00000563
14.6 0.4407 14.6 0.00000223
26
Voltage (V)
4
2
0
-2 0 2 4 6 8 16 -Voltage(V)
-4 Time (sec)
-6
-8
-10
-12
27
4.2. 3 DC Motor and Prototype experiment
This is the final experiment that determine the full result of this portable
piezoelectric generator. In this experiment, the full prototype, will be tested on a
de motor at frequency of 32 Hz. Figure 20 shows of how this piezoelectric
generator actually produce electricity in this experiment.
DC Motor Produce
vibr~ti()n v.-hE!n moving,
Jl
The vibration will vibrate
the piezoelectric
generator.
J.l
When vibrate, the
ph~zseleGtriG Will Greate
voltage and current.
J.l
Electricity produced and
will be fed on a charging
circuit.
·- --
:cr~
~·
J__L
When fully charged, the
energy will be usei:l to
charge handphone.
28
In this experiment, an empty ot discharged capacitor is used to be charged.
This capacitor actually represent the battery and will determine the whether the
voltage and current produced is enough to charge capacitor or not. Figures 21 and
22 below show the result of the graph obtained from this experiment. Due to long
data, the table will not be included in this report.
2.00[+00
L50E·t00
I
LOOE+OO -
_ ,. .,.", I
5.00E-01
0.00[+00
0 20 40 60 80 100
-S.OOE-01
I
Figure 21: Voltage Vs Time
~----------~urr~~~ ~s Time
I 0.000003 -- - · -· - --
1 0.0000025 -- -
I o.ooooo2 -:--
1 0.0000015 -
I o.ooooo1
1 o.oooooo5
-Current (A)
I o
0 40 60 80 100
-SE-07
I I
29
4.3 Discussion
From experiments 1 and 2, the voltage produced is quite high. Using the
DC motor, the voltage produced is approximately at constant 2 V. This value is
actually the value of two piezoelectric elements which means that 2 V is the value
of total voltage when the piezoelectric is put in series connection. Indeed, this
voltage can go more higher than that because from the manual experiment, the
voltage can reach until 10 V. It shows that the voltage produced is basically
depends on how much the piezo element can vibrate. The more vibration it gets,
the higher the voltage can produce. The target for this project is to ensure that the
voltage 11nd current produced can be used directly to charge at least a cellular
phone. For that purpose, the required voltage and current needed is 5V at I OOmA.
As for the current, from both experiments, the value of the current is very
low. The value of the current can be said vary from 0.000001 A until 0.000008 A.
This is equal to 1!!A until 811A. This value is too low for any direct applications.
This is because of the piezoelectric does not produce high current Due to the very
low current is the reason why it still cannot be used to generate a large scale of
electricity such as solar and hydro. So, the current produced is not enough to
charge a cellular phone. Theoretically, to charge a cellular phone, the current
required is at least around 100 rnA. From both experiments, it can be concluded
that the piezoelectric do produce high voltage but very low current value. Thus,
the piezoelectric cannot be directly used to charge a cellular phone without any
external circuit. Due to this situation, the generator will be used to store energy
first. This is demonstrated by charging a capacitor.
30
4.3.2 Experiment 3
As for the third experiment, which is using the prototype and the full
circuit, it can be seen that the graph produced is actually in charging mode. When
the piezoelectric starts to vibrate, the voltage produce is ar.ound 2.2 V. But when it
pass through the rectifier circuit, there is voltage drop occur. This is because the
the diodes actually have internal resistance, and thus have voltage drop. When
measured at the bridge output, the reading is around 0.74 V. But at the input, the
reading is 2.1 V. When the value from the input minus the value from the output,
it gives 1.36 V. This 1.36 Vis actually the voltage drop in the circuit. So that 0.74
V is the l!(:rual O\ltp\lt valm: from the bridge circuit. As for the C\lrrent, the vallle is
still the same, which is around 4uA. Then when it pass through the capacitor of 11!
Farad, the graph produce a charging graph. This shown that the voltage and the
current produced is actually enough to charge the battery.
From the graph, the graph is increased and when the capacitor has been
fully charged, the graph will decrease because it will discharge. The process of
charge and discharge is so fast because the value of the capacitance used is small,
which is l!!F. When lower value of capacitance is used, it will charge and
discharge very fast, because it cannot hold the charge for longer time. The reason
for using lower value of capacitance is because to prove that the voltage and
current produced is enough to charge the capacitor. Bigger capacitor value such as
1 Farad can be used iii this experiment, but it requites longer time to show the
charging graph. Because when the capacitor is bigger, the time taken to charge the
capacitor become longer and thus the graph obtained will be slow.
31
4.3.3 Justification ofResult
From all experiments, it can be seen that the current produced is not
enough to directly charge a cellular phone. This is because the current is too small
and not sufficent, even to light up a single LED. Because of this situation, the
current and voltage produced will be stored first in a battery. This is done by
looking at the third experiment, the values are enough to at least charge a
capacitor. The graph in experiment 3 shows that the voltage and current actually
has charged the capacitor, although it is not charging consistently due to the
inconsistent of vibration. The charging time will depend on the value of the
current supply. The bigger the value of the current, the faster it will charge and
thus will result in less time to charge. Meanwhile, if the current is very smail, then
it takes longer time to charge. The energy stored in the capacitor will then be used
to charge acellular phone or other electronic devies. The average output from the
piezogenerator is given below:
P=IV (11)
Where P is the power, I is the current and V is the voltage. Taking average
voltage of0.74V and 5uA, substitute in the above equation gives:
P = 5uA x 0.74V
= 3.7uW
Based on this result, the power will be stored first in a battery, and then the
battery will be used for other purposes. As for the efficiency is calculated below:
(12)
=24.67%
32
The result of efficiency is very low and can be considered as not efficient
enough. There are several factors that cause the low performance of this
piezoelectric generator. The first one is because the it produce large voltage but
with an extremely low current. When current low, it will affect the performance of
the generator. Another reason is because the power is dissipated by electronic
devices such as diodes, which will resulting in lower efficiency. From overal
experiment, it can be said that the generator is able to charge the capacitor.
33
CHAPTERS
5.1 Conclusion
34
5.2 Recommendations
35
REFERENCES
<http://www.spiritus-temporis.com/piezoelectricity/applications.html>
<http://en.wikipedia.org/wiki/Piezoelectricity>
<http://en. wikipedia.org/wiki/Piezoelectricity>
[4] Piezoelectricity
<http://en. wikipedia.org!wiki!Piezoelectricity>
[5] Jorge Chapa, 2008, Energy Generating Floors to Power Tokyo Subways
<http://www.inhabitat.com/2008/12/ll/tokyo-subway-stations-get-
piezoelectric-floors/>
<http://envirothink.wordpress.com/2008/12/12/human-energy-powers-
japanese-subway-stationf>
<http://www.spiritus-temporis.com/piezoelectricity/applications.htrnl>
<http://www.spiritus-temporis.com/piezoelectricity/applications.html>
36
[9 ] Ingo Kuehne, Alexander Frey, Djordje Marinkovic, Gerald Eckstein and
Helmut Seidel, 7 March 2007, Power MEMS- A Capacitive Vibration to
Electrical Energy Converter With Built-in Voltage.
<http://www.sciencedirect.com >
<http://en.wikipedia.org/wiki/Elastic_modulus>
37
APPENDIX
38
Gantt Chart For FYP 2
2 Testing.the circuit .·
'
3 Analysis ~
...a:
! .
ID
4 Submission of Progress Report a:
ti...
' 5 Submission of Draft Report .
' ...
:~:
. Ill
..
9
6 Submission of Technical Paper :i:
8 VIVA
!
D' Process
39