efficiency analysis of wireless power transmission system using magnetic resonant coupling

Efficiency analysis of wireless power transmission system using magnetic resonant coupling

A SubmittedBy

1. Rashid, Md. Rezwanur ID: 11-19510-32. Hussain, Md. Muzammel ID: 11-19546-33. Newaz, Alvi ID: 11-19558-34. Un-Noor, Mirza Md. Ragib ID: 11-19720-3

Under the Supervision of

Shuvra Saha

FacultyChoose a item.American International University - Bangladesh

Department ofElectrical and Electronic Engineering

Faculty of Engineering

Semester , December, 2014

American International University - Bangladesh

Efficiency analysis of wireless power transmission system using magnetic resonant coupling

submitted to the Electrical and Electronic Engineering Department of the Engineering Faculty,

American International University - Bangladesh (AIUB) in partial fulfillment of the requirements for the

degree of Bachelor of Science in Electrical and Electronic Engineering.

1. Rashid, Md. Rezwanur ID: 11-19510-32. Hussain, Md. Muzammel ID: 11-19546-33. Newaz, Alvi ID: 11-19558-34. Un-Noor, Mirza Md. Ragib ID: 11-19720-3

A

Department ofElectrical and Electronic Engineering

Faculty of Engineering

Semester ,

December, 2014

American International University - Bangladesh

DECLARATION

This is to certify that this is our original work. No part of this work has been submitted elsewhere partially or fully for the award of any other degree or diploma. Any material reproduced in this project has been properly acknowledged.

Students’ names & Signatures

1. Rashid, Md. Rezwanur

_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

2. Hussain, Md. Muzammel

_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

3. Newaz, Alvi

_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

4.

_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _

© Faculty of Engineering, American International University-Bangladesh (AIUB) i

APPROVAL

The Thesis titled “

” has been submitted to the following respected

members of the Board of Examiners of the Faculty of Engineering in partial fulfillment of the

requirements for the degree of of Electrical and Electronic Engineering on by the

following students and has been accepted as satisfactory.

1. Rashid, Md. Rezwanur ID: 11-19510-3

2. Hussain, Md. Muzammel ID: 11-19546-3

3. Newaz, Alvi ID: 11-19558-3

4. Un-Noor, Mirza Md. Ragib ID: 11-19720-3

_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ SupervisorShuvraSahaFacultyChoose Faculty DesignationFaculty of EngineeringAmerican International University-Bangladesh

_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ Prof. Dr. ABM Siddique HossainDeanChoose Faculty DesignationFaculty of Engineering

American International University-Bangladesh _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ External SupervisorAbu Hena Md. ShatilFacultyChoose Faculty DesignationFaculty of EngineeringAmerican International University-Bangladesh

_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _Dr. Carmen Z. LamagnaVice Chancellor

© Faculty of Engineering, American International University-Bangladesh (AIUB) ii

American International University-Bangladesh

ACKNOWLEDGEMENT

We would like to thank a few people for their support and motivation that helped us to finish this thesis

successfully and in time.

We take this opportunity to express our profound gratitude and deep regard to our guide supervisor

Shuvra Saha, Faculty of Engineering, American International University–Bangladesh (AIUB) for this

exemplary guidance, monitoring and constant encouragement throughout the course of our work.All his

advice has been invaluable.

We would like to appreciate Dr. Carmen Z. Lamagna honorable Vice Chancellor, American International

University–Bangladesh (AIUB) for her outstanding efforts in improving the academic system of AIUB

and also like to thank Prof.Dr. ABM Siddique Hossain, Dean, of Engineering, American International

University –Bangladesh (AIUB).

We are grateful to our external supervisor Abu Hena Md. Shatil for kindly agreeing to examine our

project. His suggestions regarding the project were insightful.

We would like to thank our beloved friends Apon, Tanjim and Bappy who encouraged and supported us

throughout to produce a good thesis.

Lastly, we thank our parents, brothers, sisters for their constant encouragement without which this project

would not be possible.

© Faculty of Engineering, American International University-Bangladesh (AIUB) iii

1. Rashid, Md. Rezwanur

2. Hussain, Md. Muzammel

3. Newaz, Alvi

4. Un-Noor, Mirza Md.

Ragib

TABLE OF CONTENTS

DECLARATION........................................................................................................................................IAPPROVAL..............................................................................................................................................IIACKNOWLEDGEMENT........................................................................................................................IIILIST OF FIGURES...................................................................................................................................3LIST OF TABLES.....................................................................................................................................7ABSTRACT..............................................................................................................................................8

CHAPTER 1..................................................................................................................................................9

INTRODUCTION...........................................................................................................................................91.1. Introduction.................................................................................................................................91.2. Historical Background..............................................................................................................10

1.2.1. Earlier Research..................................................................................................................................101.2.2. Resent Research..................................................................................................................................111.2.3. State of the art technology..................................................................................................................14

1.3. Future Scope of This Study.......................................................................................................181.3.1. Future Scopes......................................................................................................................................181.3.2. Recommendations...............................................................................................................................19

1.4. Limitation of the Study.............................................................................................................191.5. Advantage over Traditional Method.........................................................................................191.6. Objective of this Work..............................................................................................................20

1.6.1. Primary objectives..............................................................................................................................201.6.2. Secondary Objectives.........................................................................................................................20

1.7. Introduction to this Thesis.........................................................................................................21

CHAPTER 2................................................................................................................................................22

THEORY AND EQUATIONS........................................................................................................................222.1. Introduction...............................................................................................................................222.2. Geometry of helical coil............................................................................................................22

2.2.1. Diameter..............................................................................................................................................23

2.3. Equivalent circuit parameters of helical coil.............................................................................242.3.1. Inductance of a helical coil.................................................................................................................252.3.2. AC resistance of a helical coil...........................................................................................................272.3.3. Capacitance of helical coil..................................................................................................................282.3.4. Mutual inductance between helical coils............................................................................................29

2.4. Flat Spiral Ring coil:.................................................................................................................292.5. Parallel two coil scheme...........................................................................................................31

2.5.1. Solving circuit.....................................................................................................................................32

2.6. Parallel three coil scheme.........................................................................................................342.7. Parallel four coil scheme...........................................................................................................36

CHAPTER 3................................................................................................................................................39

SIMULATION AND RESULT ANALYSIS......................................................................................................393.1. Introduction...............................................................................................................................39

© Faculty of Engineering, American International University-Bangladesh (AIUB) 1

3.2. Parallel Two Coil Circuit Model...................................................................................................403.2.1. MATLAB Code and Explanation.......................................................................................................41

3.2.1.1. MATLAB code for Helix...........................................................................................................413.2.1.2. MATLAB code for pancake.......................................................................................................443.2.1.3. Efficiency calculation.................................................................................................................45

3.2.2. MATLAB Simulated Results and Interpretation................................................................................473.2.2.1. For helical coil............................................................................................................................473.2.2.2. For pancake coil..........................................................................................................................51

3.2.3. COMSOL Simulations........................................................................................................................533.2.3.1. Two-Coil System Setup..............................................................................................................533.2.3.2. Two-Coil Simulation..................................................................................................................543.2.3.3. Design improvements I – Flat Spiral Coil System Setup...........................................................613.2.3.4. Design Improvements II-Flat Spiral Coil with resonator...........................................................72

3.2.4 Theoretical Power transmission at Radio-Frequency using 10pF capacitor.......................................83

3.3. Conclusion................................................................................................................................84

CHAPTER 4................................................................................................................................................85

PHYSICAL IMPLEMENTATION AND MEASURED DATA..............................................................................854.1. Introduction...............................................................................................................................854.2. Practical experiment setup........................................................................................................854.3. Helical Coil...............................................................................................................................86

4.3.1. Coil wound around cardboard core.....................................................................................................864.3.1.1. Measured data for 1 KΩ load resistor.........................................................................................874.3.1.1. Measured data for 10 KΩ load resistor.......................................................................................90

4.3.2. Coil wound around plastic PVC core.................................................................................................934.3.2.2. Measured data for 10 KΩ load resistor.......................................................................................964.3.2.3. Measured data for 1 KΩ load resistor.........................................................................................97

4.3.3. Flat Spiral Ring Coil...........................................................................................................................98

4.4. Conclusion..............................................................................................................................101

CHAPTER 5..............................................................................................................................................102

DISCUSSIONS AND CONCLUSIONS..........................................................................................................1025.1. Discussions..............................................................................................................................102

5.1.1. Comparison of Simulation Data with practical.................................................................................102

5.2. Suggestion for Future Work....................................................................................................1025.2.1. Consideration of high frequency components..................................................................................1035.2.2. Use of an E-class amplifier...............................................................................................................1035.2.3. Introducing different coil parameters into the practical implementation.........................................1035.2.4. Wireless power transmission at higher frequencies..........................................................................1035.2.5. Integration of Metamaterials.............................................................................................................1045.2.6. Use of larger coils.............................................................................................................................104

5.3. Conclusions.............................................................................................................................104

REFERENCES:.........................................................................................................................................105

APPENDIX............................................................................................................................................107


LIST OF FIGURES

FIG 1.1: THE WITRICITY PHYSICS RESEARCH GROUP [2].............................................................11

FIG 1.2: EFFICIENCY VS. DISTANCE GRAPH FOR POWER TRANSMITTED [2]..........................12

FIG 1.3: WIRELESSLY CHARGED DEVICES [7]..................................................................................14

FIG 1.4: ELECTRONIC DEVICES POWERED BY PROXI [7]..............................................................15

FIG 1.5: PROXI-POINT WIRELESS CONNECTOR [9]..........................................................................16

FIG 1.6: WIRELESSLY CHARGED CAR [7]..........................................................................................17

FIG 1.7: IDT WIRELESS POWER ICS [12].............................................................................................18

FIG 2.1(A): COIL GEOMETRY................................................................................................................22

FIG 2.2.1(A): COIL TOP VIEW [13].........................................................................................................23

FIG 2.3(A): EQUIVALENT CIRCUIT OF THE COIL.............................................................................24

FIG 2.3.1(A): DIAGRAM OF CURRENT SHEET INDUCTOR [13]......................................................25

FIG 2.4.1(A): GEOMETRY OF A PANCAKE COIL [20]........................................................................29

FIG 2.4.1(B): INDUCTANCE CALCULATION PARAMETER [21]......................................................30

FIG 2.4(A): BASIC BLOCK DIAGRAM OF TWO COIL SCHEME.......................................................31

FIG 2.4(B): EQUIVALENT CIRCUIT OF TWO COIL SCHEME...........................................................32

FIG 2.4.1(A): MESH ANALYSIS OF TWO COIL SCHEME..................................................................33

FIG 2.5(A): BASIC BLOCK DIAGRAM OF THREE COIL SCHEME...................................................34

FIG 2.5(B): EQUIVALENT CIRCUIT OF TWO COIL SCHEME...........................................................35

FIG 2.5(C): EQUIVALENT MESH ANALYSIS CIRCUIT OF THREE COIL SCHEME......................35


FIG. 2.6(A): BLOCK DIAGRAM OF FOUR COIL SCHEME.................................................................36

FIG 2.6(B): EQUIVALENT CIRCUIT FOUR COIL SCHEME...............................................................37

FIG 2.6(C): EQUIVALENT MESH ANALYSIS CIRCUIT OF FOUR COIL SCHEME........................37

FIG 3.1: EQUIVALENT CIRCUIT FOR WIRELESS POWER TRANSMISSION.................................40

FIG 3.2: MULTISIM REPRESENTATION OF THE BASIC MODEL....................................................40

FIG 3.3: EFFICIENCY VS. DISTANCE GRAPH FOR DIFFERENT NUMBER OF TURNS...............47

FIG 3.4: DISTANCE VS. EFFICIENCY FOR DIFFERENT DIAMETER..............................................49

FIG 3.5: DISTANCE VS. EFFICIENCY FOR DIFFERENT LOAD (ZL)...............................................50

FIG 3.6: DISTANCE VS. EFFICIENCY FOR DIFFERENT LOAD (PANCAKE).................................51

FIG 3.7: DISTANCE VS. EFFICIENCY FOR DIFFERENT TURNS AND DIAMETER.......................52

FIG 3.5: COIL CIRCUIT DIAGRAM........................................................................................................53

FIG 3.6 COIL GEOMETRY -3D VIEW....................................................................................................55

FIG 3.7: COIL GEOMETRY-TOP VIEW..................................................................................................55

FIG 3.8: POWER TRANSMISSION EFFICIENCY AT RESONANT FREQUENCY............................56

FIG 3.9(A): MAGNETIC FLUX DENSITY AT D=100 MM....................................................................57

FIG 3.9(B): MAGNETIC FLUX DENSITY AT D=140 MM....................................................................57

FIG 3.10(A): MAGNETIC FIELD AT D=100 MM...................................................................................58

FIG 3.10(B): MAGNETIC FIELD AT D=140 MM...................................................................................58

FIG 3.14: FLAT SPIRAL COIL.................................................................................................................61

FIG 3.15(A) 3D VIEW (B) TOP VIEW COIL GEOMETRY....................................................................63

FIG 3.16 POWER TRANSMISSION EFFICIENCY AT RESONANT FREQUENCY...........................64


FIG 3.17 (A) MAGNETIC FLUX DENSITY AT D=300 MM (B) TOP VIEW.......................................65

FIG 3.18 (A) MAGNETIC FLUX DENSITY AT D=400 MM (B)TOP VIEW........................................66

FIG 3.19 (A) MAGNETIC FIELD AT D=300 MM (B)TOP VIEW..........................................................67

FIG 3.20 (A) MAGNETIC FIELD AT D=400 MM (B)TOP VIEW..........................................................68

FIG 3.22 (A) ELECTRIC FIELD AT D=400 MM (B)TOP VIEW............................................................70

FIG 3.23 POWER TRANSMISSION EFFICIENCY AT DIFFERENT LOAD RESISTOR....................71

FIG 3.24: OVERALL EFFICIENCY..........................................................................................................71

FIG 3.25 EQUIVALENT CIRCUIT FOR 3 COIL DESIGN.....................................................................72

FIG 3.26 (A) COIL GEOMETRY (B) CLOSER LOOK AT THE RESONATOR AND THE RECEIVER

73

FIG 3.27 POWER TRANSMISSION EFFICIENCY AT RESONANT FREQUENCY...........................74



FIG 3.30 (A) MAGNETIC FIELD AT D=300 MM (B) TOP VIEW.........................................................77

FIG 3.31 (A) MAGNETIC FIELD AT D=400 MM (B) TOP VIEW.........................................................78

FIG 3.32 (A) ELECTRIC FIELD AT D=300 MM (B) TOP VIEW...........................................................79

FIG 3.33 (A) ELECTRIC FIELD AT D=300 MM (B) TOP VIEW..........................................................80

FIG 3.34 (A) POWER TRANSMISSION EFFICIENCY (B) OVERALL EFFICIENCY........................82

FIG 3.35 POWER TRANSMISSION AT 2.95 MHZ & 10PF EXTERNAL CAPACITOR.....................83

FIG 4.0: EXPERIMENTAL SETUP...........................................................................................................85

FIG 4.1: PARALLEL TWO COIL CIRCUIT MODEL.............................................................................86

FIG 4.2(A): OSCILLOSCOPE OUTPUT FOR 1KΩ LOAD RESISTOR.................................................88© Faculty of Engineering, American International University-Bangladesh (AIUB) 5

FIG 4.2(B): OSCILLOSCOPE OUTPUT FOR 1KΩ LOAD RESISTOR.................................................88

FIG 4.3: EFFICIENCY VS. DISTANCE CURVE FOR 1KΩ LOAD RESISTANCE..............................89

FIG 4.4(A): OSCILLOSCOPE OUTPUT FOR 10KΩ LOAD RESISTOR...............................................90

FIG 4.4(B): OSCILLOSCOPE OUTPUT FOR 10KΩ LOAD RESISTOR...............................................91

FIG 4.5: EFFICIENCY VS. DISTANCE CURVE FOR 10KΩ LOAD RESISTANCE............................92

FIG 4.6: PARALLEL TWO COIL CIRCUIT MODEL.............................................................................93

FIG 4.7(A): OUTPUT OBTAINED FROM HELICAL COIL WITH PVC PIPE AS CORE....................94

FIG 4.7(B): OUTPUT OBTAINED FROM HELICAL COIL WITH PVC PIPE AS CORE....................95

FIG 4.8: EFFICIENCY VS. DISTANCE CURVE FOR 10KΩ LOAD RESISTANCE............................96

FIG 4.9: EFFICIENCY VS. DISTANCE CURVE FOR 1KΩ LOAD RESISTANCE..............................97

FIG 4.10(A): FLAT SPIRAL RING DESIGN............................................................................................98

FIG 4.10(B): FLAT SPIRAL RING DESIGN............................................................................................99

FIG 4.11: EFFICIENCY VS. DISTANCE FOR FLAT SPIRAL COIL...................................................100

FIG 4.12: OSCILLOSCOPE OUTPUT FOR FLAT SPIRAL COIL.......................................................101


LIST OF TABLES

TABLE 2.1: PROXIMITY FACTOR Ψ.....................................................................................................28

TABLE 3.1: DATA FOR DISTANCE VS. EFFICIENCY (DIAMETER = 0.10066)...............................47

TABLE3.2: DISTANCE VS. EFFICIENCY FOR DIFFERENT DIAMETER.........................................49

TABLE 3.3: DISTANCE VS. EFFICIENCY FOR DIFFERENT LOAD (ZL)..........................................50

TABLE 3.4 DISTANCE VS. EFFICIENCY FOR DIFFERENT LOAD (PANCAKE)............................51

TABLE 3.5 DISTANCE VS EFFICIENCY FOR DIFFERENT TURNS AND DIAMETER..................52

TABLE 3.3: PARAMETERS USED IN COMSOL...................................................................................53

TABLE 3.4: PARAMETERS FOR 2-COIL FLAT SPIRAL DESIGN......................................................62

TABLE 3.5: PARAMETERS FOR 3 COIL...............................................................................................72

TABLE 4.1: MEASURED VALUES FOR 1 KΩ RESISTOR...................................................................89

TABLE 4.2: MEASURED VALUES FOR 10 KΩ RESISTOR.................................................................91

TABLE 4.3: MEASURED VALUES FOR 10 KΩ RESISTOR.................................................................96

TABLE 4.4: MEASURED VALUES FOR 1 KΩ RESISTOR...................................................................97

TABLE 4.5: MEASUREMENT FOR FLAT SPIRAL COIL...................................................................100


ABSTRACT

The main goal of our research was to see the effect distance has on the efficiency of a medium range (few

meters) wireless power transmission system and to suitably vary these different parameters and the

structure of the coil in order to maximize efficiency. Our main area of focus was Magnetic Resonant

Coupling. The research was undertaken on the efficiency of parallel circuit models for two coil resonant

magnetic coupled circuits. In order to improve the efficiency of the system we integrated three coil system

and flat spiral coils into the circuit. Our work has been done mainly with MULTISIM, MATLAB and

COMSOL. Since our work was mainly dedicated to improving the efficiency of the system, we have

varied the coil parameters to see its effect on efficiency. We have also varied the coupling coefficient and

plotted it against distance to show its variation with distance. All the circuits were designed using

MULTISIM. We practically implemented the two coil system using a variation of two different types of

helical coils- one with a cardboard core and another with a core made of PVC, and also implemented the

flat spiral coil structure. The main aim of the experimental setup was to ensure that the practical data

matched the trend set by the theoretical data obtained from our simulation software. We hope our designs

of the system can help in the practical implementation of the system in the future and make it more viable

for use in everyday life.


Chapter 1

Introduction

1.1.Introduction

The benefit of a wireless power transmission system is obvious; it can transmit power over varying

distances without the need of wires. Removing the cable between a power source and a load is very

important in many applications; e.g. for a plug-in hybrid vehicle or for a plug-in electric vehicle battery

charger [1]. In the early 20th century, Nikola Tesla made huge strides in schemes towards transporting

power wirelessly. However, typical embodiments (e.g., Tesla coils) involved undesirably large electric

fields [2]. With the emergence of autonomous devices (laptops, cell phones, robots etc.) over the last

decade, wireless power has reemerged as a very important and a much required medium of power

transmission. It enables new applications of implantable devices in several different fields including

military, medicine and more, where power sometimes is needed to be transmitted without the need of

wires. It also prevents the loss of energy while transmission and during distribution. [3] Much of this

power is wasted during transmission from power plant generators to the consumer. The resistance of the

wire used in the electrical grid distribution system causes a loss of 26-30% of the energy generated. This

loss implies that our present system of electrical distribution is only 70-74% efficient. The main reason for

power loss during transmission and distribution is the resistance of wires used for grid. The efficiency of

power transmission can be improved to certain level by using high strength composite over head

conductors and underground cables that use high temperature super conductor but, the transmission is still

inefficient. We have to think of alternate state-of-art technologies to transmit and distribute the electricity

and wireless power transmission one such method.

[4]The action of an electrical transformer is the simplest instance of wireless energy transfer. The primary

and secondary circuits of a transformer are electrically isolated from each other. The transfer of energy

takes place by electromagnetic coupling through a process known as mutual induction.

Power can wirelessly be transmitted in many different methods such as resonant induction coupling,

magnetic resonant coupling, using microwaves etc. While all of them do result in power transmission,

inductive coupling can only be used to transmit power over very short distances and hence is not always

suitable for use. So the range of the device is small and hence unsuitable. Also, the system becomes more

inefficient as the distance between source and load increases. While microwaves can also be used to


transmit power over medium and long range distance, its ill effects on human health are a major source of

concern and the diameter of the antennae needs to be in the order of kilometers. Solar power satellites

(SPS) are one way of transmitting power wirelessly over long distances. Another problem with

transmitting power using lasers and microwaves is that power needs to be transmitted along a line of sight.

So any blockade will prevent transmission of power.

Power is transmitted along three different ranges of distance-short range, medium range and long range.

Short range is considered to be a few centimeters and transmitting power wirelessly in this range is an

inefficient and expensive method. Medium range can be considered up to a few meters and is a suitable

distance to transmit power wirelessly. Long range is considered in the range of kilometers.

The area of research of this paper is magnetic resonant coupling and it is a fairly efficient system and can

be used to transmit power to distances in the range of meters (medium range). In this paper we have

researched upon the series and parallel circuit models for wireless power transmission and tried to derive

an equation containing only the circuit parameters and the distance of power transmission. We have

integrated split ring resonators into the basic model of our circuit to make the system more efficient.

1.2.Historical Background

1.2.1. Earlier Research

[5] Wireless power transfer [WPT] was established with the pioneering work on electromagnetism

by the 19th century physicists, who showed that an alternating current produces a magnetic field

and vice versa. Nikola Tesla made significant and well ahead of the time contributions to wireless

power transfer in the late 19th century and at the early 20th century. He has demonstrated a

successful WPT system that powered electronic devices [5].

Nicola Tesla proposed theories of wireless power transmission in the late 1800s and early 1900s.

One of his more spectacular displays involved remotely powering lights in the ground at his

Colorado Springs experiment station by transmitting 100 million volts of high-frequency electric

power wirelessly over a distance of 26 miles at which he lit up a bank of 200 light bulbs and ran

one electric motor. Tesla claimed that only 5% of the transmitted energy was lost in the process

[6]. The Wardenclyffe Tower, also known as the Tesla tower, was the site for Tesla’s

demonstration,


http://home.howstuffworks.com/light-bulb.htm

Earlier research also included RFID tags and the world's first passive RFID system was

demonstrated at Los-Alamos National Lab in 1973.

Prof. Shu Yuen (Ron) Hui invented a planar wireless charging pad for charging portable consumer

electronic products in 2000. A patent was filed on "Apparatus and method of an inductive battery

charger,”. Later in 2001 Prof. Shu Yuen (Ron) Hui and Dr. S.C. Tang researched using the EM

shield consisting of a thin layer of ferrite and a thin layer of copper sheet. It enabled the

underneath of the future wireless charging pads to be shielded with a thin EM shield structure with

thickness of typically 0.7mm or less.

Also in 2001, Prof. Ron Hui's team demonstrated that the coreless PCB transformer can transmit

power close to 100W.

1.2.2. Resent Research

Recent research on wireless power transmission includes work done WiTricity physics research

group in 2007. Led by Prof. Marin Soljacic at MIT, they sent power wirelessly to light a 60W light

bulb with 40% efficiency at a 2 meter (6.6 ft) distance with two 60 cm-diameter coils.

1. Fig 1.1: The WiTricity physics research group [2]


http://en.wikipedia.org/wiki/Marin_Soljacic

http://en.wikipedia.org/wiki/WiTricity

http://en.wikipedia.org/wiki/RFID

In Fig: 1.1 we can see the group with members of the team that performed the experiment

obstructing the direct line of sight between the coils; front row: Peter Fisher (left) and Robert

Moffatt; second row: Marin Soljacic; third row: Andre Kurs (left), John Joannopoulos and

Aristeidis Karalis.

2. Fig 1.2: Efficiency vs. Distance graph for power transmitted [2]

In 2008Intel reproduced the original 1894 implementation of electrodynamic induction and Prof.

John Boys group's 1988 follow-up experiments, by successfully lighting a nearby light bulb

wirelessly with an efficiency of 75%.

In 2009 POWERMAT Technologies introduced wireless charging systems, that worked with a

combination of radio-frequency identification (RFID) and electromagnetic induction. Palm

launched the Palm Pre Smartphone with the Palm Touchstone wireless charger. The Wireless

Power Consortium announced they are nearing completion for a new industry standard for low-

power (which is eventually published in August 2010) inductive charging. A simple analytical

electrical model of electrodynamic induction power transmission was also proposed and applied to

a wireless power transfer system for implantable devices. Lasermotive used the diode laser to win

$900k NASA prize in power beaming, breaking several world records in power and distance, by


http://en.wikipedia.org/wiki/Lasermotive

http://en.wikipedia.org/wiki/Inductive_charging

http://en.wikipedia.org/wiki/Wireless_Power_Consortium

http://en.wikipedia.org/wiki/Wireless_Power_Consortium

http://en.wikipedia.org/w/index.php?title=Palm_Touchstone&action=edit&redlink=1

http://en.wikipedia.org/wiki/Palm_Pre

http://en.wikipedia.org/wiki/Electromagnetic_induction

http://en.wikipedia.org/wiki/Radio-frequency_identification

http://en.wikipedia.org/wiki/Wireless_charging

http://en.wikipedia.org/wiki/Powermat_Technologies

http://en.wikipedia.org/wiki/Intel

transmitting power wirelessly over a kilowatt more than several hundred meters. Sony also showed

a wireless electrodynamic-induction powered TV set, 60 W over 50 cm.

More recently in 2012 "Bioelectromagnetics and Implantable Devices" group in University of

Utah, USA developed an efficient resonance based wireless power and data transfer system for

biomedical implants. The design achieved more than twice the efficiency and frequency

bandwidth compared to conventional inductive link approach and was extendable to other

industrial "smart" wireless power transfer system. Also, Christopher Tucker, Kevin Warwick and

William Holderbaum of the University of Reading, UK developed a highly efficient, compact

power transfer system safe for use in human proximity.

In 2013 a fully integrated wireless power receiver is demonstrated in CMOS process by Meysam

Zargham and P.G. Gulak. The designed prototype did not require any off-chip components or

post-processing steps. The demonstrated single-chip prototype is only a few millimeters on each

side, mass producible and inexpensive

The latest researches include using compact size METAMATERIALS, to enhance the power

transfer efficiency of wireless powered systems. The proposed applications include short-range

wireless power transfer to biomedical implants and wireless charging. Also the first demonstration

of resonance based wireless power transfer system used to reduce the electromagnetic energy

absorption (SAR) inside the human tissue was done on March this year.


http://en.wikipedia.org/wiki/Kevin_Warwick

1.2.3. State of the art technology

Recently many devices have hit the market that can be charged wirelessly.

3. Fig 1.3: Wirelessly charged devices [7]

Among the recent devices the Nokia Lumia 920, HTC Droid DNA, LG Nexus 4 etc are examples

of top-tier phones that can be charged without the need of wires. Such systems are more

convenient as we do not need to carry a charger around and instead can charge on the go. With

automation being of vital importance this is the way forward in the future.


4. Fig 1.4: Electronic devices powered by PROXI [7]

Fig 1.4 shows many electronic devices being charged simultaneously by a POWER BY PROXITM

wireless charger. Their motto is “The power to unplug” and they have been allowing us to do that

by providing us with real world, science-based, resonant wireless power solutions since 2007 [8].

Their wireless power devices include wireless chargers, wireless control systems and wireless

sensors. They solve continuity of power/data delivery and maintenance problems. They allow

recharging of multiple batteries from a single power transmitter and allow delivery of wireless

power to a battery management system when the moving half of the application is in a rest or

neutral position [9].

Powerbyproxi takes a different approach to wireless power with its patented Proxiwave

technology. It uses transmitter and receiver coils to respectively transmit and receive power

between a power transmitter (PTx) and power receiver (PRx). These coils are analogous to

antennas used for radio communication. A converter, powered by a AC supply is used to drive the

PTx coil. The Proxy Wave power controller regulates the power flow from the receiving PRx coil

to the target electrical device or electronics, depending on their specific power requirements [4].


5. Fig 1.5: Proxi-Point Wireless Connector [9]

Fig 1.5 shows a wireless connector, The Proxi-Point 12, which is a standalone electrical device

that enables transfer of power and data across any non-metallic material. The Proxi-Point is a next

generation resonant solution providing a reliable and maintenance free alternative to traditional

unreliable power cables, coil cords and connectors. In addition it can be used to enable non-

contact recharging of batteries. Proxi-Point 12 is a ideal for battery charging with the ability to

deliver 12V up to a distance of 25mm, while the Proxi-Point 150 is able to deliver 150 Watts up to

38mm at high efficiency [9].

The Proxi-Ring Wireless Slip Ring is the world’s first high efficiency, frictionless wireless power

slip ring capable of supplying power to rotating, highly mobile industrial equipment. It is a

standalone electrical device that enables transfer of power and data across an electrical rotary joint

referred to as a slip ring, electrical swivel, rotary electrical interface, commutator or a collector.

The Proxi-Ring is designed as a next generation resonant solution to replace existing mechanical

slip rings – providing a reliable and maintenance free alternative that doesn’t rely friction based

metal and/or carbon brush contacts to enable power and data transfer. Wherever high-value,

mission critical solutions require power and data to be transferred across a rotating joint, we can

replace an existing slip ring with our wireless power slip ring [10].


http://powerbyproxi.com/products/proxi-point-150/

http://powerbyproxi.com/products/proxi-point-12/

6. Fig 1.6: Wirelessly charged car [7]

Recently Toyota has announced that it will begin actual verification testing of its new wireless

battery-charging system for electric vehicles, one that charges the battery of a plug-in hybrid or a

pure-electric car by having the car park on top of it. This technology would eliminate the need for

physically plugging in an electric car or a hybrid. It also has the potential to act as a universal

charging station, reducing the need for multiple charging stations and plug standards [11].

Volvo has also been working on an identical system that works along the same principle.


IDT has also been producing IC’s that can transmit power wirelessly. Fig 1.7 shows these IC’s.

7. Fig 1.7: IDT Wireless Power ICs [12]

1.3.Future Scope of This Study

The future scope of this study is to be able to be an integral part of this fast growing market and giving

rise to a more efficient and effective world. The ability to create a world based on this is remarkable and a

study into the technology will definitely not be futile rather will be late into the race, as many companies

are already innovating and have established themselves at the forefront of this technology.

1.3.1. Future Scopes

The technology is a necessity not only because the world will be better without wires but because

it has many potential uses in many different sectors. Being able to transmit and receive power

wirelessly will give huge leap in research done on implantable devices in several different fields

including military, medicine etc. Also it will allow countries greater transmission of power as

losses in the wire, which is a high percentage, to be negated. In the future many more devices can

be wirelessly charged than what is imaginable today. That will allow applications such as a

universal bus system, where many devices can be wirelessly charged when they are located in a

certain region within the range of the system. Such systems can be very useful. It will be

particularly useful since distance of power transmission between charging station and the device


can be varied using different methods. So problems will not arise when the device needs to

charged immediately and the charging station isn’t within reach.

1.3.2. Recommendations

We are at the point in time when wireless power transmission has become a necessity. Not only

because of the fact that wires are disruptive, but because if power can be wirelessly transmitted over

long distances a lot of the losses that occur in wires can be accounted for and hence, a lot more power

can be distributed all the while more efficiently. The applications of technology that uses this

principle are limitless and they will make our work much easier while consuming even less power.

1.4.Limitation of the Study

The major limitation of this research topic is the cost involved with practical implementation of wireless

power systems. Although no wires will be required, building wireless power systems will be very costly

business. With existing technology it will be very difficult to build such systems, e.g. interference of

microwave with present communication systems is difficult. More efficient energy distribution systems

and sources are needed by both developed and under developed nations but taking the cost into

consideration it will not be cost effective.

Power was also delivered in the KHz range in this thesis instead of MHz range. Although MHz ranges

would have allowed increased power transfer the equipments would have been more expensive and more

complex.

1.5.Advantage over Traditional Method

Cost of electrical energy used by the consumer will be less and the landscape can be rid of wires, cables

and transmission towers. The electrical energy can be transmitted more economically without wires to any

distance across land, so there will be no transmission and distribution loss. It will increase freedom of

choice of both receiver and transmitters. Power failure due to short circuit and fault on cables would never

exist in the transmission. Power theft would be not possible at all. Wireless charging would be more

common too. Vehicles could also be driven using wireless power, eradicating fossil fuels and limiting the

harm they cause to the environment.


1.6.Objective of this Work

The purpose of this work is to be able to embrace the next leap in technology and help transmit power

more efficiently. We have designed models of the basic parallel magnetic resonance circuits to analyze the

many different parameters associated with them. We have made two coil, three coil and four coil models

alongside a flat spiral ring structure and measured their corresponding efficiencies with changing distance.

We have also compared between them to prove which is better. We have compared practical data for the

basic model with the simulated data to see if the trend in values obtained is consistent and if the data is

reliable. All this has been done to put forward a comprehensive case for efficient wireless power

transmission.

8.

1.6.1. Primary objectives

To explore the capabilities of wireless power transfer by Magnetic Resonance Coupling and make

a model for efficient power transfer over medium range distance.

9.

1.6.2. Secondary Objectives

To ensure more efficient power transfer with different designs of the parallel circuit model and

correspondence of the physical and simulated results.


1.7.Introduction to this Thesis

The report is divided into 5 chapters in order to elaborate on each segment of the functions and scope

surrounding the work. These chapters are followed by appendices which will help with any further added

detail surrounding the study itself.

Chapter 1 provides a detailed understanding of the evolution of this technology and its timeline down to

the present day idea we hold, along with all the research surrounding this.

Chapter 2 is about the different theories and equations associated to the whole thesis. This contains the

introduction to the different systems used and the understanding of the different circuit and coil

parameters.

Chapter 3 contains the design that is followed in building the whole project and the simulation data

obtained from the various simulation softwares used.

Chapter 4 contains the output of the physical implementation of the designed coil. It explains what was

observed while the experiment was conducted.

Chapter 5 explains the discussions and conclusion that are drawn from the whole thesis along with the

future scope of the project. Recommendations and limitations that are observed will be discussed and the

possible potential will be explored as well.

10.


Chapter 2

Theory and Equations

1.8.Introduction

In this chapter, the analytical model of magnetic resonant coupling wireless power transmission is

developed through circuit theory. The model is made under the assumption of low internal resistance of

circuit component excepting the coil and some particular type of resonator (inductance and capacitance of

coil) equivalent circuit. The high frequency source is considered to be directly connected to the wireless

power transmitter coil and external capacitance is used to control the resonant frequency of the system. In

the kHz to MHz range the frequency dependent component becomes a significant part of the circuit.Two

types of transmitter and receiver coils are observed. 1) Transmitter and receiver coils are both helical coils

with same resonant frequency (Part 2.2 – 2.3).2) Transmitter and receiver coils are both pancake coils

with same resonant frequency (Part 2.4). Calculation of the equivalent circuit parameter of the coil and

geometric properties of a helical coil have also been discussed.

1.9.Geometry of helical coil

The coil used is a helical coil with a diameter Diam, pitch p, height hand n number of turns. The radius of

the wire used is a. The coil geometry is shown in figure 2.1(a)

11. Fig 2.1(a): Coil geometry


The total length of the coil l can be found from the equation (2.2.1)

l=√( πnDiam )2+h2(2.2.1)[13]In these parameters the effective value of diameter Diam changes depending on coil turns, pitch and

frequency used. A short description on calculating Diam is given.

1.9.1. Diameter

Figure 2.2.1(a) represents a helical coil with finite dimensions. Here a is the radius of the coil wire.

12. Fig 2.2.1(a): Coil top view [13]

The conventional formulae calculate Diama as the diameter of the coil. But according to [13] that is

not right. Even at low frequency conduction path along the inside surface of the coil (Diama–

Diamw) is lesser than conduction path the outside surface of the coil (Diama +Diamw). Also the

stretching of wire, while producing the coil, increases the resistivity of the outside pass. So,

effective loop diameter has to be modified due to the tendency of the current density to move

towards the inside surface of the coil. Also in high frequency two other components skin effect

and proximity effect becomes evident. Considering this entire phenomenon in [13] the effective

diameter is calculated according to (2.2.1.1)

Diam=Θ ( Diamo−Diam∞ )+Diam∞ (2.2.1.1)

where ,

Diamo=Diam a(1−( 2aDiam a )

2) (2.2.1.2)


Diam∞=

Diam o+ 2 Diam min

( P2 a

−1)1+

2

( P2 a

−1) (2.2.1.3)

Diam min=Diama−¿2a +4 an

(2.2.1.4)

Θ=2δ i(1−exp −[ a2δ i ]

3.8)1

3.8 (1− y )(2.2 .1.5)

where , y= 0.0239

(1+1.67 ( z0.036−z−0.72)2)4 , z= a2.552 δ i

, δi=√ ρπf μ0

Here ρ is the resistivity of the material, f, the frequency of operation, and δi is the skin

depth. This formula comes from the observation that Diammin is the absolute minimum

effective diameter of the helical coil, so Diam∞ (effective diameter at very high frequency)

must lie somewhere between Diamo (the effective current diameter for a low frequency

case) and Diammin. Further, Θ is used as the weighting factor to evaluate the effective

diameter on the specified frequency.

1.10. Equivalent circuit parameters of helical coil

The coil discussed is a helical coil. In kHz to MHz range there are many different coil parameters which

become significant. According to [13] the helical coil can be represented using the model shown in figure

2.3(a)

13. Fig 2.3(a): Equivalent circuit of the coil.


Where C, Rac and L is the capacitance, ac resistance & inductance of the coil respectively. These

parameters have both frequency dependent and frequency independent components.

1.10.1. Inductance of a helical coil

The analysis of inductance calculation is started from considering the current sheet inductor model

shown in figure 2.3.1(a).

14. Fig 2.3.1(a): Diagram of current sheet inductor [13]

Such a solenoid is assumed to have an infinitely thin conducting wound wire (one layer) with no

spacing between the turns (nevertheless the turns are electrically isolated). The main characteristic

of such a coil is that at low frequencies they have a uniform magnetic field distribution along their

length. According to [13] if these specifications are met the inductance of the coil can be

expressed as(2.3.1.1)

Ls=μπ Diam2n2

4 h(2.3.1.1)

Where Diam is the coil diameter, n is number of turns, h is height of the coil and μ is magnetic

permeability. The current sheet model is a theoretical model, but by using this model the formula

for the actual inductance of a coil can be calculated. This calculation can be divided into two parts,

frequency independent and frequency dependent. [13]

First the frequency independent parameters are discussed. The coil in Figure 2.1(a) has finite size

(round wire with radios a and height h). And there is spacing between the coil turns (pitch

p).When coil length is comparable to its diameter, the assumption of uniform field distribution is

not valid. In 1909 H. Nagaoka introduced coefficient KL [9] to consider this non-uniformity

(2.3.1.2) [13]

K L=2h

πDiam¿ (2.3.1.2)


With this correction (2.3.1.1) can be modified into the following equation.

Ls=μπ Diam2n2

4 hkL(2.3.1.3) [13]

Now for real coils a coefficient Ks to consider the round shape of the coil and another coefficient

Km to consider the mutual inductance between the turns of the coil must be added. [17]

k m=ln (2 π )−32−

ln (n )6 n

−0.33084236n

− 1

120 n3+ 1

504 n5−0.0011923

n7+ 0.0005068

n9

(2.3.1.3)

k s=32−ln( p

a ) (2.3.1.4)

Including these modifications the inductance of the coil becomes

L=L s−μnDiam

2(k¿¿ s+k m)¿(2.3.1.5) [17]

Besides these parameters there are frequency dependent parameters also. The frequency dependent

part of inductance is internal inductance Li. It is an imaginary part of skin effect and it decreases

rapidly as the frequency increases. But at low frequency it is not negligible. It is proportional to

wire length l and also to the number of turns n. But external inductance is proportional to n2.So

effect of internal inductance is significant for short coils only. Internal inductance is approximated

as (2.3.1.6). [13]

Li=μ0 δi

4 πa (1−exp −[ a2δ i ]

3 . 8)1/3 .8

(1− y ) l (2.3.1.6)

Finally putting all these parameters into consideration the inductance L of a helical coil can be

expressed as

L=L s−μnDiam

2( ks+k m )+Li (2.3.1.7) [13]


1.10.2. AC resistance of a helical coil

The AC resistance Rac has four components the DC resistance Rdc component, the component due

to the skin effect (Θ), the component due to the proximity effect (Ψ), and for very high frequencies

a radiated resistance component (Rr) must be added. [13]

Rac=Rdc ΘΨ+R r(2.3.2.1)

Where,

Rr=√ μ0

ϵ 0 π12

n2(ωDiam2c )

4

+ 2

3 π2 (ωhc )

2 (2.3.2.2)

Rdc=ρl

π a2 , Θ= a2

(2 a δi−δi2 )

It should be noted that in (2.3.2.2) represents speed of light. [13]

The equations ofRac, Rr , Rdc and Θare given in [13] but the value of proximity factor (Ψ) is not

directly given. Instead it has been taken from the Table 2.3.2.1 given in [13]. Here, it is important

to note that Table 2.3.2.1 is applicable only when the number of turns is large (≥ 30). The coils

observed in this thesis follow this restriction.

15.

16. Table 2.1: Proximity factor Ψ


p/(2a)

h/D1 1.111 1.25 1.43 1.66 2 2.5 3.33 5 10

0 5.31 3.73 2.74 2.12 1.74 1.44 1.2 1.16 1.07 1.020.2 5.45 3.84 2.83 2.2 1.77 1.48 1.29 1.19 1.08 1.020.4 5.65 3.99 2.97 2.28 1.83 1.54 1.33 1.21 1.08 1.030.6 5.8 4.11 3.1 2.38 1.89 1.6 1.38 1.22 1.1 1.030.8 5.8 4.17 3.2 2.44 1.92 1.64 1.42 1.23 1.1 1.031 5.55 4.1 3.17 2.47 1.94 1.67 1.45 1.24 1.1 1.032 4.1 3.36 2.74 2.32 1.98 1.74 1.5 1.28 1.13 1.044 3.54 3.05 2.6 2.27 2.01 1.78 1.54 1.32 1.15 1.046 3.31 2.92 2.6 2.29 2.03 1.8 1.56 1.34 1.16 1.048 3.2 2.9 2.62 2.34 2.08 1.81 1.57 1.34 1.165 1.0410 3.23 2.93 2.65 2.27 2.1 1.83 1.58 1.35 1.17 1.04∞ 3.41 3.11 2.815 2.51 2.22 1.93 1.65 1.39

51.19 1.05

1.10.3. Capacitance of helical coil

The capacitance of the helical coil is also a frequency dependent component. In 1947 R.G.

Medhurst [18], by numerous experiments found a semi-empirical formula which calculates the self

capacitance and high frequency resistance of single layer solenoids. His formula, however, was

acceptable only for coils with solid polyester cores. So, for general cases (any core material), his

formula must be modified, resulting in equation (2.3.3.1). [13]

C=4 ϵ0 ϵ rx h

π 1+kc (1+ϵri

2ϵ rx)1+( h

πnDiam )2

Where,

k c=0.717439( Diamh )+0.933048( Diam

h )3/2

+0.106( Diamh )

2


1.10.4. Mutual inductance between helical coils

The mutual inductance between tow coils can be defined using the formula

M 12=1

I 1 I 2∫vol

( μH 1. H 2 ) dv(2.3.3.1) [19]

Where, M12 indicates the mutual inductance between coil 1 and 2. I1 and I2 are the current through

the coils 1 and 2. H1 is field resulting from I1(when I2 = 0) and H2 is field resulting from I2 (when I1

= 0). Interchanging the subscripts does not change the value of the equation. So M12 = M12=M.

According to [13] for two helical coils situated on the same axis of cylindrical symmetry and the

condition Diam<<λ (λ is the wavelength) is met the mutual inductance can be calculated as

M ≈π2

μ0( Diam1

2Diam2

2 )2

n1n2

d3

(2.3.3.1)

1.11. Flat Spiral Ring coil:

The geometry of a Flat Spiral Ring (pancake) coil is showed in the figure 2.4.1

17. Fig 2.4.1(a): Geometry of a Pancake coil [20]

Here W is the coil width. Rin is coil inner radios and Rout is coil outer radius.


The length of the coil can be determined by using the formula

l=π ( Rout2−Rin2)∗Rw (2.4 .1 ) [24]

Here, Rw is wire radius.

The inductance can be approximated using the formula

L=Rh2 n2

8 Rh+11W(2.4.2)[21]

Here, Rh = Rin + (W/2), n is the number of turns.

It should be noted that the values of Rh and W are in inches. And L is in micro Henry.

18. Fig 2.4.1(b): Inductance calculation parameter [21]

According to [21] there is no need to calculate the self capacitance of such coils because the capacitor

added to decrease the resonant frequency to the KHz – MHz is a lot bigger than the self capacitance.

The ac resistance Rac of the coil can be estimated from the equation.

Rac=√2 Rsπd

¿(2.4.3)[22]

Where, d is the diameter of wire.

Rs= 1δσ

, δ= 1

√πfμσ,q= d

√2σ [22]


Ber (q )∧Bei (q )are the real and imaginary part of Bessel function. The ' sign denotes first derivative.

Details about Bessel function are given in Appendix B.

The mutual inductance can be

M=uo n2 n1 d1

2 d22

2√(d22+ X2 )3

[20]

Here subscript 1 and 2 denotes the transmitter and the receiver coils. X is the distance between coils.

1.12. Parallel two coil scheme

In figure 2.4(a) basic block diagram of the two coil scheme is shown. In this model both of the coils have

the same resonant frequency. This causes energy to oscillate between the magnetic field of the inductor

and electric field of the capacitor. According to [13] the energy transmission occurs because of

intersection of magnetic field between the source coil and load coil. There is no intersection of electrical

energy because all electrical energy concentrates in the capacitors.

19. Fig 2.4(a): Basic block diagram of two coil scheme.

20.

The equivalent circuit of this block diagram is shown in Fig 2.4(b)


21. Fig 2.4(b): Equivalent circuit of two coil scheme

Here Cext1and Cext2 are the external capacitances connected to control the resonant frequency of the coils.

C1 and C2 are the self capacitances of respective coils. M denotes the mutual inductance between the coils,

VS is source voltage and ZL is load impedance.

1.12.1. Solving circuit

Calculating the resonant frequency of the model is an easy task. The resonant frequency can be

expressed by equation (2.4.1.1)

f c=1

2π √L C eq

, (2.4.1.1)

Where, Ceq = C + Cext For helical coil

Ceq = Cext For pancake coil.

For this model to work the resonant frequency of receiver and transmitter have to be same.

Now if we perform mesh analysis on the circuit shown in Fig 2.4(b) we can translate it to the

circuit shown in Fig 2.4.1(a).


22. Fig 2.4.1(a): Mesh analysis of two coil scheme.

Here the mutual inductance M has been represented in the circuit loop by the dependable voltage

sources. From this circuit we get the mesh equations

I1 (jX ceq1)+I2 (-jX ceq1)=Vs………………………………………………. .. (i)

I1 (-jX Ceq1 )+I2 (Rac1+j XL 1+jXCeq1 )+ I 3( jX M)=0 ...……………………. (ii)

I2 (- jX M )+I 3 (Rac2+jXL2 +jXCeq2 )+ I 4(−jX Ceq2)=0 ..…………………... (iii)

I3(−jX Ceq2 )+ I 4 ( jX Ceq2+ZL )=0.…………………………………………(iv)


From these equations the values of I1 and I4 can be obtained. The solving method is discussed in

appendix A.

So the input power, Pin = V*I1

Output power, Pout = ZL*(I4)2

And overall efficiency,η= PinPout

=V∗I1

ZL∗¿¿ (2.4.1.2)

1.13. Parallel three coil scheme

In case of the two coil model if we do not match the load with the impedance of the power source the

power transfer efficiency falls very sharply. Also if the load has a reactive part it will cause the receiver

circuit to go out of resonance. This is a big disadvantage because the system can only work for a specific

amount of load. So for different loads we need to readjust the resonant frequency or value of external

capacitance. To go around this problem the three coil model may be implemented. In this model the

transmitter coil is coupled with the resonator coil using magnetic resonance coupling (they have the same

resonant frequency). And the resonator is coupled with the receiver coil using magnetic induction

coupling (they have different resonant frequency). If all the coils have same resonant frequency, the

resonator coil may also be used as a repeater to increase efficiency.). The power will be supplied in the

resonant frequency of the resonator and source. The block diagram of this model is shown in Fig 2.5(a)

23. Fig 2.5(a): Basic block diagram of three coil scheme.


The equivalent mesh analysis circuit of this block diagram is shown in Fig 2.4(b)

24. Fig 2.5(b): Equivalent circuit of two coil scheme

This circuit is similar to the circuit described in section 2.4. The components carry the same meaning. The

middle part is the equivalent circuit of the resonator. M1 is mutual inductance between transmitter coil

and resonator coil. M2 mutual inductance between resonator and receiver coil. And M3 is the mutual

inductance between transmitter coil and receiver coil. The resonant frequency of the different blocks can

be found according to equation (2.4.1.1). Now representing the mutual inductance by voltage source we

get the circuit shown in Fig 2.5(c).

25. Fig 2.5(c): Equivalent mesh analysis circuit of three coil scheme

From here we get the following mesh equations

I1 (jX ceq1)+I2 (-jX ceq1)=Vs ………………………………………………. .. ……. (i)

I1 (−jX Ceq1)+I 2(Rac1+j XL1 +jXCeq1)+ I 3 ( jX M 1 )+ I 4( jX M 3)=0 ...…………... (ii)

I2 (− jX M 1)+I 3 (Rac2+jXL2 +jX Ceq2 )+ I 4( jX M 3)=0 ………………………….. (iii)

I2 (−j XM 2 )+ I3 (− jX M 3 )+I 4 (Rac3+j XL3+jX Ceq3 )+ I 5 (−jX Ceq3 )=0………...…. (iv)


I 4 (−jX ceq3)+I 5(jX ceq3+ZL )=0 …………………………………………………... (v)

From the equations the values of I1 and I5 can be obtained. The solving method is discussed in appendix A.



And overall efficiency η= PinPout

=V∗I1

ZL∗¿¿(2.5.1)

The three coil scheme has been simulated using COMSOL only and no analytical simulation was done

because this thesis does not include inductive coupling theoretical calculation.

1.14. Parallel four coil scheme

The three coil scheme solved the problem of connecting variable load. But there is still a problem. If the

impedance of source changes it can also change the resonant frequency of source which will drastically

reduce overall efficiency. So we need to have a fixed voltage source for a system. If we change the

voltage source with a source having different impedance the system may become inefficient. To solve this

problem we can couple resonator1 with transmitter using magnetic induction (do not have same resonant

frequency), resonator1 and resonator 2 is coupled by magnetic resonance coupling (have same resonant

frequency), resonator2 with receiver using magnetic induction (do not have same resonant frequency).

The power will be supplied in the resonant frequency of the resonators. Fig 2.6(a) shows the block

diagram of the model.

26. Fig. 2.6(a): Block diagram of four coil scheme.


Fig 2.6(b) shows the equivalent circuit of this block diagram.

27. Fig 2.6(b): Equivalent circuit four coil scheme

This circuit is similar to the circuit described in section 2.4. The components carry the same meaning. The

middle part is the equivalent circuit of the resonator. M1 is mutual inductance between transmitter and

resonator1. M2 is the mutual inductance between resonator1 and resonator2. M3 is the mutual inductance

between resonator and receiver. M4 is the mutual inductance between resonator2 and transmitter. M5 is

the mutual inductance between transmitter and receiver. M6 is the mutual inductance between resonator1

and receiver. The resonant frequency of the different blocks can be found according to equation (2.4.1.1).

Now representing the mutual inductance by voltage source we get the circuit shown in Fig 2.6(c).

28. Fig 2.6(c): Equivalent mesh analysis circuit of four coil scheme


From this circuit we get the mesh equations:

I1 (jX ceq1)+I2 (−jX ceq1)=Vs ………………………………………………. .. …… ………...…

(i)

I1 (−jX Ceq1)+I 2(Rac1+j XL1 +jXCeq1)+ I 3 ( jX M 1 )+ I 4 ( jX M 4 )+ I 5( jX M 5)=0 ...…………….. (ii)

I2 (− jX M 1)+I 3 (Rac2+jXL2 +jX Ceq2 )+ I 4 ( jX M3 )+ I 5 ( jX M 6 )=0 ……………………………. (iii)

I2 (− jX M 4 )+I3 (− jX M 2)+I 4 (Rac3+jXL3 +jX Ceq3 )+ I 5 ( jX M 3 )=0 ...…………………………(iv)

I2 (−j XM 5 )+I3 (− j X M 6)+ I 4 (− jX M3 ) +I5 (Rac4+j XL4 +jX Ceq4 )+ I 6 (−jX Ceq4 )=0….…………

(v)

I5 (−jX ceq4)+I 6 (jX ceq4+ZL )=0 …………………………………………………........................

(vi)

From the equations the values of I1 and I5 can be obtained. The solving method is discussed in appendix A.



And overall efficiency η= PinPout

=V∗I1

ZL∗¿¿ (2.6.1)

The four coil scheme has been simulated using COMSOL only and no analytical simulation was done

because this thesis does not include inductive coupling theoretical calculation.


Chapter 3

Simulation and Result Analysis

29.

1.15. Introduction

This segment introduces the simulation results of the various softwares used. Mainly MATLAB and

COMSOL were used to find out our simulated results. Also as an alternative process to solve the circuits

using MULTISIM has also been discussed. The code was written on MATLAB and the values of different

circuit components were found from the code. Values of certain parameters were also obtained using

MATLAB. Simulation of 2-Coil System was done in MATLAB. MATLAB computes the overall wireless

power transmission system numerically and hence some physical conditions were ignored and some

approximations were taken into consideration when the code was written. COMSOL MULTIPHYSICS is

a finite element analysis, solver & simulation software. Multiple types of physical condition can be

combined together and can be put to a single solution here in COMSOL.

MATLAB estimated the parameters that were needed to make a WPT system valid and those parameters

were used to define the physics in COMSOL. These parameters were used to implement the model and to

give the WPT system a much more valid and verified physical condition and at the end, a very clear

projection of EM fields around the coils was obtained.

Here it needs to be noted that COMSOL takes into consideration the variables such as Geometry, Fields

(both EM Fields & Magnetic Fields) & materials, where on the other hand MATLAB computes the whole

WPT systems numerically.


30.3.2. Parallel Two Coil Circuit Model

31. Fig 3.1: Equivalent circuit for wireless power transmission

32.

Above is the simple circuit representation of the basic wireless power transmission system. Using

MULTISIM the following circuit was implemented:

33. Fig 3.2: MULTISIM representation of the basic model


In MULTISIM model we can simulate mutual inductance using the arbitrary spice block. From here

values of the required currents can be measured. But this method is much time consuming and not as

accurate as COMSOL. So this method was rejected and MATLAB was used to get a faster approximation.

And COMSOL was used for the physical simulation.

34.

1.15.1. MATLAB Code and Explanation

1.15.1.1. MATLAB code for Helix

a=0.00066; % Wire radius

Diam=0.1+a; %Diameter of coil

d=0.04; %Distance between coils

h=0.09; %Coil Height

n=30; %Number of turns

This part of the code defines the coil parameters and geometry. The wire radius was set at0.00066

meters and the coil height at 0.09 meters. The diameter was taken as 0.1+a (wire radius) meters, distance

between coil as 0.04 meters or 4 cm. The wire had 30 turns initially.

n1=n; %for coil 1

n2=n; %for coil 2

diam1=diam; %diameter of coil 1

diam2=diam; %diameter of coil 2

Here the number of turns of the coils in the primary (transmitter) side and the secondary (receiver) side

was defined to be equal. This ensures there is no change in the value of the inductance of the coils. Also,

since the number of turns is equal on both sides the value of induced voltage will be comparable to

supplied voltage.


p=h/n; %coil Pitch

This was used to define the pitch of the coil. This is the distance between the centers of two adjacent

turns.

f=15*10^3; %Frequency

u0=1.256637061*10^-6; %Permeability of vacuum

E0=8.854187817*10^-12; %Permittivity of vacuum

Erx=E0*1.000589; %Permittivity of material sorrowing coil(Air)

Eri=2*E0; %Permittivity of material inside coil (PVC)

row=1.68*10^-8; %Conductivity of wire(copper)

The different permittivities were set for the different mediums in question. The frequency was set at 1

KHz. The conductivity of the wire, made of wire in both the practical implementation and simulation, is

defined by ‘row’. The material inside the coil was taken as wood and hence its permittivity was used.

The coil was placed in vacuum (in ideal conditions) and hence the permittivity of vacuum was used as

the sorrowing material.

Zl=1000; %load resistance

The load resistance was set at 1000 ohms.

u=1.25663760*10^-6; %PVC

This defined the permittivity of the medium the coil was wound around. It is to be noted that

nonmagnetic materials have a relative permittivity close to unity. So the permittivity of these materials

can be equal to air. So wood simulates the properties an air core using PVC core properly.


shi=5.8; %proximity factor

This was taken from the proximity factor table to define the proximity factor (shown in Table2.3.2.1)

The section after this point calculated the equivalent circuit properties of the coil.

%Code to find inductance start

kL=2*h/(pi*diam)*((log(4*diam/h)-0.5)*(1+0.383901*(h/diam)^2)+0.017108*((h/diam)^4)/

(1+0.258952*((h/diam)^2))+0.093842*(h/diam)^2+0.002029*(h/diam)^4-0.000801*(h/diam)^6);

Ls=u*pi*diam^2*n^2/(4*h)*kL;

ks=3/2-log(p/a);

km=log(2*pi)-3/2-(log(n)/(6*n))-(0.33084236/n)-1/(120*n^3)+1/(504*n^5)-(0.0011923/

n^7)+(0.0005068/n^9);

di=sqrt(row/(pi*f*u0));

z=a/(2.552*di);

y=0.0239/((1+1.67*(z^0.036-z^-0.72)^2)^4);

l=sqrt((pi*n*diam)^2+h^2);

Li=(u0*di)/(4*pi*a)*(1-exp(-(a/(2*di))^3.8))^(1/3.8)*(1-y)*l;

L=Ls-(u*n*diam/2*(ks+km))+Li;

%end

%Code to find parasitic capacitance start

kc=0.717439*(diam/h)+0.933048*(diam/h)^(3/2)+0.106*(diam/h)^2;

Cext=4*Erx*h*(1+kc*(1+(Eri/2*Erx))*(1+(h/(pi*n*diam))^2));

%end

%Code to find Rac start

Rr=sqrt(u0/E0)*(pi/12)*(n^2*((2*pi*f)*diam/(2*10^8))^4+3/(3*pi^2)*(2*pi*f*h/(2*10^8)));

Rdc=(row*l/(pi*a^2));

theta=(a^2)/(2*a*di-di^2);

Rac=Rdc*theta*shi+Rr;

%end


M=pi/2*u0*(diam1/2*diam2/2)^2*n1*n2/d^3; %mutual inductance

C=(1/(L*(2*pi*f)^2-Cext)); %value of capacitance added parally for resonance at f

k=M/L; %Coupling coefficient.

1.15.1.2. MATLAB code for pancake

This part denotes the coil parameters and system parameters

ri=0.05;%inner radious of coilw=.0396;%width of coilr=ri+w;%outer radious of coildout=2*r;rw=0.00066;%radious of wirerh=ri+(w/2);%radious of coil to half widthu0=4*pi*(10^-7); % Permeability of vacuumn=30; %number of turnsd=0.05; % distance between coilsl=(pi*((r^2)-(ri^2)))/(0.00162); %Length of coil.f=10.20*10^3; %frequencyZl=1000; %load

This part calculates the equivalent circuit parameters

%AC resistance Rac approximation%%%%%%%%%sigma =1/(16.78*10^-9);delta = 1/sqrt(pi*f*u0*sigma);q=2*rw/sqrt(2*delta);Rs=1/(sigma*delta);

%%%% Berq = Ber(q) , Beiq = Bei(q), DBerq = Ber'(q)&DBeiq = Bei'(q)

Berq = (2^(1/2)*exp((2^(1/2)*q)/2)*(cos((2^(1/2)*q)/2 - pi/8) + cos((2^(1/2)*q)/2 - (3*pi)/8)/(8*q)))/(2*pi^(1/2)*q^(1/2));

Beiq = (2^(1/2)*exp((2^(1/2)*q)/2)*(sin((2^(1/2)*q)/2 - pi/8) + sin((2^(1/2)*q)/2 - (3*pi)/8)/(8*q)))/(2*pi^(1/2)*q^(1/2));

DBerq = (exp((2^(1/2)*q)/2)*(cos((2^(1/2)*q)/2 - pi/8) + cos((2^(1/2)*q)/2 - (3*pi)/8)/(8*q)))/(2*pi^(1/2)*q^(1/2)) - (2^(1/2)*exp((2^(1/2)*q)/2)*(cos((2^(1/2)*q)/2 - pi/8) + cos((2^(1/2)*q)/2 - (3*pi)/8)/(8*q)))/(4*pi^(1/2)*q^(3/2)) - (2^(1/2)*exp((2^(1/2)*q)/2)*((2^(1/2)*sin((2^(1/2)*q)/2 - pi/8))/2 + cos((2^(1/2)*q)/2 - (3*pi)/8)/(8*q^2) + (2^(1/2)*sin((2^(1/2)*q)/2 - (3*pi)/8))/(16*q)))/(2*pi^(1/2)*q^(1/2));

DBeiq = (exp((2^(1/2)*q)/2)*(sin((2^(1/2)*q)/2 - pi/8) + sin((2^(1/2)*q)/2 - (3*pi)/8)/(8*q)))/(2*pi^(1/2)*q^(1/2)) + (2^(1/2)*exp((2^(1/2)*q)/2)*((2^(1/2)*cos((2^(1/2)*q)/2 - pi/8))/2 - sin((2^(1/2)*q)/2 - (3*pi)/8)/(8*q^2) + (2^(1/2)*cos((2^(1/2)*q)/2 -


(3*pi)/8))/(16*q)))/(2*pi^(1/2)*q^(1/2)) - (2^(1/2)*exp((2^(1/2)*q)/2)*(sin((2^(1/2)*q)/2 - pi/8) + sin((2^(1/2)*q)/2 - (3*pi)/8)/(8*q)))/(4*pi^(1/2)*q^(3/2));

%%%bessels end%%%%

Ractemp = ((Berq*DBeiq)-(DBerq*Beiq))/((DBerq^2)+(DBeiq^2));Rac = sqrt(2)*Rs*Ractemp/(pi*2*rw);%acresistance end%Inductance approximation%rh= half winding width, w is width, n number of turns%all units in inches so is multiplied by 39.3701 Ltemp=((rh*39.3701)^2)*(n^2)/((8*(rh*39.3701))+(11*(w*39.3701)));L=Ltemp*(10^-6); % L in micro henry so multiplied by 10^-6

%Mutual inductance M startM1=u0*n*n*(dout^4)*pi;M2=2*sqrt(((dout^2)+d^2)^3);M=M1/M2;end

1.15.1.3. Efficiency calculation

%Efficiency equation Start Ceq1 = Ceq;%Ceq = C + Cext for Helical coil and Ceq = Cext for pancake coil. Ceq2 = Ceq1; L2=L; L1=L; Rac1=Rac; Rac2=Rac;omega=2*pi*f;Xm=omega*M; XL1 = omega*L1; XL2 = omega * L2; XCeq1 = -(1/(omega*Ceq1)); XCeq2 = -(1/(omega*Ceq2));%loop1A(1,1)=1i* XCeq1;A(1,2)=-1i* XCeq1;A(1,3)=0;A(1,4)=0;%loop2A(2,1)=-1i*XCeq1;A(2,2)=(1i* XCeq1)+(1i*XL1)+Rac1;A(2,3)=1i*Xm;A(2,4)=0;%loop3A(3,1)=0;A(3,2)=-1i* Xm;


A(3,3)=Rac2+(1i*XL2)+(1i*XCeq2);A(3,4)=-(1i*XCeq2);%loop4A(4,1)=0;A(4,2)=0;A(4,3)=-(1i*XCeq2);A(4,4)=(1i*XCeq2+Zl);

B=[10 0 0 0]'; I=inv(A)*B; Eff=100*(abs(I(4)^2*Zl)*cos(angle(I(4)*Zl)))/(10*abs(I(1))*cos(angle(I(1))));35.

36.

37.

38.

39.

40.

41.

42.

43.

44.

45.

46.

47.

48.

49.

50.

51.

1.15.2. MATLAB Simulated Results and Interpretation© Faculty of Engineering, American International University-Bangladesh (AIUB) 46

1.15.2.1. For helical coil

52. Table 3.1: Data for distance vs. efficiency (Diameter = 0.10066)

n=30 n=35 n=40Distance(m) Efficiency% Efficiency% Efficiency%

0.05 33.49725587 44.36379311 54.29181310.07 32.91509335 43.51548801 53.06646830.09 25.0171426 32.69678757 38.73325520.11 10.51114145 13.58604532 15.64775120.13 3.887208186 4.996491905 5.704027530.15 1.473107692 1.876399712 2.11334312

53. Fig 3.3: Efficiency vs. Distance graph for different number of turns

As we can see clearly from the above diagram, the efficiency of a parallel two coil system

increases as the number of turns is increased. This is due to the fact that with increased turns the

pitch of the coil will decrease since pitch of coil is inversely proportional to number of turns.

Hence, the centers of the coils are closer together and this will ensure a more uniform flux. Also,

with an increase in the value of the number of turns the value of self inductance, Ls, and the

coefficient of mutual inductance, km, will increase. An increase in km will cause the mutual © Faculty of Engineering, American International University-Bangladesh (AIUB) 47

inductance between the transmitter and receiver coils to increase and this will increase the

coupling coefficient. With greater coupling more power will be available at the load and this will

increase the efficiency.

All the graphs, irrespective of the number of turns follow a similar shape As the two coils are

moved further apart the efficiency falls since an increase in distance leads to less coupling between

the coils. So as coupling coefficient, k, decreases, the efficiency will fall. This is due to the

receiver coil receiving less power from the transmitter coil due to less coupling.

For all the number of turns seen the maximum efficiency is reached at a range of distance between

5 cm to 7 cm. Within this range of separation the transmitter and receiver coils are at an optimum

distance apart and hence the value of coupling coefficient is greatest.

54.

55.

56.

57.

58.

59.

60.

61.

62.

63.

64.

65.

66. Table3.2: Distance vs. Efficiency for different diameter


Diameter = 0.08066 Diameter = 0.10066 Diameter = 0.12066Distance(m) Efficiency% Efficiency% Efficiency%

0.05 25.11808726 33.49725587 41.324899020.07 21.61975283 32.91509335 41.203605160.09 8.553003509 25.0171426 38.818352910.11 2.602689389 10.51114145 26.005511730.13 0.793459113 3.887208186 11.59355820.15 1.488931668 1.473107692 4.902978377

67. Fig 3.4: Distance vs. Efficiency for different diameter

As we can see with increasing coil diameter the efficiency of the system increases.

68.

69.

70.

71.

72.

73.

74. Table 3.3: Distance vs. Efficiency for different Load (ZL)


Zl=100 ohm Zl=1000 ohm Zl=10000 ohmDistance(m) Efficiency% Efficiency% Efficiency%

0.05 81.97631283 33.4972559 4.7974896280.07 62.665056 32.9150933 4.7621652740.09 20.82057346 25.0171426 4.0977133370.11 5.414164712 10.5111414 2.0876895330.13 -0.156758209 3.88720819 0.8326102250.15 4.76498846 1.47310769 0.355132616

75. Fig 3.5: Distance vs. Efficiency for different Load (ZL)

76.

1.15.2.2. For pancake coil


77. Table 3.4 Distance vs. efficiency for different load (pancake)

PANCAKE Zl=100 ohm Zl=1000 ohm Zl=10000 ohmDistance(m) Efficiency% Efficiency% Efficiency%

0.03 98.92995371 99.96314761 99.740442030.13 97.47245709 99.9477657 99.740288190.23 80.92408505 99.71153995 99.737912810.33 32.43596703 95.97459485 99.697964380.43 9.630554645 69.51072519 99.209481790.53 3.245782458 30.87548991 95.30338020.63 1.263832323 12.53629198 78.149961740.73 0.553565853 5.527292859 48.231282910.83 0.26632627 2.663687546 25.633714770.93 0.138188393 1.38371643 13.64697644

78. Fig 3.6: Distance vs. efficiency for different load (pancake)

79. Table 3.5 Distance vs efficiency for different turns and diameter


PANCAKE n=30 , diameter = 0.1792(m) n=35, diameter = 0.1861 n=40, diameter = 0.2056Distance(m) Efficiency% Efficiency% Efficiency%

0.03 99.96314761 99.9666847 99.961704060.13 99.9477657 99.94442035 99.940580310.23 99.71153995 99.6495242 99.742906960.33 95.97459485 95.47430664 97.577637450.43 69.51072519 68.13771867 81.44653950.53 30.87548991 30.17644786 44.480956360.63 12.53629198 12.3152549 19.524612720.73 5.527292859 5.452961014 8.8465204410.83 2.663687546 2.635688887 4.3230470950.93 1.38371643 1.37207772 2.265877244

80. Fig 3.7: Distance vs. efficiency for different turns and diameter

In case of pancake coils, changing the number of turns automatically changes the diameter.

1.15.3. COMSOL Simulations

1.15.3.1. Two-Coil System Setup


81. Fig 3.5: Coil Circuit Diagram

In the Global definition, Parameters for Parallel Resonance Circuit are defined as below:

82. Table 3.3: Parameters used in COMSOL

Name Value Description

R 50 (mm) Radius of Coil

Rw 0.66 (mm) Radius of Wire

D 200 (mm) Distance between Coil

N 30 Coil Turns

H 150(mm) Coil Height

Geometry- 2D-axissymetrcial were chosen, 3D design is much more sophisticated due to its requirement

of more boundary condition and a broader mesh area. One circle & two rectangles were selected, the

circle (C1) has the radius “2*d+2*Rw” and the two rectangles (R1,R2) have width of “2*Rw” & Height

of “H”.They were positioned in such a way that they were d[mm] away from each other. Then the whole

geometry was selected to build, where the circle (C1) represents domain 1, and R1 & R2 represents

domain 2 & 3 consecutively.

Materials-COMSOL has a library consisting of various materials, from there copper & air were chosen,

domain 2 & domain 3 were selected for copper, and domain 1 was selected for air.


Physics-COMSOL have a wide range of built-in Physics, from there Magnetic field, where in the

magnetic field, Multi-turn coil domain 2 & 3 were selected, domain 2 & 3 contains the Rectangles R1 &

R2 which represents the overall cross section of the coil. Then Electrical Circuits (transmitter & receiver)

were selected from the Physics, the components were connected according to node number, 1 uF

capacitors were selected to mimic the parallel resonance component selected for transmitter were –

voltage source (20v-AC), capacitor (1uF),a resistor(~0.001 ῼ) & external I vs. U circuit, which

represents’ the coil R1, here a resistor of 0.001 ῼ was selected because of the coil resistance. Component

selected for the receiver were – capacitor, load resistor, a small resistor (~coil resistance) & external I vs.

U circuit, which represents the coil R2. All of the components were connected in parallel.

Mesh-COMSOL divides the whole system into smaller area such as Free Triangular, Free Tetrahedral etc.

Mesh was done, free triangular mesh was selected for the “remaining” geometry, and element size was

selected as “extremely fine”.

Study-For study, frequency domain was selected. At first a range of frequencies were selected to find the

resonant frequency. Parametric sweep was used to analyze the model at different “d” (distance between

coils) and at different load resistor.

1.15.3.2. Two-Coil Simulation

Range of frequencies was used to search for the resonant frequency and it was found at 18.15 Khz. A

simple technique was followed to find the resonant frequency, data of receiver & transmitter coil power

were acquired at different range of frequencies, and efficiency vs. range of frequencies was plotted.


83. Fig 3.6 Coil Geometry -3D View

84. Fig 3.7: Coil Geometry-Top View


85. Fig 3.8: Power Transmission Efficiency at resonant frequency


86. Fig 3.9(a): Magnetic Flux Density at d=100 mm

87. Fig 3.9(b): Magnetic Flux Density at d=140 mm© Faculty of Engineering, American International University-Bangladesh (AIUB) 57

88. Fig 3.10(a): Magnetic Field at d=100 mm

89. Fig 3.10(b): Magnetic Field at d=140 mm© Faculty of Engineering, American International University-Bangladesh (AIUB) 58

Fig 3.11(a): Electric Field at d=100 mm

Fig 3.11(b): Electric Field at d=140 mm


The coil at the right side of the diagrams is the transmitter coil and the left side coil is the receiver coil,

circuit used for the simulation was shown as schematic in page 51, two transfer distance was used to test

the coil, (d=100mm & 140 mm) & different types of load resistor were used (0.1K , 1k, 10k).

Fig 3.12: Power Transmission Efficiency at different load Resistor

Fig 3.13: Overall Efficiency


The Fig 3.11 of the previous page is the Power Transfer Efficiency Curve. It was plotted using COMSOL

data. Efficiency was calculated as (total power received/total power sent) and the Fig 3.12 is the overall

efficiency curve. It was plotted as (power at the load/power at the source). Also, it was observed that the

2-Coil works well at minimal distance. Efficiency was maximum for 0.1k load resistor at minimal

distance but efficiency drops rapidly as distance between two coil increases. Efficiency drop is least for 1k

load resistor.

1.15.3.3. Design improvements I – Flat Spiral Coil System Setup

The geometry of the previous 2-Coil system was- two helical coil placed facing opposite to each other and

it was observed that the efficiency was not satisfactory. Also the range of power transmission was

compromised. The low amount of Magnetic Flux Linkage between the coil were the cause for the low

efficiency and it was found that these low flux linkage was due to the geometrical shape of the coil, this

problem can be minimized by redefining the coil geometry. A new model was designed that was the Flat

Spiral Coil, it was also known as Tesla Coil developed by Nikola Tesla around 1891 for experimental

purpose. Same circuit was used[Fig-3.5],the only difference were the replacement of the helical coils with

these Flat Spiral Coil.

90. Fig 3.14: Flat Spiral Coil


91. Table 3.4: Parameters for 2-Coil Flat Spiral Design

R 50[mm] Inner Radius

N 30 Coil turns

Rw 0.66[mm] Cross sectional wire radius

H N*Rw + R Outer Radius

D 100[mm] Distance between coils

Res 1000 ῼ Load Resistance

(a)


(b)

92. Fig 3.15(a) 3D view (b) Top view Coil Geometry

Geometry-Similar to the previous 2-Coil design, One circle & two rectangles were selected, the circle

(C1) has the radius “2*d+2*Rw” and the two rectangles (R1, R2) have width of “H” & Height of “2*Rw”

Physics & Mesh were similar to the previous design

Study-Efficiency curve was plotted at different range of frequency to find the resonant frequency (~10.21

KHz)then distance sweep were used to plot efficiency curve over distance.


93. Fig 3.16 Power Transmission Efficiency at Resonant Frequency


(a)

(b)

94. Fig 3.17 (a) Magnetic Flux Density at d=300 mm (b) Top View


(a)

(b)

95. Fig 3.18 (a) Magnetic Flux Density at d=400 mm (b)Top View


(a)

(b)

96. Fig 3.19 (a) Magnetic Field at d=300 mm (b)Top View


(a)

(b)

97. Fig 3.20 (a) Magnetic Field at d=400 mm (b)Top View


(a)

(b)

Fig 3.21 (a) Electric Field at d=300 mm (b)Top View


(a)

(b)

98. Fig 3.22 (a) Electric Field at d=400 mm (b)Top View


The coil at the right side of the diagrams or at the top one is the transmitter coil and the left side or the

bottom coil is the receiver coil, circuit used for the simulation was shown as schematic in page 51, two

transfer distance were used to test the coil, (d=300mm & 400 mm) & different types of load resistor were

used (0.1K, 1k, 10k) as parametric sweep.

99. Fig 3.23 Power Transmission Efficiency at different load Resistor

100. Fig 3.24: Overall efficiency


Fig 3.23 is the Power Transmission Efficiency Curve. It was plotted by using the COMSOL data (power

received/power sent) and Fig 3.24 is the overall efficiency curve which was plotted by taking (power

across load/source power), it can be inferred that the overall efficiency increased in this flat spiral coil

model. The efficiency was good at larger distance when 1k load was used (ῃ ~17.5 % at d=300mm). This

improvement in efficiency was due to greater magnetic flux linkage between the coils. The efficiency

drop follows the same trend with the previous 2-Coil design. The efficiency curves were steep, efficiency

drop was rapid as distance was increased. This problem was solved. Another coil model were designed

using the same Flat Spiral Coil but this time a resonator in between two coils were used.

1.15.3.4. Design Improvements II-Flat Spiral Coil with resonator

It was known from the theory that improvement of efficiency at larger distance can be significant if a third

coil is inserted between the coils. A resonator coil was introduced between the two coils which maintained

a fixed distance with the receiver coil.

101. Fig 3.25 Equivalent Circuit for 3 Coil design

102. Table 3.5: Parameters for 3 Coil

R 50[mm] Inner Radius

N 30 Coil turns

Rw 0.66[mm] Cross sectional wire radius

H N*Rw + R Outer Radius

D 100[mm] Distance between coils

Res 1000 ῼ Load Resistance


All the procedure for running the simulation were same except the introduction of the resonator. The

distance between the resonator & the receiver coil was fixed, the distance was kept minimum to ensure

inductive coupling between the resonator & the receiver. The resonator was used to increase the efficiency

of the system.

(a)

(b)

103. Fig 3.26 (a) Coil Geometry (b) Closer look at the resonator and the receiver


104. Fig 3.27 Power Transmission Efficiency at resonant frequency

105.

Resonant frequency was found to be 6.68 KHz where Power Transmission Efficiency was found

maximum.


(a)

(b)

106. Fig 3.28 (a) Magnetic Flux Density at d=300 mm (b) Top view


(a)

(b)

107. Fig 3.29 (a) Magnetic Flux Density at d=400 mm (b) Top view


(a)

(b)

108. Fig 3.30 (a) Magnetic Field at d=300 mm (b) Top view


(a)

(b)

109. Fig 3.31 (a) Magnetic Field at d=400 mm (b) Top View


(a)

(b)

110. Fig 3.32 (a) Electric Field at d=300 mm (b) Top View


(a)

(b)

111. Fig 3.33 (a) Electric Field at d=300 mm (b) Top view


The coil at the right side was the transmitter coil & the left side contains the resonator and the receiver

coil. Here if we compare the efficiency at d = 300 mm with the previous simulations it can be seen that

the ῃ was 2% for the first simulation (normal 2 Coil setup) 18% for the second simulation (2 Coil Flat

Spiral) and 39% for this simulation. All the efficiency readings were taken for the load at 1kῼvariation of

efficiency due to change in load were also minimized. It can be observed from the figure that the curves

were less steep for different load. Also it was found that at d = 400 mm the ῃ was ~20% which were

negligible for the previous two simulations.

(a)


(b)

112. Fig 3.34 (a) Power Transmission Efficiency (b) Overall Efficiency


3.2.4 Theoretical Power transmission at Radio-Frequency using 10pF capacitor

It was observed that the previous simulations had resonant frequencies at Kilohertz range with 1uF

as external capacitor, that seriously compromised the effective distance of wireless transmission,

According to the theory if we can replace the capacitor with a much lower value capacitor it will

increase the resonant frequencies, thus bolster the overall power transmission efficiency. To verify

the theory a simulation was run in COMSOL. Capacitor of 10pF on both side (receiver &

transmitter) were used to mimic the resonance, resonant frequency was found at 2.95 MHz due to

low external capacitance. However this simulation was not practical because some of the factors

that occur due to this high frequency were completely ignored.

113. Fig 3.35 Power Transmission at 2.95 MHz & 10pF External Capacitor

It can be clearly seen that the range almost doubled, and efficiency drop due to variation of load

were also minimized. But the factors that were not taken into considerations while running the

simulation were the proximity effect and the skin effect, at such high frequency skin effect must be

seriously taken into account, no steps were taken to reduce this effect, the proximity effects results


in redistribution of current, causing it to flow only on the surface of the wire, at radio-frequency

this effect intensifies further. But all of these effects can be reduced practically which will be

discussed in chapter 5.

1.16. Conclusion

In conclusion, we can say that the efficiency of the flat spiral coil was greater than that of the helical coil

for our designed two coil parallel resonance model in the KHz frequency range. The range of the spiral

ring coil was greater too. In the MHz range increased amount of power was transmitted with greater

efficiency over longer distances.


Chapter 4

Physical Implementation and Measured Data

1.17. Introduction

This chapter introduces the physical implementation of the basic two coil parallel resonance circuit. The

physical implementation was carried out only to see if the practical data, for our design of the coil,

matched the trend set by the simulated outputs. As we just wanted to ensure that the trend found from the

simulated data was correct, amplifiers and Litz wire principles were not applied to the physical design.

Two different types of coil were made to see the variation in efficiency with changing distance. One was a

helical coil and another flat spiral coil. We also made two different types of helical coil- one with the coil

wound around a cylindrical cardboard structure and another with the coil wound around a PVC pipe. For

all the coils, current and voltage was measured in both the transmitter and receiver side and these values

were used to calculate efficiency. For all the coils the number of turns, inner diameter of coil, pitch, the

load resistances and the capacitor values were kept constant.

1.18. Practical experiment setup

The circuit was connected as shown in the figure below. The voltage across the 1 ohm resistors were

observed by a millimeter. As V = IR and R = 1 ohm so the value of V gave us the current in the wire. One

ohm resistance was selected because it was the minimum resistance available and its value was

insignificant comparing to the load resistance.

114. Fig 4.0: experimental setup.

115.


116.

1.19. Helical Coil

1.19.1. Coil wound around cardboard core

117. Fig 4.1: Parallel two coil circuit model

118.

Fig 4.1 shows the parallel two coil circuit implemented using two helical coils wrapped around in

cylindrical cardboard structure. These two coils were used to find the practical efficiency of the system as

the distance was varied.


1.19.1.1. Measured data for 1 KΩ load resistor

First the circuit was set up s shown in Fig 3.1. The values of capacitance used for both the

transmitter and receiver capacitor was 1 µF and the load resistance (ZL) used was 1 KΩ. The

connection to the frequency generator was given to the transmitter coil. Both the receiver and

transmitter were connected to a digital oscilloscope. The distance of separation of the two coils

was noted down. The resonant frequency, calculated from our MATLAB data, was used to find the

variation in efficiency with distance of separation. This value was 16 KHz. After this frequency

was supplied to the transmitter coil, transmitter voltage and receiver voltage was noted down from

the oscilloscope. The current on both the transmission and receiver side was measured using a

Multimeter. For the transmission side the current was measured across the capacitors, with the

Multimeter probes connected in series with it. For the receiver side the probes were connected to

the load resistor to find the receiver current. After writing down all the values of current and

voltage the efficiency was calculated from the formula,

Efficiency=(V R *IR )/(V T * IT )

The distance of separation of the two coils was then changed and the values of current and voltage

was measured again to calculate the efficiency.

The output (receiver side) was connected to load resistor and is shown by the Channel 1 output

(yellow wave) in Fig 4.2(a) and 4.2(b) and the input was connected to the capacitor in the

transmission side and is shown as the Channel 2 output (blue wave) in the same figures.


119. Fig 4.2(a): Oscilloscope output for 1KΩ load resistor

120.

121. Fig 4.2(b): Oscilloscope output for 1KΩ load resistor

122.


123. Table 4.1: Measured values for 1 KΩ resistor

Distance (cm)

VT, Transmitter Voltage(mV)

VR, Receiver Voltage(mV)

IT, Transmitter Current (mA)

IR, Receiver Current (mA)

Efficiency (%)

5.5 960 264 5.79 4.4 20.97.5 940 112 3.4 4.2 14.7

10.5 720 96 6.03 4.4 9.7311 740 88 9.25 4.2 5.4

11.5 760 88 7.23 4.5 7.2112.5 680 68 7.88 4.1 5.213.5 680 52 7.65 4.2 4.214 720 48 9.15 4.2 3.06

14.5 640 34.2 21.1 4.1 1.04

4 6 8 10 12 14 160

5

10

15

20

25

Distance

Effici

ency

124. Fig 4.3: Efficiency vs. Distance curve for 1KΩ load resistance

As we can see from Fig 4.3, the efficiency of the system decreased as the distance of separation was

increased. The experimental values obtained were comparable to the values of efficiency obtained from

COMSOL at those distances. These values however were not completely accurate because the high

frequency components, Rac and parasitic capacitance, were not taken into consideration. If an amplifier

had been used the values would have been much more presentable. Since just the trend was to be

examined an amplifier was not considered.



The efficiency was again measured for varying units of distance for a 10 KΩ load resistor. The number of

turns on primary and secondary winding was kept the same as before to keep the analysis of efficiency

only varying to distance and no other factors. Similarly the coil pitch was kept constant at 0.5 cm; the

same cardboard coils were used as before so as to ensure that the cylindrical structures had the same inner

diameter. All the other coil parameters remained unchanged. Only the load resistance was changed to 10

KΩ. Resonant frequency used as the same as before (16 KHz). The value of capacitor on both the

transmitter and receiver side remained unchanged. The same procedure was followed as mentioned

before.

The output (receiver side) was connected to load resistor and is shown by the Channel 1 output (yellow

wave) in Fig 4.2(a) and 4.2(b) and the input was connected to the capacitor in the transmission side and is

shown as the Channel 2 output (blue wave) in the same figures.

125. Fig 4.4(a): Oscilloscope output for 10KΩ load resistor


126. Fig 4.4(b): Oscilloscope output for 10KΩ load resistor

127.


Distance (cm)


VR, Receiver Voltage (mV)



Efficiency (%)

5.5 1320 536 6.21 3.9 25.57.5 1280 492 7.82 4.1 20.14

10.5 1380 400 9.82 3.6 10.6311 1320 412 13.76 3.6 8.17

11.5 1440 404 14.31 3.8 7.4512.5 1380 312 10.87 3.8 8.1113.5 1280 224 10.6 3.9 6.114 1280 220 16.17 3.7 4.04

14.5 1000 112 19.43 3.8 2.19129.


5 6 7 8 9 10 11 12 13 14 150

5

10

15

20

25

30

Distance

Effici

ency


131.

As we can see from Fig 4.5 the variation of efficiency with changing distance does follow the trend

obtained earlier in the book for simulated data. Hence the data was satisfactory.

However, while conducting the experiment we noticed that our coil, at times, received interference from

the 50 Hz AC supply lines inside the walls; as the two coils did not couple and even at resonant frequency

the oscilloscope showed a frequency of 50 Hz.

Additionally, with increased load resistance we observed more harmonic distortion in our output even

though the overall efficiency of the system was greater. This can be seen in Fig 4.4(a) and 4.4(b).

Increased interference with the AC supply line of 50 Hz can be one possible explanation for this, since the

system did not have proper lagging and hence would be prone to resonance with the 50 Hz AC supply.

Another possible reason can be the fact that Litz wire was not used. A Litz wire would have ensured that

the skin effect, which occurs at high frequencies, to be minimized. Increased skin effect would be a reason

for increased distortion. Also, the parasitic capacitance and proximity effect could have an effect since the

pitch was small. If the wires are too close these two effects would be greater at high frequencies and

would cause increased distortion.


To ensure more ideal conditions the coils were reconstructed with a PVC pipe acting as core. The

permittivity of the pipe is more comparable to wood and hence provided much more satisfactory values of

efficiency at the same distances.

1.19.2. Coil wound around plastic PVC core

132. Fig 4.6: Parallel two coil circuit model

The circuit was reconstructed with two PVC pipes replacing the cardboards as cores. The same procedure

was followed to find the efficiency with changing distances. All the other parameters and values of circuit

components were kept the same as with the cardboard core helical coils in order to ensure uniformity in

obtained readings.

Again the output (receiver side) was connected to the load resistor and is shown by the Channel 1 output

(yellow wave) in Fig 4.6 and the input was connected to the capacitor in the transmission side and is

shown as the Channel 2 output (blue wave) in the same figure.


133. Fig 4.7(a): Output obtained from helical coil with PVC pipe as core

134.


135. Fig 4.7(b): Output obtained from helical coil with PVC pipe as core

136.

137.

138.




Distance (cm)





Efficiency (%)

5.5 536 200 6.6 4.8 27.17.5 656 156 6.6 4.4 15.9

10.5 688 88 6.3 5.4 10.911 688 88 8.4 4.5 6.9

11.5 688 84 6.4 4.2 8.212.5 700 64 6.4 4.1 5.913.5 700 68 8.1 4.2 514 708 64 8.4 4.2 4.5

14.5 704 44 8.4 4.1 3.05

140.

141.


143.

144.

145.


5 6 7 8 9 10 11 12 13 14 150

5

10

15

20

25

30

Distance

Effici

emcy

146.

147.

148.



Distance (cm)





Efficiency (%)

5.5 420 204 6.3 4.4 33.927.5 540 184 6.4 4.3 22.89

10.5 476 84 6.2 4.2 11.9511 620 100 8.5 4.3 8.2

11.5 616 76 6.5 4.1 7.812.5 612 72 8.1 4.4 6.413.5 588 64 6 4.2 7.614 632 60 8.3 4.5 6.3

14.5 652 52 6.3 4.7 6.1

5 6 7 8 9 10 11 12 13 14 150

5

10

15

20

25

30

35

40

Distance

Effici

emcy


151.


As we can see from Fig 4.8 and Fig 4.9, the trend found matches the trend of the simulated data. In both

the curves the efficiency decreases as the distance of separation is increased. The efficiency of the system,

at similar distances, increased with the increase in load resistance.

1.19.3. Flat Spiral Ring Coil

152. Fig 4.10(a): Flat Spiral Ring design


153. Fig 4.10(b): Flat Spiral Ring design

154.

The flat spiral rings were designed as shown above. Like the helical coils they were placed at varying

distances and their current and voltage readings taken. The voltage and current readings were taken in the

receiver and transmitter side. The resonant frequency was again 16 KHz. A 100 Ω load resistor was used.

As before the load was connected across Channel 2 and input across Channel 1.


155. Table 4.5: Measurement for flat spiral coil

Distance (cm)





Efficiency (%)

5.5 428 224 6.2 4.9 41.367.5 424 172 6.4 4.8 30.4

10.5 416 116 6.6 4.8 20.2811 424 90 6.8 4.5 14.05

11.5 440 90 6.9 4.5 13.3412.5 424 66 6.7 4.4 10.2213.5 440 62 6.5 4.2 9.114 416 40 6.3 4.5 6.86

14.5 440 29 6.2 4.1 4.3515 440 16 6.4 4.2 2.39

4 6 8 10 12 14 160

5

10

15

20

25

30

35

40

45

Distance

Effici

ency

156. Fig 4.11: Efficiency vs. Distance for flat spiral coil

Again we can see that even for this coil the trend matches the trend set by the simulated data.

Comparing the efficiency values for the 100 Ω load resistors of the two helical coils- cardboard and PVC;

and this spiral coil we can see that the spiral coil has higher efficiency at the same corresponding values.

The decrease in efficiency with increasing distance is also more uniform.


157. Fig 4.12: Oscilloscope output for flat spiral coil

1.20. Conclusion

We can conclude from the results obtained that as the value of the load resistance was increased the

system became more efficient. However, for all four cases the values obtained for the two coil system

matched the trend obtained from the simulation data. Although the values obtained were only

approximates and not accurate, they were satisfactory as they were comparable to the simulation results.

The flat spiral coil provided greater efficiency than the helical coils at a load resistance of 100 Ω.

Chapter 5


Discussions and Conclusions

1.21. Discussions

The thesis, at its completion, proved that power can indeed be transmitted wirelessly with good enough

efficiency. Even though our practical data were just approximates, systems with better designs and less

prone to interference from outside AC sources can provide even more accurate data at increased

efficiency. Our simulated data shows that using wireless power transmission power can be transmitted

from short to medium range distances at appropriate efficiencies. The simulation data was obtained from

MATLAB which provided the numerical output only. COMSOL was also used and that provided us with

much more appropriate values and values more befitting to our experimental data. Our experimental

outputs matched the theoretical ones and hence it proves the trend obtained was correct and the thesis

successful.

1.21.1. Comparison of Simulation Data with practical

Comparing the simulated data we see that the trend of decreasing efficiency with increasing distance

matches for MATLAB, COMSOL and practical data. The coils made for the practical data were not a

perfect match with model considered in simulation but the resonant frequency was observed close to the

frequency calculated in simulation.

158.

1.22. Suggestion for Future Work

The successful working of this thesis sets the ground for further enhancements and upgrades onto this idea

and the expansion of wireless power transmission to make it more viable for transmitting power more

efficiently over longer distances. This creates possibilities and space for exploration into new innovations

that can be added to further improve the idea, adding immense potential to the idea which is worth

considering for future implementations.

1.22.1. Consideration of high frequency components


If the high frequency components such as the parasitic capacitance, Rac, proximity effect and skin

effect are considered during the physical implementation of the system, more satisfactory values

can be obtained. Using a Litz wire will ensure that the skin effect in minimized and that will

increase the efficiency as the harmonic distortions at higher frequencies will be reduced. With

lower harmonic distortion less power will be lost as noise and more can be transmitted

successfully to the receiver winding.

A Litz wire consists multiple strands of thin wires that are insulated and twisted together to help

reduce skin effect and proximity effect. If skin effect occurs, current at high frequencies flow at

the surface of the conductor. This will reduce the magnetic field inside the wire which will affect

the self inductance of the wire. This effect on the internal inductance was ignored in our practical

implementation and hence no work was done in the MHz range.

1.22.2. Use of an E-class amplifier

If an E-class amplifier is used at the transmission side, the power of the transmitted signal will be

increased and this means that more power will be available to the receiver coil. This will mean

more power can be received.

1.22.3. Introducing different coil parameters into the practical implementation

More coil parameters can be introduced into the practical implementation to ensure that efficiency

different types of coil can be measured to ensure that the study is more comprehensive. Coils of

different shapes, differing number of turns and differing coil parameters such as-inner diameter of

coil, pitch etc., can be used and their efficiencies found to endure that the study is much more wide

and takes into consideration all forms of coil parameters.

1.22.4. Wireless power transmission at higher frequencies

Power transmission at higher frequencies, such as the MHz or Ghz ranges, will allow greater

amount of power to be transmitted and make certain that the study can be done on varying

resonant frequencies for the same coil designs.

1.22.5. Integration of Metamaterials


Metamaterials can be used with the existing coil design to further increase the efficiency of the

system and make it more commercially useful.

1.22.6. Use of larger coils

Larger coils can be used to transmit greater amounts of power over longer distances. If the coil can

be wounded more uniformly on cores that have permittivity close to that of vacuum, than wireless

power transmission can be done more efficiently over longer distances for larger units of power

transfer.

1.23. Conclusions

In this book a design for two coil parallel circuit model was proposed and implemented. Three coil and

flat spiral coil systems were also examined upon to make the overall system more efficient. The proposed

design successfully transferred power efficiently over short to medium range distances with a very basic,

inexpensive design, ensuring that with increased effort and sponsorship on the field of wireless power

transmission it can be a viable long term solution to the world power necessities.

159.

160.

161.

References:


1. Seung-Hwan Lee Robert D. Lorenz, Development and Validation of Model for 95% Efficiency, 220W Wireless Power Transfer over a 30cm Air-gap, IEEE Fellow, University of Wisconsin-Madison, WEMPEC.

2. André Kurs,et al., Wireless Power Transfer via Strongly Coupled Magnetic Resonance, Science 317, 83 (2007).

3. Sanjay Kumar, Sonu kr. Singh, Sant kr. Mehta, Ranjeet kr. Singh, Sanjay kumar, Ravi Shankar pd. Dangi, WIRELESS POWER TRANSMISSION- "A PROSPECTIVE IDEA FOR FUTURE", Dr. M.G.R Educational and Research Institute University, Chennai, India.

4. Kilaru Kalyan, Shaik Avaes Mohsin, Angadi Suresh, Transmission of Power through Wireless Systems, International Journal of Engineering and Advanced Technology (IJEAT) ISSN: 2249 – 8958, Volume-2, Issue-4, April 2013.

5. Duan Zhao, Enjied Ding, Yanjun Hu, Zhifeng Sun, Design and Simulation of Multiple Coil Model for Wireless Power Transmission System, China University of Mining and Technology.

6. How Wireless Power Works. [Online]. Available: http://electronics.howstuffworks.com/everyday-tech/wireless-power.html [Cited: 10th October 2014].

7. The top six wireless charging handsets. [Online]. Available: http://www.cnet.com/news/the-top-six-wireless-charging-handsets-roundup/ [Cited: 10th October 2014].

8. Power by PROXI.[Online]. Available: http://powerbyproxi.com/about/ [Cited: 11th October 2014]

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10. Proxi-Ring Wireless Slip Ring. [Online]. Available: http://powerbyproxi.com/industrial-applications/proxi-ring/ [Cited: 11th October 2014]

11. Toyota tests wireless charging for electric cars. [Online]. Available: http://www.marketwatch.com/story/toyota-tests-wireless-charging-for-electric-cars-2014-02-18 [Cited: 11th October 2014]

12. Wireless Charging ICs, Wireless Power ICs. [Online]. Available: http://www.idt.com/products/power-management/wireless-charging-ics-wireless-power-ics [Cited: 11th October 2014]


http://www.marketwatch.com/story/toyota-tests-wireless-charging-for-electric-cars-2014-02-18

http://powerbyproxi.com/industrial-applications/proxi-ring/

http://powerbyproxi.com/industrial-applications/proxi-ring/

http://powerbyproxi.com/industrial-applications/proxi-point/

http://powerbyproxi.com/industrial-applications/proxi-point/

http://powerbyproxi.com/about/

http://www.cnet.com/news/the-top-six-wireless-charging-handsets-roundup/

http://www.cnet.com/news/the-top-six-wireless-charging-handsets-roundup/

http://electronics.howstuffworks.com/everyday-tech/wireless-power.html

http://electronics.howstuffworks.com/everyday-tech/wireless-power.html

13. Alexey Bodrov and Seung-Ki Sul, “Analysis of Wireless Power Transfer by Coupled Mode Theory (CMT) and Practical Considerations to Increase Power Transfer Efficiency” in Wireless Power Transfer - Principles and Engineering Explorations, Ki Young Kim, ED. Croatia: InTech Europe, 2012, pp. 19 - 50. [E-book] Available: Wireless Power Transfer | InTechOpen. Access Date: 09.10.14

14. T. Imura, H. Okabe, T. Uchida, Y. Hori, Study on open and short end helical antennas of wireless power transfer using magnetic resonant couplings, The 10th University of Tokyo – Seoul National University Joint Seminar on Electric Engineering, pp. 175-180, Seoul, 2010.

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http://mathforum.org/library/drmath/view/53769.html

APPENDIX

APPENDIX A

Solving circuit mesh equation

Let we have an equation

A1X+B1Y + C1Z + D1W = E1

A2X+B2Y + C2Z + D2W = E2

A3X+B3Y + C3Z + D3W = E3

A4X+B4Y + C4Z + D4W = E4

This can be written in matrix form in

¿ * [ XYZW

] = [E 1E 2E 3E 4

]So, [ X

YZW

] = ¿¿ * [E 1E 2E 3E 4

]This calculation can be done easily using MATLAB.

This can be done for any equation containing more number of variables.


APPENDIX B

Bessel function

Ber(q)= 212∗exp( 2

12∗q2 )∗( cos ( 2

12∗q2

− pi8 )+cos ( 2

12∗q2

−3∗pi8 )

8∗q)

2∗p i12∗q

12

;

[22] (note exp = e^)

Bei(q)= 212∗exp( 2

12∗q2 )∗( sin (2

12∗q2

− pi8 )+sin( 2

12∗q2

−3∗pi8 )

8∗q)

2∗p i12∗q

12

;

[22] (note exp = e^)

Using MATLAB the derivatives were found.

Ber’(q)=

exp( 212∗q2 )∗( cos (2

12∗q2

− pi8 )+cos( 2

12∗q2

−3∗pi8 )

8∗q)

2∗p i12∗q

12

−2

12∗exp ( 2

12∗q2 )∗( cos( 2

12∗q2

− pi8 )+cos( 2

12∗q2

−3∗pi8 )

8∗q)

4∗p i12∗q

32

−

212∗exp( 2

12∗q2 )∗( 2

12∗sin (2

12∗q2

− pi8 )

2+cos ( 2

12∗q2

−3∗pi8 )

8∗q2 +2

12∗sin (2

12∗q2

−3∗pi8 )

16∗q)

2∗p i12∗q

12

;

Bei’(q)=

exp( 212∗q2 )∗( sin( 2

12∗q2

− pi8 )+sin ( 2

12∗q2

−3∗pi8 )

8∗q)

2∗p i12∗q

12

+

212∗exp ( 2

12∗q2 )∗( 2

12∗cos ( 2

12∗q2

− pi8 )

2−sin( 2

12∗q2

−3∗pi8 )

8∗q2 +2

12∗cos (2

12∗q2

−3∗pi8 )

16∗q)

2∗p i12∗q

12

−2

12∗exp( 2

12∗q2 )∗( sin( 2

12∗q2

− pi8 )+sin( 2

12∗q2

−3∗pi8 )

8∗q)

4∗p i12∗q

32

;


efficiency analysis of wireless power transmission system using magnetic resonant coupling

Documents

magnetic resonant coupling

degree of bachelor

partial fulfillment

following students

original work

following respected

guide supervisor shuvra

deep regard