Bachelor- thesis, optimization of wireless power transfer coils using finite element simulation-2016

01-02-2016
BEng. Final Project
Wireless Power Transfer
Department of Electrical technology
DTU Diplom
Lautrupvang 15, 2750 Ballerup
1
Optimization of wireless power Transfer
coils using Finite Element simulation
BEng (Thesis) . Final Project
Abstract
The limit of powering devices is a huge hurdle due to the limited and unreliable wires.
Imagine a device who does not need any powering wire or even a battery, which will instead
get the power wirelessly over the air. Biometric implantations are the best example for the
current age to have the demand for such wirelessly powered devices. To make such a device
possible the transfer efficiency needs to be increased. To increase the efficiency inductor coil
needs an optimization. This is the aim of this thesis, to investigate the optimization and the
efficiency of the inductor coils using FEMM simulation software.
This report starts with historical background of Wireless Power Transfer (WPT), motivation
behind the project and the objective set to investigate efficiency and optimization WPT coils.
This report continues with a presentation of basic circuit and its theoretical framework
behind WPT, and the framework is then broken down into its basic mathematical expressions
that generates the basic variables.
Furthermore, this report covers documentation of an investigation on WPT inductor coils
using FEMM simulation software. The parameters generated from FEMM simulation models
are then, verified using Pspice simulation software for different frequency range with respect
to distance between coils.
Further, in this report the parameters generated from FEMM simulation verified by Pspice
simulations, by mathematical calculations and implementing a practical model.
Supervisor: Lars Maack
Head of studies, associate professor
Center for Bachelor of Engineering Studies
lmaa@dtu.dk
Student: Danish Bangash : s104712
BEng. Computer and Electronics Engineering
Center for Bachelor of Engineering Studies
dmab@dtu.dk

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Dedicated
to
My Parents & my brothers 

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Table of Contents
Preface..................................................................................................................................................... 6
List of Figures ......................................................................................................................................... 7
List of Tables........................................................................................................................................... 8
List of Plots ............................................................................................................................................. 9
Chapter 1 ............................................................................................................................................... 10
Introduction ....................................................................................................................................... 10
History of wireless Power Transfer................................................................................................... 10
Motivation ......................................................................................................................................... 10
Objectives.......................................................................................................................................... 11
Organization of Thesis ...................................................................................................................... 11
Variables and Abbreviations ......................................................................................................... 11
Chapter 2 ............................................................................................................................................... 12
Introduction ....................................................................................................................................... 12
Basic Circuit...................................................................................................................................... 12
Mathematical Representation of WPT Basic Circuit ........................................................................ 13
Resistance...................................................................................................................................... 13
Inductance ..................................................................................................................................... 13
Coupling Coefficient..................................................................................................................... 14
Load Resistance............................................................................................................................. 14
Reflected Load Theory.................................................................................................................. 15
Voltage Drop across Inductor Coil................................................................................................ 15
Wireless Power Transfer Efficiency of Coils................................................................................ 15
Chapter 3 ............................................................................................................................................... 16
Implementation of practical coils before simulations........................................................................ 16
Chapter 4 ............................................................................................................................................... 18
Wireless Power Transfer modelled in Finite Element Method Magnetics (FEMM) ........................ 18
FEMM Simulation......................................................................................................................... 18
Simulation Setup ........................................................................................................................... 18

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Simulation Results......................................................................................................................... 19
Conclusion..................................................................................................................................... 21
Chapter 5 ............................................................................................................................................... 22
Wireless Power Transfer (WPT) Pspice Verification........................................................................ 22
Simulation Setup ........................................................................................................................... 22
Simulation Results Primary Coil................................................................................................... 23
Simulation Results Secondary Coil............................................................................................... 24
Power Transfer Efficiency from Pspice perspective ..................................................................... 25
Time Domain Analysis ................................................................................................................... 26
Conclusion......................................................................................................................................... 28
Chapter 6 ............................................................................................................................................... 29
Wireless Power Transfer (WPT) FEMM Model Mathematical Verifications .................................. 29
Calculations................................................................................................................................... 29
Conclusion......................................................................................................................................... 33
Chapter 7 ............................................................................................................................................... 34
Practical Model Verification ............................................................................................................. 34
Practical Wireless Power Transfer Model Setup........................................................................... 34
Practical Model Results................................................................................................................. 34
Conclusion......................................................................................................................................... 35
Chapter 8 ............................................................................................................................................... 36
FEMM Multi turns Hypothesis for WPT Model After verifications................................................. 36
Hypothesis 1: Four turns Defined within FEMM block properties............................................... 36
Hypothesis 2: Four turns individual 6 mm wire method............................................................... 38
Hypothesis 3: Replacement; 6 mm wire by four 3 mm wires in the same 6 mm area .................. 40
Conclusion:........................................................................................................................................ 42
Chapter 9 ............................................................................................................................................... 43
Initial Conclusion .............................................................................................................................. 43
Simulations and calculations ......................................................................................................... 43
Practical Test................................................................................................................................. 43

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Hypothesis......................................................................................................................................... 44
Final Conclusion................................................................................................................................ 44
Future Work ...................................................................................................................................... 45
Appendix............................................................................................................................................... 46
Simulation Figures Chapter 5 (Pspice).............................................................................................. 46
Simulation Figures Primary Coil................................................................................................... 46
Simulation Figures Secondary Coil............................................................................................... 47
Simulation Figures Power transfer efficiency ............................................................................... 49
Practical Model Results figures Chapter 7........................................................................................ 51
Primary Coil Scope measurements................................................................................................ 51
Secondary Coil Scope measurements with Load .......................................................................... 53
Secondary Coil Scope measurements without Load ..................................................................... 56
Bibliography...................................................................................................................................... 58
References ......................................................................................................................................... 58
Time Plan .......................................................................................................................................... 60
Matlab Scripts for FEMM Simulations............................................................................................. 62
Matlab Script for WPT model....................................................................................................... 62
Matlab Scripts for three types of hypothesis ................................................................................. 63
Pspice AC Circuits For all tested frequencies .................................................................................... 69

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Preface
This thesis work conducted as the last part of the Bachelor of Engineering program in Computer and
Electronics Engineering at Denmark Technical University (DTU) from, 1 Feb 2016 to 7 June 2016.
An enormous amount of time and energy has been put into the investigation process, research and
studying a wide range of information around the globe. The contents of this report clarifies and
verifies the analysis of Wireless Power Transfer (WPT) coils with an assessment of its practical
applicability in terms of optimization using finite element simulation FEMM, pspice, matlab,
mathematical verification and practical coils implementation.
I would like to thank Denmark Technical University (DTU) and their authorities for providing me the
opportunity to study, BEng. Computer and Electronics program in their tremendous and outstanding
educational environment. Also giving me the opportunity to conduct my final thesis at DTU- Ballerup
Campus. It has been great pleasure to work in a professional environment.
My special thanks to Lars Maack for providing me the opportunity to work under his excellence and
tremendous supervision and providing me a project of interest. It has always been exciting to work and
have discussion on various aspects of the project. Guiding me throughout the whole session of thesis
with his feedback, advices and made sure that everything is on the right track.

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List of Figures
Figure 2.1: Basic equivalent circuit for Wireless Power Transfer (WPT) -------------------------------- 12
Figure 2.2: Equivalent circuit for Secondary Coil (WPT) ---------------------------------------------------------------------- 14
Figure 2.3: Equivalent circuit for primary Coil (WPT) ------------------------------------------------------------------------- 15
Figure 3.1: coil design for FEMM Simulation and 6 mm semi-grid coaxial copper wire. -------------------------------- 16
Figure 3.2: coil design for FEMM Simulation and 6 mm semi-grid coaxial copper wire. -------------------------------- 17
Figure 4.1: Axisymmetric model, Primary and secondary coil Simulation setup and Practical Set ---------------------19
Figure 4.2: Axisymmetric model, Primary and secondary coil Simulation result -------------------------------------------19
Figure 5.1: Pspice AC Simulation Diagram ----------------------------------------------------------------------------------------- 22
Figure 5.2: Simulation result for Primary with Real power-peak and Vpeak-peak at 211 kHz--------------------------- 46
Figure 5.3: Simulation result for Primary with Real power-peak and Vpeak-peak at 800 kHz--------------------------- 46
Figure 5.4: Simulation result for Primary side with Real power-peak, Vpeak-peak at 4 MHz---------------------------- 46
Figure 5.5: Simulation result for Primary side with Real power-peak, Vpeak-peak at 6 MHz---------------------------- 47
Figure 5.6: Simulation result for Primary side with Real power-peak, Vpeak-peak at 10 MHz--------------------------- 47
Figure 5.7: Simulation result for Secondary side with Real power-peak, Vpeak-peak at 211 kHz
with efficient load ---------------------------------------------------------------------------------------------------------------------------47
Figure 5.8: Simulation result for Secondary side with Real power-peak, Vpeak-peak at 800 kHz
with efficient load--------------------------------------------------------------------------------------------------------------------------- 48
Figure 5.9: Simulation result for Secondary side with Real power-peak, Vpeak-peak at 4 MHz
with efficient load--------------------------------------------------------------------------------------------------------------------------- 48
with efficient load-------------------------------------------------------------------------------------------------------------------------- 48
with efficient load-------------------------------------------------------------------------------------------------------------------------- 49
Figure 5.12: Power efficiency of the system at 211 kHz frequency with efficient load-------------------------------------- 49
Figure 5.13: Power efficiency of the system at 800 kHz frequency with efficient load-------------------------------------- 49
Figure 5.14: Power efficiency of the system at 4 MHz frequency with efficient load---------------------------------------- 50
Figure 5.15: Power efficiency of the system at 6 MHz frequency with efficient load---------------------------------------- 50
Figure 5.16: Power efficiency of the system at 10 MHz frequency with efficient load-------------------------------------- 50
Figure 5.17: Time Domain analysis plot at 211 kHz with max efficient Load------------------------------------------------ 27
Figure 5.18: Time Domain analysis plot at 800 kHz with max efficient Load------------------------------------------------ 27
Figure 5.19: Time Domain analysis plot at 4 MHz with max efficient Load-------------------------------------------------- 27
Figure 5.20: Time Domain analysis plot at 6 MHz with max efficient Load-------------------------------------------------- 28
Figure 5.21: Time Domain analysis plot at 10 MHz with max efficient Load------------------------------------------------ 28
Figure 5.22: Pspice AC simulation Circuits for all tested frequencies--------------------------------------------------------- 69
Figure 5.23: Pspice Time Domain Simulation Circuit for all tested frequencies-------------------------------------------- 69
Figure 7.1: Voltage drop primary coil at 211 kHz frequency------------------------------------------------------------------- 51
Figure 7.2: Voltage drop primary coil at 800 kHz frequency------------------------------------------------------------------- 51

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Figure 7.3: Voltage drop primary coil at 4 MHz frequency--------------------------------------------------------- 52
Figure 7.6: Voltage drop secondary coil at 211 kHz frequency with max efficient Load----------------------- 53
Figure 7.7: Voltage drop secondary coil at 800 kHz frequency with max efficient Load----------------------- 54
Figure 7.8: Voltage drop secondary coil at 4 MHz frequency with max efficient Load------------------------- 54
Figure 7.9: Voltage drop secondary coil at 6 MHz frequency with max efficient Load------------------------- 55
Figure 7.10: Voltage drop secondary coil at 10 MHz frequency with max efficient Load---------------------- 55
Figure 7.11: Voltage drop secondary coil at 211 kHz frequency zero load---------------------------------------- 56
Figure 7.12: Voltage drop secondary coil at 800 kHz frequency zero load---------------------------------------- 56
Figure 7.13: Voltage drop secondary coil at 4 MHz frequency zero load------------------------------------------ 57
Figure 7.14: Voltage drop secondary coil at 6 MHz frequency zero load------------------------------------------ 57
Figure 7.15: Voltage drop secondary coil at 10 MHz frequency zero load---------------------------------------- 58
Figure 8.1: Axisymmetric model Hypothesis 1, Primary and secondary coil Simulation setup--------------- 37
Figure 8.2: Axisymmetric model, Primary and secondary coil Simulation result for Hypothesis 1---------- 37
Figure 8.3: Axisymmetric model Hypothesis 2, Primary and secondary coil Simulation setup--------------- 39
Figure 8.4: Axisymmetric model, Primary and secondary coil Simulation result for Hypothesis 2---------- 39
Figure 8.5: Axisymmetric model Hypothesis 3, primary, secondary coil Simulation setup
and zoomed in primary coil------------------------------------------------------------------------------------------------- 41
Figure 8.6: Axisymmetric model, Primary and secondary coil Simulation result for Hypothesis 3 --------- 42
List of Tables
Table 1.1: Organization of thesis------------------------------------------------------------------------------------------- 11
Table 3.1: Design Limits----------------------------------------------------------------------------------------------------- 16
Table 4.1: FEMM Simulated Circuit Properties for Primary Coil at all tested frequencies------------------- 20
Table 4.2: Simulated Circuit Properties for secondary Coil at all tested frequencies--------------------------- 20
Table 5.1: Pspice AC simulation Parametric Sweep ------------------------------------------------------------------- 22
Table 5.2: Pspice AC simulation Parameters Obtained from FEMM simulation-------------------------------- 22
Table 5.3: Pspice AC Simulation circuit properties for primary coil----------------------------------------------- 23
Table 5.4: Pspice AC Simulation circuit properties for Secondary coil with max efficient Load------------- 24
Table 5.5: Pspice AC Simulation circuit properties for Secondary coil without load--------------------------- 24
Table 5.6: maximum power efficiency of the whole system with max efficient Load--------------------------- 25
Table 5.7: Pspice Time Domain analysis Load Parametric Sweep------------------------------------------------- 26
Table 5.8: Pspice Time Domain simulation Results with max efficient Load------------------------------------ 26
Table 6.1: calculation parameters from simulations for verification---------------------------------------------- 29
Table 7.1: Practical Model circuit properties for primary coil----------------------------------------------------- 34
Table 7.2: Practical Model circuit properties for Secondary coil with max efficient Load------------------- 34
Table 8.1: Hypothesis 1: Simulated Circuit Properties Primary Coil--------------------------------------------- 36
Table 8.2: Hypothesis 1: Simulated Circuit Properties for secondary Coil-------------------------------------- 36

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Table 8.3: Hypothesis 2: Simulated Circuit Properties primary Coil--------------------------------------------- 38
Table 8.4: Hypothesis 2: Simulated Circuit Properties for single turn secondary Coil------------------------ 38
Table 8.5: Hypothesis 3: Simulated Circuit Properties for primary side----------------------------------------- 40
Table 8.6: Hypothesis 3: Simulated Circuit Properties for single turn secondary Coil------------------------ 40
List of Plots
Plot 4.1: Peak Real power of primary coil as function of all tested frequencies------------------------ 20
Plot 4.2: Voltage Drop -primary coil as function of all tested frequencies------------------------------- 21
Plot 4.3: Voltage Drop -secondary coil as function of all tested frequencies----------------------------- 21
Plot 5.1: Voltage Drop -primary coil as function all tested frequencies---------------------------------- 23
Plot 5.2: Peak Real Power- Primary coil as function all tested frequencies----------------------------- 23
Plot 5.3: Voltage Drop -Secondary coil with max efficient Load as
function all tested frequencies----------------------------------------------------------------------------------- 24
Plot 5.4: Peak Real Power –Secondary Coil with max efficient Load as
function all tested frequencies----------------------------------------------------------------------------------- 25
Plot 5.5: Efficiency as function all tested frequencies------------------------------------------------------- 25
Plot 5.6: Max efficiency Load resistance as function all tested frequencies---------------------------- 26
Plot 6.1: Efficiency as function all tested frequencies------------------------------------------------------- 33
Plot 6.2: Max efficient Load resistance as function all tested frequencies------------------------------ 33
Plot 7.1 Voltage drop primary practical measurements as function all tested frequencies--------- 35
Plot 7.2 Voltage drop secondary practical measurements as function all tested frequencies------- 35
Plot 8.1: Hypothesis 1: Voltage drop primary coil as function all tested frequencies---------------- 36
Plot 8.4: Hypothesis 3: peak real power primary coil as function all tested frequencies------------ 41

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Chapter 1
Introduction
Interests for biomedical implantable devices is gaining momentum among both professionals and
research, since they offer variety of systems, Example: Automatic drug delivery, Devices to simulate
specific organs and Monitors to communicate internal vital signs to the outer world.
Though all those devices performs different tasks, one of their common issue is that of power
requirements, and it has been a researched area from past decades. This chapter introduces different
researched work in the area of wireless power transfer.
History of wireless Power Transfer
Supplying power wirelessly has been a great challenge for the scientists of the modern world through
the history of technology. Wireless power transfer is not newly emerged technology, but rather it has
been an area of interest and has been implemented and worked on since 20th
century.
Most common wireless power transfer applications by means of electromagnetic field transferring low
power known as Low Power Transmission (LPT). Over the last century, the challenge of transferring
high power at greater distances is still playing a great role of interest for the scientists, but still
implanting a practical reliable application is still pending, the reason for this is the losses associated
with greater distances.
The first practical application of wireless power transfer was, implemented in the late 1899 this
experiment was, performed by Nicola Tesla in Colorado Springs. In his experiment, he managed to
lighten up 20 incandescent lamps using Inductive Power Transfer.
Thus, several experiments has been, performed since the first Nicola tesla model.
Motivation
Transfer of wireless power has been, used since long time in biometric implants mobile phone
chargers and other short distance low power transfer using the phenomena of power transfer through
the electromagnetic field transfer.
Recently there has been a growing interest towards the innovation of a deeply challenging idea for
wireless power applications: Electronics utilities without chords. Transmission of the electrical power
utilizes it in different form of copper wires; these wires are not so reliable.
Sometimes these wires are weird especially when the apparatus is small. These wires easily gives rise
to sparking, short circuit and it may give dangerous shock. Also due to regular use of these wires, it
becomes less reliable and reduces the life span of wires. In case of biometric implants or any
application where mechanical contact is the main reason behind failure of those applications. Wireless
power transfer is the best option to overcome these types of problems.
With this type of technology, there is no longer need to worry about wires. The inventions in the area
of wireless power technology and the area of study were the motivation behind this project.

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Objectives
 The main objective of the project is to study the fundamentals of wireless power transfer in
terms of the optimization of wireless power transfer coils and the efficiency between the
transmitter and receiver coils.
 Two Copper wires (Primary and Secondary) practical implementation and measurements for
comparison with Finite Element Modelling Method Simulations.
Organization of Thesis
Chapter 1 Introduction, history, motivation and research objectives, organization of thesis
Chapter 2 Basic Circuit, Mathematical representation of basic circuit.
Chapter 3 Practical coil implementation before simulations
Chapter 4 Finite Element Method Magnetics, Simulations
Chapter 5 Pspice Verification of FEMM model
Chapter 6 Mathematical Verification of FEMM model
Chapter 7 Practical Coil Measurements and Verification of FEMM model
Chapter 8 Three types of multi turn hypothesis for optimization of coils
Chapter 9 Conclusion
Appendix Simulation images, matlab scripts, practical coil images, spice simulation results
Table 1.1: Organization of thesis
Variables and Abbreviations
WPT: Wireless power Transfer
IPT: Inductive Power Transfer
PTE: Power Transfer Efficiency
RLT: Reflected Load Theory
FEMM: Finite Element Method Magnetics
PTE : Power Transfer Efficiency
FEMM: Finite Element Method Magnetics

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Chapter 2
Introduction
Wireless power transfer (WPT) technology is also, called the inductive power transfer (IPT)
technology. It is the transmission of electrical energy from the electrical source to the electrical load
through electrical magnetic field, which eliminates the use of electrical transmission through wires.
This type of technology is very useful in those cases where the use of interconnected wires are
inconvenient and hazardous or almost impossible, wireless power transfer can be used in many
applications like biometric implants, medical sensors, or laptop chargers etc.
Indeed now a day’s wireless power transfer (WPT) used frequently in biometric implants and sensors
related to medical devices. This chapter will cover the basic circuit of wireless power transfer (WPT)
using phenomena of inductive power transmission (IPT) and related mathematical expressions that
will represent the basic circuit of wireless power transfer (WPT).
Basic Circuit
Electromagnetic induction is the phenomena behind the wireless power transfer (WPT) technology or
the inductive power transfer (IPT). [Figure 2.1] shows the basic equivalent circuit for WPT.
Figure 2.1: Basic equivalent circuit for Wireless Power Transfer (WPT)
The transfer of electrical energy via magnetic flux coupling over a large airgap between the primary
coil and the secondary coil is very weak, which results in very poor coupling factor between the
primary coil and the secondary coil.

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Mathematical Representation of WPT Basic Circuit
In this section of the report, there will be use of [Figure 2.2] and [Figure 2.3] as equivalent circuits of
Wireless power transfer (WPT) for [Figure 2.1] in relations to the Mathematical expressions for WPT
used to derive the required parameters.
Resistance
Resistance, defined as the opposition to pass current through a conductor. Losses will always be
present when a current moves through a conductor. The power dissipated by the resistor will be in the
form of heat and given by:
Pdiss = I2
∗ R [2.1]
Series resistance of Inductor Coils
An Ideal inductor have no resistance or energy losses but in reality inductors have windings and those
windings creates resistance known as winding resistance which depends on material of wires. Since
the winding resistance appears as series with the inductor, which is often called series resistance.
AC series resistance of an inductor estimated by the product of resistivity of a conductor and length of
the conductor over the effective cross sectional area.
Rac−series =
ρl
Aeff
[2.2]
𝝆 : is the resistivity of a conductor
𝒍 : is the length of the conductor
𝑨_𝒆𝒇𝒇: is the effective cross sectional area
Where
Aeff = δπd = √
ρL
πfµ0
∗ 𝜋𝑑 [2.3]
𝛅: is the skin effect depth
µ 𝟎: is the absolute magnetic permeability of the conductor
Inductance
Inductance is a property of a conductor. Electromagnetic definition of inductance L is the ratio of
magnetic flux linkage λ to the current I
L =
λ
I
[2.4]
Inductance of Looped Coil
In electronics, inductor make use of the principle described by [2.5]. A changing current flows through
the windings of an inductor, creating a changing magnetic field. Each winding of the inductor captures
the flux and produces an induced voltage; back EMF that is self-inductance:
Lloop = N2
µ0µr (
D
2
) ∗ (ln (
8∗D
d
) − 2 [2.5]

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Inductor Quality Factor
The inductor series resistance converts electric current through the coil into heat, which causes a loss
in inductive quality. The quality factor of an inductor is the ratio of its inductive reactance to its
resistance at a specific frequency.
Quality factor is a measure on how ideal an inductor is and defined by:
Q =
2πfL
R
[2.6]
Mutual Inductance
The mutual inductance “M” can be, expressed by:
M = K ∗ √LP ∗ LS [2.7]
Coupling Coefficient
Where “K” is the coupling coefficient between two coils primary coil, which is the transmitter, and the
secondary coil, which is the receiver can expressed by “K”.
K = √
LP
LS
∗
VS
Vp
 Zero Load [2.8]
Hence LP represents the measurement inductance of the primary coil. Where as LS is the value of
measurement inductance from the secondary coil. The voltage drop across the secondary coil is VS
and the voltage drop across the primary side of the circuit represented by VP.
Load Resistance
Figure 2.2: Equivalent circuit for Secondary Coil (WPT)
[Figure 2.3] gives an overview of secondary coil components. Using reflected load theory the two
equivalent circuits are set to a frequency of operation. It assumes that the efficiency of the energy
transfer maximized, if the load resistance chosen according to [2.9]:
R 𝐿 = √(R S
)2 + (ωLS)2
[2.9]

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Reflected Load Theory
Reflected load theory (RLT) has been widely used to analyze transformers. RLT also applied to
wireless power transfer systems. Reflected Load Theory (RLT) states that the load present in the
secondary coil affects the amount of current that flows through the primary coil. This load is not
visible to the primary coil with the same actual value of load, but instead as a function of load value of
secondary coil which is the sum of series resistance of secondary coil and load resistance of the
secondary coil. [Figure 2.3] gives an overview of the Reflected Load Theory (RLT).
R′
= (R 𝑆 + R 𝑃) ∗ k2
[2.10]
Where, RL [2.9] and K [2.8]
Thus,
R′
= [R 𝑃 + (√(R 𝑆)2 + (ωL 𝑆)2)] ∗ K2
[2.11]
Figure 2.3: Equivalent circuit for primary Coil (WPT)
Voltage Drop across Inductor Coil
Voltage drop across the coils estimated as:
V = XL ∗ I [2.12]
Where XL is inductive reactance, which is proportional to the sinusoidal signal frequency and the
inductance: Which depends on the shape of the inductor.
XL = 2πfL [2.13]
Wireless Power Transfer Efficiency of Coils
In order to calculate the efficiency of the power transfer, the theory of energy conversion is applied.
Efficiency =
Pout
Pin
=
Pout
PRs−Prim+PRs−Sec+Pout
[2.14]

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Chapter 3
Implementation of practical coils before simulations
This chapter contains practical looped coil implementation. Practical results for both coils presented in
[Chapter 7] after obtaining the required parameters from FEMM [Chapter 4] for verification Design limit
were set to keep system small, make use of materials that are reasonable in price, available and narrow
the scope of simulations. To keep size of coils small, coil radius was limited to 17.2 cm; the thickness
of the wire is set to 6 mm in radius for both primary and secondary coils. Copper (Cu) wires used for
both coils, Copper (Cu) is known to form good inductors. Due to limitations by availability of driver
circuit for real tests, frequency is set in the range of 211 kHz - 10 MHz and peak-peak current limited
to 0.2 A. [Table 3.1] summarizes the design limits.
Coil Radius 𝟏𝟕. 𝟐 𝐜𝐦
Coil type Spherical
Wire type Semi-rigid coaxial
Wire diameter 6 mm
Wire Material Copper Cu
frequency 211 kHz – 10 MHz
Table 3.1: Design Limits
Figure 3.1: coil design for FEMM Simulation and 6 mm semi-grid coaxial copper wire.

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Figure 3.2: coil design for FEMM Simulation and 6 mm semi-grid coaxial copper wire.
 [Figure 3.1] shows actual single looped practical coil design, and its dimension.
 [Figure 3.2] represents both coils at a distance of 5 cm.

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Chapter 4
Wireless Power Transfer modelled in Finite Element Method Magnetics
(FEMM)
The simulation of Wireless power transfer model carried out in FEMM simulation software controlled
by Matlab. FEMM is a finite element method program with emphasis on magnetics, which is an ideal
program for magnetics problems before any practical implementation. Matlab is a numerical
computing environment, ideal for implementing analytical expressions and combining them into a
simulator.
The basic circuitry framework presented in [Chapter 2], a script carried out for FEMM using matlab with
different frequency starting from 211 kHz to the limit of 10 MHz with an input peak-peak current
of 0.2 A. In the sections below are the simulated results and parameters of the inductor coils, with
respect to 5 cm distance.
FEMM Simulation
Simulations carried out at different frequencies. The task for the simulation is to find required
parameters for inductor coils, which gives as big power transfer as possible at a specific frequency at
the same time keeping efficiency at reasonable levels. These parameters shows that quality factor is
dependent on the frequency, coil inductance and resistance of the coil. Coupling coefficient [2.8]
depends on inductance of primary and secondary coils, distance between primary and secondary coils
and ratio between output voltage of primary and secondary coil. Coil inductance and resistance can be
broken down to its geometrical and material properties. Parameters are coil type, coil radius, wire
radius, wire type, frequencies and material.
Simulation Setup
Model of power transfer has a symmetry along the separation axis. Therefore, coils designed as 2D-
axisymmetric. Five problems for five different frequency readings (211 kHz, 800 kHz, 4 MHz, 6
MHz, 10 MHz) are simulated. Turns ratio between primary and secondary coil is set to one. The
distance between primary coil and secondary coil is set to 5 cm. A Matlab script carried out to control
FEMM, which makes things a lot easier and quicker.

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Figure 4.1: Axisymmetric model, Primary and secondary coil Simulation setup and Practical Set
Simulation Results
Figure 4.2: Axisymmetric model, Primary and secondary coil Simulation result

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𝑭𝒓𝒆𝒒𝒖𝒆𝒏𝒄𝒚 𝑰 𝑷 𝑽 𝑷 𝑳 𝑷 𝑹 𝑷 𝑹𝒆𝒂𝒍 𝑷𝒐𝒘𝒆𝒓 𝒑𝒆𝒂𝒌 𝑫𝒊𝒔𝒕𝒂𝒏𝒄𝒆
𝟐𝟏𝟏 𝒌𝑯𝒛 0.2 A 0.096 V 360 nH 0.003788 Ω 75 µW 5 cm
𝟖𝟎𝟎 𝒌𝑯𝒛 0.2 A 0.36 V 359 nH 0.007403 Ω 148 µW 5 cm
𝟒 𝑴𝑯𝒛 0.2 A 1.80 V 358 nH 0.0171 Ω 342 µW 5 cm
𝟔 𝑴𝑯𝒛 0.2 A 2.70 V 358 nH 0.0211 Ω 422 µW 5 cm
𝟏𝟎 𝑴𝑯𝒛 0.2 A 4.5 V 358 nH 0.027 Ω 550 µW 5 cm
Table 4.1: FEMM Simulated Circuit Properties for Primary Coil at all tested frequencies
Frequency 𝑰 𝑺 𝑽 𝑺 𝑳 𝑺 𝑹 𝑺 𝑹𝒆𝒂𝒍 𝑷𝒐𝒘𝒆𝒓 𝒑𝒆𝒂𝒌 𝑫𝒊𝒔𝒕𝒂𝒏𝒄𝒆
𝟐𝟏𝟏 𝒌𝑯𝒛 0 A 0.019 V 360 nH 5 cm
𝟖𝟎𝟎 𝒌𝑯𝒛 0 A 0.073 V 5 cm
𝟒 𝑴𝑯𝒛 0 A 0.36 V 5 cm
𝟔 𝑴𝑯𝒛 0 A 0.55 V 5 cm
𝟏𝟎 𝑴𝑯𝒛 0 A 0.92 V 5 cm
Table 4.2: Simulated Circuit Properties for secondary Coil at all tested frequencies
Simulations made for the Wireless Power Transfer (WPT) system coils equivalent to [Figure 2.1] and.
[Figure 3.2] shows an overview of the coils setup, the disk below represents the transmitter coil (primary
coil) and the disk above represent the receiver coil (secondary coil). [Figure 4.2], [Table 4.1] and [Table 4.2]
show the results of the simulation for five frequency readings (211 kHz, 800 kHz, 4 MHz, 6 MHz, 10
MHz).
Plot 4.1: Peak Real power of primary coil as function of all tested frequencies

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Plot 4.2: Voltage Drop -primary coil as function of all tested frequencies
Plot 4.3: Voltage Drop -secondary coil as function of all tested frequencies
Conclusion
 As seen from FEMM, simulation results [Table 4.1] and [Table 4.2] when an increase in
frequency, there is an increase in voltage drop at the primary side and secondary side with
respect to distance.
In addition, there is an increase in real power when frequency is increased and series
resistance gets bigger with higher frequency.
 It is obvious that real power or other parameters are not visible other than voltage drop across
secondary side. FEMM software takes secondary coil as and open circuit when there is zero
current defined for the secondary coil whilst not known. Until there is a load connected to it
and unfortunately, it is not possible to connect a load in FEMM. For that purpose, Pspice
simulation software used to verify results obtained for the primary circuit and generate the
coupling coefficient using ratio between VP and VS from FEMM simulation. In Pspice, a
dummy load connected to secondary circuit to measure power and other related parameters
associated with secondary circuit. In [Chapter 5], there will be use of derived circuit parameters
[Table 4.1] to create a model for Pspice simulations.
 [Plot 4.1] gives a brief overview of real power across the primary coil at all tested frequencies
along with voltage drop across primary coil [Plot 4.2]. Which clearly indicates raise of power
across primary circuit when there is an increase in frequency. In addition, voltage drop
increases with the change in frequency across secondary coil [Plot 4.3].

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Chapter 5
Wireless Power Transfer (WPT) Pspice Verification
In this Chapter, Pspice simulation carried out to verify the parameters generated from FEMM simulation
as discussed in [Chapter 4]. Components selection for Pspice simulation circuit are equivalent to the
parameters from FEMM with five frequency readings, each frequency reading generates their own
Parameters. An overview of the components at specific frequency is shown [Table 4.2], following with
Pspice simulation results [Table 4.3], [Table 4.4] and [Table 4.5].
Figure 5.1: Pspice AC Simulation Diagram
𝑷𝒂𝒓𝒂𝒎𝒆𝒕𝒆𝒓𝒔 𝑺𝒕𝒂𝒓𝒕 𝑽𝒂𝒍𝒖𝒆 𝑬𝒏𝒅 𝑽𝒂𝒍𝒖𝒆
𝑹_𝑳𝒐𝒂𝒅_𝟐𝟏𝟏𝒌𝑯𝒛 𝟎. 𝟑 Ω 𝟎. 𝟔 Ω
𝑹_𝑳𝒐𝒂𝒅_𝟖𝟎𝟎𝒌𝑯𝒛 𝟏. 𝟔 Ω 𝟏. 𝟗 Ω
𝑹_𝑳𝒐𝒂𝒅_𝟒𝑴𝑯𝒛 𝟖. 𝟖 Ω 𝟗. 𝟏 Ω
𝑹_𝑳𝒐𝒂𝒅_𝟔𝑴𝑯𝒛 𝟏𝟑. 𝟐 Ω 𝟏𝟑. 𝟔 Ω
𝑹_𝑳𝒐𝒂𝒅_𝟏𝟎𝑴𝑯𝒛 𝟐𝟐. 𝟐 Ω 𝟐𝟐. 𝟔 Ω
Table 5.1: Pspice AC simulation Parametric Sweep
Simulation Setup
With all components selected, the simulation circuit implemented in Pspice equivalent to [Figure 2.1] and
[Figure 3.2] and [Figure 4.1]. Setting up Vac to 0.2 A, along with a parametric sweep set to start value and end
value for load resistance [Table4.1]. [Table 4.2] gives an overview of design limits with respect to its
frequency and optimal load RL calculated by [2.9]. The parameters for the coils obtained from FEMM
simulation as discussed in [Chapter 4]
𝑭𝒓𝒆𝒒𝒖𝒆𝒏𝒄𝒚 𝑳𝒑 𝑳𝒔 𝑹𝒑 𝑹𝒔 𝑹𝑳
211 𝑘𝐻𝑧 360 nH 360 nH 0.003788 Ω 0.003788 Ω 0.5 Ω
800 𝑘𝐻𝑧 359 nH 359 nH 0.007403 Ω 0.007403 Ω 1.8 Ω
4 𝑀𝐻𝑧 358 nH 358 nH 0.0171 Ω 0.0171 Ω 9.05 Ω
6 𝑀𝐻𝑧 358 nH 358 nH 0.0211 Ω 0.0211 Ω 13.5 Ω
10 𝑀𝐻𝑧 358 nH 358 nH 0.027 Ω 0.027 Ω 22.5 Ω
Table 5.2: Pspice AC simulation Parameters Obtained from FEMM simulation

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Simulation Results Primary Coil
In Pspice, the AC analysis carried out to study the behavior of the Primary Coil circuit. What is
important is that voltage and power behaves similar to [Table 4.1]. Comparing the results obtained from
FEMM simulation and Pspice simulation there is a slight difference in voltage drop, but the real power
in primary coil FEMM simulation matches with the real power obtained from the Pspice simulation at
the tested frequency range. [Figure 4.1] to [Figure 4.5] are the simulation plots for primary coil at frequency
range 𝟐𝟏𝟏 𝐤𝐇𝐳, 𝟖𝟎𝟎 𝐤𝐇𝐳, 𝟒 𝐌𝐇𝐳, 𝟔 𝐌𝐇𝐳 𝐚𝐧𝐝 𝟏𝟎 𝐌𝐇𝐳 [Table 5.3] is the overview of the results
obtained for primary circuit matched with FEMM simulation results in [Table 4.1].
𝑭𝒓𝒆𝒒𝒖𝒆𝒏𝒄𝒚 𝑰 𝑷 𝑽 𝑷 𝑳 𝑷 𝑹 𝑷 𝑹𝒆𝒂𝒍 𝑷𝒐𝒘𝒆𝒓 𝒑𝒆𝒂𝒌 𝑫𝒊𝒔𝒕𝒂𝒏𝒄𝒆 𝑲
𝟐𝟏𝟏 𝒌𝑯𝒛 0.2 A 0.094 V 360 nH 0.003788 Ω 75.6 µW 5 cm 0.2
𝟖𝟎𝟎 𝒌𝑯𝒛 0.2 A 0.35 V 359 nH 0.007403 Ω 148 µW 5 cm 0.2
𝟒 𝑴𝑯𝒛 0.2 A 1.80 V 358 nH 0.0171 Ω 342 µW 5 cm 0.2
𝟔 𝑴𝑯𝒛 0.2 A 2.70V 358 nH 0.0211 Ω 422 µW 5 cm 0.2
𝟏𝟎 𝑴𝑯𝒛 0.2 A 4.3 V 358 nH 0.027 Ω 540 µW 5 cm 0.2
Table 5.3: Pspice AC Simulation circuit properties for primary coil
Plot 5.1: Voltage Drop -primary coil as function all tested frequencies
Plot 5.2: Peak Real Power- Primary coil as function all tested frequencies
0,00E+00
1,00E-04
2,00E-04
3,00E-04
4,00E-04
5,00E-04
6,00E-04
2,11E+05
8,00E+05
4,00E+06
6,00E+06
1,00E+07
Realpower_Primar
y

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Simulation Results Secondary Coil
In Pspice, the AC analysis carried out to study the behavior of the Secondary Coil circuit. What is
important is that voltage behaves similar to [Table 4.2] and the power dissipation in the secondary coil
circuit to get the power efficiency of the whole system. Comparing the Voltage drop results obtained
from FEMM simulation [Table 4.2] with Pspice simulation, there is a slight difference in voltage drop.
To obtain the real power in secondary coil a dummy load is connected to the secondary circuit,
calculated by [2.9] for 𝟐𝟏𝟏 𝐤𝐇𝐳, 𝟖𝟎𝟎 𝐤𝐇𝐳, 𝟒 𝐌𝐇𝐳, 𝟔 𝐌𝐇𝐳 𝐚𝐧𝐝 𝟏𝟎 𝐌𝐇𝐳 . [Figure 5.6] to [Figure 5.10] are
the simulation plots for secondary coil at frequency 𝟐𝟏𝟏 𝐤𝐇𝐳, 𝟖𝟎𝟎 𝐤𝐇𝐳, 𝟒 𝐌𝐇𝐳, 𝟔 𝐌𝐇𝐳 𝐚𝐧𝐝 𝟏𝟎 𝐌𝐇𝐳
[Table 5.4] gives an overview of the results obtained for secondary coil with respect to load resistance.
Frequency 𝑰 𝑺 𝑽 𝑺 𝑳 𝑺 𝑹 𝑺 + 𝑹 𝑳 𝑹𝒆𝒂𝒍 𝑷𝒐𝒘𝒆𝒓 𝒑𝒆𝒂𝒌 𝑫𝒊𝒔𝒕𝒂𝒏𝒄𝒆 𝑲
𝟐𝟏𝟏 𝒌𝑯𝒛 0A 0.014 V 360 nH 0.00378 Ω + 0.5 Ω 189 µW 5 cm 0.2
𝟖𝟎𝟎 𝒌𝑯𝒛 0 A 0.050 V 359 nH 0.007403 Ω + 1.8 Ω 718.7 µW 5 cm 0.2
𝟒 𝑴𝑯𝒛 0 A 0.3 V 358 nH 0.0171 Ω + 9.05 Ω 3.591 mW 5 cm 0.2
𝟔 𝑴𝑯𝒛 0 A 0.4 V 358 nH 0.0211 Ω + 13.5 Ω 5.41 mW 5 cm 0.2
𝟏𝟎 𝑴𝑯𝒛 0 A 0.64 V 358 nH 0.027Ω + 22.5 Ω 8.96 mW 5 cm 0.2
Table 5.4: Pspice AC Simulation circuit properties for Secondary coil with max efficient Load
Frequency 𝑰 𝑺 𝑽 𝑺 𝑳 𝑺 𝑹 𝑺 𝑹𝒆𝒂𝒍 𝑷𝒐𝒘𝒆𝒓 𝒑𝒆𝒂𝒌 𝑫𝒊𝒔𝒕𝒂𝒏𝒄𝒆 𝑲
𝟐𝟏𝟏 𝒌𝑯𝒛 0 A 0.014 V 360 nH 0.00378 Ω 1.4294 µW 5 cm 0.2
𝟖𝟎𝟎 𝒌𝑯𝒛 0 A 0.050 V 359 nH 0.007403 Ω 2.9510 µW 5 cm 0.2
𝟒 𝑴𝑯𝒛 0 A 0.3 V 358 nH 0.0171 Ω 6.8129 µW 5 cm 0.2
𝟔 𝑴𝑯𝒛 0 A 0.4 V 358 nH 0.0211 Ω 8.4546 µW 5 cm 0.2
𝟏𝟎 𝑴𝑯𝒛 0 A 0.64 V 358 nH 0.027 Ω 10.766 µW 5 cm 0.2
Table 5.5: Pspice AC Simulation circuit properties for Secondary coil without load
Plot 5.3: Voltage Drop -Secondary coil with max efficient Load as function all tested frequencies
1,00E-02
1,00E-01
1,00E+00
1,00E+05 1,00E+06 1,00E+07
V_Secondary

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Plot 5.4: Peak Real Power –Secondary Coil with max efficient Load as function all tested frequencies
Power Transfer Efficiency from Pspice perspective
In this section of report, maximum peak power output for Wireless Power Transfer (WPT) system will
be generated and the efficiency of the system for the tested frequencies will be derived. [Table 5.6] gives
an overview of maximum peak power and its efficiency with respect to distance and load resistance
[2.9]. [Figure 5.11] to [Figure 5.15] are the Pspice simulation plots for tested frequencies.
(𝟐𝟏𝟏 𝐤𝐇𝐳, 𝟖𝟎𝟎 𝐤𝐇𝐳, 𝟒 𝐌𝐇𝐳, 𝟔 𝐌𝐇𝐳 𝐚𝐧𝐝 𝟏𝟎 𝐌𝐇𝐳).
Frequency 𝑷 𝑴𝒂𝒙−𝒑𝒆𝒂𝒌 𝜼 𝑫𝒊𝒔𝒕𝒂𝒏𝒄𝒆 𝑲 𝑹𝑳
𝟐𝟏𝟏 𝒌𝑯𝒛 710.524 mW 71 % 5 cm 0.2 0.5 Ω
𝟖𝟎𝟎 𝒌𝑯𝒛 826.130 m W 82 % 5 cm 0.2 1.8 Ω
𝟒 𝑴𝑯𝒛 911.346 mW 91 % 5 cm 0.2 9.0 Ω
𝟔 𝑴𝑯𝒛 926.290 mW 93 % 5 cm 0.2 13.5 Ω
𝟏𝟎 𝑴𝑯𝒛 942.162 mW 94 % 5 cm 0.2 22.5 Ω
Table 5.6: maximum power efficiency of the whole system with max efficient Load
Plot 5.5: Efficiency as function all tested frequencies

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Plot 5.6: Max efficiency Load resistance as function all tested frequencies
Time Domain Analysis
 Time domain simulation performed pspice to verify AC simulation in Pspice where [Table 5.7]
are the Load parameters for tested frequencies.
 Time domain simulation results [Table 5.8] verifies peak real power across the load resistor
performed by Ac sweep simulation, with a minute difference which is almost neglect able
 [Table 5.8] gives an overview of the peak real power result with respect to the calculated load
resistance and tested frequencies.
𝑷𝒂𝒓𝒂𝒎𝒆𝒕𝒆𝒓𝒔 𝑺𝒕𝒂𝒓𝒕 𝑽𝒂𝒍𝒖𝒆 𝑬𝒏𝒅 𝑽𝒂𝒍𝒖𝒆
𝑹_𝑳𝒐𝒂𝒅_𝟐𝟏𝟏𝒌𝑯𝒛 𝟎. 𝟑 Ω 𝟎. 𝟓 Ω
𝑹_𝑳𝒐𝒂𝒅_𝟖𝟎𝟎𝒌𝑯𝒛 𝟎. 𝟓 Ω 𝟏. 𝟖Ω
𝑹_𝑳𝒐𝒂𝒅_𝟒𝑴𝑯𝒛 𝟕. 𝟎 Ω 𝟗. 𝟎 Ω
𝑹_𝑳𝒐𝒂𝒅_𝟔𝑴𝑯𝒛 𝟖. 𝟓. Ω 𝟏𝟑. 𝟓 Ω
𝑹_𝑳𝒐𝒂𝒅_𝟏𝟎𝑴𝑯𝒛 𝟏𝟐. 𝟓 Ω 𝟐𝟐. 𝟓Ω
Table 5.7: Pspice Time Domain analysis Load Parametric Sweep
Frequency 𝑳 𝑺 𝑹 𝑺 + 𝑹 𝑳 𝑹𝒆𝒂𝒍 𝑷𝒐𝒘𝒆𝒓 𝒑𝒆𝒂𝒌 𝑫𝒊𝒔𝒕𝒂𝒏𝒄𝒆 𝑲
𝟐𝟏𝟏 𝒌𝑯𝒛 360 nH 0.00378 Ω + 0.5 Ω 186 µW 5 cm 0.2
𝟖𝟎𝟎 𝒌𝑯𝒛 359 nH 0.007403 Ω + 1.8 Ω 743.7 µW 5 cm 0.2
𝟒 𝑴𝑯𝒛 358 nH 0.0171 Ω + 9.05 Ω 3.591 mW 5 cm 0.2
𝟔 𝑴𝑯𝒛 358 nH 0.0211 Ω + 13.5 Ω 5.41 mW 5 cm 0.2
𝟏𝟎 𝑴𝑯𝒛 358 nH 0.027Ω + 22.5 Ω 8.96 mW 5 cm 0.2
Table 5.8: Pspice Time Domain simulation Results with max efficient Load
1,00E-01
1,00E+00
1,00E+01
1,00E+02
1,00E+05 1,00E+06 1,00E+07
R_Load

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Figure 5.17: Time Domain analysis plot at 211 kHz with max efficient Load
Figure 5.18: Time Domain analysis plot at 800 kHz with max efficient Load
Figure 5.19: Time Domain analysis plot at 4 MHz with max efficient Load

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Conclusion
 As seen from Pspice simulation results [Table 5.3] and [Table 5.4], as there is increase in the
frequency, there is an increase in voltage drop at the primary side and the secondary side. The
results obtained from Pspice simulations verifies that FEMM simulation and Pspice simulation
has neglect able difference between the results.
 In addition, there is an increase in the real power as frequency is increased and the series
resistance gets bigger with higher frequency, which verifies the results obtained from FEMM
simulation for primary coil circuit.
 To see the real power on the secondary side a dummy load is connected to the secondary
circuit which is calculated by [2.9] for the tested frequencies and the load resistance parameter
is also generated by FEMM simulation. It concludes that efficiency at high frequency 10 MHz
is approx.92 % , compared to efficiency at the lowest frequency 211 kHz that is 71 % it is
clear that power transfer is more efficient when operating at high frequencies than low
frequencies [Table 5.6].
 In addition, [Chapter 6] verifies simulations from FEMM and Pspice mathematically.

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Chapter 6
Wireless Power Transfer (WPT) FEMM Model Mathematical Verifications
All parameters derived from FEMM [Chapter 4] and Pspice simulations [Chapter 5] are verified
mathematically using mathematical expressions from [Chapter 2].
Calculations
𝐹𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 𝑉𝑝 𝑉𝑠 𝐿𝑝 𝐿𝑠 𝑅𝑠 𝑅𝑝
211 𝑘𝐻𝑧 0.095 V 0.019 360 nH 360 nH 0.003788 Ω 0.003788 Ω
800 𝑘𝐻𝑧 0.36 V 0.073 359 nH 359 nH 0.007403 Ω 0.007403 Ω
4 𝑀𝐻𝑧 1.80 V 0.36 358 nH 358 nH 0.0171 Ω 0.0171 Ω
6 𝑀𝐻𝑧 2.70 0.55 358 nH 358 nH 0.0211 Ω 0.0211 Ω
10 𝑀𝐻𝑧 4.5 0.92 358 nH 358 nH 0.027 Ω 0.027 Ω
Table 6.1: calculation parameters from simulations for verification
Inductance of Coil
Using equation [2.3], self-inductance of coil calculated as:
Where N = 1, D = 17.2 cm, d = 6 mm, µ0 = 4 ∗ π ∗ e−7
, µr = 1
Hence
Lloop = 4 ∗ π ∗ e−7
(
17.2∗e−2
2
) ∗ (ln (
8∗17.2∗ e−2
6∗e−3
) − 2 [5.1]
Lloop = 371 nH [5.2]
Coupling Coefficient” k”
Using equation [2.8] coupling coefficient derived as:
K = (1 ∗
0.019
0.073
) ∗ 100% [5.3]
K = 0.2 = 20 % [5.4]
The results above assumes that the coupling is very low at distance of 5 cm at all tested frequencies.
Mutual Inductance” M”
Mutual inductance derived by [2.7]
M = 0.2 ∗ √371 nH ∗ 371 nH [5.3]
Where both coils have the same inductance [Table 5.1]
Therefore, the mutual inductance calculated as:

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M = 74 nH [5.4]
Primary coil and secondary coil quality factor” Qp, Qs” for all tested frequencies
Due to both coils having same inductance and resistance, it assumes that
𝐿 𝑃 = 𝐿 𝑆 = L
And 𝑅 𝑃 = 𝑅 𝑃 = R
The quality factor for primary and secondary coil derived by [2.6] calculated as:
For 𝟐𝟏𝟏 𝐤𝐇𝐳:
Qp&s =
2∗π∗211 kHz∗371 nH
0.0034
= 144.6 [5.5]
For 𝟖𝟎𝟎 𝐤𝐇𝐳:
Qp&s =
2∗π∗800 kHz∗371 nH
0.0070
= 266.4 [5.6]
For 𝟒 𝐌𝐇𝐳:
Qp&s =
2∗π∗4 MHz∗371 nH
0.015
= 621.6 [5.7]
For 𝟔 𝐌𝐇𝐳:
Qp&s =
2∗π∗6 MHz∗371 nH
0.020
= 699.3 [5.8]
For 𝟏𝟎 𝐌𝐇𝐳:
Qp&s =
2∗π∗10 MHz∗371 nH
0.023
= 1.0𝑒3
[5.9]
Series Resistance of inductor Coils
The series resistance of coils calculated using equation [2.2] and [2.3] for all tested frequencies to verify
the simulation results [Chapter 4] and [Chapter 5].
ρ = 1.678e−8
Ωm
l = 17.2e−2
∗ pi = 54e−2
cm
µ0 = 4πe−7
H/m
Rac−series =
(1.678𝑒−8∗54𝑒−2 )
√
1.678𝑒−8
𝜋∗211𝑒3∗(4𝑒−7∗𝜋)
∗𝜋∗6𝑒−3
= 0.0034 [5.10]

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Rac−series =
(1.678𝑒−8∗54𝑒−2 )
√
1.678𝑒−8
𝜋∗800𝑒3∗(4𝑒−7∗𝜋)
∗𝜋∗6𝑒−3
= 0.0070 [5.11]
Rac−series =
(1.678𝑒−8∗54𝑒−2 )
√
1.678𝑒−8
𝜋∗4𝑒6∗(4𝑒−7∗𝜋)
∗𝜋∗6𝑒−3
= 0.0015 [5.12]
Rac−series =
(1.678𝑒−8∗54𝑒−2 )
√
1.678𝑒−8
𝜋∗6𝑒6∗(4𝑒−7∗𝜋)
∗𝜋∗6𝑒−3
= 0.020 [5.13]
Rac−series =
(1.678𝑒−8∗54𝑒−2 )
√
1.678𝑒−8
𝜋∗10𝑒6∗(4𝑒−7∗𝜋)
∗𝜋∗6𝑒−3
= 0.023 [5.14]
Voltage drop of inductor coil
The voltage drop across the inductor coil calculated using equation [2.12] and [2.13] for all tested
frequencies to verify the simulation results [Chapter 4] and [Chapter 5].
It is assumed that XL = RL Thus:
Vprimary = 2 ∗ π ∗ 211 kHz ∗ 371 nH ∗ 0.2 = 0.095 V [5.15]
Vprimary = 2 ∗ π ∗ 800 kHz ∗ 371 nH ∗ 0.2 = 0.37 V [5.16]
Vprimary = 2 ∗ π ∗ 4 MHz ∗ 371 nH ∗ 0.2 = 1.8 V [5.17]

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Load Resistance” RL”
Using equation [2.9], the load resistance calculated for all tested frequencies:
RL = √(0.0034)2 + (2 ∗ π ∗ 211 kHz ∗ 371 nH)2 = 0.49 Ω [5.20]
RL = √(0.007)2 + (2 ∗ π ∗ 800 kHz ∗ 371 nH)2 = 1.86 Ω [5.21]
RL = √(0.015)2 + (2 ∗ π ∗ 4 MHz ∗ 371 nH)2 = 9.3 Ω [5.22]
RL = √(0.020)2 + (2 ∗ π ∗ 6 MHz ∗ 371 nH)2 = 13.9 Ω [5.23]
RL = √(0.023)2 + (2 ∗ π ∗ 10 MHz ∗ 371 nH)2 = 23.3 Ω [5.24]
Wireless Power Transfer Efficiency for all tested frequencies
The power efficiency of the system for all tested frequencies derived by [2.14] using peak real power
value from [Table 5.3], [Table 5.4] and [Table 5.5]
Efficiency =
Pout
Pin
=
189 µW
75.6 µWPeak+1.4294 µW +189 µW
= 710.4 mW ∗ 100 = 71 % [5.25]
Efficiency =
Pout
Pin
=
718.7 µW
148 µWPeak+2.9510 µW +718.7 µW
= 826.4 mW ∗ 100 = 82 % [5.26]
Efficiency =
Pout
Pin
=
3.591 mW
342 µWPeak+6.8129 µW +3.591 mW
911.5 mW ∗ 100 = 91% [5.27]
Efficiency =
Pout
Pin
=
5.41 mW
422 µWPeak+8.4546 µW +5.41 mW
= 926.3 mW ∗ 100 = 93% [5.28]

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Efficiency =
Pout
Pin
=
8.96 mW
550 µWPeak+10.766 µW +8.96 mW
= 941.1 mW ∗ 100 = 94% [5.29]
Conclusion
Plot 6.1: Efficiency as function all tested frequencies
Plot 6.2: Max efficient Load resistance as function all tested frequencies
 [Plot 6.1] and [Plot 6.2] is an overview of mathematical results for all tested frequency which
verifies that the results obtained from simulations and mathematical calculation has
approximation of results to conclude that the simulations and the theoretical calculation can
have a zero difference or the difference can be neglected.
1,00E-01
1,00E+00
1,00E+01
1,00E+02
1,00E+05 1,00E+06 1,00E+07
R_Load

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Chapter 7
Practical Model Verification
This chapter contain results of practical model WPT tests implemented in [Chapter 3] that verifies the
results obtained from FEMM simulation [Chapter 4] and pspice simulation [Chapter 5]
Practical Wireless Power Transfer Model Setup
The WPT model designed in [Chapter 3] built, and serves the source for the required measurements. The
supply voltage taken from a function generator with a current limitation of 0.2 A, and the AC signal
used to trigger at the tested frequency for 10 V peak to peak. The single looped coils were
implemented before carrying out FEMM simulations with the purpose of having a real practical model
as a prototype to simulate on using FEMM [Chapter 4]. In addition, load resistors added to the secondary
side according to the frequency of required parameters. [Table 7.1] is an overview of results obtained
from the practical model WPT along with [Table 7.2] are the results obtained for secondary coil circuit.
Practical Model Results
Primary Coil
𝑭𝒓𝒆𝒒𝒖𝒆𝒏𝒄𝒚 𝐕𝐏 𝐋 𝐏 𝐑 𝐏 𝐃𝐢𝐬𝐭𝐚𝐧𝐜𝐞 𝐊
𝟐𝟏𝟏 𝒌𝑯𝒛 0.094 V 360 nH 0.003788 Ω 5 cm 0.2
𝟖𝟎𝟎 𝒌𝑯𝒛 0.36 V 360 nH 0.007403 Ω 5 cm 0.2
𝟒 𝑴𝑯𝒛 1.80 V 360 nH 0.0171 Ω 5 cm 0.2
𝟔 𝑴𝑯𝒛 2.70 V 360 nH 0.0211 Ω 5 cm 0.2
𝟏𝟎 𝑴𝑯𝒛 4.5 V 360 nH 0.027 Ω 5 cm 0.2
Table 7.1: Practical Model circuit properties for primary coil
Secondary Coil
Frequency 𝐕𝐒 𝐋 𝐒 𝐑 𝐒+ RL 𝐃𝐢𝐬𝐭𝐚𝐧𝐜𝐞 𝐊
𝟐𝟏𝟏 𝒌𝑯𝒛 0.014 V 360nH 0.00378 Ω + 0.5 Ω 5 cm 0.2
𝟖𝟎𝟎 𝒌𝑯𝒛 0.048 V 360nH 0.007403 Ω + 1.8 Ω 5 cm 0.2
𝟒 𝑴𝑯𝒛 0.30 V 360nH 0.0171 Ω + 9.05 Ω 5 cm 0.2
𝟔 𝑴𝑯𝒛 0.39 V 360nH 0.0211 Ω + 13.5 Ω 5 cm 0.2
𝟏𝟎 𝑴𝑯𝒛 0.64 V 360nH 0.027Ω + 22.5 Ω 5 cm 0.2
Table 7.2: Practical Model circuit properties for Secondary coil with max efficient Load

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Conclusion
Plot 7.1 Voltage drop primary practical measurements as function all tested frequencies
Plot 7.2 Voltage drop secondary practical measurements as function all tested frequencies
 To conclude, practical model results [Table 7.1] and [Table 7.2] clearly indicates resemblance
between the FEMM simulations [Chapter 4] and Pspice Simulations [Chapter 5].
 The scenario of practical model implementation verifies that FEMM simulation software can
give good results as in real world model before even building the real world model.
 There are some deviations in practical results compared to FEMM simulation results, which
are to be expected due to the quality of materials and components used. Fine results can be
achieved by good quality of coils and other components.
1,00E-02
1,00E-01
1,00E+00
1,00E+01
1,00E+05 1,00E+06 1,00E+07
V_Primary

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Chapter 8
FEMM Multi turns Hypothesis for WPT Model After verifications
As concluded FEMM is a valid software with respect to magnetics problems. FEMM used to perform
more experiments to make the system more efficient. Previously one turn coil were used, while
keeping one-coil turn increasing in the frequency was the conclusion to obtain better power efficiency.
Now question arises: What if the coil turns are increased while keeping frequency low?, for the sake of
argument this chapter will cover three types of hypothesis FEMM can offer for carrying out
simulations for multi turns coils. Due to lack of time, the three types of hypothesis analyzed briefly,
while keeping multi turns limited to the primary coil with respect to all tested frequencies [Table 3.1]
Hypothesis 1: Four turns Defined within FEMM block properties
𝟐𝟏𝟏 𝒌𝑯𝒛 0.2 𝐴 1.63 𝑉 6.15 µ𝐻 0.0063 𝛺 126 µ𝑊 5 𝑐𝑚
𝟖𝟎𝟎 𝒌𝑯𝒛 0.2 𝐴 6.18 𝑉 6.15 µ𝐻 0.0066 𝛺 132 µ𝑊 5 𝑐𝑚
𝟒 𝑴𝑯𝒛 0.2 𝐴 30.9 𝑉 6.15 µ𝐻 0.0073 𝛺 147 µ𝑊 5 𝑐𝑚
𝟔 𝑴𝑯𝒛 0.2 𝐴 46.4𝑉 6.15 µ𝐻 0.0076 𝛺 153 µ𝑊 5 𝑐𝑚
𝟏𝟎 𝑴𝑯𝒛 0.2 𝐴 77.3 𝑉 6.15 µ𝐻 0.0081 𝛺 163 µ𝑊 5 𝑐𝑚
Table 8.1: Hypothesis 1: Simulated Circuit Properties Primary Coil
Frequency 𝑰 𝑺 𝑽 𝑺 𝑫𝒊𝒔𝒕𝒂𝒏𝒄𝒆
𝟐𝟏𝟏 𝒌𝑯𝒛 0.2 𝐴 0.077 𝑉 5 𝑐𝑚
𝟖𝟎𝟎 𝒌𝑯𝒛 0 𝐴 0.294 𝑉 5 𝑐𝑚
𝟒 𝑴𝑯𝒛 0 𝐴 1.5 𝑉 5 𝑐𝑚
𝟔 𝑴𝑯𝒛 0 𝐴 2.2 𝑉 5 𝑐𝑚
𝟏𝟎 𝑴𝑯𝒛 0 𝐴 3.6 𝑉 5 𝑐𝑚
Table 8.2: Hypothesis 1: Simulated Circuit Properties for secondary Coil
Plot 8.1: Hypothesis 1: Voltage drop primary coil as function all tested frequencies
1,00E+00
1,00E+01
1,00E+02
1,00E+05 1,00E+06 1,00E+07
V_Primary

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Figure 8.1: Axisymmetric model Hypothesis 1, Primary and secondary coil Simulation setup
Figure 8.2: Axisymmetric model, Primary and secondary coil Simulation result for Hypothesis 1
 [Table 8.1] shows the hypothetical results for using multi turns for WPT primary coil.
 [Plot 7.1] indicates how voltage drop increases at primary when more turns added with respect to
frequency
 It is not clear yet that real power is the correct power using this hypothesis. It might be the
mesh size or precision solver that not give precise power at primary side, which is lack in this
hypothesis until a deep analysis made to form precise simulation clarify the problem.
However, the rest of parameters are vital with mathematical calculations using [Chapter 2].

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Hypothesis 2: Four turns individual 6 mm wire method
𝟐𝟏𝟏 𝒌𝑯𝒛 0.2 𝐴 1 𝑉 4.0 µ𝐻 0.029 𝛺 591 µ𝑊 5 𝑐𝑚
𝟖𝟎𝟎 𝒌𝑯𝒛 0.2 𝐴 4 𝑉 3.9 µ𝐻 0.060 𝛺 1.2 𝑚𝑊 5 𝑐𝑚
𝟒 𝑴𝑯𝒛 0.2 𝐴 20 𝑉 3.9 µ𝐻 0.14 𝛺 2 𝑚𝑊 5 𝑐𝑚
𝟔 𝑴𝑯𝒛 0.2 A 30 V 3.9 µH 0.17 Ω 3.5 mW 5 cm
𝟏𝟎 𝑴𝑯𝒛 0.2 A 50 V 3.9 µH 0.23 Ω 4 mW 5 cm
Table 8.3: Hypothesis 2: Simulated Circuit Properties primary Coil
Frequency 𝑰 𝑺 𝑽 𝒔 𝑫𝒊𝒔𝒕𝒂𝒏𝒄𝒆
𝟐𝟏𝟏 𝒌𝑯𝒛 0.2 A 0.064 V 5 cm
𝟖𝟎𝟎 𝒌𝑯𝒛 0 A 0.24 V 5 cm
𝟒 𝑴𝑯𝒛 0 A 1.22 V 5 cm
𝟔 𝑴𝑯𝒛 0 A 1.83 V 5 cm
𝟏𝟎 𝑴𝑯𝒛 0 A 3.0 V 5 cm
Table 8.4: Hypothesis 2: Simulated Circuit Properties for single turn secondary Coil
 [Table 8.3] shows the hypothetical results for using multi turns for WPT primary coil with air gap
between wires of a coil.
 [Plot 8.2] indicates how voltage drop increases at primary when the wires of a coil has gap
between them
 This method can be useful only if coils are gaped mostly happened when thick wires are used
or maybe a requirement of having gap between wires of a coil then it is a useful method to
1,00E+00
1,00E+01
1,00E+02
1,00E+05 1,00E+06 1,00E+07
V_Primary

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simulate on such gaped coils but to say that it gives a better result for such types of wires can
only be assumed.
Figure 8.3: Axisymmetric model Hypothesis 2, Primary and secondary coil Simulation setup

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Hypothesis 3: Replacement; 6 mm wire by four 3 mm wires in the same 6 mm area
𝟐𝟏𝟏 𝒌𝑯𝒛 0.2 A 1.45 V 5.4 µH 0.054 Ω 1.1 mW 5 cm
𝟖𝟎𝟎 𝒌𝑯𝒛 0.2 A 5.5 V 5.4 µH 0.11 Ω 2.1 mW 5 cm
𝟒 𝑴𝑯𝒛 0.2 A 27.3 V 5.4 µH 0.24 Ω 4.8 mW 5 cm
𝟔 𝑴𝑯𝒛 0.2 A 41.0 V 5.4 µH 0.3 Ω 6.1 mW 5 cm
𝟏𝟎 𝑴𝑯𝒛 0.2 A 68.3 V 5.4 µH 0.4 Ω 7.8 mW 5 cm
Table 8.5: Hypothesis 3: Simulated Circuit Properties for primary side
Frequency 𝑰 𝑺 𝑽 𝑺 𝑫𝒊𝒔𝒕𝒂𝒏𝒄𝒆
𝟐𝟏𝟏 𝒌𝑯𝒛 0 A 0.077 V 5 cm
𝟖𝟎𝟎 𝒌𝑯𝒛 0 A 0.29 V 5 cm
𝟒 𝑴𝑯𝒛 0 A 1.47 V 5 cm
𝟔 𝑴𝑯𝒛 0 A 2.2 V 5 cm
𝟏𝟎 𝑴𝑯𝒛 0 A 3.7 V 5 cm
Table 8.6: Hypothesis 3: Simulated Circuit Properties for single turn secondary Coil
1,00E+00
1,00E+01
1,00E+02
1,00E+05 1,00E+06 1,00E+07
V_Primary

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Plot 8.4: Hypothesis 3: peak real power primary coil as function all tested frequencies
 [Table 8.5] shows the hypothetical results for using multi turns for WPT primary coil.
 [Plot 8.3] indicates how voltage drop increases at primary coils if more wires are used in same
area of WPT coil 6 mm [Figure 8.5] and [Figure 8.6] which is another way making WPT coil and in
fact it can give better and efficient results.
 Due to lack of deep analysis on these phenomena, it can only be an assumption that this way
of making coils can give better results.
Figure 8.5: Axisymmetric model Hypothesis 3, primary, secondary coil Simulation setup and zoomed in primary coil
1,00E-03
1,00E-02
1,00E-01
1,00E+05 1,00E+06 1,00E+07
Real Power

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Conclusion:
 To conclude, which one of the three types of assumptions made above is better way to
simulate on wireless power transfer coils is hard at this point until a deep analysis is carried
out, which is a project on its own. It can only be assumed that all three types of methods give
good results as looking at the simulation setups for all three types clearly indicates that it fairly
depends on the type of the coil used for WPT.
 If coils are looped and tightly coupled the [Hypothesis 1], will be useful tool to simulate on such
coil and can give better and precise results according to theory [Chapter 2], which can make
system more efficient even at low frequencies.
 If the wires of a coil have gap between them then [Hypothesis 2] will give good results [Table 8.3],
as seen in [Figure 8.4] those gaps can matter a lot regarding the efficiency of the system. To have
a better system minute details have to be taken into account.
 In addition, if the case is that four 3 mm wires are used in same area as the single looped coil
[Figure 4.1] which is 6 mm, then [Hypothesis 3] will do the job more precisely than the two types
mentioned above.
 Finally, it is all dependent on the need of the type of coils, simulations will be carried out
accordingly using FEMM simulation software and validly the results will be obtained as
expected.

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Chapter 9
Initial Conclusion
This chapter summarizes the work done in this thesis with perspective to software, theory, practical
implementation and documentation processes and possible future work in the area of wireless power
transmission. The main conducted features related to the optimization of wireless power transfer coils
are as followed:
 The wireless power transfer model extended with the theory [Chapter 2] and implemented
FEMM simulation model [Chapter 4] with actual material and geometrical properties as input
parameters [Chapter 3]. An optimization technique applied through increase in frequency.
 In addition, the parameters obtained from FEMM simulation used to create the Pspice model
[Chapter 5] for verification of FEMM results and obtained real power simulation results for
secondary coil.
 Verifying the result of FEMM simulation and obtaining the real power for the secondary coil
using Pspice the process extended to additional verifications of the power efficiency and other
related parameters using mathematical expression [Chapter 6] related to theoretical aspects of
wireless power transfer systems for the power transfer efficiency between both coils.
Simulations and calculations
Choosing design limits that makes the system reasonable sized coils using the geometrical and
material properties for the coils [Figure 3.1] a FEMM model simulation [Figure 4.1] carried out [Figure 4.2] for
a set of frequencies [Table 3.1] to obtain a set of optimized parameters for each of tested frequencies [Table
4.1] [Table 4.2] . A Pspice model [Figure 5.1] carried out for each frequency using parametric sweep [Table 5.1]
for load and verified FEMM simulation results obtained from FEMM simulation. In addition, power
parameters for secondary coil obtained [Table 5.4], which were not visible in FEMM simulation results
[Table 4.2] other than the voltage drop of secondary coil because FEMM considering secondary coil as
an open circuit due to zero current defined for secondary side. Power transfer efficiency for the whole
system simulated in Pspice for all tested frequencies resulting 71% for the lower frequency 211 kHz
and 94% for the highest frequency 10 MHz for a single looped coil [Table 5.6]. In addition, mathematical
calculation carried out using theoretical expressions from [Chapter 2] to verify the results obtained from
FEMM simulation and Pspice simulation theoretically [Chapter 6]. Some deviation expected between
results obtained from FEMM, Pspice and mathematical calculations, because some components
expressions were approximations. However, the similarity between the curves with respect to tested
frequencies gives FEMM simulation software validity.
Practical Test
The practical measurements will always differ from the simulations because of an approximated
practical model and difference in the load resistance calculated and the resistors obtained from
component shop at campus have a little bit of difference due to zero availability of precise
components. In [Chapter 7] it is clearly visible that even there is slight difference between the calculated

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components and practically used components the difference in the results obtained from FEMM
simulation [Chapter 4] Pspice simulations [Chapter 5] and mathematical calculations [Chapter 6] along with the
practical measurements [Chapter 7], almost neglect able difference. Which is not much to have any sort
of impact on the results and verification of FEMM simulation; it is still valid that FEMM simulation
software is to rely on. FEMM is a lot compact, easy to use and controlled by matlab to generate plots
and other results required for magnetic problems. Although the difference can be eliminated by having
a professionally made coils by a manufacturer and precise components matching the calculated
components, which is the same as generated from FEMM simulation.
Hypothesis
Three types of hypothesis [Chapter 8] simulated in FEMM simulation after verifying the software as valid
for magnetics problems. As seen from [Chapter 8], that each of the technique hypothetically can provide a
better and efficient result for multi turn coils. It is important to take into account that if there were tight
coupling between the turns of the coil [Hypothesis 1] would be a better option to obtain better results,
which is to define the turns into the block parameters associated with FEMM software. In addition if
there is a gap between the turns due to thick wires or even thin wires but if the requirements is the gap
between the turn then [Hypothesis 2] can give a better and efficient result compared to [Hypothesis 1]. If more
wires are used in same area as single looped coil, [Figure 4.1] which is 6 mm, then [Hypothesis 3] expected
to give a precise and efficient result for simulating WPT systems in FEMM simulation software. The
reason why three types of methods [Chapter 8] are hypothesis is that due to lack of time the chances for
digging deep into those phenomena’s and analysis has been cutoff even though it’s not a project scope
but a good discussion panel in FEMM for simulating different types of coils.
The results obtained from those multi turn hypothesis [Chapter 8] clearly indicates that more turns in a
coil increases the voltage drop across the coils and so is the real power across the coils.
Final Conclusion
FEMM simulation software gives a way to optimize coils and power transfer efficiency for a system
given the design limits. Coil optimized to a specific frequency with a higher efficiency rate and higher
power transfer using single looped coil compared to lower frequencies. In that sense the objective of
the project thesis have met in all four cases FEMM simulation [Chapter 4], Pspice simulation [Chapter 5],
mathematical calculations [Chapter 6] and Practical measurements [Chapter 7]. Which verifies the fact that
FEMM simulation software is a good freeware for magnetics problems and using FEMM for further
investigation of optimization of wireless power transfer coils and the power transfer efficiency.
Pspice simulations and more deep analysis of the hypothesis can extend the work done in [Chapter 8] so
that they can be verified and will be a lot useful in future for different shapes and types of coils which
also gives a good review on FEMM being bold and open for different types of coils. However, at this
point it can only be assumed! that the three types of methods described in [Chapter 8] gives more
efficient and fine results.

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Future Work
The model can possibly be improved by adding more turns to the coil at low frequencies due to the
fact that, qualitatively at low frequencies and within the limits increasing the number of turns N
improves Q because L varies as N2
while R varies linearly with N. Which is verified hypothetically in
[Chapter 8] that more turn can give more power, but a deep analysis is required in future to conclude the
assumptions made regarding the hypothesis carried out in [Chapter 8]. Similarly, increasing radius (r) of
the inductor improves the Q as well, because L varies as r2
and R varies linearly with r. Both of these
predictions assumes that the diameter of the coils remains the same so both predictions proportionally
uses more copper.
To obtain precise results professionally manufactured components, exact tuning as well as doing the
measurements with a network analyzer would be a good idea.

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Appendix
Simulation Figures Chapter 5 (Pspice)
Simulation Figures Primary Coil
Figure 5.2: Simulation result for Primary with Real power-peak and Vpeak-peak at 211 kHz
Figure 5.3: Simulation result for Primary with Real power-peak and Vpeak-peak at 800 kHz
Figure 5.4: Simulation result for Primary side with Real power-peak, Vpeak-peak at 4 MHz

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Simulation Figures Secondary Coil
Figure 5.7: Simulation result for Secondary side with Real power-peak, Vpeak-peak at 211 kHz with efficient load

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Figure 5.8: Simulation result for Secondary side with Real power-peak, Vpeak-peak at 800 kHz with efficient load
Figure 5.9: Simulation result for Secondary side with Real power-peak, Vpeak-peak at 4 MHz with efficient load

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Simulation Figures Power transfer efficiency
Figure 5.12: Power efficiency of the system at 211 kHz frequency with efficient load
Figure 5.13: Power efficiency of the system at 800 kHz frequency with efficient load

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Figure 5.14: Power efficiency of the system at 4 MHz frequency with efficient load

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Practical Model Results figures Chapter 7
Primary Coil Scope measurements
Figure 7.1: Voltage drop primary coil at 211 kHz frequency
Figure 7.2: Voltage drop primary coil at 800 kHz frequency

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Figure 7.3: Voltage drop primary coil at 4 MHz frequency

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Secondary Coil Scope measurements with Load
Figure 7.6: Voltage drop secondary coil at 211 kHz frequency with max efficient Load

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Figure 7.7: Voltage drop secondary coil at 800 kHz frequency with max efficient Load
Figure 7.8: Voltage drop secondary coil at 4 MHz frequency with max efficient Load

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Secondary Coil Scope measurements without Load
Figure 7.11: Voltage drop secondary coil at 211 kHz frequency zero load
Figure 7.12: Voltage drop secondary coil at 800 kHz frequency zero load

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Figure 7.13: Voltage drop secondary coil at 4 MHz frequency zero load

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Bibliography
James W. Nilsson Electric Circuits Fourth Edition
http://www.femm.info/Archives/doc/manual42.pdf
http://www.femm.info/Archives/doc/octavefemm.pdf
References
1) https://en.wikipedia.org/wiki/Inductor
2) http://www.witricity.com.
3) http://www.wirelesspowerconsortium.com.
4) http://olev.kaist.ac.kr/en/
5) https://en.wikipedia.org/wiki/Vacuum_permeability
6) https://www.eeweb.com/toolbox/coil-inductance/
7) https://en.wikipedia.org/wiki/Electrical_reactance
8) https://en.wikipedia.org/wiki/Magnetic_flux
9) https://en.wikibooks.org/wiki/Circuit_Theory/Inductors
10) http://www.learnabout-electronics.org/ac_theory/reactance61.php

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11) http://meettechniek.info/passive/inductance.html
12) http://eit.lm1.dk/23434lmaweblog3901/notes/simulation-of-magnetics/femm4-2-
magnetic-simulation-examples/
13) http://www.electronics-tutorials.ws/inductor/mutual-inductance.html
14) http://www.ijritcc.org/download/1435302043.pdf
15) https://en.wikipedia.org/wiki/Copper_wire_and_cable
16) http://powerelectronics.com/alternative-energy/optimize-wireless-power-transfer-link-
efficiency-part-1
17) https://www.wirelesspowerconsortium.com/technology/quality-factor.html
18) http://www.softschools.com/formulas/physics/efficiency_formula/29/
19) http://www.allaboutcircuits.com/textbook/alternating-current/chpt-11/true-reactive-and-
apparent-power/
20) https://www.physicsforums.com/threads/how-to-calculate-resistance-inductance-
impedance-and-capacitance-of-coil-in-ac.658646/
21) http://chemandy.com/calculators/round-wire-ac-resistance-calculator.htm
22) http://www.egnret.ewg.apec.org/workshops/EVWorkshop/[2]%20Inductive-power-
transfer.pdf

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Time Plan
Project week From
From 1st
Feb – 7th
June
Dates Phase Task
1 01-02-2016 – 05-02-2016 Research Project plan, Meeting
with LMA 01-02-2016
Project scope
discussion
2 08-02-2016 – 12-02-2016 Research Report structure,
meeting with LMA 08-
02-2016 report
discussion and project
plan
3 15-02-2016 - 19-02-2016 Project definition and
planning
Chapter 1:
Abstract, Introduction,
Report. Meeting with
LMA 15-02-2015
general discussion on
Finite Element
simulation Modeling
and circuit for
Wireless Power
Transfer (WPT
4 22-02-2016 – 26-02-2016 Project definition and
planning
Report: History of
WPT, Motivation
5 29-02-2016 – 04-03-2016 Project definition and
planning
Objectives,
Organization of thesis,
Discussion with Lars
Maack
6 07-03-2016 – 11-03-2016 Practical Model Plan
for WPT
Coil research for
primary coil (TX coil)
7 14-03-2016 – 18-03-2016 Practical Model of
WPT
Implementation of
primary coil (TX coil)
Measurements of the
primary coil using
impedance analyzer
Testing the Primary
coil measurements on
the scope
8 21-03-2016 – 25-03-2016 FEMM Model for
WPT, WPT Report
Generating FEMM
model for the primary
side for comparison
with the practical
model of primary side.

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Report: Chapter 2
Introduction.
9 28-03-2016 – 01-04-2016 WPT Report: Basic Circuit for IPT
10 04-04-2016 – 08-04-2016 WPT Report: Mathematical
representation of basic
circuit
Meeting with Lars
Maack regarding
FEMM, report and
basic circuit
11 11-04-2016 – 15-04-2016 Practical Model for
WPT
Coil research for
secondary side,
implementation of
secondary coil.
12 18-04-2016 – 22-04-2016 Secondary Coil
Measurements
Measurements of the
secondary coil using
impedance analyzer
13 25-04-2016 – 29-04-2016 Testing Practical
Model
Time to test the
primary and secondary
coil and the transfer of
power between both
coils providing an
input from the function
generator down in the
Lab-
: A meeting with Lars
to have discussion on
the practical model.
14 02-05-2016 – 06-05-2016 Testing Practical
Model
Measurements of the
system in the Lab
15 09-05-2016 – 13-05-2016 Final FEMM model
for WPT.
Finalizing the FEMM
model for both
primary and secondary
side.
16 16-05-2016 – 20-05-2016 Comparison Comparison of the
whole System:
Mathematically,
Practically, and
FEMM simulation.
Discussion with Lars
Maack
17 23-05-2016 – 27-05-2016 Final Look up: Report,
measurements,
simulations.
Final check up on
everything.
Discussions with Lars

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Maack would be
needed,
18 30-05-2016 – 03-06-2016 Finalizing report
19 06-05-2016 – 07-06-2016 Finalizing Project
report , delivery
Matlab Scripts for FEMM Simulations
Matlab Script for WPT model
openfemm;%opens femm
create(0);%create a new document 0 is for megnetic problem
mi_probdef(211e3,'millimeters','axi',1e-008,31,30,(0)); % Define Problem
%//////////////////////////////////////////////////////////////////////////
%////Create Outer Core////////
mi_addnode(0,-180);%--- from 0 to -180 mm y axis
mi_addnode(0,180); %--- from 0 to +180 mm y axis
mi_addsegment(0,-180,0,180); % add 360 mm of segment from -180 to 180 on y axis
mi_addarc(0,-180,0,180,180,3);
mi_addblocklabel(50,-30);
mi_selectlabel(50,-30);%---- Selcting the label
mi_setblockprop('Air',1,0,'',0,0,0);%---> defining bllock properties
mi_clearselected; %----> clear all selected items
%////////////////////////////
%//////Primary Coil////////
mi_addnode(80.5,-0);
mi_addnode(86,-0);
mi_addarc(80.5,-0,86,-0,180,1);
mi_addarc(86,-0,80.5,-0,180,1);
mi_addblocklabel(83.25,-0);
mi_selectlabel(83.25,-0);%---- Selcting the label
mi_setblockprop('Copper',1,0,'Primary Coil',0,0,1);%---> defining bllock properties
%///////////////////////////
%///////Secondary Coil/////
mi_addnode(80.5,50);
mi_addnode(86,50);
mi_addarc(80.5,50,86,50,180,1);
mi_addarc(86,50,80.5,50,180,1);
mi_addblocklabel(83.25,50);
mi_selectlabel(83.25,50);%---- Selcting the label
mi_setblockprop('Copper',1,0,'Secondary Coil',0,0,1);%---> defining bllock properties
%///////////////////////////
%////Boundary Properties////
mi_addboundprop('Boundary',0,0,0,0,0,0,0,0,3);%--->Add boudary properties

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63
mi_selectarcsegment(0,-180);
mi_setarcsegmentprop(1,'Boundary',0,0);%---- Defining boundary prop to arcs
mi_clearselected;
%///////////////////////////
%///Get Materials///////////
mi_getmaterial('Air');
mi_getmaterial('Copper');
%///////////////////////////
%/////Circuit Properties////
mi_addcircprop('Primary Coil',0.2,1);
mi_addcircprop('Secondary Coil',0,1);
%///////////////////////////
mi_saveas('WirelessPowerTransferModel1.FEM');
mi_analyze(1);
mi_loadsolution;
mo_showdensityplot(1,0,6e-5,4e-10,'mag');
mo_savebitmap('Wirlesspowertransfer.bmp')
Matlab Scripts for three types of hypothesis
Hypothesis 1:
%//////////////////////////////////////////////////////////////////////////
mi_addarc(0,-180,0,180,180,3);
%////////////////////////////
mi_addnode(86,-0);
mi_addarc(80.5,-0,86,-0,180,1);
mi_addarc(86,-0,80.5,-0,180,1);

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64
%///////////////////////////
mi_addnode(86,50);
mi_addarc(80.5,50,86,50,180,1);
mi_addarc(86,50,80.5,50,180,1);
mi_addblocklabel(83.25,50);
mi_selectlabel(83.25,50);%---- Selcting the label
mi_setblockprop('Copper',1,0,'Secondary Coil',0,0,1);%---> defining bllock properties
%///////////////////////////
%////Boundary Properties////
mi_addboundprop('Boundary',0,0,0,0,0,0,0,0,3);%--->Add boudary properties
mi_selectarcsegment(0,-180);
mi_setarcsegmentprop(1,'Boundary',0,0);%---- Defining boundary prop to arcs
mi_clearselected;
%///////////////////////////
%///Get Materials///////////
mi_getmaterial('Air');
mi_getmaterial('Copper');
%///////////////////////////
%/////Circuit Properties////
mi_addcircprop('Primary Coil',0.2,1);
mi_addcircprop('Secondary Coil',0,1);
%///////////////////////////
mi_saveas('WirelessPowerTransferModel1.FEM');
mi_analyze(1);
mi_loadsolution;
mo_showdensityplot(1,0,6e-5,4e-10,'mag');
mo_savebitmap('Wirlesspowertransfer.bmp')

01-02-2016
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65
Hypothesis 2
%//////////////////////////////////////////////////////////////////////////
mi_addarc(0,-180,0,180,180,3);
%////////////////////////////
mi_addnode(80.5,-6.25);
mi_addnode(86.5,-6.25);
mi_addnode(80.5,-12.50);
mi_addnode(86.5,-12.50);
mi_addnode(80.5,-18.75);
mi_addnode(86.5,-18.75);
mi_addarc(80.5,-0,86.5,-0,180,1);
mi_addarc(86.5,-0,80.5,-0,180,1);
mi_addarc(80.5,-6.25,86.5,-6.25,180,1);
mi_addarc(86.5,-6.25,80.5,-6.25,180,1);
mi_addarc(80.5,-12.50,86.5,-12.50,180,1);
mi_addarc(86.5,-12.50,80.5,-12.50,180,1);
mi_addarc(80.5,-18.75,86.5,-18.75,180,1);
mi_addarc(86.5,-18.75,80.5,-18.75,180,1);
mi_addblocklabel(83.25,-6.25);
mi_selectlabel(83.25,-6.25);%---- Selcting the label
%///////////////////////////
mi_addnode(86,50);
mi_addarc(80.5,50,86,50,180,1);
mi_addarc(86,50,80.5,50,180,1);

Bachelor- thesis, optimization of wireless power transfer coils using finite element simulation-2016

Bachelor- thesis, optimization of wireless power transfer coils using finite element simulation-2016

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