circuit optimization for underwater power transfer
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FACULDADE DE ENGENHARIA DA UNIVERSIDADE DO PORTO
Circuit Optimization for UnderwaterPower Transfer
Francisco Ricardo Pinto Gonçalves
MESTRADO INTEGRADO EM ENGENHARIA ELECTROTECNICA E DECOMPUTADORES
Supervisor: Prof. Cândido Duarte
Co-supervisor: Dr. Luís Pessoa
July 28, 2016
c© Francisco Ricardo Pinto Gonçalves, 2016
Abstract
Wireless power transfer (WPT) has started with Nikola’s Tesla idea to provide the world withfree wireless power. The idea of transmitting wireless power is a hot research topic and a wellstudied area. Throughout the years, commercial devices using WPT have began to appear; elec-trical toothbrushes, induction stoves, solar powered satellites and radio have been in our quotidianfor quite some time. Although they are highly available and researched, those techniques focusmainly in two main transfer mechanisms: magnetic induction and in electromagnetic radiationmode.
The method chosen to realise underwater wireless power transfer in this work will be inductivecoupling, using two planar coils operating at 100 kHz due to their good behaviour in underwateroperation.
Hence, this is the transfer mechanism which suits the purpose of this work: supplying anautonomous underwater vehicle, or a remotely operated vehicle. This is because of the difficultieswhile operating in underwater, such as guaranteeing a stable vehicle position, high power losses,skin effect on coils, coil fouling, circuits and eddy current losses. All of those have an increasedeffect in salt water transmission compared to the air one.
The author of this work proposes to develop an adaptive underwater wireless power transfersystem, as well as developing and optimising underwater wireless power transfer by means of anew circuit topology for multi resonant power transfer.
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Resumo
O conceito de transmissão de potência sem fios, foi fortemente impulsionado com a ideiapioneira de Nikola Tesla, de distribuir energia elétrica sem fios, sem custos para todo o mundo.
Sendo este conceito um tópico de pesquisa bastante explorado hoje em dia. Ao longo dosanos, aparelhos comerciais que se baseiam em transmissão de potência sem fios começaram aaparecer; fornos de indução, máquinas de barbear, satélites carregados por energia solar e rádiosencontram-se nas nossas vidas há já algum tempo.
Estas tecnologias estão bastante presentes hoje em dia e focam-se principalmente em doismecanismos de transmissão: indução magnética e radiação electromagnética.
Nesta tese o método escolhido será indução magnética, através de acoplamento indutivo entredois inductores planares operando a uma frequência de 100kHz.
Sendo este o mecanismo que mais se adapta ao intuito deste trabalho: carregar sem fios umveículo autónomo submarino, ou um veículo submarino operado remotamente. Isto deve-se aofacto das dificuldades de operar debaixo de água, tais como: garantir uma posição estável doveículo, perdas joule, efeito pelicular nos indutores, corrosão nos indutores, perdas nos circuitos ecorrentes de Foucault. Sendo que estes factores se agravam quando passamos do ar para a água.
Com base no que foi dito, nesta tese propõe-se o desenvolvimento de um sistema adaptativode regulação de tensão na carga sem fios, assim como desenvolver um circuito que optimise atransferência de potência para a carga.
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Agradecimentos
Começando por reconhecer que o desenvolvimento desta tese não ocorreu da maneira maislinear possível, gostaria de começar por agradecer em primeiro lugar ao meu orientador CândidoDuarte por me ter apresentado este tema de dissertação e por toda a ajuda desde o primeiro diade trabalho nesta tese assim como pela paciência que teve quando nem tudo corria da melhormaneira, para ele os meus mais sinceros agradecimentos pois sem a sua paciência e encorajamentoo trabalho não teria acabado desta maneira.
Em segundo lugar gostaria de agradecer à minha família em especial ao meu pai e à minha mãepois foram os pilares da minha educação, formando-me no ser humano que sou hoje, dando-metodo o apoio necessário e indispensável para a conclusão deste curso.
Aos meus amigos do secundário, sem nenhuma ordem particular, Freitas, Ruben, Edu, Pedro,Ana, Bruna, Carolina, Sofia, Ana Sofia e Andreia.
Aos técnicos dos laboratórios pela paciência e ajuda com o desenvolvimento e debug dasPCB’s.
Ao pessoal do núcleo de microelectrónica pela companhia aquando dos jogos da seleção noEURO 2016.
Gostaria de agradecer de um modo especial à Elisa e à Sara por todo o apoio que me deramnestes últimos anos. Principalmente à Elisa obrigado por tudo, obrigado por estares sempre lá paramim por acreditares em mim mesmo quando eu não acreditei, foste indispensável neste percursoe nunca me vou esquecer disso.
À minha namorada Carolina por todo o apoio que me deu desde o primeiro dia, por todo ocarinho, por estar sempre lá quando eu precisei, por todos os cafés e jantares, por todas as quotesdos Friends, por todos os gifs e snaps que me ajudaram a fazer deste percurso mais leve e fácil deaguentar.
Gostaria de dedicar esta tese à minha avó Leopoldina da Conceição Gonçalves por ser a minhafonte de luz nos momentos mais escuros.
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‘Let the future tell the truth, and evaluate each one according to his work and accomplishments.The present is theirs; the future, for which I have really worked, is mine.”
Nikola Tesla
Contents
1 Introduction 11.1 Classification of WPT Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.2 Underwater Power Transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2.1 Main Objectives of this Work . . . . . . . . . . . . . . . . . . . . . . . 71.2.2 Document Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2 State of the Art 92.1 General ways to realise WPT . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.2 Converters and Rectifiers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122.3 Impedance Matching . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
3 Problem Characterisation 153.1 The Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.1.1 Load Determination . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153.1.2 Transformer Configuration . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.2 Proposed Solution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243.2.1 Coupled Mode Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . 243.2.2 Circuit Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 263.2.3 Adaptive Regulation System . . . . . . . . . . . . . . . . . . . . . . . . 263.2.4 Multi Resonant System . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
4 An Adaptive System for Underwater Wireless Power Transfer 294.1 Proposed Underwater WPT System . . . . . . . . . . . . . . . . . . . . . . . . 304.2 Implementation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
5 Multi Resonance System 375.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 375.2 UWPT System Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 385.3 Proposed Circuit Topology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 395.4 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
6 Conclusion 496.1 Main Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 496.2 Thesis Scientific Contributions . . . . . . . . . . . . . . . . . . . . . . . . . . . 496.3 Future Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
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viii CONTENTS
List of Figures
1.1 Categories of WPT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31.2 Circuits models for wireless power transfer . . . . . . . . . . . . . . . . . . . . 51.3 Losses in air and fresh water with respect to the distance of transmission . . . . . 61.4 Figure comparing efficiency in salt water and air . . . . . . . . . . . . . . . . . . 7
2.1 WPT System topology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92.2 Common Topologies used to implement WPT . . . . . . . . . . . . . . . . . . . 102.3 Half wave and full wave rectifier . . . . . . . . . . . . . . . . . . . . . . . . . . 102.4 Comparison between the new WPT method witricity and traditional inductive cou-
pling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.5 Common block diagram for an enery harvesting system . . . . . . . . . . . . . . 11
3.1 Overall system topology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153.2 Accurate Electrical Battery model . . . . . . . . . . . . . . . . . . . . . . . . . 163.3 Half Bridge Rectifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163.4 Block diagram of the measurement setup . . . . . . . . . . . . . . . . . . . . . . 173.5 Set-up to characterise the output impedance of the system . . . . . . . . . . . . . 183.6 Load electrical characterisation, respective to the first 25 minutes . . . . . . . . . 203.7 Load electrical characterisation respective to full charge plots . . . . . . . . . . . 213.8 Battery electrical characteristics plots . . . . . . . . . . . . . . . . . . . . . . . 223.9 Battery current and voltage full charge plots . . . . . . . . . . . . . . . . . . . . 233.10 Equivalent transformer model known as “Tee”-Model . . . . . . . . . . . . . . . 243.11 Coils top and side view . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253.12 Overview of the system in which this thesis is inserted . . . . . . . . . . . . . . 25
4.1 WPT system block diagram. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304.2 Class-D series-series driver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314.3 Load modulation signals for regulating Vout . . . . . . . . . . . . . . . . . . . . . 314.4 Pictures of the experimental set-up for an adaptive UWPT . . . . . . . . . . . . 324.5 Proposed adaptive system. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334.6 Frequency variation plot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 344.7 Osciloscope waveforms of the pulse sense and load regulation . . . . . . . . . . 35
5.1 UWPT system configuration for charging the batteries of an AUV. . . . . . . . . 385.2 UWPT system with the “tee” model of coupling coils. . . . . . . . . . . . . . . . 385.3 Cascade L network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405.4 Virtual resistance R vs load resistance RL . . . . . . . . . . . . . . . . . . . . . . 405.5 Basic network to develop the proposed topology . . . . . . . . . . . . . . . . . . 405.6 Circuit successive simplifications . . . . . . . . . . . . . . . . . . . . . . . . . . 42
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x LIST OF FIGURES
5.7 Circuit model for the proposed network topology. . . . . . . . . . . . . . . . . . 425.8 Complete UWPT topology. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 445.9 Output voltage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 445.10 Simulation results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 465.11 Maximum repetitive voltage . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
List of Tables
3.1 Comparison between 18 V and 21 V charging . . . . . . . . . . . . . . . . . . . 193.2 Variation of the input resistance with the capacity of the batteries . . . . . . . . . 19
4.1 Voltage regulation results with deviations on Vdd and RL. . . . . . . . . . . . . . 35
5.1 Simplification expressions for the circuit at f = 3 f0. . . . . . . . . . . . . . . . . 435.2 Parameter values according to the values arbitrated in (5.1)–(5.3), f0 = 100kHz,
RL = 10Ω, α = 2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 455.3 Performance comparison for RL = 10Ω and equal VRRM. . . . . . . . . . . . . . 46
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xii LIST OF TABLES
Symbols and Abbreviations
AC Alternating CurrentATX Advanced Technology eXtendedAUUV Autonomous Underwater Unmaned VehiclesAUV Autonomous Underwater VehiclesBRIA Bidirectional Reflectance Impedance AnalysisCMT Coupled Mode TheoryCT Circuit TheoryDC Direct CurrentESR Equivalent Series ResistanceIMN Impedance Matching NetworksPSU Power Supply UnitPWM Pulse Width ModulationQ Quality FactorRF Radio FrequencySCMR Strongly Coupled Magnetic ResonanceUWPT Underwater Wireless Power TransferVNA Vector Network AnalyserWPC Wireless Power ChargesWPT Wireless Power TransferZVDS Zero-Voltage Derivative SwitchingZVS Zero-Voltage Switching
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Chapter 1
Introduction
Wireless power transfer (WPT) is the concept of transferring power between a source and a
load, without wires, using time-varying electromagnetic fields [1]. WPT as an idea has existed
for over a century. It started in 1864 with Maxwell’s theoretical work on electromagnetic waves,
combining two other important scientific contributions [2], i.e.: André-Marie Ampère’s discover
that an electric current produces an magnetic field; and the electromagnetic induction unveiled
by Michael Faraday. Later, Heinrich Hertz was challenged by his doctoral advisor, Hermann
von Helmholtz, to participate on a contest aiming at experimentally demonstrate the Maxwell’s
equations. Hertz showed the existence of electromagnetic waves moving at the speed of light,
but only after the contest expired [3, pp.95–106]. Finally, it was Nikola Tesla who came with
the concept of transferring wireless power [4]. Nikola Tesla’s first breakthroughs were mentioned
in three patents, two submitted in 1899 and issued in 1901 [5, 6], and the third one published
in 1905 [7]. His idea was to use the Earth as a natural medium to transfer wireless power [7].
The original concept was using stationary-waves generators, with different wave lengths, spaced
in a judicious way in order to divide the Earth in electrical identical regions [7]. The people at
home would have a device tuned at one of those frequencies, which would grant them electrical
power [7]. The idea never leaved scientist minds and has been researched ever since.
The exponential growth of electronic devices of the last decades has led to a situation in which
a normal person can easily have five electronic devices in their bags, such as: mobile phone,
computer, tablet, smart watch and an iPod or something similar. Charging several devices simulta-
neously requires an individual charger for each. With the use of WPT one can reduce the charger
count to only one, connected to the power grid [8].
But there is a lot more to take advantage from WPT. With the appearance of affordable elec-
trical cars for the world population an industry is rising due to the need for wireless power charg-
ers (WPC) for vehicles. It is foreseen that in the shortcoming future, parking spots at shopping
centers where WPC will be placed so that the battery refills without the need to go to an actual
power station [9].
Also in health care WPT can play an important role, for instance when it comes to biomedical
implantable devices such as pacemakers, cochlear implants, deep brain neuro stimulators, gastric
1
2 Introduction
stimulators, etc [10]. Nowadays these devices are mostly limited by power supply issues, i.e.
no one wants to be often charging a small device underneath his body, which requires a regular
medical procedure and besides excessively exposes the body to radioactive fields. Therefore, the
need for better WPT systems in these context is highly required to solve some existing problems
such as: the need to adapt the transmission coil to be flexible in order to adapt to the body tissue,
which degrades the power transfer efficiency, the misalignment that does not allow for the maximal
power transfer efficiency, the fact that the body cannot be exposed to high magnetic fields, among
others [11].
WPT is also present in energy harvesting, which is the process of gathering energy from am-
bient sources and its main goal is to extend the lifetime of the battery in wireless devices, leading
to in the future battery free devices [12]. These devices generally operate in the radio frequency
band (RF) and aim to convert radio frequency waves, generally in the megahertz region, into direct
current (DC) in order to provide power to the system [13].
In the present work, the focus will be on WPT for autonomous underwater vehicles (AUVs).
This type of vehicles is very important on today’s sea patrolling. Their common routines include
things such as: habitat monitoring, ocean current measurement, wave height and wave velocity
measurements [14]. These task are done by traveling a considerable amount of miles underwa-
ter while gathering, processing, and sending data to either a control station or another AUV. To
replenish their power supplies, human intervention is required. Being able to charge them au-
tonomously by means of a power dock is fundamental to the development and swiftness of these
operations [15, 9].
1.1 Classification of WPT Systems
WPT can be categorized in terms of field range, which can be far-field range (radiative)
and near-field (non-radiative) [10, 16]. The former describes the electromagnetic radiationmode (microwave power transmission and laser) [17]. The latter comprises capacitive coupling(due to the coupling of an electric field) [18, 19] and two types of magnetic field coupling: mag-netic inductive coupling and strongly coupled magnetic resonance [15, 20, 10]. Fig. 1.1 sum-
marizes these categories.
Far-field systems operate in the region beyond two wavelengths (2λ ) of the antenna [21],
where the electric and magnetic fields are perpendicular to each other and propagate as an electro-
magnetic wave. The power leaves the emitter independently if there is a receiver or not, which is
not the most efficient approach. Electromagnetic radiation can be directed, by reflection or refrac-
tion into beams. Using a high-gain antenna or an optical system to concentrate de radiation. Some
examples can be found as microwaves or light waves [22, 16].
On the other hand, near-field is where the range is less than λ or 2λ of the antenna [21]. Here
the electric and magnetic fields are separate and the power can be transferred in both ways, i.e. via
electric fields by capacitive coupling between metal electrodes [18, 19], or by means of magnetic
fields such as inductive coupling between coils [10]. These are non-radiative fields because if there
1.1 Classification of WPT Systems 3
Figure 1.1: Categories of WPT.
is not a receiving object (coil, electrode) within the coupling range, no power leaves the transmitter.
The geometry, alignment and quality of the coils from both devices, receiver and transmitter,
sets the optimalfrequency of operation and the range of transmission. These techniques are not
suitable for long-range power transmission because the electrical and magnetic fields decrease
exponentially with distance (besides other energy loss issues) [10, 17].
Near-field systems can be still subdivided in short and mid range. Short range considers a
distance less than λ from the antenna [21] and it is where non-resonant capacitive or inductive
coupling transfer optimal power. On the other hand, mid range is usually defined as λ to 2λ
distances [21]. It is where resonant capacitive and inductive coupling transfer show optimal power
transfer. This is because resonant systems rely on evanescent waves, which increase the range of
transmission due to reduced losses on the adjacent objects (since usually they are not resonant).
As the physical mechanisms for near-field WPT system are significantly different for short and
mid ranges, they are summarized next.
• Short-range near field:
– Capacitive coupling – uses two electrodes one for the transmitter and one for the
receiver. They form a capacitor with the space between them as the dielectric. It
uses a high-frequency and high-voltage driver to excite the transmitter to generate an
alternating electric field that will eventually induce an alternating potential by elec-
trostatic induction, which is the redistribution of the electrical charges in a object
causing an alternate current (AC) to flow in the load circuit. The power transferred
4 Introduction
increases with frequency and capacitance between the plates. The transfer efficiency
is affected by surrounding objects and the transfer power is low compared to other
mechanisms [18, 19, 17, 16].
– Magnetic inductive coupling – the power is transferred between two coils that form
a transformer. The transmitter coil is excited with an AC current that produces an
oscillating magnetic field. That field passes through the receiving coil, where an al-
ternating electromotive force is induced and produces an AC current in the receiver.
Here the power transferred increases with frequency and the mutual inductance (M)
between the coils. The coupling strength is usually quantified by the so called “cou-
pling factor” k, given by M√L1L2
, which is a dimensionless parameter. The maximum k
is unitary and occurs when the coils are perfectly enclosed and aligned, thus the power
transfer is maximum [1, 15, 17, 16]. Electromagnetic induction transfer efficiency and
transfer power are usually very high, but the transfer distance is within the centimeter
level. This technique is usually employed in commercial electrical toothbrushes and
induction stoves.
• Mid-range near field:
– Strongly coupled magnetic resonance (SCMR) – the power transfer principle is the
same as in magnetic induction. However, here resonant coils are employed to achieve
better performance at greater distances where magnetic inductive coupling fails. Fig.
represents a SCMR system, where a driving loop excites the transmitting coil, which
is in resonance with the receiving coil. The coils have a high quality factor (Q) to
achieve a good resonance. SCMR transfer power and transfer efficiency are lower that
inductive coupling, but the transfer distance can be within a few meters. More detail
on WPT circuit topology can be seen in [17, 16].
In the present work, WPT will be addressed using magnetic coupling. The goal is being able
to use WPT for charging an AUV batteries. This poses particular challenges in power transfer,
essentially due to the medium, which is salt water.
1.2 Underwater Power Transfer
Sub sea power transfer has been studied and developed for many years. The conventional
approach consists on the use of plugged connectors from the docking station to the device, which
is usually an AUV [15]. By using plugged connectors there is the need to remove the AUV from
out of the water, therefore reducing the vehicle autonomy by making it travel a predefined route in
order to get data and be charged, also increasing the vehicle maintenance. In order to increase the
AUV operational lifetime, inductive wireless power transfer is being used to recharge the vehicles
batteries while underwater, using wireless connectors inside of the vehicle eliminating therefore
the need for electrical plugs [23].
1.2 Underwater Power Transfer 5
+− VS
RS
C2R2
L2 L3
R3 C3
RL
(a)
+− VS
RS
C2R2
L2 L3
R3
C3 L4
R4 C4
LL
(b)
Figure 1.2: Figures describing the power transfer model. In the first the two coils form a transformer andthe energy is transferred between them through inductive coupling. In the second figure there are threecoils, where the first can be seen as a drive loop that excites the second coil so it is put in resonance withthe third one and resonant power transfer is done. (a) Two coil wireless power transfer schematic; (b) Threecoil wireless power transfer schematic.
While the premise to recharge AUV’s batteries wirelessly is simple and bring many benefits
as stated above, there is always the other side of the coin, meaning that there are several contrains
and complications in using WPT for this process. Those constrains fall into two categories: one is
because as WPT is also realized on air it shares the same contrains, while the other is due to the
fact that the transmission mean is the water [24].
The losses shared with transmitting power in the air are [15]:
• Copper loss in coils – this phenomenon happens due to the AC resistance of the coils and
the load resistance. To minimize this effect, wires with low AC resistance should be used.
It can also be done by lowering the resonant frequency, but this is not always possible.
• Semiconductor losses in circuits – occurs in the circuit components, generally in the rec-
tifier, and it can be reduced by structural changes of the circuits (better circuit layout, or
better choice of circuit components).
• Skin effect – occurs in the conductor surfaces due to opposing eddy currents. They are
present on the shell of the conductors. As long as the gap between the shell and coil is wide
enough there should be no major power loss here. Although it rises problems in the self
inductance of the coils.
6 Introduction
0 1 2 3 4 5 60
20
40
60
80
100
120
Distance (m)
Pa
th L
oss (
dB
)
Figure 1.3: This figure shows the losses in air and fresh water with respect to the distance of transmission.As fresh water and air share almost the same permetivity the lines are represented toghether.
• Air or Water as dieletric – as reported in [25] air and water share the same permettivity
and therefore the losses either in water and in the air are relatively the same as shown in
picture 1.3 in respect to equation 1.1. Although as seen in 1.3 the attenuation for fresh water
and air are equivalent, when using salt water as a medium the attenuation does not remain
the same, since the salt water has a different permitivity and conductivity. Figure 1.4 shows
the different results when using salt water or air [24].
LMI(r)'−10log(
Nta3t a3
r
4Nrr6
)(1.1)
While in underwater we have several kinds of different losses and constrains as well [8, 9, 26,
23]:
• AUV stabilization – when operating underwater the AUV stabilization (docking) in the
docking station is a difficult process and affects the WPT efficiency, since the optimal alig-
ment and separation distance cannot be guaranteed. Inductive coupling power transfer is
used in underwater applications due to close range efficiency and being able to operate in
frequencys that allow a good WPT efficiency while operating underwater since water has a
very high attenuation for frequencies above 1MHz.
• Bio-fouling – underwater exposure of the coils also leads to some bio-fouling on them. As
so the best type of coating to make the coils invulnerable or at least without the least marine
fouling is an important aspect when designing an UWPT system. This has implications with
the coils because a certain amount of bio-fouling, leads to corrosion creating shorts between
the coils changing the coil quality factor, therefore their optimal resonating frequency which
represents a change in the efficiency of the system.
• Thermal dissipation – is the ability of the coils to dissipate a determined amount of heat
while rising their own temperatures. This is an aspect that allows the UWPT designer to
1.2 Underwater Power Transfer 7
5 10 15 20 25 30 35 40 45 50 550
10
20
30
40
50
60
70
80
90
Distance (m)
Eff
icie
ncy (
%)
Air
Water
Figure 1.4: This figure shows the efficiency for two different means of propagation,i.e, salt water and airrespective to the separation distance [24].
choose between the coils coatings available, the one which leads to the lesser rise of tem-
perature for the same amount of power dissipation.
• Thermal and bio-fouling – the factors stated above are never present by their own. Hence
the best coating material that dissipates the least heat and generates the least amount of
bio-fouling is the one that should be chosen.
• Coil quality factor – this factor should be maximized in order to transfer the maximum
power and efficiency. The coil quality factor depends only on the coil itself.The quality
factor varies with the material used as well as with the medium that surrounds it and with
the coil core.
1.2.1 Main Objectives of this Work
As discussed above the WPT concept is a hot research topic. The challenges that this kind of
system propose are not yet solved and the usual way to tackle this kind of problems is to optimise
the WPT system towards an optimal load. Although this approach is challenging at a scientific
level it lacks the real world systems, i.e., when working with an UWPT system the load varies in a
wide range of values. Hence, the load variation problem is not yet solved nor is being researched
in a way that tries to optimise a wide range of load values. With all that being said it is clear
that underwater wireless power transfer is an interesting topic of research in several areas, such
as: coil manufacturing, frequency selection, coil geometry and alignment, efficency optimization,
load variation, among others.
With the development of this work the author has the following objectives:
• Study and propose a wireless method for regulating the load voltage in order to be constant.
• Implement such method and analyse its results making use of a common WPT topology
scheme.
8 Introduction
• Study and analyse the common topologies to realise WPT and ackowledge their function-
ing.
• Optimise UWPT by means of a different topology or scheme.
• Design and implement a different topology for realising UWPT.
1.2.2 Document Outline
This work is organized as follows the next chapter 2 refers to the state of the art in WPT
systems. The next chapter 3 is where the problem that this dissertation will tackle is characterised,
followed by 4 where an adaptive system for wireless power transfer is developed and implemented.
The final chapters are the chapter 5 where the multi resonant topology introduced by this thesis is
analysed and chapter 6 is the conclusion chapter.
Chapter 2
State of the Art
This chapter will cover the state of the art for wireless power transfer techniques. Some
RF (AC)-DC converters will be covered. The overall topology of a WPT system is represented on
figure 2.1. The complete system is complex, however, in this work, only the electronic part will
be studied. There will be made a crossover between high frequency RF-DC converters i.e. GHz,
and converters used in the lower frequency spectrum,i.e.,in the range of MHz to kHz. Adaptive
impedance matching techniques will be covered as well, meaning that adaptive techniques are a
interesting area of research.
Figure 2.1: Figure describing the topology of a WPT wireless power transfer system. From left to right,top to bottom, there is the AC-DC transformer, because usually the power comes from the wall and it is ACpower, it can be power from a DC battery as well. Next there is the DC-RF amplifier to drive the sourcethe resonator, this can be made with class E inverters. The impedance matching networks (IMN), are usedto couple, efficiently, the source and device resonators. The source and device resonators are two coils thatare used to transfer wireless power. Finally, the RF-DC rectifier, is the device used to convert the RF signalreceived to DC which supplies the load.
2.1 General ways to realise WPT
One of the usual ways to achieve WPT is using one of the following topologies: series-seriesFig 2.2 (a), series-parallel Fig 2.2 (b), parallel-series Fig 2.2 (c) or parallel-parallel Fig 2.2 (d)
these names refer to the position of the capacitors used along with the coils.
This topologies are then used with a half wave or a full wave rectifier in order to provide a
constant DC level do the load. That is the way of converting a sinusoidal wave into a DC level
9
10 State of the Art
CSV+
V−
CS
RLoad
(a)
CSV+
V−
CP RLoad
(b)
CP
i
CS
RLoad
(c)
CP
i
CP RLoad
(d)
Figure 2.2: In this figures the common WPT topologies are shown. Figure (a) shows the series-series topol-ogy, in (b) the series-parallel is shown, whereas (c) shows the parallel-series and (d) depicts the parallel-parallel topology.
signal. A half wave rectifier can be seen in figure 2.3 (a) and it is usually made of a single diode as
signal rectifier, whereas in full wave rectifiers two to four diodes are used to make a full rectifying
circuit 2.3 (b).
(a)
+
−
(b)
Figure 2.3: In this figure a half wave rectifier and a full wave rectifier are shown, in (a) a half wave rectifieris shown whereas in (b) is represented a full wave rectifier in bridge topology.
In [8] a full bridge rectifier was used with parallel-parallel compensation like in Fig 2.2 (d).
Here they made a comparison between the novel witricity, i.e. SCMR and the old induction cou-
pling method. The efficiencies where 85% in SCMR vs. 65% in induction coupling at 2cm.
Whereas at mid range, which is where the SCMR has the best results, the efficiency was 73% in
SCMR and 23% in induction coupling. Which shows a good overall efficiency using full-bridge
rectifiers more detail can be seen in figure 2.4.
In [27] the researchers used also a full-bridge rectifier charge the supercapacitors. In this
work the attempt was to show that it was possible to make an array of ocean buoys powered
electromagnetically. They have shown that a pair of 50F with 2.7V rated voltage super-capacitors
can be charged within 10 minutes, using a PWM of 40kHz. To implement the full-bridge rectifier
2.1 General ways to realise WPT 11
2 3 4 5 6 7 8 9 10 112
4
6
8
10
12
14
16
18
Distance (cm)
Vo
ut (
V)
Vout
Witricity
Vout
Normal
2 3 4 5 6 7 8 9 10 110
1
2
3
4
5
6
7
8
9
Distance (cm)
Po
ut (
W)
Pout
Witricity
Pout
Normal
Figure 2.4: In this figures a comparison between novel witricity and the old inductive coupling methodis presented. Figure (a) shows the comparison in terms of output voltage and in (b) the output power isplotted.
four Schottky diodes where used. They also demonstrated that power and data can be transferred
using the same power line.
In [28] a half bridge rectifier was implemented. The purpose of this work was RF-DC energy
harvesting from the environment the conceptual block diagram is on figure 2.5. Here the operating
frequency was between 935.2 and 959.8 MHz. The half bridge rectifier was cascaded to a voltage
multiplier. The voltage multiplier design was of a Villard network. This voltage multiplier was
constituted of four stages therefore the output voltage, was VO = RORL
+ 1n . And it was shown that
using this kind of receiver it was possible to power a small device with 2.1V being the optimal
Figure 2.5: This figure represents the most common concept for energy harvesting from the medium. Theband-pass-filter is used to select the desired operating frequency, the energy conversion module is used toamplify the output voltage, then is filtered using a half bridge configuration
12 State of the Art
output voltage for a 100 load.
In [29] a full bridge rectifier was used. The overall efficiency was 50% for 5cm. The work
done here was to power a AUUV by means of eddy currents propagation. Here the authors used
dieletric assisted antennas, to transfer long range high-efficient underwater wireless charging sys-
tem, referring to figure 2.1 instead of the coils as resonators they used antennas with a size of 24cm
x 24cm x 1.5cms.
In [30] a comparison between low (25mW ) and high (25W ) power links was made. The RF-
DC rectifier was made using a full bridge rectifier. The overall efficiency to a low power link, at
close distance, was 80%, whereas a high power link manages to get, at the same distance, near 96%
efficiency. Series-series and series-parallel resonance were studied in this article, figures 2.2 (a)
and (b) respectively.
In [31] there was used a full bridge rectifier. The goal was to design a high power and high
efficiency WPT. It was achieved to a 295W a 75.7% efficiency with forced air cooling. To a 69W
a 74.2% efficiency was achieved. The operating frequency was 134kHz and the system was an
inductive coupling system.
In [23] it was also used a full bridge rectifier. The operating frequency was 136kHz to a 75W
transfer power. The objective was to power a UUV at a low spacing i.e. 2 inches. The crossover
between air and water was also made and it was shown that for frequencies below 250kHz there
was little difference between air and water as seen in the previous chapter.
When studying the optimal transfer topology for electrical vehicles [32] with a 3.3kW output
power. The authors thoroughly studied the common circuit topologies in order to find what was the
best to be used with electrical vehicles. They concluded that the series-series and parallel-series
topologies are the ones that make the best power converters for WPT systems.
2.2 Converters and Rectifiers
In the last years there was a change of paradigm when designing WPT systems. Topologies
like class-E2 converters, class-DE converters, also those topologies alone,i.e., only applied on the
receiver or on the transmitter started to be explored extensively. This has to do with the fact that
class-E operate at zero-voltage switching (ZVS) and zero-derivative switching (ZDS) making them
almost lossless in the switching zone, although to operate with that behaviour class-E systems
have a narrowband frequency of operation [31] and are greatly influenced by the load reflected
impedance.
Comparing with full bridge or half bridge rectifiers, where one can achieve a reasonable higher
efficiency, there are various concerns about power losses due to Ron of the diodes, meaning that
when there is enough voltage to turn on the diode, power losses on them must be taken into
account. Another aspect when using class-E rectifiers, is that only one transistor is used, reducing
the space of printed circuit board used to rectify the circuit.
2.3 Impedance Matching 13
As said before class-E2 converters have been an extensive area of research, so only the papers
which showed the most interesting scientific level and were able to demonstrate good results will
be documented.
In 2014 [33, 34] delevoped analytical procedures to develop and design class-E rectifiers. This
devices are low power devices using frequencies in the range 1MHz. In [33] a efficiency of 65.9%
was achieved at mid range.
Where in the class-DE approach a efficiency of 79.1% was achieved. This kind of approach
allows for efficient transfer ratio at higher frequencies. It also allows a higher separation rate
between the transmitter and receiver coil.
In 2015 [35] developed a work using a class-E rectifier in a SCMR system. This system
achieved a high efficiency, 94.43% at 800kHz. This was also a low power system delivering 10-W
to the load. A state space analysis was made in order to model and design the system.
Also in [36] a tuning method for class-E rectifier was proposed and thoroughly analysed,
making them suitable for WPT.
2.3 Impedance Matching
As it will be seen later, most of the circuits that are present in AUV’s do not have a constant
load, hence, the topologies proposed above are not suitable when there is the need to have a high
efficiency in a wide load range. To solve that problem impedance matching techniques are used to
provide a broadband load efficiency.
In [37] ABCD transmission matrixes are used to modelate each block of the wireless power
transfer system. After that two distinct algorithms are used in order to maximise the power trans-
fer efficiency of two magnetically coupled resonators at a single frequecy of operation. The al-
gorithms used are the ideal conjugate match algorithm which is used to select each component of
the matching network, as well as the parasitic match optimization algorithm, this one extracting
non-ideal components from the matching networks.
Whereas in [38] methods for matching adaptatively in the near field are studied. The main
variables that this study comprises are the frequency of operation and the load impedance. Al-
though they conclude that making simultaneous matching networks is the way that provides the
best transfer efficiency, it is in theory unfeasible since there are a lot of components that need to
be changed in a short period of time. The frequency tracking method is a good way to deliver the
most power to the system at the near field, however in the far field the method is not so effective.
This paper proposes a way with a complex load matched at target distance to achieve good power
transfer efficiency at the far field.
14 State of the Art
Chapter 3
Problem Characterisation
3.1 The Problem
3.1.1 Load Determination
The main goal of this project is to, wirelessly, charge the batteries of an AUV . As will be
discussed in chapter 2, the whole WPT system is complex. In 3.1 the system architecture that will
be simulated in this chapter to model the load impedance is represented. It is constituted from an
input sinusoidal signal, which refers to the AC signal received in the coil. Also from the rectifier,
this is the device used to rectify the AC voltage signal into a DC level signal. It can be made from
several topologies, that depend from a wide range of factors [39, 40]. Some of those are: the load
type, which can be AC or DC, the voltage level at the input, the input signal frequency, among
others. The voltage control mechanism is also a part from the system. This is used to regulate the
voltage signal, which is delivered to the battery supply system. It is a must to have this device,
since the voltage delivered must be a DC signal with constant levels without many oscillations not
to damage the battery supply system. The battery supply system is then connected to the batteries,
2 in this case.
Figure 3.1: In the figure there is presented the overall system topology covered in this work. From theleft to the right, the system is composed by: the receiver coil, the rectifier, the voltage regulation (control)system (mechanism) and the battery supply system, which is then connected to two batteries.
As stated above one of the factors that highly influence the efficiency of the system is the
load. The reason can be seen in [41], where it shows that different batteries have a different
resistance value, that changes with the state of charge and with the material in which the battery
is made. Also when operating in an AUV there will be various loads to be charged, naming
some: embedded control main board, that usually requires 5 W of power at 5 V DC, the inertial
measurement unit, that requires 0.78 W of power at 12 V DC, among others. Therefore, in order to
15
16 Problem Characterisation
design the system, the load variation must be known in order to measure it the battery impedance
value will be experimentally determined [42].
RSelf−Discharge
+CCapacity−
VSOC
Ibat −+
VOC(VSOC)
RSeries
RTransientS
CTransientS
RTransientL
CTransientL
Figure 3.2: This figure shows the accurate battery model proposed by Rincon-Mora in [41].
From picture 3.1 one can see that the voltage regulation mechanism is also an fundamental part
of the system because a constant voltage level must be delivered to the batteries. So developing
an efficient rectifier system, is the key to make an overall efficient system. In order to achieve
optimal efficiency in the rectifier, the load must be known since its efficiency depends on the load
that is attached to it. In figure 3.3 a simple half-bridge rectifier is shown. It is one of the simplest
rectifiers designs available, the load dependency is visible in the voltage decay rate τ = RC, and
from figure 3.2 it is clear that when designing an electrical model the load must be known [41].
(a) (b)
Figure 3.3: In figure (a) a simple half-bridge rectifier is presented. It is constituted by a diode, and a RCparallel circuit to maintain the voltage level within a constant τ = RC. In figure (b) the wave forms of asimple half-bridge rectifier are presented.
Therefore, to design and optimise the system, the output impedance must be known and char-
acterised. The elements that compose our load are: one BBDC-02R from OceanServer and two
BA-95HC-FL. The former is a dual battery controller with ATX power supply, this device manages
the battery charging scheme. The latter are two batteries also from OceanServer. The BBDC-02R
requires a constant 18V DC power supply to charge the batteries, it can draw up to 4A to be used
in charging the batteries. The batteries characteristics are: smart Li-Ion battery pack with 95WHr,
14.4V nominal voltage, 6.6AHr and flying lead.
So in order to use those elements as a load, there was the need to characterise them in terms
3.1 The Problem 17
Figure 3.4: Block diagram of the measurement setup.
of impedance. In order to do that, the set-up that is presented in picture 3.5(a) was set. The set-
up works as follows: the power supply unit (PSU), supplies the constant DC voltage required to
charge the batteries, then the voltmeter is connected in parallel to the board in order to measure
the input voltage, the ammeter is connected in series to the board to measure the input current.
Using Ohm’s law V = RI we can derive the input resistance. The input current and voltage were
measured manually without fixed timed intervals. The values were annotated whenever a change
either in the input current or voltage was detected. The BBDC-02R is connected to the PC through
a RS−232 serial cable connected to a RS-232/USB converter. The data received from the board is:
the number of batteries connected, the battery status, the voltage in each battery, the current being
drawn, or supplied from the batteries, the individual battery temperature, the individual status of
charge of the batteries, the capacity of each battery, estimated in Ampere-Hour, the total current
being either supplied or drawn from the system, as well as the power, the arithmetical average of
the charge, a status message stating whether the battery is being charged or discharged and finally
the time to fully charge or discharge the batteries. The data is received from the board within
a two seconds interval, then crossing the data received from the board and the ammeter and the
voltmeter was needed in order to compare if the real impedance that was seen from our system
was consistent with the values received from the board schematic, the block diagram can be seen
in figure 3.4.
To fully characterise the input resistance, a set of measurements was made. Starting from
13 V up to 18 V and then a separate 21 V charging of the battery was made to see how the
input resistance changes when the input voltage changes. The results obtained from the manual
measurements, which correspond to the input impedance, are characterized in 3.6. Those are
from the first 25 minutes of charging, only the initial minutes of charging were plotted due to the
18 Problem Characterisation
(a) (b)
Figure 3.5: In figure (a) the set-up used to charge the batteries is presented. It is made from a BBDC−02Rmodule and two batteries. The power supply unit provides a constant DC voltage and to measure the inputimpedance of the battery system a ammeter and a voltmeter were connected to the system. In (b), the circuitused to discharge the batteries is illustrated. In order to discharge the batteries within an acceptable timerange, a rheostat was the load chosen to do so. To measure the output resistance a voltmeter and a ammeterwere connected to the set-up.
following factors:
• One is that the 13 V , 14 V and 15 V curves stop within the first 25 minutes, i.e. those
voltages can’t charge the battery making the current go to 0 A.
• Another is that while charging at 16 V the current decays to 2 A within 25 minute. After
that time the batteries charge up to 8% and if we wanted to charge them to full charge it
would take more than 4 hours, assuming that that voltage can fully charge them, although
will be seen later that this voltage can not charge the batteries.
• The last is that the remaining 17 V , 18 V , 21 V curves do not change much from that time
onwards so representing them in a 25 minute temporal resolution gives greater detail in the
measurements curves.
From the graphs in figures 3.8, 3.7, it can then be concluded that in terms of voltage:
• With voltages from 13 to 17 V , the batteries can not be fully charged. This is explained by
looking at the 2 full charge curves in figure 3.9, one can see that the final voltage values in
the batteries is around 16.7 V , so the DC-DC step-down rectifier present will not be able to
work, since it needs a voltage difference in the order of 0.5 A (experimentally determined)
to supply a minimal current to charge the batteries.
• Therefore the remaining voltages are able to fully charge the batteries.
Making the analysis from table 3.1 and figure 3.7, to the current drawn from the source it
comes that:
• The maximum current drawn from the source is around 3.8 A, at 18 V and 3.21 A at 21 V .
3.1 The Problem 19
• The current lines are parallel and grow in amplitude until the voltage from the power supply
reaches 18 V as seen in figures 3.8, 3.9, after that value the current starts to drop.
Regarding the input resistance, the data in table 3.2 shows that the resistance has three stages:
• The first when the battery is fully discharged, that value is high in the dozens of Ω, here
the batteries are charged at the minimal rate to support with a low current being drawn the
system only to make the circuit operational.
• The second comes as the circuit board is fully operational and a high current is supplied to
it. Here the impedance value is almost constant and has a starting point of 4.5 Ω and in the
final end is around 6 Ω.
• The third and last stage is when the battery capacity reaches 90%, here the impedance starts
to grow again to the dozens of Ω.
That data is corroborated from the graphics in figure 3.7 and figure 3.9 were the resistance
graph starts high in the dozens of Ω then falls to around 5 Ω and when the capacity reaches 90%,
it starts to rise again to the dozens of Ω.
Regarding the power supplied by the PSU , it remains constant, when the battery capacity
goes from 1% to the 90%. Looking to the power graph, it can be seen why the current does not
rise when the voltage roses up to 21 V , that has to do with the fact that the input power is limited
to be approximately 60 W . It is on that power level that the curves of 18 V and 21 V match.
Table 3.1: Here the comparison between 18 V and 21 V charging can be seen. The most significantdifference is in the time it takes to charge, with a difference of 20 minutes between the two. The finalvoltage which the batteries stay is around the same. The maximum current drawn from the power supplyvaries around 0.58 A, which corresponds to a variation of 15.3%. The maximum power drawn from thepower supply unit varies 2.35 W and corresponds only to a variation of 3.57% of the maximum powerbeing drawn from the power supply unit.
Timeto Charge
FinalVoltage
MaximumCurrent
MaximumPower
18 V 4h3m22s 16.79 V 3.79 A 65.85 W21 V 3h40m21s 16.72 V 3.21 A 63.50 W
Table 3.2: Variation of the input resistance with the capacity of the batteries table. Here it can be seenthat the input resistance of the board varies with the capacity of the batteries. The input resistance can begrouped in three groups, one when the battery has 0% capacity, another for the 1% through the 90% ofcapacity and a final group when the capacity goes from 90% to 100%.
ResistanceC=0%
ResistanceC=1%
ResistanceC=50%
ResistanceC=90%
ResistanceC=100%
18 V 35.8Ω 4.35Ω 5.3Ω 5.8Ω 23.5Ω
21 V 46.1Ω 7.6Ω 6.1Ω 7.5Ω 40Ω
20 Problem Characterisation
(a) (b)
(c) (d)
Figure 3.6: Load electrical characterisation, respective to the first 25 minutes. In (a) there is plotted thevoltage variation over the time. In (b) the current is plotted over the time, here it can be seen that the currentstarts to grow from 0.5 A to around 3 A. The 17 V and the 18 V curves go a little higher, while the 21 Vstays at 3 A.In graph (c) the Power is plotted and it can be seen that the three higher voltage plots deliver thesame power for some time, but then the 17 V graph starts to deliver less power, as the time goes by. Whenit comes to the input resistance, which is plotted in graph (d), it can be seen that for the first 25 minutes ithas two well defined stages. One on the first seconds of charging, which it achieves dozens of ohms, then itfalls to around to units of Ω.
3.1 The Problem 21
(a) (b)
(c) (d)
Figure 3.7: Load electrical characterisation respective to full charge plots. Here the same plots as above areplotted but only for the voltages of 18 and 21 V . The most significant difference for the plot where only thefirst 25 minutes of charging are plotted is that here the resistance can be defined in three stages. One for thefirst seconds and another until the battery capacity reaches 90%. In the power graph it can be seen that bothinput voltages deliver around the same power. Which says that increasing the voltage does not increasesthe amount of power delivered to the load. Another important factor is that the time to charge differs in 20minutes, the slower one is the 18 V . And the amount of time required to charge 90% is around 3 hours andthe last 10% is one hour at 18 V and 40 minute at 21 V .
22 Problem Characterisation
(a) (b)
(c) (d)
Figure 3.8: Battery electrical characteristics plots. Here the 25 first minutes of charging are plotted.In (a)the voltage is plotted. Here it can also be seen that the battery voltage increases from around 10 V to 16V in that period. In (b) the current for the curves of 13, 14 and 15 V drops to 0 A, which means that thosevoltages can not charge the batteries. To higher voltages the current delivered is almost the same, sincethe DC-DC regulator tries to deliver always the maximum current to the load and here is around 4 A. Forthe 17 V current curve, the current is irregular and can not always match the 18 and 21 V curves. Thepower delivered to the load in (c) has a maximum of 60 W for the first minutes, and for the two highervoltage curves. The battery resistance plotted in (d) has, the same stages as the total load resistance, but hasdifferent, smaller, values.
3.1 The Problem 23
(a) (b)
Figure 3.9: Battery current and voltage full charge plots. In (a) the voltage of the battery is plotted it startsfrom a value of around 10 V and ends with the same value for both of them, 16.7 V . In (b) the currentdelivered to the batteries is plotted and it can be seen why the 21 V charges the batteries faster. That is dueto the fact that it can maintain a current of around 4 A delivered to the loads for a longer time.
24 Problem Characterisation
3.1.2 Transformer Configuration
In order to realise UWPT a transformer is needed, in this work it will be composed by two
planar coils. The coils are optimised for a resonant frequency of 100Khz and that is achieved
at a distance of 4cm which gives a coupling factor (k) of ' 0.304, the coils have both an equal
number of turns (15) and a radius of 8cm in figure 3.11 the coils used to realise UWPT can be seen.
To determine the coils self inductance a vector network analyser (VNA) was used and the coils
characteristics are presented next. The equivalent model of the transformer that will be used to
modulate the coils electrical behaviour is the “Tee”-Model presented in figure 3.10, this model is
used widely for analysing WPT systems. In the figure 3.10 L1 and L2, are the coils self inductances
which in this case are equal, have a value of 12.7 µ H, and Lm represents the mutual inductance
having itself a value of 5.548 µ H, the coils themselves have an equivalent series resistance (ESR)
of ' 118mΩ. To make the coils suitable to realize UWPT connectors from both sides were sealed
and a varnish was applied to electrically isolate the coils from the salt water.
L1
Lm
L2
Figure 3.10: “Tee” model of coupling coils.
In summary the problem that this work will tackle is inserted in the context of the figure 3.12.
The coils that will be used are presented in figure 3.11, inverter used is made from a class-D
topology from Infineon Technologies, the load is variable from 4.5Ω to roughly 40Ω, the other
elements are meant to be designed this includes the impedance matching schemes either on the
emitter and in the receiver, as well as the voltage control mechanism and the rectifier.
3.2 Proposed Solution
Before introducing the solution that will be endorsed in this thesis, some background on how
the power transfer and transfer efficiency can be modulated, using the two most common ap-
proaches. First coupled mode theory will be used to describe the system, then an approach using
circuit theory will be made.
3.2.1 Coupled Mode Theory
To describe the interchange between the coils in coupled mode theory(CMT) can be used.
CMT focus on the electromagnetic coupling modes of waves as described in [43, 10]. Using CMT
3.2 Proposed Solution 25
4cm
(a)
16cm
(b)
Figure 3.11: The figure shows the coils used to realise UWPT, in (a) the side view is shown one can seethat the separation distance between the coils is 4cm and in (b) the top view is represented here the numberof turns (15) and the radius (8cm) are shown.
Figure 3.12: This figure shows the overall system that this work will have to analyse and try to optimise.From the left to the right we have the inverter usually a class-D inverter, then the impedance matchingnetworks usually made from a common topology, the coils that won’t be a focus of optimisation in thisdissertation, finally the load and rectifier such components will be a source of design.
to describe this type of system this is the set of linear equations obtained [17, 10]:
am(t) = (iωm−Γm)am(t)+ ∑n6=m
ikmnan(t)+Fm(t) (3.1)
Here the indices represent different resonant objects. The variable am(t), represent the modal
energy amplitude, ωm the resonant frequency, Γm the intrinsic decay rate, models the losses of the
system, k represents the coupling coefficient and Fm(t) represents the driving term [17].
The transfer efficiency and transfer power can be described in CMT as [17, 10]:
η =ΓL |an(t)|2
Γm |am(t)|2 +(Γn +ΓL) |an(t)|2(3.2)
PL = 2ΓL |an(t)|2 (3.3)
If the system is operating in non-resonant state, the system driving angular frequency ω is not equal
to the resonant angular frequency ωr. Assuming the energy decay rate and the coupling coefficient
are constant the derivative of the transfer efficiency η with respect to the driving angular frequency
26 Problem Characterisation
ω is non-existent. Which means that the optimal transfer efficiency occurs in the resonant state.
Taking the derivative of the transfer power PL with respect to the driving angular frequency ω , the
optimization conditions based on maximizing the transfer power shows that the frequency splitting
phenomenon appears [17]:
ω = ωr,∂PL
∂ω= ωr±
√k2−0.5Γ2
m−0.5(Γn +ΓL)2 (3.4)
3.2.2 Circuit Theory
Using the circuit theory (CT) method, the approach made to the system is through the mutual
inductance [17]. Therefore it is a method which is simpler and easy to analyse. This is a well
studied method and his basic structures are series-series and parallel-parallel compensation. The
full analysis and design can bee seen in [20]. Here as shows only series-series compensation
will be shown for example and comprehension. The circuit is a two coil model where Rs, R2(R3),
L2(L3),C2(C3), M23 and RL, represent, respectively, the internal resistance of the voltage source, the
coil parasitic resistances, the coil self-inductances, the resonant capacitors, the mutual inductance
and the load resistance.
Applying the bidirectional reflectance impedance analysis (BRIA) method, Vre f can be defined
as the reflected voltage source form the primary coil onto the secondary coil, Rre f the reflected
impedance from the secondary coil to the primary coil, Z2 (Z3) the primary (secondary) impedance
of the coils and ω as the system driving angular frequency [17, 20].
With this in mind we can describe the reflected impedance from the secondary coil into the
primary coil, the system efficiency and power transfer as follows [17, 20]:
Rre f =ω2M2
23R3 +RL
(3.5)
η =ω2M2
23RL
[(R3 +RL)(ω2M223 +(R3 +RL)(R2 +RS))]
(3.6)
PL =ω2M2
23V 2s RL
[(ω2M223 +(R3 +RL)(R2 +RS))]2
(3.7)
These are the basic equations that allow us to describe this kind of system recurring to CT.
Comparing CT to CMT it is possible to see that both methods are equivalent and can be used to
describe the system either in resonant and in non-resonant state, more on this at [17].
3.2.3 Adaptive Regulation System
With the system analysed it should be clear that the frequency at which the system operates
changes the efficiency of the system, therefore the output voltage as well. Building on that and that
the batteries require a constant voltage over 18 V to be charged this work will propose a method
to deliver a constant voltage to the load based on frequency variation.
3.2 Proposed Solution 27
3.2.4 Multi Resonant System
Analysing the plots of the magnitude response of series-series and the parallel-series com-
pensation the optimal frequency of operation is within a bandwidth. Although that may seem a
reasonable approach, when someone designs a driver for a WPT system, it is generally designed
with a square wave input. The fourier series of the square wave comprises the fundamental fre-
quency and all the odd harmonics 3.8, therefore those WPT systems, only transmit power at the
fundamental frequency, having therefore an efficiency limitation before hand.
FN(x) =4π
N
∑n=1
sin((2n−1)xsin(2n−1)
(3.8)
With this work we propose a topology for multi-resonance making use of also the third harmonic
frequency of the square waves, trying to achieve with that a higher power throughput wideband
load variation in respect to the series-series compensation and parallel-series, as well as a higher
overall efficiency when compared to those topologies.
28 Problem Characterisation
Chapter 4
An Adaptive System for UnderwaterWireless Power Transfer
Recently, wireless power transfer (WPT) based on resonance has met a wide range of appli-
cation scenarios [44]. WPT has been addressed in wireless battery charging of smartphones [45],
medical implants [46], and electrical vehicles [47, 48]. Such systems rely on nonradiative short-
range power transfer, normally comprising one or more pairs of coils that are magnetically cou-
pled. These coupling coils operate in resonance to allow a higher energy power transfer, being
usually modeled as transformers. Fig. 4.1 depicts a block diagram for a conventional WPT system.
A driver is employed at the primary side, which can be implemented using different techniques,
such as class-D inverters or class-E drivers, whereas at the secondary side, a half- or full-bridge
with diodes can be employed to obtain the dc voltage output. The matching networks allow the
impedance transformation at the resonant frequency. Following the rectifier, voltage regulation is
usually provided to support load variations.
Resonant WPT systems are generally subject to several parameter variations, e.g. due to time-
varying distance between coupling coils, unpredictable load variation demands, or any other me-
chanical or electrical uncertainties that may affect resonance [49]. This is particularly severe in
circuits with high load quality factors, i.e. where power can be solely transferred across a narrow
frequency bandwidth, but the WPT system has almost no tunability capabilities at all. To overcome
component variations and still provide a constant output voltage, the authors in [50] make use of
a magnetic amplifier to tune the inductance in an LCL pickup circuit. In [51], a reconfigurable
system four-coil WPT system is presented in which maximum efficiency is sistematically tracked
by sensing voltage and current to adjust the driver switching frequency. Adaptive approaches need
to be adopted to circumvent possible parameter deviations in practical implementations, which
may prevent the system from proper operation when resonance or other parameters are slightly
different from expected. However, performing parameter tuning in the complete system requires
interchanging information between the power transmitter and load circuitry. Recently reported
works [52, 53] rely on wireless communications to exchange data for WPT closed-loop optimiza-
tion control, but such additional wireless data interfaces are not simple to provide in some cases,
29
30 An Adaptive System for Underwater Wireless Power Transfer
inverter
rectifier
powersupply
matchingnetworkregulation
voltageload
networkmatching
RL
couplingcoils
Figure 4.1: WPT system block diagram.
specially in underwater applications in which operation at high frequencies imply intolerable en-
ergy losses. This chapter addresses the power regulation of a dc output with an adaptive approach
to look up for the optimum frequency to achieve a target voltage. The proposed system aims at
providing a wireless power link in sea water with output voltage regulation established without ad-
ditional links. The next section addresses the proposed system and the following section presents
measurement results from the practical implementation.
4.1 Proposed Underwater WPT System
The proposed system aims at wireless powering devices in the deep sea for monitoring pur-
poses. To prevent excessive losses due to the conductivity of salt water [24], low frequency is
adopted for operation, i.e. around 100kHz. The series-series driver topology is preferred due to
its simplicity and to easier a stable voltage at the secondary side [48]. Fig. 4.2(a) depicts a con-
ventional series-series class-D resonant driver. Signals vhs and vls represent the driving signals of
the high- and low-side power MOSFETs. The coupling coils are represented as a “tee” model in
which the auto inductances are L1 = L2 = (1−k) ·L, and the mutual inductance is Lm = k ·L, with
k as the coupling factor. The capacitors C1 and C2 are usually equal valued, and define the res-
onance frequency. Fig. 4.2(b) shows the frequency response of the series-series resonant system
with a rectifier, i.e. it represents the output dc voltage Vout vs target voltage Vre f if the switching
frequency of the driver is statically swept. Each line represents a different load (the load increases
monotonically towards the lines to the top), having a peak relatively close to the resonance fre-
quency fo.
We proposed a voltage regulation algorithm based on hill climbing, using the frequency as
the control variable. As such, we incrementally change the frequency within a certain range,
preferably in the left side of fo, i.e. f ∈ [ fmin; fo] as exemplified by the circles represented in
Fig. 4.2(b). This implies a load range in which the regulated voltage at RL,min occurs at nearly
fo, although additional limitations may arise in the practical implementation. This optimization
can compensate for deviations in the resonance frequency in a given range. However, to change
the frequency, the driver has to be able to determine the output voltage, whether it is within an
acceptable regulation interval or not. The input current can be used to optimize the operation of a
power stage [54]. To do so, we propose load modulation in which the output voltage is compared
4.1 Proposed Underwater WPT System 31
CL RLLc
vhs
Vdd
vls Lm
L1C1 L2
C2coilscoupling
D
load
(a)
f/fo
0.85 0.9 0.95 1 1.05 1.1 1.15
Vou
t/Vref
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
(b)
Figure 4.2: (a) Series-series resonant driver topology with rectifier and (b) its typical frequency response.
0 150 t−t0(µs)
Vout > Vref
2×10650100
Vout < Vref
0 50 t−t0(µs)200150 2×106
Figure 4.3: Load modulation signals for regulating Vout .
to a reference (Vre f ), and takes two different actions if the voltage is above or below a certain
tolerance. As such, we provide short-circuits to the load for a predefined time so that, at the
primary side, abrupt changes in the current drawn from the power source Vdd can be sensed. Two
fixed-time pulses (duration at “high” state of 50 µs) are generated, spaced by 100 and 150 µs in
case of Vout being above and below, respectively. Following the two pulses, the sensing is disabled
for 2sec., so that the driver can update its switching frequency (see Fig. 4.3).
In a series-series driver topology, the higher the load, the higher the voltage (and current). This
behavior implies that for the load modulation, short circuits are preferred to avoid increasing the
power consumption for modulation purposes. On the primary side, current is sensed to determine
changes within the predefined periodicity.
There is still the case in which the secondary has no power to operate and the primary side
32 An Adaptive System for Underwater Wireless Power Transfer
rectifier
variableload
driver andsensing
(a)
couplingcoils
salt water
(b)
Figure 4.4: (a) Test setup and (b) coupling coils in a saline water container.
may assume the load is regulated. In order to prevent this case, we propose to have short-circuits
from time to time as an “I’m alive!” signal (just a periodic pulse), indicating the secondary is
still powered and properly regulated. In the absence of detection of such signals, the frequency
is increased towards fo until the primary senses the secondary again. Note that if even if the
secondary is working, and the primary cannot sense changes in current, this is interpreted that
there is no regulation.
In order to generate the variable switching frequency, sense the output voltage and input cur-
rent two micro-controllers are used. It should be mentioned that this does not necessarily represent
an overhead as some sort of digital processors is always required at both ends. The ADCs from the
microcontrollers are used to sense the voltage at the load and the current variations at the primary
side. The algorithm is partitioned into the two microcontrollers, being possible to keep track of
the time information about the power delivery at the secondary.
4.2 Implementation 33
µC2RL
REG
rectifier
driver
vhs
vlsµC1
Vdd
sense
debug/variablemonitoring
current
VS
Vout
111Vout
load bufferbuffer
Rs
Figure 4.5: Proposed adaptive system.
4.2 Implementation
A prototype for the proposed system has been implemented and tested in salt water – see
Fig. 4.5 for the complete system representation. At the driver side, the microcontroller is an
XMC4200 (µC1), and at the load side the microcontroller is an XMC1300 (µC2), both from In-
fineon Technologies. The load voltage is sensed from a voltage divider (1:11) by a 12-bit ADC,
whereas the reference voltage is internally generated at (µC2). The generated signals at the micro-
controller make use of a CCU4 timer with 10kHz clock frequency. For the power supply of µC2
a LM317 is used as regulator (REG), and a resistor Rs is placed in series with the load modula-
tion transistor to avoid the discharge of the rectifier capacitance to a level in which µC2 would be
turned off.
The inverter in the driver employs two BSZ060NE2LS OptiMOS power MOSFETs (from
Infineon Technologies), with reduced conduction resistance (Ron < 8.0mΩ). Load modulation is
achieved by switching the power MOSFET IR LML0060TRPBF (Ron ' 116mΩ) connected to
ground, using a 5V pulse generated by the microcontroller, buffered with a single power-supply
opamp. The microcontroller at the output requires a minimum voltage of 6V in order to start
operating. In case of power off, the lack of periodic detection of “I’m alive” signals forces the
driver to transmit higher power.
Current sensing is performed at the high-side transistor using a current shunt monitor at a
0.050Ω resistor, with the AD8219 from Analog Devices, driving the 12-bit ADC of the microcon-
troller. Fig. 4.4(a) shows the test setup with driver and rectifier systems, and and instrumentation.
Fig. 4.4(b) shows the coupling coils immersed in saline water (2g/liter of salt). A spiral geometry
with 15 turns has been adopted targeting low conduction losses in the water medium [55]. The
distance between coils is 4.0cm (16cm outer diameter) and the coupling factor indirectly obtained
from scattering parameter measurements is about 0.30.
34 An Adaptive System for Underwater Wireless Power Transfer
Figure 4.6: Frequency variable monitored in the driver-side microcontroller during output voltage regula-tion.
The algorithm was implemented in Digital Application Virtual Engineer (DAVETM), i.e. the
development platform for XMCTM, which is an Eclipse-based integrated development environ-
ment (IDE). It was used the software µC/ProbeTM XMCTM developed by Micrium, which allows
to read and write the memory of the microcontroller during run-time and visualize the acquired
data. For instance, during the load regulation procedure, the switching frequency tracking pro-
vided at the driver (synthesized by the microcontroller) is plotted in Fig. 4.6.
Table 4.1 summarizes the measurement results for extreme and central cases of supply voltage
and load ranges. The regulation error is measured according to Vre f = 7.5V as target voltage,
and the tune deviation ∆ ftune is obtained based in fo = 100kHz. The efficiency comprises all the
system losses, except for the microcontroller at the driver side, which is powered by a different
power supply for debugging purposes. Fig. 4.7a) depicts the case when the output voltage is
superior to Vre f . Hence, two pulses are generated by the load modulation circuit (signal in yellow)
and are detected by the current-sense circuitry in the driver (signal in blue). This process denotes
some noisy behavior essentially due to the switching action of the class-D driver. In a different
time scale, Fig. 4.7b) shows five iterations in the voltage regulation process at the load, ending at
an output voltage close to Vre f . The periodic abrupt voltage changes along the first iterations are
due to load modulation, whereas the last ones, when the voltage is already close to Vre f , are due to
alive signals with lower frequency.
4.2 Implementation 35
Table 4.1: Voltage regulation results with deviations on Vdd and RL.
RL Vdd eVout ∆ ftune Pin Eff.(Ω) (V) (%) (kHz) (W) (%)
6.0 6.0 -3.0 3.24 52.637.1 8.0 3.7 -5.5 3.09 52.7
10.0 5.9 -7.2 3.20 53.16.0 0.1 0.0 3.60 60.7
25.8 8.0 4.0 -4.0 3.84 61.410.0 4.9 -6.0 3.87 62.16.0 6.4 0.0 3.76 55.0
30.8 8.0 7.2 -5,0 3.63 57.910.0 1.3 -7.0 3.13 59.9
(a)
(b)
Figure 4.7: (a) Pulse sense and (b) load regulation.
36 An Adaptive System for Underwater Wireless Power Transfer
Chapter 5
Multi Resonance System
5.1 Introduction
Despite the concept of wireless power transfer (WPT) being around since the beginning of the
20th century (with the pioneer work of Nikola Tesla [5, 6]), only during the past decade the idea
had met substantial developments [11, 56, 57, 58, 31]. WPT has been revived with a new diversity
of applications, such as battery refilling systems for electric vehicles [58], powering of RFID
tags [59], and battery charging of consumer electronics or implantable medical devices [60, 11].
In our case, the purpose of application is to recharge a small-scale autonomous underwater vehicle
(AUV) in saline waters [61] (Fig. 5.1). The use of underwater WPT (UWPT) alleviates the need of
human assistance for plugging in and out electrical connectors in the docking station. Instead, the
AUV batteries can be recharged at deep underwater with reduced maintenance demands, thereby
improving the autonomy of the vehicle.
Recent WPT systems rely on non radiative power using magnetically coupled coils separated
at some distance (from mm to several cm), operating at resonance [57, 56]. In these systems, the
most common approaches for driver architectures are: the half-bridge inverter (class D), class-E
inverter, and current-mode driver (inverse class D). Although the current-mode driver yields zero-
voltage switching (ZVS), it has the disadvantage of an excessive voltage stress at the drains of the
transistors, hence degrading the power utilization factor [62]. As for the class-E inverter, besides
ZVS, in its typical operation it also allows zero-voltage-derivative switching (ZVDS) [63], and
produces more than one and a half output power than the class D for the same voltage supply and
load [31]. However, again this comes at the expense of an increased peak voltage at the drain,
which is more than three times its supply voltage. Another obstacle in the use of the class-E driver
is the high sensitivity to load resistance variations [36] that brings the operation to regimes where
ZVS and ZVDS conditions cannot be achieved.
In power applications, the class-D inverter is the most classical approach, essentially due to its
simplicity in design and control [54], and for having no implications on the voltage stress (since the
switching-node peak voltage equals the supply-voltage value). Typically, in a resonant inductive
driver, the class-D inverter makes use of one of two different matching networks connected to
37
38 Multi Resonance System
powersupply
rectifierinverter matching
RL
batteries/regulation
loadmatching
VS
docking station AUVcoils
Figure 5.1: UWPT system configuration for charging the batteries of an AUV.
Lmvsmatchingnetwork
L1 L2
matchingnetwork
RL
Figure 5.2: UWPT system with the “tee” model of coupling coils.
the coils, namely the series-series and series-parallel configurations [31]. The former topology
consists on a capacitor added in series to each coil, whereas the latter differs only on the receiver
side, with the second capacitor connected in parallel with the load [64]. Both approaches might
not provide reasonable degrees of freedom in terms of design space to mitigate the compromise
between power delivery and efficiency. Moreover, it is not simple to accommodate a wide range
of certain parameters. Since any WPT system will vary either at the distance between coils (with
direct impact on the coupling factor) or the load (or even both), design strategies are required to
overcome an expected variability. The lack of topological alternatives is also critical particularly
when the design of the coils for the inductive link is carried out apart from the remaining system,
i.e. the driver and rectifier optimization procedures are constrained by the coils chosen. In the
present work we introduce a new coupling network for existent coils and optimize the system for
a square wave voltage excitation from a class-D driver. The proposed network topology is suitable
for UWPT, being able to optimize the load variation due to the charge phase of the batteries at the
rectifier side.
5.2 UWPT System Description
When the AUV arrives at the docking station, a retention mechanism is set to keep the vehicle
still at a fixed position, minimizing possible fluctuations and settling the adequate alignment be-
tween the AUV and the recharging system. This means we can assure a nearly constant (although
loose) coupling factor (k) during the recharge phase (k'0.304 for a distance of 4cm between
coils). On the other hand, the highly conductive properties of the seawater as transfer medium
prevent the usage of high frequencies for UWPT operation. The operating frequency was chosen
at f0 = 100kHz and spiral coupling coils were manufactured in order to achieve their maximum
unloaded quality factor around f0. The coils are represented by the equivalent circuit of a trans-
former comprised by L1, L2 and Lm, as depicted in Fig. 5.2.
5.3 Proposed Circuit Topology 39
The inductors L1 and L2 are equal-valued self inductances, and Lm represents the mutual in-
ductance. The coil parameters for the UWPT system are given below
L = 18.25 µH (5.1)
L1 = L2 = (1− k) ·L = 12.7 µH (5.2)
Lm = k ·L = 5.548 µH (5.3)
In Fig. 5.2, RL represents the input impedance of the rectifier. In fact, this value should re-
flect the current required by the charging process of the batteries (hence, RL varies in time) and
should be influenced by the conduction angle of the rectification diode as well [65]. As such, both
matching networks must be carefully designed according to the load profile.
At the other end, the source vs represents the input excitation, given here as a sinusoidal volt-
age. Some works optimize the coupling network assuming such a sinusoidal input and for demon-
stration purposes validate it using a vector network analyzer, but for a more realistic scenario the
driver will apply either square voltage or current waveforms at the input (or other formats, but
rarely sinusoidal). For the reasons referred earlier in introduction, we will make use of a class-D
inverter, hence in such a case vs in Fig. 5.2 then represents a square wave at f0. The design of the
remaining UWPT system will be constrained to the specifications of the coupling coils mentioned
above.
5.3 Proposed Circuit Topology
Since the square wave at the output of the inverter comprises non-null odd harmonics, for the
proposed circuit instead of establishing resonance only at the fundamental frequency f= f0, we
will provide resonance at f=3 f0 as well. This brings the benefit of lowering the reverse peak
voltage at the rectifier diode and, as a consequence, it allows us to increase the power supply at
the inverter if there is still some margin below the maximum voltage ratings of the transistors. We
will make use of low loaded quality-factor (Q) networks [66], aiming at broadband matching to
easier the finding a solution for simultaneous resonance. Fig. 5.3 depicts a cascade L network, in
which we make the parallel reactance of the first L leg coincident with the mutual inductance of
our coupling coils. The resistor R represents a “virtual resistor”, which will be used as basic design
parameter. Its value can be arbitrated in a range limited by Rs and RL. If we consider Rs<R<RL1,
then Q is given by
Q =R
ω0Lm=
√RL
R−1 (5.4)
where ω0 = 2π f0. The equation above leads to
R3− (ω0Lm)2(RL−R) = 0 (5.5)
1The other possibility RL < R < Rs is not addressed here because it leads to a solution in which RL<1Ω, i.e. in theorder of the equivalent series resistance of inductors, which can be reflected in a low power efficiency.
40 Multi Resonance System
RLXp2
Xs2
R
Rs
vs
Xs1
Xp1=Xm
Figure 5.3: Cascade L network as the basis to develop the proposed topology.
RL (Ω)
0 5 10 15 20 25 30 35 40 45 50
R (Ω
)
0
1
2
3
4
5
6
7
8
Figure 5.4: Virtual resistance R vs load resistance RL for ω0Lm ' 3.486Ω.
Lm RLCp2vs
RsCs1 Ls2
(a)
vs RL
L2
Cp2
Cx2Rs L1Cx1
Lm
(b)
Figure 5.5: Basic network to develop the proposed topology: (a) cascade L network; and (b) modifiednetwork to include the coupling coils.
The solution for (5.5) is plotted in Fig. 5.4 admitting (5.3). For a given RL profile one can choose
R from (5.5) to derive the remaining components.
Let us go back to Fig. 5.3 where we assume that the reactance Xp2 denotes a capacitor in
parallel with the load, i.e. Xp2 = 1/(ω0Cp2) and
Cp2 =Q
ω0RL(5.6)
5.3 Proposed Circuit Topology 41
One should use an inductor to complete the second L leg at Xs2. The respective reactance is
determined as follows
Xs2 = R ·Q (5.7)
Fig. 5.5(a) depicts the arbitrated passives in place of the reactances shown in Fig. 5.3. However,
since in fact we have a transformer in the coupling network, we need to compensate for the existent
inductance, L2. Therefore, admitting Xs2 < ω0L2, we need to add in series Cx2
Cx2 =1
ω20 L2−ω0RQ
(5.8)
As for Xs1, first an equivalent series resistance is determined to maximize the bandwidth, i.e.
imposing R as the geometric mean of Rs and RL [66], from which results
Rs =R2
RL(5.9)
then
Xs1 =RL
R2 Q (5.10)
Since there is already L1 from the coupling coil, one should compensate it to achieve the required
Xs1. This means a capacitor is needed in series with the value given next
Cx1 =1
ω20 L1 +ω0
R2
RLQ
(5.11)
Fig. 5.5(b) shows the complete network for which, according to the procedure just given, the
impedance seen from vs should be 2Rs at f = f0.
In order to achieve resonance also at f=3 f0, we proceed with successive impedance trans-
formations in order to achieve a simplified circuit seen from the input. We start by noting that
Q3 = 3ω0RLCp2 = 3Q (5.12)
and proceed with the first parallel-to-series transformations and vice versa. Table 5.1 summarizes
all the intermediate steps and its correspondence to Fig. 5.6. We make use of the required equality
for the quality factor of parallel and series networks, i.e. Qp = Qs, let us denote here by Q. Hence,
in terms of resistance: Rp = Rs(1+Q2); and for the reactance: Xp = Xs(1+1/Q2
). The subscripts
“s” and “p” denote either “series” or parallel, respectively.
Fig. 5.6(a) shows the first step of the simplification. The subsequent procedure is a series-to-
parallel transformation that leads to Fig. 5.6(b). Fig. 5.6(c) corresponds to the most simple circuit,
with a load input equivalent resistance Ri3 at f = 3 f0, and similarly an equivalent reactance Xi3.
Hence, for the desired resonance, Xi3 = 0. To achieve this condition, we add in series with the
42 Multi Resonance System
vs
L2Rs L1Cx1
Lm RLs
Cs2Cx2
(a)
Rpyvs
Rs L1Cx1
Lm Xpy
(b)
vs Ri3
Rs Xi3
(c)
Figure 5.6: Simplifications for the circuit in Fig. 5.5(b) valid only for f = 3 f0.
RL
L1
Lm
L2Rs
vsCα
Cx1
Lα
Cx2
Cp2
Figure 5.7: Circuit model for the proposed network topology.
input a parallel LC tank (LαCα ), as shown in Fig. 5.7. Let us consider 1 < α < 3 so that
(αω0)2 =
1LαCα
(5.13)
The key idea here is to force an open circuit at a frequency f = α f0, between the fundamental and
the third harmonic. The impedance added by the LC tank is
Zα( jω) =jωLα
1−(
ω
α ω0
)2 (5.14)
which means that Zα( jω) is inductive at ω = ω0 and capacitive at ω = 3ω0. At the fundamental
frequency we need to add a negative reactance in series Za to establish resonance at ω = ω0, i.e.
Za( jω) =1
jωCa(5.15)
5.3 Proposed Circuit Topology 43
Table 5.1: Simplification expressions for the circuit at f = 3 f0.
Cs2 (1+1/Q23)Cp2
Fig. 5.6(a) RLs1
1+Q23RL
Cxs2Cx2Cs2
Cx2+Cs2
Xsy 3ω0L2− 13ω0Cxs2
Fig. 5.6(b)Qy Xys/RLs
Rpy RLs(1+Q2y)
Xpy Xsy(1+1/Q2y)
X j3ω0LmXpy
3ω0Lm+Xpy
Fig. 5.6(c)Q j Rpy/X j
Ri3Rpy
1+Q2j
Xi3 X jQ2
j
1+Q2j+3ω0L1− 1
3ω0Cx1
and1
jω0Ca+ j
ω0Lα
1−1/α2 = 0 (5.16)
Ca =(1−1/α
2) · 1ω2
0 Lα
(5.17)
This can be included in Cx1. Let us denote it as Cx1,
Cx1 =Cx1 ·Ca
Cx1 +Ca(5.18)
So, in order to have Xi3 = 0,
Xi3 +Zα( j3ω0)−1
3ω0Ca= 0 (5.19)
which, replacing Ca by its dependence on Lα and developing it further, leads to
Lα =38· Xi3
ω0· (1−α2)(α2−9)
α4 (5.20)
Fig. 5.9 depicts the response (voltage at RL) to a 1V signal excitation at the input of the circuit
(vs in Fig. 5.7) when the frequency is swept, for different values of α (this is in fact equivalent
to S21). There is a clear trade-off between the bandwidth at f0 and 3 f0. To ensure reasonable
44 Multi Resonance System
Lm
Cx1 L1Cx2
Cp2 Lc CL RL
Lα
Cα
L2Ron
Ron2CjVS
coilsinverterload
couplingrectifier &
Figure 5.8: Complete UWPT topology.
normalized frequency
1 2 3 4 5
voltage g
ain
(dB
)
-60
-50
-40
-30
-20
-10
0
10
20
30
1.1
1.4
1.7
2
2.3
2.6
2.9
Figure 5.9: Output voltage for different values of α when the network is excited by an AC voltage source.
insensitivity to frequency deviations α can be chosen with values 1.7 to 2.3. It should be mentioned
also that although at 3 f0 the voltage gain is superior to the case f = f0, in a square waveform the
third harmonic is much smaller than the fundamental component ('-9.5dB).
5.4 Results and Discussion
Fig. 5.8 depicts the complete UWPT system, including the class-D inverter and the rectifier.
For simulation purposes, the transistors in the inverter are modelled as switches operating in op-
posite phases, each one having a finite conduction resistance Ron and output capacitance C j. At
the load, a Schottky barrier rectifier is employed, with Lc as a choke to provide a dc path, and a
large CL to filter the ripple at RL. Table 5.2 shows the parameter values for a network designed
according to the procedure presented in last section. Spice models for the components (diode
MBRS540T3 from Onsemi) were used in the Cadence Virtuoso analog design environment to
simulate the proposed circuit topology using Cadence Spectre simulator. Series-series and series-
parallel topologies were also included in simulations for reference.
Figs. 5.10(a) and (b) show the results for the efficiency and power delivery for a load sweep
(each line correspond to a different set of component values). The thick black line corresponds
to the design of the topology with RL = 10Ω (R = 4.144Ω), as shown in Table 5.2. Based on
this first choice, the compromise between power-delivery and efficiency may be changed – the
5.4 Results and Discussion 45
Table 5.2: Parameter values according to the values arbitrated in (5.1)–(5.3), f0 = 100kHz, RL = 10Ω,α = 2.
Parameter Value UnitR 4.144 Ω
Rs 1.717 Ω
Q 1.189 —Cp2 189.20 nFLs2 7.840 µHCx2 521.01 nFCx1 158.80 nFQ3 3.566 —Cs2 204.07 nFRLs 0.729 Ω
Cxs2 146.64 nFXsy 20.325 Ω
Qy 27.883 —Rpy 567.44 Ω
Xpy 20.351 Ω
X j 6.908 Ω
Q j 82.143 —Ri3 0.084 Ω
Li3 14.594 µHLα 15.392 µHCα 41.142 nFCa 123.43 nFCx1 69.448 nF
thinner lines around correspond to deviations up and down to ±50%, denoted by R+L and R−L .
All the simulations were performed with fixed power supply (10V) and fixed duty ratio (50%)
for the switches. To better infer about the voltage at the diode, the maximum repetitive reverse
voltage (VRRM) was obtained for each operation condition. Fig. 5.11 depicts the simulation results,
denoting less VRRM required in the proposed topology. Thus, if there is still room available at the
driver side, the power supply can be increased, improving also the power delivery. We explored
such a case with RL = 10Ω. In the proposed topology, we increased the power supply until we
achieved the same VRRM at the diode as in the series-series topology shown in Fig. 5.11. The
results are summarized in Table 5.3, indicating more power at the load for the same voltage stress
at the diode rectifier when using our topology.
46 Multi Resonance System
RL (Ω)
10 20 30 40 50
eff
icie
ncy (
%)
20
30
40
50
60
70
80
90
series-series
series-parallel
proposed topology
RL-
RL+
(a)
RL (Ω)
10 20 30 40 50
ou
tpu
t p
ow
er
(W)
0
2
4
6
8
10
12
14
16
18
series-series
series-parallel
proposed topology
RL+
RL-
(b)
Figure 5.10: Simulation results for (a) power efficiency, and (b) power delivery to the load. R−L and R+L
indicate that, in (5.5), RL ∈ [5 : 9] and RL ∈ [11 : 15], respectively.
Table 5.3: Performance comparison for RL = 10Ω and equal VRRM .
topology power supply efficiency output power VRRM
series-series 10V 71.21% 11.98W 40.23Vseries-parallel 17V 68.10% 15.51W 40.22V
proposed 14V 75.65% 17.58W 40.24V
5.4 Results and Discussion 47
RL (Ω)
10 20 30 40 50
VR
RM (
V)
5
10
15
20
25
30
35
40
45
50
series-series
series-parallel
proposed topology
RL-
RL+
Figure 5.11: Maximum repetitive reverse voltage (VRRM). R−L and R+L keep the same meaning as in
Fig. 5.10.
48 Multi Resonance System
Chapter 6
Conclusion
6.1 Main Conclusions
This work focused in UWPT systems to power the batteries of an AUV. Since there are a
lot of similarities between UWPT and WPT in the air, a crossover was made between both ap-
proaches, the systems features and problems were identified and studied. This thesis is within
the Electrotechnical Engineering area and therefore, the system was analysed and developed with
resource to electronic methods. After the problem was analysed and characterised in chapter 3 and
its main problems were identified the author started to work on the proposed objectives given in
the introduction. The first objective that was worked on consisted in a wireless way for regulating
the load voltage in order to be constant. This was accomplished in chapter 4 were a solution was
proposed and implemented. An algorithm, for voltage regulation, was implemented into two µ
controllers from Infineon Technologies and when applied to an UWPT system made from two
coils with series-series compensation. More detail can be seen in chapter 4. Then a solution to
optimise UWPT by means of a different topology or scheme was found in chapter 5, were a multi-
resonance was designed and thoroughly analysed. There the design method is presented as well
as a comparison with well documented approaches in realising WPT is presented.
6.2 Thesis Scientific Contributions
In the development of this thesis two distinct scientific contributions were made.
• While developing a system to regulate the voltage wirelessly through the water. Here load
modulation was used to communicate from the receptor to the emitter to control the load
voltage. With this adaptive system few components are needed to be added to the original
system in order to maintain a constant voltage level in the load.
• Another contribution was when a multi-resonant system was being developed to realise
UWPT. In here a design approach is presented as well as compared with other circuit topolo-
gies.
49
50 Conclusion
6.3 Future Work
For future work it will be necessary to optimise the produced PCB’s in order to reduce their
size and eliminate high frequency problems that rose, such as in the driver side the ringing prob-
lem. Test the multi-resonance system is also a goal since only simulated results are presented in
this work. In respect to the adaptive load voltage regulation system, there is room for algorithm
optimization, as well as implementing a half-duplex communication mechanism.
Bibliography
[1] A. Gopinath, “All about transferring power wirelessly,” Electronics For You E-zine (EFY
Enterprises Pvt. Ltd.), vol. 2, 2013.
[2] J. C. Maxwell, “A dynamical theory of the electromagnetic field,” Philosophical Transac-
tions of the Royal Society of London, vol. 155, pp. 459–512, 1865.
[3] H. Hertz and W. Kelvin, Electric waves. Macmillan London, 1893.
[4] W. C. Brown, “The history of power transmission by radio waves,” IEEE Transactions on
Microwave Theory and Techniques, Sep 1984.
[5] N. Tesla, “Method of intensifying and utilizing effects transmitted through natural media.”
Nov 1901, US Patent 685,953.
[6] ——, “Apparatus for utilizing effects transmitted from a distance to a receiving device
through natural media.” Nov 1901, US Patent 685,955.
[7] ——, “Art of transmitting electrical energy through the natural mediums.” Apr 1905, US
Patent 787,412.
[8] S. L. Ho, J. Wang, W. N. Fu, and M. Sun, “A comparative study between novel witricity
and traditional inductive magnetic coupling in wireless charging,” IEEE Transactions on
Magnetics, vol. 47, 2011.
[9] M. Kesler and C. Mccarthy, “Highly resonant wireless power transfer in subsea,” Witricity
White Paper, 2012.
[10] A. Kurs, A. Karalis, R. Moffatt, J. D. Joannopoulos, P. Fisher, and M. Soljacic, “Wireless
power transfer via strongly coupled magnetic resonances,” Science, vol. 317, 2007.
[11] B. Lee, M. Kiani, and M. Ghovanloo, “A triple-loop inductive power transmission system for
biomedical applications,” IEEE Transactions on Biomedical Circuits and Systems, vol. 10,
no. 1, pp. 138–148, Feb 2016.
[12] S. Scorcioni, L. Larcher, and A. Bertacchini, “Optimized cmos rf-dc converters for remote
wireless powering of rfid applications,” in 2012 IEEE International Conference on RFID
(RFID), April 2012, pp. 47–53.
51
52 BIBLIOGRAPHY
[13] K. You, H. Kim, M. Kim, and Y. Yang, “900 mhz cmos rf-to-dc converter using a cross-
coupled charge pump for energy harvesting,” in 2011 IEEE International Symposium on
Radio-Frequency Integration Technology (RFIT), Nov 2011, pp. 149–152.
[14] G. V. Tibajia and M. C. Talampas, “Development and evaluation of simultaneous wireless
transmission of power and data for oceanographic devices,” in 2011 IEEE Sensors, Oct 2011,
pp. 254–257.
[15] J.-g. Shi, D.-j. Li, and C.-j. Yang, “Design and analysis of an underwater inductive coupling
power transfer system for autonomous underwater vehicle docking applications,” Journal of
Zhejiang University-SCIENCE C (Computers & Electronics), vol. 15, 2014.
[16] S. S. Valtchev, E. N. Baikova, and L. R. Jorge, “Electromagnetic field as the wireless trans-
porter of energy,” Facta universitatis - series: Electronics and Energetics, vol. 25, no. 3, pp.
171–181, 2012.
[17] X. Wei, Z. Wang, and H. Dai, “A critical review of wireless power transfer via strongly
coupled magnetic resonances,” Energies, vol. 7, 2014.
[18] J. Kim and F. Bien, “Electric field coupling technique of wireless power transfer for electric
vehicles,” in IEEE TENCON Spring Conference, Apr 2013, pp. 267–271.
[19] V. Kasturi, S. Deng, T. Hubing, and D. Beetner, “Quantifying electric and magnetic field
coupling from integrated circuits with TEM cell measurements,” in IEEE International Sym-
posium on Electromagnetic Compatibility (EMC’2006), vol. 2, Aug 2006, pp. 422–425.
[20] L. Sandrolini, U. Reggiani, G. Puccetti, and Y. Neau, “Equivalent circuit characterization
of resonant magnetic coupling for wireless transmission of electrical energy,” International
Journal of Circuit Theory and Applications, vol. 41, 2013.
[21] A. Umenei, “Understanding low frequency non-radiative power transfer,” Wireless Power
Consortium contribution by Fulton Innovation LLC, vol. 7575, 2011.
[22] L. Summerer and O. Purcell, “Concepts for wireless energy transmission via laser,” Euro-
peans Space Agency (ESA)-Advanced Concepts Team, 2009.
[23] V. Bana, M. Kerber, G. Anderson, J. D. Rockway, and A. Phipps, “Underwater wireless
power transfer for maritime applications,” in 2015 IEEE Wireless Power Transfer Conference
(WPTC). IEEE, 2015, pp. 1–4.
[24] A. Askari, R. Stark, J. Curran, D. Rule, and K. Lin, “Underwater wireless power transfer,” in
2015 IEEE Wireless Power Transfer Conference (WPTC), May 2015, pp. 1–4.
[25] Z. Sun and I. F. Akyildiz, “Magnetic induction communications for wireless underground
sensor networks,” IEEE Transactions on Antennas and Propagation, vol. 58, no. 7, pp. 2426–
2435, July 2010.
BIBLIOGRAPHY 53
[26] K. Mazloomi, N. Sulaiman, S. A. Ahmad, and N. A. M. Yunus, “Analysis of the frequency
response of a water electrolysis cell,” Int. J. Electrochem. Sci, vol. 8, pp. 3731–3739, 2013.
[27] J. Lin, X. fei Li, Q. Zhang, and H. biao Xiang, “Construction of contactless power feeding
system for ocean buoy,” in 2011 7th International Conference on Wireless Communications,
Networking and Mobile Computing (WiCOM), Sept 2011, pp. 1–4.
[28] K. Devi, M. Norashidah, C. Chakrabarty, and S. Sadasivam, “Design of an RF-DC conver-
sion circuit for energy harvesting,” in 2012 IEEE International Conference on Electronics
Design, Systems and Applications (ICEDSA), Nov 2012, pp. 156–161.
[29] K. Shizuno, S. Yoshida, M. Tanomura, and Y. Hama, “Long distance high efficient underwa-
ter wireless charging system using dielectric-assist antenna,” in Oceans - St. John’s, 2014,
Sept 2014, pp. 1–3.
[30] G. Vandevoorde and R. Puers, “Wireless energy transfer for stand-alone systems: a
comparison between and low high power applicability,” Sensors and Actuators A: Physical,
vol. 92, no. 1—3, pp. 305 – 311, 2001, selected Papers for Eurosensors XIV. [Online].
Available: http://www.sciencedirect.com/science/article/pii/S092442470100588X
[31] Z. N. Low, R. Chinga, R. Tseng, and J. Lin, “Design and test of a high-power high-efficiency
loosely coupled planar wireless power transfer system,” IEEE Transactions on Industrial
Electronics, vol. 56, no. 5, pp. 1801–1812, May 2009.
[32] S. Jeong, J. Jung, K. A. Kim, and J. Kim, “Analytical investigation of optimal wireless power
transfer topology for electric vehicles,” in 2015 IEEE PELS Workshop on Emerging Tech-
nologies: Wireless Power (WoW), June 2015, pp. 1–5.
[33] T. Nagashima, X. Wei, and H. Sekiya, “Analytical design procedure for resonant inductively
coupled wireless power transfer system with class-DE inverter and class-E rectifier,” in 2014
IEEE Asia Pacific Conference on Circuits and Systems (APCCAS), Nov 2014, pp. 288–291.
[34] T. Nagashima, K. Inoue, X. Wei, E. Bou, E. Alarcon, M. Kazimierczuk, and H. Sekiya,
“Analytical design procedure for resonant inductively coupled wireless power transfer system
with class-E2 DC-DC converter,” in 2014 IEEE International Symposium on Circuits and
Systems (ISCAS), June 2014, pp. 113–116.
[35] P.-K. Luk, S. Aldhaher, W. Fei, and J. Whidborne, “State-space modeling of a class ee con-
verter for inductive links,” IEEE Transactions on Power Electronics, vol. 30, no. 6, pp. 3242–
3251, June 2015.
[36] S. Aldhaher, P. C. K. Luk, and J. F. Whidborne, “Tuning class E inverters applied in inductive
links using saturable reactors,” IEEE Transactions on Power Electronics, vol. 29, no. 6, pp.
2969–2978, Jun 2014.
54 BIBLIOGRAPHY
[37] Y. Lim, H. Tang, S. Lim, and J. Park, “An adaptive impedance-matching network based on a
novel capacitor matrix for wireless power transfer,” IEEE Transactions on Power Electronics,
vol. 29, no. 8, pp. 4403–4413, Aug 2014.
[38] J. Park, Y. Tak, Y. Kim, Y. Kim, and S. Nam, “Investigation of adaptive matching methods
for near-field wireless power transfer,” IEEE Transactions on Antennas and Propagation,
vol. 59, no. 5, pp. 1769–1773, May 2011.
[39] L. Jianyu, T. Houjun, and G. Xin, “Frequency splitting analysis of wireless power transfer
system based on t-type transformer model,” Elektronika ir Elektrotechnika, vol. 19, no. 10,
pp. 109–113, 2013.
[40] N. K. Trung, T. Ogata, S. Tanaka, and K. Akatsu, “Pcb design for 13.56mhz half-bridge
class d inverter for wireless power transfer system,” in 2015 9th International Conference on
Power Electronics and ECCE Asia (ICPE-ECCE Asia), June 2015, pp. 1692–1699.
[41] M. Chen and G. A. Rincon-Mora, “Accurate electrical battery model capable of predicting
runtime and iv performance,” IEEE transactions on energy conversion, vol. 21, no. 2, pp.
504–511, 2006.
[42] C. H. Lee, J. T. Yang, and J. A. Jiang, “Assessment of pem fuel cells-based dc/dc power con-
version for applications in auvs,” IEEE Transactions on Aerospace and Electronic Systems,
vol. 46, no. 4, pp. 1834–1847, Oct 2010.
[43] E. D. Denman, “Coupled mode theory,” Journal of Mathematical Analysis and Applications,
vol. 21, 1968.
[44] S. Y. Ron Hui, “Magnetic resonance for wireless power transfer [a look back],” IEEE Power
Electronics Magazine, vol. 3, no. 1, pp. 14–31, Mar 2016.
[45] K. Y. Kim, C. Yoon, N. Y. Kim, J. Choi, Y. H. Ryu, D. Z. Kim, K. S. Song, C. H. Ahn,
E. Park, Y. K. Park, and S. Kwon, “Magnetic resonance wireless power transfer system for
practical mid-range distance powering scenario references,” in IEEE International Confer-
ence on Consumer Electronics (ICCE’2013), Jan 2013, pp. 175–176.
[46] J. C. Chiao, “Batteryless wireless gastric implants,” in IEEE 15th Annual Wireless and Mi-
crowave Technology Conference (WAMICON’2014), Jun 2014, pp. 1–4.
[47] S. Li and C. C. Mi, “Wireless power transfer for electric vehicle applications,” IEEE Journal
of Emerging and Selected Topics in Power Electronics, vol. 3, no. 1, pp. 4–17, Mar 2015.
[48] C.-S. Wang, O. H. Stielau, and G. A. Covic, “Design considerations for a contactless electric
vehicle battery charger,” IEEE Transactions on Industrial Electronics, vol. 52, no. 5, pp.
1308–1314, Oct 2005.
BIBLIOGRAPHY 55
[49] J. Oiler, G. Anderson, V. Bana, A. Phipps, M. Kerber, and J. D. Rockway, “Thermal and
biofouling effects on underwater wireless power transfer,” in 2015 IEEE Wireless Power
Transfer Conference (WPTC), May 2015, pp. 1–4.
[50] J. U. W. Hsu, A. P. Hu, and A. Swain, “A wireless power pickup based on directional tuning
control of magnetic amplifier,” IEEE Transactions on Industrial Electronics, vol. 56, no. 7,
pp. 2771–2781, Jul 2009.
[51] Y. Cao, Z. Dang, J. A. A. Qahouq, and E. Phillips, “Dynamic efficiency tracking controller
for reconfigurable four-coil wireless power transfer system,” in IEEE Applied Power Elec-
tronics Conference and Exposition (APEC’2016), Mar 2016, pp. 3684–3689.
[52] H. Li, J. Li, K. Wang, W. Chen, and X. Yang, “A maximum efficiency point tracking con-
trol scheme for wireless power transfer systems using magnetic resonant coupling,” IEEE
Transactions on Power Electronics, vol. 30, no. 7, pp. 3998–4008, Jul 2015.
[53] T. D. Yeo, D. Kwon, S. T. Khang, and J. W. Yu, “Design of maximum efficiency tracking
control scheme for closed loop wireless power charging system employing series resonant
tank,” IEEE Transactions on Power Electronics, vol. PP, no. 99, pp. 1–1, To be published
2016.
[54] P. Amaral, C. Duarte, and P. Costa, “On the impact of timer resolution in the efficiency
optimization of synchronous buck converters,” International Journal of Power Electronics
and Drive Systems, vol. 6, no. 4, pp. 693–702, Dec 2015.
[55] F. Gonçalves, C. Duarte, and L. M. Pessoa, “A novel circuit topology for underwater wireless
power transfer,” in International Conference on Systems Informatics, Modelling and Simula-
tion, Riga, Latvia, Jun 2016, pp. 181–186.
[56] J. Dai and D. C. Ludois, “A survey of wireless power transfer and a critical comparison of
inductive and capacitive coupling for small gap applications,” IEEE Transactions on Power
Electronics, vol. 30, no. 11, pp. 6017–6029, Nov 2015.
[57] S. Hui, W. Zhong, and C. Lee, “A critical review of recent progress in mid-range wireless
power transfer,” IEEE Transactions on Power Electronics, vol. 29, no. 9, pp. 4500–4511,
Sept 2014.
[58] J. Shin, S. Shin, Y. Kim, S. Ahn, S. Lee, G. Jung, S.-J. Jeon, and D.-H. Cho, “Design
and implementation of shaped magnetic-resonance-based wireless power transfer system for
roadway-powered moving electric vehicles,” IEEE Transactions on Industrial Electronics,
vol. 61, no. 3, pp. 1179–1192, March 2014.
[59] C. R. Valenta and G. D. Durgin, “Harvesting wireless power: Survey of energy-harvester
conversion efficiency in far-field, wireless power transfer systems,” IEEE Microwave Maga-
zine, vol. 15, no. 4, pp. 108–120, Jun 2014.
56 BIBLIOGRAPHY
[60] T. Sun, X. Xie, and Z. Wang, Wireless Power Transfer for Medical Microsystems, ser.
SpringerLink : Bücher. Springer New York, 2013.
[61] N. A. Cruz and A. C. Matos, “The MARES AUV, a modular autonomous robot for environ-
ment sampling,” in OCEANS 2008, Sep 2008, pp. 1–6.
[62] D. Oliveira, C. Duarte, V. G. Tavares, and P. G. de Oliveira, “Design of a current-mode
class-D power amplifier in RF-CMOS,” in Proceedings of the XXIV Conference on Design
of Circuits and Integrated Systems (DCIS’2009), Zaragoza, Spain, Nov 2009, pp. 418–422.
[63] T. Nagashima, X. Wei, E. Bou, E. Alarcón, M. K. Kazimierczuk, and H. Sekiya, “Analysis
and design of loosely inductive coupled wireless power transfer system based on class-E2
DC-DC converter for efficiency enhancement,” IEEE Transactions on Circuits and Systems—
Part I: Regular Papers, vol. 62, no. 11, pp. 2781–2791, Nov 2015.
[64] M. Kiani and M. Ghovanloo, “A figure-of-merit for designing high-performance inductive
power transmission links,” IEEE Transactions on Industrial Electronics, vol. 60, no. 11, pp.
5292–5305, Nov 2013.
[65] X. Zhang, L. E. Larson, P. M. Asbeck, and R. A. Langridge, “Analysis of power recycling
techniques for RF and microwave outphasing power amplifiers,” IEEE Transactions on Cir-
cuits and Systems—Part II: Analog and Digital Signal Processing, vol. 49, no. 5, pp. 312–
320, May 2002.
[66] J. Love, RF Front-End: World Class Designs. Newnes, 2009.
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