circuit optimization for underwater power transfer

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.

i

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.

iii

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.

v

vi

‘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

vii

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

ix

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

xi

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

xiii

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


(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


(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 .


(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.


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


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.

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


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.


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.

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.


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)


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


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)


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


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.


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.

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.

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