characterization and optimization of a wireless power...

Bachelor’s degree final-year project – Proyecto Fin de Grado

Degree in Electrical Engineering – Grado en Ingeniería Eléctrica

Characterization and optimization of a wireless power transmission system by means of resonant

coupling

Donostia / San Sebastián, 23rd May 2014 Iñigo García de Madinabeitia Merino

ii

Acknowledgements

I wish to thank many people for their contribution to this project, without whom this project

would not have been accomplished.

Firstly, to my family for their support in the good and bad moments has been crucial all

throughout these years. I would like to thank my father, Pedro García de Madinabeitia, who

worked day and night on countless occasions and showed great passion for everything he ever

tried to accomplish.

Secondly, I would like to thank Juan Ignacio Sancho, the director of this final year project, for

helping me make this possible.

Thirdly, I wish to thank Luis Fontán for his patient guidance, enthusiastic encouragement and

useful critiques of my work. He has been a perfect tutor and teacher, and I learned much more

than engineering with him.

Besides, I want to thank all my friends, those who I met in school and have been part of my life

for so many years, those that I have met in university, that although it seems to have been

such a short time, they have become very good friends, and all the rest that I have met along

the way.

Last but not least, José Macayo and Javier García, people who searched for everything I asked

them and made my internship at CEIT easier, Iñaki Ortego and José Martín Echeverría,

researchers in CEIT who gave me their sincere opinion about everything they could help me

with.

From the bottom of my heart, thank you.

iii

Abstract

Currently, there are multiple ways of transferring energy, such as Plug-DC, Plug-AC, inductive,

capacitive and resonant coupling. Although wireless energy transmission has been widely

studied throughout the last two centuries, recent appearance and incipient importance of

electric mobility has pushed this to a higher level. After an analysis of the possible alternatives,

it is seen that RF resonant coupling is not widely studied. This study starts with a finite element

simulation in order to obtain the needed data and size the system optimally, and, thus, an air-

core 1-turn coil system is built to do so. Air-core systems do not have any problem with

saturation, and are much lighter than metal-core systems. Coil size and gap between them is

chosen with data from the simulation, and results are experimentally verified. The presented

results show that RF resonant coupled energy transmission is robust, as tolerance regarding

axial gap and radial misalignment, as impedance and frequency can be changed to optimize

every axial and radial configuration.

v

Contents

Preliminary phase .......................................................................................................................... 1

Historical background ............................................................................................................... 1

Electromagnetic theory ......................................................................................................... 2

Resonance ............................................................................................................................. 5

Introduction to the studies and goals ....................................................................................... 6

Design 1 ................................................................................................................................. 6

Design 2 ................................................................................................................................. 6

Equipment ................................................................................................................................. 7

Network analyzer .................................................................................................................. 7

Signal generator .................................................................................................................... 7

Rheostat ................................................................................................................................ 8

Amplifier ................................................................................................................................ 8

Lux meter .............................................................................................................................. 9

Power meter ........................................................................................................................ 10

Power sensor ....................................................................................................................... 10

Oscilloscope ......................................................................................................................... 11

Quickfield ............................................................................................................................ 11

Simulation phase ......................................................................................................................... 13

Results of Quickfield simulation .............................................................................................. 13

Self-inductance calculation ..................................................................................................... 15

Experimental phase ..................................................................................................................... 16

Measurement of self-inductances .......................................................................................... 16

Design 1 ............................................................................................................................... 16

Design 2 ............................................................................................................................... 19

Series resonance measurement .............................................................................................. 20

Mutual inductance calculation ................................................................................................ 22

Impedance matching ............................................................................................................... 24

Calculation of transmission efficiency ..................................................................................... 28

Study of transmission and reflection efficiencies as a function of the axial gap .................... 29

Illuminance study .................................................................................................................... 31

vi

Equations ............................................................................................................................. 33

DC studies ................................................................................................................................ 34

DC waveforms ..................................................................................................................... 34

Power vs. Signal generator power ...................................................................................... 35

Power vs. Signal generator frequency ................................................................................ 37

Power vs. Axial gap .............................................................................................................. 39

Power vs. Radial misalignment ........................................................................................... 42

Conclusions and future work ...................................................................................................... 45

List of Figures .............................................................................................................................. 46

List of pictures ............................................................................................................................. 48

List of Tables ................................................................................................................................ 48

Bibliography ................................................................................................................................ 49

1

Preliminary phase

Historical background

Originally electricity and magnetism were thought of as two separate forces. J.C Maxwell

changed this vision in 1873 when Treatise on Electricity and Magnetism was published.

Electromagnetic fields have been studied since their discovery.

H.C. Ørsted noticed the induction phenomenon in 1820. His findings resulted in intensive

research throughout the scientific community in electrodynamics. They influenced A.M.

Ampère's developments of a single mathematical form to represent the magnetic forces

between current-carrying conductors. Many well-known scientists have researched on this

phenomenon, such as M. Faraday, O. Heaviside and H. Hertz.

Later on, E.B. Rosa, F.W. Grover, L. Cohen, H.L. Curtis and C.M. Sparks published many papers for the Department of Commerce and Labor of the USA regarding numerical calculations of inductances, and H. Nagaoka did the same in Japan. In 1894, Nikola Tesla used resonant inductive coupling to wirelessly light up phosphorescent and incandescent lamps at the 35 South Fifth Avenue laboratory, and later at the 46 E. Houston Street laboratory in New York City. In the 1940s, radio engineering began to be crucial due to the Second World War. F.E. Tenman published “Radio Engineers’ Handbook” in 1943, reference book about inductances and their use in radio engineering. After that, RFID technologies have been developed as a natural evolution, reducing size and increasing functionality for use in identification and combined with electronics. Even so, things are changing, and the appearance of the electric vehicle is turning that evolution towards bigger and more powerful coils, which could be seen as a return to the 1900s. This is not strictly like that, since power electronics are playing a very important role and capacitances are being used in order to increase the transmission efficiency and power capability of the system by making it resonant.

This Bachelor’s degree final-year project will characterize a Wireless Energy Transmission

system at radio frequency to see the advantages and disadvantages compared to power

electronics frequencies.

2

Electromagnetic theory

As said in [1], understanding of the procedures of power transfer requires an understanding of

the physical principles of magnetic phenomena. Every moving charge, such as electrons in

wires or in vacuum, producing a flow of current, is associated with a magnetic field. The

intensity of the magnetic field can be demonstrated experimentally by the forces acting on a

magnetic compass, as Ørsted did, or a second electric current. The magnitude of the magnetic

field is described by the magnetic field strength H regardless of the material properties of the

space.

∑ ∮

If the measuring point is moved away from the center of the coil along the coil axis, the

strength of the field H will decrease as the axial distance is increased. A more in-depth

investigation shows that the field strength in relation to the radius (or area) of the coil remains

constant up to a certain distance and then falls rapidly. In free space, the decay of field

strength is approximately 60 dB per decade in the near field of the coil, and flattens out to 20

dB per decade in the far field of the electromagnetic wave that is generated [1].

The total number of lines of magnetic flux that pass through the inside of a circular coil, for

example, is the magnetic flux Φ. Magnetic flux density B is a variable related to area A.

Magnetic flux is expressed as:

A magnetic field, and thus a magnetic flux Φ, will be generated around a conductor of any

shape. This will be particularly intense if the conductor is in the form of a loop. Normally, there

3

is not one conduction loop, but N, of the same area A, through which the same current I flows.

Each of the conduction loops contributes the same proportion Φ to the total flux ψ.

∑

The ratio of the interlinked flux ψthat appears in an area enclosed by current I, to the current

in the conductor that encloses it, is denoted by inductance L.

Inductance is one of the characteristic variables of conductor loops (coils). The inductance of a

coil depends totally upon the material properties of the space that the flux flows through and

the geometry of the layout.

If a second coil (area A2) is located in the proximity of coil 1 (area A1), through which a current

is flowing, this will be subject to a proportion of the total magnetic flux Φ flowing through A1.

The two circuits are connected together by this partial flux or coupling flux. The magnitude of

the coupling flux Φ21 depends upon the geometric dimensions of both conductor loops, the

position of the conductor loops in relation to one another, and the magnetic properties of the

medium in the layout. Similarly to the definition of the self-inductance L of a conductor loop,

the mutual inductanceM21 of conductor loop 2 in relation to conductor loop 1 is defined as the

ratio of the partial flux Φ21 enclosed by conductor loop 2, to the current I1 in conductor loop 1:

∮

Similarly, there is also a mutual inductance M12. Here, current I2 flows through the conductor

loop 2, thereby determining the coupling flux Φ12 in loop 1. The following relationship applies:

Mutual inductance describes the coupling of two circuits via the medium of a magnetic field,

and is always present between two electric circuits. Its dimension and unit are the same as for

inductance.

4

Mutual inductance is a quantitative description of the flux coupling of two conductor loops.

The coupling coefficient k is introduced so that we can make a qualitative prediction about the

coupling of the conductor loops independent of their geometric dimensions. The following

applies:

√

The coupling coefficient always varies between the two extreme cases 0 ≤ k ≤ 1.

k=0: Full decoupling due to great distance or magnetic shielding.

k=1: Total coupling. Both coils are subject to the same magnetic flux Φ. The

transformer is a technical application of total coupling, whereby two or more coils are

wound onto a highly permeable iron core.

5

Resonance

Electrical resonance occurs in an electric circuit at a particular frequency as a consequence of

the cancellation of the reactances of circuit elements with each other. In some circuits this

happens when the impedance between the input and output of the circuit is minimal.

Resonant circuits can generate higher voltages and currents than are fed into them.

Resonance of a circuit involving capacitors and inductors occurs because the collapsing

magnetic field of the inductor generates an electric current in its windings that charges the

capacitor, and then the discharging capacitor provides an electric current that builds the

magnetic field in the inductor. This process is repeated continually.

√

Inductors are typically constructed from coils of wire, the resistance of which is not usually

desirable, so Litz wire can be used to minimize it, and it has a significant effect on the circuit.

This way, a new parameter Q is defined.

The higher Q is, the better energy transmission there will be, as losses would be smaller and

mutual inductance bigger. Q is normally kept between 10 and 100 for wireless energy

transmission.

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

6

Introduction to the studies and goals

In order to give an understandable cohesion to this project, it will be divided into Simulation

and Experimental phases.

In the Simulation phase, a finite element calculation program, Quickfield, will be used to

characterize the electromagnetic flux linking between coils and to calculate the inductance.

After that, in the Experimental phase, this inductance calculation will be revised. Furthermore,

resonance frequency will be measured, as well as mutual inductance. Later on, an impedance

matching will be performed. The main results will be the RF efficiency, the illuminance study

and DC efficiency.

In order to calculate the performance ratios, the radio frequency amplifier will not be

considered. The focus will be on characterizing and optimizing the wireless energy

transmission. Thus, algorithms linking resonance frequency with secondary impedance, axial

gap and radial misalignment could be developed.

After this, conclusions will be obtained, and, with these, a guideline for future work will be

designed.

Design 1

This study will be performed with a one-loop circular coil, with a radius of 30 centimeters. The

goal is to reach a good efficiency, 75%, at 15 centimeter axial distance, i.e. a gap-diameter

ratio of ¼. The resonance frequency is 6.7MHz.

Design 2

This will be a scaled model, with a 2 cm radius, and the goal is to find if the inductances are a

function of the square the number of turns reliably, so that the same know-how in every case

with a ¼ gap-diameter ratio could be applied. The gap will be 1 cm.

7

Equipment

Network analyzer

A network analyzer is an instrument that measures the network parameters of electrical

networks. Today, network analyzers commonly measure s–parameters because reflection and

transmission of electrical networks are easy to measure at high frequencies, but there are

other network parameter sets such as y-parameters, z-parameters, and h-parameters.

Network analyzers are often used to characterize two-port networks such as amplifiers and

filters, but they can be used on networks with an arbitrary number of ports.

The two basic types of network analyzers are:

Scalar network analyzer (SNA) : measures amplitude properties only

Vector network analyzer (VNA): measures both amplitude and phase properties

The chosen model is a HP 8714ET VNA [Picture 1], giving:

Narrowband and broadband detection

100 dB dynamic range

Real-time sweep speeds (40 ms/sweep)

Integrated T/R test set

Synthesized source with 1-Hz resolution

Standard LAN interface

Standard Internal Agilent Instrument BASIC (IBASIC)

Picture 1: HP 8714ET VNA

Signal generator

Signal generators are electronic devices that allow the user to test equipment, such as

antennas, with different waveforms and frequencies. In this case, as a power amplifier will be

used, the rated power of the generator is not a key factor.

The chosen model is a HP E4432B digital signal generator [Picture 2] giving:

Frequency: 250 kHz to 3.0 GHz

Power: 0 to 20 dBm

8

RF modulation bandwidth up to 35 MHz

Optional dual arbitrary waveform generator and/or real-time I/Q baseband generator

40 MHz sample rate and 14-bit I/Q resolution

1 Msample (4 MB) memory for waveform playback and 1 Msample (4 MB) memory for waveform storage

Custom digital modulation (>15 variations of FSK, MSK, PSK, and QAM),AM, FM, phase modulation, pulse modulation, and step/list sweep (frequency and power)

Picture 2: HP E4432B signal generator

Rheostat

It is an adjustable resistor used in applications that require the adjustment of current or the

varying of resistance in an electric circuit. The rheostat can adjust generator characteristics,

dim lights, and start or control the speed of motors. Its resistance element can be a metal wire

or ribbon, carbon, or a conducting liquid, depending on the application. For average currents,

the metallic type is most common; for very small currents, the carbon type is used; and for

large currents the electrolytic type, in which electrodes are placed in a conducting fluid, is

most suitable. A special type of rheostat is the potentiometer.

The chosen model is an Instituto Torres Quevedo M-54-02 [Picture 3], giving a maximum of

100Ω and 2.5A. It can be seen in Picture 3.

Picture 3: Instituto Torres Quevedo M-54-02 rheostat

Amplifier

An amplifier is an electronic device that increases the power of a signal. It takes energy from

a power supply and controls the output to match the input signal shape but with

larger amplitude. In this sense, an amplifier modulates the output of the power supply.

9

The chosen model is an Amplifier Research 30W1000B [Picture 4], giving a maximum of 30W

from 1 to 1000 MHz. The Model 30W1000B is a portable, self-contained, air-cooled,

broadband, solid state amplifier designed for applications where instantaneous bandwidth and

high gain are required.

Picture 4: Amplifier Research 30W1000B

Lux meter

The lux is the SI unit of illuminance, measuring luminous flux per unit area. It is equal to

one lumen per square meter. In photometry, this is used as a measure of the intensity, as

perceived by the human eye, of light that hits or passes through a surface. It is analogous to

the radiometric unit watts per square meter, but with the power at each wavelength weighted

according to the luminosity function, a standardized model of human visual brightness

perception.

Examples:

Illuminance Surfaces illuminated by:

0.0001 lux Moonless, overcast night sky (starlight)

0.002 lux Moonless clear night sky with airglow

0.27–1.0 lux Full moon on a clear night

3.4 lux Dark limit of civil twilight under a clear sky

50 lux Family living room lights (Australia, 1998)

80 lux Office building hallway/toilet lighting

100 lux Very dark overcast day

320–500 lux Office lighting

400 lux Sunrise or sunset on a clear day.

1000 lux Overcast day; typical TV studio lighting

10000–25000 lux Full daylight (not direct sun)

32000–100000 lux Direct sunlight

10

The chosen model is a TES 1332 [Picture 5], giving a measuring range of

200/2000/20000/200000 Lux and a resolution of 0.1 Lux.

Picture 5: TES 1332 lux meter

Power meter

When measuring electric power at RF frequencies, we need a special device, called microwave

power meter. Usually, a microwave power meter will consist of a measuring head which

contains the actual power sensing element, connected via a cable to the meter proper, which

displays the power reading. The head needs a power sensor. Different power sensors can be

used for different frequencies or power levels. Historically, the means of operation in most

power sensor and meter combinations was that the sensor would convert the microwave

power into an analogue voltage which would be read by the meter and converted into a power

reading. Several modern power sensor heads contain electronics to create a digital output and

can be plugged via USB into a PC which acts as the power meter.

Power sensor

The chosen model is an Agilent 9304A [Picture 6].

Low frequency coverage (9 kHz to 6 GHz) for EMC/EMI test applications such as the radiated immunity test (IEC61000-4-3)

High sensitivity (-60 to +20 dBm) and fast measurement speed to reduce the time taken to calibrate radiated field uniformity and EMC/EMI test receivers

Measure transmitter power and receiver sensitivity at Very Low Frequency (VLF) to microwave frequencies

11

Picture 6: E9304A power sensor

Oscilloscope

A digital storage oscilloscope is an oscilloscope which stores and analyses the

signal digitally rather than using analogue techniques. It is now the most common type of

oscilloscope in use because of the advanced trigger, storage, display and measurement

features which it typically provides.

The selected oscilloscope is an Agilent DSO1052B [Picture 7], with specifications:

Up to 1 GSa/s sample rate

Up to 16 kpts memory

5.7-inch color LCD display with wide viewing angle

Simultaneous viewing of main and zoomed waveforms

Picture 7: Agilent DSO1052B oscilloscope

Quickfield

QuickField is a finite element analysis software package running on Windows platforms. It is

developed and distributed by Tera Analysis Ltd. QuickField is available as a commercial

program or as a free Student Edition with limited functionality. Main applications

include computer simulations of electromagnetic fields for scientific and industrial purposes,

and use as a teaching aid in the college and university electromagnetic or physics courses.

12

Analysis types:

AC, DC and transient electromagnetics

Electrostatics, DC, AC and transient electric analysis

Steady-state and transient heat transfer

Stress analysis

Coupled multiphysics

QuickField combination of simplicity and power makes it a popular tool for using by

researchers in famous scientific centers. The impressive list of publications, referencing to

QuickField proves that.

Modern scientific researches often require simulations, both of the phenomena under study,

and new tools and equipment to be used in research. From this point of view any of

applications, listed in the Industrial section of this website may related to science. And vice

versa – modern engineering often involves scientific research to be performed.

Also, universities involve students in research works, so scientific and educational uses are

often going together.

13

Simulation phase

Results of Quickfield simulation

By means of axial symmetry, simulations have been done with the following results. The next

graph is obtained by keeping the primary (sender) coil still with a radius of 30 cm. The

secondary (receiver) coil varies in radius and axial gap between sender and receiver. Magnetic

flux [Figure 1] and flux density [Figure 2] are represented in Y-axis.

Figure 1: Axial magnetic flux density as a function of receiver coil radius and axial gap

0,00E+00

2,00E-06

4,00E-06

6,00E-06

8,00E-06

1,00E-05

1,20E-05

0,0 10,0 20,0 30,0 40,0 50,0 60,0 70,0 80,0

Axi

al m

agn

eti

c fl

ux

de

nsi

ty [

T]

Receiver coil radius

15 cm gap

22.5 cm gap

30 cm gap

60 cm gap

14

Figure 2: Axial magnetic field intensity as a function of receiver coil radius and axial gap

These plots suggest that the usual rule of thumb which says that B and H are constant until the

gap is as big as the coil diameter can be used only in certain cases. For instance, this can only

be applied in the 15 cm gap case.

An explanation may be found in the fact that the flux is not as directed as it would be in a

longer coil consisting of more turns. These coils consist of one turn and a single layer, so the

flux is much freer and it is harder to capture.

0

1

2

3

4

5

6

7

8

9

0,0 10,0 20,0 30,0 40,0 50,0 60,0 70,0 80,0

Axi

al m

agn

eti

c fi

eld

inte

nsi

ty [

A/m

]

Receiver coil radius

15 cm gap

22.5 cm gap

30 cm gap

60 cm gap

15

Self-inductance calculation

As this circle-shaped one loop coil is not the most common kind, numerous calculations have

been made with many different equations designed for a variety of specific types of

applications, sizes and specifications.

The first reference will be the inductance value the Quickfield built-in impedance wizard gives,

2.0539 µH [Figure 3].

Figure 3: Quickfield snapshot

Besides, to be able to compare and contrast this data, Radio Engineers’ Handbook [2] has been

consulted. It is found that:

(

)

, where D is the diameter of the circular loop and d is the diameter of a round conductor, both

of them in inches. µ is the permeability of the wire and δ is the skin-effect delta. This formula

was developed from [3] and [4]. δ can be found in [5] as follows:

√

, where f is the frequency, µ is the permeability and σ is the conductivity of the material.

These calculations give an inductance value of 2.06 µH.

16

Experimental phase

Measurement of self-inductances

A Smith chart of the coil impedance spectrum is plotted with a HP8714ET VNA.

Design 1

With 6 mm2 wire, and one turn in a single layer, the

theoretically calculated inductance is 2.06 µH in the

previous section. It will be seen if this is a correct

guess for our system or there are big differences in

the real built model [Picture 8].

The empirically obtained screenshots are the

following:

This shows that inductance at 6.7 MHz is higher

than expected, 2.54µH [Figure 4].

At 0.3 MHz [Figure 5], the value is still higher than expected, but smaller than at 6.7 MHz, due

to the smaller skin-effect delta at lower frequencies.

It is also noticed that the system is never self-resonant in that range of frequencies, but it turns

out to be an open circuit around 20 MHz, so working around this point should be avoided.

This study will be repeated with 2 turns now.

Figure 5: screenshot with 1 turn at 0.3 MHz Figure 4: screenshot with 1 turn at 6.7 MHz

Picture 8: practical implementation of the coils.

17

Figure 6: screenshot with 2 turns at 0.3 MHz

Figure 7: screenshot with 2 turns at 6.7 MHz

In figures 4, 5, 6 and 7 it is seen how the one-turn inductance value is quite stable in the

analyzed frequency range, but this phenomenon doesn’t happen with a two-turn coil. An

inductance ratio, f, is defined, which is helpful for comparing inductance growth with the

number of turns at any frequency.

At 300 kHz, the multiplication factor is

18

At 6.7MHz it is

Due to its proximity to the open-circuit position in the Smith chart, theoretical results are not

directly applicable here, because it is predicted that inductance is a function of , being the

number of turns, so should be 4 in an ideal case.

With this data, the following capacitances in order to make the system series-resonant at

6.7MHz are needed:

;

The studies will go on only with the 1-turn coils, as the procedure with the 2-turn coil would be

analogous.

19

Design 2

With 1.5 mm2 wire and 3 layers, 5 turns each, the theoretically calculated inductance is 10 µH.

Experimentally, the results are 12.46 µH in coil 1 [Figure 8] and 10.27 µH in coil 2 [Figure 9] at

600kHz.

Figure 8: Smith diagram of coil 1, from 0.3 to 20 MHz

Figure 9: Smith diagram of coil 2, from 0.3 to 20 MHz

With this data, the following capacitances are needed in order to make the system resonant at

600 kHz:

;

From now on, there will be no further study of design 2.

20

Series resonance measurement

A 4 unit 220 pF capacitor system is mounted, divided into 2 parallel strings of 2 capacitors in

series each string [Picture 9], owing to the fact that one

only ceramic capacitor cannot handle with the working

voltage that will be dealt with:

√

√

When the coil is connected in series with the capacitor system, the desired 6.7 MHz resonance

is obtained, as well as the values of R and L [Figure 10].

Picture 9: detail of the constructed capacitor system

21

Figure 10: screenshot with the capacitor system and 1-turn coil at 6.7 MHz. The resistance is 1.044Ω and the reactance is 90.56 mΩ

Now that the complete system is resonating at the objective frequency, the reflection

coefficient will be considered. It is minimum at 6.7MHz [Figure 11], but the reflection value is

too high, -0.362 dB, to consider it well adapted. It must be under -10 dB to be an acceptable

adaptation.

Figure 11: screenshot with the capacitor system and 1-turn coil at 6.7 MHz. It is seen that the surroundings are in the lowest point of the plot.

22

Mutual inductance calculation

In order to get numerical values of the mutual inductance, many books have been consulted,

such as [3], [4] and [6]. After the evaluation of the results, the latter one, [6], by H.L. Curtis and

C.M. Sparks, is chosen.

Axial gap

Method 15 cm 22,5cm 30cm 60cm

Mu

tual

in

du

ctan

ce

Graphical 3,30E-07 2,10E-07 1,50E-07 4,50E-08

Tabulated 3,22E-07 2,03E-07 1,48E-07 4,26E-08

Table 1: Different results with methods taken from [6]

0,00E+00

5,00E-08

1,00E-07

1,50E-07

2,00E-07

2,50E-07

3,00E-07

3,50E-07

0 10 20 30 40 50 60 70

Mu

tual

Ind

uct

ance

[H

]

Axial gap [cm]

Mutual inductance vs. axial gap

Graphical method

Tabulated method

Exponencial(Tabulated method)

Figure 12: Mutual inductance profile depending on the axial gap

23

By means of the tabulated results [Table 1], an exponential approximation of the tabulated

data is obtained.

This equation will be useful in the analyzed range. At the same time, it is observed that the

graphical and tabulated methods are closer to each other with bigger gaps.

24

Impedance matching

Due to the fact that all of the measuring equipment has a characteristic impedance of 50 Ω, an

impedance matching will be done so that reflections can be avoided. As the mutual impedance

is small compared to the self-inductances, it will not be considered in the impedance matching.

Thus, the matching calculation will be performed only with self-inductances and will be refined

empirically. In order to do the adaptation, a series-parallel capacitance system will be used.

Figure 13: adaptation circuit schematic

From the schematic of the circuit that will be used [Figure 13], the characteristic impedance is

obtained with this equation:

Thus, the chosen capacitances are:

√

√

( )

( √

)

Even though this theoretical model gives that C1s= 236.67 pF and C2s= 3.559 nF if RL=0.875 Ω

and LL= 2.54 µH, results show that this is not exactly applicable, due to the components not

25

being ideal. Apart from that, capacitors will be changed to SMD ones. Each capacitor and

additional cable has its own parasitic inductance and resistance. In addition, the adaptation

with the whole system mounted will be performed, i.e. with a 50Ω in series, to simulate the

effect that it would have, if already adapted. With this model, the impedance seen by the

primary coil is 65 Ω at 6.7 MHz.

Therefore, along with empirical result, the adapting capacitances are tuned reaching a

reflection coefficient of -22.697 dB [Figure 14] and primary impedance of 50.31 Ω at 6.7 MHz

[Figure 15]. There capacitances are C1s=282.8pF and C2p=1.53nF, as shown in Picture 10.

Picture 10: detail of the practical implementation of the adaptation.

Figure 14: it is observed that adaptation is good around the resonance frequency, giving -22.697 dB

26

Figure 15: Smith chart with series-parallel resonance, 282.8pF in series and 1.53nF in parallel. 50 Ω resistance in secondary.

As soon as the 50 Ω resistance is replaced by the VNA reception input, the impedance viewed

by the VNA output changes in the whole range of frequencies, 60.30 Ω at 6.7 MHz [Figure 16],

due to the error tolerance of the resistance to be much smaller. The VNA introduces

measuring imperfections, but the resonance frequency is still the same.

The reflection coefficient is bigger [Figure 17] in comparison with the previous case with the

resistance, but is below -10 dB, so it will be considered as well-adapted.

Figure 16: Smith chart with series-parallel resonance, 282.8pF in series and 1.53nF in parallel. VNA reception input in secondary.

27

Figure 17: logarithmic diagram of reflection and transmission coefficients. VNA in secondary.

28

Calculation of transmission efficiency

As it can be seen in Figure 18, the transmission coefficient at 6.7 MHz is S21= -1.28 dB.

Figure 18: logarithmic diagram of transmission coefficient with VNA in secondary.

With these results, and knowing that

, the efficiency ratio

is obtained, giving a result of η = 74.47 % at 6.7MHz.

29

Study of transmission and reflection efficiencies as a function of the

axial gap

Now that a procedure to find the reflection and transmission efficiencies has been found, the

next step is the analysis of these as a function of the axial gap between the coils. X is defined

as the axial gap in equations.

As shown in Figure 19, the transmission is maximal in the range from 10 to 13 cm, and,

furthermore, there is no difference bigger than 1% there. The transmission efficiency is

approximated in the working range by:

Figure 19: transmission efficiency vs. Axial gap

Figure 20: non-reflection efficiency vs. Axial gap

66

68

70

72

74

76

78

80

10 12 14 16 18

Effi

cie

ncy

[%

]

Gap [cm]

Transmission efficiency

92

93

94

95

96

97

98

99

10 12 14 16 18

Effi

cie

ncy

[%

]

Gap [cm]

No-reflection efficiency

30

On the other hand, in Figure 20, the reflection is minimal between 14 and 15 cm, and drops

sharply at lower and higher values of the gap. The no-reflection efficiency is approximated in

the working range by:

Figure 21: total efficiency vs. Axial gap

When those two partial efficiencies are combined, the total performance is obtained [Figure

21]. The maximum value is 76.12% at 13 cm, and is stable above 76% from 12.5 to 13.5 cm.

Moreover, 75% efficiency is achieved from 12 cm to 14.5 cm.

This can be explained with S11 (reflection) and S21 (transmission) separately: before 12.5 cm, S21

is quite good, but S11 is very low, and above 15 cm both drop sharply. The total efficiency is

approximated in the working range by:

62

64

66

68

70

72

74

76

78

10 12 14 16 18

Effi

cie

ncy

[%

]

Axial gap [cm]

Total efficiency

31

Illuminance study

In order to have a visual result, an illuminance study will be performed. To do so, a TES 1332lux

meter will be used.

The impedance will be different since the bulb, incandescent and meant to be used for an anti-

condensation beacon, is 15W, 24VDC, rated, giving a DC impedance of 38.4 Ω.

The Illuminance vs. signal generator power [Figure 22] and Illuminance vs. frequency [Figure

23] studies were measured at 2cm distance, and Illuminance vs. axial gap [Figure 24] and

Illuminance vs. radial misalignment [Figure 25] studies were measured at a very close distance,

with the lux meter touching the bulb.

As these figures show, there is a clear resonance around 6.7 MHz and the decrease of received

power with radial misalignment is quite linear. The equations in Figure 22 and Figure 24 are

complicated, but the supposition in the first is that the power amplifier saturates and amplifies

differently depending on the input amplitude, it is not linear.

Figure 22: Illuminance vs. Signal generator power. Frequency: 6.7 MHz, Axial gap: 15 cm, axes aligned.

0

2000

4000

6000

8000

10000

12000

0 5 10 15

Illu

min

ance

[Lu

x]

Signal generator power [dBm]

Illuminance vs. signal generator power

32

Figure 23: Illuminance vs. Frequency. Signal generator power: 10 dBm, Axial gap: 15 cm, axes aligned.

Figure 24: Illuminance vs. Axial gap. Signal generator power: 10dBm, Frequency: 6.7 MHz, axes aligned

0

1000

2000

3000

4000

5000

6000

6,55 6,6 6,65 6,7 6,75 6,8

Illu

min

ance

[Lu

x]

Frequency (MHz)

Illuminance vs. frequency

0

10000

20000

30000

40000

50000

60000

70000

80000

90000

100000

7,5 9,5 11,5 13,5 15,5 17,5 19,5

Illu

min

ance

[Lu

x]

Gap (cm)

Illuminance vs. axial gap

33

Figure 25: Illuminance vs. radial misalignment. Signal generator power: 10 dBm, Frequency: 6.7 MHz, Axial gap: 13 cm

Equations

If illuminance is defined as y and the variable in the x-axis as x, equations will be approximated

in each case.

1. Illuminance vs. signal generator power:

2. Illuminance vs. frequency:

3. Illuminance vs. axial gap:

4. Illuminance vs. radial misalignment:

0

5000

10000

15000

20000

25000

0 5 10 15

Illu

min

ance

[Lu

x]

Radial misalignment [cm]

Illuminance vs. radial misalignment

34

DC studies

As consumption in cars and most household goods is made in DC, rectification must be done in

order to prove that wireless energy transmission systems can satisfy those demands. In this

case, a diode-bridge rectifier is used with a capacitance in parallel, so that ripple is minimized.

Resonance frequency is around 6.7 MHz, making it impossible to work with conventional

diodes. Schottky diodes will be used instead, along with polyester film 10uF FACO capacitors.

This way, power, voltage and current will be measured, using a rheostat which can vary its

resistance between 20 and 65 Ω.

It is remarkable that the added capacitance in the rectifier changes the impedance adaptation,

making it out of tune.

DC waveforms

Figure 26: DC current (yellow) and voltage (green) waveforms without parallel capacitance added to the diode bridge rectifier.

35

Figure 27: DC current (yellow) and voltage (green) waveforms with 20 µF parallel capacitance added to the diode bridge rectifier.

Power vs. Signal generator power

In Figure 28, Figure 29 and Figure 30, it is observed that power, current and voltage are mostly

linear in the range from 1 to 16 dBm. From 16 to 19 dBm, the amplifier cannot handle such big

signals by amplifying them linearly, so there is saturation.

Figure 28: Secondary DC power vs. signal generator power at 15 cm axial gap and 6.7 MHz

0

1

2

3

4

5

6

7

8

9

10

0 5 10 15 20

Re

ceiv

ed

po

we

r [W

]


Secondary DC power vs. signal generator power at 15 cm axial gap and 6.7 MHz

20 Ω

30 Ω

38 Ω

45 Ω

50 Ω

55 Ω

65 Ω

36

Figure 29: Secondary DC current vs. signal generator power at 15 cm axial gap and 6.7 MHz

Figure 30: Secondary DC voltage vs. signal generator power at 15 cm axial gap and 6.7 MHz

0

0,1

0,2

0,3

0,4

0,5

0,6

0,7

0 5 10 15 20

Cu

rre

nt

[A]


Secondary DC current vs. signal generator power at 15 cm axial gap and 6.7 MHz

20 Ω

30 Ω

38 Ω

45 Ω

50 Ω

55 Ω

65 Ω

0

5

10

15

20

25

0 5 10 15 20

Vo

ltag

e [

V]


Secondary DC voltage vs. signal generator power at 15 cm axial gap and 6.7 MHz

20 Ω

30 Ω

38 Ω

45 Ω

50 Ω

55 Ω

65 Ω

37

Power vs. Signal generator frequency

In Figure 31, Figure 33 and Figure 34, new results are shown. There is a clear increase of the

received power around 6.4 MHz, instead of the previous 6.7 MHz. Figure 32 shows the

maximum efficiency achieved with every load impedance studied and at which frequency was

that.

Figure 31: Secondary DC power vs. signal generator frequency at 10 dBm signal generator power and 15 cm axial gap

0

5

10

15

20

25

30

6 6,2 6,4 6,6 6,8 7 7,2 7,4

Re

ceiv

ed

po

we

r [W

]

Signal generator frequency [MHz]

Secondary DC power vs. signal generator frequency at 10 dBm signal generator power

and 15 cm axial gap

20 Ω

30 Ω

38 Ω

45 Ω

50 Ω

55 Ω

65 Ω

38

Figure 32: Secondary DC maximal efficiency vs. signal generator frequency at 10 dBm signal generator power and 15 cm axial gap

Figure 33: Secondary DC current vs. signal generator frequency at 10 dBm signal generator power and 15 cm axial gap

68,78%

72,20%

74,82%

69,22%

65,85%

64,47%

58,94%

57,00%

62,00%

67,00%

72,00%

77,00%

6,3 6,4 6,5 6,6

Max

imal

eff

icie

ncy


Secondary DC maximal efficiency vs. signal generator frequency at 10 dBm signal generator power and 15 cm axial gap

20 Ω

30 Ω

38 Ω

45 Ω

50 Ω

55 Ω

65 Ω

0

0,2

0,4

0,6

0,8

1

1,2

6 6,2 6,4 6,6 6,8 7 7,2 7,4

Cu

rre

nt

[A]


Secondary DC current vs. signal generator frequency at 10 dBm signal generator power

and 15 cm axial gap

20 Ω

30 Ω

38 Ω

45 Ω

50 Ω

55 Ω

65 Ω

39

Figure 34: Secondary DC voltage vs. signal generator frequency at 10 dBm signal generator power and 15 cm axial gap

Power vs. Axial gap

Figure 35, Figure 37 and Figure 38 show how received power, current and voltage vary as the

axial gap and load impedance does. Thus, the maximal efficiency at 15cm is achieved with 38

Ω. A useful consequence is displayed in Figure 36. If the system can vary its secondary

impedance, optimality can be obtained along a wide range of axial gaps.

0

5

10

15

20

25

30

35

40

6 6,2 6,4 6,6 6,8 7 7,2 7,4

Vo

ltag

e [

V]


Secondary DC voltage vs. signal generator frequency at 10 dBm signal generator power

and 15 cm axial gap

20 Ω

30 Ω

38 Ω

45 Ω

50 Ω

55 Ω

65 Ω

40

Figure 35: Secondary DC power vs. axial gap at 6.4 MHz and 10 dBm signal generator power

Figure 36: Secondary DC maximal efficiency vs. axial gap at 6.4 MHz and 10 dBm signal generator power

0

5

10

15

20

25

30

8 10 12 14 16 18 20

Re

ceiv

ed

po

we

r [W

]

Axial gap [cm]

Secondary DC power vs. axial gap at 6.4 MHz and 10 dBm signal generator power

20 Ω

30 Ω

38 Ω

45 Ω

50 Ω

55 Ω

65 Ω

71,75% 72,20%

74,82%

70,55%

70,14%

67,87%

66,14%

65,00%

67,00%

69,00%

71,00%

73,00%

75,00%

12,5 13,5 14,5 15,5 16,5 17,5

Max

imal

eff

icie

ncy

Axial gap [cm]

Secondary DC maximal efficiency vs. axial gap at 6.4 MHz and 10 dBm signal generator

power

20 Ω

30 Ω

38 Ω

45 Ω

50 Ω

55 Ω

65 Ω

41

Figure 37: Secondary DC current vs. axial gap at 6.4 MHz and 10 dBm signal generator power

Figure 38: Secondary DC voltage vs. axial gap at 6.4 MHz and 10 dBm signal generator power

0

0,2

0,4

0,6

0,8

1

1,2

8 10 12 14 16 18 20

Cu

rre

nt

[A]

Axial gap [cm]

Secondary DC current vs. axial gap at 6.4 MHz and 10 dBm signal generator power

20 Ω

30 Ω

38 Ω

45 Ω

50 Ω

55 Ω

65 Ω

0

5

10

15

20

25

30

35

40

8 10 12 14 16 18 20

Vo

ltag

e [

V]

Axial gap [cm]

Secondary DC voltage vs. axial gap at 6.4 MHz and 10 dBm signal generator power

20 Ω

30 Ω

38 Ω

45 Ω

50 Ω

55 Ω

65 Ω

42

Power vs. Radial misalignment

The variations of received power, current and voltage owing to radial misalignment are shown

in Figure 39, Figure 41 and Figure 42. Similarly to axial gap, radial misalignment optimality is

achieved by choosing the right impedance for each distance. Figure 40 shows how efficiency

varies along a range of distances, keeping almost flat if the optimal impedance is chosen (2%

decrease if the misalignment is varied a 26.7% of the radius).

Figure 39: Secondary DC power vs. radial misalignment at 6.4 MHz , 15 cm axial gap and 10 dBm signal generator power

0

5

10

15

20

25

30

0 5 10 15 20

Re

ceiv

ed

po

we

r [W

]


Secondary DC power vs. radial misalignment at 6.4 MHz , 15 cm axial gap and 10 dBm

signal generator power

20 Ω

30 Ω

38 Ω

45 Ω

50 Ω

55 Ω

65 Ω

43

Figure 40: Secondary DC maximal efficiency vs. radial misalignment at 6.4 MHz , 15 cm axial gap and 10 dBm signal generator power

Figure 41: Secondary DC current vs. radial misalignment at 6.4 MHz , 15 cm axial gap and 10 dBm signal generator power

72,38% 73,30% 74,82%

69,22%

66,84% 66,84%

64,47%

55,00%

60,00%

65,00%

70,00%

75,00%

0 2 4 6 8 10

Max

imal

eff

icie

ncy


Secondary DC maximal efficiency vs. radial misalignment at 6.4 MHz , 15 cm axial gap

and 10 dBm signal generator power

20 Ω

30 Ω

38 Ω

45 Ω

50 Ω

55 Ω

65 Ω

0

0,2

0,4

0,6

0,8

1

1,2

0 5 10 15 20

Cu

rre

nt

[A]


Secondary DC current vs. radial misalignment at 6.4 MHz , 15 cm axial gap


20 Ω

30 Ω

38 Ω

45 Ω

50 Ω

55 Ω

65 Ω

44

Figure 42: Secondary DC voltage vs. radial misalignment at 6.4 MHz , 15 cm axial gap and 10 dBm signal generator power

0

5

10

15

20

25

30

35

40

0 5 10 15 20

Vo

ltag

e [

V]


Secondary DC voltage vs. radial misalignment at 6.4 MHz , 15 cm axial gap


20 Ω

30 Ω

38 Ω

45 Ω

50 Ω

55 Ω

65 Ω

45

Conclusions and future work

1. In order to handle with more power, resonance frequency should be dramatically

decreased, so that power electronics are more efficient.

2. A way to do so is by having a coil with more turns; the more turns, the better the

magnetic flux will be directed, meaning a smaller leakage flux. This will also decrease

the resonance frequency.

3. Energy should be always rectified in the secondary, as efficiency only decreases from

76.12% to 74.82%. Batteries and inverters can have their energy supply from this DC

source.

4. Change the coil setting to a matrix. This way, smaller coils could be used, increasing

modularity, and a failure in one of them would have a much less important effect

when regarding the whole system. Further research is recommended to verify the

electromagnetic behavior of this setting.

5. An optimization process should be developed, in order to get the optimal

transmission frequencies for the primary and impedance for the secondary. If the

system can vary these, influences of axial and radial distances are minimized and the

system becomes more robust and adaptive.

46

List of Figures

Figure 1: Axial magnetic flux density as a function of receiver coil radius and axial gap ........... 13

Figure 2: Axial magnetic field intensity as a function of receiver coil radius and axial gap ........ 14

Figure 3: Quickfield snapshot ...................................................................................................... 15

Figure 4: screenshot with 1 turn at 6.7 MHz ............................................................................... 16

Figure 5: screenshot with 1 turn at 0.3 MHz ............................................................................... 16

Figure 6: screenshot with 2 turns at 0.3 MHz ............................................................................. 17

Figure 7: screenshot with 2 turns at 6.7 MHz ............................................................................. 17

Figure 8: Smith diagram of coil 1, from 0.3 to 20 MHz ............................................................... 19

Figure 9: Smith diagram of coil 2, from 0.3 to 20 MHz ............................................................... 19

Figure 10: screenshot with the capacitor system and 1-turn coil at 6.7 MHz. The resistance is

1.044Ω and the reactance is 90.56 mΩ ....................................................................................... 21

Figure 11: screenshot with the capacitor system and 1-turn coil at 6.7 MHz. It is seen that the

surroundings are in the lowest point of the plot. ....................................................................... 21

Figure 12: Mutual inductance profile depending on the axial gap ............................................. 22

Figure 13: adaptation circuit schematic ...................................................................................... 24

Figure 14: it is observed that adaptation is good around the resonance frequency, giving -

22.697 dB .................................................................................................................................... 25

Figure 15: Smith chart with series-parallel resonance, 282.8pF in series and 1.53nF in parallel.

50 Ω resistance in secondary. ..................................................................................................... 26

Figure 16: Smith chart with series-parallel resonance, 282.8pF in series and 1.53nF in parallel.

VNA reception input in secondary. ............................................................................................. 26

Figure 17: logarithmic diagram of reflection and transmission coefficients. VNA in secondary. 27

Figure 18: logarithmic diagram of transmission coefficient with VNA in secondary. ................. 28

Figure 19: transmission efficiency vs. Axial gap .......................................................................... 29

Figure 20: non-reflection efficiency vs. Axial gap ....................................................................... 29

Figure 21: total efficiency vs. Axial gap ....................................................................................... 30

Figure 22: Illuminance vs. Signal generator power. Frequency: 6.7 MHz, Axial gap: 15 cm, axes

aligned. ........................................................................................................................................ 31

Figure 23: Illuminance vs. Frequency. Signal generator power: 10 dBm, Axial gap: 15 cm, axes

aligned. ........................................................................................................................................ 32

Figure 24: Illuminance vs. Axial gap. Signal generator power: 10dBm, Frequency: 6.7 MHz, axes

aligned ......................................................................................................................................... 32

Figure 25: Illuminance vs. radial misalignment. Signal generator power: 10 dBm, Frequency: 6.7

MHz, Axial gap: 13 cm ................................................................................................................. 33

47

Figure 26: DC current (yellow) and voltage (green) waveforms without parallel capacitance

added to the diode bridge rectifier. ............................................................................................ 34

Figure 27: DC current (yellow) and voltage (green) waveforms with 20 µF parallel capacitance

added to the diode bridge rectifier. ............................................................................................ 35

Figure 28: Secondary DC power vs. signal generator power at 15 cm axial gap and 6.7 MHz ... 35

Figure 29: Secondary DC current vs. signal generator power at 15 cm axial gap and 6.7 MHz .. 36

Figure 30: Secondary DC voltage vs. signal generator power at 15 cm axial gap and 6.7 MHz .. 36

Figure 31: Secondary DC power vs. signal generator frequency at 10 dBm signal generator

power and 15 cm axial gap.......................................................................................................... 37

Figure 32: Secondary DC maximal efficiency vs. signal generator frequency at 10 dBm signal

generator power and 15 cm axial gap......................................................................................... 38

Figure 33: Secondary DC current vs. signal generator frequency at 10 dBm signal generator


Figure 34: Secondary DC voltage vs. signal generator frequency at 10 dBm signal generator


Figure 35: Secondary DC power vs. axial gap at 6.4 MHz and 10 dBm signal generator power 40

Figure 36: Secondary DC maximal efficiency vs. axial gap at 6.4 MHz and 10 dBm signal

generator power ......................................................................................................................... 40

Figure 37: Secondary DC current vs. axial gap at 6.4 MHz and 10 dBm signal generator power 41

Figure 38: Secondary DC voltage vs. axial gap at 6.4 MHz and 10 dBm signal generator power 41

Figure 39: Secondary DC power vs. radial misalignment at 6.4 MHz , 15 cm axial gap and 10

dBm signal generator power ....................................................................................................... 42

Figure 40: Secondary DC maximal efficiency vs. radial misalignment at 6.4 MHz , 15 cm axial

gap and 10 dBm signal generator power .................................................................................... 43

Figure 41: Secondary DC current vs. radial misalignment at 6.4 MHz , 15 cm axial gap and 10


Figure 42: Secondary DC voltage vs. radial misalignment at 6.4 MHz , 15 cm axial gap and 10


48

List of pictures

Picture 1: HP 8714ET VNA ............................................................................................................. 7

Picture 2: HP E4432B signal generator .......................................................................................... 8

Picture 3: Instituto Torres Quevedo M-54-02 rheostat ................................................................ 8

Picture 4: Amplifier Research 30W1000B ..................................................................................... 9

Picture 5: TES 1332 lux meter ..................................................................................................... 10

Picture 6: E9304A power sensor ................................................................................................. 11

Picture 7: Agilent DSO1052B oscilloscope .................................................................................. 11

Picture 8: practical implementation of the coils. ........................................................................ 16

Picture 9: detail of the constructed capacitor system ................................................................ 20

Picture 10: detail of the practical implementation of the adaptation. ....................................... 25

List of Tables

Table 1: Different results with methods taken from [6] ............................................................. 22

49

Bibliography

[1] K. Finkenzeller, “RFID Handbook: Fundamentals and Applications in Contactless Smart Cards and Identification”, John Wiley and Sons Ltd. , Second edition, 2003, ISBN: 0-470-84402-7

[2] F.E. Tenman, “Radio Engineers’ Handbook”, McGraw-Hill Book Company, 1st edition , 1943

[3] E.B. Rosa and F.W. Grover, “Bulletin of the Bureau of Standards”, Vol.8, Department of Commerce and Labor, 1912

[4] E.B. Rosa and L. Cohen, “Bulletin of the Bureau of Standards”, Vol. 4, Department of Commerce and Labor, 1907-1908

[5] T. Youbok Lee, “Antenna Circuit Design for RFID Applications”, Microchip Technology Inc., 2003

[6] H.L. Curtis and C.M. Sparks, “Scientific papers of the Bureau of Standards N. 492: Formulas, tables and curves for computing the mutual inductance of two coaxial circles”, Vol. 10, Department of Commerce, Washington, 1924

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