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
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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.
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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.
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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
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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
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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.
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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.
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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.
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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.
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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
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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.
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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
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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
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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.
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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.
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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
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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
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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.
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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.
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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
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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.
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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.
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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
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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.
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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
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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.
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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
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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.
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Figure 17: logarithmic diagram of reflection and transmission coefficients. VNA in secondary.
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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
]
Signal generator power [dBm]
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]
Signal generator power [dBm]
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]
Signal generator power [dBm]
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
Signal generator frequency [MHz]
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]
Signal generator frequency [MHz]
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]
Signal generator frequency [MHz]
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
]
Radial misalignment [cm]
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
Radial misalignment [cm]
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]
Radial misalignment [cm]
Secondary DC current 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
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]
Radial misalignment [cm]
Secondary DC voltage 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
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
power and 15 cm axial gap.......................................................................................................... 38
Figure 34: Secondary DC voltage vs. signal generator frequency at 10 dBm signal generator
power and 15 cm axial gap.......................................................................................................... 39
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
dBm signal generator power ....................................................................................................... 43
Figure 42: Secondary DC voltage vs. radial misalignment at 6.4 MHz , 15 cm axial gap and 10
dBm signal generator power ....................................................................................................... 44
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