máster universitario en electrónica...

Universidad Politécnica de Madrid

Centro de Electrónica Industrial

Escuela Técnica Superior de Ingenieros Industriales

Departamento de Automática, Ingeniería Electrónica e Informática Industrial

Máster Universitario en Electrónica Industrial

WIRELESS POWER TRANSFER: CONTROL ALGORITHM TO

TRANSFER THE MAXIMUM POWER

Autor: Javier Rojas Urbano

Tutor: Pedro Alou Cervera

Septiembre, 2016

Trabajo Fin de Máster

I

ACKNOWLEDGMENT

To my future wife Nataly Valencia, our dream, our life together has been always

the principal objective to meet this challenge. It has been a long road and many times it

became difficult, however, your support, your companionship and comprehension was

my impulse to overcome any obstacle and move on. You have always been an inspiration

and your unconditional love has given me the strength to complete this challenge and be

together forever. My Naty, my partner, my friend, my counselor and my complement to

happiness, you will always be the guiding light for our family. Thank you for believe and

trust in me.

To my parents, Arturo Rojas and Carmita Urbano, thanks for yours teachings, you

have been an example in every stage of my life, your advices have been valuable to pursue

and achieve this goal, thanks for always giving me your support.

To Pedro Alou for your support as tutor, your ideas and advice have been

valuables in the project’s development, thanks for your time and effort.

To Secretaria Nacional de Educación Superior, Ciencia, Tecnología e Innovación,

SENESCYT, and Ecuador Government, for its support as the scholarship’s sponsor to

study in Spain and have the opportunity to improve my knowledge in my career, bring it

to Ecuador and in a future collaborate to Ecuador’s progress.

II

PREFACE

This job is developed as part of “Health aware enhanced range wireless power

transfer systems", known as ETHER. It is a cooperation project where Universidad

Politécnica de Madrid (UPM) and Universidad Politécnica de Cataluña (UPC) research

groups are mainly involved. ETHER objective is to develop a wireless power transfer

system for medical applications, specifically a pacemaker charger to improve patient’s

lifestyle decreasing the number of required operations to replace pacemaker battery. This

job was developed in Centro de Electrónica Industrial (CEI) from UPM together with

Carlos Terciado, who works on his final grade job.

Wireless power transmission refers to energy transmission from a source to a

receiver located at a determined distance without the use of cables or conductors, it is

useful where the use of conducting cables is not possible or not preferred, and it provides

mobility and flexibility for consumer electronics. It could deliver power to rotating and

highly mobile industrial equipment, mission critical systems in wet or dirty environments.

WPT isn’t a new concept, in 1893, Nikola Tesla demonstrated the illumination of

vacuum bulbs without using wires at the World Columbian Exposition in Chicago. In

2007, a team at the Massachusetts Institute of Technology (MIT) was successful in

transferring the power wirelessly at a mid-range. They lit a bulb of 60 W at a range of 2

m. In 2014, the Korea Advanced Institute of Science and Technology (KAIST) scientists

had transferred power wirelessly using dipole coil resonant system. The Volvo Group is

working on the possibility of developing a dynamic charging solution for city buses. [1]

The wireless transmission of power can be achieved using electromagnetic

radiation, magnetic coupling and electric field coupling. The magnetic coupling mode is

mainly used for short-range. It is produced when two coils are in close proximity to each

other, magnetic flux caused by current flowing through one coil links itself with the other.

This induces a voltage in the other coil, by the phenomenon known as mutual induction.

Magnetic coupling WPT technologies that are based on two coupled magnetic

resonators to transfer power over distance are knowledge as Resonant Inductive Coupling

(RIC). RIC system has the advantage of obtaining high currents and producing more

magnetic coupling field, increasing the energy transmission distance between the two

coils, which ranged from a few centimeters to over 2.5 [m]. [2]

PREFACE

III

Previous jobs on ETHER project like [3] and [4] had determined operational

parameters and circuit topology. The WPT system determined is a RIC system that consist

of several parts, it includes a high frequency Inverter, the magnetic coupling system,

including primary and secondary coils and resonant capacitors, high frequency active

Rectifier and a DC-DC converter as a voltage regulation module. An additional proposal

includes a third resonant tank that acts as a bridge increasing WPT separation distance,

general concept of these topologies are represented in Figure 1.

InverterPrimary

Resonant Tank

Secondary Resonant

Tank

Active Rectifier

DC-DC converter

(a)

InverterPrimary

Resonant Tank

Secondary Resonant

Tank

Active Rectifier

DC-DC converter

Third Resonant

Tank

(b)

Figure 1. ETHER WPT topologies. (a) Two resonant tanks. (b) Three resonant tanks

This job looks for determining the active power behavior in a RIC system and

propose an adequate control algorithm to achieve the maximum active power transfer in

any perturbation condition to obtain a fast battery charge, it considers as principal

perturbations the resonant components change, because degradation or tolerance, and

coils separation distance variation, because mobility application parameters, they affect

the inductive coupling and vary induced voltage and transferred power.

An equivalent model is determined to analyze the resonant coupling circuit and

determine adequate control variables, a voltage source and an impedance represent the

induced voltage, and the active rectifier and DC-DC converter are represented by a

voltage source. To analyze the circuit, the first harmonic approximation is valid because

it is operating at resonance frequency, Active power behavior is analyzed and control

variables are determined and its influence is explored in Chapter 2. Adequate control

variables expressions to determine the maximum active power operation point are

acquired and graphically analyzed with Matlab. A Simulink simulation includes the active

rectifier as a first validation.

PREFACE

IV

Chapter 3 describes the control variables and active power behavior validation

through simulations that include the effect of the inverter and active rectifier switching.

3 commercial coils set from Würth Elektronik are characterized to obtain proper and

mutual inductances required for the model’s application. The complete circuit scheme is

simulated in SIMPLIS to acquire a more realistic active power’s behavior, the variation

of the control variables is implemented to obtain different results and determine the

absolute maximum power operation point. These results are compared with theoretical

behavior and optimal control values determined with equations acquired in Chapter 2.

Additionally an experimental setup is designed, components’ sizing and selection

criteria are described. The experimental results and its analysis with respect to simulation

results are shown to obtain a practical validation. The experimental process is developed

with the coils’ set 2 because its current’s limits and maximum active power achievable.

In Chapter 4 the control algorithm proposal is described, the control actions are

determined according to the control variables influence analysis. The algorithm control

concept is based on a derivative calculus criteria to find the absolute maximum in a

function. Flux diagram is shown and the algorithm is tested with simulations in Matlab

because it allows to simulate power and control stage together.

Finally, Chapter 5 shows the conclusions extracted from each job step and suggest

some future lines that can be implemented as a job continuation or recommendations to

obtain better results in new implementations.

Keywords: Wireless Power Transfer (WPT), Algoritmo de Control, Marcapasos,

Enlace Resonante Inductivo, Resonant Inductive Coupling (RIC), witricidad, Máxima

Transferencia de Potencia.

UNESCO codes: 3322 (tecnología energética), 3306.01, 3306.02, 3306.09,

3307.19, 3311.10.

V

GENERAL INDEX

1. INTRODUCTION .............................................................................................. 2

1.1 Wireless Power Transfer. ................................................................................... 4

1.2 Resonant inductive coupling .............................................................................. 5

2 CONTROL VARIABLES DETERMINATION.............................................. 10

2.1 RIC System Equivalent Model ........................................................................ 10

2.2 Behavior Analysis ............................................................................................ 16

2.2.1 Graphical Analysis .......................................................................... 16

2.2.2 Equivalent Model Simulation Analysis .......................................... 19

3 CONTROL VARIABLES VALIDATION ...................................................... 26

3.1 Inductive Coupling Characterization ............................................................... 26

3.2 Analysis with Equivalent Model ...................................................................... 30

3.3 RIC System Complete Simulation. .................................................................. 32

3.4 Experimental Resonant Inductive Circuit Design............................................ 42

3.4.1 Primary and Secondary Current Limits .......................................... 42

3.4.2 Resonant capacitors ......................................................................... 44

3.4.3 Mosfet selection .............................................................................. 47

Inverter .................................................................................................. 47

Active Rectifier ..................................................................................... 48

3.5 Experimental Results ....................................................................................... 49

3.5.1 Prototyping Setup ............................................................................ 49

GENERAL INDEX

VI

3.5.2 Experimental Results ...................................................................... 51

4 CONTROL ALGORITHM .............................................................................. 58

4.1 Algorithm concept ........................................................................................... 58

4.2 Flux diagram .................................................................................................... 61

4.3 Algorithm control test ...................................................................................... 64

5 CONCLUSIONS AND FUTURE LINES ....................................................... 70

5.1 Conclusions ...................................................................................................... 70

5.2 Future lines ...................................................................................................... 72

6 LIST OF FIGURES .......................................................................................... 75

7 LIST OF TABLES ........................................................................................... 79

8 APPENDIX A. Matlab Scripts ......................................................................... 80

9 APPENDIX B. Wurten coils data sheets .......................................................... 85

10 REFERENCES ................................................................................................. 86

Chapter 1

INTRODUCTION

CHAPTER 1. INTRODUCTION

2 UNIVERSIDAD POLITÉCNICA DE MADRID (UPM)

1. INTRODUCTION

Present job is developed in the Industrial Electronic Center (CEI) from Madrid’s

Polytechnic University (UPM) as a part of ETHER collaboration project, "Health aware

enhanced range Wireless Power Transfer (WPT) systems”. ETHER objective is to

develop a wireless power transfer system to reach energy transmission in distances

between 10 [cm] to 10 [m], considered as near and far field. The System should provide

from 10 [mW] to 10 [W] of power using magnetic fields. The WPT system is going to be

designed for medical applications.

ETHER Project proposes a pacemaker with wireless charge development to

improve life style in hearth malfunction patients. This proposal reduces the number of

risks and operations required for battery change in actual pacemakers. A wireless power

transfer system charges continuously a pacemaker battery while the patient is sitting down

on a sofa or resting in bed, maximum power transfer is required to ensure maximum

charge in any patient position with respect to the energy transmitter.

Figure 2. ETHER project scheme. [3]

WPT systems have been widely studied for medical applications, especially for

biomedical implants where power and data transfer are required, wired power and data

transfer is possible with transcutaneous wires into the body but it reduces the patient’s

quality of life especially for long-term monitoring applications.

Realization of a medical wireless power system take into account the inclusion of

sensors and electronics of the implanted biomedical device as the load. Commonly loads

begins with a power management unit followed by integrating electronics, and ends with

sensors and actuators.

WIRELESS POWER TRANSFER

JAVIER ROJAS URBANO 3

Implant units are portable, therefore they are powered by a battery; it makes

energy transfer efficiency a critical aspect to consider in the system level design, studies

in this area shows that the inductive link is the weakest point of the system, but it depends

on constructive and physical parameters so efficiency in the implant power management

unit is the improvement objective to obtain a better power transfer. [5]

Figure 3. Pacemarker implant.

ETHER Project is developed in collaboration with some research groups that work

in parallel:

Centro de Tecnología Biomédica (CTB) from UPM, its studies are focused

in possible wireless technology health impact because the use of magnetic

fields at high frequencies.

Departamento de Ingeniería Electrónica from Cataluña’s Polytechnic

University (UPC), they are in charge of the near field WPT.

Grupo de Ingeniería de Radio (GIRA) from UPM, they are in charge of the

far field WPT using radio frequency.

Grupo de Electrónica Industrial del Centro de Electrónica Industrial

(CEI) from UPM, its research is focused in the power electronics required to

near and medium WPT.

In each research group previous jobs have been developed and they establish

operational parameter, limits and explores possible solutions that accomplishes ETHER

objectives and focus on a pacemaker application to improve patient’s lifestyle. In this way

present job explores the active power variation and the possibility to obtain a maximum

power transfer control strategy, It identifies adequate control variables and validate them

with system simulations and an experimental setup.



Previous research like [3] or [4] and ETHER work group research has established

operational parameters where the power transfer required is between 10[mW] and 10[W]

for separation distances between 10[cm] and 10[m] with a transmission frequency of

500[kHz] or 7[MHz] that accomplish electromagnetic exposure limits in SAR; frequency

limits were established by Madrid Polytechnic Biotechnology Center.

1.1 Wireless Power Transfer.

Wireless power transfer, commonly known as WPT, consists in energy transfer

between two physically separate points without cables or any conductor. It is

advantageous than energy transmission techniques using wires from the point of safety,

reliability, low maintenance, and long product life. In [6] Nicolas Tesla proposes that

wirelessly transfer power is possible between two coils using the principle of magnetic

resonance and near-field coupling.

Figure 4. Inductive transfer power concept.

When two coils are in close proximity to each other, magnetic flux caused by

current flowing through one coil links itself with the other. This induces a voltage in the

other coil, by the phenomenon known as mutual induction. It is based on Ampere and

Faraday’s law on which transformers and induction motor works, however in a WPT

system a considerable separation distance between primary and secondary coil is

expected, therefore the leakage flux is thevmore and coupling coefficient is low,

producing poor power transfer. [7]

The wireless transmission of power can be achieved using three modes of

coupling: magnetic coupling, electromagnetic radiation and electric field coupling. WTP

systems can be classified considering the separation distance between transmitter and

receiver, in this way there are far field systems and near field systems

Far field system is when separation distance is bigger than one antenna

wavelength or ten times the transmitter diameter; magnetic and electric fields are



perpendicular and act like an electromagnetic wave, it has omnidirectional behavior and

low efficiency because transmitter is always transferring energy. In the far field radiated

techniques are used, it includes microwaves and laser technologies. Microwave wireless

power transmission is a wide range process in which long distance electric power

transmission becomes possible. Laser wireless power transmission is done by using laser

beam which acts as a source. The laser beam of high intensity is thrown from some

specific distance to the load end. [1]

Near field coupling refers to short separation distance between reception and

emission sides, the distance is less or equal than transmitter diameter. The Energy isn’t

radiated, electric and magnetic fields are separated and transmitter doesn´t transfer energy

when the receptor isn’t in a determined range of distance. The magnetic coupling mode

is mainly used. The power transferred and the efficiency of power transfer is high, but it

has distance limitations. Electric field coupling uses the redistribution of the surface

charge. A high voltage and a high frequency source generate an alternating electric field

to excite the transmitter and couples with the receiver to transfer energy wirelessly [6] [9]

Figure 5. Near field coupling scheme.

1.2 Resonant inductive coupling

Inductive coupling power transfer, also known as ICPT was described in section

1.1, it is applied in short separation distance between transmitter and receiver with good

efficiency, ICPT drawback is that transsmited energy decrease exponecially with

distance, in order to obtain a considerable power transfer in bigger separation distance

resonant inductive coupling, RIC, can be used.

It is a technique to improve energy transmission and include middle separation

distances, where distance is bigger than transmitter diameter. It uses resonance in

transmitter and receiver to obtain bigger currents and produce a stronger magnetic field,

it improves the inductive coupling and increase power transfer with distance. [10]



In order to obtain a RIC system, capacitors are included in the circuit to obtain a

resonant tank that resonate at the same frequency in transmission and reception sides, it

reduce circuit impedance and depends only on its parasitic resistance so coils with high

Q quality factor and capacitors with low ESR are required.

Figure 6. RIC system structure. [3]

RIC systems are very sensitive to distance variations and to conductive interfering

objects, a high Q allows an efficient power transfer in big distances and gives freedom in

relative position between coils, sometimes it is called Highly Resonant Wireless Power

Transfer (HR-RPT). This technology has 40% efficiency approximate in middle distances

and is less than 1% in big distances, ten times transmitter diameter. [3]

Resonant capacitor can be connected in either series or parallel with coils, a total

of four topology could be obtained: Series-Series (SS) topology, Series-Parallel (SP)

topology, Parallel-Series (PS) topology and Parallel-Parallel (PP) topology. [11]

Series-Series. Resonant capacitor is in series with coil in both sides of the RIC.

Output Voltage is a function of current in the receiver side.

Series-Parallel. Resonant capacitor is in series with transmitter coil and in parallel

with receiver coil. Output voltage is equal to the receiver resonant capacitor

voltage.

Parallel-Series. Resonant capacitor is in parallel with transmitter coil and in series

with receiver coil. Output Voltage is a function of current in the receiver side.

Parallel-Parallel. Resonant capacitor is in parallel with transmitter and receiver

coil. Output voltage is equal to the receiver resonant capacitor voltage.



Figure 7. RIC topologies. (a) Series-Series. (b) Series Parallel. (c) Parallel -Series. (d)

Parallel-Parallel. [3]

Each topology has its own advantages and disadvantages, some of them are

explored in [11] and [7], topology selection depends on application, in this job series-

series topology is selected according to [3], all topologies can be analyzed with reflected

load theory and its voltage and current expressions can be obtained.

Table 1. Electric parameters for RIC topologies. [3]

Chapter 2

CONTROL VARIABLES

DETERMINATION

CHAPTER 2 CONTROL VARIABLES DETERMINATION


2 CONTROL VARIABLES

DETERMINATION

This section describes the methodology applied to obtain a control strategy in the

WPT system, the behavior of the active power in a RIC system is analyzed to obtain the

control variables, its influence on active power is analyzed to determine the best way to

modify them, no matter what condition or circuit parameter has changed.

The equations for the control variables are obtained from an equivalent model, a

Matlab script validate them with a numerical analysis, the graphs of the power variation

in a determined range of each control variable are used to explore the behavior of the

active power and the existence of an absolute maximum. The analysis of the circuit

parameters influence in the control variables allows to obtain a proper control strategy.

Simulink simulation allows analyze more complete circuit to include the effect of

others circuit parameters and more realistic behavior of the circuit including square

waveforms.

2.1 RIC System Equivalent Model

In the job presented in [12], the first harmonic approximation in the wireless

power transfer system is used to analyze active power variation and coupling between

primary and secondary inductors in a RIC scheme.

(a)



(b)

Figure 8. Resonant circuit scheme. (a) First harmonic approximation equivalent circuit . (b)

Circuit model with two equivalent sources to model the inductive coupling.

The output of the circuit is connected to a load 𝑍𝐿, the real and imaginary parts

represent the active and reactive power transfer. A control of 𝑍𝐿 is required to obtain the

maximum power transfer.

𝑍𝐿 = 𝑅𝐿 + 𝑗𝑋𝐿.

(1)

𝑍𝑂 = 𝑍𝑆 +𝑋𝑀

2

𝑍𝑃

(2)

𝑍𝐿 = 𝑍𝑂∗

(3)

𝑍𝐿 =𝑉𝐿

1

𝐼𝐿1 =

4

𝜋

|𝑉𝐿|

|𝐼𝐿|(cos(𝜑) − 𝑗𝑠𝑖𝑛(𝜑))

(4)

According to equation (4) 𝑍𝐿 can be controlled with voltage and current across it, it is

possible when 𝑍𝐿 is considered as an equivalent representation of an active rectifier and DC-DC

converter, the amplitude of the voltage and current across 𝑍𝐿 (|𝑉𝐿|, |𝐼𝐿|) and the phase

angle between them (φ) can be controlled with control signals and duty cycle in the active

rectifier and DC-DC converter respectively.



Figure 9. Circuit scheme to include the control variables.

A specific value of 𝑍𝐿 produces the maximum active power in the load, in [12] the

expressions for optimal values of 𝜑, |𝑉𝐿| and |𝐼𝐿| are determined, but a small analysis in

the equivalent circuit shows that a change in |𝑉𝐿| produce a change in |𝐼𝐿|, in the same

way a change in 𝜃 produce a change in 𝛾 and 𝜑, since 𝜑 = 𝜃 − 𝛾 where , 𝜃 is the 𝑉𝐿 phase

and 𝛾 is the 𝐼𝐿 phase, both of them referred to the input voltage in the resonant inductive circuit

𝑉𝐼𝑁.

It means that the control could be realized only with variation in |𝑉𝐿| and 𝜃, parameters

of the DC-DC converter and active rectifier respectively, so they can be stablished as

control variables. To analyze this idea 𝑉𝐿 is represented by a sinusoidal voltage source,

connected to an equivalent circuit which represents the resonant inductive circuit voltage

transfer, it is obtained with the Thevenin’s equivalent theorem, this is represented in

Figure 10.

Figure 10. Circuit to analyze |𝑽𝑳| and 𝜽 as Active Power control variables.

The Thevenin’s equivalent voltage and impedance are obtained using classical

circuit analysis in the circuit showed in Figure 8. (b) where 𝑉𝐼𝑁 is the circuit reference



and its phase is 0°. The open and short circuit equivalents showed in Figure 11 are used

to determine respective values.

(a)

(b)

Figure 11. (a) Open circuit equivalent. (b) Short circuit equivalent.

𝑉𝑇𝐻 = 𝑗𝑋𝑀𝐼𝑃 → 𝐼𝐿 = 0 (5)

𝑉𝑇𝐻 =𝑤𝑀|𝑉𝑖𝑛|

𝑍𝑃 ⌊90°

(6)

𝑍𝑇𝐻 =𝑉𝑇𝐻

𝐼𝐿 (7)

𝑍𝑇𝐻 = [(𝑤𝑀)2

𝑍𝑃+ 𝑍𝑆] ⌊𝛿

(8)



𝛿 is the phase angle of 𝑍𝑇𝐻 and its value is obtained evaluating the expression of

𝑍𝑇𝐻 with real and imaginary part of 𝑍𝑃 and 𝑍𝑆. With this expressions the active power in

𝑉𝐿 can be obtained as follows:

𝑃 = 𝑅𝑒𝑆 (9)

𝑆 = 𝑉𝐿 . 𝐼𝐿∗

(10)

𝐼𝐿 =𝑉𝑇𝐻⌊90° − 𝑉𝐿⌊𝜃

𝑍𝑇𝐻⌊𝛿

(11)

𝐼𝐿 = −𝑉𝐿 . cos(𝜃 − 𝛿) − 𝑉𝑇𝐻. sin(𝛿) + 𝑗(𝑉𝐿 . sin(𝜃 − 𝛿) − 𝑉𝑇𝐻. 𝑐𝑜𝑠(𝛿))

𝑍𝑇𝐻

(12)

𝑃 =1

𝑍𝑇𝐻(𝑉𝑇𝐻,𝑅𝑀𝑆. 𝑉𝐿,𝑅𝑀𝑆. 𝑠𝑖𝑛(𝜃 + 𝛿) − 𝑉𝑇𝐻,𝑅𝑀𝑆

2. 𝑐𝑜𝑠(𝛿)) (13)

It’s clear that 𝑃 = 𝑓(𝑉𝐿 , 𝜃) and 𝐼𝐿 = 𝑔(𝑉𝐿 , 𝜃) because 𝑉𝑇𝐻, 𝑍𝑇𝐻 and 𝛿 are defined

by the circuit parameters. Looking the equation (6) and (8), the maximum voltage transfer

in the inductive coupling is when 𝑉𝑇𝐻 is a maximum and 𝑍𝑇𝐻 minimum, it can be

achieved with the minimum value of the primary and secondary impedance, 𝑍𝑃 and 𝑍𝑆,

so the best option is to work in the resonance frequency for both sides of the circuit, this

feature is explored in [8] and [13].

According to equation (13) the variation of the active power has sinusoidal

behavior, and a maximum can be achieved with optimal value of |𝑉𝐿| and 𝜃, according to

the first derivate theorem they can be found when the derivate expression of each control

variable is equal to zero.

𝜕𝑃

𝜕𝑉𝐿=

1

𝑍𝑇𝐻(𝑉𝑇𝐻,𝑅𝑀𝑆𝑠𝑖𝑛(𝜃 + 𝛿) − 2𝑉𝑇𝐻,𝑅𝑀𝑆. 𝑐𝑜𝑠(𝛿))

(14)

𝜕𝑃

𝜕𝑉𝐿= 0 → 𝑉𝐿.𝑜𝑝𝑡 =

𝑉𝑇𝐻

2

sin (𝜃 + 𝛿)

cos (𝛿)

(15)

𝜕𝑃

𝜕𝜃=

1

𝑍𝑇𝐻(𝑉𝑇𝐻,𝑅𝑀𝑆. 𝑉𝐿,𝑅𝑀𝑆. 𝑐𝑜𝑠(𝜃 + 𝛿))

(16)



𝜕𝑃

𝜕𝜃= 0 → 𝜃𝑜𝑝𝑡 =

𝜋

2− 𝛿

(17)

According to Equation (15) and (17) a sinusoidal behavior of the active power

variation for each control variable is expected, and a possible control strategy based in

the derivative calculus could be determined. Equation (15) and (17) shows for each

control variable the existence of a unique maximum and when the optimal value is

reached in both of them the absolute maximum for the active power is obtained.

Since 𝑉𝐿 is the amplitude of the firs harmonic of voltage in the secondary active

rectifier, the relation with the DC voltage 𝑉𝑟 specified in Figure 9 needs to be included.

𝑉𝑇𝐻 depends on |𝑉𝑖𝑛|, voltage amplitude of the first harmonic from the primary inverter

and the relation with the DC voltage 𝑉𝑠 showed in Figure 9 also needs to be included in

the analysis to have controllable expressions for the control variables because 𝑉𝑠 and 𝑉𝑟

can be modified in the circuit.

(a)

(b)

Figure 12. Square and first harmonic waveforms in (a) primary inverter (b)

secondary active rectifier.

|𝑉𝑖𝑛| =4

𝜋

𝑉𝑠

2=

2

𝜋𝑉𝑠

(18)



|𝑉𝐿| =4

𝜋𝑉𝑟

(19)

𝑉𝐿.𝑜𝑝𝑡 =4

𝜋𝑉𝑟 =

𝑤𝑀2𝜋 𝑉𝑆

𝑍𝑃

2.sin (𝜃 − 𝛿)

cos (𝛿) (20)

𝑉𝑟,𝑜𝑝𝑡 =𝑤. 𝑀

4. 𝑍𝑃. 𝑉𝑆.

sin (𝜃 − 𝛿)

cos (𝛿)

(21)

In this job 𝑉𝑟 is considered as a DC voltage source, however, in the complete

circuit it is the output voltage from a DC-DC converter so its optimal equation must be

used to calculate the optimal value of duty cycle, 𝐷𝑜𝑝𝑡, in a converter with 𝑉𝑙 as a DC

input voltage

2.2 Behavior Analysis

In order to have a clearer idea about the behavior of the active power with control

variables determined in 2.1 and in different circuit parameters’ scenarios, the problem is

solved using a Matlab script to include numerical values in the equations. It obtains graphs

to analyze the interaction of each control variable in the complete system and determine

which one is principal or critical to control.

Additionally to obtain a more realistic analysis a Simulink simulation is developed

to include more electric circuit parameters and obtain comparable results with the first

harmonic approximation and analyze its precision.

2.2.1 Graphical Analysis

The equivalent circuit showed in Figure 9 is solved using the classical circuit

analysis theory where electrical variables are expressed as phasors to make a sinusoidal

analysis. The objective is a behavior analysis, so the voltage and impedance values are

selected around 1 to obtain a per unit system, it avoid the influence of frequency and

results can be generalized.

A Matlab script solves the circuit for different electrical parameters with a swept

of 𝜃 while |𝑉𝐿| is kept constant, Thevenin’s impedance value changes on its imaginary



part to analyze the influence of resonant circuit parameters. Active power graphs are

generated to visualize its behavior with the variable parameters.

Table 2. Parameters used in the Matlab script.

Circuit

Parameter Description

𝑉𝑇𝐻 𝑉𝐼𝑁 = 1⌊0°. Its value is kept constant in each case, it’s the circuit

reference.

𝑍𝑇𝐻 𝑅𝑇𝐻 = 1 is kept constant in each case, 𝑋𝑇𝐻 vary from -1.5 to 1.5

in steps of 0.5, each case is analyzed individually.

𝑉𝐿 In each case there is a phase swept from -180° to 180° and the

magnitude vary in steps around its optimal for each 𝑍𝑇𝐻 value.

The values of 𝐼𝐿 in the circuit, S and P in the voltage source 𝑉𝐿 are calculated for

each value of 𝜃, P is saved in a vector, then a circuit parameter like 𝑋𝑇𝐻 and 𝑉𝐿 are

changed and the calculus is developed again, the script plots some graphs in the same axis

to compare them and allows a results analysis with a clear vision of the power behavior

in the circuit.

To select variation of |𝑉𝐿 |, its optimal value is calculated with the equation (15)

and a step before and after are determined for the first calculus case. For simulation

|𝑉𝐿 | = 0.5, 0.55, 0.6 are established for calculus in concordance with (22)

𝑍𝑇𝐻 = 1 + 𝑗0.5 → 𝜃𝑜𝑝𝑡 = 63.44° → |𝑉𝐿 | 𝑜𝑝𝑡 = 0.56

(22)

(a)

-200 -100 0 100 200-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4Xth=0.5

phi (angulo de V2)

Active P

ow

er

P

VL=0.5

VL=0.55

VL=0.6

-200 -100 0 100 200-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3Xth=0.55

phi (angulo de V2)

Active P

ow

er

P

VL=0.5

VL=0.55

VL=0.6

-200 -100 0 100 200-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3Xth=0.6

phi (angulo de V2)

Active P

ow

er

P

VL=0.5

VL=0.55

VL=0.6



(b)

(c)

Figure 13. Plots obtained with the Matlab script. (a) Phase swept for different amplitude

with positive values for 𝑿𝑻𝑯, (b) Zoom in figure (a), (c ) phase swept for different amplitude

with negative values for 𝑿𝑻𝑯.

Figure 13 shows the active power sinusoidal behavior for each control variable

and circuit condition, validating the equations obtained before. It’s clear the existence of

a unique maximum point with an optimal |𝑉𝐿| and 𝜃 . In Figure 13 (a) the optimal 𝜃 is

less 63.44° while in Figure 13 (c) is 116.56°, this result validate equation (17). Figure 13

(b) shows a zoom of figure (a), the maximum active power in the first one is 0.25 with an

optimum 𝑉𝐿 of 0.55 validating the equations. It also shows that different circuit

parameters require an adjustment in the optimal control variables.

0 20 40 60 80 1000.2

0.21

0.22

0.23

0.24

0.25

0.26Xth=0.5

phi (angulo de V2)

Active P

ow

er

P

VL=0.5

VL=0.55

VL=0.6

0 20 40 60 80 1000.2

0.21

0.22

0.23

0.24

0.25

0.26Xth=0.55

phi (angulo de V2)

Active P

ow

er

P

VL=0.5

VL=0.55

VL=0.6

0 20 40 60 80 1000.2

0.21

0.22

0.23

0.24

0.25

0.26Xth=0.6

phi (angulo de V2)

Active P

ow

er

P

VL=0.5

VL=0.55

VL=0.6

-200 -100 0 100 200-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4Xth=0.5

phi (angulo de V2)

Active P

ow

er

P

VL=0.5

VL=0.55

VL=0.6

-200 -100 0 100 200-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3Xth=0.55

phi (angulo de V2)

Active P

ow

er

P

VL=0.5

VL=0.55

VL=0.6

-200 -100 0 100 200-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3Xth=0.6

phi (angulo de V2)

Active P

ow

er

P

VL=0.5

VL=0.55

VL=0.6



According to the graphs a change in |𝑉𝐿| doesn’t affect the optimal value of 𝜃 and

also shows that active power is more affected by 𝜃 than |𝑉𝐿|, so as a control strategy 𝜃

optimal must be found first and then |𝑉𝐿| optimal using the equations (15) and (17).

Figure 14. Plots for different values of 𝑿𝑻𝑯.

Figure 14 is obtained to compare the effect of changes in the circuit parameters’,

once the maximum power point is reached a change in the equivalent impedance produces

a small change in the power, so a small adjust is required and the control has enough time

to produce it since the difference in power isn’t bigger.

2.2.2 Equivalent Model Simulation Analysis

Simulink integrates some electric elements to implement a more complete circuit

in order to analyze a realistic behavior of the circuit. The active rectifier is included. To

control 𝜃 its control signals are synchronized with the Thevenin’s voltage phase. A DC

voltage source is included to control |𝑉𝐿|, together act as a square voltage source with

variable phase and voltage to control the power in the circuit.

Figure 15. Thevenin’s equivalent and active rectifier used in Simulink.

-200 -100 0 100 200-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3VL=0.5

phi (angulo de V2)

Act

ive

Pow

er P

Xth=0.5

Xth=1

Xth=1.5

-200 -100 0 100 200-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6VL=0.55

phi (angulo de V2)

Act

ive

Pow

er P

Xth=0.5

Xth=1

Xth=1.5

-200 -100 0 100 200-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4VL=0.6

phi (angulo de V2)

Act

ive

Pow

er P

Xth=0.5

Xth=1

Xth=1.5



𝑍𝑇𝐻 is represented with a RLC load to include changes in the imaginary part, so

an analysis of tolerance and degradation in reactive elements can be included. The

universal bridge is selected to act as an ideal switch full bridge without consider the

parasitic effects and switching power losses because the analysis objective is the behavior,

not the numerical values.

Figure 16. Active Rectifier control signals generator.

The Simulink circuit showed in Figure 16 is the control signal generator for the

active bridge, it takes the Thevenin’s voltage phase as an input and generates square

waveforms with a specific delay based in the values of ‘phi’ and ‘Tsw’, variables’ names

for 𝜃 and for the switching period respectively, it also generates a variable dead time. The

circuit is valid for −180° ≤ 𝑝ℎ𝑖 ≤ 180°.

Figure 17 . Output Power measurement’s circuit.

Simulink makes a continuous time simulation, the current and voltage’s

continuous data are acquired and multiplied point by point to obtain the instantaneous

power, the mean value is calculated to determine the active power, this value is stored in



a vector only at the end of simulation, in the circuit steady state. It is obtained with the

circuit in Figure 17.

A Matlab script controls the simulation in Simulink, it allows to specify the circuit

and simulation parameters, simulation runs four times the switching period to obtain

steady state values. The script modifies, simulate and acquire data from Simulink to

obtain a complete plot of the active power in the complete range of 𝜃 and for some 𝑉𝐿

values, enough to validate conclusions from the past sections

Figure 18. Complete circuit scheme in Simulink

Simulink circuit components’ described above are integrated in the complete

circuit scheme showed in Figure 18. Simulation waveforms are monitoring with the scope

Simulink tool and the active power data, Po, is sent to the workspace and stored. Figure

19 shows waveforms for different values of θ, the phase difference obtained with the

circuit is noticed in the graphs.



Figure 19. Waveforms obtained in Simulink.

Waveforms for VL, IL and P don’t show sinusoidal behavior because the

introduction of the active rectifier, the active power shows stability at the end of the

simulation time validating the acquisition criteria of this data at this time.

(a) (b)

Figure 20. Active Power as a function of control 𝜽 for different values of |𝑽𝑳|. (a) Plot

obtained with Simulink simulation, (b) Plot obtained with Matlab script circuit solver.

-200 -150 -100 -50 0 50 100 150 200-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

-200 -100 0 100 200-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4Xth=0.5

phi (angulo de V2)

Act

ive

Pow

er P

VL=0.5

VL=0.55

VL=0.6

-200 -100 0 100 200-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3Xth=0.55

phi (angulo de V2)

Act

ive

Pow

er P

VL=0.5

VL=0.55

VL=0.6

-200 -100 0 100 200-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3Xth=0.6

phi (angulo de V2)

Act

ive

Pow

er P

VL=0.5

VL=0.55

VL=0.6



Plots are similar and shows the same behavior analyzed in the past section

validating the equivalent model and conclusions. The introduction of the active filter

doesn’t affect the active power behavior, the difference in the values is justified because

𝑉𝐿 isn’t sinusoidal source and Simulink simulation requires the introduction of frequency,

but plots are valid to determine the existence of the absolute maximum and validate the

equations for the optimal values of the control variables and control strategy in a more

realistic scenario.

Chapter 3

CONTROL VARIABLES

VALIDATION

CHAPTER 3 CONTROL VARIABLES VALIDATION


3 CONTROL VARIABLES VALIDATION

In this section the equivalent model and equations described in Section 2.1 are

validated with a RIC system implementation. Commercial inductors designed for wireless

power transfer applications from Würth Elektronik are selected. Transmission and

reception coils with theirs self- inductance are together in a set, so its characterization is

developed to obtain the inductive coupling parameters and RIC circuit components.

With the switching frequency established in ETHER project mentioned in chapter

1. and the inductive coupling parameters, the equivalent model is determined and its

power transfer capacity is explored. For each coupled inductor´s set the control variables

optimal values are calculated and analyzed to suggest the most suitable set for an

experimental implementation and validation.

SIMPLIS simulation is developed with the inductive coupled circuit parameters

to obtain approximated results with respect a practical setup because the primary inverter

and secondary active rectifier are included. Simulation data can be used as an intermediate

comparison between the equivalent model and a practical setup.

Finally, components selection for an experimental setup is described, voltage and

current limits are considered because in a RIC system they can become bigger,

additionally switching losses are considered for an adequate power measurement.

3.1 Inductive Coupling Characterization

Würth Elektronik eiSos is a member of the Wireless Power Consortium (WPC)

and Alliance for Wireless Power (A4WP) now known as “Rezence” and has been

developing various wireless transmitter and receiver coils compliant with Qi standard in

proprietary solution. Because of its experience six of its coils are acquired, they are

individual elements so sets of two are performed to stablish an inductive coupling.

Figure 21. Coils from Würth Elektronik.



Table 3. Transmitter and receiver coils

Refererence

Würth

Elektronik

Element’s

code

𝑳

[𝒖𝑯] 𝑸

𝑰𝑹,𝒎𝒂𝒙

[𝑨]

𝑰𝑺𝑨𝑻

[𝑨]

𝑹𝑫𝑪,𝒎𝒂𝒙

[Ω]

𝒇𝑹𝒆𝒔

[𝑴𝑯𝒛]

Transmitter

TX1 760308100141 10 180 9 16 0.03 11

TX2 760308100110 24 180 6 10 0.1 5

TX3 760308101105 3.3 30 3 6 0.083 20

Receiver

RX1 760308102207 8 30 5 10 0.08 16

RX2 760308101220 12.6 20 1.1 2.5 0.34 19

RX3 760308101216 6.6 10 0.5 1 0.44 32

In order to obtain controlled conditions, transmitter and receiver coils are putting

together in a way that 0.5 [cm] separation distance is kept constant, datasheet specifies

the inductance value in each coil, it and other values are sowed in Table 3 , however in

the set the value of self-inductance and mutual inductance at specific frequency needs to

be determined.

Figure 22 . Coil’s construction set.

Table 4. Coils sets

Set number Transmission Coil Reception Coil

1 760308100141 760308101220

2 760308101105 760308101216

3 760308100110 760308102207



An impedance analyzer is used to determine the set resonance frequency with

open circuit measurements in both sides of the coil’s set. For all coils sets the proper

resonance frequency is below 4 [MHz], ETHER project’s specifications establishes

operating frequency of 500[kHz] or 5[MHz] so the first one is chosen as operating

frequency.

Figure 23. Measurements in the impedance analyzer.

At operation frequency and with the impedance analyzer resistance and

inductance are measured, coils set configuration and measurements to determine the

inductive coupling parameters are developed according to the procedure specified in [14].

Table 5 shows the measurements obtained for the three test approach.

Table 5. Measurement obtained from the coils set with an impedance analyzer

Frequency [Hz] 5.00E+05

Coils set SET 1 SET 2 SET 3

R1 [ohm] 3.11E-01 1.73E-01 3.19

Locp [uH] 10.55 3.68 36.99

Lsc [uH] 9.88 3.62 16.31

Locs [uH] 13.36 7.37 12.35

R2 [ohm] 1.41 1.38 1.51

Locp is the measurement at transmission side with reception side in open circuit.

Locs is the measurement at reception side with transmission side in open circuit.

Lsc is the measurement at transmission side with reception side in short circuit

R1 is the resistance measurement in transmission side

R2 is the resistance measurement in reception side



Figure 24. Inductive coupling equivalent model

𝐿𝑃 = 𝐿𝑂𝐶𝑃 (23)

𝐿𝑆 = 𝐿𝑂𝐶𝑆 (24)

𝑀 = √(𝐿𝑂𝐶𝑃 − 𝐿𝑆𝐶). 𝐿𝑂𝐶𝑆 (25)

𝑅𝑃 = 𝑅1 (26)

𝑅𝑆 = 𝑅2 (27)

𝐶𝑟 =1

(2𝜋𝑓)2. 𝐿

(28)

Equations from (23) to (27) are applied in each coil set and theirs parameters are

obtained. To complete the resonant inductive circuit resonant capacitors are calculated at

500 [kHz] with equation (28), Table 6 shows the characterization results.

Table 6. Inductive coupling sets models

Coil Set R1 [Ω] Cr1 [F] L1 [uH] M [uH] L2 [uH] Cr2 [F] R2[Ω]

SET 1 0.31113 9.60E-09 10.55 2.99 13.36 7.58E-09 1.41

SET 2 0.17275 2.75E-08 3.68 0.66 7.37 1.37E-08 1.38

SET 3 3.19 2.74E-09 36.99 15.98 12.35 8.20E-09 1.51

Set 3 has the biggest value of M, it’s the better coupling set and according to the

equivalent model it could produce the best power transfer, however, in resonance the

impedance depends only on its resistance value, set 2 has the less impedance and could

produce a good power transfer.



3.2 Analysis with Equivalent Model

Coil set’s parameters are used in the equations of the equivalent model and the

generated active power and optimal values for control variables are calculated to predict

its behavior in concordance with the model described in section 2.1.

Frequency parameter is determined by ETHER project and the criteria mentioned

in section 3.1. ETHER project also defines input voltage and output active power

parameters, however, to obtain a measurable active power inclusive with considerable

switching losses an input voltage 𝑉𝑆 = 15.7 [𝑉] is used to obtain a |𝑉𝑖𝑛| = 10 [𝑉]

according to equation (18). Output active power isn’t considered a specified numeric

value because this job tries to extract the maximum active power whatever condition.

Table 7 shows the values obtained from the equivalent model.

Table 7. Equivalent model values for each coupling set.

|𝑽𝑻𝑯| ⌊𝑽𝑻𝑯 |𝒁𝑻𝑯| 𝜹 𝜽𝒐𝒑𝒕 𝑽𝒓𝒐𝒑𝒕 Pmax [W]

SET 1 302.09 90.0 285.36 0.0 90.0 118.63 39.9774

SET 2 120.93 90.0 26.6 0.0 90.0 47.49 68.7221

SET 3 157.39 90.0 791.69 -2.55E-13 90.0 61.81 3.9112

Set 2 shows the biggest maximum active power, it’s reasonable because it has the

less equivalent impedance. Set 1 has the biggest voltage transfer but its equivalent

impedance is big, it reduces the power transfer capability. Set 3 presents the less power

transfer principally because it has the biggest equivalent impedance.

The value of 𝜃𝑜𝑝𝑡 is 90° for all coil’s set, it’s because in resonance 𝛿 = 0. The

Value of |𝑉𝐿|𝑜𝑝𝑡 is different in each set, set 1 requires a big voltage value while set 2 and

3 are relatively closer. Set 3 is the less attractive because its lower maximum active power,

in a practical setup the inclusion of power losses could reduce this value and make it

difficult to measure, for this reason set 1 and 2 seems the most suitable, control voltage

in set 2 is easy to obtain so it could be the best choice for a practical setup.

Consider tolerance and degradation of capacitors in time, it’s important to analyze

its variation over the maximum active power and the control variables to achieve it. A

variation of ±10% in the reception side resonance capacitor is analyzed in its results are

showed in Table 8 and Table 9.



Table 8. Equivalent model values with +10% variation in reception side resonant capacitor


SET 1 302.0985 90.0 285.38 0.7661 89.2 118.60 39.9776

SET 2 120.9300 90.0 26.727 4.517 85.5 47.05 68.5984

SET 3 157.3867 90.0 791.70 0.2553 89.7 61.80 3.9110

Table 9. Equivalent model values with -10% variation in reception side resonant capacitor


SET 1 302.1000 90.0 285.39 -0.9363 90.9 118.59 39.9789

SET 2 120.9320 90.0 26.768 -5.5151 95.5 46.83 68.5878

SET 3 157.3867 90.0 791.7 -0.312 90.3 61.80 3.9110

Variation in resonant capacitor affects to the equivalent impedance, apparently the

module variation is minimum because its real component still dominating, but phase

shows a change, it isn’t bigger, but 𝜽𝒐𝒑𝒕 and |𝑽𝑳|𝒐𝒑𝒕 require a small adjust to obtain the

maximum active power at this condition. The minimum active power change shows a

tolerance range for the control action because its variation is less than 1%.

To explore the active power behavior in each coupled inductor set its variation

graphs are obtained with variation of 𝜽 and 𝑽𝑳 according to equation (13). They are shown

in Figure 25 and allow to analyze the expected behavior in a practical setup.

(a)

-200.0000

-150.0000

-100.0000

-50.0000

0.0000

50.0000

-200 -100 0 100 200

Active power variation

Vr=90 Vr=118 Vr=118.63 Vr=119 Vr=140



(b)

(c)

Figure 25. Active power variation in coupled inductor sets. (a) Set 1 (b) Set 2 (c) Set 3.

3.3 RIC System Complete Simulation.

Simplis simulation allows the inclusion of the primary inverter, coupling effect,

secondary active rectifier and control signals in a complete simulation, it allows to obtain

similar results than a practical setup of the circuit and it can be considered as a valid

comparison and validation method for the equivalent model described in section 2.1.

The analysis realized in [8], [4] and [13] is based on a “T model” for coupled

inductors, it is determined by quadrupoles theory; however theory shows that “T Model”

is a coupled circuit analysis tool and when the mutual inductance is bigger enough it’s

not physically realizable because it requires negative inductance.

-250.0000

-200.0000

-150.0000

-100.0000

-50.0000

0.0000

50.0000

100.0000

-200 -100 0 100 200


Vr=45 Vr=47 Vr=47.49 Vr=48 Vr=50

-15.0000

-10.0000

-5.0000

0.0000

5.0000

-200 -150 -100 -50 0 50 100 150 200


Vr=55 Vr=61 Vr=61.81 Vr=62 Vr=65



Figure 26. T model for coupled inductors.

Coupled inductors sets used in this work have a small separation distance, as

mentioned in section 3.1, and its mutual inductance has a big value specially in set 3, for

this reason “T model is discarded in this analysis and the 3 sets of coupled inductors are

simulated with the model showed in Figure 24.

Inverter and active rectifier are simulated with ideal switches and its on resistance

is set to 1 [uΩ] to avoid the effect of switching power losses and obtain comparable results

with the equivalent model’s results. Simulation includes control signals generators based

in comparators, active rectifier control includes a control circuit that is synchronized with

inverter control to obtain a phase control, and the voltage amplitude is simulated and

controlled with a DC voltage source.

Simulations are executed in the same conditions than section 3.2 to compare

results, multi- step simulation helps to obtain a phase swept in active rectifier, power

probe measures the instantaneous power in DC voltage, 𝑉𝑟, simplis tools are used to

determine the active power with the mean value of instantaneous power in each

simulations. The process is repeated for different 𝑉𝑟 values, they are changed manually.

(a)



(b)

Figure 27. Simplis simulation scheme. (a) Power stage and resonant inductive model. (b)

Control signals generators.

Figure 27 shows the circuit implemented in Simplis for simulation, figure (a)

shows the complete power stage with the measurement probes to monitor its behavior;

figure (b) shows the control stage, it includes a dead time generator to analyze a real

behavior with control signals. To obtain comparable values with equivalent model, dead

time isn’t considered because it influence on |𝑉𝐿|.

Figure 28. Waveforms obtained with simplis for Set 1 in maximum power conditions .

Ip / A

Y2

-10

-6

-2

2

6

10

time/uSecs 2uSecs/div

0 2 4 6 8 10 12

Vin / V

Y1

-0

2

4

6

8

10

12

14

Is / m

A

Y2

-800

-600

-400

-200

0

200

400

600

800


0 2 4 6 8

Vo /

V

Y1

-60

-40

-20

0

20

40

60


0 2 4 6 8 10

Pout

/ W

-30

-20

-10

0

10

20

30

40

50



Figure 28 shows waveforms of voltage and current on both sides of the circuit for

set 1 with optimal control variables’ values instead of Figure 29 which has a different

value of θ; primary current shows a sinusoidal shape because the circuit is switching at

the resonance frequency, θ variation doesn’t affect the shape but in optimal conditions

this current is in phase with the input voltage and produce maximum magnetic field and

coupling. Secondary current isn’t sinusoidal because the active rectifier phase shift, but

in optimal conditions it has less distortion and it will produce more active power than

reactive power at the output. Instantaneous power has negative values because the

secondary current waveform however in optimal condition negative area is minimum so

power transferred to the load is bigger. Active power is obtained with the mean value of

instantaneous power waveform.

Figure 29. Waveforms obtained with simplis for Set 1 with θ=30°.

Waveforms for the other coil sets are similar than the figures analyzed and

generates same observations. For each coils set a table with numerical values and its

graphs are presented to compare with model values obtained in section 3.2.

Ip /

A

Y2

-8

-4

0

4

8


0 2 4 6 8 10

Vin

/ V

Y1

-0

4

8

12

Is /

A

Y2

-1

-0.6

-0

0.6

1


0 2 4 6 8 10

Vo /

V

Y1

-60

-20

20

60


0 2 4 6 8

Pou

t /

W

-40

-20

0

20

40

60



Table 10. Active power data in Simplis simulation and equivalent model for Set 1

VL

VL

phi

90.00 118.00 118.63 119.00 140.00

90.00 118.00 118.63 119.00 140.00

-180

Sim

plis

sim

ula

tio

n

-23.177 -39.836 -40.263 -40.515 -56.072

Equ

ival

en

t m

od

el

-23.0082 -39.5513 -39.9748 -40.2245 -55.6741

-150 -53.324 -79.363 -80.000 -80.376 -102.967 -53.3365 -79.3151 -79.9509 -80.3253 -102.8515

-120 -73.853 -106.182 -106.960 -107.418 -134.663 -75.5383 -108.4242 -109.2154 -109.6811 -137.3877

-90 -84.03 -119.622 -120.474 -120.976 -150.732 -83.6648 -119.0789 -119.9269 -120.4261 -150.0288

-60 -75.738 -108.75 -109.544 -110.012 -137.834 -75.5383 -108.4242 -109.2154 -109.6811 -137.3877

-30 -53.293 -79.321 -79.959 -80.334 -102.918 -53.3365 -79.3151 -79.9509 -80.3253 -102.8515

0 -23.15 -39.801 -40.227 -40.478 -56.029 -23.0082 -39.5513 -39.9748 -40.2245 -55.6741

30 6.996 -0.275174 -0.490 -0.617 -9.134 7.3201 0.2124 0.0013 -0.1238 -8.4967

60 29.434 28.853 29.086 28.757 25.455 29.5220 29.3215 29.2658 29.2320 26.0395

90 36.987 39.209 39.210 39.207 37.874 37.6484 39.9762 39.9774 39.9770 38.6806

120 29.411 27.533 27.466 27.424 23.928 29.5220 29.3215 29.2658 29.2320 26.0395

150 6.965 -0.315 -0.531 -0.658 -9.182 7.3201 0.2124 0.0013 -0.1238 -8.4967

180 -23.177 -39.836 -40.236 -40.514 -56.072 -23.0082 -39.5513 -39.9748 -40.2245 -55.6741

-200

-150

-100

-50

0

50

-200 -100 0 100 200

Simplis simulation, P

VL=90 VL=118 VL=118.63 VL=119 VL=140



Figure 30. Active power variation in Simplis simulation and equivalent model for Set 1.

Table 10 and Figure 30 show that simulation data obtained are similar with the

equivalent model values, variation between them is less than 1% and shows 𝑉𝐿 and θ

dependence. It validates completely the equivalent model and its control variables. In

Figure 31 is noticed that a 10 [V] variation in 𝑉𝐿 produce a small variation in the

maximum active power, it means that this control variable produces a small power

variation compared with θ.

Figure 31. Variation of maximum active power with 𝑽𝑳.

In Figure 32 a comparison of simulation and equivalent model is shown, both

curves are coincident in almost each point, it means that equivalent model analysis is

valid for a practical setup behavior analysis. Data obtained with the others setups show

the same behavior with respect the equivalent model, it confirms the validation of the

model for different circuit cases and generalized it. This data and graphs are shown in the

next tables and figures to firm up the validation.

-200.0

-150.0

-100.0

-50.0

0.0

50.0

-200 -150 -100 -50 0 50 100 150 200

Equivalent model, P

Vr=90 Vr=118 Vr=118.63 Vr=119 Vr=140

36.5

37

37.5

38

38.5

39

39.5

0.00 50.00 100.00 150.00

Pmax variation, Simplis simulation

37.5

38.0

38.5

39.0

39.5

40.0

40.5

0.00 50.00 100.00 150.00

Pmax variation, equivalent model



Figure 32. Comparison between simplis simulation and equivalent model in set 1 .


VL

VL

phi

45.00 47.00 47.49 48.00 50.00

45.00 47.00 47.49 48.00 50.00

-180

Sim

plis

sim

ula

tio

n

-63.309 -69.018 -70.454 -71.964 -78.042

Equ

ival

ent

mo

del

-61.7069 -67.3138 -68.7247 -70.2087 -76.1813

-150 -128.559 -137.168 -139.315 -141.565 -150.543 -126.8270 -135.3282 -137.4481 -139.6702 -148.5370

-120 -176.272 -187.001 -189.667 -192.458 -203.557 -174.4982 -185.1181 -187.7572 -190.5195 -201.5050

-90 -193.418 -204.91 -207.762 -210.748 -222.608 -191.9471 -203.3425 -206.1715 -209.1316 -220.8927

-60 -175.313 -186 -188.656 -191.436 -202.492 -174.4982 -185.1181 -187.7572 -190.5195 -201.5050

-30 -126.908 -135.444 -137.572 -139.803 -148.708 -126.8270 -135.3282 -137.4481 -139.6702 -148.5370

0 -61.41 -67.035 -68.450 -69.939 -75.933 -61.7069 -67.3138 -68.7247 -70.2087 -76.1813

30 3.839 1.115 0.410 -0.339 -3.432 3.4132 0.7005 -0.0013 -0.7473 -3.8257

60 51.551 50.948 50.762 50.554 49.581 51.0844 50.4904 50.3077 50.1020 49.1423

90 68.698 68.857 68.858 68.843 68.632 68.5333 68.7148 68.7221 68.7142 68.5300

120 50.593 49.947 49.751 49.531 48.516 51.0844 50.4904 50.3077 50.1020 49.1423

150 2.188 -0.609 -1.332 -2.1 -5.267 3.4132 0.7005 -0.0013 -0.7473 -3.8257

180 -63.309 -69.018 -70.454 -71.964 -78.042 -61.7069 -67.3138 -68.7247 -70.2087 -76.1813

-140.0

-120.0

-100.0

-80.0

-60.0

-40.0

-20.0

0.0

20.0

40.0

60.0

-200 -100 0 100 200

Maximum Active Power Comparison

SIMPLIS_MAXEQVMAX





-250

-200

-150

-100

-50

0

50

100

-200 -150 -100 -50 0 50 100 150 200


Vr=45 Vr=47 Vr=47.49 Vr=48 Vr=50

-250

-200

-150

-100

-50

0

50

100

-200 -150 -100 -50 0 50 100 150 200

Equivalent model, P

Vr=45 Vr=47 Vr=47.49 Vr=48 Vr=50

-250

-200

-150

-100

-50

0

50

100

-200 -100 0 100 200

Maximum active power comparison

SIMPLIS_MAXEQVMAX




VL

VL

phi

55.00 61.00 61.81 62.00 65.00

55.00 61.00 61.81 62.00 65.00

-180

Sim

plis

sim

ula

tio

n

-3.784 -4.662 -4.788 -4.818 -5.299

Equ

ival

ent

mo

del

-3.0971 -3.8097 -3.9116 -3.9357 -4.3257

-150 -6.542 -7.178 -7.883 -7.922 -8.552 -6.5776 -7.6699 -7.8230 -7.8591 -8.4390

-120 -9.824 -11.357 -11.571 -11.621 -12.429 -9.1254 -10.4957 -10.6863 -10.7312 -11.4501

-90 -11.2 -12.882 -13.116 -13.171 -14.052 -10.0580 -11.5300 -11.7343 -11.7825 -12.5522

-60 -9.282 -10.708 -10.907 -10.953 -11.716 -9.1254 -10.4957 -10.6863 -10.7312 -11.4501

-30 -5.921 -6.983 -7.130 -7.164 -7.751 -6.5776 -7.6699 -7.8230 -7.8591 -8.4390

0 -3.906 -4.797 -4.924 -4.955 -5.442 -3.0971 -3.8097 -3.9116 -3.9357 -4.3257

30 -1.04 -1.615 -1.701 -1.721 -2.049 0.3833 0.0504 -0.0002 -0.0123 -0.2125

60 2.302 2.003 1.966 1.958 1.807 2.9312 2.8762 2.8631 2.8599 2.7986

90 4.105 4.14 4.145 4.139 4.120 3.8637 3.9105 3.9112 3.9111 3.9007

120 2.475 2.332 2.303 2.287 2.193 2.9312 2.8762 2.8631 2.8599 2.7986

150 -0.882 -1.392 -1.466 -1.484 -1.776 0.3833 0.0504 -0.0002 -0.0123 -0.2125

180 -3.784 -4.662 -4.788 -4.818 -5.299 -3.0971 -3.8097 -3.9116 -3.9357 -4.3257

-15

-9

-3

3

-200 -150 -100 -50 0 50 100 150 200


Vr=55 Vr=61 Vr=61.81 Vr=62 Vr=65





-15

-9

-3

3

-200 -150 -100 -50 0 50 100 150 200

Equivalent model, P

Vr=55 Vr=61 Vr=61.81 Vr=62 Vr=65

-14

-12

-10

-8

-6

-4

-2

0

2

4

6

-200 -150 -100 -50 0 50 100 150 200

Maximum active power comparison

SIMPLIS_MAXEQV MAX



3.4 Experimental Resonant Inductive Circuit Design.

In this section an experimental setup is proposed to validate the active power

behavior and control variables optimal values. Electronic elements to implement it are

dimensioned, with this objective inductive coupling parameter determined for the 3 coil

sets available are used in conjunction with simulation results. Considering that efficiency

isn’t taking into account, power losses are not included in the analysis, however a small

analysis is required to obtain active power values bigger enough to be measured in the

output with conventional measurement devices.

3.4.1 Primary and Secondary Current Limits

The ideal case is test an experimental setup in the same conditions than

simulations were developed, with the same variation range for θ and 𝑉𝑟 including the

maximum active power point. Coils sets have defined its maximum current’s limits in

their respective datasheets, they are considered to determine an operation range in the

experimental setup.

In section 3.2 set 2 was recommended for an experimental setup considering its

maximum power and control variables requirements. Simplis simulations are used to

determine the maximum currents, it occurs at maximum active power.

Figure 37. Primary and secondary current in maximum active power condition for set 2.

Currents limits from coils datasheet are:

𝐼𝑃,𝑚𝑎𝑥 = 6 [𝐴]

𝐼𝑆,𝑚𝑎𝑥 = 1 [𝐴]



RMS currents from Figure 37 are:

𝐼𝑃,𝑟𝑚𝑠 = 1.63 [𝐴]

𝐼𝑆,𝑟𝑚𝑠 = 21.69 [𝐴]

𝐼𝑆,𝑟𝑚𝑠 > 𝐼𝑆,𝑚𝑎𝑥, it shows that Secondary coil can’t manage the current and it isn’t

possible to implement it. Because this limitation circuit parameters are changed until

limitations of the current are satisfied.

𝑉𝑠 = 5[𝑉] 𝑎𝑛𝑑 𝑉𝑟 = 3[𝑉] → 𝐼𝑝,𝑟𝑚𝑠 = 1.92 [𝐴]

𝐼𝑠,𝑟𝑚𝑠 = 0.926[𝐴]

𝑃𝑚𝑎𝑥 = 2.5 [𝑊]

In this case limitations of the current are satisfied, but the maximum active power

is lower and could be a problem with inclusion of switching power losses, it discards set

2 for an experimental setup. In Section 3.2 set 1 was not recommended because its

maximum output active power requires a 𝑉𝑟,𝑜𝑝𝑡=120[v], however, to obtain a behavior

analysis 𝑉𝑟,𝑜𝑝𝑡 could be limited until 60 [V] and its power and currents could be analyzed.

For set 1 with 𝑉𝑠 = 15.7 [𝑉] 𝑎𝑛𝑑 𝑉𝑟 = 60 [𝑉]


0 2 4 6 8 10

Ip /

A

-8

-6

-4

-2

0

2

4

6

8


0 2 4 6 8 10

Is /

A

-1

-0.8

-0.6

-0.4

-0.2

-0

0.2

0.4

0.6

0.8

1



Figure 38. Waveforms for Set 1 with 𝑽𝒔 = 𝟏𝟓. 𝟕 [𝑽] 𝒂𝒏𝒅 𝑽𝒓 = 𝟔𝟎 [𝑽]

𝐼𝑝,𝑟𝑚𝑠 = 5.83 [𝐴]

𝐼𝑠,𝑟𝑚𝑠 = 0.59[𝐴]

𝑃𝑚𝑎𝑥 = 30.26 [𝑊]

Currents limits from coils datasheet are:

𝐼𝑃,𝑚𝑎𝑥 = 9 [𝐴]

𝐼𝑆,𝑚𝑎𝑥 = 1.1 [𝐴]

Set 1 in this condition shows high output active power, its current limits are

satisfied and active power is bigger enough with in a wide variation range of the control

variables making it the recommended set and conditions for an experimental setup.

3.4.2 Resonant capacitors

In section 3.1 capacitance for resonant capacitors where defined to produce

resonance at frequency determined in ETHER project. At maximum active power

condition, voltage across the capacitor needs to be tolerate and its own resonance

frequency needs to be bigger enough keep its capacitive behavior.

To obtain low ESR and high resonance frequency film capacitors are considered,

Figure 39 shows the frequency behavior of Metallized Polypropylene Film Capacitors

(MKP) from TDK, it shows that capacitors resonance frequency is bigger than 500 [kHz]

making them suitable for this application

The voltage across resonant capacitor in maximum active power condition is

determined with the RMS value of the waveform obtained with simplis simulation. Figure

40 shows voltage waveforms where the voltage across the primary resonant capacitor and

secondary resonant capacitor are 𝑉𝐶𝑟𝑝,𝑟𝑚𝑠 = 191.72 [𝑉] 𝑎𝑛𝑑 𝑉𝐶𝑟𝑠,𝑟𝑚𝑠 = 28.08 [𝑉]

respectively.


0 2 4 6 8 10

Pou

t / W

-40

-20

0

20

40

60



Figure 39. Impedance Z vs Frequency f for Film capacitor MKP from TDK.

Figure 40. Voltage across resonant capacitor in primary a nd secondary side

The Capacitors must manage this voltage at 500 [kHz], voltage capacitor’s

maximum voltage rating decrease with frequency, after review some capacitors

datasheets, 𝑉𝐶𝑟𝑝,𝑟𝑚𝑠 can’t be accomplished with a unique component; a series capacitor

array is proposed to reduce the required maximum voltage. Array showed in Figure 41

reduce the voltage rating in 1/3 for each capacitor.

Figure 41. Capacitors array

In concordance with Figure 41 in primary side 3 capacitors of 28.8 [nF], 70

[Vrms] @ 500 [kHz] are required, to obtain more accurate capacitance value a parallel

array is proposed like Figure 42 (a), this parallel-series capacitors array accomplishes the



requirements for the primary side. Secondary side hasn’t maximum voltage problems,

however an array is required to accomplish the capacitance required, it is shown in Figure

42 (b).

(a) (b)

Figure 42. Capacitor Arrays. (a) Primary resonant capacitor (b) Secondary resonant

capacitor.

Capacitors selected are 22 [nF] series B32654, 6.8 [nF] series B32651 and 2.2

[nF] series B32652 from TDK; all of them are capable to manage minimum 70 [Vrms] at

500 [kHz] according its datasheets graphs, it is showed in Figure 43.

Figure 43. Maximum Voltage rating variation with frequency for resonant

capacitors. [15]



3.4.3 Mosfet selection

Inverter and active rectifier require Mosfets selection in function of currents and

voltages at maximum power condition, although power behavior is the objective power

losses analysis is developed to select the lowest power losses Mosfet to obtain measurable

power. Simplis simulation is used to determine operational specifications and power

losses are determined in concordance with [16] calculation guide.

Inverter

Figure 44, Drain source voltage and drain current in inverter mosfets.

According to Figure 44 Mosfet inverter requirements are 𝑉𝐷𝑆,𝑚𝑎𝑥 > 15.7 [𝑉]

and 𝐼𝐷,𝑅𝑀𝑆 > 4.13 [𝐴], commercial Mosfet that accomplish this specification are

analyzed to determine which one produce less power losses. Table 13 shows power losses

obtained and the components analyzed, according to it Mosfet IPP015N04N from

Infineon is the most suitable option because it has the less power losses and satisfies the

requirements.

Table 13. Inverter Mosfet power losses comparison.

Mosfet Model IPP015N04N G IRF7430 AUIRF8409

Total Power Losses [W] 3.19 7.22 5.40



Active Rectifier

Figure 45. Drain source voltage and drain current in active rectifier mosfets.

According to Figure 44 Figure 45 Mosfet’s active rectifier requirements are

𝑉𝐷𝑆_𝑚𝑎𝑥 > 60 [𝑉] and 𝐼𝐷,𝑅𝑀𝑆 > 0.417 [𝐴], like inverter analysis commercial Mosfet are

compared. According to Table 14 Mosfet PSMN3R5 from NXP Semiconductors is the

most suitable option because it has the less power losses and satisfies the requirements.

Table 14. Active Rectifier Mosfet power losses comparison.

Mosfet model PSMN3R5 CSD19506KCS IRFB3077

Total power losses [W] 5.113 11.35 5.63

With this Mosfets total power losses expected in the inverter and active rectifier

are approximate 27 [W], it is a high value because the high switching frequency but it

allows to obtain enough output power to validate the active power behavior.



3.5 Experimental Results

In this section an experimental setup for a RIC system is implemented with

voltage levels and components dimensioned and selected in sections 2.13.1 and 3.426.

Furthermore, the acquired active power measurement results are plotted to show its

behavior. These results are compared with the theoretical and simulated behavior

obtained in previous section.

3.5.1 Prototyping Setup

To obtain an experimental validation of the equivalent model and power behavior,

a RIC system has been implemented, it is intended to operate at 500 [kHz] as resonance

frequency. Coils set 2 and its resonance capacitors form primary and secondary resonant

tanks, they are driven by an inverter and an active rectifier, respectively, like the circuit

simulated in Simplis, Figure 27, but taking account Mosfets and capacitor selection

described in section 3.4.

𝑉𝑟 is a DC power supply connected at the output of the system, it can’t receive

current, so a resistance is connected in parallel with 𝑉𝑟 to establish a current way when

the RIC system is transferring energy from primary to the secondary side, acting like a

battery; for a proper function, resistance is dimensioned to demand the double of the

available power in this operation’s condition, 50 [W].

To stabilizing input and output voltage two capacitors, 𝐶1 = 22[𝑢𝐹]𝑎𝑛𝑑 𝐶2 =

47[𝑛𝐹] are in the inverter input and at active rectifier output, 𝐶3 = 22[𝑢𝐹]𝑎𝑛𝑑 𝐶4 =

47[𝑛𝐹]. The digital control of the whole RIC system has been implemented on an external

Digital Signals Processor (DSP) board [Piccolo user manual]. A schematic overview of

the entire system

(a)



(b)

Figure 46. Schematic illustration of the experimental setup. (a) Transmitter, (b) Receptor.

To validate the equivalent model power behavior a DSP generates primary and

secondary control signals to drive the inverter switches, Q1 and Q2, as well the active

rectifier switches, Q3 to Q6. This prototype is intended to demonstrate the sinusoidal

behavior of the output active power with respect to 𝑉𝑟 𝑎𝑛𝑑 𝜃 variations, so 𝑉𝑟 is manually

controlled with the DC voltage supply level control, it is changed constantly to keep its

value constant while 𝜃 vary. 𝜃 variation is obtained with a delay between inverter and

active rectifier control signals.

The Experimental setup is intended to operate in open loop, 𝜃 vary from 10° to

180 ° in steps of 10° while 𝑉𝑟 is kept constant, inverter and active rectifier voltage and

current waveforms are monitored with an oscilloscope to verify its phase shift, output

active power is indirectly measured with active rectifier output current determined by

current measurements from the resistance 𝑅1 and 𝑉𝑟, DC voltage source.

Figure 47. Experimental Setup



3.5.2 Experimental Results

In order to obtain the active power behavior, power measurements are taken each

10° and then are plotted. A secondary open circuit test is developed to determine if the

circuit is at resonance, Figure 48 shows the existence of a phase shift between primary

current and voltage in this condition, it means that system isn’t in resonance, it could be

because actual switching frequency isn’t system resonance frequency. However analysis

is performed because the objective is determine active power behavior.

Figure 48. Primary voltage and current waveforms with secondary in open circuit.

This phase shift produces a variation in circuit impedances, introducing actual

frequency in the equivalent model and applying equation (17) a 𝜃𝑜𝑝𝑡 = 112.5° is

obtained, it means that for any value of 𝑉𝑟 the maximum active power should be obtained

at 𝜃𝑜𝑝𝑡. Figure 49 to Figure 51 shows voltage and current´s waveforms obtained for θ

values of 10°, 100° and 150°. Each figure (a) shows inverter and active rectifier voltages

on the same graph to verify the existence of θ. Figure (b) shows primary voltage and

current in the same graph while the figure (c) shows secondary waveforms, these figures

shows phase shift existence in each case. A quick comparison shows that this waveforms

are very similar with waveforms obtained in Simplis simulations.

(a)



(b)

(c)

Figure 49. RIC system with 10° phase shift . (a) Primary and Secondary voltages , (b) Primary

voltage and current , (c) Secondary voltage and current .

(a)

(b)



(c)

Figure 50. RIC system with 100° phase shift. (a) Primary and Secondary voltages, (b)

Primary voltage and current, (c) Secondary voltage and current.

(a)

(b)

(c)


Primary voltage and current, (c) Secondary voltage and current.



Figure 50 shows that current and voltage are in phase at both sides of the RIC

system, it means that the system is at resonance and power transfer must be in its

maximum value, it is also noticed that for 𝜃 < 𝜃𝑜𝑝𝑡, primary side has capacitive behavior,

the current leads to the voltage, while secondary side has inductive behavior, the current

lags to the voltage. When 𝜃 > 𝜃𝑜𝑝𝑡 the system behavior is in the opposite way.

(a) (b)

(c) (d)

Figure 52. Active Power vs θ . (a) Vr=7.5 [V], (b) Vr=10 [V], (c) Vr=12.5 [V], (d) Vr=15 [V].

Figure 52 shows the results obtained with the experimental setup, in each figure

the active power shows a sinusoidal behavior, it validates the results obtained with the

equivalent model and simulations. It is also noticed that maximum active power is

obtained at 115 [°] approximately in each case, this result is very similar with the 𝜃𝑜𝑝𝑡

calculated in these conditions.

Furthermore, it can be seen that while 𝑉𝑟 increases the active power also increases,

Figure 53 shows it clearly, if this result are compared with figures obtained in section 3.3,

the experimental setup's active power show the same behavior obtained with the

equivalent model and simulation, this validates completely the sinusoidal active power

behavior and the influence of the control variables (𝑉𝑟 , 𝜃).

-4.0

-3.0

-2.0

-1.0

0.0

1.0

2.0

3.0

4.0

0 50 100 150 200P [

W]

Ѳ [°]

Vr=7.5

-6.0

-4.0

-2.0

0.0

2.0

4.0

0 50 100 150 200

P [

W]

Ѳ [°]

Vr=10

-8.0

-6.0

-4.0

-2.0

0.0

2.0

4.0

6.0

0 50 100 150 200

P [

W]

Ѳ [°]

Vr=12.5

-10.0

-8.0

-6.0

-4.0

-2.0

0.0

2.0

4.0

6.0

0 50 100 150 200

P [

W]

Ѳ [°]

Vr=15



Figure 53. Experimental setup active power variation.

A frequency swept is developed with the DSP until resonance frequency is found

in the secondary open circuit test. In this operation point the experiment is repeated with

the same conditions as in the last experiment.

Figure 54. Experimental results in experimental setup reson ance frequency.

Figure 54 shows that when the circuit is operating at resonance frequency the

maximum active power is achieved with 𝜃 = 90°, it validate this job because in resonance

reactive impedance is annulated and Thevenin’s equivalent impedance only has real part.

-10.0

-8.0

-6.0

-4.0

-2.0

0.0

2.0

4.0

6.0

0 50 100 150 200

P [

W]

θ [°]

Experimental P variation

Vr=7.5

Vr=10.0

Vr=12.5

Vr=15.0

-0.4

-0.3

-0.2

-0.1

0.0

0.1

0.2

0.3

0.4

0 50 100 150 200P[W

]

Ѳ [°]

Vr=5

-4.0

-3.0

-2.0

-1.0

0.0

1.0

2.0

0 50 100 150 200

P [

W]

Ѳ [°]

Vr=7.5

Chapter 4

CONTROL

ALGORITHM

CHAPTER 4 CONTROL ALGORITHM


4 CONTROL ALGORITHM

This section describes an algorithm scheme to keep the maximum output active

power in the resonant inductive circuit described in previous sections, the algorithm

works with control variables proposed (𝑉𝑟, 𝜃) to contrast changes in circuit parameters,

especially the capacitance variation because of tolerance or degradation.

Flux diagram shows required actions and it is validated with simulations in

simulink controlled with a Matlab script because it offers a simplex and fast way to test

it. Algorithm validation is developed with a comparison of maximum conditions achieved

with the algorithm and maximum conditions predicted by equations (17) and (21).

4.1 Algorithm concept

The algorithm is based on the sinusoidal behavior of active power, section 2.2.1

shows that as a first action a 𝜃 adjust is required and with its optimal value 𝑉𝑟 can be

adjusted. Circuit parameters variation isn’t detected so the algorithm proposes a constant

adjust in determined time intervals, it is a valid option because in section 3.2 was

demonstrated that active power variation is only a small percentage and a fast adjustment

isn’t necessary.

Figure 55. Algorithm control concept in a sinusoidal waveform.

Figure 55 shows that in a sinusoidal waveform the maximum can be achieved

when the first derivate is equal to 0, measurements and comparisons of active power with

small variations of control variables allows to detect the operation point in the active

power curve and determine the appropriate control action. This process is valid for both

control variables because active power variation with both of them is sinusoidal.



(a)

(b)

(c)



(d)

Figure 56. Operation point scenarios (a) scenario 1 , growing, (b) scenario 2 , decreasing, (c)

scenario 3, minimum, (d) scenario 4 , maximum.

Figure 56 shows the possible operation point scenarios, they are valid for both

control variables. It’s clearer than small increments and decrements of control variable

around actual value and active power measurements in each point are required to

determine the actual operating point and the respective control action, they are described

in Table 15.

Table 15. Control action in function of operation point.

Scenario Condition Control action

Scenario 1 𝑃𝐿 < 𝑃𝑎 < 𝑃𝑅 Increment X, keep Y constant

Scenario 2 𝑃𝐿 > 𝑃𝑎 > 𝑃𝑅 Decrement X, keep Y constant

Scenario 3 𝑃𝐿 > 𝑃𝑎; 𝑃𝑎 < 𝑃𝑅 Increment X, keep Y constant

Scenario 4 𝑃𝐿 < 𝑃𝑎; 𝑃𝑎 > 𝑃𝑅 No action

𝑃𝑎 = 𝑓(𝑋, 𝑌), 𝑎𝑐𝑡𝑢𝑎𝑙 𝑎𝑐𝑡𝑖𝑣𝑒 𝑝𝑜𝑤𝑒𝑟 𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑚𝑒𝑛𝑡

𝑃𝐿 = 𝑓(𝑋 − ∆𝑋, 𝑌), 𝑙𝑒𝑓𝑡 𝑎𝑐𝑡𝑖𝑣𝑒 𝑝𝑜𝑤𝑒𝑟 𝑣𝑎𝑟𝑖𝑎𝑡𝑖𝑜𝑛 𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑚𝑒𝑛𝑡

𝑃𝑅 = 𝑓(𝑋 + ∆𝑋, 𝑌), right 𝑎𝑐𝑡𝑖𝑣𝑒 𝑝𝑜𝑤𝑒𝑟 𝑣𝑎𝑟𝑖𝑎𝑡𝑖𝑜𝑛 𝑚𝑒𝑎𝑠𝑢𝑟𝑒𝑚𝑒𝑛𝑡

𝑋 = 𝑐𝑜𝑛𝑡𝑟𝑜𝑙 𝑣𝑎𝑟𝑖𝑎𝑏𝑙𝑒 𝑚𝑎𝑛𝑖𝑝𝑢𝑙𝑎𝑡𝑒𝑑

𝑌 = 𝑐𝑜𝑛𝑡𝑟𝑜𝑙 𝑣𝑎𝑟𝑖𝑎𝑏𝑙𝑒 𝑐𝑜𝑛𝑠𝑖𝑑𝑒𝑟𝑒𝑑 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡

Active power is a two variable function, the control algorithm manipulates one at

a time, for this reason control action is referred to X and Y because they are valid for both

𝑉𝑟 𝑜𝑟 𝜃. In section 2.2.1 was demonstrated that θ is faster and produces bigger active



power changes compared with 𝑉𝑟, for this reason algorithm control consider as a first step

θ optimization and the with 𝜃𝑜𝑝𝑡 as a constant 𝑉𝑟 optimization is developed. It’s clear that

algorithm objective is that operation point reaches scenario 4 conditions.

4.2 Flux diagram

In concordance with section 4.1 criteria, the control algorithm needs to identify

the actual operation scenario and execute an appropriate control action for both control

variables in the order mentioned previously until absolute maximum active power is

reached, then adjust process is executed again in a determined time interval.

START

ACTUAL OPERATION POINT MEASURMENTS

( θa, Vra, Pa )

OPTIMAL θ DETERMINATIONVra CONSTANT

OPTIMAL Vr DETERMINATIONΘ opt CONSTANT

OPTIMAL θ OPERATION POINT MEASURMENTS

( θa, Vra, Pa )

END

(a)



POWER VARIATION ACQUISITIONChange θ to Θa- θ; measure P=PLChange θ to Θa+ θ; measure P=PR

PL < Pa < PR

PL > Pa > PR

PL > PaAND

PR > Pa

PL < PaAND

PR < Pa

θ = 0.5°

θ = - 0.5°

θ = 0.5°

OPTIMAL θ START

END

STORE θoptimal

(b)



POWER VARIATION ACQUISITIONChange θ to Θa- θ; measure P=PLChange θ to Θa+ θ; measure P=PR

PL < Pa < PR

PL > Pa > PR

PL > PaAND

PR > Pa

PL < PaAND

PR < Pa

Vr = 1 [V]

Vr = - 1 [V]

Vr = 1 [V]

OPTIMAL Vr START

END

STORE Vroptimal

(c)

Figure 57. Algorithm flux diagram. (a) Principal routine. (b) Optimal 𝜽 subroutine. (c)

Optimal 𝑽𝒓 subroutine.



4.3 Algorithm control test

Section 3.3 validates the equivalent model for the resonant inductive circuit

studied, in this model the algorithm test is developed with a script in Matlab that controls

a simulink simulation similar to section 2.2.2 process. Matlab script executes the control

actions specified in the flux diagram, acting as a circuit controller, it generates the

appropriate control signals for the equivalent power circuit simulated in Simulink.

Each simulation is developed with 𝜃 = 20° 𝑎𝑛𝑑 𝑉𝑟 = 10 [𝑉] as initial conditions,

Figure 58 shows graphs obtained for simulation with coils set 1, they show the control

variables variation until find the optimal values according to the flux diagram. The

algorithm validation is clear because its action allow to find the maximum active power

point. Table 16 shows a comparison of the values between equivalent model and

algorithm test, it shows that algorithm test is capable to find optimal control variables

values according to the equivalent model.

(a)

-2 0 2 4 6 8 1024

24.1

24.2

24.3

24.4

24.5

24.6

24.7optimal phi process, Vr is constant

Phi

Active P

ow

er,

Po [

W]



Figure 58. Algorithm test results in coils set 1 , (a) 𝜽 optimization. (b) 𝑽𝒓 Optimization.

Table 16. Algorithm Test comparison for set 1.

Equivalent Model Algorithm test

Output Active Power [W] 39.98 31.7413

Optimal 𝑽𝒓 [V] 118.63 120.95

Optimal 𝜽 [°] 90 90.5

Angle difference is produced by the control algorithm sensibility. Matlab script

uses ∆𝜃= 0.5° 𝑎𝑛𝑑 ∆𝑉= 1 [𝑉], however this values could be optimized to produce faster

results or to increase optimization sensibility. Simulations for set 2 and 3 are developed

for a complete validation in different circuit parameter, its results are showed in Figure

59.

60 70 80 90 100 110 120 13024

25

26

27

28

29

30

31

32Optimal Vr process, phi is constant

Vr [V]

Active P

ow

er,

Po [

W]



(a)

-2 0 2 4 6 8 10

24.5

24.55

24.6

24.65

24.7

24.75

24.8

24.85


Phi

Active P

ow

er,

Po [

W]

10 15 20 25 30 35 40 45 5020

25

30

35

40

45

50

55Optimal Vr process, phi is constant

Vr [V]

Active P

ow

er,

Po [

W]



(b)

Figure 59. Algorithm test results. (a) coils set 2, (b) c oils set 3.

-2 0 2 4 6 8 101.105

1.11

1.115

1.12

1.125


Phi

Active P

ow

er,

Po [

W]

10 20 30 40 50 60 701

1.5

2

2.5

3

3.5Optimal Vr process, phi is constant

Vr [V]

Active P

ow

er,

Po [

W]



Table 17. Algorithm Test comparison for set 1.

|

SET 2 SET 3|

Equivalent

Model

Algorithm

test

Equivalent

Model

Algorithm

test

Output Active

Power [W] 68.7221 54.5639 3.9112 3.1054

Optimal 𝑽𝒓 [V] 47.49 48.38 61.81 63.03

Optimal 𝜽 [°] 90 90.5 90 90.5

Table 16 and

Table 17 values shows that control algorithm proposal has been validated with

simulation for the 3 coils sets because optimal values reached are too close with the values

obtained with the equivalent model and difference can be justified because the inclusion

of first harmonic approximation, it generalize its function so it can be valid for any

coupled inductor array and it requires only output active power and control variables

monitoring.

Chapter 5

CONCLUSIONS

AND

FUTURE LINES

CHAPTER 5 CONCLUSIONS AND FUTURE LINES


5 CONCLUSIONS AND FUTURE LINES

In this chapter principal conclusion obtained from this job are shown, they are

extracted from the different analysis and simulations developed and explained in previous

chapters, they summarize principal results obtained in this job in accordance with its

objectives, additionally recommendations about next steps in ETHER project and some

possible improvements are shown.

5.1 Conclusions

ETHER separation distance specifications require wireless power transfer in the

middle range classification, so a resonant inductive coupling system (RIC) has to be

implemented because it produces higher currents in transmission coil, therefore magnetic

flux is bigger, increasing mutual coupling, it induces a bigger voltage in the receiver coil.

On the receiver side, a resonant tank at the same frequency is implemented to produce

higher currents with induced voltage, producing a high power transfer.

The proposed circuit for WPT uses square voltages because of the inverter, active

rectifier and DC-DC converter, however, it’s a RIC system where the reactive impedance

is cancelled because of resonance, the resonant tanks act like a filter and makes possible

the circuit analysis with the first harmonic approximation where voltages and currents are

considered sinusoidal and phasors's theory is applicable.

In [12], the efficiency for a specific active power is maximized with optimal

values of voltage level in an active rectifier, current in receiver resonant tank and phase

shift between these voltage and current, φ, however, in this job an additional analysis

shows that the receiver's resonant tank current and the phase shift, φ, can be controlled

by the active rectifier's voltage level and its phase, then they can be established as control

variables simplifying the control and required measurements.

A RIC system can be analyzed with an equivalent model where the resonant

coupling is represented by its Thevenin’s voltage and impedance

equivalent, 𝑉𝑇𝐻 𝑎𝑛𝑑 𝑍𝑇𝐻, and the load, active rectifier and DC-DC converter can be

represented by a sinusoidal voltage source, defined by its voltage level and

phase, 𝑉𝐿 𝑎𝑛𝑑 𝜃 respectively, any coupling parameter’s change, because of tolerance or

degradation, will be reflected in Thevenin’s values and the equivalent circuit’s current

and power could be modified or controlled with 𝑉𝐿 𝑎𝑛𝑑 𝜃.



ETHER proposes a pacemaker’s wireless charger where the transmitter coil is on

a sofa or bed and receiver coil is inside pacemaker, a possible system perturbation is that

patients could be sitting or lying in any position and change it in time, it means that the

separation distance could vary constantly and according to the equivalent model, it

modifies the induced voltage , 𝑉𝑇𝐻. Other perturbation source is resonant capacitor’s

change because of its own degradation in time or tolerance, it will vary the thevenin’s

impedance, 𝑍𝑇𝐻.

Equivalent model’s analysis shows that maximum active power is a function of

coupling parameters and control variables, 𝑃 = 𝑓(𝑉𝑇𝐻, 𝑍𝑇𝐻 , 𝑉𝐿 , 𝜃), perturbations will

change maximum power available so this job proposes as a compensation action keep the

maximum power transfer, in any condition, to achieve maximum charge in a pacemaker

battery in any condition, using optimal values for 𝑉𝐿 𝑎𝑛𝑑 𝜃.

Equivalent model’s analysis shows that active power could be a two variable

function because coupling parameters are considered constant because they can’t be

manipulated, so 𝑃 = 𝑓( 𝑉𝐿, 𝜃), the partial derivatives help to determine active power

behavior individually with each control variable, it shows that in both cases active power

has a sinusoidal behavior, for each control variable a maximum power operation point

can be found and a unique absolute maximum can be achieved with the optimal

combination of 𝑉𝐿 𝑎𝑛𝑑 𝜃.

An Equivalent model with a coils set characterization at a specific frequency allow

to find operational conditions as maximum power, currents and induced voltages but

especially, it allows to identify and determine the control variable’s values and its

required changes when a resonant capacitor’s variation is considered. It establishes

operational parameters for a coil set and allow to know required elements for a RIC

system.

Simulation allows to include more realistic parameters to obtain a validation

method for equivalent model’s results, in this job this comparison is developed in three

coils set and comparison shows that equivalent model is a valid analyze tool and method

to determine the operational characteristics in any WPT system working as a RIC system.

Active Power variation’s analysis shows that optimal 𝑉𝐿 depends on 𝜃, for this

reason the absolute maximum power point requires that optimal 𝜃 is found first and then

𝑉𝐿 is adjusted, for this reason the control algorithm proposed finds the maximum active

power in this way. Small power variations are produced by coupling parameter’s change

so control actions can be developed in time intervals and obtain a good power transfer.

CHAPTER 5 CONCLUSIONS AND FUTURE LINES


Active power in a RIC system has a sinusoidal behavior so the first derivative's

test can be applied to find its operation point and its absolute maximum, in this way

producing small variations of power with a small increment and decrement in control

variables the value of the first derivate can be found and the location of the operation

point in power curve can be determined, in that way, an adequate control action can be

defined.

In order to simulate and evaluate a control action, that requires some math

operations and comparisons, Matlab is a good option because with Simulink a power

electronic circuit can be simulated while a Matlab script can execute operations and

comparisons determining required control signals and controlling Simulink simulation,

in this way Matlab allows to simulate power and control circuits for test or as a quick

prototyping.

The equivalent model and the determined control variables have been validated

with simulations and experimental results because the obtained values have the behavior

predicted by deduced equations, therefore the model can be used for RIC system’s

analysis and design. It also can be used to design an adequate controller for any circuit

variable like voltage, current or power and obtain a determined behavior.

5.2 Future lines

This job proposes a control strategy to obtain maximum active power transfer in

any condition, an immediate future work should implement this algorithm in a controller

like a DSP or FPGA to work in high frequency, appropriate power sensor must be selected

to obtain close loop function. This work could validate the control strategy and determines

the most suitable control variable’s variation for a better system accuracy and an adequate

control execution time interval that allows a faster optimal point determination.

This job is at 500[kHz] resonance frequency, however ETHER project parameters

suggest also 7 [GHz] as resonance frequency, a future work could consider components

selection at this frequency, it could reduce the prototype size and increase the power

transfer. Adequate drivers considerations and control signals generators should be

determined to obtain better power transmission in this frequency.

Next job could include power losses study in the active rectifier and DC-DC

converter because of the high frequency operation, it produces higher switching losses, it

could include a topology improvement and adequate switch selection to take advantage

of the power transfer, it also could include SMD components selection and considerations

because the receiver needs to be smaller as actual pacemakers.



Coil’s construction could be considered as a next project or part of one to improve

the induced voltage, shape and size could be explored to obtain the best coupling

considering separation distance requirements and biological limits in ETHER project, the

job shown in [5] explores some alternatives and could be taken as an initial job.

Control strategy focuses in receiver resonant tank power and assumes that

resonance is kept in any circumstance, however, resonant capacitor in transmitter side

could change and a control that keep circuit in resonance should be implemented.

As part of ETHER project a prototype is required to explore some biological

effects of a RIC system in the human body with experiments coordinated by CTB, they

are in charge to determine some circuit operation’s limits related to electrical parameters

but specially frequency effects on human health.

6 LIST OF FIGURES

Figure 1. ETHER WPT topologies. (a) Two resonant tanks. (b) Three resonant tanks . III

Figure 2. ETHER project scheme. [3] .............................................................................. 2

Figure 3. Pacemarker implant. .......................................................................................... 3

Figure 4. Inductive transfer power concept. ..................................................................... 4

Figure 5. Near field coupling scheme. .............................................................................. 5

Figure 6. RIC system structure. [3] .................................................................................. 6

Figure 7. RIC topologies. (a) Series-Series. (b) Series Parallel. (c) Parallel-Series. (d)

Parallel-Parallel. [3] .......................................................................................................... 7

Figure 8. Resonant circuit scheme. (a) First harmonic approximation equivalent circuit.

(b) Circuit model with two equivalent sources to model the inductive coupling. .......... 11

Figure 9. Circuit scheme to include the control variables. ............................................. 12

Figure 10. Circuit to analyze 𝑽𝑳 and 𝜽 as Active Power control variables. .................. 12

Figure 11. (a) Open circuit equivalent. (b) Short circuit equivalent. ............................. 13

Figure 12. Square and first harmonic waveforms in (a) primary inverter (b) secondary

active rectifier. ................................................................................................................ 15

Figure 13. Plots obtained with the Matlab script. (a) Phase swept for different amplitude

with positive values for 𝑿𝑻𝑯, (b) Zoom in figure (a), (c) phase swept for different

amplitude with negative values for 𝑿𝑻𝑯. ...................................................................... 18

Figure 14. Plots for different values of 𝑿𝑻𝑯. ................................................................ 19

Figure 15. Thevenin’s equivalent and active rectifier used in Simulink. ....................... 19

Figure 16. Active Rectifier control signals generator..................................................... 20

Figure 17. Output Power measurement’s circuit. ........................................................... 20

Figure 18. Complete circuit scheme in Simulink ........................................................... 21

Figure 19. Waveforms obtained in Simulink. ................................................................ 22

CHAPTER 6 LIST OF FIGURES


Figure 20. Active Power as a function of control 𝜽 for different values of |𝑽𝑳|. (a) Plot

obtained with Simulink simulation, (b) Plot obtained with Matlab script circuit solver.22

Figure 21. Coils from Würth Elektronik. ....................................................................... 26

Figure 22. Coil’s construction set. .................................................................................. 27

Figure 23. Measurements in the impedance analyzer..................................................... 28

Figure 24. Inductive coupling equivalent model ........................................................... 29

Figure 25. Active power variation in coupled inductor sets. (a) Set 1 (b) Set 2 (c) Set 3.

........................................................................................................................................ 32

Figure 26. T model for coupled inductors. ..................................................................... 33

Figure 27. Simplis simulation scheme. (a) Power stage and resonant inductive model. (b)

Control signals generators. ............................................................................................. 34

Figure 28. Waveforms obtained with simplis for Set 1 in maximum power conditions. 34

Figure 29. Waveforms obtained with simplis for Set 1 with θ=30°. .............................. 35


........................................................................................................................................ 37

Figure 31. Variation of maximum active power with 𝑽𝑳. .............................................. 37

Figure 32. Comparison between simplis simulation and equivalent model in set 1. ..... 38


........................................................................................................................................ 39



........................................................................................................................................ 41


Figure 37. Primary and secondary current in maximum active power condition for set 2.

........................................................................................................................................ 42

Figure 38. Waveforms for Set 1 with 𝑽𝒔 = 𝟏𝟓. 𝟕 𝑽 𝒂𝒏𝒅 𝑽𝒓 = 𝟔𝟎 𝑽 ........................... 44

Figure 39. Impedance Z vs Frequency f for Film capacitor MKP from TDK. .............. 45

Figure 40. Voltage across resonant capacitor in primary and secondary side ................ 45



Figure 41. Capacitors array ............................................................................................ 45

Figure 42. Capacitor Arrays. (a) Primary resonant capacitor (b) Secondary resonant

capacitor.......................................................................................................................... 46

Figure 43. Maximum Voltage rating variation with frequency for resonant capacitors.

[15] ................................................................................................................................. 46

Figure 44, Drain source voltage and drain current in inverter mosfets. ......................... 47

Figure 45. Drain source voltage and drain current in active rectifier mosfets. .............. 48

Figure 46. Schematic illustration of the experimental setup. (a) Transmitter, (b) Receptor.

........................................................................................................................................ 50

Figure 47. Experimental Setup ....................................................................................... 50

Figure 48. Primary voltage and current waveforms with secondary in open circuit. ..... 51


Primary voltage and current, (c) Secondary voltage and current. .................................. 52





Figure 52. Active Power vs θ. (a) Vr=7.5 [V], (b) Vr=10 [V], (c) Vr=12.5 [V], (d) Vr=15

[V]. .................................................................................................................................. 54

Figure 53. Experimental setup active power variation. .................................................. 55

Figure 54. Experimental results in experimental setup resonance frequency. ............... 55

Figure 55. Algorithm control concept in a sinusoidal waveform. .................................. 58

Figure 56. Operation point scenarios (a) scenario 1, growing, (b) scenario 2, decreasing,

(c) scenario 3, minimum, (d) scenario 4, maximum. ...................................................... 60

Figure 57. Algorithm flux diagram. (a) Principal routine. (b) Optimal 𝜽 subroutine. (c)

Optimal 𝑽𝒓 subroutine. .................................................................................................. 63

Figure 58. Algorithm test results in coils set 1, (a) 𝜽 optimization. (b) 𝑽𝒓 Optimization.

........................................................................................................................................ 65

CHAPTER 6 LIST OF FIGURES


Figure 59. Algorithm test results. (a) coils set 2, (b) coils set 3. .................................... 67

7 LIST OF TABLES

Table 1. Electric parameters for RIC topologies. [3] ....................................................... 7

Table 2. Parameters used in the Matlab script. ............................................................... 17

Table 3. Transmitter and receiver coils .......................................................................... 27

Table 4. Coils sets ........................................................................................................... 27

Table 5. Measurement obtained from the coils set with an impedance analyzer ........... 28

Table 6. Inductive coupling sets models ........................................................................ 29

Table 7. Equivalent model values for each coupling set. ............................................... 30

Table 8. Equivalent model values with +10% variation in reception side resonant

capacitor.......................................................................................................................... 31

Table 9. Equivalent model values with -10% variation in reception side resonant capacitor

........................................................................................................................................ 31

Table 10. Active power data in Simplis simulation and equivalent model for Set 1 ..... 36

Table 11. Active power data in Simplis simulation and equivalent model for Set 2 ..... 38

Table 12. Active power data in Simplis simulation and equivalent model for Set 3 .... 40

Table 13. Inverter Mosfet power losses comparison. ..................................................... 47

Table 14. Active Rectifier Mosfet power losses comparison. ........................................ 48

Table 15. Control action in function of operation point. ................................................ 60

Table 16. Algorithm Test comparison for set 1. ............................................................. 65

Table 17. Algorithm Test comparison for set 1. ............................................................. 68

8 APPENDIX A. MATLAB SCRIPTS

Active Power Behavior Script

clc clear all

%------DATOS PARA EL CIRCUITO -------- fsw=500000;%frecuencia de switcheo Tsw=1/fsw;%periodo de switcheo w=2*pi*fsw;%frecuencia angular V1=157.4;%voltaje de entrada, tiene 0° phi_V1=0; %V=input('Ingrese el valor de la tension V2: ')

%phi=0;%Desfase de V2 R=0;%Resistencia de Z en ohm L=0*(1/w);%Inductancia de Z en H, L=0_Np Inductor C=(1/(792*w));%Capacitancia de Z en F, C=inf_No Capacitor %C=inf; %-------- DETECCIÓN DE PUNTO DE OPERACIÓN ----------- Color=['r','g','b','y','c','m','k','y','m','c','r','g','b']; i=0; for V=50:5:60 i=i+1; j=0; for phi=-180:5:180 j=j+1; tsim=num2str(4/fsw);%periodos para la simulación set_param('TFMMAT','StopTime',tsim) simOut =

sim('TFMMAT','SaveOutput','on','OutputSaveName','Ja'); Po_aux=simOut.get('Po');%adquiere el valor de Potencia [m,n]=size(Po_aux); Po(j)=Po_aux(m-1);%Medida Potencia Actual

end vector_phi=-180:5:180; plot(vector_phi,Po,Color(i)) hold on end



Control Algorithm Script

Main Function

Clc

clear all

%------DATOS PARA EL CIRCUITO -------- fsw=500000;%frecuencia de switcheo Tsw=1/fsw;%periodo de switcheo w=2*pi*fsw;%frecuencia angular V1=157.3867;%voltaje de entrada, tiene 0° phi_V1=0; V=input('Ingrese el valor de la tension V2: ')

R=0; L=0*(1/w);%Inductancia de Z en H, L=0_Np Inductor C=1/(791.69*w);%Capacitancia de Z en F, C=inf_No Capacitor

%-------- DETECCIÓN DE ANGULO DE OPERACIÓN ----------- Lazo=0;%variable que indica que se vaia: 0=phi; 1=V phi_actual=10;%Medida Desfase actual

accion=0; vector_phi(1)=phi_actual;%primer valor vector de phi j=1;%Contador de pasos stop=0;%Permite iniciar la busqueda stop_aux=0;%Permite saber q aun no hay posible máximo %incremento=incremento1; %Empieza la busqueda a pasos largos

while stop==0

phi=vector_phi(j); Po_actual= Medir(fsw,Tsw,w,V1,phi_V1,R,L,C,V,phi) vector_Po(j)=Po_actual;%primer valor vector de Po

phi=vector_phi(j)+0.5; Po1= Medir(fsw,Tsw,w,V1,phi_V1,R,L,C,V,phi) phi=vector_phi(j)-0.5; Po2= Medir(fsw,Tsw,w,V1,phi_V1,R,L,C,V,phi) [accion_aux,accion, incremento1,

incremento2]=determinar(accion,Lazo,vector_Po(j),Po1,Po2);

if accion==0 stop=1;%ES MAXIMO,PARAR BUSQUEDA else j=j+1; phi=vector_phi(j-1)+incremento1 vector_phi(j)=phi; end

end

%***********GRAFICA Po vs phi******************* plot(vector_phi,vector_Po,'*-r') title('con V2 introducida por teclado, barrido en desfase') xlabel('Desfase Phi (V2 respecto V1)') ylabel('Potencia activa')

CHAPTER 8 APPENDIX A. MATLAB SCRIPTS


hold on Po1_MAX=vector_Po(j)%almacena la primera Po Maxima phi_MAX=vector_phi(j)%almacena el angulo de Po Maxima plot(phi_MAX,Po1_MAX,'o-k') %unica el punto máximo

%-------- DETECCIÓN DE VOLTAJE DE OPERACIÓN ----------- Lazo=1;%variable que indica que se vaia: 0=phi; 1=V %EL VALOR DE VOLTAJE INICIAL YA SE CONOCE, VARIABLE V phi=phi_MAX; V_actual=V; Po_actual= Po1_MAX;%inicia desde la primera potencia maxima vector_V(1)=V_actual;%primer valor vector de phi j=1;%Contador de pasos stop=0;%Permite iniciar la busqueda stop_aux=0;%Permite saber q aun no hay posible máximo incremento=incremento1; %Empieza la busqueda a pasos largos contador=0;

while stop==0

%**********REVISION POSIBLE MAXIMO************ %Determina si hay máximo o falso máximo V=vector_V(j)+0.05; Po1= Medir(fsw,Tsw,w,V1,phi_V1,R,L,C,V,phi) V=vector_V(j)-0.05; Po2= Medir(fsw,Tsw,w,V1,phi_V1,R,L,C,V,phi) [accion_aux,accion, incremento1,

incremento2]=determinar(accion,Lazo,vector_Po1(j),Po1,Po2);

if accion~=accionaux contador=contador+1; end

if contador>15 accion=0; end

if accion==0 stop=1;%ES MAXIMO,PARAR BUSQUEDA else if accion_aux==0%continuar buscando a pasos cortos(Máximo

cercano) incremento=incremento2; stop=0; stop_aux=0; V=vector_V(j); else incremento=incremento1;%continuar buscando a pasos

largos(Falso máximo) stop=0; stop_aux=0; V=vector_V(j); end end

end

%***********GRAFICA Po vs phi******************* figure



plot(vector_V,vector_Po1,'*-r') title('con phi_MAX constanre, barrido en Voltaje') xlabel('V (V)') ylabel('Potencia activa') hold on Po2_MAX=vector_Po1(j)%almacena la primera Po Maxima V_MAX=vector_V(j)%almacena el angulo de Po Maxima plot(V_MAX,Po2_MAX,'o-k') %unica el punto máximo

Medir Fuction

function Po = Medir(fsw,Tsw,w,V1,phi_V1,R,L,C,V,phi)

tsim=num2str(4/fsw);%periodos para la simulación set_param('TFMMAT','StopTime',tsim) simOut = sim('TFMMAT','SaveOutput','on','OutputSaveName','Ja'); Po_aux=simOut.get('Po');%adquiere el valor de Potencia [m,n]=size(Po_aux); Po=Po_aux(m-1);

end

Determinar Function

function [accion_aux,accion,incremento1, incremento2] =

determinar(accion,Lazo,Po_actual,Po1,Po2) accion_aux=0;

if Po1>Po_actual && Po2<Po_actual accion=1; else if Po1<Po_actual && Po2>Po_actual accion=2; else if Po1>Po_actual && Po2>Po_actual accion_aux=1; accion=accion;

else if Po1<Po_actual && Po2<Po_actual accion=0; else accion=0; end end end end

switch accion case 1 if Lazo==0 incremento1=0.5; incremento2=0.1; else incremento1=1; incremento2=1; end

CHAPTER 8 APPENDIX A. MATLAB SCRIPTS


case 2 if Lazo==0 incremento1=-0.5; incremento2=-0.1; else incremento1=-1; incremento2=-1; end

case 0 incremento1=0; incremento2=0; end end

9 APPENDIX B. WURTEN COILS DATA

SHEETS

Dimensions: [mm]

Scale - 1:1,5

53,3

± 1,

1

40,7 ± 2

6,0 ref.

10,0 ± 21

2

53,3 ± 1,1 42,8 ± 2

6,5

max

.

Heat shrinkbleTubing (black)

Recommended Land Pattern: [mm]

Scale - 1:1,5

1 25,0 min.

O 2,0

Schematic:

Electrical PropertiesProperties Test conditions Value Unit Tol.Inductance 125 kHz/ 10 mA L 10 μH ±10%

Q-factor 125 kHz/ 10 mA Q 200

Rated Current ΔT = 40 K IR 9 A max.

Saturation Current ISAT 16 A typ.

DC Resistance @ 20°C RDC 0.028 Ω typ.

DC Resistance @ 20°C RDC 0.03 Ω max.

Self Resonant Frequency fres 11 MHz

General InformationProperties Value

It is recommeded that the temperature of the component does not exceed +105°C under worstcase conditions

Operating Temperature TOP -20 °C up to +105 °C

Storage Temperature (in originalpackaging) TS -20 °C up to +60 °C

Test conditions of Electrical Properties: 20°C, 33% RH if not specified differently

Würth Elektronik eiSos GmbH & Co. KGEMC & Inductive Solutions

Max-Eyth-Str. 174638 WaldenburgGermanyTel. +49 (0) 79 42 945 - 0

[email protected]

CREATED CHECKED GENERAL TOLERANCE PROJECTIONMETHOD

WE WE DIN ISO 2768-1m

DESCRIPTION

WE-WPCC Wireless PowerCharging Transmitter Coil ORDER CODE

760308141SIZE REVISION STATUS DATE BUSINESS UNIT PAGE

5353 001.001 Draft 2015-12-01 1/6

This electronic component has been designed and developed for usage in general electronic equipment only. This product is not authorized for use in equipment where a higher safety standard and reliability standard is especially required or where a failure of the product is reasonably expected to cause severe personal injury or death, unless the parties have executed an agreement specifically governing such use. Moreover Würth Elektronik eiSos GmbH& Co KG products are neither designed nor intended for use in areas such as military, aerospace, aviation, nuclear control, submarine, transportation (automotive control, train control, ship control), transportation signal, disaster prevention, medical, public information network etc.. Würth Elektronik eiSos GmbH & Co KG must be informed about the intent of such usage before the design-in stage. In addition, sufficient reliability evaluation checks for safetymust be performed on every electronic component which is used in electrical circuits that require high safety and reliability functions or performance.

Typical Inductance vs. Current Characteristics:

0.0

2.0

4.0

6.0

8.0

10.0

12.0

0.0 5.0 10.0 15.0 20.0

Ind

ucta

nce [

µH

]

Current [A]

Typical Inductance vs. Frequency Characteristics:

1

10

100

10 100 1000 10000

Ind

ucta

nce [

µH

]

Frequency [kHz]



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DESCRIPTION



5353 001.001 Draft 2015-12-01 2/6


Q-Factor vs. Frequency:

0

40

80

120

160

200

10 100 1000 10000

Q-f

ac

tor

Frequency [kHz]

Typical Temperature Rise vs. Current Characteristics:

0.0

5.0

10.0

15.0

20.0

25.0

30.0

35.0

40.0

45.0

0.0 2.0 4.0 6.0 8.0 10.0 12.0

Tem

pera

ture

Ris

e [

K]

Current [A]



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DESCRIPTION



5353 001.001 Draft 2015-12-01 3/6


Classification Wave Soldering Profile:Temperature

Time

Tp

tp

Ts maxTs typical

Ts min

First Wave

Preheat area Cool down area

Second Wave

typical temperature proceduremin temperature proceduremax temperature procedure

Classification Wave Soldering Profile:Profile Feature Pb-Free Assembly Sn-Pb AssemblyPreheat Temperature Min 1) Ts min 100 °C 100 °C

Preheat Temperature Typical Ts typical 120 °C 120 °C

Preheat Temperature Max Ts max 130 °C 130 °C

Preheat Time ts from Ts min to Ts max ts 70 seconds 70 seconds

Peak temperature Tp 250 °C - 260 °C 235 °C - 260 °C

Time of actual peak temperature tpmax. 10 secondsmax. 5 seconds each wave

max. 10 secondsmax. 5 seconds each wave

Ramp-down Rate, Min ~ 2 K/ second ~ 2 K/ second

Ramp-down Rate, Typical ~ 3.5 K/ second ~ 3.5 K/ second

Ramp-down Rate, Max ~ 5 K/ second ~ 5 K/ second

Time 25°C to 25°C 4 minutes 4 minutes

1) refer to EN61760-1:2006refer to EN 61760-1:2006



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DESCRIPTION



5353 001.001 Draft 2015-12-01 4/6


Cautions & Warnings:The following conditions apply to all goods within the product series of WE-WPCC of Würth Elektronik eiSos GmbH & Co. KG:

General:All recommendations according to the general technical specifications of the data sheet have to be complied with.

The usage and operation of the product within ambient conditions, which probably alloy or harm the wire isolation, has to be avoided.

If the product is potted in customer applications, the potting material might shrink during and after hardening. The product is exposed to thepressure of the potting material with the effect that the core, wire and termination is possibly damaged by this pressure and so theelectrical as well as the mechanical characteristics are endangered to be affected. After the potting material is cured, the core, wire andtermination of the product have to be checked if any reduced electrical or mechanical functions or destructions have occurred.

The responsibility for the applicability of customer specific products and use in a particular customer design is always within the authority ofthe customer. All technical specifications for standard products do also apply to customer specific products.

Cleaning agents that are used to clean the customer application might damage or change the characteristics of the component, body, pinsor termination.

Direct mechanical impact to the product shall be prevented as the ferrite material of the core could flake or in the worst case it could break.

Product specific:

Follow all instructions mentioned in the data sheet, especially:

• The soldering profile has to be complied with according to the technical wave soldering specification, otherwise this will void thewarranty.

• Reflow soldering is not applicable. Wave soldering is recommended.• All products shall be used before the end of the period of 12 months based on the product date code, if not a 100% solderability can´t

be ensured.• Violation of the technical product specifications such as exceeding the nominal rated current will void the warranty.• Due to heavy weight of the component, strong forces and high accelerations might have the effect to damage the electrical connection

or to harm the circuit board and will void the warranty.

The general and product specific cautions comply with the state of the scientific and technical knowledge and are believed to be accurateand reliable; however, no responsibility is assumed for inaccuracies or incompleteness.



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DESCRIPTION



5353 001.001 Draft 2015-12-01 5/6


Important Notes

The following conditions apply to all goods within the product range of Würth ElektronikeiSos GmbH & Co. KG:

1. General Customer Responsibility

Some goods within the product range of Würth Elektronik eiSos GmbH & Co. KG contain statements regarding general suitability for certainapplication areas. These statements about suitability are based on our knowledge and experience of typical requirements concerning theareas, serve as general guidance and cannot be estimated as binding statements about the suitability for a customer application. Theresponsibility for the applicability and use in a particular customer design is always solely within the authority of the customer. Due to thisfact it is up to the customer to evaluate, where appropriate to investigate and decide whether the device with the specific productcharacteristics described in the product specification is valid and suitable for the respective customer application or not.

2. Customer Responsibility related to Specific, in particular Safety-Relevant Applications

It has to be clearly pointed out that the possibility of a malfunction of electronic components or failure before the end of the usual lifetimecannot be completely eliminated in the current state of the art, even if the products are operated within the range of the specifications.In certain customer applications requiring a very high level of safety and especially in customer applications in which the malfunction orfailure of an electronic component could endanger human life or health it must be ensured by most advanced technological aid of suitabledesign of the customer application that no injury or damage is caused to third parties in the event of malfunction or failure of an electroniccomponent. Therefore, customer is cautioned to verify that data sheets are current before placing orders. The current data sheets can bedownloaded at www.we-online.com.

3. Best Care and Attention

Any product-specific notes, cautions and warnings must be strictly observed. Any disregard will result in the loss of warranty.

4. Customer Support for Product Specifications

Some products within the product range may contain substances which are subject to restrictions in certain jurisdictions in order to servespecific technical requirements. Necessary information is available on request. In this case the field sales engineer or the internal salesperson in charge should be contacted who will be happy to support in this matter.

5. Product R&D

Due to constant product improvement product specifications may change from time to time. As a standard reporting procedure of theProduct Change Notification (PCN) according to the JEDEC-Standard inform about minor and major changes. In case of further queriesregarding the PCN, the field sales engineer or the internal sales person in charge should be contacted. The basic responsibility of the

customer as per Section 1 and 2 remains unaffected.

6. Product Life Cycle

Due to technical progress and economical evaluation we also reserve the right to discontinue production and delivery of products. As astandard reporting procedure of the Product Termination Notification (PTN) according to the JEDEC-Standard we will inform at an early stageabout inevitable product discontinuance. According to this we cannot guarantee that all products within our product range will always beavailable. Therefore it needs to be verified with the field sales engineer or the internal sales person in charge about the current productavailability expectancy before or when the product for application design-in disposal is considered. The approach named above does notapply in the case of individual agreements deviating from the foregoing for customer-specific products.

7. Property Rights

All the rights for contractual products produced by Würth Elektronik eiSos GmbH & Co. KG on the basis of ideas, development contracts aswell as models or templates that are subject to copyright, patent or commercial protection supplied to the customer will remain with WürthElektronik eiSos GmbH & Co. KG. Würth Elektronik eiSos GmbH & Co. KG does not warrant or represent that any license, either expressed orimplied, is granted under any patent right, copyright, mask work right, or other intellectual property right relating to any combination,application, or process in which Würth Elektronik eiSos GmbH & Co. KG components or services are used.

8. General Terms and Conditions

Unless otherwise agreed in individual contracts, all orders are subject to the current version of the “General Terms and Conditions of WürthElektronik eiSos Group”, last version available at www.we-online.com.



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DESCRIPTION



5353 001.001 Draft 2015-12-01 6/6


Dimensions: [mm]

Scale - 1:1,6

2,0q

47,0

O50,0

± 1,

1O

15,0

± 0,

1O

5,0 ref.43,0 ± 2

18,0 6,0 ref.

10,0 ± 21

2

40,0 ± 248,0 ± 1,1

Heat shrinkableTubing (black)

3,2

max

.6,

0m

ax.


Scale - 1:1,5

1 25,0 min.

O 2,0

Schematic:















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DESCRIPTION



Ø 50 001.001 Draft 2015-12-01 1/6



0.0

5.0

10.0

15.0

20.0

25.0

30.0

0.0 2.0 4.0 6.0 8.0 10.0 12.0

Ind

ucta

nce [

µH

]

Current [A]


1

10

100

10 100 1000 10000

Ind

ucta

nce [

µH

]

Frequency [kHz]



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DESCRIPTION



Ø 50 001.001 Draft 2015-12-01 2/6



0

40

80

120

160

200

240

10 100 1000

Q-f

ac

tor

Frequency [kHz]


0.0

10.0

20.0

30.0

40.0

50.0

60.0

70.0

80.0

0.0 2.0 4.0 6.0 8.0 10.0

Tem

pera

ture

Ris

e [

K]

Current [A]



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DESCRIPTION



Ø 50 001.001 Draft 2015-12-01 3/6



Time

Tp

tp

Ts maxTs typical

Ts min

First Wave


Second Wave
















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DESCRIPTION



Ø 50 001.001 Draft 2015-12-01 4/6









Product specific:









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DESCRIPTION



Ø 50 001.001 Draft 2015-12-01 5/6


Important Notes










5. Product R&D





7. Property Rights






[email protected]



DESCRIPTION



Ø 50 001.001 Draft 2015-12-01 6/6


Dimensions: [mm]

Scale - 1:1

Heat shrinkableTubing (black)

2,8

max

.

20,5 max. 49,0 ± 3,0

10,0 ± 2,0

6,0 ref.


Scale - 1:1,5

1 25,0 min.

O 2,0

Schematic:

Electrical PropertiesProperties Test conditions Value Unit Tol.Inductance 125 kHz/ 10 mA L 3.3 μH ±10%






Self ResonantFrequency fres 20 MHz

General InformationIt is recommeded that the temperature of the component does not exceed +105°C under worst

case conditions


Storage Temperature (inoriginal packaging) TS -20 °C up to +60 °C




[email protected]


SSt CSo DIN ISO 2768-1m

DESCRIPTION



Ø 20 001.000 Draft 2016-03-17 eiSos 1/6



0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0

Ind

ucta

nce [

µH

]

Current [A]


1

10

100

10 100 1000 10000 100000

Ind

ucta

nce [

µH

]

Frequency [kHz]



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DESCRIPTION



Ø 20 001.000 Draft 2016-03-17 eiSos 2/6



0

20

40

60

80

100

120

10 100 1000 10000

Q-f

ac

tor

Frequency [kHz]


0.0

10.0

20.0

30.0

40.0

50.0

60.0

0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0

Tem

pera

ture

Ris

e [

K]

Current [A]



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DESCRIPTION



Ø 20 001.000 Draft 2016-03-17 eiSos 3/6



Time

Tp

tp

Ts maxTs typical

Ts min

First Wave


Second Wave


Classification Wave Soldering Profile:Profile Feature Pb-Free Assembly Sn-Pb AssemblyPreheat Temperature Min Ts min 100 °C 100 °C











refer to EN61760-1:2006



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DESCRIPTION



Ø 20 001.000 Draft 2016-03-17 eiSos 4/6









Product specific:









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DESCRIPTION



Ø 20 001.000 Draft 2016-03-17 eiSos 5/6


Important Notes










5. Product R&D





7. Property Rights






[email protected]



DESCRIPTION



Ø 20 001.000 Draft 2016-03-17 eiSos 6/6


Dimensions: [mm]

Scale - 2:1

3,0

5,0 ± 2,0

25,0 ± 2,017,0 ± 0,3O

detail A

0,82

±0,2

Copper Coil

Release Paper

Doublefaced Adhesive Tape

Ferrite Sheet

PET

Glue

A

Recommended Hole Pattern: [mm]

1 22,0 min.

O 1,0

Scale - 1:1,5

Schematic:


Q-factor 125 kHz/ 10 mA Q 20 typ.

Rated Current ΔT = 40 K IR 1.1 A max.

Saturation Current ISAT 2.5 A typ.











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DESCRIPTION

WE-WPCC Wireless PowerCharging Receiver Coil ORDER CODE


Ø 17 001.001 Draft 2015-12-01 1/6



0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Ind

ucta

nce [

µH

]

Current [A]


1

10

100

1000

10 100 1000 10000 100000

Ind

ucta

nce [

µH

]

Frequency [kHz]



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DESCRIPTION



Ø 17 001.001 Draft 2015-12-01 2/6



0

10

20

30

40

10 100 1000 10000

Q-f

ac

tor

Frequency [kHz]


0.0

10.0

20.0

30.0

40.0

50.0

60.0

70.0

0.0 0.3 0.6 0.9 1.2 1.5 1.8

Tem

pera

ture

Ris

e [

K]

Current [A]



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DESCRIPTION



Ø 17 001.001 Draft 2015-12-01 3/6



Time

Tp

tp

Ts maxTs typical

Ts min

First Wave


Second Wave
















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DESCRIPTION



Ø 17 001.001 Draft 2015-12-01 4/6


Cautions and Warnings:

The following conditions apply to all goods within the product series of WE-WPCC ofWürth Elektronik eiSos GmbH & Co. KG:

General:

All recommendations according to the general technical specifications of the data sheet have to be complied with.





Direct mechanical impact to the product shall be prevented as the core material could flake or in the worst case could break.

Product specific:


• The soldering profile has to be complied with according to the technical reflow soldering specification, otherwise this will void thewarranty.







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DESCRIPTION



Ø 17 001.001 Draft 2015-12-01 5/6


Important Notes










5. Product R&D





7. Property Rights






[email protected]



DESCRIPTION



Ø 17 001.001 Draft 2015-12-01 6/6


Dimensions: [mm]

Scale - 3:1

5 ±2,0

6,0 ± 0,3 25,0 ±2,0

2,5

2,0

max

. Copper Coil

Epoxy

PET

Ferrite Sheet

Adhesive Tape

Release Paper

detail A

Release Tape

A


1 22,0 min.

O 1,0

Scale - 1:1,5

Schematic:



Rated Current ΔT = 40 K IR 0.5 A max.












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DESCRIPTION



Ø 6 001.000 Draft 2015-12-10 1/6



0,0

1,0

2,0

3,0

4,0

5,0

6,0

7,0

8,0

0,0 0,2 0,4 0,6 0,8 1,0 1,2

Ind

ucta

nce [

µH

]

Current [A]


1

10

100

1000

10 100 1000 10000 100000

Ind

ucta

nce [

µH

]

Frequency [kHz]



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DESCRIPTION



Ø 6 001.000 Draft 2015-12-10 2/6



0

10

20

10 100 1000 10000

Q-f

ac

tor

Frequency [kHz]


0.0

10.0

20.0

30.0

40.0

50.0

0.0 0.2 0.4 0.6 0.8 1.0

Tem

pera

ture

Ris

e [

K]

Current [A]



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DESCRIPTION



Ø 6 001.000 Draft 2015-12-10 3/6



Time

Tp

tp

Ts maxTs typical

Ts min

First Wave


Second Wave
















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DESCRIPTION



Ø 6 001.000 Draft 2015-12-10 4/6




General:







Product specific:









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DESCRIPTION



Ø 6 001.000 Draft 2015-12-10 5/6


Important Notes










5. Product R&D





7. Property Rights






[email protected]



DESCRIPTION



Ø 6 001.000 Draft 2015-12-10 6/6


Dimensions: [mm]

40 ±0,3

40±0

,3

detail B

0,45

2x O

5 ref.

0,9

ref.

5re

f.

25u1

1,2

±0,3

with

adh

esiv

e ta

pe

B

Scale - 1:1,5


1 22,0 min.

O 1,0

Scale - 1:1,5

Schematic:















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DESCRIPTION



4040 001.001 Draft 2015-12-01 1/6



0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

8.0

9.0

0.0 2.0 4.0 6.0 8.0 10.0 12.0

Ind

ucta

nce [

µH

]

Current [A]


1

10

100

10 100 1000 10000 100000

Ind

ucta

nce [

µH

]

Frequency [kHz]



[email protected]



DESCRIPTION



4040 001.001 Draft 2015-12-01 2/6


Q-factor vs. Frequency:

0

20

40

10 100 1000

Q-f

acto

r

Frequency [kHz]


0.0

5.0

10.0

15.0

20.0

25.0

30.0

35.0

40.0

45.0

0.0 1.0 2.0 3.0 4.0 5.0 6.0

Tem

pera

ture

Ris

e [

K]

Current [A]



[email protected]



DESCRIPTION



4040 001.001 Draft 2015-12-01 3/6



Time

Tp

tp

Ts maxTs typical

Ts min

First Wave


Second Wave
















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DESCRIPTION



4040 001.001 Draft 2015-12-01 4/6




General:







Product specific:









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DESCRIPTION



4040 001.001 Draft 2015-12-01 5/6


Important Notes










5. Product R&D





7. Property Rights






[email protected]



DESCRIPTION



4040 001.001 Draft 2015-12-01 6/6


10 REFERENCES

[1] S. R. A. Bolonne, A. K. K. Chanaka, G. C. Jayawardhana, I. H. T. D. Lionel

y D. P. Chandima, Wireless Power Transmition for Multiple Devices,

Moratuwa: Department of Electrical Engineering, University of Moratuwa.

[2] F. Ye, Q. Chen y W. Chen, Analysis and Design of Magnetic Coupling

Structure in Wireless Power Transmission System, Fuzhou: College of

Electrical Engineering and Automation. Fuzhou University.

[3] M. Guifford, "Transferencia de Energía Inalámbrica para Alimentación de

un Marcapasos: Análisis del Enlace Resonante Inductivo." Trabajo de Fin

de Carrera (ETSII - UPM), 2015.

[4] D. Cabrera, WPT: Control para Máxima Transferencia de Potencia con

Enlace Resonante Inductivo, Madrid: ETSII - UPM, 2016.

[5] C. D. Gurkan Yilmaz, An Efficient Wireless Power Link for Implanted

Biomedical Devices via Resonant Inductive Coupling, RFIC Group, Ecole

Polytechnique Federale de Lausanne.

[6] N. Tesla, "The Transmission of Electrical Energy Without Wires", Electrical

World and Engineer, 1905.

[7] K. B. S. Kiran, S. Brahma, S. K. Parida y R. K. Behera, Analysis of Inductive

Resonant Coupled WPT System using Reflected Load Theory, Indian

Institute of Technology Patna., 2014.

[8] M. Guifford, Transferencia de Energía Inalámbria para Alimantación de un

Marcapasos: Análisis del Enlace Resonante Inductivo, Madrid: ETSII -

UPM, 2015.

[9] Saurabh, D. Kapur y R. J, Wireless Power Trnasmission for Solar Input,

Vellore: School of Electrical Engineering, VIT University.



[10] T. Nagashima, X. Wei, E. Bou, E. Alarcón y H. Sekiya, Analytical Design

for Resonant Inductive Coupling Wireless Power Transfer System with

Class-E inverter and class-DE Rectifier, Fukuoka University, UPC

BacelonaTech.

[11] K. Aditya, M. Youssef y S. S. Williamson, Analysis of Series-Parallel

Resonant Inductive Coupling Circuit using the Two-port Network Theory,

University of Ontario-Institute of Technology, 2015.

[12] A. Berger, A Wireless Charging System Applying Phase-Shift and

Amplitude.

[13] M. G. S. Heredia, Transferencia Inalámbrica de Energía Mediante

Acoplamiento Inductivo Resonante en el Ambito de los Marcapasos,

Madrid: ETSIME - UPM, 2016.

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máster universitario en electrónica...

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