Copyright by Ick-Jae Yoon 2012

The Dissertation Committee for Ick-Jae Yoon Certifies that this is the approved version of the following dissertation:

Realizing Efficient Wireless Power Transfer in the Near-Field Region Using Electrically Small Antennas

Committee:

Hao Ling, Supervisor

Andrea Alù

Ross Baldick

Heinrich Foltz

Ali Yilmaz

Realizing Efficient Wireless Power Transfer in the Near-Field Region Using Electrically Small Antennas

Ick-Jae Yoon, B.S.; M.S.

Dissertation Presented to the Faculty of the Graduate School of The University of Texas at Austin in Partial Fulfillment of the Requirements for the Degree of

Doctor of Philosophy

The University of Texas at Austin August 2012

Dedicated to my dearly beloved family Acknowledgements

There are many people who deserve recognition for their contribution to the success of this dissertation from my four years at the University of Texas. First of all, I would like to express my deepest appreciation to my supervisor and mentor, Dr. Hao

Ling, who introduced me to the beauty of electromagnetics through my Ph.D. study. His exemplary guidance with deep insight, broad and profound knowledge, encouragement, patience, and open perspective to my ideas inspired me to mature academically. Without his supervision, I would never have produced meaningful results from my Ph.D. research, and for that I will always be grateful. I also thank him for being with me during the ups and downs of my four years in Austin. I would also like to thank my committee members – Dr. Andrea Alù, Dr. Ross Baldick, Dr. Heinrich Foltz, and Dr. Ali E. Yilmaz for their time and helpful suggestions on my dissertation. My appreciation also goes out to my fellow research group members over the years: Dr. Hosung Choo, Dr. Sungkyun Lim, Dr. Youngwook Kim, Dr. Shobha S. Ram, Dr. Yang Li, Dr. Nicholas J. Whitelonis, Mr. Shang-Te Yang, Mr. Aale Naqvi, Mr. Bong W. Jun, and Mr. Chenchen Li for their helpful and invaluable discussions.

Last, I can never thank my parents enough for their endless love, encouragement and unconditional support in all aspects of my life. Finally, thanks to my wife, Jungin, for her love, support and patience while I pursued my Ph.D.

ICK -JAE YOON The University of Texas at Austin August 2012 v Realizing Efficient Wireless Power Transfer in the Near-Field Region Using Electrically Small Antennas

Ick-Jae Yoon, Ph.D.

The University of Texas at Austin, 2012

Supervisor: Hao Ling

Non-radiative wireless power transfer using the coupled mode resonance phenomenon has been widely reported in the literature. However, the distance over which such phenomenon exists is very short when measured in terms of wavelength. In this dissertation, how efficient wireless power transfer can be realized in the radiating near- field region beyond the coupled mode resonance region is investigated. First, electrically small folded cylindrical helix (FCH) dipole antennas are designed to achieve efficient near-field power transfer. Measurements show that a 40% power transfer efficiency (PTE) can be realized at the distance of 0.25 λ between two antennas in the co-linear configuration. These values come very close to the theoretical upper bound derived based on the spherical mode theory. The results also highlight the importance of antenna radiation efficiency and impedance matching in achieving efficient wireless power transfer. Second, antenna diversity is explored to further extend the range or efficiency of the power transfer. For transmitter diversity, it is found that a stable PTE region can be created when multiple transmitters are employed at sufficiently close spacing. For receiver diversity, it is found that the overall PTE can be improved as the number of the receivers is increased. vi Third, small directive antennas are investigated as a means of enhancing near- field wireless power transfer. Small directive antennas based on the FCH design are also implemented to enhance the PTE. It is shown that the far-field realized gain is a good surrogate for designing small directive antennas for near-field power transfer.

Fourth, to examine the effects of surrounding environments on near-field coupling, an upper bound for near-field wireless power transfer is derived when a transmitter and a received are separated by a spherical material shell. The derived PTE bounds are verified using full-wave electromagnetic simulation and show good agreement for both TM mode and TE mode radiators. Using the derived theory, lossy dielectric material effects on wireless power transfer are studied. Power transfer measurements through walls are also reported and compared with the theory. Lastly, electrically small circularly polarized antennas are investigated as a means of alleviating orientation dependence in near-field wireless power transfer. An electrically small turnstile dipole antenna is designed by utilizing top loading and multiple folding. The circularly polarization characteristic of the design is first tested in the far field, before the antennas are placed in the radiating near-field region for wireless power transfer. It is shown that such circularly polarized antennas can lessen orientation dependence in near-field coupling.

vii Table of Contents

List of Tables ...... x

List of Figures ...... xi

CHAPTER 1: INTRODUCTION ...... 1

CHAPTER 2: ACHIEVING THEORETICAL POWER TRANSFER EFFICIENCY BOUND USING ELECTRICALLY SMALL ANTENNAS ...... 6

2.1 Introduction ...... 6

2.2 Power flow between antennas in different regions ...... 7

2.3 Theoretical bound for near-field power transfer and antenna design considerations ...... 9

2.4 Design of electrically small, folded cylindrical helix (FCH) antennas ...... 16

2.5 Near-field power transfer simulation and measurement ...... 20

2.6 Summary ...... 24

CHAPTER 3: WIRELESS POWER TRANSFER ENHANCEMENT USING TRANSMITTER DIVERSITY AND RECEIVER DIVERSITY ...... 26

3.1 Introduction ...... 26

3.2 Near-field power transfer bound under transmitter diversity ...... 27

3.3 Power transfer simulation and measurement ...... 32

3.4 Near-field power transfer under receiver diversity ...... 38

3.5 Summary ...... 41

CHAPTER 4: WIRELESS POWER TRANSFER ENHANCEMENT USING SMALL DIRECTIVE ANTENNAS ...... 43

4.1 Introduction ...... 43

4.2 Feasibility and antenna design considerations ...... 45

4.3 Design of an electrically small FCH Yagi ...... 47

viii 4.4 Power transfer simulation and measurement ...... 56

4.5 Summary ...... 60

CHAPTER 5: INVESTIGATION OF NEAR -FIELD WIRELESS POWER TRANSFER IN THE PRESENCE OF LOSSY DIELECTRIC MATERIALS ...... 62

5.1 Introduction ...... 62

5.2 Derivation of upper PTE bound ...... 62

5.3 Validation and Results ...... 67

5.4 Summary ...... 79

CHAPTER 6: ALLEVIATING ORIENTATION DEPENDENCE IN NEAR-FIELD WIRELESS POWER TRANSFER USING SMALL , CIRCULAR POLARIZATION ANTENNAS ...... 80

6.1 Introduction ...... 80

6.2 Review of the half wavelength turnstile antenna ...... 82

6.3 Design of electrically small turnstile dipole antenna ...... 86

6.4 PTE values using electrically small turnstile dipole antenna ...... 97

6.5 Summary ...... 99

CHAPTER 7: CONCLUSIONS AND FUTURE WORK ...... 101

Appendix A ...... 104

Bibliography ...... 107

ix List of Tables

Table 3.1 : Measured Resonant Frequency and Input Resistance of the Fabricated

FCH Dipoles...... 33

Table 4.1 : Optimized Design Dimension Parameters...... 49

x List of Figures

Figure 1.1 : Power transfer efficiency vs. distance between two electrically small

meander antennas operating at 43MHz...... 3 Figure 2.1 : Power flow between transmitting and receiving antennas. (a) Coupled mode region: d=0.05 λ. (b) Radiating near-field region: d=0.3 λ. (c) Far-

field region: d=1.0 λ...... 8

Figure 2.2 : Two small antennas in free space for wireless power transfer...... 9 Figure 2.3 : PTE bound versus distance for different radiation efficiencies and antenna orientations. (a) Radiation efficiency of small dipole

(TM 10 )=1.0. (b) Radiation efficiency of small dipole (TM10 )=0.7...... 14 Figure 2.6 : Simulated and measured input impedance of the folded cylindrical helix

dipole. (a) Input resistance. (b) Input reactance...... 19 Figure 2.7 : Photos of the outdoor measurement setup. Each FCH is connected to a

2:1 transformer balun. (a) θ=0. (b) θ=π/2...... 21 Figure 2.8 : Simulated and measured PTE of two FCH-FCH dipoles. (a) θ=0. (b)

θ=π/2...... 22 Figure 2.9 : Real part of the optimal load values with two folded cylindrical helix

dipole antennas ( Zin =48.9 Ω) for collinear ( θ=0) and parallel ( θ=π/2)

configurations...... 24 Figure 3.2 : PTE bound for transmitter diversity (two transmitters and one receiver) in the parallel configuration. The two transmitters are separated by the

fixed distance D. (a) D=0.7 λ. (b) D=1.0 λ...... 30

xi Figure 3.3 : Optimal load value ( Zopt ) for the PTE bound with 0.7 λ separation

between the transmitters (Figure 3.2a case), with respect to Za=0.079-

11270j [ Ω]...... 31 Figure 3.4 : NEC simulation setup for the two-transmitter and one-receiver scheme

using electrically small folded cylindrical helix dipoles. The antennas

are in the parallel configuration...... 33

Figure 3.5 : Photo of the measurement setup...... 34 Figure 3.6 : Simulated and measured PTE for transmitter diversity using three FCH

dipoles...... 35 Figure 3.7 : Four-transmitter and one-receiver scheme. (a) PTE bound. (b) NEC

simulation using electrically small folded cylindrical helix dipoles...... 36 Figure 3.8 : PTE bound and NEC simulation result for receiver diversity (1-Tx, 2-

Rx). (a) θ=0. (b) θ=π/2...... 39 Figure 3.9 : Power distribution with single transmitting FCH and multiple receiving

FCH dipoles. (a) 1-Rx, (b) 2-Rx, and (c) 4-Rx...... 40 Figure 4.1 : PTE simulation setup using two-element idealized superdirectivity

arrays...... 46 Figure 4.2 : PTE enhancement in the near-field region using an idealized

superdirective array...... 47

Figure 4.3 : Initial small Yagi antenna design before optimization ...... 48 Figure 4.4 : Theoretical expectation of directivity with two-infinitesimal dipole

array...... 50 Figure 4.5 : Small FCH Yagi design. (a) NEC model. (b) Photo of the fabricated

antenna...... 52

xii Figure 4.6 : Simulation and measurement results of input impedance from the

designed FCH Yagi antenna. (a) Resistance. (b) Reactance...... 53 Figure 4.7 : Simulation and measurement results of return loss from the designed

FCH Yagi antenna...... 54 Figure 4.8 : Simulation and measurement results from the designed FCH Yagi

antenna. (a) Realized gain. (b) Front-back ratio...... 55 Figure 4.9 : Measurement setup. (a) FCH Yagi-FCH Yagi. (b) FCH Yagi-FCH

dipole...... 57 Figure 4.11 : PTE comparison: FCH dipole-FCH dipole, FCH Yagi-FCH dipole and

FCH Yagi-FCH Yagi...... 59 Figure 4.12 : PTE comparison: PTE with transmitter diversity, receiver diversity and

directive antennas...... 60 Figure 5.1 : Coupled small antennas. Transmit antenna enclosed by a finite-

thickness spherical shell of material with a receive antenna in free space. ..63 Figure 5.2 : PTE prediction using the derived theory and FEKO when the shell is

filled with body fluid material ( εr=69.037 and tan δ=1.965). (a) r1=0.05 λ

and τ=0.05 λ (b) r1=0.015 λ and τ=0.05 λ...... 68

Figure 5.3 : PTE under human body fluid material (r1=0.1 λ and τ=0.05 λ). (a) TM and TE mode comparison. (b) Stored electric and magnetic energy

distribution for small loop (TE mode)...... 71

Figure 5.4 : PTE degradation by the thickness of the shell ( r1=0.1 λ). (a) Co-linear

configuration. (b) Parallel configuration...... 72 Figure 5.5 : Normalized optimal load impedance (Zopt) for shell problem with

respect to Za (εr =4, tan δ=0.2, r1=0.1 λ and τ=0.25 λ). (a) Co-linear

configuration. (b) Parallel configuration...... 75 xiii Figure 5.6 : Through-exterior wall PTE measurement. (a) Setup. (b) Results...... 77

Figure 5.7 : Through-interior wall PTE measurement. (a) Setup. (b) Results...... 78 Figure 6.1 : Antenna misalignment. (a) Lateral misalignment. (b) Angular

misalignment. (c) Combination of lateral and angular misalignment...... 80

Figure 6.2 : Half-wavelength turnstile dipole. Voltage source is at the center...... 83 Figure 6.3 : Simulation result of a turnstile dipole antenna. (a) Absolute axial ratio

intensity along the length of the dipole elements. (b) Axial ratio vs.

frequency. (c) Input impedance...... 85 Figure 6.4 : Small circular polarization antenna with top loading disc. (a) Structure.

(b) Absolute axial ratio intensity along the length of the dipole elements. ..87 Figure 6.5 : Small circular polarization antenna with top loading disc and folded arm. (a) Structure. (b) Absolute axial ratio intensity along the length of

the dipole elements...... 90 Figure 6.6 : Fabricated circular polarization antennas (Tx and Rx). One shows the

front side and the other one shows the back side...... 91 Figure 6.7 : Simulation and measurement results for the designed circular polarization antenna. (a) Axial ratio. (b) Return loss. (c) Input reactance.

(d) Input resistance...... 93 Figure 6.8 : Circular polarization characteristic measurement. (a) Setup. (b)

Transmission loss. (c) Magnitude ratio. (d) Phase difference...... 96

Figure 6.9 : PTE simulation setup. (a) Identical orientation. (b) Oriented at 45 ...... 98

Figure 6.10 : PTE simulation for polarization mismatch case...... ° 99 Figure A.1 : Balun de-embedding setup. ( *ADT2-1T 2:1 transformer from Mini-

Circuits used as a balun.) ...... 104

Figure A.2 : T-network of a balun...... 105 xiv Chapter 1: Introduction

The dream of delivering power wirelessly over a significant distance has been around since the early days of electromagnetism. In the early 1900’s, Tesla carried out his famous experiment on power transmission over long distances by radio waves [1]. He built a giant coil (200-ft mast and 3-ft-diameter copper ball positioned at the top) resonating at 150 kHz and fed it with 300 kW of low frequency power. However, there is no clear record of how much of this power was radiated into space and whether any significant amount of it was collected at a distant point. Over the years, wireless power delivery systems have been conceived, tried and tested by many [2]-[8]. For very short

ranges, the inductive coupling mechanism is commonly exploited. This is best

exemplified by non-contact chargers and radio frequency identification (RFID) devices

operating at 13 MHz [9]. Such systems are limited to ranges that are less than the device

size itself. For long distance wireless power delivery, directed radiation is required,

which dictates the use of large aperture antennas. This line of thinking is best exemplified

by NASA’s effort to collect solar power on a single satellite station in space and relay the

collected power via microwaves to power other satellites in orbit [3]. In addition to

needing large antennas, this scheme requires uninterrupted line-of-sight propagation and

a potentially complicated tracking system for mobile receivers.

In 2007, MIT physicist Solja čić and his group demonstrated the feasibility of

efficient non-radiative wireless power transfer (WPT) using two resonant loop antennas

[10]. Since then, there has been much interest from the electromagnetics community to

1 more closely study this phenomenon [11]-[25]. It was found that when two antennas are very closely spaced, they are locked in a coupled mode resonance phenomenon. In this coupled mode region, the two antennas see each other’s presence strongly, and very high power transfer efficiency (PTE) can be attained (see Figure 1.1). The term magnetic resonance coupling is often used to describe this phenomenon, although such coupled mode resonance can exist in antenna systems dominated by either magnetic or electric coupling, as shown in [11]. It was also found that to maximize the power transfer the antennas need to have low radiation loss so that power is not lost to the radiation process.

However, such a coupled mode region is very short when measured in terms of electrical wavelength. Due to the strong coupling between the antennas, the frequency at which resonance occurs is also shifted from the original resonant frequency of the antennas.

This frequency splitting phenomenon is a function of the antenna spacing. Moreover, an optimal load impedance exists for achieving maximum transfer efficiency. This value again changes as a function of the distance between the antennas. All of these characteristics make design of an optimal system for efficient WPT rather challenging.

When the distance between the two antennas increases, the coupled mode resonance phenomenon disappears, and the antennas behave like traditional transmitting

(Tx) and receiving (Rx) antennas in the near field (see Figure 1.1). Beyond the coupled mode region, the PTE decreases rapidly as a function of distance. Nevertheless, sufficiently high PTE values might still be maintained for such coupling to be useful for power transfer.

Figure 1.1: Power transfer efficiency vs. distance between two electrically small meander antennas operating at 43MHz.

The physics beyond the coupled mode region is significantly easier to interpret.

There have been works on the coupling properties of antennas in the near-field region, though the interest was not for WPT. In the 1970’s, theoretical and practical aspects of the spherical near-field antenna measurement were extensively studied at the Technical

University of Denmark [26]. Yaghjian formulated a coupling equation between a Tx and

Rx antenna pair by the spherical wave expansion [27]. To more accurately estimate the coupling in the near-filed region, heuristic corrections to the far-field Friis formula were also attempted by adding a gain reduction factor [28] or by adding higher order distance terms [29]. More recently, attention was turned to WPT in this region. Lee and Nam presented a theoretical PTE bound for WPT in the near-field region under the optimal load condition [30]. They applied the spherical mode theory to study the coupling 3 between two electrically small antennas. It was found that a 40% PTE value can be theoretically achieved at a distance of 0.26 λ in the co-linear configuration of electric dipole antennas, while the same PTE value was obtained at 0.067 λ based on the MIT

experiment using two resonant, multi-turn helices under coupled mode operation [10].

Therefore, if practical antennas can be realized to achieve the PTE bound of Lee and

Nam, the distance for efficient WPT can be significantly extended over the current state

of the art. This could potentially benefit a number of applications including RFID [31]-

[35], biomedical implants [36]-[39], and electric car charging [40]-[41]. However, at

frequencies where the electrical wavelength is tens of meters or more, designing

physically compact antennas becomes a real challenge.

The design of electrically small but highly efficient antennas is a research topic

that has been well investigated in the past decade [42]-[45]. Among the various small

antenna designs, the most well-known is the folded spherical helix (FSH) by Best [44]. In

his design, four arms are wound helically along a spherical surface and the arms are

connected at the top. Such design uses multiple folds to step up the radiation resistance.

The reported size of kr is 0.38 (where k is the free-space wave number and r is the

minimum size of the imaginary sphere enclosing the antenna). The FSH monopole

antenna yields a low Q (32) and high radiation efficiency η (98.6%) despite its small size.

The folded cylindrical helix (FCH) has also been investigated [46]-[48]. Although it does

not achieve as low a Q-factor as that of the FSH, it has a form factor that is easier to construct and handle.

4 This dissertation focuses on the radiating near-field region beyond the coupled mode resonance region. In particular, it will be shown that electrically small antennas can be designed to realize efficient WPT in the radiating near field. This dissertation is organized as follows. In Chapter 2, it is shown that the theoretical bound derived in [30] can be approached by the use of two electrically small but highly efficient FCH dipoles.

In Chapter 3, transmitter and receiver diversity is discussed as a means to extend the range or efficiency of the near-field power transfer. The theoretical PTE bounds are derived under transmitter diversity and receiver diversity and such bounds are achieved experimentally using actual FCH dipoles. In Chapter 4, electrically small, directive antennas are investigated as a means of increasing the range or power transfer efficiency in the near-field region. Chapter 5 investigates dielectric material effects on near-field

WPT. An analytic PTE bound is derived when a Tx antenna is surrounded by a finite thickness material shell and an Rx antenna is outside the shell. Using the derived theory, lossy dielectric material effects on WPT are studied for both TM and TE mode radiators.

Chapter 6 describes the design of electrically small, circular polarization antennas to alleviate orientation dependence in near-field WPT. The final chapter presents conclusions and discusses potential future studies that could follow from the work presented here.

5 Chapter 2: Achieving theoretical power transfer efficiency bound using electrically small antennas

2.1 INTRODUCTION

Since the feasibility of non-radiative WPT over short ranges using two resonant antennas was demonstrated in [10], many works have been published in the electromagnetics community [11]-[25]. In [11], the coupled mode behaviors of two electrically small meander antennas were investigated. It was found that when two antennas are very closely spaced, they are locked in a coupled mode resonance phenomenon. In this coupled mode region, the two antennas see each other’s presence strongly, and very high PTE can be attained (above 80%). It was also found that to maximize the power transfer, the antennas need to have small radiation resistances so that power is not lost to the radiation process. However, attempts to design antennas to extend the distance over which such coupled mode phenomenon can be maintained have proven to be rather difficult [13].

When the distance between the two antennas increases, the coupled mode resonance phenomenon disappears, and the antennas behave like traditional Tx and Rx antennas in the near field. The physics beyond the coupled mode region is significantly easier to interpret. It is under this premise that the spherical mode theory for electrically small antennas was applied to study the coupling between two antennas in this region

[30]. A theoretical PTE bound was presented under the optimal load condition.

Furthermore, it was shown that high antenna radiation efficiency is needed to maximize the power transfer beyond the coupled mode region. However, to date no experimental 6 validation has been provided. In this chapter, it is demonstrated experimentally that the theoretical PTE bound derived in [30] can be indeed be realized by the design of efficient, electrically small antennas.

This chapter describes the use of FCH antennas to achieve the upper PTE bound derived in [30]. First, the theoretical PTE bound is reviewed. Then the design specifications including the radiation efficiency, antenna orientation, and input impedance of the antenna for maximum power transfer beyond the coupled mode region are discussed. The FCH dipole is next designed based on the Numerical Electromagnetics

Code (NEC). Two prototypes are constructed and tested. The PTE between the two antennas are simulated and measured. The results are compared with the theoretical bound.

2.2 POWER FLOW BETWEEN ANTENNAS IN DIFFERENT REGIONS

We begin by studying the power transfer mechanism in the coupled mode region, the radiating near-field region and the far-field region. In Figure 2.1, the real part of the complex Poynting’s vector with two very short ( λ/50) Tx and Rx dipoles is plotted in dB

scale. In all three figures, the Tx antenna is at the center and the distance between the

antennas is chosen as 0.05 λ, 0.3 λ and 1.0 λ to represent the three regions, respectively. A

load value for optimal power transfer is assumed in each case. It is shown in Figure 2.1a

that the power flowing out of the Tx antenna is channeled into the Rx antenna due to their

strong coupling. In contrast, Figure 2.1c shows that the power flowing out of the Tx

antenna is very similar to that of a stand-alone dipole antenna since the coupling amount

7 between the antennas is very weak. In the radiating near-field region shown in Figure

2.1b, it is observed that the shape of the power flow is in-between those in the other two regions.

(a) (b)

-20 -20

1 d=0.05 λ 1 d=0.3 λ -40 -40

0.5 -60 0.5 -60 λ 0 -80 λ 0 -80 z, z,

-0.5 -100 -0.5 -100

-120 -120 -1 -1

-140 -140 -1 -0.5 0 0.5 1 -1 -0.5 0 0.5 1 x, λ x, λ

(c)

-20

1 d=1.0 λ -40

0.5 -60

λ 0 -80 z,

-0.5 d -100

-120 -1

-140 -1 -0.5 0 0.5 1 x, λ

Figure 2.1: Power flow between transmitting and receiving antennas. (a) Coupled mode region: d=0.05 λ. (b) Radiating near-field region: d=0.3 λ. (c) Far-field region: d=1.0 λ.

8 2.3 THEORETICAL BOUND FOR NEAR -FIELD POWER TRANSFER AND ANTENNA DESIGN CONSIDERATIONS

Before discussing antenna design for demonstrating the theoretical PTE bound in

[30], its analytical derivation is first reviewed and verified. To derive the maximum possible PTE for two small antennas in free space as shown in Figure 2.2, [30] assumed that only the TM 10 or TE 10 mode spherical harmonic is transmitted and received by a small electric or magnetic dipole antenna. It is also assumed that the scattering by the antenna itself can be ignored due to its small size. In this review, the terminal of Tx antenna is port 1 and that of the Rx antenna is port 2.

Rx r θθθ ε µ Tx εεo, µµo, ko

Figure 2.2: Two small antennas in free space for wireless power transfer.

Under these assumptions, Nam and Lee described the coupling network between the two antennas as a Z-matrix. For Z11 and Z22 , they are set to have the input impedance

of a stand-alone antenna Za. To determine Z21 , the radiated power from port 1 is related to

the power received at port 2. The power of the outward traveling spherical modes is

expressed as:

9 1 ∗ 1 = × sin = || (2.1) 2 2

1 = | | + 2 where is the radiation resistance of the Tx antenna, I1 is the current at the feed of the Tx antenna, and and are complex coefficients of the TM 10 and TE 10 modes being radiated by the Tx antenna. The fields are represented in a general form as [49]-

[50]:

= + (2.2)

= +

where is the wave impedance in free space and and are the spherical vector wave functions. The subscripts and indicate the even and odd variants of the corresponding mode in the coordinate. Using the addition theorem of spherical wave functions, the radiated field from the Tx antenna can be re-expressed in terms of impinging spherical modes on the Rx antenna for the TM 10 and TE 10 modes as ∙ and , where is the translation coefficient [51]: ∙

10 (2.3) = cos ℎ + cos ℎ

where is the spacing between the antennas in free space, is the angle of the Rx antenna with respect to the Tx antenna (see Figure 2.2), is the wave number, = 2/ is the associated Legendre function of the first kind, and is the cos ℎ spherical Hankel function of the second kind. The maximum receivable power at the Rx antenna is expressed as (2.4) by the Thevenin equivalent circuit with the input impedance of the Rx antenna and the source voltage, :

(2.4) 1 | | = + = 2 2 2 8

where is the radiation efficiency of the Rx antenna. The magnitude of = for the given problem is obtained from (2.1) and (2.4) as:

(2.5) | | = = ∙ ||

By the fact that the spherical mode coefficient and the current over a small antenna have the same uniform phase and by invoking reciprocity, it is obtained that:

11 (2.6) = = ∙ = ∙ ∙

From the Z parameters for the given two port network, the input impedance of the Tx antenna is given by:

(2.7) = − +

where ZL is a load impedance value at the Rx antenna. Since the input power to the network is , the power delivered to the load is: = | |

(2.8) 1 1 = || = 2 2 +

where IL is the current at the load of the Rx antenna. The PTE is defined as the ratio of

the power dissipated in the load of the Rx antenna to the input power accepted by the Tx

antenna:

(2.9) || /2 = = = || /2 +

12 The maximum PTE is found when the load values satisfy and , = 0 = 0 which leads the optimum load for maximum power transfer. The final maximum PTE bound in free space takes on the following simple, closed-form expression:

|| = (2.10) 2 − + 41 − − = ∙ 3 1 1 1 = ∙ − sin + 3 cos − 1 ∙ + ∙ 2

In the above expression, is the free-space wave number. The bound holds = 2/ true for a small electric dipole or a small magnetic dipole antenna.

The PTE bound vs. distance (measured in wavelengths) is computed using (2.9) and (2.10) and plotted in Figure 2.3 for different ɳ (1.0 and 0.7) and θ (0 and π/2) values.

The theory is verified using NEC simulation with two very short ( λ/50) dipoles placed in the near-field region. The radiation efficiency, , of the antennas is varied by changing the conductivity of the wires in NEC. The Linville load, which is the optimal load to achieve maximum power transfer for a general two-port network, is calculated and utilized at each distance. Its detailed derivation is found in [52] and will not be repeated here. It is found from Figure 2.3 that the theory shows very good agreement with the NEC simulation.

13 (a)

10 0

10 -1 =1.0)

eff -2 η 10

PTE ( PTE Theory( θ=0) 10 -3 NEC( θ=0) Theory( θ=π/2) NEC( θ=π/2)

10 -1 10 0 Distance, λ

(b)

10 0

10 -1 =0.7)

eff -2 η 10

PTE ( PTE Theory( θ=0) 10 -3 NEC( θ=0) Theory( θ=π/2) NEC( θ=π/2)

10 -1 10 0 Distance, λ

Figure 2.3: PTE bound versus distance for different radiation efficiencies and antenna orientations. (a) Radiation efficiency of small dipole (TM 10 )=1.0. (b) Radiation efficiency of small dipole (TM 10 )=0.7.

14 It is observed that higher PTE is achieved when the two antennas are in the co- linear configuration ( θ=0 ) than when they are in the parallel configuration ( θ=λ/2 ) up to a distance of 0.4 λ. This is clearly a feature unique to the near-field region, since two electric dipoles cannot couple to each other in the collinear configuration in the far field.

Beyond this distance, our usual far-field intuition takes hold, i.e., antennas couple much more strongly in the parallel instead of the co-linear configuration.

Several additional antenna design implications can be inferred from Figure 2.3.

First, it is observed that PTE decreases rapidly as ɳ decreases, implying that antennas with high radiation efficiency are needed to achieve the best results. It is crucial that any dissipative losses in the antenna are small relative to the radiated power. For example, simply using very short dipoles will not be a good choice to realize efficient power transfer since they have small radiation resistance and thus poor radiation efficiency when constructed using real conductors. Another important consideration is impedance matching. The PTE bounds in Figure 2.3 are derived by assuming a different optimal load value is used at every distance. Any deviation from this optimal load will critically lower the realizable PTE. In the far field, the optimal load is simply the conjugate of the input impedance of the receiving antenna. In the coupled mode region, this conjugate matching condition is strongly violated. Fortunately, the conjugate matching condition is only weakly perturbed in the near-field region, since the antennas are not strongly coupled.

Therefore, enforcing the conjugate matching condition leads to a good design choice for power transfer in the near field, without the need for a complex matching network that is a function of antenna separation. If a 50 Ω load is desirable from a practical point of 15 view, the receiving antenna can be designed to have an input impedance of 50 Ω to approach the PTE bound. The same antenna design, when used for the transmit antenna, will also present a convenient impedance for the transmitter circuitry.

2.4 DESIGN OF ELECTRICALLY SMALL , FOLDED CYLINDRICAL HELIX (FCH) ANTENNAS

To approach the theoretical PTE bound using electrically small antennas, it is desired to design highly efficient antennas with a 50 Ω input impedance. As discussed in

Chapter 1, the FCH is one such candidate with a good form factor and a well-understood design methodology. Since the radiation resistance of an electrically small antenna drops quadratically as a function of its height, the FCH design uses the folding concept to step up the small radiation resistance to improve the radiation efficiency and provide good matching. When N multiple folding arms are used for a highly symmetrical antenna

structure, equal currents are induced on all the arms, resulting in a radiation resistance

2 (Rrad ) that scales approximately as N while the loss resistance ( Rloss ) is increased only by

a factor of N, thus leading to a high radiation efficiency [45].

Figure 2.4 shows the designed FCH dipole operating at 200MHz based on 18- gauge copper wires. The diameter and height of the antenna are chosen to be approximately equal and are confined to a maximum dimension of 10.5cm. The antenna fits within a kr =0.31 sphere. NEC is utilized in the antenna modeling. The number of turns (1.25-turn) and the number of arms (4-arm) are chosen to reach the input impedance target of 50 Ω while achieving a resonant frequency of 200MHz. The resulting antenna

16 has an input resistance of 48.9 Ω with a corresponding of 0.93 based on NEC simulation.

Figure 2.4: The designed 1.25-turn, 4-arm folded cylindrical helix dipole.

In Figure 2.5, the ratios of the electric field strengths, | Er(d,θ=0 )|/|Eθ(d,θ=π/2 )| are plotted versus distance d from the antenna for both the designed FCH dipole and an infinitesimal dipole. It is observed that the field strength ratios out of the two antennas are same for distances beyond 0.2 λ, meaning that the fields from the designed FCH dipole is dominated by the lowest TM 10 mode. It is also seen that the Er field strength along θ=0 is larger than the Eθ field strength along θ=π/2 up to a distance of 0.4 λ. This explains why a higher PTE is achieved for the co-linear configuration than the parallel configuration up to a distance of 0.4 λ in Figure 2.3.

17 3 designed FCH infinitesimal dipole

)| 2.5 /2 π = θ 2 r, ( θ E 1.5 )|/|

=0 1 θ r, (

r 0.5 |E

0 0.2 0.4 0.6 0.8 1 λ Distance,

Figure 2.5: Electric field strength ratios of the designed folded cylindrical helix dipole and an infinitesimal dipole.

Two FCH dipoles based on the above design are built and tested. They are constructed by winding copper wires on paper support. During testing, the feed point for each FCH is connected to a 2:1 transformer balun, which is characterized separately. The balun is then de-embedded from the measurement to obtain the S 11 of each antenna.

Figure 2.6 compares the simulated and measured input impedances. As can be seen in

Figure 2.6, the measured results are shifted slightly downward by 5 MHz from the simulation. This is due to fact that the wire windings in the built antennas are slightly longer than the design. However, the input resistances are still measured to be 49.1 Ω and

48.9 Ω, respectively, at their resonant frequencies. This pair of antennas is used as the Tx

and Rx antennas in the PTE measurement.

18 (a)

150 Sim. Meas.(Tx) Meas.(Rx)

Ω 100

50 Resistance, Resistance,

0 170 180 190 200 210 220 230 240 250 Frequency, MHz

(b)

3000 Sim. Meas.(Tx) 2000 Meas.(Rx)

Ω 1000

-1000 Reactance, Reactance,

-2000

-3000 170 180 190 200 210 220 230 240 250 Frequency, MHz

Figure 2.6: Simulated and measured input impedance of the folded cylindrical helix dipole. (a) Input resistance. (b) Input reactance. 19 2.5 NEAR -FIELD POWER TRANSFER SIMULATION AND MEASUREMENT

The PTE between the two designed FCH antennas is simulated using NEC as well

as measured. In the simulation, a 50-Ω resistive load is placed on the receive FCH. This is in contrast to what was done in 2.2 for the short dipole simulation, where the Linville optimal load ( ZLinv ) was used. In this manner, any potential impedance mismatch between the receiver and the load is reflected in the resulting PTE value. The center-to-center distance between the two FCHs is varied from 0.15m to 2m. The resonant frequency splits into an even and an odd mode when the two antennas are at very close range of the coupled mode region and returns to the stand-alone resonant frequency when they are far apart. It was reported in [11] that the even mode always shows a slightly lower PTE than the odd mode, and this also holds true for the FCH-FCH coupling for both θ=0 and

θ=π/2 configurations. For the measurement, the FCH dipoles are mounted on 2m-high tripods and measured using a vector network analyzer. Outdoor measurement is performed to minimize any possible environmental effects. Figure 2.7 shows the photos for the outdoor measurement setup. PTE is calculated from the measured S-parameters as

2 2 |S 21 | /(1-|S 11 | ). The two baluns are again de-embedded to obtain the S 21 between the two

antennas (See Appendix A). Both the co-linear and parallel configurations are simulated

and measured.

20 (a)

(b)

Figure 2.7: Photos of the outdoor measurement setup. Each FCH is connected to a 2:1 transformer balun. (a) θ=0. (b) θ=π/2.

21 (a)

10 0

Theoretical bound -1 (ηηη=1.0 & ηηη=0.7 ) 10 ) =0 θ

10 -2 PTE(

10 -3 FCH-FCH simulation FCH-FCH measurement

10 -1 10 0 Distance, λ

(b)

10 0

Theoretical bound -1 (ηηη=1.0 & ηηη=0.7 ) 10 ) /2 π = θ 10 -2 PTE(

10 -3 FCH-FCH simulation FCH-FCH measurement

10 -1 10 0 Distance, λ

Figure 2.8: Simulated and measured PTE of two FCH-FCH dipoles. (a) θ=0. (b) θ=π/2.

22 Figure 2.8 shows the simulated (solid lines) and measured (dots) PTE results versus distance in wavelength. The PTE bounds from (2.10) shown earlier in Figure 2.3 are re-plotted as dotted-lines for comparison. It is observed that the simulated FCH-FCH results nearly approach the theoretical PTE bound with . The minor = 100% difference between them can be attributed to the slightly less than ideal radiation

efficiency of the real FCH antenna ( ) and the small mismatch between the = 93% receive antenna and the load. It is also observed from Figure 2.8a that the simulated PTE curve begins to deviate more from the reference when the two antennas = 100% are very close to each other. This deviation is due to the increasing difference between

the optimal Linville load ZLinv and the resistive 50 Ω load when the antennas begin to couple tightly at closer as observed in Figure 2.9, which shows the real part of the ZLinv with two FCH dipoles. It is also observed that such difference is more severe for the collinear configuration which is resulted in more degradation from the PTE bound with

at close range than the parallel configuration. = 100% The measured FCH-FCH results (shown as dots in both Figure 2.8a and Figure

2.8b) follow the simulation results fairly well. The discrepancy is likely caused by the non-negligible physical size of the balun boxes and the slight misalignment during the measurement. They are slightly higher for the co-linear configuration and slightly lower for the parallel configuration. This is likely caused by the balun boxes, which have a non- negligible physical size, and the slight misalignment during the measurement, which becomes more severe at larger distances. In Figure 2.8a, a power decay rate of about -3.8

23 is estimated for the measurement from 0.2 λ to 0.75 λ. For the θ=π/2 configuration in

Figure 2.8b, the measured power decay rate is about -1.8 from 0.1 λ to 0.6 λ.

130 θ=0 120 θ=π/2 110

100 Ω 90 ], ],

opt 80

Re[Z 70

40 0 0.2 0.4 0.6 0.8 1 1.2 1.4 λ Distance,

Figure 2.9: Real part of the optimal load values with two folded cylindrical helix dipole antennas ( Zin =48.9 Ω) for collinear ( θ=0) and parallel ( θ=π/2) configurations.

2.6 SUMMARY

In this chapter, it has been demonstrated that electrically small antennas can be designed to approach the theoretical bounds derived in [30] for WPT beyond the coupled mode region. Two FCH dipoles were built and characterized before the PTE between them was measured. The measured results showed a PTE of 40% at a distance of 0.25 λ in the co-linear configuration, very close to the theoretical bound. For comparison, the meander monopole antennas reported in [11] showed a 40% PTE at a distance of 0.044 λ

(0.31m at 43MHz) in the parallel configuration. 24 This chapter highlights the role of the theoretical bound in guiding antenna design. It also underscores the importance of electrically small and highly efficient antenna design in achieving highly efficient power transfer in the radiating near-field region. In next two chapters, possible ways are explored to further extend the range or efficiency of the power transfer.

25 Chapter 3: Wireless power transfer enhancement using transmitter diversity and receiver diversity

3.1 INTRODUCTION

In this chapter, to use receiver and/or transmitter diversity (see Figure 3.1) is investigated as one way to the range or efficiency of the power transfer in the near-field region. Multiple receiver scenarios have been studied in the coupled mode region to power multiple devices simultaneously from a single source [17]-[18]. Multiple transmitting and receiving coils have also been investigated for device charging at very close range [19]. This chapter focuses attention on transmitter and receiver diversity in the radiating near-field region.

(a) (b)

Tx#1 Rx Tx#2 Rx#1 Tx Rx#2

( ( ( ( (

( ( ( ( ( ( (

d d d1 d2 1 2

Figure 3.1: Diversity configuration. (a) Transmitter diversity. (b) Receiver diversity.

In certain applications, it may be reasonable to use multiple transmitters, e.g., embedding antennas in multiple walls of a room to service a user in the room. This offers the possibility to extend the efficiency or range of the transfer. First, the PTE bound for the multiple transmitter scheme is derived by using a multiport network extension of the 26 results shown in Chapter 2. A numerical search for the optimal load is performed to determine the maximum achievable PTE bound. The resulting bound shows that a stable region in PTE can be created for a sufficiently close spacing between the transmitters.

Next, electrically small FCH dipoles with high efficiency are designed and simulated with a 50-Ω load. It is shown that the simulated results from the FCH design can

approach the derived bound well. Measurements are performed using three fabricated

FCH dipoles at 194.5 MHz and compared to the theoretical bound and simulation. The

theoretical bound and simulation results of the four-transmitter and one-receiver case are

also presented. The multiple receiver scheme is also studied by using the same approach

for the transmitter diversity. It is found that the PTE bound is extended as the number of

receivers is increased, as expected. However, some rippling of the PTE curve is observed

due to the coupling of the antennas at closer range. It is also shown that the derived

bound can be approached by the use of the designed FCH dipoles in simulation.

3.2 NEAR -FIELD POWER TRANSFER BOUND UNDER TRANSMITTER DIVERSITY

To begin, the PTE for multiple transmitters and a single receiver is defined as the

ratio of the power dissipated in the load to the total power accepted by the transmit

antennas. For the two transmitter case, this is given as:

(3.1) ∙ || /2 = ∗ ∗ ∙ /2 + ∙ /2

27 where Zload is the load impedance, I3 is the current at the load of the receiving antenna

(port 3), V1, V2 are the input voltages and I1, I2 are the currents at the feed points of the transmitting antennas (ports 1 and 2). With specified input voltages at the transmitter ports and a given load, the terminal currents can be obtained once the 3-by-3 Z-matrix of the network is known:

(3.2) = − ∙

The Z-matrix can be calculated by extending the closed form, mutual impedance between two electrically small dipole antennas derived in [30] to the multiport case as follows:

(3.3) , = = ∙ , ≠

In (3.3), the self impedance is approximated by Za, the stand-alone impedance of a small dipole, which can be calculated using the induced EMF method [52]. T is described

in (2.10). To compute the upper PTE bound, the optimal value for Zload , Zopt needs to be found. However, the closed form solution (i.e., the Linville load) used in Chapter 2 is only available for a two-port network. For three ports or more, a numerical optimization can be performed instead. Based upon (3.1) through (3.3), a local search for Zopt to reach

the maximum PTE is carried out with the antenna configuration shown in Figure 3.1a.

28 The separation of the transmitters is fixed as D and a single receiver is moved between

them. The antennas are in the parallel configuration ( θ=π/2) and the radiation efficiencies

are set to 100%. To compute the bound, the optimal load is found numerically at every

receiver position, with the conjugate value of the input impedance of the receiving

antenna as the initial guess. The same input voltages are assumed ( V1=V2) at the two transmitters. For Za, a value of 0.079-11270j [ Ω] is used, which is the input impedance for a λ/50 dipole computed by the induced EMF method.

(a)

1 2-Tx,1-Rx( θ=π/2) 0.9 1-Tx,1-Rx( θ=π/2) 0.8

0.7

0.6 d 0.5 D=0.7 λ 0.4 PTE bound PTE 0.3

0.2

0.1

0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 λ d,

29 (b)

1 2-Tx,1-Rx( θ=π/2) 0.9 1-Tx,1-Rx( θ=π/2) 0.8

0.7

0.6 d 0.5 D=1.0 λ 0.4 PTE bound PTE 0.3

0.2

0.1

0 0 0.2 0.4 0.6 0.8 1 λ d,

Figure 3.2: PTE bound for transmitter diversity (two transmitters and one receiver) in the parallel configuration. The two transmitters are separated by the fixed distance D. (a) D=0.7 λ. (b) D=1.0 λ.

Figure 3.2 shows the maximum PTE bounds derived in this manner when the

transmitters are 0.7 λ and 1.0 λ apart, respectively. The theoretical PTE bound for the

single transmitter case is also plotted by dashed lines for reference in both figures. In

Figure 3.2a, it is interesting to see that a very stable PTE region can be created as a

function of the receiver position d. A PTE of 22% is maintained over a 0.2 λ–0.5 λ region between the two transmitters. This is also significantly improved from that of the single transmitter case. In this region, the fields due to the two transmitters add constructively since the receiver distance from the two transmitters is small. However, at larger spacing

30 between the transmitters, rippling starts to appear due to the expected standing wave interference. This is shown in Figure 3.2b for D=1.0 λ.

x 10 4 0.2 1.14 Ω Ω ], ], ], ], 0.1 opt opt Z Z Im[ Re[

0 1.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 λ d,

Figure 3.3: Optimal load value ( Zopt ) for the PTE bound with 0.7 λ separation between the transmitters (Figure 3.2a case), with respect to Za=0.079-11270j [ Ω].

Several comments are in order on the PTE bound for the multiple transmitter case

shown in Figure 3.2. First, it is found that the PTE bound is not sensitive to the particular

choice of Za when the optimal load is used. Second, the real and imaginary parts of the optimal load value Zopt corresponding to Figure 3.2a are shown in Figure 3.3. It is observed that Zopt is also rather stable in the flat PTE region of 0.2 λ – 0.5 λ. In particular, its numerical value is close to the conjugate of the input impedance of the stand-alone antenna. An important implication of this observation is that if to use a constant 50-Ω

31 load is desired, then it is acceptable to design the receiving antenna to have an input impedance of 50 Ω to approach the upper PTE bound in the region. Lastly, as was found

from the previous work in Chapter 2, lower radiation efficiency lowers the PTE

significantly. Therefore, the antennas should be designed to have radiation efficiency as

close to 100% as possible.

3.3 POWER TRANSFER SIMULATION AND MEASUREMENT

It is demonstrated through simulation and measurement that the derived PTE bound can be approached using actual antennas. The same electrically small FCH dipoles designed in Chapter 2 are used. The antenna has an input resistance of 48.9 Ω with a corresponding radiation efficiency of 93% and fits inside a kr =0.31 sphere at 200MHz.

Three identical FCH dipoles are used in the NEC simulation and the setup is shown in

Figure 3.4. Two FCH dipoles are used as transmitting antennas with a separation of

1.05m (0.7 λ at 200MHz, as measured between the two antenna ports), and an FCH dipole

with a fixed 50-Ω resistive load is used as the receiving antenna. The position of the receiving antenna is changed between the transmitters from 0.15m to 0.90m. PTE is calculated using (3.3) at a fixed frequency of 200MHz.

For measurement, three FCH dipoles are built by winding copper wires on paper support. The three antennas are tuned to have approximately the same resonant frequency and 50 Ω input resistance. A 2:1 transformer balun is connected to each antenna in the

measurement. The balun is characterized and de-embedded to obtain the S 11 of each

32 antenna. The measured resonant frequencies and input resistances of the antennas are listed in Table 3.1.

Figure 3.4: NEC simulation setup for the two-transmitter and one-receiver scheme using electrically small folded cylindrical helix dipoles. The antennas are in the parallel configuration.

Table 3.1: Measured Resonant Frequency and Input Resistance of the Fabricated FCH Dipoles. f0, MHz Rin , Ω

Tx#1 194.4 61.66

Tx#2 194.5 63.52

Rx 194.5 55.28

The FCHs are mounted on 2m high tripods and measured using a VNA. The two transmitting FCH dipoles are separated by 1.08m (0.7 λ at 194.5MHz) and the receiving one is moved from 0.15m to 0.90m by steps of 0.05m as shown in Figure 3.5. To obtain the 3-by-3 scattering matrix at each position, each antenna is terminated by a 50 Ω load 33 alternately while the other two are connected through the baluns to the two ports of the

VNA. The baluns are then de-embedded to obtain the S-parameters. Finally, the PTE is calculated from the measured S-parameters as:

(3.4) | + | = 1 − | + | + 1 − | + |

where ports 1 and 2 are for the transmit antennas and port 3 is for the receive antenna.

Figure 3.5: Photo of the measurement setup.

The simulated and measured PTE results across distance in wavelength are shown in Figure 3.6. The PTE bound in Figure 3.2a is re-plotted as the solid line for reference.

The simulation result using FCH dipoles ( ) is plotted as circles. The stable 34 = 93% PTE region can be clearly observed from 0.2 λ to 0.5 λ, which approaches the theoretical

PTE bound well. The small gap between them is caused by the slightly less than ideal

radiation efficiency of the real FCH design and the mismatch between the load and the

receive antenna. When the receiver comes close to either transmitters (i.e. the region 0.1 λ

– 0.2 λ and 0.5 λ – 0.6 λ), the PTE falls sharply off from the theoretical bound. This fall off is due to an impedance mismatch, as the optimal load is no longer well represented by the fixed 50 Ω load when the antennas begin to couple tightly at closer range. This statement can be confirmed from Figure 3.3, where it is seen that the real part of the optimal load impedance deviates significantly from the value at the center region within 0.2 λ from each transmitter.

1 2-Tx,1-Rx PTE bound(Fig.7a) 0.9 Sim.( η=93% for FCH dipoles) 0.8 Sim.( η=70% for FCH dipoles) Measured 0.7

0.6

0.5 PTE 0.4

0.3

0.2

0.1

0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 λ d,

Figure 3.6: Simulated and measured PTE for transmitter diversity using three FCH dipoles.

35 The measured PTE values are plotted as dots in Figure 3.6. They closely follow the trend of the simulation, showing the same stable PTE region. However, the measured

PTE level is about 3% lower than the simulation. This is caused mainly by the lower radiation efficiencies of the fabricated FCH dipoles. To confirm this, the PTE is simulated using the same FCH dipoles with an of 70% (simulated by lowering the wire conductivity in NEC) and is plotted as squares in Figure 3.6. It shows an even lower

PTE level than the measurement. Wheeler cap measurement of the actual FCH dipoles is

also carried out and find their radiation efficiencies to be in the 80% to 90% range.

Therefore, it is concluded that the lower radiation efficiencies of the built antennas are

the main cause of the lower PTE values as compared to the simulation. This highlights

the importance of high antenna efficiency for achieving efficient near-field power

transfer.

(a) (b)

0.5 0.5 0.9 0.9

0.8 0.4 0.8 0.4

0.7 0.7 0.3 0.3 0.6

0.6 λ λ , , , , d 0.5 d 0.5 0.2 0.2 0.4 0.4

0.1 0.3 0.1 0.3 0.2 0.2

0.1 0.2 0.3 0.4 0.5 0.1 0.2 0.3 0.4 0.5 d, λ d, λ

Figure 3.7: Four-transmitter and one-receiver scheme. (a) PTE bound. (b) NEC simulation using electrically small folded cylindrical helix dipoles.

36 Finally, the two-transmitter and single-receiver case is extended to four transmitters and a single receiver over a two-dimensional region. The same method used for the two transmitter case is used for the PTE derivation except that a 5-port network is considered. The four transmitters are located at the corners of a square region in Figure

3.7. The length of the diagonal region is set to 0.7 λ and a single receiver is moved within the region. Again the optimal load for maximum power transfer is found through a numerical search. The derived PTE bound is plotted as a two-dimensional intensity plot in Figure 3.7a. It is seen that a stable PTE of 50% is generated within a region of size

0.3 λ at the center. Next, actual FCH dipoles are used in the PTE calculation. The optimal

load value at each position is also replaced by a fixed 50-Ω load at the receive FCH

dipole and the result is shown in Figure 3.7b. The same trends as the two transmitter case

are observed. First, when the receiver comes closer to each transmitter, the PTE again

falls sharply from the theoretical bound. This is again caused by the impedance mismatch

of using the fixed 50 Ω load when the antennas begin to couple tightly at close range.

Second, despite the slightly lower value (41%) from the PTE bound due to the imperfect radiation efficiency and load mismatch, the stable PTE region is created along the center region. Thus transmitter diversity can potentially be applied to provide a stable service region for one (or more) mobile receiver(s).

37 3.4 NEAR -FIELD POWER TRANSFER UNDER RECEIVER DIVERSITY

The PTE bound for receiver diversity can also be derived by using the same approach for the transmitter diversity. For two receivers, only the PTE definition is different and is given as:

(3.5) , ∙ || /2 + , ∙ || /2 = ∗ ∙ /2

where port 1 is the transmitter and ports 2 and 3 are the receivers. Zload,2 and Zload,3 are the load impedances.

(a)

0 10

10 -1 ) =0 θ d d 10 -2 PTE ( PTE

PTE bound (1-Tx,2-Rx) 10 -3 PTE bound (1-Tx,1-Rx) NEC sim. for 1-Tx,2-Rx

10 -1 10 0 Distance, λ

38 (b)

0 10

10 -1 ) /2 π = θ

-2 10 d d PTE ( PTE

PTE bound (1-Tx,2-Rx) 10 -3 PTE bound (1-Tx,1-Rx) NEC sim. for 1-Tx,2-Rx

10 -1 10 0 Distance, λ

Figure 3.8: PTE bound and NEC simulation result for receiver diversity (1-Tx, 2-Rx). (a) θ=0. (b) θ=π/2.

Figure 3.8 shows the PTE bounds for the co-linear and parallel configurations. In these plots, the distances between the transmitter and the two receivers are set to be equal to simplify the calculation. The result of this constraint is that the optimal load impedances at the two receiving antennas are the same, thus simplifying the numerical search. The efficiencies of the antennas are set as 100%. The PTE bounds for the single transmitter and single receiver case are plotted in dashed lines for reference. As expected, the PTE bound is extended under receiver diversity. However, some rippling of the PTE curve can be seen due to coupling of the antennas. NEC simulation using three FCH dipoles ( Rin =48.9 Ω, ɳ=93% and kr =0.31) with fixed 50-Ω loads is also carried out and

39 the result is plotted as dots in Figure 3.8. Not surprisingly, it follows the PTE bound well as it did in the single-transmitter single-receiver scenario.

(a) (b)

2 10 2 10

5 5 1.5 1.5 0 0 1 1 -5 -5 0.5 0.5 -10 -10

0 -15 0 -15 Z, m Z, Z, m Z, -20 -20 -0.5 -0.5 -25 -25 -1 -1 -30 -30 -1.5 -1.5 -35 -35

-2 -40 -2 -40 -2 -1 0 1 2 -2 -1 0 1 2 X, m X, m

(c)

2 10

5 1.5 0 1 -5 0.5 -10

0 -15 Z, m Z, -20 -0.5 -25 -1 -30 -1.5 -35

-2 -40 -2 -1 0 1 2 X, m

Figure 3.9: Power distribution with single transmitting FCH and multiple receiving FCH dipoles. (a) 1-Rx, (b) 2-Rx, and (c) 4-Rx.

40 The real part of the complex Poynting’s vector is plotted in dB scale in Figure 3.9 to see the change in power distribution with multiple transmitters. The Tx FCH dipole is located at the center and all the Rx FCH dipoles with 50-Ω load are 0.5m (0.33 λ) away from it in all figures. Note that the Z-axis in the figures is in along with θ=0, so the

antennas are in the co-linear configuration for the Rx FCH dipoles located at Z=0.5m and

Z=-0.5m. And the Rx FCH dipoles at X=0.5m and X=-0.5m in Figure 3.9c form parallel

configuration to the Tx FCH dipole antenna. Figure 3.9a shows the power flowing out of

the Tx FCH dipole to a single RX FCH dipole in the collinear configuration and it is

observed in Figure 3.9b and Figure 3.9c that this power flowing is hardly changed in the

presence of other Rx antennas. It supports the observation in Figure 3.8 that the PTE is

increased as the number of receivers increased in the radiating near-field region. It is

found from Figure 3.9c, in which both the co-linear and parallel configurations of the

antennas are, that this feature holds true for the mixed configuration scenarios as well.

3.5 SUMMARY

In this chapter, the upper bound for near-field power transfer under multiple transmitters and multiple receivers has been derived. The derivation uses a multiport extension of the coupling limit derived previously in [30]. A numerical search for the optimal load for maximum power transfer was carried out to compute the upper bound.

For transmitter diversity, results showed a stable PTE region for the two-transmitter scenario, in contrast to the monotonic decay of the single transmitter case. It was then demonstrated through simulation and measurement that such a bound can be approached

41 by using efficient, electrically small, folded cylindrical helix dipoles. The measurement showed a 17% PTE values over a 0.3 λ region between the two transmitters, corroborating

the theory and simulation. Results from the four-transmitter case illustrated that the stable

PTE region can be extended to two-dimensional space. For receiver diversity, it was

found that the PTE bound is extended as the number of receivers is increased. It was also

shown that such bound can be approached by using highly efficient electrically small

antennas. Generalization to the case of multiple transmitters and multiple receivers is

reported in [53].

42 Chapter 4: Wireless power transfer enhancement using small directive antennas

4.1 INTRODUCTION

Another possible way to enhance the range or efficiency of near-field WPT is to

use spatial focusing antennas. For stand far-field applications, there has been

considerable interest recently in the realization of electrically small, supergain arrays in

the end-fire direction [54]-[56]. Yaghjian et al. [54] reported on the theory, simulation

and measurement of electrically small supergain arrays in the end-fire direction. A two-

element array was demonstrated by using two electrically small resonant antennas spaced

0.1 λ apart. Since two identical elements are used, supergain is achieved at a frequency that is slightly off resonance and a lumped capacitor is needed to achieve input impedance matching. Bayraktar et al. [55] used a particle swarm optimization to miniaturize a 3-element Yagi antenna. In the optimized design, the length of the reflector is reduced to 0.27 λ and the spacing is 0.11 λ between the reflector and the driver. Lim and

Ling [56] demonstrated a two-element, closely spaced Yagi antenna using electrically small, folded monopole elements. The structure was optimized by a genetic algorithm to maximize gain and at the same achieve good impedance matching without the need for any lumped element loading. The measured realized gain is 8.81dB in the monopole configuration, with a total volume of 0.065 λ 0.095 λ 0.095 λ. In subsequent works × × [57]-[58], the antenna beam was also made reconfigurable by the addition of multiple parasitic elements and switches.

43 While the role of directivity is very clearly described by the Friis transmission formula in the far field, spatial focusing in the near field is not as well understood [28]-

[29]. In the derivation of the upper bound for near-field power transfer in [30], only the lowest TM 10 or TE 10 mode was considered. In this chapter, small directive antenna is investigated to see whether it can be used as a means of increasing the range or PTE of near-field power transfer. This chapter begins with a feasibility test of using electrically small Yagi antennas (for standard far-field application) for improving the coupling in the radiating near-field region. Parasitic implementation of two-element superdirectivity arrays with optimal load for maximum power transfer is employed for this study. PTE enhancement is observed by the test and it is found that the radiation resistance should be increased sufficiently to use such superdirectivity arrays in practice. Next, the two- element superdirective array is realized using an FCH structure as an array element for a reflector-type Yagi design. The antenna design is optimized for far-field realized gain using a local search. After checking its performance in the far-field region in terms of the realized gain, the designed antennas are put in the radiating near-field region for near- field WPT. It is demonstrated through simulation and measurement that the PTE enhancement in the radiating near-field region using superdirective arrays can be approached by the practical design of FCH Yagi antennas except for very close range of the antennas. Lastly, the PTE improvement is compared with the cases using FCH dipole antennas in Chapter 2.

44 4.2 FEASIBILITY AND ANTENNA DESIGN CONSIDERATIONS

The feasibility of near-field coupling enhancement using directive antennas designed for far-field application is first tested. Uzkov showed that the end-fire directivity of a periodic linear array of N isotropic radiators can approach N2 as the spacing between elements decreases, provided the magnitude and phase of the input excitations are properly chosen [59]. Such a directivity value represents the so-called

“superdirectivity” when compared to the maximum attainable directivity for isotropic elements spaced half-wavelength apart, especially because the directivity increases as the length of the linear array becomes smaller [60]. Thus, the directivity of a two-element array of isotropic radiators would approach a value of four, i.e., 6 dB higher than that of a single isotropic radiator. Parasitic implementation of superdirectivity is also feasible. For example, a two-element, 0.02 λ spacing Yagi antenna with a driver and a reflector each about half-wavelength (driver: 0.4781 λ and reflector: 0.49 λ) shows a directivity of 7.2dB

in the far field [58].

This configuration is chosen for both the Tx and Rx antennas in the radiating

near-field PTE simulation as shown in Figure 4.1. Under no conductor losses and with

the optimal load (ZLinv ) for maximum coupling at every distance, the PTE between two such antennas is calculated. This particular antenna configuration under no conductor loss and with the optimal load will be called an “idealized superdirective array” in subsequent discussions.

45 ≈λ/2

Distance, λ

Figure 4.1: PTE simulation setup using two-element idealized superdirectivity arrays.

The calculated PTE is shown by a solid line in Figure 4.2. PTE enhancement is observed from 0.1 λ as compared to the PTE bound derived for small antennas, which is

plotted by a dashed line. At far distances, the enhancement approaches about 11 dB,

which is well predicted by the Friis far-field formula (2 (7.2dB-1.76dB)). While the × solid line in Figure 4.2 shows an impressive improvement in PTE performance when directive antennas are used, there are practical implementation issues. First, when the optimal load is replaced by a fixed 50-Ω load, the PTE degrades sharply, as marked by

the first arrow in Figure 4.2. Second, the PTE degrades even more if conductor loss is

considered, as marked by the second arrow in Figure 4.2. These degradations are similar

to the well-known pitfalls in realizing superdirective antennas for far-field applications,

namely, an idealized superdirective array often comes with a large impedance mismatch

and low radiation efficiency when implemented in practice. Therefore, to capture the

46 benefit of high directivity for near-field power transfer, one must pay careful attention to antenna design. First, the radiation efficiency of the antenna should be high to minimize the conductor loss effect. Second, the input impedance of the antenna needs to be close to

50 Ω for impedance matching to a standard 50-Ω resistive load. Finally, it is desirable that the antenna size be as small as possible.

10 0

-1 Conductor loss Z Ω 10 L=50 (2) /2) π (1) = θ

-2 PTE ( PTE 10

PTE for idealized superdirective array PTE bound for small dipole -3 10 10 -1 10 0 Distance, λ

Figure 4.2: PTE enhancement in the near-field region using an idealized superdirective array.

4.3 DESIGN OF AN ELECTRICALLY SMALL FCH YAGI

In this section, an electrically small Yagi antenna designed based on the FCH

dipole is presented to achieve good directivity, radiation efficiency and impedance

matching. The antenna is comprised of two elements, a driver and a reflector. Each

element is an FCH structure that has been thoroughly discussed in previous chapters and

47 as shown in Figure 4.3. The dimensions of the antenna including the height (h r, h d) and the radius (r r, r d) of each element, the spacing (s) between the two elements and the number of arms are optimized using a local optimizer in conjunction with NEC. The far- field realized gain, which accounts for directivity, radiation efficiency and matching, is chosen to be the objective function.

Figure 4.3: Initial small Yagi antenna design before optimization

The optimized antenna design and a photo of the fabricated antenna are shown in

Figure 4.4. The optimized design parameters are given in Table 3.1. The antenna feed is located at the center of one arm in the driver. The wire length of one arm in the driver is

85 cm (0.57 λ at 200MHz) and that of the reflector is slightly longer at 92 cm (0.61 λ at

200MHz). The entire antenna fits inside a kr =0.95 sphere, where r is the radius of the imaginary sphere that encloses the entire antenna. A copper wire radius of 0.5mm (18-

48 AWG) is chosen for both elements. The optimized Yagi antenna has an input resistance of 50.9 Ω at resonance with a corresponding radiation efficiency of 96%. The maximum simulated directivity, gain and realized gain in the forward direction at 200MHz are 6.76,

6.61 and 6.60dB, respectively. The front-to-back ratio is 12.3dB.

Table 4.1: Optimized Design Dimension Parameters. hr 34.74cm s 19.90cm

rr 4.75cm Number of arms 3

(reflector)

hd 35.37cm Number of arms 2

(director)

rd 4.28cm Number of turns 1.25

(reflector and director)

To confirm that the directivity of the designed antenna is at or close to theoretical expectation values, the directivity of two-infinitesimal dipole array is calculated. With the far field formula of an infinitesimal dipole, the directivity toward the forward direction can be expressed as:

49 = (4.1)

∙ ∙ ∙ ∙ ∙ ∙

where α and β are the real and imaginary part of the current ratio at the reflector and the driver ( Iref /Idri ), respectively. s is the spacing between the two elements and θ and φ are the azimuth and elevation angle, respectively.

Directivity, dB 1 7 0.9

0.8 6

) 0.7 5 dri 0.6 /I 0.5 4 ref I 0.4 3 0.3 : Im( : β 0.2 2 0.1 1 0 -1 -0.8 -0.6 -0.4 -0.2 0 α:Re( I /I ) ref dri

Figure 4.4: Theoretical expectation of directivity with two-infinitesimal dipole array.

Using (4.1), directivity is plotted versus alpha and beta in Figure 4.4 when s=0.133λ, which is corresponding to s=19.9cm from the optimized dimension. It is

50 observed that the theoretical maximum directivity is about 7dB when (α, β) = (-0.96,

0.32). This is expressed in the magnitude ratio of 1.01 and phase difference of 161.57 . ° From the optimized antenna simulation, the current ratio at 200 MHz is read as

1.10 ∠147.57 , which is slightly off from the theoretical maximum point and shows the ° directivity of 6.76dB. This point is also expressed as ( α, β) = (-0.85, 0.54), and the theoretical directivity at this point is observed as 6.64dB in Figure 4.4. The slight difference might be caused by the coupling due to the physical dimension of the antenna.

Even though the designed antenna does not show the desired current ratio for maximum directivity exactly, it is confirmed that the current ratio of the optimized Yagi antenna is very close to the theoretical maximum point of a two element array design.

(a)

(b)

Figure 4.5: Small FCH Yagi design. (a) NEC model. (b) Photo of the fabricated antenna.

A prototype of the antenna in Figure 4.5a is built by winding copper wires on paper support as shown in Figure 4.5b. The position of the reflector and driver parts is held in place by Styrofoam. The two small metal tips in the driver are connected to a 2:1 transformer balun in the measurement. The balun is characterized and de-embedded to obtain the S 11 of the antenna. Figure 4.6 shows the simulated and measured input impedances. Other than a slight downward shift of 5MHz, the measured results show good agreement with the simulation. The input resistance is measured as 56.0 Ω at its resonant frequency of 195.3MHz. The simulated and measured return loss plots are shown in Figure 4.7. The -10dB impedance bandwidth is measured to be 9.69%, which is in good agreement with the 9.75% in the simulation. 52 (a)

400

350

300

250 Ω

, , 200 in R 150

100

50 measurement NEC 0 160 180 200 220 240 Frequency, MHz

(b)

600

400

200 Ω

, , 0 in X -200

-400 measurement NEC -600 160 180 200 220 240 Frequency, MHz

Figure 4.6: Simulation and measurement results of input impedance from the designed FCH Yagi antenna. (a) Resistance. (b) Reactance.

53 0

-5

-10

-15

-20

-25

-30 Return Loss, dB Loss, Return -35

-40 measurement NEC -45 160 180 200 220 240 Frequency, MHz

Figure 4.7: Simulation and measurement results of return loss from the designed FCH Yagi antenna.

(a)

-5

-10 Realized gain, dB gain, Realized -15 measurement NEC -20 160 180 200 220 240 Frequency, MHz

54 (b)

5 Front-back ratio, dB ratio, Front-back 0 measurement NEC -5 160 180 200 220 240 Frequency, MHz

Figure 4.8: Simulation and measurement results from the designed FCH Yagi antenna. (a) Realized gain. (b) Front-back ratio.

The simulated and measured realized gain and front-to-back ratio are plotted in

Figure 4.8. The measured realized gain is 6.2dB at 195.3MHz, which is lower than the simulated realized gain by 0.4dB. Minor RF interference noises can be observed at 175,

215, and 225MHz due to the outdoor environment. The front-to-back ratio is measured as

14.5dB at 195.3MHz in Figure 4.8b, which is slightly higher than the simulated value of

12.3dB. The peaks above the resonant frequencies in both the measurement and simulation are due to a null in the backward direction.

55 4.4 POWER TRANSFER SIMULATION AND MEASUREMENT

PTE values are simulated and measured using the two designed FCH Yagi antennas. A 50-Ω resistive load is placed on the receiving antenna in the NEC simulation.

The distance between the antennas is measured as that between the centers of the two

antennas. The photos for the outdoor measurement setup are shown in Figure 4.9. The

2 2 PTE is calculated from the measured S-parameters as |S 21 | /(1-|S 11 | ).

The simulated PTE results with the two FCH Yagi antennas with a fixed 50-Ω resistive load are shown as solid dots in Figure 4.10. The PTE calculated with the idealized superdirective array (i.e. without conductor loss and with optimal load at every distance) in Figure 4.2 is re-plotted for reference. The dashed line is the Friis far field formula with two 7.2dB antennas. It is observed that the simulated PTE between the FCH

Yagis follows the trend of the idealized superdirective array for spacing greater than 0.3 λ.

The discrepancy between the two is mainly caused by the lower directivity and radiation efficiency of the designed antennas as compared to the idealized superdirective array.

When the two Yagi antennas are spaced less than 0.3λ, the PTE between them is rather

degraded. This is due to the strong coupling between the antennas, which causes the

current distribution on each Yagi antenna to deviate from its stand-alone design for high

directivity. The measured results are plotted as open circles and they show reasonable

agreement with the simulation. Both the simulation and measurement show that 40%

PTE is achieved at a distance of 0.45 λ based on the center-to-center distance definition.

56 (a)

(b)

Figure 4.9: Measurement setup. (a) FCH Yagi-FCH Yagi. (b) FCH Yagi-FCH dipole

10 0 ) /2 π

= -1 θ 10 PTE( PTE for idealized superdirective array Simulation (Two FCH Yagis,Z =50 Ω) L Friis (Directivity=7.2dB) Measurement (Two FCH Yagis,Z =50 Ω) L -2 10 10 -1 10 0 Distance, λ

Figure 4.10: Simulated and measured PTE for FCH Yagi-FCH Yagi.

To see the improvement in PTE by using directive antennas in the near-field region, the PTE results in Figure 4.10 are compared to those from using FCH Yagi (Tx)-

FCH dipole (Rx) and FCH dipole (Tx)-FCH dipole (Rx) in Figure 4.11. The simulated values are plotted as lines and the corresponding measurement results are plotted as dots.

At 0.45 λ, the PTE difference between the FCH Yagi-FCH Yagi coupling and FCH dipole-FCH dipole coupling is 9.11 dB, showing good enhancement, though it is slightly lower than the 9.7 dB in the far field. This statement is also supported by the measurement results, which follow the simulation results fairly well.

58 0 10

10 -1 /2) π = θ PTE ( PTE

-2 FCH dipole-FCH dipole(Z =50 Ω) 10 L FCH Yagi-FCH dipole(Z =50 Ω) L FCH Yagi-FCH Yagi(Z =50 Ω) L

0.3 1 λ Distance,

Figure 4.11: PTE comparison: FCH dipole-FCH dipole, FCH Yagi-FCH dipole and FCH Yagi-FCH Yagi.

Lastly, the PTE enhancement using directive antennas is compared with that using transmitter diversity or receiver diversity discussed in Chapter 3. In Figure 4.12, the PTE bounds from the two-transmitter and one-receiver, one-transmitter and two-receiver, and the PTE for two idealized superdirective arrays are plotted for the parallel configuration

(θ=π/2). It is shown that the PTE is increased more with two directive antennas than with

the two-receiver case using small dipole antennas for the region beyond 0.15 λ. It is also shown that the PTE using two idealized superdirective arrays is higher than the stable

PTE region achieved by the two-transmitter case with small dipole antennas. Therefore, it may be possible to use superdirective arrays as transmitters in a transmitter diversity scenario to further elevate the efficiency in the stable PTE region.

PTE bound for 2-Tx,1-Rx PTE bound for 1-Tx,2-Rx PTE for idealized superdirective array 1

0.8 /2) π = θ 0.6 PTE( 0.4

0.2

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 λ Distance,

Figure 4.12: PTE comparison: PTE with transmitter diversity, receiver diversity and directive antennas.

4.5 SUMMARY

In this chapter, superdirective array has been investigated as a means of increasing the range in near-field WPT and PTE. The feasibility of enhancing PTE using directive antennas has been tested first with idealized superdirve arrays and such improvement has been realized by design of electrically small, highly directive FCH Yagi antennas. From this study, it was observed that the far-field realized gain can be used as a good surrogate for designing small directive antennas for near-field power transfer. This is an important practical consideration, since using PTE directly as the cost function is computationally more expensive and can lead to different designs at different distances.

However, it is also worth to note that this PTE improvement comes at the price of

60 antenna size, as the designed FCH Yagi has about a three-fold increase in kr as compared

to that of the FCH dipole.

61 Chapter 5: Investigation of near-field wireless power transfer in the presence of lossy dielectric materials

5.1 INTRODUCTION

While WPT in free space has been well studied thus far, the interactions of near fields with materials also need to be quantified to address practical deployment issues.

There are several works that have been reported so far regarding material effects on WPT based on numerical simulations or measurements [36], [61]-[65]. In this chapter, an analytic PTE bound in the radiating near-field region when a small Tx antenna is enclosed by a material shell and a small Rx antenna is located outside in free space is derived. Extending the work presented in Chapter 2, the derivation considers an additional pair of incoming and outgoing spherical waves within the spherical shell. Both the lowest order TM and TE mode radiator cases are considered. The derived bound is compared against full-wave simulation and shows good agreement in PTE. Next, lossy dielectric material effects on WPT with the lowest TM (i.e., a dipole) or TE (a loop) mode radiators are examined using the theory. Finally, through-wall power transfer measurement results are reported using two FCH dipoles and compared to the theory.

5.2 DERIVATION OF UPPER PTE BOUND

The derivation begins from the theoretical PTE bound between two small

antennas in free space as shown in Figure 2.1. The PTE definition and the derived

formula are given in (2.9) and (2.10).

Rx r ε µ εεo, µµo, ko Tx θθθ r2 r1 εεε µµµ k o, o, o τττ ε µ εεs, µµs, ks

Figure 5.1: Coupled small antennas. Transmit antenna enclosed by a finite-thickness spherical shell of material with a receive antenna in free space.

For the problem at hand (shown in Figure 5.1), the Tx antenna is enclosed by a finite-thickness spherical material shell (possibly lossy). The Tx antenna is placed at the center of the interior free space region and a single Rx antenna is located outside in free space. In Figure 5.1, r1 is the radius of the inside sphere, τ is the thickness of the shell,

and r2 is the radius of the outside sphere (i.e. r2=r1+τ). In the PTE derivation, it is assumed that only the lowest TM10 or TE 10 spherical mode is radiated from the source

and the scattering from the Tx and Rx antennas is negligible due to their small size. As it

will be seen, this latter assumption is valid as long as the two antennas are not very

closely spaced. It is worth mentioning that a similar problem with a double-negative

metamaterial shell was formulated earlier in [66] in order to determine the far-field

radiated power and the reactance of the antenna. Here, our focus is on the power transfer

between the two antennas in the near-field region. 63 To obtain the PTE to the given problem, the intensity of the fields outside the shell from a small Tx electric dipole located at the origin that generates only the TM 10 mode is first calculated. The magnetic vector potential is given as:

: cos ∙ 1 ∙ + ≤ (5.1) = cos ∙ : + : ≤ ≤ cos ∙ : ≥

where and are the wave numbers in free space and = = in the shell, respectively. is the associated Legendre function of the first kind, cos is the alternative spherical Hankel function of the second kind, and = ℎ and are alternative spherical Bessel functions of the = = first and second kind. an:TM , bn:TM and cn:TM are the coefficients of the standing waves inside the shell ( ) and dn:TM is that of the outgoing wave outside the shell ( ). ≤ ≥ The amplitude of the incident wave from the source is set to 1. n is equal to 1 in (5.1)

since only the lowest spherical wave mode is excited by the source. By calculating the

field expressions for Eθ and Hφ in each region based on Ar and enforcing the continuity of

the tangential fields at r=r1 and r=r2, the following matrix equation is found and the coefficients can be determined:

64 − − 0 1 1 1 : − − 0 : : 0 − : (5.2) 1 1 1 0 −

− 1 = − 0 0 where and . The prime symbol in (5.2) denotes derivative = / = / with respect to the argument of the function.

After obtaining d1:TM , the same procedure as [30] can be taken to arrive at the

PTE. First, the X in (2.10) is replaced by:

(5.3) : = ∙ : ∙

Before arriving at the desired PTE expression, the input power accepted by the Tx antenna inside the shell must be obtained. This can be found in closed form as:

(5.4) 1 ∗ = × ∙ 2 65 ∗ 4 ∗ ∗ = ∙ + : ∙ ∙ + : ∙ 3

For comparison, the input power to the Tx antenna in free space is:

1 ∗ = × ∙ (5.5) 2

∗ 4 = ∙ ∙ 3

Note that both and are independent of r. Finally the desired PTE expression for the material shell case is obtained by modifying (2.10) by the ratio of and . The final expression is given by:

: ∗ ∙ (5.6) ∗ = ∗ ∗ + : ∙ ∙ + : ∙

|: | × 2 − : + 41 − : − :

A similar bound for the TE case can be derived by the use of duality and is given

as:

66 : ∗ ∙ (5.7) ∗ = ∗ ∗ + : ∙ ∙ + : ∙

|: | × 2 − : + 41 − : − :

where and d1:TE represents the coefficient of the TE 10 mode : = ∙ : ∙ outside the shell, which can be found by solving the dual of (5.6).

5.3 VALIDATION AND RESULTS

The derived analytic formulas are first compared against numerical simulation

using the method of moments solver in FEKO. Human body fluid is chosen as the

material for the shell. The relative permittivity (εr) and loss tangent ( tan δ) of the body

fluid are chosen respectively as 69.037 and 1.965 at 200MHz [67]. Both the radius of the

inner shell r1 and the thickness of the shell τ are first set as 0.05 λ. The radiation efficiency

ηeff is set to 1. Under these conditions, the predicted PTEs by the theory are shown as solid lines in Figure 5.2a. Both TM and TE mode cases are plotted for the co-linear ( θ=0) and parallel ( θ=π/2) configurations of antennas.

67 (a)

-1 10

-2 10

-3 10

-4 10 θ=π/2 PTE

-5 10

Theory: TM mode -6 10 FEKO: small dipole Theory: TE mode FEKO: small loop θ=0 -7 10 0.15 0.3 0.6 0.9 1.2 1.5 1.8 Distance, λ

(b)

0 10

-2 10

-4 10 θ=π/2 PTE -6 10

-8 Theory: TM mode 10 FEKO: small dipole θ Theory: TE mode =0 FEKO: small loop -10 10 0.08 0.15 0.3 0.6 0.9 1.2 1.5 1.8 Distance, λ

Figure 5.2: PTE prediction using the derived theory and FEKO when the shell is filled with body fluid material ( εr=69.037 and tan δ=1.965). (a) r1=0.05 λ and τ=0.05 λ (b) r1=0.015 λ and τ=0.05 λ.

68 In the FEKO simulation, a λ/50-long dipole is used for both the Tx inside the shell and the Rx outside the shell for the TM mode validation. For the TE mode, the dipoles are replaced by loops with a diameter of λ/50. It is assumed that there is no conductor

loss for the antennas. After calculating the Z-matrix at each position of the Rx antenna,

the Linville method [52], [61] is utilized to obtain the maximum PTE at each distance

between the two antennas. The numerically calculated PTEs using FEKO are plotted as

crosses in Figure 5.2a. It is observed that the predicted PTEs from the theory and FEKO

agree very well at distances beyond 0.2 λ. However, the two results start to deviate from each other at closer range. This is because of the weak-coupling assumption made in the derivation, which is not valid for very closely spaced antennas. Next, the derived formula is tested when the radius of the inner shell r1 is 0.015 λ to see if it works even for such an

extremely small enclosure. The thickness τ is kept as 0.05 λ. Under this condition, the predicted PTEs by the theory and FEKO are respectively plotted by solid lines and crosses in Figure 5.2b. It is shown that the two PTEs still agree well at distances beyond

0.2 λ for both configurations.

Next the difference in PTE between the TM and TE modes is examined. The shell is filled with the same material. In Figure 5.3a, the PTE bounds predicted by the theory are plotted by solid lines for both TM and TE modes when the material shell extends from 0.1 λ to 0.15 λ from the Tx antenna (i.e. r1=0.1 λ and τ=0.05 λ). The theoretical PTE

bound for the free space case is also plotted by dotted lines for reference. It is clearly

observed that all PTEs for both the TM and TE mode radiators in the presence of material

are significantly degraded in comparison to the free space case. This is due to the high 69 relative permittivity and dielectric loss of the material. It is also interesting to note that the power transfer using TM mode radiators is more efficient in this configuration than the TE mode case. This is contrary to the common belief that a loop (TE mode) antenna produces predominantly magnetic stored energy in the near-field, and therefore is not as strongly affected by a dielectric material. To explain this phenomenon, the stored electric energy density (w e) and magnetic energy density (w m) of a small horizontal loop in free

space along the θ=π/2 direction are plotted in Figure 5.3b. It is seen that w m is higher than we up to 0.1 λ. Therefore, power transfer using loops (TE mode radiators) should be less

affected by a dielectric material when it is in the very near-field region. This was indeed

the cases shown in Figure 5.2a and Figure 5.2b, where the dielectric shell is located

within 0.1 λ of the Tx antenna. In those cases, the TE mode exhibits a higher PTE than the

TM mode. The shell considered in Figure 5.3a (0.1 λ -0.15 λ) occupies the region of space where w e is slightly higher than w m in Figure 5.3b. This explains why the TM mode radiators display a higher PTE than the TE mode ones. Extrapolating this argument, no difference between the TE and TM cases is expected when a dielectric shell is located beyond 1 λ from the Tx antenna. The results predicted by the analytic formula indeed

show this to be the case.

70 (a)

0 10 θ π -1 free space, = /2 10

-2 10 θ -3 free space, =0 10 θ=π/2 PTE -4 10

-5 10

-6 10 TM mode θ=0 TE mode -7 10 0.15 0.3 0.6 0.9 1.2 1.5 1.8 Distance, λ

(b)

-2 10 W e -4 W

3 10 m

-6 10

-8 10

-10 10

-12 Stored energy density (TE), J/m (TE), densityenergy Stored 10

-14 10 -2 -1 0 1 10 10 10 10 Distance, λ

Figure 5.3: PTE under human body fluid material ( r1=0.1 λ and τ=0.05 λ). (a) TM and mode comparison. (b) Stored electric and magnetic energy distribution for small loop (TE mode).

71 (a)

0 10 τ=0.02 λ τ=0.04 λ τ=0.08 λ -2 10

=0) -4 θ 10 PTE(

-6 10

-8 10 0.15 0.3 0.6 0.9 1.2 1.5 1.8 Distance, λ

(b)

0 10 τ=0.02 λ τ=0.04 λ τ=0.08 λ -2 10 /2) π

= -4

θ 10 PTE(

-6 10

-8 10 0.15 0.3 0.6 0.9 1.2 1.5 1.8 Distance, λ

Figure 5.4: PTE degradation by the thickness of the shell ( r1=0.1 λ). (a) Co-linear configuration. (b) Parallel configuration.

72 In Figure 5.4, the PTEs of the TM mode radiators vs. different shell thickness are plotted when the shell is filled with the body fluid material. The inner radius r1 is fixed as

0.1 λ. It is shown that the PTE decreases with shell thickness, as expected. The

degradation approximately follows e-2ατ , where α is the attenuation constant inside the

shell due to the non-zero loss tangent. The same trend is observed for both the co-linear

and the parallel configuration of the antennas.

WPT measurements are carried out through walls to examine the effect of

materials on the PTE and to corroborate the theory. Even though the measurement

geometry is for a planar wall while the theory is derived based on a spherical shell, such

comparison should provide an assessment on the predictive value of the derived

theoretical bound. Two types of walls are tested: a 37.5cm-thick exterior brick wall and a

13cm-thick interior wall made of wood panel and sheetrock.

Before the measurement, it is worth to note that all the PTE values predicted by

the theory assume 100% antenna radiation efficiency and an optimal load impedance

value ( Zopt ) for maximum power transfer at each distance between the antennas. It was

shown in [61] that the Zopt values in the radiating near-field region are fairly well

approximated by a single resistive load, which is the conjugate of the input impedance of

the Rx antenna. To see if such finding for free space is still valid when a material is

placed between the antennas, the optimal load values across distance when the shell is

filled with a dielectric concrete material with εr=4 and tan δ=0.2 [68] is calculated. The

inner radius r1 and the thickness τ are chosen as 0.1 λ and 0.25 λ, respectively. The

73 formula for calculating the optimal load impedance for antennas in free space [30] is modified for the shell problem. For the TM mode, the result is:

(5.8)

1 = 1 − : − : 4

1 = : − 2 where Xshell:TM is given in (5.3).

The optimal impedance under the setup is normalized with respect to the input impedance Za of a free-standing Rx antenna and plotted in Figure 5.5. It is seen that the

real part of the normalized optimal load impedance in Figure 5.5a is close to one while

the imaginary part in Figure 5.5b is close to zero until it comes close to the edge of the

shell. These behaviors are similar to those observed when the antennas are in free space

[61]. Therefore, an Rx antenna with a 50 Ω input impedance attached to a fixed 50 Ω load should come close to maximizing the PTE. In the WPT measurement, a pair of FCH dipole antennas designed previously in [61] is used. The design has an electrical size of kr =0.31, a radiation efficiency ηeff of 93% and an input impedance of 48.9 Ω at 200MHz

from simulation. The actual measured resonant frequency is 194.4 MHz for both antennas

and the input resistances are measured as 57.57 Ω and 53.51 Ω for the Tx and Rx FCHs,

respectively.

74 (a)

1.2 θ=0 1.15 θ=π/2

1.1

1.05

1 ], normalized ],

opt 0.95 Re[Z 0.9

0.85

0.8 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Distance, λ

(b)

0.06 θ=0 0.04 θ=π/2

0.02

-0.02 ], normalized ],

opt -0.04 Im[Z -0.06

-0.08

-0.1 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 Distance, λ

Figure 5.5: Normalized optimal load impedance (Zopt) for shell problem with respect Za (εr =4, tan δ=0.2, r1=0.1 λ and τ=0.25 λ). (a) Co-linear configuration. (b) Parallel configuration.

75 For the exterior wall measurement, the Tx FCH is fixed at 15cm ( r1=0.1 λ) from one side of the wall and the Rx FCH is placed at different distances on the other side of the wall. The thickness of the concrete wall is 37.5cm ( τ=0.25 λ). The two antennas are mounted on 2-m-high tripods and measured using a vector network analyzer in both the co-linear and parallel configurations. The PTE is calculated from the measured S-

2 2 parameters as |S 21 | /(1-|S 11 | ) at 194.4MHz. Two baluns are characterized and de- embedded to obtain the S-parameters between the two antennas. The photograph for the measurement setup for the parallel configuration is shown in Figure 5.6a and the measured results for both configurations are plotted as dots in Figure 5.6b. Even though the measurement geometry is for a planar wall, the theoretical results for the spherical shell are plotted for reference. One set of curves is for free space and another set is for a material shell with εr =4, tan δ =0.2, r1=0.1 λ and τ=0.25 λ. It is observed that the measured

PTEs are degraded from the free space bound, and approximately follow the bounds of the material shell.

(a)

76 (b)

-1 10

θ=π/2

-2 10

θ=0 PTE

-3 10

Theory (TM mode, ε =4 & tan δ=0.2) r Exterior wall measurement Theory (TM mode, ε =1 & tan δ=0.0) r -4 10 0.5 0.6 0.7 0.8 0.9 1 Distance, λ

Figure 5.6: Through-exterior wall PTE measurement. (a) Setup. (b) Results.

(a)

77 (b)

-1 10

θ=π/2

-2 10 PTE θ=0

Theory (TM mode ε =4 & tan δ=0.2) r -3 10 Interior wall measurement Theory (TM mode, ε =1 & tan δ=0.0) r

0.5 0.6 0.7 0.8 0.9 1 Distance, λ

Figure 5.7: Through-interior wall PTE measurement. (a) Setup. (b) Results.

An interior wall measurement is also carried out in a similar manner. The wall

thickness is 15cm ( τ=0.1 λ) and the Tx FCH dipole is 22.5cm ( r1=0.15 λ) away from the

wall. The measurement setup for the parallel configuration is shown in Figure 5.7a and

the results for both configurations are plotted as dots in Figure 5.7b. The theoretical

results for the spherical shell are plotted as dashed lines (free space) and solid lines ( εr

=4, tan δ =0.2, r1=0.15 λ and τ=0.1 λ). It is observed that the measurement results are overall slightly lower than the free space PTE and higher than the theory values for concrete. These through-wall measurement results show the approximate predictive value of the derived theoretical bounds.

78 5.4 SUMMARY

In this chapter, an analytic upper bound for near-field wireless power transfer when the Tx is surrounded by a spherical material shell has been derived. The formulation is based on the free space PTE bound derived previously, and considered an additional pair of incoming and outgoing spherical waves within the shell. After converting the field expression into a mutual impedance parameter, a power transfer efficiency expression was obtained. The theory was validated against numerical simulation from FEKO. It was shown that both TM and TE mode radiators are affected by lossy dielectric materials. Finally, PTE degradation in the presence of a wall was shown through measurement and compared with the theory.

79 Chapter 6: Alleviating orientation dependence in near-field wireless power transfer using small, circular polarization antennas

6.1 INTRODUCTION

In addition to material effects on near-field WPT, the issue of orientation dependence should be examined in considering practical deployment of WPT systems.

As shown in Chapter 2, the achievable PTE value is dependent on the orientation of antennas. The maximum PTE is achieved in the co-linear configuration up to a distance of 0.4 λ between antennas while the parallel configuration is needed for distances beyond

0.4 λ. The work in Chapter 2 ignores any losses in power transfer due to misalignment or polarization mismatch between the antennas.

(a) (b) (c)

Figure 6.1: Antenna misalignment. (a) Lateral misalignment. (b) Angular misalignment. (c) Combination of lateral and angular misalignment.

Recently, some research results have been published regarding the antenna misalignment issue in near-field WPT. The antenna misalignment can be described by lateral misalignment, angular misalignment and a combination of the two. They are 80 shown in Figure 6.1. In [32], an analytical solution for the PTE of loosely coupled inductive links under lateral and angular coil misalignment has been derived. In [69], the relationships among the PTE and several parameters of the WiTricity power transfer system were analyzed using finite element simulations. Both works point to the fact that antenna misalignment is an inherent problem of near-field WPT. Significant impairment to the PTE was shown analytically and numerically. To overcome such degradation, Lee et al. proposed to implement an adaptive matching circuit composed of inductors and variable capacitors at the transmitting loop antenna [70]. It was shown that such a method can improve the PTE by 48% in comparison to a WPT system without such a technique for the axial misalignment case.

The polarization mismatch loss between linearly polarized antennas can be considered as a form of angular misalignment. It can cause orientation dependence in

PTE for near-field WPT. Circularly polarized (CP) antennas have been used in standard far-field applications such as satellite and terrestrial point-to-point communications systems (e.g. GPS) in order to maximize the polarization efficiency component of the link budget. In this chapter, it will be investigated that whether small, CP antennas can be used as a means of alleviating orientation dependence in near-field WPT. This chapter focuses on cross dipole antennas, or the so-called turnstile dipole antennas, which can achieve CP without the use of external 90-degree phase shifters [71]-[72]. In particular, the design of electrically small turnstile antennas is investigated for near-field WPT.

81 Electrically small turnstile antennas for far-field applications have been reported so far. They include cavity backed structure [73]-[74], double-sided cross dipole [75], metamaterial inspired design [76]-[78], etc.

This chapter is organized as follows. First, the working principles of a λ/2- turnstile CP antenna are reviewed. Second, an electrically small, turnstile CP antenna is designed using the top loading and folding concept. FEKO simulation in conjunction with a local numerical search is utilized to optimize for the axial ratio (AR) and impedance matching. Simulation results are compared with measurement results in terms of return loss, input impedance and CP performance. Lastly, PTEs are simulated and measured for the designed and fabricated antennas. It is shown that CP characteristics can still be useful in alleviating polarization mismatch in near-field power transfer.

6.2 REVIEW OF THE HALF WAVELENGTH TURNSTILE ANTENNA

A λ/2-cross dipole, or the turnstile dipole antenna, is composed of two orthogonal

linearly polarized (LP) dipoles. One of them is slightly longer than half wavelength while

the other one is slightly shorter than half wavelength as shown in Figure 6.2.

Theoretically, such a composition can satisfy the CP condition in the boresight direction

at the resonant frequency of half wavelength [79]. For example, if the input impedances

of the two LP dipoles are 50+50i Ω and 50-50i Ω, respectively, then the total input impedance of the turnstile antenna is 50 Ω since it is connected in parallel. Also the currents on both of the LP dipoles are of equal amplitude and in phase quadrature ( ) ±90° under the excitation voltage, satisfying the condition for AR of 1. To confirm this

82 numerically, the AR of the antenna versus the half-length of each dipole (i.e. l x and l y) is

plotted in Figure 6.3a.

Figure 6.2: Half-wavelength turnstile dipole. Voltage source is at the center.

In this work, the AR of the polarized wave is defined as the ratio of the minor axis to the major axis to avoid an excessively large number for the LP case. Therefore, the AR of the perfect CP is 1 while that of the perfect LP is 0. It is also assumed that there are no conductor losses on the wires. A target frequency is set as 200 MHz. It is shown in Figure

6.3a that AR values of 0.6-0.8 are observed at some antenna length combinations. Among these possible lengths, the smallest antenna dimension is given by lx=0.27 λ and ly=0.23 λ or vice versa. Since the AR is very sensitive to the length of the antennas, a local search is run with these lengths as the initial guess to maximize the AR at 200 MHz. Figure 6.3b

83 shows that an AR of 0.99 is achieved with (l x, l y)=(0.2601 λ, 0.2264 λ) at 200 MHz. Figure

6.3c shows the input impedance versus frequency of the resulting design. It is interesting

to note that the impedance bandwidth of the design is actually broadened in comparison

to that of a single λ/2-dipole antenna. This is because each LP dipole’s resonant frequency is shifted slightly upward or downward, resulting in a flat reactance region close to the zero crossing when they are connected in parallel. However, the limiting performance of this design is the CP bandwidth, which is much narrower than its impedance bandwidth. The input impedance at 200MHz is 74.9-1.9i Ω, very similar to

that of a half-wavelength dipole.

(a)

1 0.8

0.7

0.75 0.6

0.5 λ 0.5 0.4 ly, ly,

0.3

0.25 0.2

0.1

0.25 0.5 0.75 1 lx, λ

84 (b)

0.9

0.8

0.7

0.6

0.5 AR

0.4

0.3

0.2

0.1

0 150 160 170 180 190 200 210 220 230 240 250 Frequency, MHz

(c)

150

100

Ω 50

-50 Input impedance, Input

-100 Real Imaginary -150 150 200 250 Frequency, MHz

Figure 6.3: Simulation result of a turnstile dipole antenna. (a) Absolute axial ratio intensity along the length of the dipole elements. (b) Axial ratio vs. frequency. (c) Input impedance.

85 6.3 DESIGN OF ELECTRICALLY SMALL TURNSTILE DIPOLE ANTENNA

The feasibility of designing a turnstile CP antenna by the combination of two half wavelength dipole antennas has been reviewed and confirmed in the previous section.

Next, it is considered how to make such a CP antenna electrically small. The practical design issue is how to overcome the poor radiation performance and narrow impedance bandwidth that typically comes with miniaturization while maintaining the proper current ratio on each small LP element for CP.

(a)

86 (b)

0.12 0.3

0.11 0.25 0.1

0.2 0.09

λ 0.08 0.15 ly, ly,

0.07 0.1 0.06

0.05 0.05

0.04 0.04 0.06 0.08 0.1 0.12 lx, λ

Figure 6.4: Small circular polarization antenna with top loading disc. (a) Structure. (b) Absolute axial ratio intensity along the length of the dipole elements.

There are two well-known techniques to overcome the small radiation resistance of electrically small antennas. The first one is to employ a top loading at each end of the dipole antenna to provide self-resonance characteristic on small antennas [80]. The second one is to use multiple folding to provide high radiation efficiency as described in

Chapter 2. The impedance bandwidth of the electrically small turnstile antennas will not be narrow due to their intrinsic characteristic as shown in the previous section. However, the CP bandwidth will be narrower since the proper current ratio for CP is dominated by the electrical size of the antenna and thus needs to be examined. In addition to this, the

AR itself is very sensitive to the length of the antennas. Therefore, to find a desired

87 current ratio, a numerical search is utilized in the design process after achieving enough radiation resistance by top loading and multiple folding techniques. The design is carried out using FEKO again in conjunction with a local numerical search engine fminsearch in

MATLAB.

The design is shown in Figure 6.4a, which is created by adding top loading discs at both ends of a 0.1 λ small dipole antenna. The operating frequency is chosen as 200

MHz. PEC is used for the disc since the height of the disc is assumed to have zero

volume. A copper wire radius of 0.5mm (18-AWG) is chosen. The diameter of the

loading disc is fixed to have 95% of the dipole length to prevent any possible overlap

during the geometry optimization. The kr value of the initial design is 0.44. To check the

feasibility of CP performance at such a small size, the AR is plotted according to the

length of the dipole (lx, ly). In Figure 6.4b, it is found that 0.3 AR is observed at (lx,

ly)=(0.057 λ, 0.053 λ) where lx and ly is the half length of each dipole with disc loading. A local search is carried out to maximize the AR using this point as the initial guess to maximize the AR. An AR of 0.97 is obtained at (lx, ly)=(0.0544 λ, 0.0531 λ). However,

the corresponding input impedance is very low at 6.1+2.7i Ω, meaning that only the self-

resonance characteristic is achieved without a sufficiently high radiation resistance.

Therefore, the number of arms on each dipole antenna is increased. Since the input

resistance with a single arm with disc loading is 6.1 Ω, a three-arm design is chosen as

shown in Figure 6.5a. The set of additional folded arms for each LP dipole antenna

element is located in parallel with it as shown in the figure. The distance from the excited

dipole to each arm and the distance between the arms in the disc plane are set to pl. It is 88 fixed as 0.005m for now. The length of the folded arms is same with each excited dipole.

As it was done for the single arm with disc loading case, AR is plotted according to the length of the dipole in Figure 6.5b. The AR of 0.64 is observed at (lx, ly)=(0.063 λ,

0.060 λ). A local search with this point as an initial guess with the same objective function finds an AR of 0.97 at (l x, l y)=(0.0633 λ, 0.0608 λ), with an input impedance of 38.5+39.4i

Ω. It is worthwhile to note that the antenna dimensions are slightly increased with the added folding arms.

(a)

89 (b)

0.12 0.6 0.11

0.5 0.1

0.09 0.4

λ 0.08

ly, ly, 0.3

0.07 0.2 0.06

0.1 0.05

0.04 0.04 0.06 0.08 0.1 0.12 lx, λ

Figure 6.5: Small circular polarization antenna with top loading disc and folded arm. (a) Structure. (b) Absolute axial ratio intensity along the length of the dipole elements.

Lastly, to have a better matching with respect to 50 Ω, the location of the folded arm pl in Figure 6.5a is added as a variable in the numerical search. To find a good initial guess for the numerical search, the objective function K=|1-|AR||+|S 11 | values are checked first along with lx, ly and pl. It is found that the minimum K of 0.4181 is obtained with

(lx, ly, pl)=(0.11m, 0.115m, 0.05m). A local search with this point as an initial seed gives

|S 11 | of 0.2721 and AR of 0.9993 at the resonant frequency 200 MHz with (lx, ly, pl)=(0.1097m, 0.1158m, 0.0516m). Its corresponding kr is 0.67. It is seen that the optimized parameters are not very far from the initial seed value, showing that the small turnstile design is very sensitive to the dimensions. The optimized CP design out of the

90 local search is fabricated as shown in Figure 6.6. Two antennas are built, one as the Tx and one as the Rx, using AWG-18 copper wire and copper tape. Copper tape is used for the loading discs, which are supported by cardboards. A 50-cm long ruler is placed together for size comparison. The metal tip shown at the center of the antenna is for the balun connection. Again, the balun is characterized and de-embedded to obtain the S- parameters at the feeding port of the antenna in the measurement process, similar to what was used in the previous chapters.

Figure 6.6: Fabricated circular polarization antennas (Tx and Rx). One shows the front side and the other one shows the back side.

The simulated AR, return loss and input impedance are plotted in solid lines in

Figure 6.7. The measured return loss and input impedance are plotted in dashed lines. It is shown in Figure 6.7a that the AR is 0.99 at 200 MHz and the 3dB-AR bandwidth is about

3%. The -10dB impedance bandwidth is 8.25% as shown in Figure 6.7b.

91 (a)

1 FEKO 0.9

0.8

0.7

0.6

0.5 AR 0.4

0.3

0.2

0.1

0 120 140 160 180 200 220 240 Frequency, MHz

(b)

-5

Return Loss, dB Loss, Return -10

FEKO Rx Measurement Tx Measurement -15 120 140 160 180 200 220 240 Frequency, MHz

92 (c)

800 FEKO 600 Tx Measurement Rx Measurement

400 Ω 200

0 Reactance,

-200

-400

-600 120 140 160 180 200 220 240 Frequency, MHz

(d)

1200 FEKO Tx Measurement 1000 Rx Measurement

800 Ω

600

Resistance, 400

200

0 120 140 160 180 200 220 240 Frequency, MHz

Figure 6.7: Simulation and measurement results for the designed circular polarization antenna. (a) Axial ratio. (b) Return loss. (c) Input reactance. (d) Input resistance.

93 From the measurement result, two things are observed. First, the resonant frequency is shifted downward by 20 MHz from the simulation. This is likely caused by fabrication inaccuracy. Second, the measured impedance bandwidth is narrower than the simulation by half (i.e. bandwidth=4.1%), which happened during the tuning process for

CP performance of the fabricated antennas. It will be discussed later in the CP performance measurement part. In addition to the bandwidth, another feature of the designed antenna can be found in Figure 6.7c, which shows the simulation and measurement values of the input reactance. It is observed from the simulation that the two frequency points for X=0 (193 MHz) and AR=1 (200 MHz) are off by 7MHz or the ratio of 0.97. The frequency where X=0 is 175 MHz from the measurement, therefore, it can be inferred that a good CP characteristic would be observed around 181MHz. Lastly, from Figures 6-7b, c and d, it is observed that the two fabricated antennas show very similar impedance characteristics and the measured input impedance of the Tx antenna is

26.1+30.5i Ω and the Rx antenna is 30.7+23.4i Ω at 181MHz.

To measure the CP performance of the fabricated antennas, a λ/2-long LP dipole is employed as the receiver and rotated in 30 steps from 0 to 330 as shown in Figure ° ° ° 6.8. The vertical position of the dipole antenna (the position shown in the photo) is

designated as 0 . During the test, each CP antenna is used as the transmitter in a fixed ° orientation, while the LP dipole is used as the receiver and rotated. The distance between

the two antennas is fixed at 1.8m, to ensure that the antennas are in the far-field region.

94 (a)

(b)

Transmission Loss: Tx antenna 160 -15

165

170 -20

175

180 -25

185

190 -30 Frequency, MHz Frequency, 195

200 -35

205

210 -40 0 50 100 150 200 250 300 Angle, deg

Transmission Loss: Rx antenna 160 -15

165

170 -20

175

180 -25

185

190 -30 Frequency, MHz Frequency, 195

200 -35

205

210 -40 0 50 100 150 200 250 300 Angle, deg

95 (c)

2 Tx Measurement 1.8 Rx Measurement 1.6

1.4

1.2

0.8 Magnituderatio 0.6

0.4

0.2

0 120 140 160 180 200 220 240 Frequency, MHz

(d)

300 Tx Measurement 200 Rx Measurement

100

-100

Phase difference, deg Phasedifference, -200

-300

-400 120 140 160 180 200 220 240 Frequency, MHz

Figure 6.8: Circular polarization characteristic measurement. (a) Setup. (b) Transmission loss. (c) Magnitude ratio. (d) Phase difference.

96 2 2 2 The measured transmission loss, defined as |S 21 | /|1-|S 11 | |/|1-|S 22 | | is shown in

Figure 6.8b for both of the CP antennas. The color intensity is in dB scale and transmission loss is plotted versus frequency and angle of the LP dipole antenna. It is shown that a very stable transmission loss is observed at 180 MHz for all rotation angles of the LP dipole antenna, meaning that the fabricated antennas show good CP performance. Also for each fabricated CP antenna, the ratio of the received signals when the dipole antenna is at 0 (vertical polarization) and 90 (horizontal polarization) is ° ° measured and plotted in Figs. 6-7c and d. It is observed that at 181 MHz, the magnitude ratio between the two polarizations is about 1 and the phase difference (vertical to horizontal) is about -100 for both antennas, confirming a left-handed CP performance. ° During the measurement, the smaller dipole element in both CP antennas was retuned by

increasing the disc size to improve the CP performance. This resulted in a narrower

impedance bandwidth, which is why the impedance bandwidth of the measured antenna

in Figure 6.7b is less than that of the simulation.

6.4 PTE VALUES USING ELECTRICALLY SMALL TURNSTILE DIPOLE ANTENNA

In this section, the PTE is simulated and measured using the designed electrically small turnstile dipole antennas under near-field and far-field conditions. In Figure 6.9, the two PTE simulation setups to observe the ability of alleviating polarization dependence in the near-field region using the designed CP antennas are shown. On the left is when the two antennas are in identical orientation, and on the right they are oriented at a 45 degree

97 angle with respect to each other. The distance is defined as from center to center of the antennas and varied from 0.15 λ to 1.3 λ.

(a) (b)

Figure 6.9: PTE simulation setup. (a) Identical orientation. (b) Oriented at 45 . °

The PTE values based on the configurations in Figure 6.9 are simulated and plotted in Figure 6.10 as solid lines. For comparison, two linearly polarized FCH dipole antennas in Chapter 2 are also tested under the same scenarios (in the parallel configuration). Their PTE results are plotted by dashed lines. It is observed that, under perfect alignment, the PTE values using the CP antennas is almost the same as that of the

FCH dipoles. The only exception is the small drop at a single distance when the antennas are at 0.2 λ. Under the misaligned scenario, the PTE for the LP FCH antennas drop by the expected 3dB in the far field. Closer in (<0.2 λ), the drop is less than a factor of two. The 98 PTE for the small CP antennas show the expected orientation independence in the far field. There is essentially no difference between the 0 and 45 cases for a separation ° greater than 0.3 λ. There is some orientation dependence at closer range. This could be

due to the fact that the current ratio on the antennas is varied from its best CP

performance as the two antennas are closely spaced and coupled to each other strongly.

Nevertheless, it is confirmed that CP property is still a good characteristic to alleviate

polarization mismatch in power transfer in the radiating near-field region.

0 10 ° FCH-FCH (Rx rotate 0 ) ° FCH-FCH (Rx rotate 45 ) ° CP-CP (Rx rotate 0 ) ° -1 CP-CP (Rx rotate 45 ) 10 /2) π = θ

PTE( -2 10

-3 10 0.15 0.3 0.6 0.9 1.2 d, λ

Figure 6.10: PTE simulation for polarization mismatch case.

6.5 SUMMARY

In this chapter, an electrically small turnstile dipole antenna has been designed using full-wave simulation in conjunction with a local optimizer to investigate whether

99 circular polarization antennas can be used in alleviating orientation dependence problem in near-field wireless power transfer. It was found that a circular polarization antenna can be designed and realized in an electrically small size and such a polarization characteristic is useful to avoid polarization mismatch problem in near-field wireless power transfer.

100 Chapter 7: Conclusions and Future Work

The use of the coupled mode resonance phenomenon for non-radiative wireless power is being studied intensively and many works have been reported. However, the distance over which such phenomenon exists is very short when measured in terms of wavelength. This dissertation focused on the near-field region beyond the coupled mode resonance region as a means of efficient wireless power transfer (WPT). In Chapter 2, the theoretical power transfer efficiency (PTE) bound was demonstrated by the design of electrically small, highly efficient folded cylindrical helix (FCH) dipole antennas. A 40%

PTE was achieved at the distance of 0.25 λ between the antennas in the co-linear configuration. In Chapter 3, to further extend the range or efficiency of the power transfer, transmitter diversity and receiver diversity were investigated. For transmitter diversity, it was found that a stable PTE region can be created when multiple transmitters are sufficiently closely spaced. Subsequently, such a stable PTE region was demonstrated using electrically small FCH dipoles. The measurement results highlighted the importance of maintaining high antenna radiation efficiency in realizing efficient WPT.

For receiver diversity, it was found that the PTE can also be improved as the number of the receivers is increased. In Chapter 4, small directive antennas were investigated to see whether they can be used as a means of enhancing near-field WPT. It was found that the range of efficiency can indeed be enhanced by using small directive antennas. It was also shown that the far-field realized gain is a good surrogate for designing small directive antennas for near-field power transfer. Chapter 5 and Chapter 6 discuss the topics related to practical deployment issues. In Chapter 5, to examine the effects of surrounding 101 environments on the near-field coupling, an analytic upper bound for near-field WPT when the transmitter is surrounded by a spherical material shell was derived. The derived formulas for both TM and TE mode radiators showed good agreement with full-wave simulation results. Lossy dielectric material effects on the near-field WPT were studied using the derived theory. It was found that TE mode radiator is less affected by the presence of dielectric material in power transfer only when the radiator is extremely close to the material. There was no difference in PTE between the TE and TM mode radiators when dielectric material is located beyond 1 λ from the transmitting antenna. In Chapter

6, electrically small circularly polarized antennas were investigated to alleviate the

orientation dependence problem in near-field coupling. An electrically small, turnstile

dipole antenna was designed and tested in the far-field region. Then the ability to reduce

orientation dependence in near-field WPT by the use of this design was quantified.

To conclude this dissertation, several potential extensions and future research

topics are suggested. First, it would be interesting to study whether an optimal frequency

exists for maximizing the range or efficiency of the transfer. 200 MHz was chosen for all

of the examples in this dissertation as a matter of convenience in the measurements. A

lower frequency would naturally lead to a longer absolute range in the power transfer.

However, maintaining high antenna efficiency and physical size while reducing the

operating frequency also becomes more challenging. Therefore, an optimal frequency

may exist by considering the different practical implementation constraints (e.g., wire

radius, antenna size). Some work has recently been reported along this line in [36].

102 Second, investigation on efficient near-field coupling to implanted devices could be an interesting and practical topic. One important issue in WPT is its interactions with surrounding materials for practical deployment. In Chapter 5, such effects with arbitrary lossy dielectric materials for TM and TE mode radiators have been quantified using the spherical mode theory. This line of research can be extended for high dielectric and lossy materials such as the human body. The closed-form formula derived in Chapter 5 is useful in predicting the efficiency degradation in power transfer under lossy dielectric materials at a given distance. Therefore, the formula can serve as a useful antenna design guide for powering implanted biomedical devices in the human body. The feasible antenna size and the corresponding resonant frequency can be estimated in this manner.

Then proper antenna systems can be designed and built to meet the condition for efficient

WPT. The formula can be further extended for multi-layers problem to analyze more complex and realistic situations. For this type of study, standard material parameters of human body are recommended [83]. Another topic of interest along the same line is the safety issue of WPT systems. Electromagnetic exposure to humans from WPT systems must be properly addressed. The fact found in Chapter 5 that the interaction between TE mode radiators and surrounding dielectric material is less only when the material is placed less than 0.1 λ from the radiator can be exploited.

103 Appendix A

Two-port S-parameters ( ) can be measured using a vector network analyzer and be transformed into ABCD matrix ([ ) with respect to Z0=50 Ω:

(A.1) =

Each matrix term in (A1) is represented in Figure A.1.

path loss antenna-antenna

50 Ω 100 Ω 50 Ω cable *balun balun cable

[ABCD] [ABCD] [ABCD] A B C

Figure A.1: Balun de-embedding setup. ( *ADT2-1T 2:1 transformer from Mini-Circuits used as a balun.)

can be characterized from the S-parameters of the balun alone. Since the balun can be modeled as a two-port T-network as shown in Figure A.2, the balun needs to be measured three times with the output of open, short, and matched load (100-Ω), respectively.

104 Za Zb

port1 Zc port2

Figure A.2: T-network of a balun.

After calculating Zopen , Zshort , and Zload with the measured data and from Figure A.2, they

can be solved for Za, Zb, and Zc such as [81]:

= −

= − (A.2) −

100 × − = − 1 − −

and they can be transformed into [82]. can be calculated using the same method. Then is obtained by:

(A.3) =

105 and finally, the desired S-parameters is conversed from with respect to 50Ω.

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113 Vita

Ick-Jae Yoon was born on August 31 st 1980 in Seoul, Republic of Korea. He received his B.S. and M.S. degrees in Electrical and Electronic Engineering from Yonsei

University, Seoul, Korea in August 2003 and August 2005, respectively. From July 2005 to August 2008, he worked as a research engineer at Samsung Advanced Institute of

Technology (SAIT) of Samsung Electronics, Co., Yongin, Korea. He carried out research on antennas and active/passive RF circuits for mobile applications.

Since August 2008, he has been a graduate student and a research assistant in the

Dept. of Electrical and Computer Engineering at the University of Texas at Austin and working toward the Ph.D. degree.

Permanent email: [email protected]

This dissertation was typed by the author.

114