An energy harvesting antenna array for the 28 ghz band

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An Energy Harvesting Antenna Array for the

28 GHz Band

by

Hidai Arnulfo C´ardenas Herrera

Thesis submitted in partial fulfillment of the requirements for the degree of:

M.Sc. in Electronics

from the

Instituto Nacional de Astrof´ısica, ´Optica y Electr´onica (INAOE) December 2019

Santa Mar´ıa Tonantzintla, Puebla

Advisor:

Dr. Roberto Stack Murphy Arteaga

c

The author grants INAOE permission for reproducing and distributing copies of this thesis in its entirety or in parts mentioning the source.

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Abstract

Recently, electromagnetic harvesting technologies have attracted the attention as an en-ergy source for the future. The key element of an RF enen-ergy harvesting system (EHS) is the rectenna, which is a combination between a rectifying circuit and an antenna. The antenna receives the electromagnetic power and the rectifying circuit converts it to DC electric power.

The research on antennas for EHS have been focused on frequencies below 10 GHz and only some of them in tens of GHz. The antennas for EHS that work below 10 GHz currently have many sources of energy, but the trade-offis their large size. Therefore, it is important to harvest energy at higher frequencies with a large amount of energy available. The new 5G network, which works about the 28 GHz band (27.5-28.35 GHz) and nearby frequencies, will be available in 2020, It will provide a large amount of available energy to be harvested.

In this work, due to its light weight, easy integration into circuits and low cost, a 2x2 microstrip antenna array with circular polarization to harvest electromagnetic energy at 28 GHz band is proposed. The array has two resonance bands, one of 6.61 GHz (25.07-31.68 GHz) and a second one of 0.92 GHz (34.83-35.75 GHz). The bandwidth of the circular polarization is 0.73 GHz (27.75-28.49 GHz). At 28 GHz, an axial ratio of 0.91 dB and a gain of 10.4 dBi are presented.

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Resumen

Recientemente, las tecnolog´ıas de recolección electromagnética (EHS) han atra´ıdo la atención como fuente de energ´ıa para el futuro. El elemento clave de un sistema de recolección de energ´ıa de RF es la rectenna, que es una combinación entre un circuito rectificador y una antena. La antena recibe la energ´ıa electromagnética y el circuito recti-ficador la convierte en energ´ıa eléctrica de CC.

Las investigaciones sobre antenas para EHS se han centrado en frecuencias inferiores a 10 GHz y sólo algunas de ellas en décadas de GHz. Las antenas para EHS que funcionan por debajo de 10 GHz actualmente tienen muchas fuentes de energ´ıa, pero tienen gran tamaño. Por lo tanto, es importante cosechar energ´ıa en frecuencias más altas con una gran cantidad de energ´ıa disponible. La nueva red 5G, que funciona en la banda de 28 GHz (27.5-28.35 GHz) y frecuencias cercanas, estará disponible en 2020 y proporcionará una gran cantidad de energ´ıa para ser cosechada.

En este estudio, debido a su peso ligero, fácil integración en circuitos y bajo costo, se propone un arreglo de 2x2 antenas de microstrip con polarización circular para recolección de energ´ıa electromagnética en la banda de 28 GHz. El arreglo tiene dos bandas de reso-nancia, una de 6.61 GHz (25.07-31.68 GHz) y una segunda pequeña de 0.92 GHz (34.83-35.75 GHz). El ancho de banda de la polarización circular es 0.73 GHz (27.75-28.49 GHz). A 28 GHz, se presenta una relación axial de 0.91 dB y ganancia de 10 dBi.

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Acknowledgements

Foremost, I thank to my parents and siblings who are always with me and without them I would not have enough motivation to achieve the goals proposed so far. Thank you for good vibes and affection that you grant me, which is a great support all the time.

I thank Dr. Roberto Stack Murphy Arteaga for his guidance on the research work presented here.

I’m also grateful to Consejo Nacional de Ciencia y Tecnolog´ıa (CONACYT) for provid-ing me with the scholarship # 852405 and the CONACYT project # 285199 for supportprovid-ing my studies.

I finally thank the Instituto Nacional de Astrof´ısica, ´Optica y Electr´onica (INAOE) for allowing me to be one of his students .

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List of Figures

1.1 Harvest system block diagram. . . 2

2.1 Antenna as a transition device [16] . . . 8

2.2 Transmission – line Thevenin equivalent of an antenna in transmitting

mode [16] . . . 9

2.3 (a) Radiation lobes and beamwidths of an antenna pattern. (b) Linear plot

of power pattern and its associated lobes and beamwidths [16] . . . 11

2.4 Typical changes of antenna amplitude pattern shape from reactive near

field toward the far field [18] . . . 12

2.5 Two- and three-dimensional directivity patters of a 2 dipole. [16] . . . 15

2.6 Rotation of a plane electromagnetic wave and its polarization ellipse at

z=0 as a function of time [16] . . . 17

2.7 Polarization figure traces of an electric field extremity as a function of

time for a fixed position. (a) Linear. (b) Circular. (c) Elliptical. [19] . . . 18

2.8 Main dimensions of Microstrip path antenna. (W) Width and (L) length

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2.9 Representative shapes of microstrip patch elements [16]. . . 20

2.10 Microstrip antenna equivalent circuit. . . 21

2.11 Square patch arrangements for circular polarization [20] . . . 22

2.12 Single-feed arrangements for circular polarization of rectangular microstrip

patches [16] . . . 22

2.13 Circular polarization for a square patch with thin slots on patch (c =

W/2.72=L/2.72, d=c/10=W/27.2=L/27.2), and by trimming opposite

corners of a square patch [16]. . . 23

2.14 Circular polarization by making circular patch slightly elliptical [16] . . . 23

2.15 Square patch arrangements for circular polarization [23],[24] . . . 25

3.1 (a) CP patch array antenna configuration. (b) Photograph of the fabricated

prototype [26] . . . 29

3.2 Simulation and measurement results of (a) impedance matching and (b)

axial ratio of the CP array from 22 GHz to 28 GHz [26] . . . 30

3.3 Simulated and measuredS11 parameters of the proposed CP antenna

ar-rays: (a) LHCP and (b) RHCP [27] . . . 31

3.4 Simulated and measured radiation performance of the proposed CP

an-tenna arrays against the frequency band: (a) LHCP and (b) RHCP [27] . . 31

3.5 (a) Side view of the proposed CP antenna array and (b) photograph of the

fabricated antenna arrays: LHCP (left) antenna array and RHCP (right)

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3.6 Geometries of LHCP (top) and RHCP (down) antenna elements with

dif-ferent configurations: (a) substrate # 1; (b) substrate # 2; (c) copper plate;

and (d) substrate # 3 [27] . . . 32

3.7 Proposed MMW energy harvesting antenna: a) simulated prototype with design parameters; b) fabricated prototype [28] . . . 33

3.8 (a) Return loss plot and (b) peak gain vs frequency plot of the proposed MMW energy harvesting [28] . . . 34

3.9 Proposed printed slot antenna. (a) Top view, (b) side view and (c) a close-up view of the cross slot in the parasitic patch. (d) Photograph of the fabricated prototype [29] . . . 34

3.10 Measured and full-wave simulated reflection coefficients of the proposed printed slot antenna [29] . . . 35

4.1 (a) Antenna and (b)S11parameters of the first design stage (W1=3.0) . . 39

4.2 Radiation pattern of stage 1 . . . 40

4.3 (a) Antenna and (b)S11parameters of the second design stage . . . 41

4.5 (a) Antenna and (b)S11parameters of the third design stage . . . 42

4.6 Axial ratio (dB) vs frequency of the third design stage. . . 42

4.7 Radiation pattern of Stage 3 . . . 43

4.8 (a) Antenna and (b)S11parameters of the fourth design stage . . . 43

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4.11 Displacement of the electric field in an antenna . . . 45

4.12 (a) 2x2 antenna Array dimensions and (b) 2x2 antenna Array with

con-nector and coordinate system . . . 46

4.13 S11parameters of the 2x2 antenna Array . . . 47

4.14 3-D Gain pattern of the array at (a) 25 GHz, (b) 28 GHz, (c) 31.6 GHz

and (d) 35.2 GHz) . . . 47

4.15 Gain pattern of (a) electrical and magnetic plane, (b) Co-Polarization

and Cross-Polarization in the electrical plane and (c) Co-Polarization and

Cross-Polarization in the magnetic plane at 28 GHz . . . 48

4.16 Axial ratio vs frequency of the array . . . 49

5.1 1492-02A-6 connector dimensions. All dimensions are in inches. All

angles are in degrees. Dimensions shown in brackets are in millimeters [43] 51

5.2 RT/duroid launch dimension. All dimensions are in inches. All angles are

in degrees [44] . . . 52

5.3 Taper (version 1), Optimized Taper (version 2) and No Taper TDR. This

optimization is from another substrate, it is only shown by way of example

[45] . . . 52

5.4 (a) Array drawn on copper foil, (b) manufactured array, (c) manufactured

array compared to 50 cents Mexican coin and (d) manufactured array with

its connector . . . 53

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5.6 Normal distribution of absolute error . . . 54

5.7 Vector Network Analyzer Anritsu with calibration kit . . . 55

5.8 ParametersS11simulated and measured from antenna array . . . 56

5.9 Simulation and measurement of the first resonance band of the array . . . 56

5.10 Simulation and measurement of the second resonance band of the array . 57

5.11 (a) Circular wave port to excite coaxial and (b) rectangular wave port to

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List of Tables

2.1 5G frequencies close to 28GHz band . . . 24

3.1 Dimensions of the antenna array . . . 29

3.2 Dimensions of Two CP antenna elements (Units: mm) [27] . . . 31

3.3 Design Parameters of proposed MMW antenna [28] . . . 33

3.4 Dimensions of the printed slot antenna elements (Units: mm) . . . 35

3.5 Antennas in the 5G band . . . 36

4.1 Dimensions of antenna design stages . . . 40

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Chapter 1 Introduction

1.1 Motivation

Recently, energy harvesting technologies, which transform a small amount of energy into electric power, have attracted the attention as an energy source for the future. These energy harvesting technologies extract power from different sources, such as: sunlight, mechanical vibration, thermal gradients, convection flows, electromagnetic waves and other forms of harvestable energy [1, 2, 3]. Electromagnetic waves are also considered one of the principal energy sources.

Electromagnetic energy produced by humans is located on the range from Hz to EHz, but the largest amount of energy available is in the GHz range. For instance, AM radio (600 KHz – 1.6 MHz) is placed in the range of MHz, Mobile Phones (900 MHz – 2.4GHz) and radar (1-100 GHz) are based in the range of GHz, and Medical X-ray is in the range of EHz. All this electromagnetic energy is available to be harvested, but the largest amount of recyclable ambient electromagnetic energy can be found in densely populated urban zones, where mobile devices work in GHz or decades of GHz. Therefore, the system used to harvest electromagnetic energy, must do so at the frequencies with the greatest amount

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of energy available.

The key element of an RF energy-harvesting system is the rectenna [4], which is a combination between a rectifying circuit and an antenna. The antenna receives the elec-tromagnetic power and the rectifying circuit converts it to DC electric power. Figure1.1

shows a rectenna’s block diagram, where a low pass filter (LPF) and matching network blocks are included. Since the rectifier is made with a diode, which is an active device, the intermodulation products (IMPs) need to be eliminated with an LPF. Generally, in rectifiers a larger amount of energy available at the input will produce a larger amount of energy available at the output.

Figure 1.1: Harvest system block diagram.

In order to capture as much as possible RF power, antenna arrays are generally used as the receiving components of the rectennas, for these collect more incoming RF energy. The array structure improves the efficiency by focusing the beam toward the transmitter antenna, but at lower frequencies, by considering numerous available sources, to apply an array could reduce the power harvested by the antenna (narrower beamwidth). In any case, the use of an antenna array seems to be the most promising solution to provide more RF power [5].

Since the power density of ambient RF energy is extremely small, it is very challenging to design RF energy harvesting systems with satisfying RF-to-dc power conversion effi -ciencies. Transmitted power is limited by government regulations and received power is attenuated due to free-space loss. Because of these limitations, wireless power harvesting is mainly suitable for portable low-power applications, for example a low-power wireless sensor. In general, portable devices have small dimensions. Therefore, the rectenna should

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have small dimensions as well. This results in a small antenna area and, consequently, a low amount of received power.

1.2 Problem description

With the development of remotely powered passive devices (RPPD) [6] and low-power electronic circuits (LPEC), the use of energy harvesting systems (EHS’s) has increased. Remotely powered passive devices, for example, modern biomedical implants [7], are required because the use and replacement of batteries are impractical since the chance of infection and chemical instability can increase. In LPEC the battery is the main source of energy, and the harvesting device plays a secondary but important role. Using the energy harvester, battery energy usage is limited, and the system’s lifetime is prolonged, decreasing the frequency of external battery recharge and replacement. Therefore the research on EHS has increased in the last decades.

Research on antennas for EHS has been focused on frequencies below 10 GHz, and only some of them in decades of GHz. To illustrate this, in [8] and [9] an overview of antennas for RF energy harvesting below of 10 GHz is presented. And only a few works have been reported above 10 GHz. For example, a rectenna operating at 10 GHz and 35 GHz was presented in [10], and some studies have been made at 24 GHz [11,12,13,14].

The antennas for EHS that work below 10 GHz currently have many sources of energy, but the trade-off is the large size. In a mobile network, which works from 900 MHz to 2.4 GHz, the mobile companies use many transmitters of energy, because of the great number of users. In Wi-Fi networks, that work at 2.4 GHz and 5.8 GHz, many sources of energy are based in urban zones, because Wi-Fi is available at houses and free areas, like shopping malls, airports, parks and recreational centers. Nonetheless the size of the antenna is directly proportional to the wavelength. The size of the antenna needed for these frequencies is larger than the size of the devices which are energized. Therefore, it is

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important to harvest energy at higher frequencies with a large amount of energy available.

Polarization and orientation of the incident wave is known, but the orientation of the receptor element is unknown. Electromagnetic waves coming from radio stations, cellular station towers and Wi-Fi modems have vertical polarization. The RPPD and LPEC are portable devices that when they are transported, they change their position and orientation. Therefore, to increase the amount of energy harvested, it is necessary to have a receiving antenna with circular polarization.

1.3 Proposed solution

The new 5G network, which works about the 28 GHz band (27.5-28.35 GHz) and nearby frequencies, will be available in 2020, It will provide a large amount of available energy to be harvested. In this way, 29 billion devices will be connected to Internet of Things (IoT) by 2022 [15], each of these devices will send and receive electromagnetic waves. Even a 5G Fixed Wireless Access (FWA) will try to compete with the actual Wi-Fi networks. Because of the amount of energy that will be available and the size of the antenna related with 28 GHz, energy harvesting in the new 5G network is looked forward to as an excellent option.

In this work, due to its light weight, easy integration into circuits and low cost, a 2x2 microstrip antenna array with circular polarization to harvest electromagnetic energy at 28 GHz band is proposed. Each element of the array was designed as a square patch with two corners cut out [16] and made on a Rogers RT/duroid 5880 laminate.

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1.4 Objectives

The current project satisfies the following objectives:

General

• Design and fabricate a 2x2 antenna array with circular polarization for harvesting electromagnetic energy about the 28 GHz band

Specific

• Design and simulate an antenna with circular polarization about the 28 GHz band.

• Design and simulate a 2x2 antenna array with circular polarization about the 28 GHz band.

• Fabricate the antenna array.

• Measure S parameters of the antenna array.

• Compare measurements and simulations.

• Obtain results and conclusions.

1.5 Document organization

The structure of the present document is noted below. Chapter 2 describes the central theoretical concepts regarding the methods used to design the antennas. In the following chapter, there is a general overview of antennas designed for power harvesting and for general applications, which can be used for energy collection at the 28 GHz and nearby bands. Chapter 4 is about the designing process of the antenna array, beginning with the

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design of a single antenna. Chapter 5 includes the manufacture and measurement of the antenna. Finally, the last chapter presents the main conclusions of this work and provides some future directions.

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Chapter 2 Theoretical Framework

Antennas are the elements responsible for transmitting information in the form of elec-tromagnetic waves in wireless communications. Antennas are defined as “the part of a transmitting or receiving system, designed to radiate or receive electromagnetic waves”

[17]. The electromagnetic waves received by the antennas or array of antennas can be used as information or as available energy to be harvested; that depends on the type of system in which the antenna is being used. In Figure2.1a transmitting system is observed. First the origin of the electromagnetic energy known as source is found, the electromagnetic energy is transported through a transmission line to the antenna and finally the antenna is responsible for radiating the wave to free space. From the above it is understood that an “antenna is the transitional structure between free – space and a guiding device”[16].

In order to understand the antenna, Figure 2.2 shows the Thevenin equivalent of a transmission-line of a transmission system of electromagnetic waves. Three stages of the transmission system are shown. The sourceVg as the first stage has an impedanceZg,

which in RF systems is generally 50 ohm. In a receiver energy harvesting system, the source would have to be replaced by a rectifier circuit with matching input impedance.

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Figure 2.1: Antenna as a transition device [16]

the antenna. Generally, the transmission line has the same impedance as the source and is smaller than the antenna; therefore, impedance couplers are used to transmit all the line energy to the antenna.

The final stage is the antenna, whose impedanceZAcan be represented as two resistors

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physical structure of the antenna and the resistanceRrrepresent the energy radiated by the

antenna.

Figure 2.2: Transmission – line Thevenin equivalent of an antenna in transmitting mode [16]

In addition to the characteristic impedance of the antenna, there are other characteristics that can describe the behavior of an antenna, these characteristics are called figures of merit.

2.1 Figures of merit of an antenna

The figures of merit of an antenna describe the performance of an antenna. For example; with the figures of merit can be described how the electromagnetic energy of the antenna is radiated; that is, the direction in which it is radiated (radiation pattern and directivity), the amount of energy that is radiated (radiation intensity and gain), frequencies in which the antenna is able to radiate (bandwidth) and the behavior of the radiated electric field (polarization). The figures of merit described here are not all of them, but those here give a general idea of the behavior of the antenna. A complete study of antennas and their figures of merit is done in [16].

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2.1.1 Radiation Pattern

The radiation pattern, also called the antenna pattern is defined as“the spatial distribution of a quantity that characterizes the electromagnetic field generated by an antenna”[17]. A radiation pattern in 3D and 2D is shown in Figures2.3 a and b. The distribution can be a graphic representation or a mathematical function. The graphic representation can be cast in 2 dimensions, rectangular and polar graphics, or in 3 dimensions, usually polar graphics. The term amplitude pattern, field pattern, or voltage pattern is used when the amplitude of a specific component of the electric field is plotted graphically or expressed mathematically, and the term power pattern is used when the square of the amplitude of a specific component of the electric field is plotted graphically or expressed mathematically.

The lobes, “portion of the radiation pattern bounded by regions of relative weak radi-ation intensity” [16], help to describe the radiation pattern. There are 2 types of lobes; Main lobe or major lobe and minor lobe. The types of lobes are shown in Figure2.3 b. The main lobe is the lobe in which the maximum radiation is found and the minor lobe is any other lobe that is not the main lobe. Within the minor lobes 2 types of lobes can be identified, secondary lobes in which a large amount of radiation is found, but not as much as in the main lobe and posterior lobe which is approximately 180◦_{from the main lobe.}

Figure2.3(b) indicates the Half-Power Beamwidth (HPBW) which is defined as“in a radiation-pattern cut containing the direction of the maximum of a lobe, the angle between

the two directions in which the radiation intensity is one-half the maximum value”[17], it also shows the First-Null Beamwidth (FNBW) which is“the angular separation between the first nulls of the pattern” [16]. The measurements of the radiation pattern are made in

the far field, the electric field regions of an antenna are explained below.

There are 3 regions that describe the behavior of the electric field radiated by an antenna, reactive near field, radiant near field and far field (Figure2.4).

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surround-(a)

(b)

Figure 2.3: (a) Radiation lobes and beamwidths of an antenna pattern. (b) Linear plot of power pattern and its associated lobes and beamwidths [16]

ing the antenna wherein the reactive field predominates”[17].

Radiating near-field region: “That portion of the near-field region of an antenna be-tween the far field and the reactive portion of the near-field region, wherein the angular

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field distribution is dependent upon the distance from the antenna”[17].

Far-field region: “That region of the field of an antenna where the angular field distri-bution is essentially independent of the distance from a specified point in the antenna’s

region”[17].

Figure 2.4: Typical changes of antenna amplitude pattern shape from reactive near field toward the far field [18]

2.1.2 Radiation Intensity

To understand the radiation intensity it is necessary to understand that“the power pattern of the antenna, is just a measure, as a function of direction, of the average power

den-sity radiated by the antenna” [16], where the power density is just the time average of Poynting’s vector.

The radiation intensity is defined as,“in a given direction, the power radiated from the antenna per unit solid angle”[17]. Mathematically it is expressed as2.1

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U = r2Wrad (2.1)

Where

U=radiation intensity (W/unit solid angle)

Wrad=radiation density (W/m2)

From the radiation intensity we can obtain the radiated power, as shown by (2.2).

Prad = Ω

UdΩ = Z 2π

0 Z 2π

0

U sinθdθdφ (2.2)

wheredΩ =element of solid angle= sinθdθdφ

2.1.3 Directivity

Directivity is defined as, “in a given direction, that part of the radiation intensity cor-responding to a given polarization divided by the total radiation intensity averaged over

all directions”. To know the average radiation intensity, it is enough to divide the total

power radiated by 4π. The direction of maximum radiation intensity is assumed when the direction is not specified.

The directivity is expressed as follows:

D= U U0

= 4πU

Prad

(2.3)

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Dmax= D0 =

Umax U0

= 4πUmax

Prad

(2.4)

Where

D=Directivity (dimensionless)

D0=Maximum directivity (dimensionless)

U=Radiation intensity (W/unit solid angle)

Umax=Maximum radiation intensity (W/unit solid angle)

U0=Radiation intensity of isotropic source (W/unit solid angle)

Prad=Total radiated power (W)

The directivity patterns can be done in two or three dimensions, in Figure 2.5 (a) the 2-D radiation patterns of isotropic and omnidirectional antennas are presented and in Figure 2.5 (b) the 3-D radiation patterns of isotropic and omnidirectional antennas are also presented.

2.1.4 Gain

Although the directivity describes the directional behavior of the antenna, it does not consider the efficiency of the antenna. It does not consider the losses due to the physical structure of the antenna; to consider these factors there is another figure of merit of the antenna, called gain.

The gain is defined as “ The ratio of the radiation intensity in a given direction to the radiation intensity that would be produced if the power accepted by the antenna were

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(a)

(b)

Figure 2.5: Two- and three-dimensional directivity patters of a 2 dipole. [16]

divide the power accepted by the antenna by 4π.

Gain does not consider losses by impedance and polarization mismatches, therefore it does not depend on the system with which it is measured, also if the antenna has no dissipative losses, the gain would be equal to its directivity.

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2.1.5 Bandwidth

The bandwidth of an antenna is defined as “the range of frequencies within which the performance of the antenna conforms to a specified standard with respect to some

char-acteristic”[17].

In the bandwidth the gain, the directivity, the radiation efficiency and other parameters present an acceptable value with respect to the design values of the fundamental frequency.

The bandwidth can be expressed in two different ways, broadband (2.5) or narrow band (2.6).

BW = 2 (fmax− fmin) fmax+ fmin

x100% (2.5)

BW = fmax fmin

: 1 (2.6)

2.1.6 Polarization

The polarization of the antenna in a given direction is defined as“the polarization of the wave transmitted by the antenna” [17], i.e. “that property of an electromagnetic wave describing the time-varying direction and relative magnitude of the electric-field vector;

specifically, the figure traced as a function of time by the extremity of the vector at a

fixed location in space, and the sense in which it is traced, as observed along direction

of propagation”[16]. In Figure2.6 the rotation of a plane electromagnetic wave and its polarization ellipse is shown.

There are three types of polarization, linear polarization, circular polarization and ellip-tical polarization (Figure2.7). These 3 types of polarization are defined below:

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(a)

(b)

Figure 2.6: Rotation of a plane electromagnetic wave and its polarization ellipse at z=0 as a function of time [16]

“Lineal Polarization: “A time-harmonic wave is linearly polarized at a given point in space if the electric-field (or magnetic-field) vector at that point is always oriented along

the same straight line at every instant of time”[16]. The electric field vector generally has a single component, although it can have two components with a phase shift of 180◦ or

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multiples of 180◦_.

Circular polarization: “A time-harmonic wave is circularly polarized at a given point in space if the electric (or magnetic) field vector at that point traces a circle as a function

of time”[19].The electric field vector has two components of the same magnitude and a phase shift of 90◦.

Elliptical Polarization: A time-harmonic wave is elliptically polarized if the tip of the field vector (electric or magnetic) traces an elliptical locus in space”[19]. The electric field vector can have two components of the same magnitude with a different phase angle of 90◦_{(because it would be circular polarization) or two components of di}_ff_erent

magni-tude with a different phase shift of 0◦or 180◦(because it would be linear polarization).

The direction of rotation of the circular and elliptical polarization can be right handed or left handed, if the field vector rotates clockwise, it will be right-handed polarized, and if the field vector rotates counterclockwise, it will be left-handed polarized.

(a) (b) (c)

Figure 2.7: Polarization figure traces of an electric field extremity as a function of time for a fixed position. (a) Linear. (b) Circular. (c) Elliptical. [19]

2.2 Microstrip antennas

Microstrip antennas (Figure 2.8) consist of a “thin (t<< λ0, where λ0 is the free-space wavelength) metallic strip (patch) placed a small fraction of a wave length (h << λ0,

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usually0.003λ0≤ h≤0.05λ0) above the ground plane”[16].

Figure 2.8: Main dimensions of Microstrip path antenna. (W) Width and (L) length of the patch, (h) height of the dielectric and (t) the thickness of the patch.

There are different geometries of microstrip patches. The most common are rectangular, square and circular patches. The square patch is a special case of the rectangular patch. Figure 2.9 shows the basic geometry, which is a variation or combination of the three basic patches. These different geometries change the radiation pattern, gain, polarization and bandwidth.

2.2.1 Rectangular patch

To illustrate the design of an antenna, the principal equations involved in the design are shown below. For a detailed analysis please refer to [16]. There are two basic character-istics of the patch antenna; first the size of the antenna for the desired resonant frequency and second, the input impedance. Following the methodology of microstrip antennas

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de-(a) Square (b) Rectangular (c) Dipole

(d) Circular (e) Elliptical

(f) Triangular (g) Disc sector (h) Circular ring (i) Ring sector

Figure 2.9: Representative shapes of microstrip patch elements [16]

sign, the principal equations to determine W an L are2.7and2.8.

W = 1

2fr √

µ00 r

2 r+1

(2.7)

L= 1

2fr √

re f f √

µ00 −2∆L (2.8)

Where µ0 and0 are the permittivity and permeability of vacuum,r andre f f are the

relative permittivity and effective permittivity of the dielectric, fr is the resonant frequency and∆Lis a variation in the size of the antenna because of the fringing fields.

Since for a patch antenna the maximums electric field are at the edges, each one of the edges could be like a radiating slot, and each slot is represented by a parallel equivalent admittance Y (with conductance G and susceptance B), Figure2.10. Assuming symmetry (G1 = G2) conductance of a single slot can also be obtained using the field expression

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derived from the cavity model.

Figure 2.10: Microstrip antenna equivalent circuit.

The input impedance of the antenna is described by2.9.

Rin =

1

2 (G1±G12) (2.9)

2.2.2 Methods for designing antennas with circular polarization

There are different methods to obtain circular polarization in an antenna. The methods can be a double feed phased out to the patch, a single feed but at a particular position in the patch, or making modifications directly to the patch.

In Figure2.11methods with double-feed square patches are presented to obtain circular polarization. The first method (Figure2.11 a) is to feed the patch on two adjacent sides, the power comes from a non-symmetrical T junction, the two lines are different by a length ofλ/4 that gives the two feed lines a phase shift of 90◦. In the second method (Figure2.11

b) the patch is fed in two adjacent sides, the feeding of both lines comes from a 90◦hybrid splitter, which provides the two feed lines with a phase shift of 90◦.

Figure 2.12 shows the methods to obtain antennas with circular polarization. These methods consist of placing the feed line of the patch, almost square, at a point different

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(a) Square patch driven at adjacent sides through a power divider

(b) Square patch driven at adjacent sides through a 90 hybrid

Figure 2.11: Square patch arrangements for circular polarization [20]

from the conventional. The first method is to place the feed line in a corner of the patch (Figure2.12 a). The second method consists of placing the antennas feed line at a point between the center of the patch and a corner of the antenna; depending on the position in which the power is placed the antenna presents left-handed or right-handed circular polarization (Figure2.12b y c).

(a) Nearly square patch (b) Left-hand circular (LHC)

(c) Right-hand circular (RHC)

Figure 2.12: Single-feed arrangements for circular polarization of rectangular microstrip patches [16]

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Figure2.13shows methods to obtain circular polarization in square patches modifying the geometry of the patch. The first method is to make a rectangular slot in the center of the patch, depending on the orientation of the slot, this can present left-handed or right-handed circular polarization. The second method is to cut two opposite corners of the patch, and depending on where the patch feed is placed right-handed or left-handed polarization can be attained.

(a) Right-hand (b) Left-hand (c) Trimmed square

(L=W)

Figure 2.13: Circular polarization for a square patch with thin slots on patch (c = W/2.72 = L/2.72, d = c/10 = W/27.2 = L/27.2), and by trimming opposite corners of a square patch [16]

Another method is to make an elliptical patch and feed it at an angle of 45◦ _respecting

the semimajor axis (Figure2.14), it depends the position of the feed and the axial ratio of the ellipse can be obtained left-hand or right-hand circular polarization.

(a) Elliptical with tabs

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2.3 5G network

The new 5G network will be available in 2020. It will provide a large amount of available energy to be harvested. Certainly, 29 billion of devices will be connected to Internet of Things (IoT) in 2022 [15], each of these devices will send and receive electromagnetic waves. In the world, the 5G network can be found within 3 bands, Low-Band (<3.7 GHz), Mid-Band (3.7-24 GHz) and High-Band (>24 GHz). Some countries have already defined

5G networks in the three bands, most have focused on the High-Band at frequencies near the 28 GHz band (27.5-28.35 GHz). Table2.1shows in greater detail the frequencies for the 5G network proposed and established by different countries [21]. The proposed bands will be established in the following years.

Table 2.1: 5G frequencies close to 28GHz band

Country - Zone Defined 5G spectrum (GHz) Proposed 5G spectrum (GHz)

USA 27.5-28.35 25.5-27.5, 31.8-33.4

Canada - 26.5-27.5, 27.5-28.35

Mexico 24.65-27

-Brazil - 25.25-27.5

Colombia - 25.25-27.5

Uruguay - 25.25-27.5

European Union mm 24.25-27.5

-France - 25.25-27.5

Germany - 24.25-27.5

United Kingdom - 24.25-27.5

China 24.75-27.5

-Japan 24.25-29.5

-South Korea 27.5-28.35 26.5-27.5, 28.35-29.5

Australia - 24.25-27.5

The European Union was the first to establish the 5G network of 24.25-27.5 GHz, each of the countries of the European Union will choose the most appropriate frequency for the 5G network within this frequency range. France has proposed 25.25-27.5 GHz which is within the frequencies established by the European Union but does not cover it in its

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entirety. The United States of America (USA) has established 27.5-28.35 GHz as a 5G network and has proposed to expand it from 25.5-27.5 GHz and 31.8-33.4 GHz.

The bands for the 5G network mentioned will have a lot of energy to collect, because in addition to new applications, some of the main sources of electromagnetic energy that are currently at frequencies below 6 GHz will become operational in the 5G network. Within the wireless information transmitters, which can also be considered electromagnetic en-ergy sources, are the mobile network bases and the wireless network access points (for example Wi-Fi). The mobile network bases will have to be adequate to transmit infor-mation at higher frequencies (5G network) [22][23][24] and the wireless network access points will be replaced by Fixed Wireless Access [25], which are the same concept only instead of transmit the information through coaxial cables or fiber optic, the information will be transmitted wireless.

Figure2.15shows how the transmission of information will be. Starting with an infor-mation transmission center (Figure2.15 a) transmitting to small mobile network stations (Figure2.15b), it is even observed how the small stations transmit to the buildings which have Fixed wireless Access inside.

(a) (b)

Figure 2.15: Square patch arrangements for circular polarization [23],[24]

It is important to note that each of the devices to which these sources will send informa-tion, when sending the information back they become energy sources, resulting in sources such as cell phones, computers, electronic tablets, video game consoles, etc. in addition

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to teleoperation applications (Real-time remote control of machines).

2.4 Conclusions

An analysis of figures of merit of antennas has been carried out, which will help to describe their response. The different forms of patch antennas have been explained, the rectangular patch formulas have been briefly described, and the different ways of achieving circular polarization have also been analyzed. Finally a compilation of different countries that have defined and proposed frequency bands for the 5G network was carried out.

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Chapter 3 State of the Art

Designing antennas for the 28 GHz band and nearby bands has gathered importance in recent years due to the fact that the 5G network has already been defined in these bands in different regions of the world. Harvesting antennas have been reported as general applica-tions. The harvesting antennas try to cover all the bands defined and proposed by different countries. General application antennas have focused on the 28 GHz band, although some have properties that make them good candidates for harvesting electromagnetic energy. Microstrip antennas have been popularized due to their low cost, easy integration into cir-cuits and easy development of new designs. Some of the antenna designs seek to have circular polarization, even if they do not have a broadband [26] [27], and some other an-tenna designs seek to have broadband even if they do not have circular polarization [28] [29]. Which characteristics of the antenna is more important depends on the specific ap-plication

In [26] is reported a 2x2 antenna array with circular polarization at 24 GHz (Figure

3.1 a and b). The array of antennas has a bandwidth (Figure3.2a) of 1.96 GHz (23.54-25.23 GHz) and circular polarization (AR<3 dB) from 23.9 GHz to 25 GHz (Figure3.2

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gain of 10.3 dBi. The array of 2x2 antennas has a final size of 30 mm x 30 mm and with a standard low-cost printed circuit process it is made on a Rogers RT/duroid 5880 laminated substrate 0.508 mm thick with a dielectric constant of 2.2. The simulations to obtain the optimal parameters are made in Ansoft HFSS and it is measured with a horn antenna. To obtain circular polarization each element is made as a circular patch with two rectangular notches positioned at opposite ends of the patch. If the array is split in half on the x-axis, the array is seen as two sets of two antennas. Two elements of each set are positioned angularly at 90◦with respect to each other (taking as reference the rectangular notches), these two elements are joined by a non-symmetrical T junction that provides 90◦_{of phase}

shift in the antennas supply. Finally the two sets of antennas are joined by a symmetric T-junction.

(a) (b)

Figure 3.1: (a) CP patch array antenna configuration. (b) Photograph of the fabricated prototype [26]

Table 3.1: Dimensions of the antenna array

Parameter R1 S1 W1 D

Dimension mm 2.2 0.65 0.45 8

Parameter L L1 L2 L3

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(a) (b)

Figure 3.2: Simulation and measurement results of (a) impedance matching and (b) axial ratio of the CP array from 22 GHz to 28 GHz [26]

In [27] two arrays of 1x8 elements with circular polarization are designed for the 28 GHz band. The arrays have left handed circular polarization (LHCP) and right handed circular polarization (RHCP).S11 parameters show that the array of LHCP antennas has a bandwidth of 1.54 GHz (27.4-28.94 GHz) and the array of RHCP antennas has a band-width of 1.7 GHz (27.27-28.95 GHz), Figures3.3(a) and (b) respectively. The bandwidth of the circular polarization of the LHCP (Figure 3.4 a) and RHCP (Figure3.4 b) arrays are 1.1 GHz (27.7-28.8 GHz) and 1.3 GHz (27.5-28.8 GHz) respectively. The gain peak for the LHCP array is 13.09 dBi and the gain peak for the RHCP array is 13.52 dBi. The substrate used is Rogers 4359B laminated with a thickness of 0.508 mm, dielectric con-stant of 3.66 and tangent of losses of 0.004. The thickness of the copper foil is 0.5 mm. The antenna array is designed with CTS Microwave Studio software.

To obtain circular polarization each element of the array has 3 layers of substrate and one layer of copper. The design of each layer is shown in Figure3.6and Table 3.2. The order of the layers is substrate 1, substrate 2, copper and substrate 3 as shown in Figure

3.5. All the layers have a size of 10 mm x 10 mm. The substrate 1 and substrate 2 consist of rectangular openings surrounded by circular vias, the copper layer has a circular cavity in the center and the substrate 3 has a radiating patch on the upper part. By varying the size and position of the cavities, the size and position of the radiating patches and the position of the vias, LHCP or RHCP can be obtained. The dimensions of LHCP and

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(a) (b)

Figure 3.3: Simulated and measured S11 parameters of the proposed CP antenna arrays: (a) LHCP and (b) RHCP [27]

(a) (b)

Figure 3.4: Simulated and measured radiation performance of the proposed CP antenna arrays against the frequency band: (a) LHCP and (b) RHCP [27]

RHCP antennas are presented in Table3.1

Table 3.2: Dimensions of Two CP antenna elements (Units: mm) [27]

Parameters Ws1 Ls1 Ws2 Ls2

LHCP/RHCP 0.32/0.35 3.9/3.42 0.4/0.36 5/3.88

Parameters Wp Lp Dc a

LHCP/RHCP 2.52/1.44 1.9/2.44 5/3.88 29.1/17.5

Parameters vg yp vo,xp Gx,Gy

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(a) (b)

Figure 3.5: (a) Side view of the proposed CP antenna array and (b) photograph of the fabricated antenna arrays: LHCP (left) antenna array and RHCP (right) antenna array [27]

(a) (b) (c) (d)

Figure 3.6: Geometries of LHCP (top) and RHCP (down) antenna elements with different configurations: (a) substrate # 1; (b) substrate # 2; (c) copper plate; and (d) substrate # 3 [27]

In [28] a broadband antenna is designed (Figure3.7a and b) for collecting electromag-netic energy in the 5G network. The return loss (Figure 3.8 a) shows that the antenna has two resonances with bandwidths of 3.8 GHz (15.9-19.7 GHz) and 11.5 GHz (22.5-34 GHz). Figure3.8(b) presents the peaks of gain vs frequency of the antenna, a gain peak of 8.8 dBi is presented at 34 GHz and it can be seen that a gain of 7 dBi is maintained from 27 to 31 GHz. The antenna is printed with silver ink nano particles using the inkjet

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printing technique on a flexible PET substrate with a thickness of 135 µm, a dielectric constant of 3.2 and a loss tangent of 0.022. The simulations to design the antenna are made with CST Microwave Studio Suite. In order to get broadband, the antenna is shaped like an equilateral triangle of 3.637 mm on each side with a CPW feed. The CPW feed is extended creating a rectangular opening of 10 mm x 6 mm around the triangular patch. To the ground created by the opening two symmetrical square rings of 2.2 mm x 2.2 mm are added on each side of the power line. The dimensions of the antenna are shown in Table

3.3.

(a) (b)

Figure 3.7: Proposed MMW energy harvesting antenna: a) simulated prototype with de-sign parameters; b) fabricated prototype [28]

Table 3.3: Design Parameters of proposed MMW antenna [28]

Antenna Parameters Units (mm) Antenna Parameters Units (mm) Aperture length,Ls 10 Feed length,Lf 5.6

Aperture width,Ws 6 Feed width,Wf 1

Triangle side,P=a 3.637 DGS slot width,w 0.15 DGS gap from the edge,d 2.5 Split-rig length,LS R 2.2

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(a) (b)

Figure 3.8: (a) Return loss plot and (b) peak gain vs frequency plot of the proposed MMW energy harvesting [28]

In [29] a broadband antenna with bandwidth (3.10) of 44.56 GHz (22.44 GHz - 67 GHz) is designed, the antenna has gains at 28, 38 and 60 GHz of 4.4 dBi, 6.2 dBi and 3.4 dBi. The structure was manufactured with a laminated substrate Rogers RT/duroid 5880 with a thickness of 0.127 mm and a dielectric constant of 2.2. The simulations were done in the ANSYS HFSS software. To obtain broadband the antenna is designed as a rectangular patch with an elliptical opening; within the elliptical opening there is a circular non-concentric patch. This non-concentric circular patch has a cavity in the shape of a cross. The feeding of the antenna consists of a microstrip line with a small stub. The antenna is shown in Figures3.9(a)-(d) y and the dimensions are presented in Table3.4.

(a) (b) (c) (d)

Figure 3.9: Proposed printed slot antenna. (a) Top view, (b) side view and (c) a close-up view of the cross slot in the parasitic patch. (d) Photograph of the fabricated prototype [29]

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Table 3.4: Dimensions of the printed slot antenna elements (Units: mm)

Parameters L W Wf Lf

Dimension 11.1 5 0.39 7.7 Parameters Ls Ws Rpx Rpy

Dimension 0.7 0.63 0.95 0.88 Parameters Rsx Rsy xs ys

Dimension 2.1 1.92 xp 8.6

Parameters yp Lc Wc ds

Dimension 7.9 0.7 0.21 6.87

Figure 3.10: Measured and full-wave simulated reflection coefficients of the proposed printed slot antenna [29]

Some other designs that do not have circular polarization but that have broadband and some special feature have also been designed. In [30] a dual band antenna is designed, the first bandwidth of 5.94 GHz (26.36-32.3) with gain of 13.2 dBi at 28 GHz, and the second bandwidth of 1GHz (37.4-38.4) with a gain of 14.6 dBi at 38 GHz. The remarkable feature of this antenna is that it can be excited with higher order modes. In [31] 2 arrangements of 1x8 antennas have been designed. The first arrangement, whose feature is that it is invisible, has a bandwidth of 5.55 GHz (24.23-29.78 GHz) with a gain of 6.66 dBi at 28 GHz. The second arrangement, whose feature is that it is transparent, has a width of 4.42 GHz band (25.48-29.9 GHz) and a gain of 9.16 dBi

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3.1 Summary and conclusions

In Table3.5a compilation of antennas designed and manufactured for the 5G network is presented.

The designs [28] and [29], with a bandwidth of 11.5 GHz (22.5-34 GHz) and 46 GHz (22.4-67 GHz) respectively, are the antennas that cover all of the bands proposed for the 5G network shown in Table2.1(24.25-33.4 GHz is 100%), some broadband designs [31] with 4.42 GHz and 5.55 GHz, [32] with 6 GHz and [30] with 5.94 GHz meet 48% and 66.65%, 65.57%, and 64.91% of the 5G bands. The work presented in the following chapters has a bandwidth of 6.61 GHz (25.07-31.68 GHz), and covers 72 % of the defined and proposed bands.

Designs with circular polarization are [26] with CP bandwidth of 1.1 GHz, [27] CP bandwidth of 1.1 and 1.3 GHz, and this work with 0.73 GHz.

Table 3.5: Antennas in the 5G band

Antenna Frequency Bandwidth Band Gain Polarization Number of Size (GHz) (GHz) (GHz) dBi <3 dB elements mm [26] 24 1.96 (23.54-25.23) 10.3 (24.8 GHz) 0.5 dB (24.3 GHz), 4 30x30

- 23.9-25GHz

[27] 28 LHCP 1.54 (27.4-28.94) 13.09 27.7-28.8 GHz 70x63.5x2.2 [27] 28 RHCP 1.7 (27.25-28.95) 13.52 27.5-28.8 GHz 70x63.5x2.2 [29] 28/38/60 44.6 (22.4-67) 4.4 (28 GHz) - 1 5x11.1

6.2 (38 GHz)

[28] - 3.8 (15.9-19.7) 8.8 dB (34 GHz) - 1 6.75x6.96 11.5 (22.5-34) 7 dB (27-31 GHz)

[32] 28 6 (27-33) 6-7 (27-33 GHz) - 8 11x20 [30] 28/38 5.94 (26.36-32.3) 13.2 (28 GHz) - 1 7.32x7.32

1 (37.4-38.4) 14.6 (38GHz)

[31] 28 I 5.55 (24.23-29.78) 6.66 (28 GHz) - 8 21x52 [31] 28 T 4.42 (25.48-29.9) 9.16 (28 GHz) - 8 21x52 [33] 2.4/5.5/28 0.19 (2.16-2.35) 1.95 (2.4 GHz) - 1 35x45

1.22 (4.58-5.8) 3.76 (5.5 GHz) 3.2 (26.8-30) 7.35 (28 GHz)

[34] 28 2.5 (28.2-30.7) - - 2 12x24 [35] 28 2.3 (27.3-29.6) 13.97 - 8 70x63.5 [36] 24 0.82 (24.78- 25.6) - - 1 15x27 this work 28 6.61 (25.07-31.68) 10.4 (28 GHz) 27.75-28.49 4

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Chapter 4 Design 2x2 of a Antenna Array with

Circular Polarization

An array of 2x2 microstrip patch antennas was designed for electromagnetic energy col-lection in a double band of 7.43 GHz bandwidth (24.02-31.45 GHz) and 0.44 GHz band-width (34.78-35.22 GHz). To achieve circular polarization in the array, each element was designed as a square patch with two cut corners [16]. The design requires four stages in order to obtain the desired resonance frequency and polarization. In the first stage a square patch with resonance frequency in the 28 GHz band is obtained, in the second, third and fourth stages circular polarization is obtained by cutting 2 opposite corners of the patch. The material used is Rogers RT/duroid 5880 with a dielectric height of 0.787 mm, a cop-per thickness of 18 micrometers (1/2 ounce), roughness of 0.3 micrometers rms on the top side and 0.4 micrometers rms on the dielectric side, a dielectric constant of 2.2 and a loss tangent of 0.0009. For simulation the dielectric constant and loss tangent values provided by the manufacturer are used. With respect to the roughness; the model presented in [37], which is a variation of the [38], is used to obtain the roughness correction factor, and using [39] the roughness correction factor is used to calculate the conductivity of copper as a function of frequency. The minimum requirements of the antenna are: bandwidth in the

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band of 28 GHz (27.5 - 28.35 GHz) and circular polarization at 28 GHz (AR<3dB).

4.1 Stages of single antenna design

4.1.1 First stage

In order to have a starting point in the design, equation2.8is used to find the dimensions of a square patch, this is due to the fact that in [16] it is described that the resonance frequency of a patch antenna is mainly the result of this Equation. The square patch dimension is W1=3.0 mm, by means of the equations of2.9the characteristic impedance of the square patch antenna is found and using a λ/4 coupler the antennas is coupled to a 50 ohm line. The calculated dimensions (Table 4.1) are simulated and the result obtained is shown in Figure 4.1 (b). The antenna presents a bandwidth of 2.2 GHz (26.86-29.06 GHz) and, as expected, the patch resonates closer to the 28 GHz band. The maximum gain of this design stage is 7.21 dBi and the radiation pattern is shown in Figure 4.2. The radiation pattern shows a second lobe.

(a) (b)

Figure 4.1: (a) Antenna and (b)S11parameters of the first design stage (W1=3.0)

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have linear polarization; therefore it is necessary to modify the geometry of the antenna to achieve circular polarization.

Figure 4.2: Radiation pattern of stage 1

Table 4.1: Dimensions of antenna design stages

Stage 1st 2nd 3th 4th

W1 (mm) 3.0 3.0 3.2 3.2

W2 (mm) - 2 2.2 2.2

W3 (mm) 0.27 0.27 0.8

-W4 (mm) 2.4 2.4 2.4 0.3

Z antenna (Ω) 410 410* 177.47* 139.7* Z coupler (Ω) 143.3 120.7 94.2

-Z Feed (Ω) 50 50 50 139.7

Hereafter in each stage W1 reference the size of the square patches, W2 reference to the size of the cuts in the patches, W3 reference the width of the couplers and W4 reference the width of the feeding lines.

4.1.2 Second stage

Two corners of the patch are cut (opposite each other) achieving polarization with an axial ratio of 7.35 dB and an increase in bandwidth of 2.20 GHz (20.95 - 22.02 GHz) to 4.91 GHz (29.31-34.23 GHz, Figure 4.3 b). Wide band square microstrip antennas with cut

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corners have been reported in [40] with a bandwidth of 9.15 GHz (2.95-12.1 GHz) and in [41] with two bands of 23.03-23.83 GHz and 27.41- 27.8 GHz. This design does not yet have circular polarization, therefore it is necessary to modify the dimensions of the patch and the cuts in the corners in order to obtain the polarization and preserve the resonance at the desired frequency. The maximum gain of this design stage is 8.14 dBi and the radiation pattern is shown in Figure4.4

(a) (b)

Figure 4.3: (a) Antenna and (b)S11parameters of the second design stage

4.1.3 Third stage

The size of the antenna patch is modified (Figure 4.5a) in order to obtain the best com-promise of resonance frequency and polarization.

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(a) (b)

Figure 4.5: (a) Antenna and (b)S11parameters of the third design stage

The size of the patch is increased (3.2 mm), the size of the cut in the antenna (1 mm) is preserved and the coupler widened (0.8 mm). With these modifications, bandwidth (Figure4.5b) of 5.9 GHz (25.52-31.43 GHz) and an axial ratio of 1.65 dB is achieved.

The axial ratio vs frequency is shown in Figure4.6, the antenna has circular polarization with a bandwidth of 1.56 GHz (26.83 - 28.39 GHz). This bandwidth easily covers the 28 GHz band.The maximum gain of this design stage is 7.45 dBi and the radiation pattern is shown in Figure4.7

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Figure 4.7: Radiation pattern of Stage 3

4.1.4 fourth stage

The antenna is directly coupled to a line of 139.7 ohm in order to have lines with widths more suited to the size of the antenna array (Figure 4.8). The impedance of the antenna changes from 177.47 ohm to 139.7 ohm, which indicates that the input impedance of the antenna also depends on the distance from the edge of the feed line to the trimmed edge of the antenna. As a result of the modification of the feed line, a bandwidth of 5.6 GHz (25.47-31.11 GHz) and a polarization of 2.1 dB is obtained.

(a) (b)

Figure 4.8: (a) Antenna and (b)S11parameters of the fourth design stage

The axial ratio vs frequency is shown in Figure4.9; the antenna has circular polarization with a bandwidth of 1.63 GHz (26.73 - 28.36 GHz). This bandwidth easily covers the 28 GHz band. The maximum gain of this design stage is 7.19 dBi and the radiation pattern

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is shown in Figure4.10. For this antenna design the second lobe and the main lobe are joined and even if it seems not to be a omnidirectional pattern, this design has resonance frequency and circular polarization in the 28 GHz band.

Figure 4.9: Axial ratio (dB) vs frequency of the fourth design stage

4.1.5 Right-hand and left-hand polarization

Figure4.11shows the simulation of the distribution of the electric field in the antenna at a frequency of 28 GHz. As expected, most of the electric field is at the edges of the antenna. Figure 4.11 (a) shows the behavior of a normal rectangular patch antenna, which could be represented by the transmission line model as two radiating apertures. But due to the cuts at the corners, the electric field shows a different behavior. Figures 4.11 (a)-(d) are sequential; the electric field is displaced from the feed edge towards the right uncut corner

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of the antenna (Figure4.11 b), the field continues on the right edge (Figures4.11 c y d), until reaching the opposite edge of the feed (Figure 4.11e). In the same way, the electric field that in Figure4.11(a) appeared on the edge opposite the feed, in Figure4.11(d) it is observed to have moved towards the edge of feed point. The electric field is rotating at the edges of the antenna, which indicates that the antenna has circular polarization. Since the electric field would be radiated perpendicular and outwardly of the sheet in Figure4.11, the electric field is rotating clockwise, therefore antenna is right hand polarized.

(a) (b) (c)

(d) (e)

Figure 4.11: Displacement of the electric field in an antenna

4.2 Antenna Array Design

Once obtaining an antenna having circular polarization, an array of 2x2 antennas is de-signed. The array has a bandwidth of 7.43 GHz (24.02-31.45 GHz, Figure4.13), circular polarization (Figure4.16) and a directional radiation pattern (Figure4.15). The array and

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its dimensions are shown in Figure4.12(a) and Table4.2. Since every bend and T-union increases energy losses, the array must have the least number of T-joints and must not have bends. This array is composed of four antennas, three T-junctions and fourλ/4 couplers.

(a) (b)

Figure 4.12: (a) 2x2 antenna Array dimensions and (b) 2x2 antenna Array with connector and coordinate system

Table 4.2: Dimensions of the antenna array

L (mm) W (mm)

L1 3.2 W1 0.3

L2 2.2 W2 0.75

L3 6 W3 1.02

L4 2.486 W4 2.4 L5 2.007 L6 2.993

The antenna has two resonance bands (Figure 4.13), one of 7.43 GHz (24.02-31.45 GHz) and a second small one of 0.44 GHz (34.78-35.22 GHz). Between these two res-onances there is a resonance (31.45 GHz-34.78) that does not exceed -10 dB but has resonance with values less than -8.45 dB.

Figure4.14shows the gain radiation patterns of the array at different frequencies. Fig-ure 4.14 (b) shows the radiation pattern at 28 GHz (with maximum gain of 10.4 dBi), frequency at which the antenna has a circular polarization. In Figures4.14(a) and (c) the

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Figure 4.13:S11parameters of the 2x2 antenna Array

radiation pattern is presented at 25 GHz (with maximum gain of 11.6 dBi) and 31.6 GHz (with maximum gain of 12.3 dBi), frequencies that are the beginning and end of the first resonance band. Figure4.14(d) shows the radiation pattern at 35.2 GHz (with maximum gain of 10.0 dBi), frequency that is within the second resonance band.

(a) (b)

(c) (d)

Figure 4.14: 3-D Gain pattern of the array at (a) 25 GHz, (b) 28 GHz, (c) 31.6 GHz and (d) 35.2 GHz)

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Although the best energy harvesting antenna must have an omnidirectional radiation pattern, it is explained by [42] that due to the small amounts of electromagnetic energy that can be collected and its relation to the collection efficiency, a directional antenna with high gain to an omnidirectional antenna with little gain might be preferred.The radiation patterns are different since the radiation pattern changes with the separation between an-tennas or in this case with the change in wavelength. The wavelength for 25 GHz, 28 GHz, 31.6 GHz and 35.2 GHz are 12 mm, 10 mm, 9.4 mm and 8.5 mm respectively.

The 2-dimensional gain patterns of the 28 GHz antenna array is shown in Figure4.15. Figure4.15(a) shows the total gain in the electric (with maximum gain of 10.4 dBi at 20◦) and magnetic plane (with maximum gain of 7.1 dBi at 0◦_{). The gain of Co-Polarization}

(with maximum gain of 8.6 dBi at 25◦) and Cross-Polarization (with maximum gain of 9.5 dBi at 67.5◦_{) for the electric plane is shown in Figure} _4.15 _{(b). Figure}_4.15 _{c shows}

the gain of Co-Polarization (with maximum gain of 4.1 dBi at 0◦) and Cross-Polarization (with maximum gain of 4.1 dBi at 0◦_{) for the magnetic plane.}

(a) (b) (c)

Figure 4.15: Gain pattern of (a) electrical and magnetic plane, (b) Co-Polarization and Cross-Polarization in the electrical plane and (c) Co-Polarization and Cross-Polarization in the magnetic plane at 28 GHz

The axial ratio vs frequency is presented in Figure 4.16, the bandwidth of the circular polarization is 0.73 GHz (27.75-28.49 GHz). An elliptical polarization of less than 6 dB

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Figure 4.16: Axial ratio vs frequency of the array

is observed with a bandwidth of 1.43 GHz (27.47 GHz - 28.90 GHz). At 28 GHz, an axial ratio of 0.91 dB is presented.

4.3 Conclusions

An array of antennas with circular polarization was designed for the 28 GHz band. As a result of cutting 2 corners of each patch, circular polarization and a wide band were obtained. The array is broadband with bandwidths of 7.43 GHz (24.02-31.45 GHz) and 0.44 GHz (34.78-35.22 GHz). The bandwidth of the circular polarization is 0.73 GHz (27.75-28.49 GHz). The S11 parameter meets the defined and proposed frequencies of the 5 G network in different countries, from the 24.25 GHz established by the European Union to 33.4 GHz proposed by USA, and of course it covers the 28 GHz band.

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Chapter 5 Manufacturing, Measurement and

Results

During the manufacture and measurement of an antenna, multiple errors can occur. In RF measurements, one of the most important things is to be sure that the measuring equipment (VNA) is calibrated and that the device under test (DUT) is correctly attached to the connector. With a correct VNA calibration, the effects introduced by the measurement setup are eliminated. With the correct connection between the DUT and the connector, measurement errors are avoided. In addition, all manufacturing presents errors; therefore it is important to know how much the physical dimensions of the manufactured device differ with respect to the design dimensions.

5.1 Manufacturing

In manufacturing, making a proper launch, interface between the connector and the an-tenna array, is important. Due to the working frequency, connectors 149202A-6 Southwest Microwave 2.40 mm are used, with a working frequency of up to 50 GHz. The dimensions

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of the connectors are shown in Figure5.1.

Figure 5.1: 1492-02A-6 connector dimensions. All dimensions are in inches. All angles are in degrees. Dimensions shown in brackets are in millimeters [43]

The feed line thickness (2.4mm) of the array is greater than the connector’s dielectric thickness (1.612mm), therefore it is necessary to adjust the thickness of the feed line to the connector’s dielectric [44] . The launch suggested by Southwest Microwave Company for connector 1492-02A-6 and substrate RT/duraid 5880, with copper weight of 1/2 oz, dielectric thickness of 0.031 (0.787 mm) and dielectric constant of 2.2 is shown in Figure

5.2. This type of launch is called Top Ground Microstrip. The launch is designed by SouthWest Microwave using the Time Domain Reflectometry (TDR) Test Data method (for a detailed analysis see [45] ).

An example of optimization using the TDR method is shown in [45]. Figure5.3shows the first launch setting in red, which is simply connecting the power line to the connector; the wave shows the behavior of short rather than a shunt capacitor discontinuity. A second

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Figure 5.2: RT/duroid launch dimension. All dimensions are in inches. All angles are in degrees [44]

adjustment of the power line is shown in green; the wave shows the behavior of open rather than a series inductor discontinuity. Finally, in blue, the last version is presented; even though it looks like short, it present less amplitude compared to red and green waves.

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Figure 5.3: Taper (version 1), Optimized Taper (version 2) and No Taper TDR. This optimization is from another substrate, it is only shown by way of example [45]

Finally, a standard manufacturing process is used to manufacture the antenna array (Figure5.4).

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(a) (b) (c)

(d)

Figure 5.4: (a) Array drawn on copper foil, (b) manufactured array, (c) manufactured array compared to 50 cents Mexican coin and (d) manufactured array with its connector

5.2 Measurement

Making a precise manufacture and knowing the manufacturing error is very important. This is because the dimensions of the array are very small, and an analysis of the dimen-sions is performed with the mechanical profilometry method. The method is a 2D analysis of the lines and patches. By means of a linear sweep a needle is displaced horizontally and when it encounters structures in the sweep the needle is displaced vertically, the val-ues of vertical and horizontal displacement are stored. The profilometer used is the Bruker DektakXT model (Figure5.5).

The normal distribution of the absolute error shown in Figure 5.6 has an average of 0.065 mm and a standard deviation of 0.037 mm. The normal distribution shows that 68.2 of the measurement errors are between 0.028 Micrometers and 0.102 Micrometers and 95.4 of the errors are in the range of -0.009 mm to 0.139 mm.

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Figure 5.5: Profilometer DektakXT, Bruker of the INAOE

Figure 5.6: Normal distribution of absolute error

The dispersion parameter measurements were made with an Anrisut M544Z-A VNA and calibrated with a 3658SV-Autocal automatic calibrator that uses the SOLT calibration method (Figure5.7).

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Figure 5.7: Vector Network Analyzer Anritsu with calibration kit

5.3 Results

TheS11parameters of the array are measured with the VNA, and the results are presented in Figure5.8. The measurements show that the arrangement is multiband since it has two resonance frequencies, the first resonance is a broadband and the second is a narrow band

In order to observe the resonance bands, enlarged images of the first and second bands are shown in Figure5.9and Figure5.10

In Figure5.9it can be seen that the beginning of the first resonance band in simulation is at 24.02 GHz while in measurement it is at 25.07 GHz, this difference represents an error of 4.3%. With respect to the end of the first resonance band in simulation it is at 31.45 GHz, while in measurement it is at 31.68 GHz, this difference represents an error of

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(a)

Figure 5.8: ParametersS11simulated and measured from antenna array

0.7%. Simulation has a bandwidth of 7.43 GHz (24.02-31.45 GHz) and the measurement has a bandwidth of 6.61 GHz (25.07-31.68 GHz), this bandwidth difference represents a reduction of 0.82 GHz.

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Figure 5.9: Simulation and measurement of the first resonance band of the array

In Figure 5.10 it can be seen that the start of the first resonance band in simulation is at 34.78 GHz while in measurement it is at 34.83 GHz, this difference represents a 0.1% error. With respect to the end of the second resonance band, in simulation it is at 35.22 GHz while in measurement it is at 35.75 GHz, this difference represents a 1.5% error. Simulation has a bandwidth of 0.44 GHz (34.78-35.22 GHz) and the measurement has a bandwidth of 0.92 GHz (34.83-35.75 GHz), this bandwidth difference represents a

An energy harvesting antenna array for the 28 ghz band