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Electromagnetic characterization of miniature antennas for portable devices

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Title:
Electromagnetic characterization of miniature antennas for portable devices
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English
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Aristizabal, Diana P
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Subjects / Keywords:
Self-complementary
Archimedean
Equiangular
Balun
FSS
Helical
Dissertations, Academic -- Electrical Engineering -- Masters -- USF   ( lcsh )
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bibliography   ( marcgt )
theses   ( marcgt )
non-fiction   ( marcgt )

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Abstract:
ABSTRACT: Advances in technology have placed a great emphasis on the design of broadband antennas as well as antenna miniaturization to cope with the demands of making electronic and handheld communication devices smaller and more efficient. In this thesis, the design and fabrication of a frequency independent antenna and a narrow-band planar microstrip Balun are presented. An analysis of frequency selective surfaces is also introduced in order to demonstrate their capability to miniaturize antenna thickness. Lastly, s-parameters measurements and efficiency characterization are performed to determine the radiation properties of surface mount chip inductors in order to determine the feasibility of using them as electrically small antennas.Two types of frequency independent antennas are considered due to their planar geometries, the Equiangular and Archimedean spiral antennas.^ Frequency independent antennas are radiating devices that have frequency independent impedance and pattern properties because their shape is specified only in terms of angles.The Balun is designed to meet the need of a feeding element for the Archimedean spiral antenna. A Balun is a three port device that connects an unbalanced transmission line such as a coaxial line to a balanced feed line such as the one required by two-arm spiral antennas. The Balun discussed in this work is designed to operate at 2.4 GHz with a 200 MHz bandwidth and to transform the antenna input impedance to a 50-ohm reference impedance. The main characteristics from this device that distinguish it from commercially available structures are its low cost, planarity, and compact footprint. The balancing capability of this Balun is shown by the close agreement between the measured and simulated results.^ Antennas can be potentially miniaturized in the z-direction by replacing the PEC ground plane separated from the antenna by a lambda /4 thick substrate with a frequency selective surface (FSS) structure that allows the ground plane conductor to be in close proximity to the antenna without affecting its radiation performance. The FSS layer operating at 2.4 GHz presented in this thesis is static (not tuned) and thus the overall bandwidth reduces approximately to the bandwidth obtained with the narrow-band Balun.
Thesis:
Thesis (M.S.E.S.)--University of South Florida, 2006.
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Includes bibliographical references.
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by Diana P. Aristizabal.
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Electromagnetic Characterization of Mi niature Antennas for Portable Devices by Diana P. Aristizabal A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in Electrical Engineering Department of Electrical Engineering College of Engineering University of South Florida Major Professor: Thomas M. Weller, Ph.D. Kenneth A. Buckle, Ph.D. Arthur David Snider, Ph.D. Date of Approval: October 30, 2006 Keywords: Self-Complementary, Archimedean, Equiangular, Balun, FSS, Helical Copyright 2006, Diana P. Aristizabal

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Dedication To my beloved husband Fernando Aristizab al, my daughter Sofia Aristizabal, and my parents Alberto Mora Perez and Beatriz Castro de Mora.

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Acknowledgements I would like to express my gratitude to Dr. Thomas M. Weller for his excellent support, guidance, and for granting me with the opportunity to work in such an interesting project. In addition, I want to recognize XetronNorthrop Grumman for sponsoring my research. Next, I want to thank my committee me mbers Dr. Kenneth A. Buckle and Dr. Arthur David Snider for their excellent suggest ions to improve my work. Also, I want to recognize Modelithics Inc. for providing me w ith the necessary parts for some of my measurement characterization projects, as well as for letting me use their facilities to make measurements. Finally, I want to thank my colleagues in the Antennas and Propagation Lab (412) for their great support and friendship, especi ally, Bojana Zivanovic, Suzette Presas, Saravana P. Natarajan, Alberto Rodriguez, Sam Baylis, Sergio Melais, and Srinath Balachandran.

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i Table of Contents List of Tables iii List of Figures iv Abstract x Chapter 1 Introduction 1 1.1 Overview 1 1.2 Contributions 3 Chapter 2 Frequency Independent Antennas 4 2.1 Introduction 4 2.2 Equiangular Spiral Antenna 6 2.2.1 Background Theory 7 2.2.2 Design 9 2.3 Archimedean Spiral Antenna 10 2.3.1 Background Theory 11 2.3.2 Design 13 2.4 Electromagnetic Design and Simula tions of Equiangular Spiral Antenna 14 2.4.1 S-parameter Simulations 17 2.4.2 Radiation Pattern Simulations 20 2.4.3 Antenna Parameters Simulations 25 2.5 Electromagnetic Design and Simulations of Archimedean Spiral Antenna 28 2.5.1 S-parameter Simulations 29 2.5.2 Radiation Pattern Simulations 32 2.5.3 Antenna Parameters Simulations 34 2.6 Summary and Conclusions 36 Chapter 3 Archimedean Spiral Antenna with a Narrow-Band Feed Network 38 3.1 Introduction 38 3.2 Archimedean Spiral Antenna Design 39 3.2.1 Electromagnetic Simulations of the Spiral Antenna on a Thinner Substrate 40 3.2.1.1 S-parameter Simulations 41 3.2.1.2 Radiation Pattern Simulations 43 3.2.1.3 Antenna Parameter Simulations 44

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ii 3.2.2 Electromagnetic Simulations of the Effect of Adding a Narrow-Band Feed Structure to the Spiral Antenna 46 3.2.2.1 S-parameters Simulations 49 3.2.2.2 Radiation Pattern Simulations 51 3.2.2.3 Antenna Parameters Simulations 53 3.2.3 Microwave Simulations of the Effect of Adding a Narrow-Band Feed Structure to the Spiral Antenna 55 3.3 Balun Design 60 3.3.1 Background Theory 61 3.3.2 Microwave Design and Simulations 62 3.3.2.1 Balanced Input to Unba lanced Output Transition Simulations 65 3.3.2.2 Impedance Transformation Simulations 67 3.3.3 Ground Effects Microwave and Electromagnetic Simulations 69 3.4 Fabrication 72 3.5 Measurements 73 3.5.1 S-parameters Measurements 74 3.5.2 Radiation Pattern Measurements 75 3.5.3 Balun Measurements 78 3.6 RF Coaxial Connector Electromagnetic Simulations 79 3.7 Summary and Conclusions 81 Chapter 4 Frequency Selective Surfaces 83 4.1 Introduction 83 4.2 Theory of Operation 84 4.3 Summary and Conclusions 88 Chapter 5 Miniature Coil Antennas 89 5.1 Introduction 89 5.2 Background Theory 89 5.3 Measurement Characterization 92 5.3.1 S-parameter Measurements 95 5.3.2 Efficiency Measurements 96 5.4 Summary and Conclusions 104 Chapter 6 Conclusions and Recommendations 105 6.1 Conclusions 105 6.2 Recommendations for Future Work 107 References 109

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iii List of Tables Table 2.1 Radius Equations Calcula tions for the Two-Arm Equiangular Spiral Antenna 10 Table 2.2 Calculated Design Paramete rs for the Archimedean Spiral Antenna 14 Table 2.3 Radius Equations Calcula tions for the Two-Arm Archimedean Spiral 14 Table 5.1 Calculation of Inductor Parameters 94 Table 5.2 Calculation of Wire Length for Optimal Radiation Performance 95

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iv List of Figures Figure 2.1 Antenna Defined as a Transi tion Region Between a Wave Guided by a Transmission Line and a Free-Space Wave 5 Figure 2.2 Equiangular Spiral Curve 7 Figure 2.3 Frequency-Independent Planar Self-Complementa ry Equiangular Spiral Antenna 9 Figure 2.4 Frequency-Independent Planar Self-Complementary Archimedean Spiral Antenna 13 Figure 2.5 Radiation Boundary Assignm ent for the Equiangular Spiral Antenna 16 Figure 2.6 Lumped Port Assignment fo r the Equiangular Spiral Antenna 16 Figure 2.7 S-parameter Simulations fo r the Equiangular Spiral Antenna 18 Figure 2.8 Input Impedance Simulations for the Equiangular Spiral Antenna 19 Figure 2.9 Simulated VSWR for th e Equiangular Spiral Antenna 20 Figure 2.10 Coordinate System for Antenna Analysis 21 Figure 2.11 Simulated Radiation Pattern Versus Theta at 2.4GHz for the Equiangular Spiral Antenna 24 Figure 2.12 Side, Front, and Top Views of Simulated Radiation Pattern in 3D at 2.4GHz for the Equiangular Spiral Antenna Backed by a /4 Thick Substrate 25 Figure 2.13 Side, Front, and Top Views of Simulated Radiation Pattern in 3D at 2.4GHz for the Equiangular Spiral Antenna Backed by a /4 Thick Substrate and a Ground Plane 25 Figure 2.14 Simulated Total Gain (dB) Ve rsus Frequency for the Equiangular Spiral Antenna 28

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v Figure 2.15 Simulated Axial Ratio (dB) Ve rsus Frequency for the Equiangular Spiral Antenna 28 Figure 2.16 Radiation Boundary Assignm ent for the Archimedean Spiral Antenna 29 Figure 2.17 Lumped Port Assignment fo r the Archimedean Spiral Antenna 29 Figure 2.18 S-parameter Simulations for the Archimedean Spiral Antenna with and without a Ground Plane 30 Figure 2.19 Input Impedance Simulations for the Archimedean Spiral Antenna with and without a Ground Plane 31 Figure 2.20 Simulated VSWR for the Arch imedean Spiral Antenna with and without a Ground Plane 31 Figure 2.21 Simulated Radiation Pattern Versus Theta at 2.4GHz for the Archimedean Spiral Antenna with and without a Ground Plane 33 Figure 2.22 Side, Front, and Top Views of Simulated Radiation Pattern in 3D at 2.4GHz for the Archimedean Spiral Antenna Backed by a /4 Thick Substrate 33 Figure 2.23 Side, Front, and Top Views of Simulated Radiation Pattern in 3D at 2.4GHz for the Archimedean Spiral Antenna Backed by a /4 Thick Substrate and a Ground Plane 34 Figure 2.24 Simulated Total Gain (dB) Ve rsus Frequency for the Archimedean Spiral Antenna with and without a Ground Plane 35 Figure 2.25 Simulated Axial Ratio (dB) Ve rsus Frequency for the Archimedean Spiral Antenna with and without a Ground Plane 36 Figure 3.1 Spiral Antenna Integrated with a Narrow-band Feed Network 39 Figure 3.2 Radiation Boundary Assignm ent for the Archimedean Spiral Antenna on a 31-mil Thick Substrate 41 Figure 3.3 S-parameter Simulations for the Archimedean Spiral Antenna 42 Figure 3.4 Input Impedance Simulations for the Archimedean Spiral Antenna 42 Figure 3.5 Simulated VSWR for the Archimedean Spiral Antenna 43

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vi Figure 3.6 Simulated Radiation Pattern Versus Theta at 2.4GHz for the Archimedean Spiral Antenna 44 Figure 3.7 Side, Front, and Top Views of Simulated Radiation Pattern in 3D at 2.4GHz for the Archimedean Spiral Antenna Backed by a 31-mil Thick Substrate 44 Figure 3.8 Simulated Total Gain (dB) Ve rsus Frequency for the Archimedean Spiral Antenna 45 Figure 3.9 Simulated Axial Ratio (dB) Ve rsus Frequency for the Archimedean Spiral Antenna 46 Figure 3.10 Wave Port Assignment at the Bottom of the 31-mil Thick Substrate for the Archimedean Spiral Antenna with Feeding Wires 47 Figure 3.11 Wave Port Assignment to One Side of the 31-mil Thick Substrate for the Archimedean Spiral An tenna with Feeding Twin-Strip Lines 47 Figure 3.12 Radiation Boundary Assignm ent for the Archimedean Spiral Antenna with Feeding Wires and a 31-mil Thick Substrate 49 Figure 3.13 Radiation Boundary Assignm ent for the Archimedean Spiral Antenna with Feeding Twin-Strip Lines and a 31-mil Thick Substrate 49 Figure 3.14 S-parameter Simulations for the Archimedean Spiral Antenna Backed by a 31-mil Thick Substrate 50 Figure 3.15 Input Impedance Simulations for the Archimedean Spiral Antenna Backed by a 31-mil Thick Substrate 51 Figure 3.16 Simulated Radiation Pattern Versus Theta at 2.4GHz for the Archimedean Spiral Antenna Backed by a 31-mil Thick Substrate 52 Figure 3.17 Side, Front, and Top Views of Simulated Radiation Pattern in 3D at 2.4GHz for the Archimedean Spiral Antenna Backed by a 31-mil Thick Substrate and Simu lated with Feeding wires 52 Figure 3.18 Side, Front, and Top Views of Simulated Radiation Pattern in 3D at 2.4GHz for the Archimedean Spiral Antenna Backed by a 31-mil Thick Substrate and Simulated with Feeding Twin-Strip Lines 53

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vii Figure 3.19 Simulated Total Gain (dB) Ve rsus Frequency for the Archimedean Spiral Antenna Backed by a 31-mil Thick Substrate 54 Figure 3.20 Simulated Axial Ratio (dB) Ve rsus Frequency for the Archimedean Spiral Antenna Backed by a 31-mil Thick Substrate 55 Figure 3.21 ADS Approximation of the Spiral Antenna Response when Simulated with Feeding Wires 56 Figure 3.22 S-parameters Simulations of Spiral Antenna Feeding Wires 58 Figure 3.23 ADS Approximation of the Spiral Antenna Response when Simulated with Twin-Strip Lines 59 Figure 3.24 S-parameters Simulations of Spiral Antenna Feeding Twin-Strip Lines 60 Figure 3.25 Integration of Spiral An tenna and Narrow-band Feed Network 60 Figure 3.26 Balanced and Unbalanced Modes on a Three-Wire Transmission Line 62 Figure 3.27 Input Impedance of the Spiral Antenna with Feeding Twin-Strip Lines 63 Figure 3.28 Matching Network Topology N eeded to Match the Antenna Input Impedance to 200 Ohms 64 Figure 3.29 Ideal Lumped Element Matching Network Solution 64 Figure 3.30 Ideal Versus Modelithics Johanson Models Matching Network Solution 65 Figure 3.31 Ideal Versus Modelithics Johanson Models Matching Networks 65 Figure 3.32 Balun Design 66 Figure 3.33 Balun Design Optimization in ADS to Connect a Balanced Input to an Unbalanced Output 67 Figure 3.34 S12 (phase) of Balun Design 67 Figure 3.35 Impedance Transformation Design in ADS 68 Figure 3.36 Balun Input Impedance 69

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viii Figure 3.37 Ground Effects Microwave and Electromagnetic Simulations of the Balun Design 70 Figure 3.38 Babinet’s Principle Approxima tion Between the Twin-Strip Line and CPW Structures 71 Figure 3.39 S-parameter Simulations fo r the Back-to-Back Balun Design 72 Figure 3.40 Fabricated Self-Complementary Archimedean Spiral Antenna with a Narrow-band Feed Network 73 Figure 3.41 Fabricated Back -to-Back Balun Design 73 Figure 3.42 Comparison Between Simulate d and Measured S-parameters of Archimedean Spiral Antenna 74 Figure 3.43 E-Plane Radiation Pattern M easurements of Fabricated Spiral Antenna 77 Figure 3.44 H-Plane Radiation Pattern M easurements of Fabricated Spiral Antenna 78 Figure 3.45 Measured S-parameters of Fa bricated Back-to-Back Balun Design 79 Figure 3.46 Back-to-Back Connector Design 81 Figure 3.47 S-parameter Simulations of Back-to-Back Connector Design 81 Figure 4.1 Basic Frequency Selective Surfaces 85 Figure 4.2 Cross Section and Top Vi ew of a High-Impedance Surface 86 Figure 4.3 Three-Layer High-Impedance Surface 87 Figure 5.1 Typical Geometry for a Helix 90 Figure 5.2 Six 1-Port Bonding Configurati ons Used to Characterize Surface Mount Chip Inductors as Miniature Antennas 92 Figure 5.3 Surface Mount Chip Inductor 93 Figure 5.4 S-parameters of 270 nH 0603 Coil Inductor Bonded in a 1-Port Configuration Radiating into Free Space 96 Figure 5.5 Efficiency Measurements 98

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ix Figure 5.6 S-parameters of 270 nH 0603 Coil Inductor Bonded in a 1-Port Configuration Radiating In side the Wheeler Cap 99 Figure 5.7 Radiation Efficiency of 270 nH 0603 Coil Inductor Bonded in a 1-Port Configuration 100 Figure 5.8 Input Impedance of 270 nH 0603 Coil Inductor Bonded in a 1-Port Configuration Radiating in Free Space 103

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x Electromagnetic Characterization of Mi niature Antennas for Portable Devices Diana P. Aristizabal ABSTRACT Advances in technology ha ve placed a great emphasi s on the design of broadband antennas as well as antenna miniaturizati on to cope with the demands of making electronic and handheld communica tion devices smaller and more efficient. In this thesis, the design and fabrication of a frequency i ndependent antenna and a narrow-band planar microstrip Balun are presented. An analysis of frequency select ive surfaces is also introduced in order to demonstrate their capa bility to miniaturize antenna thickness. Lastly, s-parameters measurements and effi ciency characterization are performed to determine the radiation properties of surface m ount chip inductors in order to determine the feasibility of using them as electrically small antennas. Two types of frequency independent antenn as are considered due to their planar geometries, the Equiangular and Archimedean spiral antennas. Frequency independent antennas are radiating devices that have frequency independent impedance and pattern properties because their shape is sp ecified only in terms of angles. The Balun is designed to meet the need of a feeding element for the Archimedean spiral antenna. A Balun is a three port de vice that connects an unbalanced transmission line such as a coaxial line to a balanced feed line such as the one required by two-arm spiral antennas. The Balun disc ussed in this work is design ed to operate at 2.4 GHz with

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xi a 200 MHz bandwidth and to transform th e antenna input impedance to a 50-ohm reference impedance. The main characteristics from this device that distinguish it from commercially available structures are its low cost, planarity, and compact footprint. The balancing capability of this Balun is shown by the close agreement between the measured and simulated results. Antennas can be potentially miniaturized in the z-direction by replacing the PEC ground plane separated from the antenna by a /4 thick substrate with a frequency selective surface (FSS) structur e that allows the ground plane conductor to be in close proximity to the antenna without affecting its radiation performance. The FSS layer operating at 2.4 GHz presented in this thesis is static (not tuned) and thus the overall bandwidth reduces approximately to the bandw idth obtained with the narrow-band Balun.

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1 Chapter 1 Introduction 1.1 Overview Advances in technology have led to the design of antennas capable of transmitting and/or receiving radio frequency signals at a wide frequency band, which would simplify the complexity in a wireless network design by reducing the amount of antennas necessary to cover a wide frequency range of operation. Two types of inherently broadband antennas were considered in this rese arch work due to their planar geometries, the Equiangular and Archimedean spiral an tennas. These two type s of antennas were designed as two-arm spirals. They were fe d using a feed network that connects the antenna balanced input to an unbalanced feed line. Electromagnetic an alysis of each of these antennas is presented in chapter 2 in order to establish the best working design at the frequency range of interest from 2 to 6 GHz. The optimum frequency independent antenna design as far as its fine quality radiation characteristics was c onstructed and integrated with a narrow-band feed network. Throughout chapter 3, electromagnetic and circu it level simulations were performed to investigate the effect on the antenna radia tion performance when decreasing the substrate thickness from /4 (calculated at 2.4 GHz) to 31 mils. In order to feed the two-arm spiral antenna with a narrow-band feed network, it was necessary to access the antenna feed point with vias that go to the end of the substrate and twin-strip lines to connect the

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2 balanced antenna input to the feed network. With the aim of electromagnetic simulations, the antenna performance was an alyzed all the way to the po int where it is connected to the balanced feed network. The designed narrow-band feed network consists of a Balun, which properly connects a balanced transmission line to an unbalanced transmission line. The unbalanced transmission line connects the antenna balanced feed line to an RF coaxial connector. Furthermore, the balun was measured with th e antenna at the input of the connector as well as separate from the antenna in a ba ck-to-back configuration. The RF coaxial connector was also simulated in HFSS in a tw o-port back-to-back conf iguration so as to investigate the performance of the transition from the unbalanced line to the input of the connector. In chapter 4, the background theory of ope ration for frequency selective surfaces is analyzed. A frequency sele ctive surface (FSS) is a metal surface coated with resonant structures that do not support surface waves within a frequency band. They can serve as substrates for antennas allowing them to lie directly adjacent to the ground plane surface without being shorted out. A low-frequency structure opera ting at 2.4GHz is evaluated that could potentially miniaturize the spir al antenna designed in chapter 2 in the zdirection. Advances in technology have placed a great emphasis not only on broadband antennas to cover an entire design application range but al so on antenna miniaturization to cope with the demands of making elect ronic devices smaller. In chapter 5, the fundamental limits of electrically small ante nnas are studied as far as how small an antenna can be at a particular wavelength and st ill behave as an effi cient radiating device.

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3 In addition, research and measurement character ization were oriented to investigate the feasibility of using chip inductors mounted in a 1-port configuration as electrically and physically small helical antennas operating at the frequency range of 1 to 3 GH. The research focuses on reflection coefficient and radiation efficiency measurements in order to characterize their performance as electrically small antennas. 1.2 Contributions The design of two se lf-complementary frequency i ndependent spiral antennas and a planar narrow-band Balun has been pres ented. The electromagnetic simulations and measurement characterization of these ante nnas and feed network have provided an understanding of their capabilities and limitatio ns. The main contributions from this work are the introduction of inhe rently broadband antennas achieving optimum operation, the design of a planar narrow-band Balun transfor mer operating as an efficient antenna feed network, the characterization of coil inductors as practical miniature antennas, and the study of FSS structures as potential groun d planes structures allowing antenna miniaturization.

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4 Chapter 2 Frequency Independent Antennas 2.1 Introduction An antenna is the structure associated with the transition re gion between a guided wave present in a waveguide, microstrip or transmission line and a free-space radiating wave. Thus, an antenna represents an inte rface where the convers ion of electrons on conductors to photons in space takes place. Figu re 2.1 illustrates this transition between a guided wave and a free space wave. It is desirabl e that this transmission of energy occurs with maximum efficiency. Once the transmission line separation approaches a wavelength or more, the guided wave or plan e wave traveling along the transmission line in one dimension tends to be radiated so th at the opened-out line acts like an antenna, which launches a free space wave or spherica lly expanding wave as illustrated on figure 2.1. The currents on the transmission line flow out on the transmission line and end there, but the fields associated with them continue [1]. The demands for numerous applications of electromagnetics due to the advances in technology have led to the design of broadband antennas. In 1954, Victor H. Rumsey introduced a class of structures and suggested that their patt ern and impedance properties should be independent of fre quency [2]. Rumsey’s principle states that the impedance and pattern properties of an antenna are frequency independent if the antenna shape is specified only in terms of angles [1]. Therefore, frequency independent antennas

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5 correspond to a type of structures that can be their own continuously scaled models since any characteristic length is re placed by specified angles. Figure 2.1 Antenna Defined as a Transition Region Between a Wave Guided by a Transmission Line and a Free-Space Wave [1] A successful frequency independent antenna must radiate most of the power in a finite active region so that it can be truncated with little effects on the pattern. Therefore, the currents must decay after the radiating active region. The finite active region is identified by truncation constants used to si ze the design. It must also be a transmissionline structure to carry power to the lowe r frequency end when fed from the high frequency end. Furthermore, a true frequenc y independent antenna has a constant beam width over the designed freque ncy band of operation if the ac tive region dimensions scale with wavelength [3]. Two types of frequency independent antenna s were considered due to their planar geometries, the self-complementary plan ar Equiangular and Archimedean spiral antennas. A spiral antenna is a bidirectional radiating device, which consists of a thin metal foil spiral pattern etched on a substrat e, usually fed from the center, and located over a backing cavity to either properly reflect or absorb th e energy [3]. These two types

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6 of antennas were designed as two-arm spirals since they can be fed using a fairly simple feed network that connects the antenna bala nced input to an unbalanced feed line. Both the Equiangular and Archimedean spir al antennas share a particular feature of frequency independent antennas called the self-complementary structure. The complementary structure of a metal antenna w ith input impedance Zmetal is an antenna with input impedance Zair that can be form ed with air replacing the metal and metal replacing the air of the original metal ante nna. Therefore, comple mentary antennas are similar to a positive and negative in phot ography. [4]. Then, it can be shown from Babinet’s principle that the impedances of complementary ante nnas are related by equation 2.1, where is the impedance of free space equal to 377 ohms. Z air Z metal 24 (2.1) If an antenna and its complement are actually the same, they are called selfcomplementary and are defined by equation 2.2 [4]. Z air Z metal 2 188.5ohms (2.2) Throughout this chapter, electromagnetic analysis of each of these antennas is presented in order to establis h the best working de sign at the frequency range of interest. Subsequently, the best antenna design is fabr icated and tested with a narrow-band feed network. This procedure is presented in Chapter 3. 2.2 Equiangular Spiral Antenna The self-complementary planar equiangul ar spiral antenna is considered a frequency independent antenna b ecause it satisfies the requirement that its geometry is entirely defined by angles. Additionally, th is type of antenna obeys the truncation

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7 requirement that the currents decay after the radiating active region so that the structure can be stopped without adversely aff ecting the antenna properties [3]. 2.2.1 Background Theory An equiangular spiral antenna can be defined by the spiral curve given by equation 2.3 and also shown in figure 2.2 [1], wh ere r is the radial di stance to a point P on the spiral, is the angle sweep with re spect to the x axis, and a is the spiral constant or flare rate which determines the tightness of the spiral winding [2]. The spiral curve on figure 2.2 is right-handed due to the positive value of the constant a. Likewise, lefthanded spiral curves can be obtaine d using negative values of a. r 1 a (2.3) Figure 2.2 Equiangular Spiral Curve Rotating the spiral curve r1 (equation 2.3) by a angle generates the spiral curve r2 (equation 2.4). Similarly, shifting the angle of equations 2.3 and 2.4 by 180 degrees ( ) creates the spiral curves r3 and r4 (equations 2.5 and 2.6 respectively). r 2 a () (2.4) r 3 a () (2.5)

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8r 4 a () (2.6) By metalizing the areas between spiral curves r1 and r2 (equations 2.3 and 2.4 respectively) and between spiral curves r3 and r4 (equations 2.5 and 2.6 respectively), with the other areas open, a two-arm equiangul ar spiral antenna is created as shown on figure 2.3. The arrows indicate the direction of the outgoi ng waves traveling along the conductors resulting in right-circularly polari zed (RCP) radiation outward from the page and left-circularly polarized ra diation into the page [1]. The rotation angle can be defined by equation 2.7, where the gap/arm ratio is equal to 1 for a self-complementary structure and N is the number of spiral turns [3]. Spirals with one half to thr ee turns have been found experi mentally to be relatively insensitive to the parameters “a” and [4]. Another way of descri bing the spiral curves is through the expansion factor (EF), which is de fined by equation 2.8 as the ratio of radius increase in one turn. 2 N1 gap arm (2.7) EFa2 (2.8) The high-frequency limit of operation is de termined by the spacing “d” of the input terminal [1]. The upper cutoff is limited to frequencies for which the spacing “d” of the input terminal cease to look like a point [5]. In the sa me way, the low-frequency limit of operation is determined by the overall diam eter “D” [1], which denotes the point of truncation where the total arm length is comparable to the wavelength and where the

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9 current becomes negligible [5]. Thus, for al l frequencies above the lowest frequency of operation, the pattern and impedance characte ristics are frequency independent [5]. Figure 2.3 Frequency-Independent Planar Self-Complementary Equiangular Spiral Antenna 2.2.2 Design The frequency range of inte rest is from 2 to 6 GHz. Th e equiangular spiral was designed as a two-arm spiral with the num ber of turns N equal to 2. By setting the maximum radius of the spiral “R” equal to L/4 (where L is the wavelength at the lower band edge frequency) and the minimu m radius of the spiral “r” to U/4 (where U is the wavelength at the upper freque ncy band edge), the antenna ba ndwidth is 3 to 1. This is the bandwidth we are looking fo r even though this type of antenna could provide much larger bandwidths. The flare rate “a” can be found from the maximum radius “R” as shown by equation 2.9, where 4 is the angle for two spiral turns, “c” equals 3x10^8 m/s, fL equals 2 GHz, and ereff is the effective dielectric consta nt of the dielectric material backing up the antenna. We chose the R ogers 5880 RT Duroid substrate with er equal to 2.2 for all calculations and simulations. The eff ective dielectric consta nt of this Rogers material is approximately equal to 1.61. By solving equation 2.9, we obtain a flare rate 1 The effective dielectric constant was approximated by the following formula ereff = (er+1)/2

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10 “a” equal to 1.31. The expansion factor equa ls to 5.46, and a typical value for the expansion factor is 4. From equation 2.7, we find the rotation angle to be equal to /2 for a two-turn self-complementary structure consisting of two arms. Ra4 L 4 c 4f Le reff (2.9) Table 2.1 shows the calculated radius e quations for the two-arm spiral antenna, where r1 through r4 corresponds to equations 2.3 to 2.6 respectively. Units are specified in mm. The physical dimensions of the equian gular spiral antenna are 50.5mm x 33.7mm. Table 2.1 Radius Equations Calculations for the Two-Arm Equiangular Spiral Antenna (radians) r1 (mm) r2 (mm) (radians) r3 (mm) r4 (mm) 0 0.00 1.0 0.7 3.14 1.0 0.7 /2 1.57 1.5 1.0 3 /2 4.71 1.5 1.0 3.14 2.2 1.5 2 6.28 2.2 1.5 3 /2 4.71 3.4 2.2 5 /2 7.85 3.4 2.2 2 6.28 5.0 3.4 3 9.43 5.0 3.4 5 /2 7.85 7.5 5.0 7 /2 11.00 7.5 5.0 3 9.43 11.3 7.5 4 12.57 11.3 7.5 7 /2 11.00 16.9 11.3 9 /2 14.14 16.9 11.3 4 12.57 25.3 16.9 5 15.71 25.3 16.9 2.3 Archimedean Spiral Antenna Similar to the equiangular spiral antenna, the self -complementary planar Archimedean spiral antenna is also consider ed a frequency independent antenna because it satisfies both the angle and truncation requi rements. The properties of the Archimedean spiral antenna are similar to those of th e equiangular planar spiral antenna. Their differences are in the equations defining their arms and the pa rameters used to achieve a self-complementary structure.

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11 2.3.1 Background Theory An Archimedean spiral antenna can be de fined by the spiral radius increasing uniformly with angle given by equation 2.10, where r1 is the inner radius of the spiral, ro is proportionality constant for the growth rate, and is the angle sweep with respect to the x axis [6]. r a r o r 1 (2.10) A rotation of the spiral curve of equati on 2.10 generates the other edge of the spiral arm as shown by equation 2.1 1. Similarly, shifting the angle of equations 2.10 and 2.11 by 180 degrees ( ) creates the second arm given by equations 2.12 and 2.13. r b r o 2r 1 (2.11) r c r o r 1 (2.12) r d r o 2r 1 (2.13) In order to control the frequency of operation, the outer a nd inner radius r2 and r1, respectively, must be defined. The outer radius r2 determines the low-frequency of operation, and the inner radius r1 determines the high frequency limit of operation. Equations 2.14 and 2.15 show the relation between radius and frequency of operation, where fhigh and flow are the high and low end freque ncies of the op erating range, respectively, and “c” is the speed of light eq ual to 3x10^8 m/s. In practice, the low frequency point can be greater than predicted by equation 2.15 due to reflections from the end of the spiral, which could be minimized by using resistive loading at the end of each arm or by adding conductivity loss to some pa rt of the outer turn of each arm [6].

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12 Likewise, the high frequency limit may be less than predicted by equation 2.14 due to feed region effects [6]. r 1 c 2 f high (2.14) r 2 c 2 f low (2.15) Moreover, the width of each arm and the sp acing between each turn are set equal to obtain a self-complementary structure. Th e width and space of each arm are defined by equation 2.16. Since frequency independent be havior is best achieved when the inner radius is equal to the strip widt h or spacing between turns [6], r1 is established by equation 2.17. The proportionality constant for the growth rate ro is given by equation 2.18. W r 2 r 1 4N (2.16) r 1 r 2 4N 1 (2.17) r o 2W (2.18) By metalizing the areas between spiral curves “a” and “b” (equations 2.10 and 2.11 respectively) and between spiral curves “c” and “d” (equations 2.12 and 2.13 respectively), with the other areas open, we obtain a two-arm Archimedean spiral antenna as shown on figure 2.4.

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13 Figure 2.4 Frequency-Independent Planar Self-Complementary Archimedean Spiral Antenna The radiations from the nearly equal and opposite currents at the feed point separated by the growing spiral arms cancel in the far field. When the perimeter of the turn approaches one wavelengt h, the out-of-phase currents b ecome in phase so that the currents no longer cancel in the far field. This condition continues for some distance after the 1 perimeter point [3]. The spiral radiates RHC (Right Hand Circ ular) polarization on one side and LHC (Left Hand Circular) polariz ation on the other side [3]. One of these polarizations is eliminated when the ante nna is mounted over a cavity. In order to determine the sense of the circul ar polarization, let your fingers roll in the direction of the spiral with the tips toward increasing radius and the thumb points to the pattern maximum [3]. The Archimedean spiral shown on figure 2.4 radiates RHC polarization. 2.3.2 Design The frequency range of interest is from 2 to 6GHz. By plugging these frequencies of interest into equations 2.14 to 2.18, we obt ain the parameters necessary to design the antenna. Table 2.2 shows the calculated parameters for the Archimedean spiral antenna. The number of turns “N” was se t to two. Table 2.3 shows the calculated radius equations for the two-arm spiral antenna, where ra th rough rd corresponds to equations 2.10 to 2.13

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14 respectively. Units are specified in mm. Th e physical dimensions of the equiangular spiral antenna are 53.1mm x 47.7mm. Table 2.2 Calculated Design Parameters for the Archimedean Spiral Antenna ParameterValue (mm) r1 2.653 r2 23.873 W 2.653 S 2.653 ro 1.689 Table 2.3 Radius Equations Calculations for the Two-Arm Archimedean Spiral (radians) ra (mm) rb (mm) (radians) rc (mm) rd (mm) 0 0.00 2.7 5.3 3.14 2.7 5.3 /2 1.57 5.3 8.0 3 /2 4.71 5.3 8.0 3.14 8.0 10.6 2 6.28 8.0 10.6 3 /2 4.71 10.6 13.3 5 /2 7.85 10.6 13.3 2 6.28 13.3 15.9 3 9.43 13.3 15.9 5 /2 7.85 15.9 18.6 7 /2 11.00 15.9 18.6 3 9.43 18.6 21.2 4 12.57 18.6 21.2 7 /2 11.00 21.2 23.9 9 /2 14.14 21.2 23.9 4 12.57 23.9 26.5 5 15.71 23.9 26.5 2.4 Electromagnetic Design and Simulations of Equiangular Spiral Antenna In order to perform an electromagnetic simulation of the antenna design, the program Ansoft HFSS (High Frequency Stru cture Simulator) was used. HFSS employs the Finite Element Method (FEM) for the EM simulations of arbitrary 3D volumetric passive devices [7]. Its basic mesh elemen t is a tetrahedron, which allows solving arbitrary 3D geometries involving complex curves and shapes [7]. The two-arm equiangular spiral antenna was drawn in HFSS us ing the calculated radius equations presented on table 2.1. The su bstrate was defined as the Rogers 5880 RT Duroid with er equal to 2.2. The metal thickness wa s set to 1.7 mils. Additionally, the preliminary simulations of the spiral antenna utilize the traditional /4 cavity backed implementation, which introduces a fixed length in terms of limiting the frequency

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15 independent characteristics of the antenna [8]. The /4 substrate thickness was calculated at 2.4 GHz to be equal to 24.7mm. In addition to generating a precise 3D draw ing of the antenna to be characterized, boundary conditions represent a major area of concern with efficiently and correctly modeling an antenna in HFSS. Boundary cond itions specify the field behavior on the surfaces of the problem region and object interf aces [7]. The wave equation that is solved by Ansoft HFSS is derived from the different ial form of Maxwell’s equations [7]. For these expressions to be vali d, it is assumed that the fi eld vectors are single-valued, bounded, and have continuous distribution al ong with their derivatives [7]. Then, boundary conditions define the field behavi or across discontinuous boundaries [7]. There are two types of boundaries that need to be considered and defined properly in order to accura tely simulate an antenna in HFSS. The first type of boundary is the excitation port that permits energy to flow into and out of a structure [7]. The second type of boundary is the radiation surface or absorbing boundary that enables modeling a surface as electrically open so that waves can radiate out of the structure and toward the radiation boundary [7]. When radiation boundari es are included in a structure simulation, calculated S-parameters include the effects of radiation loss [7]. In addition, the radiation boundary can be assigned to a 3D box enclosing th e radiating structure (the spiral antenna in this case) at a radial distance /4 in every direction as shown by figure 2.5.

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16 Figure 2.5 Radiation Boundary Assignment for the Equiangular Spiral Antenna There are two types of excitation boundaries in HFSS: one is external or wave port and the other one is intern al or lumped port. Since spir al antennas are conventionally fed in the center of the spiral, an initial si mple feeding was created with a lumped port assignment at the center of the spiral repr esented by a 2D recta ngular surface as shown by figure 2.6. A terminal line was defined to crea te a voltage polarity reference in the port boundary. The arrow head is synonymous with “+” and the arrow base is synonymous with “-”. Figure 2.6 Lumped Port Assignment for the Equiangular Spiral Antenna

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17 2.4.1 S-parameter Simulations The scattering matrix is used to provide a complete descri ption of an N-port network as seen at its N ports [9]. Furthe rmore, the scattering [S] matrix relates the voltage waves incident on the ports to those reflected from the ports as stated by equation 2.19, where Vn and Vn + are the amplitudes of the voltage waves reflected and incident on port n respectively [9]. For a 1-port network su ch as an antenna, the scattering parameter of interest is the reflection coefficient or S11 defined as the amplitude of the reflected voltage wave V1 coming out of port 1 to the incident voltage wave V1 + going into port 1 when all other ports are terminated in ma tched loads as shown by equation 2.20 [9]. The reflection coefficient is also represented as (1) (V2 +=0) [9]. [Vn -] = [S] [Vn +] (2.19) S11 = V1 / V1 + (V2 +=0) (2.20) The return loss (RL) in dB defined by equation 2.21 describes the reduction in the amplitude of the reflected energy as compared to the forward energy due to the mismatch between the transmission line characteristic impedance and the load impedance. When is equal to zero the load is matched to the line, so there is no reflected power and the return loss equals dB. When the magnitude of is equal to 1 all incident power is reflected, so the return loss equals 0 dB [9]. RL20 log dB (2.21) A flat metal sheet is used in many antennas as a ground plane. Therefore, simulations have been performed with a gr ound plane located approximately a quarterwavelength from the antenna, and without a ground plane, in order to compare the different and expected antenna performance. Figure 2.7 shows S11 in dB and phase for the

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18 equiangular spiral antenna having a /4 thick substrate2 with and without a ground plane present. The equiangular spiral antenna has a return loss of less than 5dB for a frequency range from 2 to 6 GHz. The effect of backing the antenna with a ground plane is illustrated by the blue trace in both plots shown on figure 2.7. For instance, the highest resonance for the antenna backed by a /4 thick substrate occurs at 2.2 GHz where S11 equals -18.6dB. Conversely, there are two dis tinctive resonances for the antenna backed by a /4 thick substrate and a ground plan e occurring at 1.9 and 4.6 GHz where S11 equals -17.61 and -17.73 dB respectively. -20 -15 -10 -5 0 1.522.533.544.555.56 Frequency (GHz)S11 (dB) No Ground Plane Ground Plane -100 -50 0 50 100 1.522.533.544.555.56 Frequency (GHz)S11 (phase) No Ground Plane Ground Plane Figure 2.7 S-parameter Simulations for the Equiangular Spiral Antenna. Red TraceAntenna Backed by a /4 Thick Substrate. Blue TraceAntenna Backed by a /4 Thick Substrate and a Gr ound Plane. Left PlotReturn Loss (dB). Right PlotReturn Loss (phase) Input impedance is defined as the impedance presented by an antenna at its terminals or the ratio of the voltage to current at a pair of terminals as demonstrated by equation 2.22, where ZA is the antenna impedance, RA is the antenna resistance, and XA is the antenna reactance at its terminals [5]. The resistive part of the antenna impedance (RA) consists of two components as shown by equation 2.23, where Rr is the radiation resistance and RL is the loss resistance of the antenna [5]. 2 The /4 thickness was calculated at 2.4 GHz for the Roge rs 5880 material (dielectric constant equal to 2.2) to be equal to 24.7 mm.

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19Z A R A jX A (2.22) R A R r R L (2.23) Figure 2.8 shows the simulated input impedance for the equiangular spiral antenna having a /4 thick substrate w ith and without a ground plane present. For a frequency-independent self-complementary sp iral, the input impedance should be flat over a wide frequency range. This trend is better represented by the antenna design without the ground plane as shown by the re d trace on both plots of figure 2.8, since the impedance follows a more constant flat trace between 3.5 and 6 GHz. 0 50 100 150 200 1.522.533.544.555.56 Frequency (GHz)Zin (real) No Ground Plane Ground Plane -100 -50 0 50 100 150 1.522.533.544.555.56 Frequency (GHz)Zin (im) No Ground Plane Ground Plane Figure 2.8 Input Impedance Simulations for the Equiangular Spiral Antenna. Red TraceAntenna Backed by a /4 Thick Substrate. Blue TraceAntenna Backed by a /4 Thick Substrate and a Ground Plane. Left PlotInput Impedance (real). Right PlotInput Impedance (imaginary) The voltage standing wave ratio (VSWR) is a measure of the mismatch of a line and can be defined by equation 2.24 to be a real number such that 1 VSWR [9]. Matched impedances give idea l power transfer that translates into a value of VSWR equal to 1. On the contrary, mismatched im pedances represent reduced power transfer that translates into a high value of VSWR. VSWR 1 1 (2.24)

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20 The voltage standing wave ratio is typically used to measure antenna bandwidth [6]. Figure 2.9 shows the simulated VSWR fo r the equiangular spiral antenna having a /4 thick substrate with and without a ground plane present. For the antenna without the ground plane present, the VSWR referenced to 50 ohms is less than 3 except for the frequency range between 2.6-3.1 GHz. On the other hand, for the antenna with a ground plane present, the VSWR referenced to 50 ohms is less than 3 except for two frequency ranges between 2.3-2.7 GHz and 4.9-6 GHz. 1 2 3 4 5 22.533.544.555.56 Frequency (GHz)VSWR No Ground Plane Ground Plane Figure 2.9 Simulated VSWR for the Equiangular Spiral Antenna. Red TraceAntenna Backed by a /4 Thick Substrate. Blue TraceAntenna Backed by a /4 Thick Substrate and a Ground Plane 2.4.2 Radiation Pattern Simulations An antenna radiation patte rn is a graphical repres entation of the radiation properties of the antenna, such as radiation intensity and dir ectivity phase or polarization, as a function of space coordinates [5]. An ampl itude field pattern is a graph of the spatial variation of the electric or magnetic fields al ong a constant radius [5]. In most cases, radiation and field patterns are determined in the far-field region, which is the region of the field of the antenna where the angular fiel d distribution is essent ially independent of the distance from the antenna [5]. The far-f ield region is commonl y taken to exist at

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21 distances greater than 2D2/ from the antenna, where D is the antenna maximum overall dimension [5]. Moreover, the radiation pattern is represented as a f unction of the standard spherical coordinate system. The spherical coordi nate system consists of a radial distance r that is maintained fixed, and two angular coordinates ( ) as shown by figure 2.10. Two-dimensional planes are used to characteri ze an antenna radiation pattern, such as the elevation plane or principal E-plane that co rresponds to the Theta angle and the azimuth plane or principal H-plane that corresponds to the Phi angle [5]. The E and H-planes are the planes containing the electric-field and magnetic-field vectors respectively as well as the direction of maximum radiation [5]. Figure 2.10 Coordinate System for Antenna Analysis The polarization of a radiated wave is defined as that property of an electromagnetic wave describing the time varyi ng direction of the electric-field vector [5]. The polarization characteri stics of an antenna can be represented by its polarization

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22 pattern, which is the spatial distribution of the polarizations of a field vector excited (radiated) by an antenna taken over its radiati on sphere [5]. At each point on the radiation sphere the polarization is usually resolved in to a pair of orthogona l polarizations, the copolarization and cross polarization [5]. There are three types of polarization; linea r, circular, and elliptical polarizations. 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 circ le as a function of time [5]. The necessary and sufficient conditions to accomplish this type of polarization are th at the electric or magnetic field vector must have two ort hogonal linear components which must have the same magnitude and a time-phase difference of odd multiples of 90 degrees [5]. Spiral antennas exhibit circular polariz ation. The sense of the spiral wrap and the direction of current flow determine the circ ular polarization sense [3]. The mode number of a spiral refers to the number of 2 (radians) or 360 (degrees) cycles that occur in the feed phasing when processing through the arms CCW (counterclockwise) [3]. For inst ance, mode 1 phases in a two-arm spiral are 0 and 180. Moreover, the phase difference moving CCW between arms is found from the mode number m and the number of arms N as shown by equation 2.25 [3]. We determine the mode radiating by the phase slope. RHC polarization prod uces a negative slope as increases (CCW rotation) [3]. We use th e convention that positive modes radiate RHC and negative modes radiate LHC and place th e negative sign in the mode expressions. phase 2 m N (2.25)

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23 “The number of arms equals the number of independent modes. An axially symmetrical antenna such as a spiral can radiate these modes when we phase the feeding of the ports to match the phase rotation of th e mode [3]”. For Instance, a two-arm spiral antenna has modes +1 and -1, which produce th e same phasing at the feed points of the spiral: 0 and 180. The spiral wrap directi on determines the polariz ation radiated [3]. Similarly, all odd-order (…, -3 -1, 1, 3, 5, …) modes have the same phasing on two feeds, which means that the two-arm spiral wi ll radiate these modes efficiently if current flows on the arms where the spiral circum ference is the same integer number of wavelengths [3]. Therefore, whenever the ci rcumference of a two-arm spiral is an oddinteger multiple of a wavelength the currents radiate. The two-arm spiral suppresses the even modes but allows ra diation of odd modes [3]. Figure 2.11 shows the simulated total far-field radiation patterns versus Theta at 2.4GHz for the equiangular spiral antenna backed by a /4 thick substrate with and without a ground plane present. The equiangular spiral antenna backed by a /4 thick substrate without the ground plane present shows an expected total gain pattern characterized by a major and a minor circular lobe. The maximum total gain at 2.4GHz is 4dB and occurs at a Theta angle equal to 180 for both 0 and 90 Phi angles due to the dielectric backing the antenna. If the dielect ric constant of the substrate backing the antenna is increased, then the maximum total ga in gets re-directed to a Theta angle of 0 because the thickness of the substrate decrease s and less energy tends to be stored in the substrate. On the other hand, the equi angular spiral antenna backed by a /4 thick substrate and a ground plane show s an expected total gain pattern characterized by a single major circular lobe and an almost non-existent minor lobe due to the presence of

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24 the ground plane. Making the ground plane infi nitely long would make the minor lobe disappear. The maximum total gain at 2.4GHz is 7dB and occurs at a Theta angle equal to 0 for both 0 and 90 Phi angles. As it is shown by figure 2.11, the presence of a ground plane redirects one-half of the radiation into the opposit e direction, improving the antenna gain by about 3dB [17]. Figures 2.12 and 2.13 show the side, front, and top views of the simulated radiation patterns in 3D at 2.4GHz for the equiangular spiral antenna backed by a /4 thick substrate without a nd with a ground plane present respectively. 330 300 270 240 210 180 150 120 90 60 0 30 -5 -4 -3 -2 -1 0 1 2 3 4 5 Phi=0deg Phi=90deg 330 300 270 240 210 180 150 120 90 60 0 30 -20 -15 -10 -5 0 5 10 Phi=0deg Phi=90deg Figure 2.11 Simulated Radiation Pattern Versus Thet a at 2.4GHz for the Equian gular Spiral Antenna. Red TracePhi = 0deg. Blue Tr acePhi = 90deg. Left PlotAntenna Backed by a /4 Thick Substrate. Right PlotAntenna Backed by a /4 Thick Substrate and a Ground Plane

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25 Figure 2.12 Side, Front, and Top Views of Simulated Radiation Pattern in 3D at 2.4GHz for the Equiangular Spiral An tenna Backed by a /4 Thick Substrate Figure 2.13 Side, Front, and Top Views of Simulated Radiation Pattern in 3D at 2.4GHz for the Equiangular Spiral An tenna Backed by a /4 Thick Substrate and a Ground Plane 2.4.3 Antenna Parameters Simulations Peak directivity or maximum directivity Do is a measure that describes only the directional properties of the an tenna, and it is therefore controlled by the pattern [5]. Do is defined as the ratio of the maximum radiation intensity from the antenna to the radiation intensity averaged over all directions, where th e averaged radiation intensity is equal to the total power radiated by the antenna divided by 4 [5]. In mathematical form, Do can

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26 be expressed as equation 2.26, where Umax is the maximum radiation intensity (W/unit solid angle) and Prad is the total radiated power (W) [5]. D o 4 U max P rad (dimensionless) (2.26) Peak Gain Go is a measure of the antenna perfor mance that takes into account the efficiency as well as the directional capabili ties of the antenna as shown by equation 2.27, where ecd is the antenna radiation efficiency (dimensionless) [5]. The antenna radiation efficiency accounts for the conduction and dielec tric efficiency, so gain does not include losses arising from impedance mismatches (reflection losses) and polarization mismatches (losses) [5]. Equation 2.28 conve rts gain from a dimensionless quantity to decibels. G o e cd D o (dimensionless) (2.27) G o dB ()10loge cd D o (2.28) Figure 2.14 shows the simulated total maxi mum gain (dB) versus frequency for the equiangular spiral antenna. The spiral antenna backed by a /4 thick substrate and without a ground plane present shows a total ma ximum gain increasing with frequency as expected. The gain increases from 3 to 12 dB between 2 to 5.4 GHz. Similarly, the spiral antenna backed by a /4 thick substrate and a ground plan e shows the increa sing trend of total maximum gain versus frequency excep t for the frequency range between 4 to 5 GHz. The gain increases from 6.7 to 11.7 dB between 2 to 6GHz. The low gain response between 4 to 5 GHz for the antenna backed by a ground plane shown suggests that at Phi = 0 and Theta =0 there is a null in the radiat ion pattern. This distortion in the radiation pattern could be due to the fact that at th is frequency range the substrate backing up the

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27 antenna is /2 electrically long instead of /4, which will put the antenna closer to the ground plane electrically. Theref ore, the image currents on the ground plane tend to cancel the currents in the antenna resulting in this low gain. Axial ratio is a very important parameter for spiral antennas since it indicates the type of polarization the antenna exhibits. More over, it is defined as the ratio of the major to the minor axis of the polarization ellipse. The axial ratio value range varies from 1 to infinity, where 1 (0 dB) indicates that the elec tric field is circularly polarized and a value of infinity indicates that th e electric field is linearly pol arized. For instance, spiral antennas should have an axial ratio less than 5dB to be considered a circularly polarized antenna with a bidirectional radiation pattern broadside to the plane of the spiral. The designed equiangular spiral an tenna radiates RHC polarizati on based on the spiral wrap direction. Figure 2.15 shows the simulated axial ratio (dB) versus frequency at the Theta and Phi angle position where total gain is maximum for the equiangular spiral antenna. The spiral antenna backed by a /4 thick substrate and wit hout a ground plane present has linear polarization from 2 to 3.5 GHz and fr om 4.5 to 6GHz. However, it has circular polarization from 3.5 to 4.5 GHz. Furtherm ore, the spiral antenna backed by a /4 thick substrate and a ground plane has linear polar ization from 2 to 2.2 GHz and from 3.1 to 5.3 GHz. It has circular pol arization from 2.3 to 3GHz and from 5.4 to 6GHz.

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28 0 2 4 6 8 10 12 14 22.533.544.555.56 Frequency (GHz)Total Gain (dB) No Ground Plane 0 2 4 6 8 10 12 14 22.533.544.555.56 Frequency (GHz)Total Gain (dB) Ground Plane Figure 2.14 Simulated Total Gain (dB) Versus Frequency for the Equiangular Spiral Antenna. Left PlotAntenna Backed by a /4 Thick Substrate Simulated at Phi = 0 and Theta = 180. Right PlotAntenna Backed by a /4 Thick Substrate and a Ground Plane Si mulated at Phi = 0 and Theta = 0 0 5 10 15 20 25 22.533.544.555.56 Frequency (GHz)Axial Ratio (dB) No Ground Plane 0 5 10 15 20 25 30 22.533.544.555.56 Frequency (GHz)Axial Ratio (dB) Ground Plane Figure 2.15 Simulated Axial Ratio (dB) Versus Frequency for the Equiangular Spiral Antenna. Left PlotAntenna Backed by a /4 Thick Substrate Simulated at Phi = 0 and Theta = 180. Right PlotAntenna Backed by a /4 Thick Substrate and a Ground Plane Si mulated at Phi = 0 and Theta = 0 2.5 Electromagnetic Design and Simulations of Archimedean Spiral Antenna The two-arm Archimedean spiral ante nna was drawn in HFSS using the calculated radius equations presented in table 2.2. The substrate was defined as the Rogers 5880 RT Duroid with er equal to 2.2. The metal thickness was set to 1.7 mils. Additionally, the preliminary simulations of the spiral antenna utilize the traditional /4 cavity backed implementation. The /4 substrate thickness was calculated at 2.4 GHz to be equal to 21.07mm.

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29 The radiation boundary was assigned to a 3D box enclosing the radiating structure (the spiral antenna in this case) at a radial distance /4 in every direction as shown by figure 2.16. Additionally, an initial simple feeding was created with a lumped port assignment at the center of the spiral represented by a 2D rectangular surface as shown by figure 2.17. A terminal line was define d to create a voltage polarity reference in the port boundary. Figure 2.16 Radiation Boundary Assignment for the Archimedean Spiral Antenna Figure 2.17 Lumped Port Assignmen t for the Archimedean Spiral Antenna 2.5.1 S-parameter Simulations Figure 2.18 shows the return loss in dB and phase for the Archimedean spiral antenna having a /4 thick substrate with and w ithout a ground plane present. The

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30 Archimedean spiral antenna has a return loss of less than 5dB for a frequency range from 2 to 6 GHz. The effect of backing the ante nna with a ground plane is illustrated by the blue trace in both plots shown on figure 2.18. For instance, the highest resonance for the antenna backed by a /4 thick substrate occurs at 2.4 GHz where S11 equals -7.9 dB. Conversely, there are two high resona nces for the antenna backed by a /4 thick substrate and a ground plane that occu r at 2.25 and 3.05 GHz where S11 equals -12.18 and -16.56 dB respectively. -20 -15 -10 -5 0 22.533.544.555.56 Frequency (GHz)S11 (dB) No Ground Plane Ground Plane -50 -25 0 25 50 75 22.533.544.555.56 Frequency (GHz)S11 (phase) No Ground Plane Ground Plane Figure 2.18 S-parameter Simulations for the Arch imedean Spiral Antenna w ith and without a Ground Plane. Red TraceAntenna Backed by a /4 Thick Substrate. Blue TraceAntenna Backed by a /4 Thick Substrate and a Ground Plane. Left PlotReturn Loss (dB). Right PlotReturn Loss (phase) Figure 2.19 shows the simulated input im pedance for the Archimedean spiral antenna having a /4 thick substrate w ith and without a ground plane present. For a frequency-independent self-complementary sp iral, the input impedance should be flat over a wide frequency range. This trend is better represented by the antenna design without the ground plane as shown by the re d trace on both plots of figure 2.19, since the impedance follows a more constant flat trace from 2 to 6 GHz.

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31 0 50 100 150 200 250 300 22.533.544.555.56 Frequency (GHz)Zin (real) No Ground Plane Ground Plane -100 -50 0 50 100 150 22.533.544.555.56 Frequency (GHz)Zin (im) No Ground Plane Ground Plane Figure 2.19 Input Impedance Simulations for the Ar chimedean Spiral Antenna with and without a Ground Plane. Red TraceAntenna Backed by a /4 Thick Substrate. Blue TraceAntenna Backed by a /4 Thick Substrate and a Ground Plane. Left PlotInput Impedance (real). Right PlotInput Impedance (imaginary) Figure 2.20 shows the simulated VSWR for the Archimedean spiral antenna having a /4 thick substrate with and without a ground plane present. For the antenna without the ground plane present, the VSWR referenced to 50 ohms is less than 3 except for the frequency range between 3.2 to 3.75GHz On the other hand, for the antenna with a ground plane present, the VSWR refe renced to 50 ohms is less than 5. 1 2 3 4 5 6 22.533.544.555.56 Frequency (GHz)VSWR No Ground Plane Ground Plane Figure 2.20 Simulated VSWR for the Archimedean Sp iral Antenna with and without a Ground Plane. Red TraceAntenna Backed by a /4 Thick Substrate. Blue TraceAntenna Backed by a /4 Thick Substrate and a Ground Plane

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32 2.5.2 Radiation Pattern Simulations The Archimedean and the equiangular spiral antennas share similar radiation pattern characteristics. For instance, they e xhibit maximum gain peaks at a theta angle equal to 180 degrees for the configuration w ithout a ground plane pr esent and at a theta angle equal to 0 degrees for the configur ation with a ground plane present, which indicates that the presence of a ground plane redirects the direction of maximum gain by 180 degrees. Also, as it is shown by figures 2.11 and 2.21, the Archimedean spiral antenna has slightly higher gain peaks than the equiangular spiral. In addition, the presence of a ground plane improved the antenna gain of the Archimedean and equiangular spiral antenn as by about 3dB at 2.4GHz. Figure 2.21 shows the simulated total far-field radiation patterns versus Theta at 2.4GHz for the Archimedean spiral antenna backed by a /4 thick substrate with and without a ground plane present. The Archimedean spiral antenna backed by a /4 thick substrate without the ground plane present shows an expected total gain pattern characterized by a major and a minor circular lobe. The maximum total gain at 2.4GHz is 4.26dB and occurs at a Theta angle equal to 180 for both 0 and 90 Phi angles. On the other hand, the Archimedean spiral antenna backed by a /4 thick substrate and a ground plane shows an expected total gain pattern characterized by a single major circular lobe and an almost non-existent minor lobe due to the presence of the ground plane. The maximum total gain at 2.4GHz is 7.11dB and oc curs at a Theta angle equal to 0 for both 0 and 90 Phi angles. Figures 2.22 and 2.23 sh ow the side, front, and top views of the simulated radiation patterns in 3D at 2.4GHz for the Archimedean spiral antenna backed by a /4 thick substrate wit hout and with a ground pl ane present respectively.

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33 30 0 60 90 120 150 180 210 240 270 300 330 -3 -2 -1 0 1 2 3 4 5 Phi=0deg Phi=90deg 330 300 270 240 210 180 150 120 90 60 0 30 -30 -25 -20 -15 -10 -5 0 5 10 Phi=0deg Phi=90deg Figure 2.21 Simulated Radiation Pattern Versus Theta at 2.4GHz for the Archimedean Spiral Antenna with and without a Ground Plane. Red Tr acePhi = 0deg. Blue TracePhi = 9 0deg. Left PlotAntenna Backed by a /4 Thick Substrate. Right PlotAntenna Backed by a /4 Thick Substrate and a Ground Plane Figure 2.22 Side, Front, and Top Views of Simulated Radiation Pattern in 3D at 2.4GHz for the Archimedean Spiral An tenna Backed by a /4 Thick Substrate

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34 Figure 2.23 Side, Front, and Top Views of Simulated Radiation Pattern in 3D at 2.4GHz for the Archimedean Spiral An tenna Backed by a /4 Thick Substrate and a Ground Plane 2.5.3 Antenna Parameters Simulations The Archimedean spiral antenna has similar gain versus frequency response to the equiangular spiral antenna. Th e increasing trend of total maximum gain with frequency is present for the equiangular and Archimedean spiral antennas regardless of the presence of a conductive ground plane. Additionally, the Ar chimedean spiral antenna holds the same low gain performance as the equiangular spir al antenna at a fre quency range where the substrate backing up the antenna is /2 electrically long instead of /4. However, this distortion in the gain is more noticeable fo r the Archimedean spiral antenna as shown by figure 2.24, which could be due to the Archimedean spiral antenna arms being closer to the edge of the substrate so the image currents on the ground plane could cancel the currents in the antenna to a greater extent. Figure 2.24 shows the simulated total maxi mum gain (dB) versus frequency for the Archimedean spiral antenna. The gain in creases from 3.66 to 7.75 dB between 2 to 5.85 GHz. Similarly, the spiral antenna backed by a /4 thick substrate and a ground plane shows the increasing trend of total ma ximum gain versus frequency except for the frequency range between 3.7 to 4.455 GHz. The gain increases from 7.2 to 11.9 dB

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35 between 2 to 5.7 GHz. The low gain response be tween 4 to 5 GHz for the antenna backed by a ground plane shown in figure 2.24 implies th at at Phi = 0 and Theta =0 there is a null in the radiation pattern. 0 2 4 6 8 10 22.533.544.555.56 Frequency (GHz)Total Gain (dB) No Ground Plane -15 -10 -5 0 5 10 15 22.533.544.555.56 Frequency (GHz)Total Gain (dB) Ground Plane Figure 2.24 Simulated Total Gain (dB) Versus Frequency for the Archimedean Spiral Antenna with and without a Ground Plane. Left PlotAntenna Backed by a /4 Thick Substrate Simulated at Phi = 0 and Theta = 180. Right PlotAntenna Backed by a /4 Thick Substrate and a Ground Plane Simulated at Phi = 0 and Theta = 0 Figure 2.25 shows the simulated axial ratio (dB) versus frequency at the Theta and Phi angle positions where total gain is maximum for the Archimedean spiral antenna backed by a /4 thick substrate. The Archimedean spiral antenna achieves circular polarization through a wider frequency range th an the equiangular sp iral antenna without a ground plane present. For instance, the Ar chimedean spiral antenna has circular polarization from 2.4 to 6.0 GHz except for the frequency range between 5.75 to 5.9 GHz where the polarization is more linear. Moreover, it also has lin ear polarization from 2.0 to 2.39 GHz. On the contrary, the equiangular spir al antenna has circular polarization from 3.5 to 4.5 GHz. Below 3.5 GHz, th e polarization is linear. The linear polarization at lower frequencies can be attributed to the reflectio ns from the end of each spiral arm [6]. The reflected waves have opposite sense polarizati on than the outward traveling waves, which has a significant impact on the ax ial ratio at the lower cutoff frequencies. The reflections

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36 from the end of each equiangular spiral arm mi ght be greater than from the end of each Archimedean spiral arm since the equiangula r spiral arms are wider at the point of truncation resulting in lin ear polarization through a wi der low frequency range. Furthermore, the Archimedean and equiangular spiral antennas achieve linear polarization through a wider freque ncy range when backed by a /4 thick substrate and a ground plane than without a ground plane presen t. For instance, the Archimedean spiral antenna has mostly linear polar ization from 2 to 6.0 GHz exce pt for the frequency ranges from 5.05 to 5.45 GHz, from 5.65 to 5.8 GHz, a nd at 4.95 GHz where it has circular polarization. In this case, the reflections from the end of each spiral arm plus the interference caused when the surface waves traveling along the ground plane reach the substrate edges are the key factors accountable for the linear polarization through a wider frequency range. 0 2 4 6 8 10 22.533.544.555.56 Frequency (GHz)Axial Ratio (dB) No Ground Plane 0 5 10 15 20 25 30 35 22.533.544.555.56 Frequency (GHz)Axial Ratio (dB) Ground Plane Figure 2.25 Simulated Axial Ratio (dB) Versus Fr equency for the Archimedean Spiral Antenna with and without a Ground Plane. Left PlotAntenna Backed by a /4 Thick Substrate Simulated at Phi = 0 and Theta = 180. Right PlotAntenna Backed by a /4 Thick Substrate and a Ground Plane Simulated at Phi = 0 and Theta = 0 2.6 Summary and Conclusions Two types of frequency independent ante nnas were designed and simulated as two-arm spirals. Simulations have been performed with a ground plane located

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37 approximately a quarter-wavelength from th e antenna, and without a ground plane. The non-ground plane configuration is the reference configuration as it is the goal to obtain similar results to this when we miniat urize the most optimal design using a high impedance frequency selective surface (FSS). Th e FSS layer will be static (not tuned) and thus the overall bandwidth will reduce re lative to the non-ground plane approach. The simulation results show that even though the Archimedean and the equiangular spiral antennas have different equations defining them, their performance characteristics are similar. For instance, the return loss, VSWR, total gain, and radiation characteristics follow similar and expected trends. Despite the fact that the simulations were performed using a substrate w ith a fixed electrical length of /4 at 2.4 GHz, both spirals showed a broadband response at the fr equency range of interest. Also, as it was expected, the presence of a ground plane a dist ance equal to a quarter wavelength away from the antenna resulted in similar radi ation responses for bot h spiral antennas. To conclude, the Archimedean spiral has a more flat input impedance response, as well as circular polarization over a greater bandwidth than the equiangular spiral. In addition, since the difference in physical size between both spirals is not significant, the Archimedean spiral appears to be the most op timal design to be miniaturized in the zdirection using an FSS. In Chapter 3, the c onstruction and testing of the Archimedean spiral antenna using a narrowband Balun is pr esented in order to va lidate the performance of the antenna at a chosen frequency of 2.4GHz.

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38 Chapter 3 Archimedean Spiral Antenna with a Narrow-Band Feed Network 3.1 Introduction In Chapter 2, the Archimedean spiral antenna was found to be the optimum frequency independent design to be constructed and integrat ed with a narrow-band feed network due to its radiation char acteristics. In order to fabricate the spiral antenna, it was necessary to use a thinner substrate than a /4 thick substrate at a chosen common wireless communication frequency of 2.4 GH z because the physical thickness of about 24.7 mm is not commercially available. Thro ughout this chapter, electromagnetic and circuit level simulations were performed to i nvestigate the effect on the antenna radiation performance when decreasing the substr ate thickness to 31 mils (0.8 mm). The Archimedean spiral antenna was simu lated using a different feed network than the ideal excitation at the antenna feed point used in Chapter 2. In order to feed the two-arm spiral antenna with a narrow-band f eed network, it was necessary to access the antenna feed point with vias that go to the end of the substrate and twin-strip lines to connect the balanced antenna input to the feed network as shown in figure 3.1. Simulations of the antenna with feeding wire s and twin-strip lines were performed using HFSS. The narrow-band feed network consists of a Balun, which connects a balanced transmission line to an unbalanced transmi ssion line [3]. The unbalanced transmission

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39 line serves as the interface between the ante nna and an RF coaxial connector. The Balun was designed and simulated using the Agilent Advanced Design Syst em (ADS) software. Furthermore, it was measured integrated with the spiral antenna as well as in a back-toback configuration. Finally, th e RF coaxial connector was also simulated in HFSS in a two-port back-to-back configura tion so as to investigate the performance of this 50-ohm unbalanced connection. Figure 3.1 Spiral Antenna Integrated with a Narrow-band Feed Network 3.2 Archimedean Spiral Antenna Design The spiral antenna simulated in Chapter 2 used a substrate with a /4 thickness calculated at 2.4GHz. Nevertheless, this thickn ess translates into a physical dimension not available for commercial dielectric subs trates such as Rogers. Therefore, new simulations were conducted with a 31 mil thick R ogers substrate, so that as to predict the antenna behavior on the subs trate used for fabrication. Similarly, the spiral antenna simulations performed in Chapter 2 used a lumped port excitation at the antenna feed point. Howe ver, to maintain the symmetrical properties of the antenna, it is necessary to feed the antenna with an electrically and geometrically balanced line [5]. In addition, this balanced line can be connected to an unbalanced line using a Balun to be able to measur e the antenna using a coaxial cable.

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40 The designed transition between the antenna feed point and the Balun consists of two wires that go from the feed point of th e spiral antenna down to the bottom of the substrate through via holes and two planar twin -strip lines that go from the feeding wires at the bottom of the substrat e to one side of the substr ate, as shown in figure 3.1. Microwave simulations in ADS were perfor med to examine the effect of adding a balanced feed line structure on the antenna performance. 3.2.1 Electromagnetic Simulations of the Sp iral Antenna on a Thinner Substrate The new substrate backing the spiral antenna was a 31-mil thick dielectric sheet manufacture by Rogers. This subs trate was chosen because of its low dielectric constant and low-loss tangent. The spiral operates as a transmission line between the arms whose length becomes significant for tightly wrappe d spirals [3]. This transmission could be analyzed as a coplanar strip transmission lin e for losses, and the equivalent dielectric constant of the transmission li ne loads the spirals and reduces the effective loop radiator size [3]. The spiral antenna simulations on a thinne r substrate presented in this section use the same lumped port excitation feed structur e used in Chapter 2, as well as the same radiation boundary assignment except for shorte r dimensions in the z-direction due to the thinner substrate thickness, as shown in figure 3.2. Simulation results will corroborate expected changes in antenna performance as far as the return loss, VSWR, and input impedance. The antenna radiation pattern is e xpected to still follow the well-known spiral antenna behavior.

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41 Figure 3.2 Radiation Boundary Assignment for the Archimedean Spiral Antenna on a 31-mil Thick Substrate 3.2.1.1 S-parameter Simulations Figure 3.3 shows S11 in dB and phase for the Archimedean spiral antenna with a /4 and a 31-mil thick substrate without a gr ound plane present. The Archimedean spiral antenna has a return loss of less than 5dB for a frequency range from 2 to 6 GHz. The effect of backing the antenna with a thinner substrate is i llustrated by the blue trace in both plots shown on figure 3.3. For instance, the highest resonance for the antenna backed by a /4 thick substrate occu rs at 2.4 GHz where S11 equals -7.9 dB. Conversely, the highest resonance for the antenna backed by a 31-mil thick substrate occurs at 2.9 GHz where S11 equals -7.13. The response of the antenna backed by th e 31-mil thick substrate looks like the response of the antenna backed by a /4 thick substrate shifte d by about 500 MHz. This shift in S11 over frequency is due to the fact that the 31-mil thick substrate has a lower effective dielectric constant than the /4 thick substrate, which in turn increases the resonant frequency. Similarly, th is predictable shift is also present in the input impedance and VSWR responses as shown by figure 3.4 and 3.5. Figures 3.4 and 3.5 show the simulated input impedance and VSWR, respectively, for the Archimedean spiral antenna with a /4 and a 31-mil thick substrate without a

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42 ground plane present. Both antenna simulati ons follow a similar trend with a flat impedance response from 2 to 6 GHz and a VSWR referenced to 50 ohms less than 3.5. -20 -15 -10 -5 0 22.533.544.555.56 Frequency (GHz)S11 (dB) lambda/4 substrate 31-mil thick substrate 0 10 20 30 40 22.533.544.555.56 Frequency (GHz)S11 (phase) lambda/4 substrate 31-mil thick substrate Figure 3.3 S-parameter Si mulations for the Archimedean Spiral An tenna. Red TraceAntenna Backed by a /4 Thick Substrate. Blue TraceAn tenna Backed by a 31-mil Thick Substr ate. Left PlotReturn Loss (dB). Right PlotReturn Loss (phase) 60 80 100 120 140 160 22.533.544.555.56 Frequency (GHz)Zin (real) lambda/4 substrate 31-mil thick substrate 0 10 20 30 40 50 60 22.533.544.555.56 Frequency (GHz)Zin (im) lambda/4 substrate 31-mil thick substrate Figure 3.4 Input Impedance Simulations for the Archimedean Spiral Antenna. Red TraceAntenna Backed by a /4 Thick Substrate. Blue TraceAntenna Backed by a 31-mil Thick Substrate. Left PlotInput Impedance (real). Right PlotInput Impedance (imaginary)

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43 1 1.5 2 2.5 3 3.5 22.533.544.555.56 Frequency (GHz)VSWR lambda/4 substrate 31-mil thick substrate Figure 3.5 Simulated VS WR for the Archimedean Spiral Ante nna. Red TraceAntenna Backed by a /4 Thick Substrate. Blue TraceAntenna Backed by a 31-mil Thick Substrate 3.2.1.2 Radiation Pattern Simulations Figure 3.6 shows the simulated far-field radi ation patterns vers us Theta at 2.4GHz for the Archimedean spiral antenna with a /4 and a 31-mil thick substrate without a ground plane present. The Archimedean spiral antenna backed by a 31-mil thick substrate shows an expected total gain pattern char acterized by two major circular lobes. The maximum total gain at 2.4GHz is 2.98dB and o ccurs at a Theta angle equal to 180 for 0 and 90 Phi angles. As expected, the maximum gain is lower for the antenna simulated on the thinner substrate, but it still occurs at the same Theta angle as the antenna with a /4 thick substrate. The thicker substrate suppresse s one of the major lobes into minor lobes, which eventually disappear when a ground pl ane is present as shown by the pattern simulations in Chapter 2. Figure 3.7 shows the side, front, and top views of the simulated radiation patterns in 3D at 2.4GHz for th e Archimedean spiral antenna backed by a 31mil thick substrate without a ground plane present.

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44 30 0 60 90 120 150 180 210 240 270 300 330 -3 -2 -1 0 1 2 3 4 5 Phi=0deg Phi=90deg 330 300 270 240 210 180 150 120 90 60 0 30 -8 -6 -4 -2 0 2 4 Phi=0deg Phi=90deg Figure 3.6 Simulated Radiation Pattern Versus Thet a at 2.4GHz for the Archim edean Spiral Antenna. Red TracePhi = 0deg. Blue Tr acePhi = 90deg. Left PlotAntenna Backed by a /4 Thick Substrate. Right PlotAntenna Backed by a 31-mil Thick Substrate Figure 3.7 Side, Front, and Top Views of Simulated Radiation Pattern in 3D at 2.4GHz for the Archimedean Spiral An tenna Backed by a 31-mil Thick Substrate 3.2.1.3 Antenna Parameter Simulations Figure 3.8 shows the simulated total maximu m gain (dB) versus frequency for the Archimedean spiral antenna. The spiral ante nna backed by a 31-mil thick substrate and without a ground plane present shows a total ma ximum gain increasing with frequency as expected. The gain increases from 2 to ~10 dB between 2 to 5.4 GHz. From 2 to 3GHz, the total maximum gain is lower than the ga in obtained with the antenna backed by a /4

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45 thick substrate. However, from 3 to 5.4GHz, the total maximum gain is higher than the gain obtained with the antenna backed by a /4 thick substrate. Figure 3.9 shows the simulated axial ratio (d B) versus frequency at the Theta and Phi angle position where total gain is maxi mum for the Archimedean spiral antenna. The spiral antenna backed by a 31-mil thick substrate and without a ground plane present has circular polarization from 3.15 to 5.9 GHz. On the contrary, from 2 to 3.1 GHz the polarization is more linear. Furthermore, from 2 to 3.5 GHz, the axial ratio is higher than the axial ratio obtained with the antenna backed by a /4 thick substrate. However, from 3.6 to 6.0 GHz, the axial ratio follows a close trend to the axial ratio obtained with the antenna backed by a /4 thick substrate. 0 2 4 6 8 10 22.533.544.555.56 Frequency (GHz)Total Gain (dB) lambda/4 substrate 31-mil thick substrate Figure 3.8 Simulated Total Gain (dB) Versus Freq uency for the Archimedean Sp iral Antenna. Red Trace Antenna Backed by a /4 Thick Substrate Simulated at Phi = 0 and Theta = 180. Blue TraceAntenna Backed by a 31-mil Thick Substrate Simu lated at Phi = 0 and Theta = 180

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46 0 2 4 6 8 10 12 14 16 22.533.544.555.56 Frequency (GHz)Axial Ratio (dB) lambda/4 substrate 31-mil thick substrate Figure 3.9 Simulated Axial Ratio (dB) Versus Fre quency for the Archimedean Sp iral Antenna. Red TraceAntenna Backed by a /4 Thick Substrate Simulated at Phi = 0 and Theta = 180. Blue TraceAntenna Backed by a 31-mil Thick Substrate Simu lated at Phi = 0 and Theta = 180 3.2.2 Electromagnetic Simulations of the Effect of Adding a Narrow-Band Feed Structure to the Spiral Antenna The effect of adding a narrow-band feed network to the spiral antenna was analyzed in HFSS in tw o stages. The first stage consists of feeding the antenna using two wires that go from the feed point of the spir al antenna down to the bottom of the substrate (31 mils away from the antenna) through vi a holes. Figure 3.10 illustrates this first feeding used that it is referred to as “ bottom feeding.” The second stage consists of feeding the antenna using two planar twin-strip lines that go from the feeding wires at the bottom of the substrate over to one side of the substrate. Eventually, a Balun will be connected to these lines with the purpose of fabricating and testing the spiral antenna. Figure 3.11 illustrates this second feeding used th at it is referred to as “side feeding.”

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47 Figure 3.10 Wave Port Assignment at the Bottom of the 31-mil Thick Substrate for the Archimedean Spiral Antenna with Feeding Wires Figure 3.11 Wave Port Assignment to One Side of the 31-mil Thick Substrate fo r the Archimedean Spiral Antenna with Feeding Twin-Strip Lines These simulations were performed using a wave port assignment instead of a lumped port because it calculates additional information regarding the port-cross section, such as characteristic impedance and complex propagation constant, th at will be later needed for the microwave simulations in ADS. Wave ports are ex ternal excitations assumed to be connected to a semi-infinite ly long waveguide that has the same crosssection and material properties as the port [7 ]. The field patterns of the traveling waves entering and exiting the port ar e computed at every frequenc y point of interest using Maxwell’s equations [7].

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48 The generalized s-parameters calculate d by HFSS must be renormalized to a constant characteristic impedance such as 50 ohms in order to match the results obtained in laboratory measurements and circuit si mulators, which use a constant reference impedance so the ports are not perf ectly matched at every frequency. The wave ports must be calibrated in orde r to determine direction and polarity of fields, to make voltage calculations, and to be able to duplicate the results of laboratory measurements in which the setup is calibra ted by removing the structure and connecting two ports together [7]. They are calibrated us ing integration lines, which serve as the path over which HFSS integrates the E-field to obtain the voltage at a wave port [7]. In [7], the procedure used by HFSS to calibrate the ports is explained in more detail. The simulations used the same radiati on boundary assignment us ed in previous simulations, except for shorter dimensions in the z and x directi ons for the bottom and side feeding respectively, since the wave por t can not be inside the radiation boundary but on the interface instead. Figures 3.12 and 3.13 show the radiation boundary assignment for the spiral antenna with a bottom and a side feeding configuration respectively. The radius of the wires feeding the antenna was defined as one quarter the desired strip width, since it represents an appropriate transformati on from strip width to wire diameter [6]. The strip width of the Archim edean spiral antenna is equal to 2.653 mm, so the wire radius is equal to 0.663 mm. The tw in strip lines feeding the antenna had a characteristic impedance of 215.96 ohm s and were 33.979 and 26.021 mm long, 0.663 mm wide, and with a gap width equal to 1.326 mm.

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49 Figure 3.12 Radiation Boundary Assignment for the Archimedean Spiral Antenna with Feeding Wires and a 31-mil Thick Substrate Figure 3.13 Radiation Boundary Assignment for the Archimedean Spiral Antenna with Feeding Twin-Strip Lines and a 31-mil Thick Substrate 3.2.2.1 S-parameter Simulations Figure 3.14 compares the return loss in dB and phase of the Archimedean spiral antenna backed by a 31-mil thick substrate with three different types of feeding configurations. The effect of feeding the antenna with wires is illustrated by the blue trace in both plots shown on figure 3.14. For instan ce, from 2 to 5 GHz, the return loss of the antenna is less than 5 dB w ith feeding wires. On the othe r hand, the return loss of the antenna with feeding twin-strip lines is great er than 5 dB from 2.2 to 3.1GHz and from 5 to 6GHz as shown by the magenta trace in both plots of figure 3.14. The differences between the three simulations are expected as a result of adding transmission line with a characteristic impedance that is not matched to the load impedance. At the frequency

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50 ranges where S11 is low for the antenna simulated with feeding wires and with twin-strip lines, the real part of the input impedance, shown in figure 3.15, is much greater than the respective characteristic impeda nce of the feeding wires (247 .2 ohms) and twin-strip lines (215.96 ohms) resulting in a greater mismatch. Figure 3.15 compares the simulated input impedance for the Archimedean spiral antenna backed by a 31-mil thick substrate with three different types of feeding configurations. The antenna with feeding wi res has a peak on the impedance from 2 to 4GHz, and then it has a flat trace characteri zed by a lower impedance as compared to the antenna simulated directly at the spiral f eed point. Similarly, the antenna with feeding twin-strip lines has a peak on the input impedance from 3.6 to 4.2 GHz, and then it has a flat trace characterized by a higher impedance as compared to the antenna simulated directly at the spiral feed point. Changes in input impedance were expected after adding feeding wires and twin-strip lines to the an tenna, since we are adding extra transmission lines. 345 26 -15 -10 -5 -20 0 Frequency (GHz)S11 (dB) 345 26 -50 0 50 -100 100 Frequency (GHz)S11 (phase) Figure 3.14 S-parameter Simulations for the Archimedean Spiral Antenna Backed by a 31-mil Thick Substrate. Red TraceAntenna Simula ted at the Antenna Feed Point. Bl ue TraceAntenna Simulated with Feeding Wires. Magenta Trace – Antenna Simulated with Feeding Twin-Strip Lines Left PlotReturn Loss (dB). Right PlotReturn Loss (phase)

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51 345 26 100 200 300 400 0 500 Frequency (GHz)Zin (re) 345 26 -100 0 100 200 -200 300 Frequency (GHz)Zin (imag) Figure 3.15 Input Impedance Simulations for the Archimedean Spiral Antenna Backed by a 31-mil Thick Substrate. Red TraceAntenna Simula ted at the Antenna Feed Point. Bl ue TraceAntenna Simulated with Feeding Wires. Magenta Trace – Antenna Simulated w ith Feeding Twin-Strip Lines. Left PlotInput Impedance (real). Right PlotInput Impedance (imaginary) 3.2.2.2 Radiation Pattern Simulations Figure 3.16 shows the simulated total far-field radiation patterns versus Theta at 2.4GHz for the Archimedean spiral antenna backed by a 31-mil thick substrate with two different types of feeding configurations. Both antenna feeding configurations (wires and twin-strip lines) show the expected total gain pattern characterized by two major circular lobes. However, the antenna with feeding wire s shows a much lower ga in versus Theta at both 0 and 90 Phi angles as compared to th e antenna with feeding twin-strip lines. For instance, the maximum total gain at 2.4GHz fo r the antenna simulated with feeding wires is -5.09 dB and occurs at a Theta angle equa l to 0 for both 0 and 90 Phi angles. The maximum total gain at 2.4GHz for the antenna simulated with feeding twin-strip lines is 2.6 dB and occurs at a Theta angle equal to 30 and at a Phi angle equal to0. Figures 3.17 and 3.18 show the side, front, and top views of the simulated radiation patterns in 3D at 2.4GHz for the Archimedean spiral ante nna backed by a 31-mil thick substrate with feeding wires and twin-s trip lines respectively.

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52 30 0 60 90 120 150 180 210 240 270 300 330 -12 -10 -8 -6 -4 -2 0 Phi=0deg Phi=90deg 330 300 270 240 210 180 150 120 90 60 0 30 -10 -8 -6 -4 -2 0 2 4 Phi=0deg Phi=90deg Figure 3.16 Simulated Radiation Pattern Versus Theta at 2.4GHz for the Archimedean Spiral Antenna Backed by a 31-mil Thick Substrate. Red TracePhi = 0deg. Blue TracePhi = 90deg. Left PlotAntenna Simulated with Feeding Wires. Right Plot – An tenna Simulated with Feeding Twin-Strip Lines Figure 3.17 Side, Front, and Top Views of Simulated Radiation Pattern in 3D at 2.4GHz for the Archimedean Spiral Antenna Backed by a 31-mil Thick Substrate and Simulated with Feeding Wires

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53 Figure 3.18 Side, Front, and Top Views of Simulated Radiation Pattern in 3D at 2.4GHz for the Archimedean Spiral Antenna Backed by a 31-mil Thick Substrate and Simulated with Feeding Twin-Strip Lines 3.2.2.3 Antenna Parameter Simulations Figure 3.19 shows the simulated total maxi mum gain (dB) versus frequency for the Archimedean spiral antenna backed by a 31-mil thick substrate with two different types of feeding configurations. Both antenn a feeding configurations (wires and twinstrip lines) show a total maximum gain incr easing with frequency as expected. However, the antenna with feed ing wires (blue trace on figure 3.19) has considerably lower gain than the antenna simulated directly at the spiral feed point (red trace on figure 3.19). On the contrary, the gain of the antenna with f eeding twin-strip lines (green trace on figure 3.19) follows a closer trend to the gain of the antenna simulated directly at the spiral feed point except for the frequency range from 2.45 to 3GHz. The peak gain variation at lower frequencies can be attributed to the refl ections from the end of each spiral arm. Based on return loss and maximum gain results, it is better to feed the antenna with wires and twin-strip lines than ju st with wires in or der to obtain an S11 greater than 5 dB and a gain response closer to the one achie ved by the antenna fed directly at the spiral feed point.

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54 Figure 3.20 shows the simulated axial ra tio (dB) versus frequency for the Archimedean spiral antenna backed by a 31-mil thick substrate with two different types of feeding configurations. The spiral antenna with feeding wires has circular polarization from 2 to 4.5 GHz. On the contrary, the antenna with feeding twin-str ip lines has linear polarization for almost the entire freque ncy range except for some narrow frequency ranges. -15 -10 -5 0 5 10 15 20 22.533.544.555.56 Frequency (GHz)Total Gain (dB) lumped port feeding feeding wires feeding twin-strip lines Figure 3.19 Simulated Total Gain (dB) Versus Freq uency for the Archimedean Sp iral Antenna Backed by a 31-mil Thick Substrate. Red Trace Antenna Simulate d at the Antenna Feed Poin t at Phi = 0 and Theta = 180. Blue TraceAntenna Simulated with Feeding Wires at Phi = 0 and Theta = 0. Green Trace – Antenna Simulated with Feeding Twin-Strip Lines at Phi = 0 and Theta = 30

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55 0 5 10 15 20 25 30 35 40 45 22.533.544.555.56 Frequency (GHz)Axial Ratio (dB) lumped port feeding feeding wires feeding twin-strip lines Figure 3.20 Simulated Axial Ratio (dB) Versus Freq uency for the Archimedean Sp iral Antenna Backed by a 31-mil Thick Substrate. Red Trace Antenna Simulate d at the Antenna Feed Poin t at Phi = 0 and Theta = 180. Blue TraceAntenna Simulated with Feeding Wires at Phi = 0 and Theta = 0. Green Trace – Antenna Simulated with Feeding Twin-Strip Lines at Phi = 0 and Theta = 30 3.2.3 Microwave Simulations of the E ffect of Adding a Narrow-Band Feed Structure to the Spiral Antenna The spiral antenna response obtained with the HFSS simulations was analyzed and approximated using ADS in order to corro borate that adding fe eding wires and twinstrip lines to the antenna f eed point does not influence th e performance by the existence of coupling effects between the spiral arms and the feeding structure. The expected results will support the presumption that th e narrow-band balanced feed line structure will have an effect on the antenna operati on only because of the fact that further transmission line is present. The first step was to approximate with circuit-level simulati ons the response of the antenna when feeding wires are added to th e spiral antenna feed point. In order to approximate the antenna’s return loss res ponse in ADS, the physical transmission line parameters of the feeding wire s were introduced into an ideal transmission line model, and the s-parameter response of the spiral antenna simulated at the feed point with a

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56 lumped port assignment was added to this transmission line model. The schematic representation of this pro cedure is shown on figure 3.21. In HFSS simulations, each port is assumed to be connected to a transmission line structure that has the same cross-section as the port [7]. Then, the complex propagation constant “ ” and the characteristic impedance of this transmission line “Zpi” are computed by HFSS. The additional physical tr ansmission line parameters of the feeding wires needed for the model in ADS are physi cal length “L” equal to 0.8738 mm, effective dielectric constant “k”, attenuation constant, dielectric loss tangent “TanD” equal to 0.0009 for the Rogers material used in the simulations, and relative permeability “Mu” equal to 1 for the Rogers material used in the simulations. Figure 3.21 ADS Approximation of the Spiral An tenna Response when Simulated with Feeding Wires The complex propagation constant “ ” is given by equation 3.1, where (nepers/meter) is the attenuation constant of a signal in the transmission structure and (radians/meter) is the phase constant associat ed with the wave [7]. Equation 3.2 converts the attenuation constant from nepe rs per meter to dB per meter.

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57 j (3.1) dB meter 20loge (3.2) The effective dielectric constant “k” is given by equation 3.3, where ko is the free space wave number, and is the imaginary component of the complex propagation constant [9]. k k o 2 (3.3) k o 2 f c (3.4) Figure 3.22 shows the comparison between the spiral antenna simulated with feeding wires and the approxima tion to this response using transmission line simulations in ADS. The differences among the simulations in HFSS and the approximation in ADS can be explained by the fact that the simula tions were obtained usi ng two different types of excitations (wave and lumped port). The second step was to approximate with circuit-level simulations the response of the spiral antenna when twin-strip lines are added from the feeding wires at the bottom of the substrate all the way to one side of the substrate. In order to approximate the antenna’s return loss response in ADS, the physical transmission line parameters of the twin-strip lines were introduced into an ideal transmission line model, and the sparameter response of the spiral antenna simu lated with two feeding wires was added to

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58 this transmission line model. The schematic re presentation of this pr ocedure is shown on figure 3.23. 345 26 -15 -10 -5 -20 0 Frequency (GHz)S11 and S22 (dB) p 345 26 -50 0 50 -100 100 Frequency (GHz)S11 and S22 (phase) Figure 3.22 S-parameters Simu lations of Spiral Antenna Feedin g Wires. Red Trace-Spiral Antenna Simulated in HFSS with Two Feeding Wires. Blue TraceApproximation Simulations in ADS of this Response. Left PlotReturn Loss (d B). Right PlotReturn Loss (phase) Besides the complex propagation constant “ ” and the characteristic impedance “Zpi” of the twin-strip transmission lines computed by HFSS, the additional physical transmission line parameters of the feeding twin-strip lines needed for the model in ADS are physical length “L” equal to 33.979 mm, eff ective dielectric cons tant “k” calculated using equation 3.3, attenuation co nstant calculated in dB per meter by equation 3.2, dielectric loss tangent “TanD” equal to 0.0009 for the Rogers material used in the simulations, and relative permeability “Mu” equal to 1 for the Rogers material used in the simulations.

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59 Figure 3.23 ADS Approximation of the Spiral Ante nna Response when Simulated with Twin-Strip Lines Figure 3.24 shows the comparison between the spiral antenna simulated with feeding twin-strip lines and the approximati on to this response using transmission line simulations in ADS. The approximation follows the same trend as the HFSS simulation, and at 2.4, 3.5, and 4.8 GHz they are an exac t match. These results confirm that adding feeding wires and twin-strip lines to the antenna feed point does not influence the performance by the existence of coupling effect s between the spiral arms and the feeding structure. The microwave simulations in ADS support the presumption that the narrowband balanced feed line structure has an effect on the antenna operation only because further transmission line is present.

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60 345 26 -15 -10 -5 -20 0 Frequency (GHz)S11 and S22 (dB) pp 345 26 -50 0 50 -100 100 Frequency (GHz)S11 and S22 (phase) Figure 3.24 S-parameters Simulations of Spiral Antenna Feeding Twin-Strip Lines. Red Trace-Spiral Antenna Simulated in HFSS with Feeding Twin-Strip Lines. Blue TraceApproximation Simulations in ADS of this Response. Left PlotReturn Lo ss (dB). Right PlotReturn Loss (phase) 3.3 Balun Design In order to fabricate the antenna to corroborate the HFSS simulations at a frequency of 2.4 GHz, we desi gned a microstrip feed that consist of a matching network and a Balun. The purpose of the Balun is to provide a balanced feed to the antenna necessary for optimum performance as well as a transition to an unbalanced feed characteristic of a microstrip design. Prio r to the microstrip feed design, antenna simulations using feeding wires and twin-strip lines were performed in HFSS to establish a suitable feeding configurati on to connect the spiral antenna to the microstrip design. In addition, the antenna simulations se rved to determine the input impedance looking into the antenna, which will be transformed to a pur ely real impedance using a matching network. Then, the impedance looki ng into the matching network will be transformed to 50 ohms by the Balun. This procedure is illust rated in figure 3.25. Figure 3.25 Integration of Spiral Antenna and Narrow-band Feed Network

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61 The Balun was designed in two phases. The first phase was to design the Balun to appropriately connect the balanced antenna input to an unbalanced output. The second phase was to design the Balun as an impedance transformer to convert Zmatched to Zo (50 ohms) as shown on figure 3.25. Moreover, a back -to-back configuration of the Balun was simulated in ADS and HFSS in order to i nvestigate possible effects from stopping the ground plane of the microstrip narrow-band f eed network at the input of the antenna. 3.3.1 Background Theory The term Balun is a combination of th e words balance and unbalanced. It is a device that connects a balanced two-conductor line to an unbalanced co axial line [1]. A twin-lead transmission line (two parallel-condu ctor line) is a symme trical line whereas a coaxial cable is inherently unbalanced [5]. A device such as a Balun can be used to balance inherently unbalanced systems by cance ling or choking the net current flow to ground on the outside part of the outer conductor of the coax line [5]. The Balun operation can be explained by th e balanced and unbalanced modes of the three-wire transmission lines. A balanced three-wire transmissi on-line mode carries equal and opposite currents in the feeder lines, where the cap acitances per unit length of the two lines to ground are the same [3]. Coax is an example of an unbalanced line structure, where the inner conductor ha s no direct capacitance to ground [3]. Figure 3.26 shows circuit representations of the fundamental modes of a threewire transmission line without showing th e ground conductor. Equal loads terminate ports 3 and 4. The unbalanced mode (equal curren t directions) is associ ated with the even mode, which applies equal voltages on ports 1 and 2 and forms a magnetic wall between the conductors becoming a virtual open circuit [3]. On the contrary the balanced mode

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62 (equal and opposite currents) is associated with the odd mode, which applies equal and opposite voltages on port 1 and 2 and set up an electric wall be tween the conductors becoming a virtual short circuit [3]. Figure 3.26 Balanced and Unbalanced Modes on a Three-Wire Transmission Line [3] A balun also blocks the un-wanted farfield radiation com ponents produced by the feeder line, whose polarizations redirect the beam peak of the antenna [3]. Only closely spaced equal and opposite currents, the balanced mode, cancel the far-f ield radiation from the currents on the feed lines [3]. 3.3.2 Microwave Design and Simulations It was desired to match the input impedance of the spiral antenna to a real value that would make the Balun easier to design. A matching network was used to eliminate the capacitive imaginary pa rt of the input impedance looki ng into the ante nna at 2.4 GHz. Figure 3.27 shows this input impedance.

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63 2.53.54.55.5 1.56.5 100 200 300 400 0 500 -100 0 100 200 -200 300 Frequency (GHz)Zin(re) m5 Zin(imag) m6 m5 freq= real(Zin1)=61.517 2.400GHz m6 freq= imag(Zin1)=-79.793 2.400GHz Figure 3.27 Input Impedance of the Spiral Antenna with Feeding Twin-Strip Lines. Red TraceZin (real). Blue TraceZin (imaginary) A lumped-element matching network was chosen for its simplicity and ease to manufacture in order to match Zant equal to 61.5-j79.8 to Zmatched equal to 200 ohms. Figure 3.28 shows the network topology necessary to match this type of load since the normalized load impedance lies outside the 1+ jx circle on the smith chart. Equations 3.5 and 3.6 were used to calculate the series reactance X and shunt susceptance B for the marching network [9], where RL is equal to 61.5 ohms, XL is equal to -79.8, and ZO is equal to 200 ohms. One of the possible so lution networks was found based on these equations consisting of a 5.3pF series cap acitor and an 8.8nH shunt inductor. The matching network was first simulated in ADS using ideal components as shown by figure 3.29.

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64 Figure 3.28 Matching Network Topology Needed to Match the Antenna Input Impedance to 200 Ohms XR L Z o R L X L (3.5) B Z o R L R L Z o (3.6) S1P SNP2 File="S11(dB)_CL.s1p" 1 Ref C C1 C=5.3 pF L L1 R= L=8.8 nH Term Term1 Z=50 Ohm Num=1 Figure 3.29 Ideal Lumped Element Matching Network Solution The Johanson 0201 surface mount chip inducto rs and capacitors were chosen to fabricate the matching network. Therefore, the matching network was also analyzed by replacing the ideal lumped element compone nts by the Modelithics ADS models of the Johanson 0201 surface mount chip inductors an d capacitors in the ADS simulations. The lumped component values in the Johanson mo dels were tuned to match the response of the matching network using ideal components as shown by figure 3.30. The final inductor and capacitor values were 2.6pF and 6.9nH resp ectively. Because of samples availability, the actual components used in the fabricat ed matching network we re a 2.7pF capacitor and a 6.8nH inductor. Figure 3.31 compares the response of the matching networks using ideal components and Modelithics models.

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65 VAR VAR4 L1=6.9 tune{ 5 to 30 by 0.1 } C1=2.6 tune{ 0.5 to 20 by 0.1 }Eqn Var S1P SNP2 File="S11(dB)_CL.s1p" 1 Ref C C1 C=5.3 pF L L1 R= L=8.8 nH Term Term1 Z=50 Ohm Num=1 S1P SNP4 File="S11(dB)_CL.s1p" 1 Ref Term Term3 Z=50 Ohm Num=3 CAP_JOH_0201_001_MDLXCLR1 JOH_0201L_C2 TanD=0.0009 T=1.7 mil Er=2.2 H=31 mil Tolerance=1.0 Subst="MSub1" C=C1 pF IND_JOH_0201_001_MDLXCLR1 JOH_L_05xxxx_L2 TanD=0.0009 T=1.7 mil Er=2.2 H=31 mil Tolerance=1.0 Subst="MSub1" L=L1 nH Figure 3.30 Ideal Versus Modelithics Johanson Models Matching Network Solution 2.252.302.352.402.452.502.55 2.202.60 100 150 200 50 250 freq, GHzreal(Zin1) m1 real(Zin3) m2 m1 freq= real(Zin1)=200.010 2.400GHz m2 freq= real(Zin3)=199.384 2.400GHz 2.252.302.352.402.452.502.55 2.202.60 0 50 100 150 -50 200 freq, GHzimag(Zin1) m5 imag(Zin3) m6 m5 freq= imag(Zin1)=1.363 2.400GHz m6 freq= imag(Zin3)=-2.141 2.400GHz Figure 3.31 Ideal Ve rsus Modelithics Johanson Models Ma tching Networks. Red TraceMatching Network Using Ideal Components. Bl ue TraceMatching Network Usin g Modelithics Models. Right PlotZin (real). Left PlotZin (imaginary) 3.3.2.1 Balanced Input to Unbalanced Output Transition Simulations Figure 3.32 shows the Balun design that will connect the spiral antenna to a coaxial 50-ohm RF connector as shown by fi gure 3.40. This type of Balun was chosen among many available designs due to its plan ar geometry and impedance transformation capabilities that will provide a balanced to unbalanced feed reference to 50 ohms without

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66 excessively increasing the design size in the Zdirection. In order to connect the balanced spiral antenna arms to an unbalanced line, th e Balun balanced lines need to be a distance /4 apart from each other. Figure 3.33 shows the ADS simulation schema tic used to optimi ze the lengths (L1 and L2) of the Balun, so that the phase di fference between S12 and S13 is 180 degrees required for a balanced feed. The lengths L1 and L2 that provided a 180 degree phase difference between S12 and S13 were 22.5 and 23 mm respectively. Figure 3.34 shows the insertion loss (phase) after the optimiza tion. The exact phase difference between S12 and S13 is 180.83 degrees at 2.4 GHz. Figure 3.32 Balun Design

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67 Term Term1 Z=50 Ohm Num=1 MLIN TL13 L=L3 mm MLIN TL17 L=L3 mm MCORN Corn5 W=Wlines mm MLIN TL14 L=L2 mm MTEE Tee3 W3=Wlines mm W2=Wlines mm W1=Wlines mm MCORN Corn6 W=Wlines mm MLIN TL16 L=L1 mm Term Term3 Z=50 Ohm Num=3 Term Term2 Z=50 Ohm Num=2 Figure 3.33 Balun Design Optimization in ADS to Connect a Balanced Input to an Unbalanced Output 2.252.302.352.402.452.502.55 2.202.60 -100 -50 0 50 100 -150 150 Frequency (GHz)phase(S(1,3)) m1 p h ase (S(1 2)) m2 m1 freq= phase(S(1,3))=89.012 2.400GHz m2 freq= phase(S(1,2))=-91.817 2.400GHz Figure 3.34 S12 (phase) of Balun Design. Re d TraceS13 (phase). Blue TraceS12 (phase) 3.3.2.2 Impedance Transformation Simulations In addition to providing a balanced feed to the self-complementary spiral antenna, the Balun design also includes a step change in impedance from 200 ohms (impedance looking into the matching network) to a 50ohm transmission line. A 100 ohm resistor

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68 was placed between ports 2 and 3 of the Ba lun on the ADS simulation to emulate the 200-ohm impedance seen looking into the ma tching network. In order to perform the impedance transformation, the transmission line length L3 needs to be /4. Figure 3.35 shows the ADS simulation schematic used to op timize the length L3 in order to transform the impedance from 200 to 50 ohms. Figur e 3.36 shows the real and imaginary input impedance looking into the Balun after the leng th optimization. The final length L3 that provided the impedance transformation was 23 mm. The width of the Balun transmission lines was optimized to 0.66 mm. The final input impedance looking into the narrow-band feed network and the spir al antenna is 51.428 + j1.34. Term Term4 Z=50 Ohm Num=4 MTEE Tee2 W3=Wlines mm W2=Wlines mm W1=Wlines mm MCORN Corn3 W=Wlines mm MLIN TL9 L=L2 mm MLIN TL12 L=L3 mm MLIN TL8 L=L3 mm R R2 R=100 Ohm MLIN TL10 L=L1 mm MCORN Corn4 W=Wlines mm Figure 3.35 Impedance Transformation Design in ADS

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69 2.252.302.352.402.452.502.55 2.202.60 47 48 49 50 51 46 52 Frequency (GHz)Zin1 (real) m3 m3 freq= real(Zin1)=51.428 2.400GHz 2.252.302.352.402.452.502.55 2.202.6 0 -5 0 5 10 -10 15 Frequency (GHz)Zin1 (imag) m4 m4 freq= imag(Zin1)=1.340 2.400GHz Figure 3.36 Balun Input Impedance. Left PlotZin (real). Right PlotZin (imaginary) 3.3.3 Ground Effects Microwave and Electromagnetic Simulations Additional simulations were performed in order to investigate the effect of stopping the ground plane conductor at the balan ced input of the Ba lun just where the balanced twin-strip lines connect. A back to back design was simulated in ADS and HFSS as shown by figure 3.37. This design cons ists of a Balun and its mirror image connected to each other through a twin-strip line. A short piece of twin-strip lines was used instead of the r eal twin-strip line connecting the antenna to the Ba lun so that the design would not become extremely long since we just wanted to check the ground effects. The design in HFSS was simulated using wave ports at both ports. The short piece of twin-strip line was desi gned with a characteristic impedance of 200 ohms and to be approximately 20 degrees long at 2.4GHz. In order to calculate the physical length and width of the twin-strip line for the HFSS simulation, a coplanar waveguide structure was used to approximate a twin-strip line structure as shown by figure 3.38. Then, Babinet’s prin ciple was used to approxi mate the characteristic impedance of the coplanar waveguide structur e, and the ADS LineCalc tool was used to calculate its physical parameters. Equation 3.7 shows Babinet’s principle formula, where

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70 o is the characteristic impedance of free space equal to 377 ohms, reff is the effective dielectric constant, Zcpw corresponds to the strip c onductor impedance of the CPW structure, and Zslot corresponds to the slot impedance of the twin-strip line structure equal to 200 ohms. The effective dielectric consta nt was approximated by equation 3.8 to be equal to 1.6, where r is the dielectric constant of th e RT/Duroid 5880 substrate equal to 2.2. Therefore, the approximated strip conduc tor impedance of the CPW structure was calculated to be equal to 111.04 ohms. The cal culated physical parameters of the twinstrip line structure were as follows: slot width was equal to 1.01 mm, strip conductor width was equal to 1.33 mm, and the length of the twin-strip line was equal to 5.9 mm. Figure 3.37 Ground Effects Microwave and Electromagnetic Simulations of the Balun Design

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71Z slot Z cpw 24 reff (3.7) reff r 1 2 (3.8) Figure 3.38 Babinet’s Principle Approximation Between the Twin-Strip Line and CPW Structures The ADS simulation represents an ideal transmission line mode l of the back-to back Balun design as opposed to the HFSS simulation that represents the actual design. Figure 3.39 shows the comparison between th e ADS and HFSS Balun design simulations. The differences among the two design simulati ons at other frequencies other than 2.4 GHz could be caused by the accuracy of the calculations used to determine the width and length of the twin-strip line for the HFSS simulation. These results give us conf idence that stopping the ground plane at the twin-strip line will not affect the performance of the microstrip narrow-band feed network at the design frequency of 2.4GHz. This design was fabricated and tested to confirm the simulation results.

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72 2.32.42.5 2.22.6 -25 -20 -15 -10 -30 -5 Frequency (GHz)S11 (dB) 2.32.42.5 2.22.6 -3 -2 -1 -4 0 Frequency (GHz)S21 (dB) Figure 3.39 S-parameter Simulations for the Back-to-Back Balun Design. Red TraceADS Simulation. Blue TraceHFSS Simulation. Left Pl otS11 (dB). Right Plot S21 (dB) 3.4 Fabrication The self-complementary Archimedean spiral antenna design was etched on a 31mil thick Rogers RT/Duroid 5880 substrate (er=2.2). Figure 3.40 shows the fabricated design implemented with the narrow-band fe ed network. The ante nna feed point was connected to the twin-strip lines at the bottom of the substrate through via holes filled with conductive silver epoxy. The Johanson su rface mount components for the matching network (series capacitor-shunt inductor) were bonded between the twin-strip lines and the balanced output of the Bal un using a re-flow process with solder paste. Finally, an RF connector was soldered to the unbalanced input of the Balun. The back-to-back Balun design shown on figure 3.37 was milled on a 31-mil thick Rogers RT/Duroid 5880 substr ate (er=2.2). The ground plan e under the twin-strip line that connects the two Baluns was also mille d. Figure 3.41 shows the fabricated design. Two RF connectors were soldered to the unbalanced inputs of each Balun.

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73 Figure 3.40 Fabricated Self-Complementary Arch imedean Spiral Antenna w ith a Narrow-band Feed Network Figure 3.41 Fabricated Back-to-Back Balun Design 3.5 Measurements In Chapter 2 and previous sections of Chapter 3, analytical methods were implemented to analyze and numerically co mpute the radiation characteristics of the Archimedean spiral antenna. S-parameters and radiation pattern measurements were performed in order to corroborate the result s obtained in the simulations. Moreover, sparameter measurements of the back-to-b ack Balun design were also performed to support the ground effects simulation results.

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74 3.5.1 S-parameters Measurements A vector network analyzer (VNA) was used to measure the s-parameters of the spiral antenna. A 1-port calibration was perf ormed at the end of a coaxial RF cable connected to port 1 of the network anal yzer. The 1-port SOL (Short-Open-Load) calibration consists of connecti ng a short, an open, and a load calibration standards to the end of the coaxial cable. Then VNA computed the calibration coeffi cients to account and correct for the loss of the path. Once the m easurement setup was calibrated, the device under test (spiral antenna) was connected to the coaxial cable through the RF connector at the unbalanced input of the Balun, and the s-pa rameters of the ante nna were recorded on the network analyzer. Figure 3.42 shows the comparison between simulated and measured S11 (dB) of the fabricated spiral antenna. At the designed frequency of 2.4 GHz, there is a 19dB of return loss with a 200 MHz 10-dB return loss bandwidth. The differences between the simulation and measur ement could be explained by the fact that the simulated spiral antenna is not matched to the feed line, but the measured spiral antenna is matched to a 50-ohm feed line. Th e spiral antenna simulations do not include the lumped-element matching network, th e Balun, and the coaxial RF connector. -25 -20 -15 -10 -5 0 2.0E+092.2E+092.4E+092.6E+092.8E+093.0E+09 Frequency (GHz)S11 (dB) Measured Simulated Figure 3.42 Comparison Between Simulated and Measured S-parameters of Archimedean Spiral Antenna. Red TraceSimulated. Blue TraceMeasured

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75 3.5.2 Radiation Pattern Measurements Far-field radiation characteristics are m easured by illuminating the test antenna by plane waves, that is waves with uniform amp litude and phase [5]. In order to approximate this ideal condition, the test antenna is sepa rated from the source antenna or illumination source by a distance equal to the inner boundary of the antenna’s far-field region [5]. This inner boundary is equal to 2D2/ where D is the antenna overall maximum dimension and is the antenna operating wavelength [5]. Radiation patterns are measured on the su rface of a constant radius sphere [5]. The standard spherical coordinate system (r, ) is used to identify any particular position on the sphere. However, only the two angular coordinates are needed for positional identification since the radial distan ce is maintained fixed. For the reason that it is impractical to measure a three-dimens ional pattern, the minimum number of twodimensional patterns needed to accurately re present the antenna radiation pattern is two [5]. A two-dimensional pattern is obt ained by fixing one of the angles ( or ) while varying the other [5]. For instance, elevati on or E-plane patterns are obtained by fixing (0 2 ) and varying (0 ), and azimuthal or H-pl ane patterns are obtained by fixing (0 ) while is varied (0 2 ) [5]. The Archimedean spiral antenna was tested in an indoor free-space antenna range or anechoic chamber. The anechoic chamber has walls covered with RF absorbers to suppress electromagnetic interference and is protected from environm ental conditions [5]. The source antenna was chosen to be a Ya gi antenna operating at 2.4 GHz. The Yagi antenna is connected to a signal source, such as a vector network analyzer. The spiral antenna was mounted to a rotational pedestal using a short semi-rigid RF coaxial cable.

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76 The rotational pedestal has the capability of rotating in various planes. The recording system is connected to the rotational mount, so that position references can be recorded simultaneously with measurements for angular positional identification [5]. Figures 3.43 and 3.44 show the radiation pa ttern measurements for the fabricated antenna characterized by two major circul ar lobes. The differences between the simulation and measurement could be explai ned by the fact that the spiral antenna simulations do not include the lumped-ele ment matching network, the Balun, and the coaxial RF connector. The Balun ground plane could have caused interference in the pattern measurement. Also, there could be s ources of error in the pattern measurement caused by the accuracy of directing the source an tenna beam directly to the spiral antenna under test.

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77 270 180 90 0 -7 -6 -5 -4 -3 -2 -1 0 1 Measured Simulated Figure 3.43 E-Plane Radiation Pattern Simulation and Measurement of Fabricated Spiral Antenna. TopE Plane Pattern. BottomAnte nna E-Plane Orientation. Red TraceSi mulation. Blue TraceMeasurement

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78 180 90 270 0 -20 -15 -10 -5 0 5 Measured Simulated Figure 3.44 H-Plane Radiation Pattern Simulation and Measurement of Fabricated Spiral Antenna. TopH Plane Pattern. BottomAnte nna H-Plane Orientation. Red TraceSi mulation. Blue TraceMeasurement 3.5.3 Balun Measurements A vector network analyzer (VNA) was used to measure the s-parameters of the back-to-back Balun design. A 2-port SOLT (Short-Open-Load-Thru) calibration was performed at the end of two coaxial RF cab les connected to port 1 and port 2 of the network analyzer by connecting a short, an ope n, and a load calibration standards to the end of each coaxial cable. Next, a thru connection was made between ports 1 and 2 through the coaxial cables. Then VNA computed the calibration coefficients to account and correct for the loss of the paths. Once our measurement setup was calibrated, the device under test (back-to-back Balun desi gn) was connected through the RF connectors

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79 at the unbalanced input of each Balun in between ports 1 a nd 2 of the VNA at the end of the coaxial cables. Then, the S-para meters were recorded on the VNA. Figure 3.45 shows the measured s-paramete rs of the back-to-back Balun design compared to the simulation results obtained with ADS. At 2.4 GHz, The S11 and S21 in dB from both simulation and measurements ar e close. For instance, S11 (dB) at 2.4GHz for the ADS design is -22.08 dB and for the me asured design is -21.11 dB. S21 (dB) at 2.4 GHz for the ADS design is -0.3 dB and for the measured design is -0.7 dB. However, there is a shift in th e response between measured data and simulations of about 50 MHz approximately. This frequency response shif t between the simulation and the measured data could be explained by the inductan ce added by the RF coaxial connectors. 2.32.42.5 2.22.6 -25 -20 -15 -10 -30 -5 Frequency (GHz)S11 (dB) 2.32.42.5 2.22.6 -3 -2 -1 -4 0 Frequency (GHz)S21 (dB) Figure 3.45 Measured S-parameters of Fabricated Back-t o-Back Balun Design. Red TraceADS Simulation. Blue TraceMeasured Data. Le ft PlotS11 (dB). Right Plot S21 (dB) 3.6 RF Coaxial Connector Electromagnetic Simulations The purpose of this section was to investig ate how RF coaxial connectors, such as the ones used for our fabricated designs, pe rform at the frequency range of interest. Therefore, the PSF-S01 end launch connector was chosen to be studied by means of electromagnetic simulations. The connector was drawn in HFSS using available dimensions from vendor’s datasheet. Dimensions that were not availa ble in the vendor’s datasheet, such as the

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80 diameter of the dielectric present between the inner and outer conductors and the diameter of the inner conductor, were meas ured using a micrometer. The dielectric present between the inner and outer conductor s was assumed to be a dielectric core material with a dielectric constant equal to 3.255. The connector was simulated in a back-toback configuration using a microstrip transmission line. The width of the microstr ip line was designed to be 50 ohms at 2.4 GHz, and the length was designed to be 64 de grees at 2.4 GHz. The ca lculated width and length were equal to 18.3 a nd 540 mils respectively. Th e substrate used for the simulations was an 8-mil thick RO4003 Rogers material with a dielectric constant equal to 3.38. Wave port assignments were used as the excitations at the input of each connector as shown by figure 3.46. We expect for a good RF connector to have a return loss of 20dB or better and an insertion loss of 0.2 dB or better at the designed frequency range of operation. Figure 3.47 shows the simulation results of the back -to-back connector design. The connector shows acceptable return and insertion loss performance to 3GHz based on the expected standards of operation for RF coaxial connectors. At our fre quency of interest of 2.4 GHz, the return and insertion loss are equal to 23.4 and 0.08 dB respectively.

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81 Figure 3.46 Back-to-Back Connector Design. Top LeftConnector Design in HFSS. Top RightAir Boundary Assignment. Bottom LeftWave Port 1 Refe rence Plane. Bottom RightWave Port 2 Reference Plane 0.51.01.52.02.53.03.5 0.04.0 -50 -40 -30 -20 -60 -10 Frequency (GHz)Return Loss (dB) 0.51.01.52.02.53.03.5 0.04.0 -0.3 -0.2 -0.1 -0.4 0.0 Frequency (GHz)Insertion Loss (dB) Figure 3.47 S-parameter Simulations of Back-to-B ack Connector Design. Left PlotReturn Loss (dB). Right PlotInsertion Loss (dB) 3.7 Summary and Conclusions With the aim of electromagnetic and circuit-level simulations, the Archimedean spiral antenna performance was successfully analyzed to the point where it is connected to the balanced feed network. It was shown th at the twin-strip line feeding configuration does not affect the radiation ch aracteristics of the antenna. It was also demonstrated that there is a trade-off in the antenna performance when the substrate backing up the antenna is reduced in thickness from an ideal /4 thickness.

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82 A narrow-band feed network involving a planar Balun was designed and simulated using the Agilent Advanced Design Sy stem (ADS) software in order to connect the antenna balanced input to an unbalan ced line for fabrica tion and measurement purposes. Furthermore, the Balun was measured with the antenna as well as separate from the antenna in a back-to-back configur ation. Both the Archimedean spiral antenna and Balun measurements agre ed with the simulations. The RF coaxial connector was also simula ted in HFSS in a two-port back-to-back configuration so as to investigate its performance at the fr equency range of interest of 2.4 GHz. Based on the expected standards of operation for RF coaxial connectors, the connector showed acceptable return and insertion loss performance to 3GHz.

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83 Chapter 4 Frequency Selective Surfaces 4.1 Introduction As it was shown on chapters 2 and 3, the radiation properties of an antenna are affected by the presence of a perfect electric conducting (PEC) ground plane. Moreover, if the antenna is placed too close to this conducting surface, the image currents cancel the currents in the antenna resulting in poor radiation efficiency [17]. In order to prevent poor radiation efficiency due to the close proxim ity of a ground plane to the antenna, a quarterwavelength space can be included between th e radiating element and the ground plane. However, this design approach brings a fixed thickness of /4 into the backing configuration that not only increases the ov erall physical dimensions of the antenna but also limits the performance of inherently br oad-band antennas such as the spiral antennas discussed in chapter 2 and 3. Metals support electromagnetic surface wa ves that bond to the interface between metal and free space and do not couple to exte rnal plane waves if the surface is smooth and flat [17]. By incorporating a special texture on a conducting surface, it is possible to alter its radio-frequency electromagnetic prop erties as well as its surface impedance [17]. This type of metal surfaces coated with resonant structures is known as frequency selective surfaces (FSS) and can serve as a substrate for antennas allowing them to lie directly adjacent to the ground plane su rface without being shorted out [18].

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84 In this chapter, the background theory of operation for frequency selective surfaces is analyzed, and a low-frequency stru cture operating at 2.4GHz is evaluated that could potentially be used to miniat urize an antenna in the z-direction. 4.2 Theory of Operation A frequency-selective surface is a surf ace which exhibits different reflection and/or transmission properties as a function of frequency [1]. Two basic types of FSS are an array of dipoles and an array of slots bo th followed by a dielectric slab. An array of resonant dipoles acts as a band-stop filter by passing waves above and below the dipole resonant frequency but not at the resona nt frequency. On the other hand, the complementary array of slots acts as a band -pass filter by passing waves at the resonant frequency of the slots but rejecting them at higher and lower frequencies. As shown by figure 4.1, the action of the dipoles is equivalent to that of a series-tuned circuit on a transmission line and that of the slots is anal ogous to a parallel tune d circuit. Therefore, the inductor and capacitor resonate at the pass or stop frequencies. Surface waves travel on a flat metal c onductor until they reach an edge where they can radiate into free space translating into a multi-path interference that can be seen as ripples in the radiation pattern [17]. On the contrary, surface waves will radiate vertically if scattered by a surface textur e. Smooth conducting sheets have low surface impedance, but a textured surface or FSS can have high surface impedance (greater than 377 ohms).

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85 Figure 4.1 Basic Frequency Selective Surfaces [1] The type of FSS described in this chapter consists of a lattice of small mushroomshaped protrusions made of metal plat es, connected to a common ground plane by vertical metal pins as shown by figure 4.2 [18] The surface impedance of this structure is characterized by an equivalent parallel resonant LC circ uit and is given by equation 4.1. At low frequencies it is inducti ve and supports transverse ma gnetic (TM) waves. At high frequencies it is capacitive and supports transverse electric (TE) waves. Near the LC resonance frequency (equation 4.2), the surface impedance is very high and electromagnetic waves are reflected with zero phase shift. In this region, waves are not bound to the surface but radiate readily in to the surrounding space. The fractional bandwidth of the gap between the TM and TE bands is given by equation 4.3 where t is the thickness of the surface and o is the wavelength at resonance.

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86 Figure 4.2 Cross Section and Top Vi ew of a High-Impedance Surface [17] Z s j L 1 2L C (4.1) o 1 LC (4.2) Bt 2 o (4.3) As the structure shown on figure 4.2 inte racts with electromagnetic waves, currents are induced in the top metal plates [17]. A capacitance is built up on the ends of the plates as a voltage is applied to the top surface. An inductance is formed by the magnetic field associated with the currents that flow around a path through the vias and bottom plate. Therefore, in a two-layer de sign such as the one shown on figure 4.2, the capacitors are formed by the fringing electric fields between adjacen t metal patches, and the inductance is fixed by the thickness of the structure.

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87 The three-layer design structure shown on figure 4.3 achieves a lower resonance frequency for a given thickness by using capacitiv e loading that consists of parallel-plate capacitors formed by the top two overlapping layers [17]. This lo w-frequency structure would work perfectly for the spiral antenna s described on chapter 2 operating at 2.4 GHz. This design can maintain a thickness of a few millimeters with a corresponding inductance of a few nanohenrys and a capacitance of several picofarads. However, by forcing a thin structure to have a low resona nce frequency, the bandwid th is also reduced. Operating bandwidths of 6 GHz are common fo r two-layer FSS structures at a design frequency of 14 GHz. Moreover, operati ng bandwidths of 400 MHz are common for three-layer FSS structures at a design freque ncy of 2.4 GHz. The overall thickness of a low-frequency FSS structure operating at 2.4 GHz can be about 4 mm, which is considered a miniature backing design for an antenna compared to the /4 thick substrate approach with a thickness of about 21 mm at 2.4 GHz. Figure 4.3 Three-Layer High-Impedance Surface [17] The high-impedance surface is particularly applicable to the field of portable hand-held communications, in wh ich the interaction between the antenna and the user can have a significant impact on antenna perf ormance. Moreover, using this ground plane structure as a shield between the antenna and the user in portable communications equipment can lead to higher antenna effici ency, longer battery life, and lower weight [17].

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88 As shown in [8], by placing a spiral antenna over a FSS structure rather than a PEC ground plane, a reduction of more than 69% in antenna height can be obtained. Furthermore, in order to maintain the inhere nt frequency-independent characteristics of a spiral antenna, varactor diodes or reversed -biased diodes can be connected between each unit cell in the periodic su rface texture and its four ne ighbors to tune the resonance frequency by changing the voltage of the diodes which adjusts the capacitance between neighboring cells as shown in [19]. 4.3 Summary and Conclusions Antennas can be potentially miniaturized in the z-direction by replacing the PEC ground plane separated from the antenna by a /4 thick substrate with a FSS structure that allows the ground plane conductor to be in close proximity to the antenna without affecting its radiation performance. This type of high impedance st ructure not only makes it possible to reduce the antenna height by at least 69%, but also pr ovides the opportunity of maintaining broad-band antenna responses by means of including tunable varactor diodes to the structure that adjusts the res onance frequency of the FSS. Lastly, a twolayer FSS structure operating at 2.4 GHz was pres ented that could serve as the substrate for the spiral antenna designs introduced in chapters 2 and 3 to make them miniature in the z-direction.

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89 Chapter 5 Miniature Coil Antennas 5.1 Introduction Advances in technology have placed a great emphasis not only on broadband antennas to cover an entire design application range but al so on antenna miniaturization to cope with the demands of making electr onic devices smaller. There are fundamental limits to how small an antenna can be at a particular wavelength and still behave as an efficient radiating device. In this chapter, the fundamental limits of electrically small antennas are studied to distinguish and ex amine the restrictions of miniature coil antennas. Research and measurement characterizati on were oriented to investigate the feasibility of using chip inductors mounted in a 1-port configuration as electrically and physically small helical antennas operating at the frequency range of 1 to 3 GH. The research focuses on reflection coefficient and radiation efficiency measurements in order to characterize coil performance as electrically small antennas. 5.2 Background Theory Antenna size with respect to the wavelengt h is the parameter that will have the major influence on the radiation characteristics such as gain, efficiency, and polarization purity [16]. An antenna is considered to be electrically small when its maximum physical dimension is small compared to the opera ting wavelength [14]. Therefore, the coil

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90 inductors used for this inves tigation are considered to be electrically small based on the physical dimensions and operating wa velengths shown on tables 5.1 and 5.2. A coil inductor can be analy zed as a helical antenna, wh ich is a conduc tor that is wound into a helical shape and properly fed at the input of the heli x [4]. Figure 5.1 shows the typical geometry for a helix with N turns, where D is the diameter of helix calculated between centers of coil material, d is the di ameter of helix conductor, S is the spacing between turns, and L is the le ngth of one turn. The length of one turn is given by equation 5.1, where C is the circumference of helix equal to D [4]. Another important parameter of the helical antenna is the pitch angle defined by equation 5.2, which is the angle formed by a line tangent to the helix wire and a plane perpendicular to the helix axis [5]. Figure 5.1 Typical Geometry for a Helix LC2S 2 (5.1) tan S C (5.2) A helix of fixed diameter collapses to a loop as the spacing between turns approaches zero ( =0) [15]. On the other hand, a he lix of fixed spacing between turns straightens out into a lin ear conductor as the diam eter approaches zero ( =90) [15].

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91 Therefore, a true helix is formed when the pitch angle is between 0 and 90 degrees (0< <90) with a circumference greater than ze ro but less than the circumference when the helix is reduced to a loop [5]. The radiation charac teristics of the antenna can be varied by controlling the size of its geomet rical properties compared to the wavelength [5]. Moreover, the input impedance is critic ally dependent upon th e pitch angle and the size of the conducting wire [5]. The coil inductors used for this investig ation can be compared to helical antennas operating in the normal mode of radiation that occurs when the dime nsions of the helix are small compared to the operating wavele ngth, and hence they have neither a wideband nor a high efficiency [15] This normal mode of operati on is related to the lowest transmission mode of operation To used to describe how an electromagnetic wave propagates along an infinitely long helix [15]. In this mode, a helix has adjacent regions of positive and negative charge separated by many turns. This is the mode that occurs on low frequency inductances [15]. A helical antenna operating in the norma l radiation mode exhibits maximum radiation broadside to the plane of the antenna and the current is assumed to be uniform in magnitude and in-phase over the entire le ngth of the helix [15]. For a small helix (L<< ), the far-field is independent of the number of turns. Th erefore, the axial ratio of the polarization ellipse can be defined as the ratio of the far-field E component of the short dipole to the far-field E component of the small loop [15]. E and E are 90 degrees out of phase. Helical antennas could have circular polariza tion instead of elliptical polarization if the magnitudes of the E and E components are equal.

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92 5.3 Measurement Characterization The inductors used for this investig ation were 0402 and 0603 Coilcraft surface mount chip inductors with inductances of 47 and 270nH respectively. The radiation efficiency varies depending upon the directio n the inductor is bonded [10]. Consequently, the responses of six 1-port configurations we re analyzed to determine the most efficient design pattern. The 0402 inductors have a rema rkable difference in the wire windings across them. The spacing between each wire tu rn changes across the inductor length, so the wire windings look more closely spaced towards one end of the coil wrap-up. Thus, this difference was taken as the reference point to bond the 0402 inductors in six different 1-port orientations. On the other hand, the 0603 inductors have a pol arity dot marked on one side of the plastic cap covering the top of the surface mount chip, which was taken as the reference point to bond these inductors in the six different 1-port orientations, as shown by figure 5.2. Figure 5.2 Six 1-Port Bonding Co nfigurations Used to Characteri ze Surface Mount Chip Inductors as Miniature Antennas

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93 Based on preliminary s-parameter meas urements, the 0402 and 0603 inductors showed a lower reflection response when bonded vertically on the side of the reference point looking away from the feed line. Also, the inducto rs bonded horizontally on the reference point side showed a promising re flection response. The best vertical and horizontal orientations were chosen for th e subsequent measurements and calculations (figure 5.3). Figure 5.3 Surface Mount Chip Induct or. LeftVertical Conf iguration. MiddleHori zontal Configuration. RightInductor Parameters Total wire length and diameter of elect rically small antennas are two of the physical properties that influence their elect romagnetic behavior. Therefore, we estimated these resonant properties based on the numbe r of turns, effectiv e length, width, and height of the inductors provided on the Coilcra ft datasheets (figure 5.3). Estimated values for total wire length and diameter were obt ained using formulas 5.3 and 5.4 respectively, where “N” is the number of turns, “E” is the effective length, “C” is the effective width, and “G” is the effective height. The estimated values are summarized on table 5.1. Moreover, the pitch angle was estimated for the 47nH 0402 and 270nH 0603 chip inductors to be equal to 6.9 and 7.7 degrees respectively. LEN 2 ()CN 2 () (5.3) d G N (5.4)

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94Table 5.1 Calculation of Inductor Parameters Inductor / Parameters E (mm) C (mm) G (mm) N d (mm) L (mm) 47nH (0402) 0.51 0.66 0.56 13 0.043 30 270nH (0603) 0.76 1.07 0.86 23 0.037 84 Strong radiation is observed when the i nductor’s wire length is approximately 0.45 o [10]. According to the calculations sh own in table 5.2, the wavelengths were corrected to account for the i nductor’s geometry, which essent ially consists of the wire being wrapped around a Teflon core. Thus, the wavelengths ( o) were divided by the square root of the dielectric constant of Teflon that is equal to 2.1. The Teflon-corrected wavelength ( g) and optimal wire length (0.45 g) values are summarized in table 5.2. By comparing the optimal 0.45 g wire lengths calculated at the radiation frequencies to the actual stretched lengths, we concluded that they match well. For instance, in the case of the 47nH 0402 inductor, the total estimated wire length is 30 mm (table 5.1), and the 0.45 g values for the vertical and horiz ontal 1-port configurations are 33 and 44 mm, respectively (table 5.2). Simi larly, for the 270 nH 0603 inductor, the estimated wire length is 84 mm (table 5.1), and the 0.45 g values for the vertical and horizontal 1-port configurations are 87 and 83 mm, respectively (table 5.2). Since we did not find an equation that relates bonding orient ation to radiation effi ciency, we used the best vertical and horizontal orientati ons found in the preliminary s-parameter measurements for subsequent measurements and radiation parameters calculations.

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95Table 5.2 Calculation of Wire Length for Optimal Radiation Performance Inductor Bonding Configuration fo (GHz) o (mm) g Teflon (mm) 0.45* g (mm) 47nH (0402) 1-port Vertical 2.861 105 72 33 47nH (0402) 1-port Horizontal 2.14 140 97 44 270nH (0603) 1-port Vertical 1.07 280 193 87 270nH (0603) 1-port Horizontal 1.12 268 185 83 5.3.1 S-parameter Measurements S-parameter measurements were performed using the best vertical and horizontal 1-port configurations with the samples ra diating into free space (figure 5.4). Samples were mounted on 59 mil thick FR4 test fixtur es, which were also used for efficiency measurements. These S-parameter measurements were also repeated with the samples inside a conducting sphere for efficiency calculation purposes. The loss factor or mismatch loss for these 1-port measurements was calculated using equation 5.5. Moreover, the loss factor of the miniature coil antennas (inductors bonded in a 1-port configuration), when radiati ng into free space as well as inside a conducting sphere (Wheeler cap), provides an in sight into the radiation e fficiency of the antennas. LF1S11 2 (5.5)

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96 Figure 5.4 S-parameters of 270 nH 0603 Coil Inductor Bonded in a 1-Port Configuration Radiating into Free Space. Top LeftBroad-band S11 (dB) Response. Top RightBroad-band Loss Factor. Bottom LeftNarrow-band S11 (dB) Reponse. Bottom RightNarrow-band Loss Factor. Red TraceInductor Bonded in a Vertical Configuration. Blue TraceInductor Bonded in a Horizontal Configuration 5.3.2 Efficiency Measurements An electrically small antenna can be represented by a lumped element circuit whose input impedance is given by equation 5.6, where RA is the real part of the antenna’s input impedance and XA is the antenna’s reactance [5]. The real part of the antenna’s input impedance is defined by equation 5.7, where Rr is the radiation resistance and RL is the loss resistance of the antenna [5]. Z A R A jX A (5.6) R A R r R L (5.7) 246 08 -2.0 -1.5 -1.0 -0.5 0.0 -2.5 0.5 Frequency (GHz)S11 (dB) 270nH 0603 (1-port Configuration) 246 08 0.0 0.1 0.2 0.3 -0.1 0.4 Frequency (GHz)Loss Factor 270 n H 0603 (1 -por t C on fi gura ti on ) Vertical Configuration Horizontal Configuration Vertical Configuration Horizontal Configuration 246 08 -2.0 -1.5 -1.0 -0.5 0.0 -2.5 0.5 Frequency (GHz)S11 (dB) 270nH 0603 (1-port Configuration) 246 08 0.0 0.1 0.2 0.3 -0.1 0.4 Frequency (GHz)Loss Factor 270 n H 0603 (1 -por t C on fi gura ti on ) Vertical Configuration Horizontal Configuration Vertical Configuration Horizontal Configuration Vertical Configuration Horizontal Configuration Vertical Configuration Horizontal Configuration m1 freq= m1=-1.092 1.070GHz m2 freq= m2=-1.839 1.120GHz 0.51.01.5 0.02. 0 -2.0 -1.5 -1.0 -0.5 0.0 -2.5 0.5 Frequency (GHz)S11 (dB) m1 m2270nH 0603 (1-port Configuration)m3 freq= m3=0.222 1.070GHz m4 freq= m4=0.345 1.120GHz 0.51.01.5 0.02. 0 0.0 0.1 0.2 0.3 -0.1 0.4 Frequency (GHz)Loss Factor m3 m4270nH 0603 (1-port Configuration)Vertical Configuration Horizontal Configuration Vertical Configuration Horizontal Configuration m1 freq= m1=-1.092 1.070GHz m2 freq= m2=-1.839 1.120GHz 0.51.01.5 0.02. 0 -2.0 -1.5 -1.0 -0.5 0.0 -2.5 0.5 Frequency (GHz)S11 (dB) m1 m2270nH 0603 (1-port Configuration)m3 freq= m3=0.222 1.070GHz m4 freq= m4=0.345 1.120GHz 0.51.01.5 0.02. 0 0.0 0.1 0.2 0.3 -0.1 0.4 Frequency (GHz)Loss Factor m3 m4270nH 0603 (1-port Configuration)Vertical Configuration Horizontal Configuration Vertical Configuration Horizontal Configuration Vertical Configuration Horizontal Configuration Vertical Configuration Horizontal Configuration

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97 The radiation resistance accounts for the ra diated power and the loss resistance accounts for the dissipated power. The total antenna efficiency eo is given by equation 5.8, where er is the reflection efficiency and ecd is the conduction and dielectric efficiency. Reflection efficien cy represents the mismatch between the transmission line and the antenna, and conduction an d dielectric efficiency repres ent dissipative losses [5]. Reflection and conduction efficiency are de fined by equations 5.9 and 5.10 respectively. e o e r e cd (5.8) e r 1 2 (5.9) e cd R r R L R r (5.10) Efficiency measurements are performed to experimentally find the loss resistance of the antenna by using the principles of the Wheeler Cap method. This method consists of placing the antenna inside a conducting shell, which effectively eliminates Rr [11]. Therefore, the resistive term of the antenna ’s input impedance given by equation 5.7 will be only determined by loss resistance RL when the antenna is measured inside the conducting shell environment. Then, the radi ation resistance can be experimentally determined by subtracting the input impedance of the antenna measured with the antenna inside the shell from the input impedance of the antenna radia ting into an anechoic environment [12]. The conducting shell or Wheeler cap used for efficiency measurements is shown in figure 5.5. This Wheeler cap consists of a rectangular cavity milled in the center of a piece of aluminum carrier. The chip inductor sample mounted on a FR4 test fixture is

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98 placed inside this cavity with the RF coaxial connector sticking out of the cavity. The size of this cavity is 3.1 cm long, 1 cm wide, and 0.5 cm deep. An RF coaxial cable was used to connect the chip inductor sample to port 1 of the Vector Networ k Analyzer to perform S-parameter measurements. Figure 5.5 Effici ency Measurements S-parameter measurements were performed with the samples inside the Wheeler cap (figure 5.5). Then, radiation efficien cy was calculated using equation 5.11, where S11wc refers to the measurements when the antennas are inside the Wheeler cap, and S11fs refers to the measurements when the an tennas are radiating into free space. Figure 5.6 shows the s-parameter measurements of the inductor antennas radiating inside the Wheeler Cap, and Figure 5.7 shows ra diation efficiency calculations. Equation 5.11 describes the constant power loss method to calculate radiation efficiency for small antennas (i.e., < /10). Equation 5.11 is proven to be mathematically equivalent to equation 5.10 [13]. This met hod assumes a constant power loss for a small antenna, with and without the Wheeler cap, whos e radiation resistance is typically small in comparison to the 50-ohm measuring syst em source resistance [13]. The constant power loss method follows the same measurem ent principles as the Wheeler Cap method and defines radiation efficiency as the ra tio of total power radiated by total power accepted by the antenna at its input terminals during radiation [5].

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99 S11 wc 2S11 fs 2 1S11 fs 2 (5.11) Figure 5.6 S-parameters of 270 nH 0603 Coil Inductor Bonded in a 1-Port Configuration Radiating Inside the Wheeler Cap. Top LeftBroad-band S11 (dB) Response. Top RightBroad-band Loss Factor. Bottom LeftNarrow-band S11 (dB) Reponse. Bottom Right Narrow-band Loss Factor. Red TraceInductor Bonded in a Vertical Co nfiguration. Blue TraceInductor Bond ed in a Horizontal Configuration m7 freq= m7=0.576 995.3MHz m8 freq= m8=0.332 1.120GHz 0.51.01.5 0.02. 0 0.0 0.2 0.4 0.6 -0.2 0.8 Frequency (GHz)Loss Factor m7 m8270nH 0603 (1-port Configuration)m5 freq= m5=-3.723 995.3MHz m6 freq= m6=-1.753 1.120GHz 0.51.01.5 0.02. 0 -4 -3 -2 -1 0 -5 1 Frequency (GHz)S11 (dB) m5 m6270nH 0603 (1-port Configuration)Vertical Configuration Horizontal Configuration Vertical Configuration Horizontal Configuration m7 freq= m7=0.576 995.3MHz m8 freq= m8=0.332 1.120GHz 0.51.01.5 0.02. 0 0.0 0.2 0.4 0.6 -0.2 0.8 Frequency (GHz)Loss Factor m7 m8270nH 0603 (1-port Configuration)m5 freq= m5=-3.723 995.3MHz m6 freq= m6=-1.753 1.120GHz 0.51.01.5 0.02. 0 -4 -3 -2 -1 0 -5 1 Frequency (GHz)S11 (dB) m5 m6270nH 0603 (1-port Configuration)m7 freq= m7=0.576 995.3MHz m8 freq= m8=0.332 1.120GHz 0.51.01.5 0.02. 0 0.0 0.2 0.4 0.6 -0.2 0.8 Frequency (GHz)Loss Factor m7 m8270nH 0603 (1-port Configuration)m5 freq= m5=-3.723 995.3MHz m6 freq= m6=-1.753 1.120GHz 0.51.01.5 0.02. 0 -4 -3 -2 -1 0 -5 1 Frequency (GHz)S11 (dB) m5 m6270nH 0603 (1-port Configuration)Vertical Configuration Horizontal Configuration Vertical Configuration Horizontal Configuration Vertical Configuration Horizontal Configuration Vertical Configuration Horizontal Configuration 246 08 -4 -3 -2 -1 0 -5 1 Frequency (GHz)S11 (dB) 270nH 0603 (1-port Configuration) 246 08 0.0 0.2 0.4 0.6 -0.2 0.8 Frequency (GHz)Loss Factor 270nH 0603 (1-port Configuration)Vertical Configuration Horizontal Configuration Vertical Configuration Horizontal Configuration 246 08 -4 -3 -2 -1 0 -5 1 Frequency (GHz)S11 (dB) 270nH 0603 (1-port Configuration) 246 08 0.0 0.2 0.4 0.6 -0.2 0.8 Frequency (GHz)Loss Factor 270nH 0603 (1-port Configuration)Vertical Configuration Horizontal Configuration Vertical Configuration Horizontal Configuration Vertical Configuration Horizontal Configuration Vertical Configuration Horizontal Configuration

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100 Figure 5.7 Radiation Efficiency of 270 nH 0603 Coil Inductor Bonded in a 1-Port Configuration. Top LeftBroad-band Response of Inductor in a Vertical Configuration. Top RightBroad-band Response of Inductor in a Horizontal Configuration. Bottom LeftNarrow-band Response of Inductor in a Vertical Configuration. Bottom RightNarrow-band Response of Inductor in a Horizontal Configuration For the vertical 270nH 0603 sample, we obt ained a very high efficiency of 91.6%, which is explained by a shift in resona nce frequency from 1.070 GHz to 995.3 MHz rather than the existence of high radiation efficiency. In ad dition, the horizontal 270nH 0603 sample showed a very low radiation efficiency of 3.8% without a shift in resonance frequency. The loss factor does not signific antly decrease when placed inside the Wheeler cap, generating this low efficiency ; in fact, in some cases the loss factor increases when measured inside the Wheeler Cap. Based on our current efficiency results, we can conclude that these coil inductors have resonant freque ncies with very low radiation efficiencies. m9 freq= m9=0.916 1.070GHz 0.51.01.5 0.02. 0 -1 0 1 -2 2 Frequency (GHz)Radiation Efficiency m9Constant Power Loss Methodm10 freq= m10=0.038 1.120GHz 0.51.01.5 0.02. 0 -1 0 1 -2 2 Frequency (GHz)Radiation Efficienc y m10Constant Power Loss Methodm9 freq= m9=0.916 1.070GHz 0.51.01.5 0.02. 0 -1 0 1 -2 2 Frequency (GHz)Radiation Efficiency m9Constant Power Loss Methodm10 freq= m10=0.038 1.120GHz 0.51.01.5 0.02. 0 -1 0 1 -2 2 Frequency (GHz)Radiation Efficienc y m10Constant Power Loss Method 246 08 -1 0 1 -2 2 Frequency (GHz)Radiation EfficiencyConstant Power Loss Method 246 08 -1 0 1 -2 2 Frequency (GHz) R a di a ti on Effi c i encyConstant Power Loss Method

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101 In order for the loss mechanisms and near fields of the antenna to behave the same way when inside the conducting sphere (Wh eeler cap) as when it is radiating in free space, the Wheeler cap s hould have a radius of /2 [10]. This radius represents the transition between the antenna’s energy-storing near-field and its radiating far-field [5]. The Wheeler cap used for the efficiency meas urements did not have the specified radius, and this could have disturbed the coil antenn as’ near fields producing the frequency shift between shielded and unshielded measurements as well as the high loss for the shielded measurements. Moreover, electrically sma ll antennas are difficult to measure properly because when they are connected to a measur ing device a current w ill flow in the outer conductor of the cable connect ing the antenna crea ting spurious radi ation [16]. This spurious radiation will freque ntly completely mask the characteristics of the antenna under test yielding results that in clude the connecting cable [16]. Antennas are resonant at a frequency where they exhibit the greatest effective volume, and their resonant Q decreases with increasing effective volume [14]. Furthermore, antennas with dimensions which are small compared to a wavelength exhibit large radiation quality factors. Radiation quality factor Q equals the antenna reactance (stored energy) divide d by the antenna resistance (radiated energy) [14]. Thus, there is more non-propagating energy stor ed than energy radiated leading to predominantly reactive input impedances. Al so, because of the large radiation quality factors, the presence of even small resistive losses leads to very low efficiencies [12]. The basic limitations of electrically sm all antennas are imposed by the free-space wavelength that the antenna element must coupl e to [5]. These limitations are derived by assuming that the entire antenna structure with a largest linear dimension of 2r is

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102 enclosed within a sphere of radius r [5]. When the sphere enclosing the antenna element becomes very small, there ex ist no propagating modes so th e Q of the system becomes very large. Thus, the fundamental limit on the electrical size of an antenna is related to the lowest achievable Q at its largest linea r dimension, which is independent of the geometrical configuration of th e antenna within the sphere of radius r [5]. The shape of the radiating element within the bounds of the sphere only determines what modes are excited [5]. The fundamental limit of elect rically small antennas is given by equation 5.12, where k is the wave number equal to 2 / and r is the radius of the sphere enclosing the antenna [16]. Q 1 kr ()3 (5.12) Figure 5.8 shows how the input impedance for the 270nH 0603 coil inductor bonded vertically and horizontally is predominantly reactive at the resonant frequencies. For instance, the inductor in a vertical conf iguration has an input impedance equal to 19.11-119.93j, and the inductor in a horizontal configuration has an input impedance equal to 35.105-113.5j. Therefore, there is more non-propagating energy stored than energy radiated.

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103 Figure 5.8 Input impedance of 270 nH 0603 Coil Inductor Bonded in a 1-Port Configuration Radiating in Free Space. Top LeftBroad-band Plot of Input Impedance for the Coil Inductor Bonded in a Vertical Configuration. Top RightBroad-band Plot of Input Impedance for the Coil Inductor Bonded in a Horizontal Configuration. Bottom LeftNarrow-band Plot of Input Impedance for the Coil Inductor Bonded in a Vertical Configuration. Bottom RightNarrow-band Plot of Input Impedance for the Coil Inductor Bonded in a Horizontal Configuration. Red TraceZin (real). Blue TraceZin (imag) In [11], the efficiency measurement of a lossy monopole consisting of a copper strip with three 10-ohm resistor s placed at interval of 1/ 6, 1/2, and 5/6 along the antenna length is presented. At 950 MHz, the measur ed antenna efficiency is about 65%. The radiation efficiency of this monopole with different copper wire diameters ranging from 0.5 to 1.6 mm is also presented in this wor k. It is shown that monopoles with largerdiameter wires measured higher efficienc y. Fort instance, a monopole with a wire diameter equal to 1.6 mm had a radiation effi ciency of 98% at 950 MHz, and a monopole with wire diameter equal to 0.5 mm had a ra diation efficiency of 87% at 950 MHz. All 0.51.01.5 0.02.0 -150 -100 -50 0 -200 50 Frequency (GHz)Zin m17 m18270nH 0603 (1-port Configuration) m17 freq= real(Zin2)=35.105 1.121GHz m18 freq= imag(Zin2)=-113.504 1.121GHz 0.51.01.5 0.02.0 -150 -100 -50 0 -200 50 Frequency (GHz)Zin m13 m14270nH 0603 (1-port Configuration) m13 freq= real(Zin1)=19.114 1.076GHz m14 freq= imag(Zin1)=-119.932 1.076GHz 12345 06 -300 -150 0 -450 150 Frequency (GHz)Zin 270nH 0603 (1-port Configuration) 12345 06 -300 -150 0 -450 150 Frequency (GHz)Zin 270nH 0603 (1-port Configuration)

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104 the monopoles presented in [11] had a length of 85 mm, and were centrally mounted on a 220 mm by 220 mm ground plane. Similarly, the radiation efficiency measurement of a modified bow-tie antenna constructed as a monopole (also called a waveguide-to-coax transition) with a large surface area to mini mize conductor losses is presented in [11]. The efficiency was found to be equal to 99.17%. These radiation efficiency values reported in the literature for small antennas c onfirm that the surface mount chip inductors used in this investigation have very low radiation efficiencies. 5.4 Summary and Conclusions The fundamental limits to how small an an tenna can be at a pa rticular wavelength and still behave as an efficient radiati ng device were studied. The restrictions of miniature coil antennas were examined by conducting S-parameters and efficiency measurements characterization. The measurem ent results show that the coil inductors have resonant frequencies with very low radi ation efficiencies, which translates into the coil inductors not using effectively the availa ble volume within the sphere of radius r enclosing them. Moreover, the coil induct ors have predominan tly reactive input impedances at the resonant frequencies, which indicate that there is more nonpropagating energy stored th an energy radiated. Finally, even though the wheeler cap used for the efficiency measurements did not have the specified radius producing the frequency shift between shielded and unshielded measurements as well as the high loss for the shielded measurements, the coil inductors still have low efficiencies becau se of the predominantly reactive input impedances that make the presence of even small resistive losses decrease the efficiency.

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105 Chapter 6 Conclusions and Recommendations 6.1 Conclusions In this research work, the design of frequency independent antennas, an Archimedean spiral antenna, and a narrow-ba nd planar couple micr ostrip Balun were presented. Moreover, the designed Archimedea n spiral antenna integrated with the narrow-band Balun was successfully fabricated and tested to validate the performance predicted by the electromagnetic simulations. An analysis of frequency selective surfaces was also conducted in order to demonstrate their capability to miniaturize an antenna overall thickness by serving as backing ground planes. Lastly, the radiation properties of surface mount chip inductors were studied to in vestigate the feasibility of using them as electrically small antennas. An Equiangular and Archimedean spiral frequency independent antennas were designed and simulated as twoarm spirals for a frequency range of operation between 2 to 6 GHz. Simulations were performed with a ground plane locat ed approximately a quarter-wavelength from the antenna, and without a ground plane, to corroborate the expected performance. It was demonstrated that the presence of a ground plane backing the antenna redirects on e-half of the radiation into th e opposite direction, which improves the antenna peak gain by about 3 dB. Furt hermore, it was shown that when spiral antennas are backed by a quarter-wavele ngth substrate without a ground conducting

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106 plane present, the radiated waves tend to get stored in the dielectric so the peak gain shifts 180 degrees in the theta direction. The simulation results showed that even though the Archimedean and the equiangular spiral antennas have different equations defining them, their performance characteristics are si milar. For instance, the return loss, VSWR, total gain, and radiation characteristics follo w similar and expected trends. However, the Archimedean spiral had a more flat input impedance response, as well as circular polarization over a greater bandwid th than the equiangular spiral Despite the f act that the simulations were performed using a substr ate with a fixed el ectrical length of /4 calculated at 2.4 GHz, both spirals showed a broadband response at the designed frequency range. With the aim of electromagnetic and circuit-level simulations, the Archimedean spiral antenna performance was successfully analyzed to the point where it was connected to the balanced feed network. It was shown that the twin-strip line feeding configuration does not affect the radiation ch aracteristics of the antenna. It was also demonstrated that there is a trade-off in the antenna performance when the substrate backing up the antenna is reduced in thickness from an ideal /4 thickness. A narrow-band feed network that consists of a planar Balun was designed and simulated using the Agilent Advanced Design Sy stem (ADS) software in order to connect the antenna balanced input to an unbalan ced line for fabrica tion and measurement purposes. Furthermore, the Balun was measured with the antenna as well as separate from the antenna in a back-to-back configur ation. Both the Archimedean spiral antenna and Balun measurements agr eed with the simulations.

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107 A two-layer Frequency selective surf ace structure operating at 2.4 GHz was presented that could serve as the substrate for the Archimedean spiral antenna design to miniaturize its overall thickness. The FSS layer is static (not tuned) and thus the overall bandwidth reduces relative to the non-ground plane approach presen ted in Chapter 2. This type of high impedance structure not only makes it possible to reduce the antenna height by at least 69%, but also provides the opportunity of main taining broad-band antenna responses by means of including tunable varactor di odes to the structure that adjusts the resonance frequency of the FSS. Lastly, the fundamental limits to how sma ll an antenna can be at a particular wavelength and still behave as an efficient ra diating device were studied. The restrictions of surface mount chip inductors operating as miniature coil antennas were examined by conducting S-parameters and efficiency measurements characterization. The measurement results showed that the coil inductors have res onant frequencies with very low radiation efficiencies, which translates into the coil inductors not using effectively the available volume within the sphere of radius r enclosing them. Moreover, the measurement results also indi cated that the coil inductors have predominantly reactive input impedances at the resonant frequencie s due to the fact that there is more nonpropagating energy stored than energy radiated. 6.2 Recommendations for Future Work The simulations, analysis, and experime ntal data presented on the previous designs have provided interesting conclusi ons and ideas for future research work. Even though it was proved that the coil inducto rs have low efficiencies because of the predominantly reactive input impedances that make the presence of even small

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108 resistive losses decrease the efficiency, ther e is an important recommendation to validate expected results. It is advised to modify the wheeler cap used for the efficiency measurements to have the required quarter wa velength radius so that the frequency shift between shielded and unshielded measurements as well as the high loss for the shielded measurements can be resolved. Finally, a significant recommendation for future work regarding the frequency selective surfaces emphasizes the electromagne tic simulation of the low-frequency design operating at 2.4 GHz to validate the background theory and analysis presented in this research work. Integrating the 2.4 GHz fre quency selective surface design with tunable varactor diodes is another important recomm endation in order to exploit the inherently broad-band characteristics of the Archimedean spiral antenna.

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109 References [1] John D. Kraus, “Antennas for All Applications,” Mc Graw Hill, 3rd Edition, New York, 2003. [2] Robert E. Collin, “Antenna Theory,” Mc. Graw Hill, 2nd Edition, New York, 1969. [3] Thomas A. Milligan, “Modern An tenna Design,” John Wiley & Sons, 2nd Edition, New Jersey, 2005. [4] Warren L. Stutzman and G. A. Thiele “Antenna Theory and Design,” John Wiley & Sons, 1st Edition, New York, 1981. [5] C.A Balanis, “Antenna Theory Anal ysis and Design,” John Wiley & Sons, 2nd Edition, New York, 1982. [6] “Chapter 2: Analysis of Archimed ean Spiral Antenna.”, M.S.E.E. thesis, scholar.lib.vt.edu/thes es/available/unrestric ted/Caswell_etd_Ch2.pdf. [7] Ansoft Electronic Design Automation Software, “High Fr equency Structure Simulator v9 User’s Guide.” [8] Jodie M. Bell and Magdy F. Iskander, “A Low-Profile Archimedean Spiral Antenna Using an EBG Ground Plane,” IEEE Antennas and Wireless Propagation Letters, vol. 3, pp. 223-226, 2004. [9] David M. Pozar, “Microwave E ngineering,” John Wiley & Sons, 2nd Edition, New York, 1998. [10] E. Benabe, “Microwave Characteriza tion and Modeling of Air Coil Inductors and Ceramic Multilayer Capacitors,” M.S.E.E. thesis, University of South Florida, Tampa, Florida, 2000. [11] R. H. Johnston, J. G. McRory, “An im proved Small Antenna Radiation-Efficiency Measurement Method,” IEEE Antennas a nd Propagation Magazine, vol. 40, No. 5, October 1998. [12] J. S. McLean, “The Radiative Prope rties of Electrically-Small Antennas.” IEEE Trans. Ant. Prop., University of Wi sconsin-Madison, Madison, Wisconsin, 1994.

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110 [13] “Cellular Handset Antenna Efficiency Measurement Using the Wheeler Cap,” Skyworks Solutions, January 2005. [14] S. R. Best, “A Discussion on the Prope rties of Electrically Small Self-Resonant Wire Antennas,” IEEE Antennas and Pr opagation Magazine, vol. 46, No. 6, December 2004. [15] Rajeswari Chatterjee, “Antenna Theo ry and Practice,” John Wiley & Sons, 1st Edition, New York, 1988. [16] A. K. Skrivervik, J. F. Zurcher, O. Staub, and J. R. Mosig, “PCS Antenna Design; The Challenge of Miniaturization,” I EEE Antennas and Propagation magazine, vol. 43, No. 4, pp12-27, August 2001. [17] D. Sievenpiper, L. Zhang, R. Br oas, N. Alexopolous, and E. Yablonovitch, “High-Impedance Electromagnetic Surfaces with a Forbidden Frequency Band,” IEEE Transactions Microw. Theo ry Tech., vol. 47, no. 11, pp. 2059–2074, Nov. 1999. [18] D. Sievenpiper, “Forward and Back ward Leaky Wave Radiation with Large Effective Aperture from a Electronically Tunable Textured Surface,” IEEE Trans. Antennas Propag., vol. 53, no. 1, pp. 236–247, Jan. 2005. [19] D. Sievenpiper, J. Schaffner, H. J. Song, R. Loo, and G. Tangonan, “Two Dimensional Beam Steering Reflector Us ing an Electrically Tunable Impedance Surface,” IEEE Trans. Antennas Propag., vol. 51, no. 10, pp. 2713–2722, Oct. 2003.


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Electromagnetic characterization of miniature antennas for portable devices
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ABSTRACT: Advances in technology have placed a great emphasis on the design of broadband antennas as well as antenna miniaturization to cope with the demands of making electronic and handheld communication devices smaller and more efficient. In this thesis, the design and fabrication of a frequency independent antenna and a narrow-band planar microstrip Balun are presented. An analysis of frequency selective surfaces is also introduced in order to demonstrate their capability to miniaturize antenna thickness. Lastly, s-parameters measurements and efficiency characterization are performed to determine the radiation properties of surface mount chip inductors in order to determine the feasibility of using them as electrically small antennas.Two types of frequency independent antennas are considered due to their planar geometries, the Equiangular and Archimedean spiral antennas.^ Frequency independent antennas are radiating devices that have frequency independent impedance and pattern properties because their shape is specified only in terms of angles.The Balun is designed to meet the need of a feeding element for the Archimedean spiral antenna. A Balun is a three port device that connects an unbalanced transmission line such as a coaxial line to a balanced feed line such as the one required by two-arm spiral antennas. The Balun discussed in this work is designed to operate at 2.4 GHz with a 200 MHz bandwidth and to transform the antenna input impedance to a 50-ohm reference impedance. The main characteristics from this device that distinguish it from commercially available structures are its low cost, planarity, and compact footprint. The balancing capability of this Balun is shown by the close agreement between the measured and simulated results.^ Antennas can be potentially miniaturized in the z-direction by replacing the PEC ground plane separated from the antenna by a lambda /4 thick substrate with a frequency selective surface (FSS) structure that allows the ground plane conductor to be in close proximity to the antenna without affecting its radiation performance. The FSS layer operating at 2.4 GHz presented in this thesis is static (not tuned) and thus the overall bandwidth reduces approximately to the bandwidth obtained with the narrow-band Balun.
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