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Arm Spiral Antennas INVESTIGATION OF CYLINDRICALLY-CONFORMED FOUR- ARM SPIRAL ANTENNAS A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in Engineering By DOUGLAS JEREMY GLASS B.S.E.P., Wright State University, 2003 2007 Wright State University WRIGHT STATE UNIVERSITY SCHOOL OF GRADUATE STUDIES June 29, 2007 I HEREBY RECOMMEND THAT THE THESIS PREPARED UNDER MY SUPERVISION BY Douglas Jeremy Glass ENTITLED Investigation of Cylindrically- Conformed Four-Arm Spiral Antennas BE ACCEPTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF Master of Science in Engineering. _________________________________ Ronald Riechers, Ph.D. Thesis Director _________________________________ Fred Garber, Ph.D. Department Chair Committee on Final Examination _________________________________ Ronald Riechers, Ph.D. _________________________________ Fred Garber, Ph.D. _________________________________ Marian Kazimierczuk, Ph.D. _________________________________ Joseph F. Thomas, Jr., Ph.D. Dean, School of Graduate Studies ABSTRACT Glass, Douglas Jeremy, M.S. Egr., Department of Electrical Engineering, Wright State University, 2007. Investigation of Cylindrically-Conformed Four-Arm Spiral Antennas. A four-arm spiral antenna offers broadband frequency response, wide beamwidths, reduced size compared to other antenna designs, and the ability to determine the relative direction of an incident signal with appropriate mode-forming. The reduced overall area projection of the four-arm spiral antenna compared to other antenna designs and the ability to be manufactured in a planar format allows the antenna to reside within an Unmanned Air Vehicle (UAV) fuselage. This thesis investigates the effects of cylindrically-conforming two different designs of a four-arm spiral antenna to reside within the fuselage of a medium-sized UAV. Theoretical predictions of antenna performance were created using the Numerical Electromagnetics Code (NEC) package and compared to measured results of flat and cylindrically-conformed four-arm spiral antennas with and without ground plane apertures. iii Table of Contents Page 1. Introduction………………………………………………………………..…………1 1.1. Thesis Motivation…………………………………………………………...……1 1.2. Thesis Objectives…………………………………………………………………1 2. Frequency-Independent Antennas……………………………………...…………..2 2.1. Theory of Frequency Independence…………………………………………..….2 2.2. Types of Frequency-Independent Antennas…………………………………...…5 2.2.1. Biconical Antennas……………………………………………………..…5 2.2.2. Log-Periodic Antennas……………………………………............…..…..8 2.2.3. Spiral Antennas……………………………………………………….….12 2.3. Modal Behavior of the Spiral Antenna…………………………………….....…19 3. Antenna System Development……………………………………….….………....26 3.1. Spiral Antenna Development………………………………………………...….26 3.1.1. Spiral Antenna Design……………………………………………...……26 3.1.2. Spiral Antenna Fabrication………………………………………...…….28 3.2. Mode-Former Development…………………………………………………….35 3.2.1. Mode-Former Design ……………………………………………………35 3.2.2. Mode-Former Fabrication ……………………………………………….36 4. Theoretical Model……………………………………………………….……….…39 4.1. Maxwell’s Equations……………………………………………………...…….39 4.2. Numerical Electromagnetics Code Discussion…………………………...……..41 4.2.1. Integral Equations……………………………………………………..…41 4.2.2. Thin Wire Approximation…………………………………………..……44 4.2.3. Method of Moments Solution Method……………………………….…..48 4.3. Numerical Electromagnetics Code Results…………………………………..…54 4.3.1. Archimedean Spiral……………………………………………….……..55 4.3.2. Cylindrically-Conformed Archimedean Spiral………………………..…66 4.3.3. Square Spiral…………………………………………………………..…76 4.3.4. Cylindrically-Conformed Square Spiral……………………………..…..86 4.3.5. Radius of Curvature Analysis of the Archimedean Spiral…………….…96 5. Measured Results…………………………………………………………..…..….102 5.1. Measurement Method………………………………………………………….102 5.1.1. Vector Network Analyzer Discussion………………………………….103 5.1.2. Reference Antenna Discussion…………………………………………104 5.1.3. Desktop Antenna Measurement System Discussion……………………105 5.2. Mode-Former Results………………………………………………………….107 iv 5.2.1. Power Pattern Phase Balance Comparison……………………………..113 5.3. Spiral Antenna Results………………………………………………...………119 5.3.1. Archimedean Spiral……………………………………………...……..120 5.3.2. Cylindrically-Conformed Archimedean Spiral…………………………125 5.3.3. Square Spiral……………………………………………………...…….130 5.3.4. Cylindrically-Conformed Square Spiral………………………………..135 5.3.5. Square Spiral within Ground Plane Aperture……………………….….140 5.3.6. Cylindrically-Conformed Archimedean Spiral within Ground Plane Aperture…………………………………………………………….…..148 6. Conclusions…………………………………………………………….…………..158 6.1. Summary of Work……………………………………………………….…….158 6.2. Recommendations for Further Study…………………………………..………159 References………………………………………………………………..……….........160 v Acknowledgements I would like to begin by thanking Dr. Ronald Riechers for all the time that he has spent guiding and motivating me to complete this task. I would also like to thank Dr. Riechers for instilling a passion for electromagnetics that has only grown over the many years that I have had the honor of being one of his students. I would also like to thank the personnel and the measurement capabilities of Spectral Energetics Incorporated. Without it, I would not have had any measured data with which to compare my theoretical model. I would also like to thank Dr. Fred Garber and the Electrical Engineering Department of Wright State University for providing me the opportunity to attain a Master of Science in Engineering. I would also like to thank Dr. Marian Kazimierczuk for taking the time to serve on my committee. Finally, I would also like to thank Mr. Barry Woods. Without his guidance, my undergraduate and graduate experience would not have been as enjoyable. My final thank you goes out to all my friends and family who encouraged me throughout my education, especially my friend Jason and my oldest brother John. I would also like to thank my friends Mark Stewart, Lamar Westbrook, and Edward Dininger for the time they spent helping me take antenna pattern measurements and my friend Dr. Chad Hagedorn for his time spent editing my thesis. Finally, to my wife Sharon, without your love, patience, and understanding, “Sweets,” none of this would have been possible. vi 1. INTRODUCTION 1.1. Thesis Motivation Developing a low-cost (disposable) and light-weight direction-finding system for use with an Unmanned Air Vehicle (UAV) is the motivation of this thesis. As the battlefield evolves around the world, the ability to locate communications of enemy combatants is one of the most relevant tasks for supporting the war-fighter. Developing an antenna for a direction-finding system with an emphasis on modularity for different mission types and broad frequency response would demonstrate the utility of such a system to the military. 1.2. Thesis Objectives The objectives of this thesis are the following: Define a suitable antenna as defined by the thesis motivation. Describe the characteristics of the antenna. Discuss the development of an antenna capable of direction-finding. Define a theoretical model capable of describing the antenna. Provide a comparison of the theoretical and measured results. 1 2. FREQUENCY-INDEPENDENT ANTENNAS 2.1 Theory of Frequency Independence Due to the ever-expanding utilization of the electromagnetic spectrum, antennas that can operate over wide frequency ranges have become increasingly desirable. As stated in Balanis [1], prior to the 1950s, antenna technology could only provide bandwidths of 2:1 or less. Afterwards though, the concept of specifying antenna geometries purely by angles instead of characteristic lengths allowed for bandwidths of 40:1 or more. If an antenna is only defined by angles, attributes such as the characteristic input impedance, field pattern, and polarization remain constant as the size of the antenna is scaled. The theory of frequency-independence, as described by the work of Rumsey [2] and Elliot [3], begins by assuming an antenna geometry within spherical coordinates (ρ,θ,φ ), where each terminal (feed point) of the antenna surface is infinitesimally close to the origin and is confined to rotation about the θ = 0 axis. To further simplify the problem, surfaces are assumed to be perfectly conducting, and the region surrounding the antenna is assumed to be infinite in extent, homogenous, and isotropic. Such a surface is described by a single curve (for a wire) or a set of curves (to define the edges of a strip) r = F(θ,φ) (2.1-1) 2 where r represents the radial distance along the curve. To define the property of scaling, start by assuming an antenna were to be scaled to operate at a frequency that is K times lower than the original antenna. The physical size of the antenna would need to be increased by a factor of K. The scaled curve is then described by r′ = KF(θ,φ) (2.1-2) where both surfaces superimpose one another after the second curve is rotated by an angle φc about the θ = 0 axis. This is shown by the following F(θ,φ +φc ) = KF(θ,φ) (2.1-3) where the rotated angle φc depends only on K. The following figure depicts three spirals that correspond to a single-arm spiral, a scaled single-arm spiral, and a scaled single-arm spiral that has been rotated to visualize congruence of the two spirals. Figure 2.1-1 Comparison of Scaled Spirals 3 To prove congruence between the two curves, begin by differentiating both sides of equation (2.1-3) with respect to both φc and φ. d dK ∂ []KF()θ,φ = []F()θ,φ = []F()θ,φ +φc (2.1-4) dφc dφc ∂φc d ∂ []KF()θ,φ
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