Size Reduction of an Uwb Low-Profile Spiral Antenna

SIZE REDUCTION OF AN UWB LOW-PROFILE SPIRAL ANTENNA DISSERTATION Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By Brad A. Kramer, M.S., B.S. ***** The Ohio State University 2007 Dissertation Committee: Approved by Professor John L. Volakis, Adviser Adjunct Professor Chi-Chih Chen Adviser Associate Professor Fernando L. Teixeira Graduate Program in Electrical and Computer Engineering c Copyright by Brad A. Kramer 2007 ABSTRACT Fundamental physical limitations restrict antenna performance based on its electrical size alone. These fundamental limitations are of the utmost importance since the minimum size needed to achieve a particular figure of merit can be determined from them. In this dissertation, the physical limitations on the size reduction of a broadband antenna is examined theoretically and experimentally. This is in contrast to previous research that focused on narrowband antennas. Specifically, size reduction using antenna miniaturization techniques is considered and explored through the ap- plication of high-contrast material and reactive loading. A particular example is the miniaturization of a broadband spiral using readily available high-contrast dielectrics and a novel inductive loading technique. Using either dielectric or inductive loading, it is shown that the size can be reduced by more than a factor of two which is close to the observed theoretical limit. To enable the realization of a conformal antenna without the loss of the antenna’s broadband characteristics, a novel ground plane is introduced. The proposed ground plane consists of a traditional metallic ground plane coated with a layer of ferrite material. It is shown that the ferrite coated ground plane minimizes the negative effects that occur when the spacing between a traditional metallic ground plane and antenna becomes electrically small. ii ACKNOWLEDGMENTS I would like to acknowledge all of my committee members, especially my advisor, Professor John Volakis for his guidance and advice. I would also like to thank Dr. Chen and Ming Lee for the interesting discussions and insight on antennas and other topics. Additionally, I would like to thank John Moniz, program officer at the Office of Naval Research, for sponsoring this work. Lastly, I would like to thank the staff and fellow students of the ElectroScience Laboratory for their support. iii VITA August 19, 1978 ............................Born - Newark, Ohio March, 2002 ................................Bachelor of Science in Electrical and Computer Engineering The Ohio State University May, 2003 - present .........................Graduate Research Associate, The Ohio State University - Columbus, OH December, 2004 ............................Masters of Science in Electrical and Computer Engineering The Ohio State University FIELDS OF STUDY Major Field: Electrical Engineering Studies in: Electromagnetics Communications and Signal Processing iv TABLE OF CONTENTS Page Abstract....................................... ii Acknowledgments.................................. iii Vita ......................................... iv ListofTables.................................... viii ListofFigures ................................... ix Chapters: 1. Introduction.................................. 1 1.1 Motivation, Challenges and Objective . 1 2. Fundamental Limitations of Electrically Small Antennas . ........ 6 2.1 Introduction .............................. 6 2.2 Directivity Limit for an Antenna of Arbitrary Size . 7 2.3 AntennaQualityFactor ........................ 9 2.4 Directivity Limit Based on Antenna Q ................ 16 2.4.1 Chu-Harrington-Taylor Normal Directivity Limit . 17 2.4.2 Maximum Directivity for a Given Antenna Q ........ 18 2.4.3 Minimum Q Antenna or Electrically Small . 23 2.5 ImpedanceBandwidthLimitations . 24 2.5.1 Passive Lossless Networks . 26 2.5.2 Active and Lossy Networks: Non-Foster Matching . 31 2.6 Extending Fundamental Limitations to Broadband Antennas.... 32 2.6.1 Fano-Bode Limit for High-Pass Response . 33 2.7 Summary ................................ 49 v 3. AntennaMiniaturization........................... 51 3.1 Importance of Electrical Size and Phase Velocity . 52 3.2 AntennaMiniaturizationConcept. 56 3.3 Performance Enhancement caused by Antenna Miniaturization . 58 3.3.1 Radiation Resistance . 60 3.3.2 Antenna Q andBandwidth .................. 61 3.3.3 ElectricalSize.......................... 68 3.4 Approach to Broadband Antenna Miniaturization . 72 3.4.1 Optimum Miniaturization Factor . 72 3.4.2 Importance of Tapered Loading Profile . 74 3.4.3 Importance of Equal LC Loading . 79 3.5 Summary ................................ 82 4. Broadband Antenna Miniaturization using Material Loading ....... 84 4.1 Introduction .............................. 84 4.2 SpiralAntenna: TheoryofOperation. 86 4.3 Spiral Antenna Miniaturization using High-Contrast Dielectrics . 89 4.3.1 Quantifying Miniaturization for a Broadband Antenna . 90 4.3.2 Impact of Dielectric Layer Dimensions . 91 4.3.3 Impact of Dielectric Constant . 96 4.4 DielectricLoadingIssues. 101 4.4.1 Impedance Reduction . 102 4.4.2 Surface Wave and Resonant Mode Issues . 107 4.5 Summary ................................ 108 5. Broadband Antenna Miniaturization via Inductive Loading ........ 110 5.1 Introduction .............................. 110 5.2 Implementation of Inductive Loading for the Spiral Antenna . 111 5.2.1 2-D Inductive Loading: Planar Meandering . 112 5.2.2 3-D Inductive Loading: Coiling . 115 5.3 3-D Inductive Loading Taper Design . 118 5.3.1 OptimalTaperProfile . 121 5.3.2 OptimalTaperLength . 129 5.4 6” Spiral Design for UHF Operation . 135 5.4.1 Selection and Optimization of Coil Parameters . 136 5.4.2 Fabrication and Measurement . 144 5.5 18” Spiral Design for VHF and UHF Operation . 148 5.5.1 Design and Optimization . 150 vi 5.5.2 Fabrication and Measurement . 155 5.6 Summary ................................ 161 6. Ferrite Coated Ground Plane for Low-Profile Broadband Antennas . 164 6.1 Introduction .............................. 164 6.2 Issues with Metallic Ground Plane or Cavity . 165 6.3 PEC Ground Plane Alternatives: EBG Structures . 172 6.3.1 Artificial Magnetic Conductors . 172 6.4 PEC Ground Plane Alternatives: Utilization of Ferrite Materials . 175 6.4.1 High Impedance Surface using Ferrites . 180 6.4.2 Ferrite Coated Metallic Ground Plane . 185 6.4.3 Potential Future Improvements . 190 6.5 Integration of Ferrite Coated PEC Ground Plane with Miniaturized Spiral .................................. 193 6.5.1 6” Diameter Spiral for UHF Operation . 194 6.5.2 18” Diameter Spiral for VHF and UHF Operation . 202 6.6 Summary ................................ 206 7. Conclusion................................... 208 7.1 SummaryandConclusions. 208 7.2 FutureWork .............................. 211 7.2.1 Low Q AntennaDesigns . .. ... .. .. .. .. .. ... 211 7.2.2 Inductively Loaded Spiral Design . 212 7.2.3 Optimization of Ferrite Coated Ground Plane . 213 Bibliography .................................... 215 vii LIST OF TABLES Table Page 2.1 Lopez’s coefficients an and bn [1]. .................... 28 viii LIST OF FIGURES Figure Page 2.1 Equivalent circuits for the (a) T Mmn and (b) TEmn modes of free space[2,3]. ................................ 12 2.2 Percent error due to calculating the minimum Q based on Chu’s ap- proximate analysis and Fante’s exact analysis. 15 2.3 Comparison of the antenna Q limit with Geyi’s minimized Q for the directional and omni-directional antenna. 21 2.4 Percent difference between the antenna Q limit and Geyi’s minimized Q for the directional and omni-directional antenna. 22 2.5 Comparison of the normal directivity limit with Geyi’s maximized directivity for the directional and omni-directional antenna........ 23 2.6 A possible band pass response for the reflection coefficient that illus- tratesBode-Fanocriterion.. 27 2.7 Percent bandwidth improvement for a given Q as a function of Γ. 30 2.8 Typical spiral antenna input impedance. 35 2.9 The ideal high-pass reflection coefficient response. 37 2.10 Matching network for an arbitrary load impedance [4]. ....... 38 2.11 Matching network and Darlington equivalent of load impedance in cascade[4]. .................................. 39 2.12 Two terminal pair reactive network [4]. 40 ix 2.13 Two reactive networks in cascade [4]. 42 ωca 2.14 In-band reflection coefficient Γ0 vs the cutoff size (ka = c ) or cutoff frequency. The cutoff size is the smallest antenna size for which Γ Γ . 47 | | ≤ | 0| 2.15 The lowest achievable cutoff frequency for a minimum Q antenna in termsoftherealizedgain. 48 3.1 Schematic diagram of a dipole antenna and coordinate system..... 53 3.2 Gaussian pulse radiation from a λ/2 dipole for θ = π/2......... 55 3.3 Gaussian pulse radiation from an electrically small dipole (h = λ/10) for θ = π/2................................. 56 3.4 Miniaturization factor as a function of the inductance per unit length foradipoleorloopantenna. 59 3.5 Comparison of the dipole radiation resistance for different miniaturiza- tionfactors. ................................ 62 3.6 Comparison of the dipole reactance referred to current maximum for differentminiaturizationfactors.. 62 3.7 Dipole radiation resistance at ka = 0.5 as a function of the miniaturization factor m. ............................. 63 3.8 Comparison of the current distribution at ka 0.5 for a 6 inch long ≈ unloaded dipole below resonance and real impedance match, below resonance and complex conjugate

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