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Electromagnetic Properties of Fractal Antennas Wright State University CORE Scholar Browse all Theses and Dissertations Theses and Dissertations 2018 Electromagnetic Properties of Fractal Antennas Jordan Jeffrey Ewing Wright State University Follow this and additional works at: https://corescholar.libraries.wright.edu/etd_all Part of the Physics Commons Repository Citation Ewing, Jordan Jeffrey, "Electromagnetic Properties of Fractal Antennas" (2018). Browse all Theses and Dissertations. 1974. https://corescholar.libraries.wright.edu/etd_all/1974 This Thesis is brought to you for free and open access by the Theses and Dissertations at CORE Scholar. It has been accepted for inclusion in Browse all Theses and Dissertations by an authorized administrator of CORE Scholar. For more information, please contact [email protected]. ELECTROMAGNETIC PROPERTIES OF FRACTAL ANTENNAS A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science By JORDAN JEFFREY EWING B.S., Slippery Rock University, 2016 2018 Wright State University WRIGHT STATE UNIVERSITY GRADUATE SCHOOL April 25, 2018 I HEREBY RECOMMEND THAT THE THESIS PREPARED UNDER MY SUPERVISION BY Jordan Jeffrey Ewing ENTITLED Electromagnetic Properties of Fractal Antennas BE ACCEPTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF Master of Science. ________________________________________________ Sarah F. Tebbens, Ph.D. Thesis Director ________________________________________________ Jason A. Deibel, Ph.D. Department Chair Committee on Final Examination _________________________ Sarah F. Tebbens, Ph.D. _________________________ Jason A. Deibel, Ph.D. _________________________ Christopher C. Barton, Ph.D. _________________________ Barry Milligan, Ph.D. Interim Dean of the Graduate School Abstract Ewing, Jordan Jeffrey. M.S. Department of Physics, Wright State University, 2018. Electromagnetic Properties of Fractal Antennas. Finite element method analysis is used to conduct electromagnetic simulations to characterize fractal antennas. This work considers wire (1D) antennas such as the triadic Koch curve, zig zag, and quadratic Koch curve of varying heights, iterations, and cross- sectional areas. Carpet (2D) antennas, including the Sierpinksi carpet, of varying heights, iterations, and deterministic and stochastic iterations are analyzed. The antenna shapes were generated in MATLAB and then modeled with finite element analysis using COMSOL Multiphysics®. The focus of this study is to determine what role various fractal patterns and iterations have on the S11 return loss and far field radiation patterns. Specifically, changes in directionality of the emitted radiation and return loss over a range of frequencies, between 0.2 to 2.2 GHz, are examined. Parameters that are manipulated to assess the influence on antenna performance include varying the fractal generator, varying the number of iterations to make more complex shapes, scaling the antennas, and varying the cross sectional area. Antennas with fractal shapes are shown to have multiple operational bandwidths and exhibit directionality changes with frequency in the far field radiation pattern. iii TABLE OF CONTENTS 1. INTRODUCTION…………………………………………………………..1 a. Fractals b. Antennas c. COMSOL Simulations i. Finite Element Method 2. METHODS………………………………………………………………….14 3. RESULTS…………………………………………………………….……..21 a. No Antenna b. 1D Antennas – Wires i. Straight Wire Antenna ii. Triadic Koch Curve iii. Quadratic Koch Curve iv. Zig-Zag Curve v. Effects of Antenna Scaling – 4, 6, 8, 10, 12 cm Heights vi. Effects of Changing Antenna Cross Sectional Area c. 2D Antennas - Carpets i. Solid Square Sheet Carpet ii. Sierpinski Carpet iii. Deterministic Sierpinski Carpets – Effects of Higher Iterations iv TABLE OF CONTENTS (Continued) iv. Deterministic Sierpinski Carpet 2nd Iteration – Effect of Edge Mount vs Corner Mount, and Full Size vs Half Size v. Stochastic Sierpinski Carpet – Effect of Changing Location of Port vi. Stochastic Sierpinski Carpet – Effect of Number of Iterations 4. CONCLUSIONS…………………………………………………………....119 a. 1D Antennas – Wires Summary b. 2D Antennas – Carpets Summary c. Future Work 5. REFERENCES………………………………………………………....124-125 6. APPENDIX A – Figures for all Wire Antennas…………………………….126 7. APPENDIX B – Figures for all Carpet Antenna……………………………146 v LIST OF FIGURES Figure page 1. Triadic Koch curve antenna shapes 4 2. The triangular Sierpinski gasket and the square 6 Sierpinski carpet. 3. S11 values for the Koch generator, which exhibits 8 multiple S11 minima 4. The 3D far-field radiation pattern of a straight 10 monopole antenna 5. Triadic Koch curve 1st iteration 3D far field 11 radiation distribution 6. Image of rod attached to heat source at the left end 14 7. Flow chart of the overall process of antenna simulation 14 8. Flow chart of the overall process within COMSOL 15 9. Screen Image of converting the .stl file to a 17 solid within COMSOL 10. Screen image of the “Model Space” is in yellow 18 11. Screen image of the far-field domain, which is 19 the spherical purple shell 12. Image of model in “Mesh” view with the study section open 21 13. No Antenna 3D Radiation Pattern and Normalized Surface 22 Electric field 14. Plot of S11 versus frequency for the straight wire 24 with 1 mm2 cross-sectional area 15. Straight Wire Antenna data 25-26 16. Triadic Koch curve antenna shapes 27 17. Plot of S11 versus frequency for the triadic Koch curve 29 generator, 1st, 2nd Iteration, and straight wire with 1 mm2 cross-sectional area vi 18. The normalized surface electric field for triadic Koch curve 30 generator, 1st iteration, and 2nd iteration 19. 2D polar far field radiation plot for the triadic Koch curve 32 Antennas 20. 2D Radiation Plot of triadic Koch curve of frequency with 34 lowest S11 minima for each shape 21. 3D Radiation distribution in the Far Field for 35 triadic Koch curve 22. Quadratic Koch curve antenna shapes 36 23. S11 values for the quadratic Koch curve generator, 38 1st, 2nd iteration, and straight wire 24. The normalized surface electric field from left to right for 39 the quadratic Koch curve generator, 1st iteration, and 2nd iteration 25. 2D polar far field radiation plot of the quadratic Koch 41 curve antennas for all frequencies analyzed 26. 2D Radiation Plot of quadratic Koch curve of frequency 44 with the lowest S11 minima for each shape 27. 3D far field radiation pattern of the quadratic Koch 45 curve of frequency with the lowest S11 minima for each shape 28. Zig Zag curve antenna shapes 46 29. S11 values for the Zig Zag curve generator, 48 1st, 2nd iteration, and straight wire antenna 30. The normalized surface electric field for Zig Zag curve 49 31. 2D polar far field radiation plot of Zig Zag curve 51 for all frequencies analyzed vii 32. 2D Radiation plot of Zig Zag curve for the frequency with the 53 lowest S11 minima for each shape 33. 3D far field radiation pattern of the Zig Zag curve for the 54 frequency with the lowest S11 minima for each shape 34. Plot of S11 verses frequency for the straight wire antenna and for 55 the triadic Koch curve 2nd iteration scaled to 4, 6, 8, 10, 12 cm and with proportional cross-sectional area 35. The normalized surface electric field for the scaled 57-58 triadic Koch curve 2nd iteration 36. 2D polar far field radiation plot for the scaled 2nd iteration 59-60 triadic Koch curve scaled for all frequencies analyzed 37. 2D Radiation Plot of triadic Koch curve scaled for the 62-63 frequency with the lowest S11 minima for each antenna length 38. 3D far field radiation pattern for the 2nd iteration 64-65 triadic Koch curve for the frequency with the lowest S11 minima for each antenna length 39. Plot of S11 verses frequency for the triadic Koch curve 67 2nd iteration for cross-sectional areas of 0.5, 1.0, 1.5, and 2.0 mm2 40. The normalized surface electric field from the triadic Koch 68-69 curve 2nd iteration with different cross sectional areas 41. 2D polar far field radiation plot of 2nd iteration 70-71 triadic Koch curve with different cross-sectional areas for all frequencies analyzed 42. 2D radiation plot of 2nd iteration triadic Koch curve 73-74 with different cross-sectional areas for the frequency with the lowest S11 minima for each shape viii 43. 3D far field radiation pattern of the 2nd iteration 75-76 triadic Koch curve with different cross-sectional areas for the frequency with the lowest S11 minima for each shape 44. Image of solid square sheet antenna 78 45. S11 verses frequency for an side-mounted solid square sheet 79 antenna 46. Analysis of a side-mounted solid square sheet antenna 80 47. S11 verses frequency for an side-mounted solid square sheet 81 antenna 48. Analysis of a corner-mounted solid square sheet antenna 82 49. Deterministic Sierpinski Carpet iterations 83 50. Stochastic Sierpinski carpets iterations 83 51. Deterministic Sierpinski Carpet 84 52. Plot of S11 verses frequency for the deterministic side 85 mounted Sierpinski carpet 2nd, 3rd, and 4th iteration 53. The normalized surface electric field for 86 Deterministic 2nd iteration Sierpinski carpet 54. 2D polar far field radiation plot for deterministic 87 2nd iteration Sierpinski carpet 55. 2D Radiation plot for deterministic 2nd iteration 88 Sierpinski carpet 56. 3D Radiation plot for deterministic 2nd iteration 89 Sierpinski carpet nd 57. Deterministic 2 iteration Sierpinski carpet shape 90 nd 58. S11 values for the deterministic 2 iteration 91 Sierpinski carpet port variations and size ix 59. The normalized surface electric fields for the 92-93 deterministic 2nd iteration Sierpinski carpet port variations and size 60. 2D polar far field radiation plot of deterministic 94-95 2nd iteration Sierpinski carpet port and size variations for all frequencies analyzed 61. 2D Radiation Plot of deterministic 2nd iteration Sierpinski 96-97 carpet port and size variations for the frequency with lowest S11 minima for each shape 62. 3D far field radiation plot of the deterministic 2nd iteration 98-99 Sierpinski carpet port and size variations for the frequency with the lowest S11 minima for each shape st 63.
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