(FDTD) Analysis of a Leaky Traveling Wave Microstrip Antenna

158 Pages·2005·2.08 MB·English

FINITE DIFFERENCE TIME DOMAIN (FDTD) ANALYSIS OF A LEAKY
TRAVELING WAVE MICROSTRIP ANTENNA
THESIS
Gregory M. Zelinski, First Lieutenant, USAF
AFIT/GE/ENG/05-24
DEPARTMENT OF THE AIR FORCE
AIR UNIVERSITY
AIR FORCE INSTITUTE OF TECHNOLOGY
Wright-Patterson Air Force Base, Ohio
APPROVED FOR PUBLIC RELEASE; DISTRIBUTION UNLIMITED.
The views expressed in this thesis are those of the author and do not reflect the official
policy or position of the United States Air Force, Department of Defense, or the United
States Government.
AFIT/GE/ENG/05-24
FINITE DIFFERENCE TIME DOMAIN (FDTD) ANALYSIS OF A
LEAKY TRAVELING WAVE MICROSTRIP ANTENNA
THESIS
Presented to the Faculty
Department of Electrical and Computer Engineering
Graduate School of Engineering and Management
Air Force Institute of Technology
Air University
Air Education and Training Command
In Partial Fulfillment of the Requirements for the
Degree of Master of Science in Electrical Engineering
Gregory M. Zelinski, B.S.E.E.
First Lieutenant, USAF
March 2005
APPROVED FOR PUBLIC RELEASE; DISTRIBUTION UNLIMITED.
AFIT/GE/ENG/05-24
FINITE DIFFERENCE TIME DOMAIN (FDTD) ANALYSIS OF A
LEAKY TRAVELING WAVE MICROSTRIP ANTENNA
Gregory M. Zelinski, B.S.E.E.
First Lieutenant, USAF
Approved:
/signed/ 21 Mar 2005
Maj Michael L. Hastriter (Chairman) date
/signed/ 21 Mar 2005
Dr. William P. Baker (Member) date
/signed/ 21 Mar 2005
Dr. Michael J. Havrilla (Member) date
/signed/ 21 Mar 2005
Dr. Andrew J. Terzuoli (Member) date
Acknowledgements
First and foremost, I’d like to thank Dr. Gary Thiele for his patience, his advice, and his
friendship. Dr. Thiele’s curiosity in this project was a source of motivation. I couldn’t
have completed much of this work without Dr. Dan Janning, Josh Radcliffe, Ken Goss,
“Cub” Corwin, John Reynolds, and all of the other “RASCAL’s” that helped fabricate
and measure antennas.
Manythankstomyadvisor, MajLarkinHastriter. His“hands-off”stylegavemethe
flexibility to learn a great deal more than I otherwise would have. Dr. Andrew Terzuoli
deserves special recognition for finding a computer with increased memory to enable larger
simulations. Thanks also to my committee for their support and direction when needed.
Finally, I’d like to thank my wife. I know it was as difficult for you as it was for me.
It’s your turn to go to school, now. To my daughters, the party is over.
Gregory M. Zelinski
iv
Table of Contents
Page
Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv
List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii
List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x
Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi
I. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Problem Statement . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 Scope . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3 Resources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.4 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
II. Background on Microstrip Leaky Traveling Wave Antennas . . . . . . 5
2.1 Traveling Waves . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 Traveling Wave Antennas . . . . . . . . . . . . . . . . . . . . 6
2.3 Antenna Characteristics . . . . . . . . . . . . . . . . . . . . . 7
2.4 Propagation Modes . . . . . . . . . . . . . . . . . . . . . . . 12
2.5 Microstrip. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.5.1 Physical Characteristics . . . . . . . . . . . . . . . . 13
2.5.2 Advantages and Disadvantages . . . . . . . . . . . . 14
2.5.3 Hybrid Modes . . . . . . . . . . . . . . . . . . . . . 14
2.6 Propagation Mechanisms . . . . . . . . . . . . . . . . . . . . 16
2.7 Menzel’s Original Antenna . . . . . . . . . . . . . . . . . . . 21
2.8 Analysis of Menzel’s Work . . . . . . . . . . . . . . . . . . . 22
III. Finite Difference Time Domain . . . . . . . . . . . . . . . . . . . . . . 25
3.1 Formulation . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
3.2 Absorbing Boundary Condition (ABC) . . . . . . . . . . . . 30
3.3 Materials specification . . . . . . . . . . . . . . . . . . . . . . 34
3.4 Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
3.5 Dispersion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.6 Geometric Distortion . . . . . . . . . . . . . . . . . . . . . . 43
3.7 Source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
v
Page
IV. Simulation Development . . . . . . . . . . . . . . . . . . . . . . . . . . 45
4.1 Hagness-Willis Code . . . . . . . . . . . . . . . . . . . . . . . 45
4.2 Copper . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
4.3 PML . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.4 Material Surrounding the Antenna . . . . . . . . . . . . . . . 47
4.5 Resolution and Cell Size . . . . . . . . . . . . . . . . . . . . . 50
4.6 Source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
4.7 Loss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
4.8 Precision . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
4.9 Full Width vs. Half Width . . . . . . . . . . . . . . . . . . . 54
4.10 Determination of Leakage Constant and Phase Constant. . . 54
4.11 Validating FDTD Code . . . . . . . . . . . . . . . . . . . . . 58
4.11.1 Transverse Resonance . . . . . . . . . . . . . . . . . 58
4.11.2 Measurements . . . . . . . . . . . . . . . . . . . . . 61
4.12 Curvature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
V. Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
5.1 Reduction of Memory for Simulation . . . . . . . . . . . . . . 70
5.2 Menzel antenna . . . . . . . . . . . . . . . . . . . . . . . . . 71
5.3 Thiele Full Width (TFW) antenna . . . . . . . . . . . . . . . 71
5.4 Modifying dimensions to meet bandwidth specifications . . . 75
5.4.1 Varying Dielectric Constant . . . . . . . . . . . . . . 75
5.4.2 Varying Height . . . . . . . . . . . . . . . . . . . . . 77
5.4.3 Varying Width . . . . . . . . . . . . . . . . . . . . . 77
5.4.4 Frequency Scaling . . . . . . . . . . . . . . . . . . . 77
5.5 Curvature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
5.6 Multiple Elements . . . . . . . . . . . . . . . . . . . . . . . . 81
5.7 Simplified Fabrication . . . . . . . . . . . . . . . . . . . . . . 83
VI. Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
6.1 Summary of Results . . . . . . . . . . . . . . . . . . . . . . . 86
6.2 Follow-on Work . . . . . . . . . . . . . . . . . . . . . . . . . 87
6.2.1 FDTD Simulation . . . . . . . . . . . . . . . . . . . 88
6.2.2 THW antenna . . . . . . . . . . . . . . . . . . . . . 89
6.2.3 Feed . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
6.2.4 S-Parameter Measurements . . . . . . . . . . . . . . 89
Appendix A. Matlab Code . . . . . . . . . . . . . . . . . . . . . . . . . . 90
Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
vi
List of Figures
Figure Page
1.1. Thiele Half Width (THW) antenna. . . . . . . . . . . . . . . . . . 3
1.2. Menzel’s original antenna [23]. . . . . . . . . . . . . . . . . . . . . 3
2.1. The effects of a reflected traveling wave . . . . . . . . . . . . . . . . 7
2.2. Illustration of the far-field distance. . . . . . . . . . . . . . . . . . . 8
2.3. The far-field pattern of a 3 λ long antenna. . . . . . . . . . . . . . . 10
2.4. The far-field pattern of a 5 λ long antenna. . . . . . . . . . . . . . . 11
2.5. The complete far-field pattern at 6.7 GHz. . . . . . . . . . . . . . . 12
2.6. Geometry of a microstrip transmission line. . . . . . . . . . . . . . 14
2.7. Microstrip feed techniques. . . . . . . . . . . . . . . . . . . . . . . . 15
2.8. Field pattern of microstrip’s fundamental mode. . . . . . . . . . . . 16
2.9. Field pattern of microstrip’s first higher order mode. . . . . . . . . 16
2.10. A typical plot of the EH propagation constant. . . . . . . . . . . . 17
1
2.11. Angle of radiation due to β and k . . . . . . . . . . . . . . . . . . . 19
x 0
2.12. The radiating fields increase moving away from the structure. . . . 19
2.13. Vector components of the surface wavenumber, k . . . . . . . . . . . 21
s
2.14. Predictions of normalized phase constant for Menzel’s antenna [29]. 23
3.1. The Yee Cell [39,43]. . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.2. UPML covering a PEC wall normal to xˆ. . . . . . . . . . . . . . . 32
3.3. Modelling PEC using electric field boundary conditions.. . . . . . . 35
3.4. Correctly modelling the width of PEC. . . . . . . . . . . . . . . . . 35
3.5. Instabilities tend to grow and multiply. . . . . . . . . . . . . . . . . 39
3.6. An instability quickly overtakes the entire computational space. . . 40
3.7. The magnitude of phase velocity error, or dispersion [39]. . . . . . 42
3.8. Geometric distortion. . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3.9. The source waveform. . . . . . . . . . . . . . . . . . . . . . . . . . . 44
vii
Figure Page
4.1. Cross-section slice of the original TFW antenna simulation. . . . . . 46
4.2. Longitudinal-section slice of the original TFW antenna simulation. 46
4.3. Extending the TFW antenna into the PML (cross-section). . . . . . 48
4.4. Extending the TFW antenna into the PML (longitudinal-section). . 48
4.5. Further reduced TFW antenna simulation (cross-section). . . . . . . 49
4.6. Further reduced TFW antenna simulation (longitudinal-section). . . 49
4.7. Error due to cell size and substrate thickness. . . . . . . . . . . . . 51
4.8. Resolution for 5-cell thick substrate. . . . . . . . . . . . . . . . . . . 52
4.9. Comparison of lossy and lossless.. . . . . . . . . . . . . . . . . . . . 53
4.10. Comparison of double and single precision. . . . . . . . . . . . . . . 53
4.11. THW antenna vs. TFW antenna. . . . . . . . . . . . . . . . . . . . 54
4.12. Determining the propagation constant from the fields. . . . . . . . . 55
4.13. The raw E data retrieved following simulation. . . . . . . . . . . . 56
z
4.14. The best-fit exponential curve. . . . . . . . . . . . . . . . . . . . . . 57
4.15. λ is much longer for lower frequencies. . . . . . . . . . . . . . . . . 57
β
4.16. The natural logarithm of the simulation data. . . . . . . . . . . . . 59
4.17. A transmission line circuit model. . . . . . . . . . . . . . . . . . . . 60
4.18. The effect of the height of the substrate on the propagation constant. 60
4.19. FDTD is in agreement with transverse resonance. . . . . . . . . . . 62
4.20. Near field probing of the THW antenna. . . . . . . . . . . . . . . . 63
4.21. Extraction of k from the near field measurements. . . . . . . . . . 63
x
4.22. Set-up used for far-field H-plane measurements. . . . . . . . . . . . 64
4.23. Far-field radiation pattern of the THW fabricated with vias. . . . . 65
4.24. Estimating k from measured data. . . . . . . . . . . . . . . . . . . 66
x
4.25. Matlab representation of curved THW antenna. . . . . . . . . . . . 67
4.26. The curved THW antenna is approximated by rectangular cells. . 68
4.27. Processing the angle data. . . . . . . . . . . . . . . . . . . . . . . . 69
viii
Figure Page
5.1. Simulation of the original Menzel antenna. . . . . . . . . . . . . . . 72
5.2. Simulation of the Menzel antenna with larger slots. . . . . . . . . . 73
5.3. The fields in the non-excited side of the TFW antenna. . . . . . . . 74
5.4. The propagation constant’s dependence on dielectric constant. . . . 75
5.5. The bandwidth as a function of substrate permittivity. . . . . . . . 76
5.6. Lower dielectric constant causes lower α . . . . . . . . . . . . . . . 76
x
5.7. The effect of the width of the conductor on the propagation constant. 77
5.8. Scaling the center frequency by a factor of four. . . . . . . . . . . . 78
5.9. The THW antenna curved with a radius of 93 mm. . . . . . . . . . 79
5.10. The THW antenna curved with a radius of 53 mm. . . . . . . . . . 80
5.11. The THW antenna curved with a radius of 42 mm. . . . . . . . . . 80
5.12. The THW antenna curved with a radius of 34 mm. . . . . . . . . . 81
5.13. Field distribution due to curvature with wall on the outside. . . . . 82
5.14. Error due to spacing between two elements. . . . . . . . . . . . . . 82
5.15. Substrate outside of wall does not affect k . . . . . . . . . . . . . . 83
x
5.16. THW antenna fabricated without vias. . . . . . . . . . . . . . . . . 84
5.17. Comparison of THW antenna with vias and with tape at 6.7 GHz.. 85
5.18. Comparison of THW antenna with vias and with tape at 7.2 GHz.. 85
ix