No abstract availableThesis (PhD (Electronic Engineering))--University of Pretoria, 2007.Electrical, Electronic and Computer Engineeringunrestricte

Theunissen, W H

Thesis (PhD (Electronic Engineering))--University of Pretoria, 2007.No abstract availableElectrical, Electronic and Computer Engineeringunrestricte

UPSpace at the University of Pretoria

Reconfigurable contour beam synthesis using a mechanical FEM surface description of dual offset reflector antenna surfaces W.B. THEUNISSEN A thesis submitted in partial fulfillment of the requirements for the degree of Philosophiae Doctor in the FACULTY OF ENGINEERING UNIVERSITY OF PRETORIA SOUTH AFRICA January 1999                                                   © University of Pretoria TABLE OF CONTENTS LIST OF FIGURES v Chapter 1: Introduction . . .. . . ... . . . ... . .. . . ... .... . .. . . . .. .... . . . . . . 1 1.1. Geostationary satellites . . . . .. . . .. . . . ... ... ... . . . . . . . . ... . .. .. . 1 1.2. Antenna systems on geostationary satellites . . . . . . . . . . . . . . . . . . . . . . 6 1.3. The mechanical finite element diffraction synthesis technique . . . . . . . 8 Chapter 2: Diffraction synthesis and radiation pattern computa tion for reflector antennas. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 2.1. Geometry of the dual reflector antenna and coordinate description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.2. Subreflector analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15 2.2.1. Calculation of specular points . .. . . . . .. . . . ... ..... ......... 15 2.2.2. Edge diffraction . .. . . .. . .. . . . .. . . .. . . . . .. . . . .. ....... . . . 21 2.3. Calculation of the far-field radiation pattern . . . . . . . . . . . . . . . . . . . . 24 2.3.1. The p-series method . ... . . . . . . . . . ..... . .. . . . ... . .. . .. . . . 24 2.3.2. The J acobi-Bessel series expansion method ... . . . . _ . . .. . _ . . . . _ 26 2.3.3. The Gaussian beam technique . . .... _ . . .. . . .. . ___ . ... . _ . . . 36 2.4. Surface expansion in terms of the Modified Jacobi polynomials .. .. .. . . .. . . _ . . _ . . . _ .. .. . _ . . .. . . ... . .. . . . . .. . ... 44 2.5. Verification of the accuracy of the developed codes .. _ . . . .. _ . . 47 2.5.1. The p-series method . . . .. . . . .. .... ... . . . _ . . . . . . . . . . . . . . 47    2.5.2. The Gaussian beam technique . .. ... . .. . .. . . . . .. .. . . . .. . .. 52 2.6. Calculation of the antenna footprint . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 Chapter 3: Optimization of the contour beam gain cost function .. .. .. .. . ... 56 3.1. Cost function . . .. . . . .. . . . .. .. . . . .. . . . . . .. .. . .. .. . . . .. . . .. . ' 56 3.2. Optimization methods ... . ... . . .. . . . .. . . . ... . . . . . . _ . _ . . ... . _ 57 3.2.1. The Steepest Gradient Solver .. . .. . _ .. . . . _ .. . .. . .. . .. ... . 57 3.2.2. The Genetic Algorithm Solver . . . . .. . . . .. _.. . .. ... . . . . . .. 58 3.3. Design of a CONUS beam . .. . .. .... . ...... . . . .. . .. . ... . . . . _ . . 60 Chapter 4: Mechanical design of the reflector ..... . _ . _ . . . . . ... .. .. . . _ .. 65 4.1. Mechanical description of the surfaces using shell elements . .. . .. .... 65 4.2. DitTraction synthesis results and mechanical design performance . . .. _ . 70 Chapter 5: Contour beam synthesis using the mechanical FEM surface description . . . . ...... . . . . . . . ... _.. . . _ . _ . . . . . _ . . . . 77 5.1. Mechanical FEM diffraction synthesis ... . ..... . . _ . _ . . _ . . . .. . . ... 77 5.2. The effect of mechanical surface properties on actuator number and placement .. . ... .. . . . . .. . . .. . . . _ . . . . . . . . . 81 5.3. Synthesis of an adjustable elliptical beam using the mechanical FEM surface description ... . .. .. . __ . . . . . . . . . . . . . 93 5.4. Synthesis of an reconfigurable beam using the mechanical FEM surface description ...... . . . .. . .... _.. . . . . . . . . . . _ . . . _ . . . 97 Chapter 6: Conclusion . .. . . ... . . . ... .. . . . . .... . .. . . _ . _ . . . . . . . . . . .. 101 References .. .... . . . _ .. _.... . . . . .. .. ..... . . . . . . . . . . . ... . ... . .. .. 103    ACKNOWLEDGEMENTS I would like to acknowledge the help and encouragement of the following people: Professors 1. Joubert and W.l Odendaal of the University of Pretoria, my study leaders, Professor W.D. Burnside of The Ohio State University ElectroScience Laboratory, for all his help and advice, Professor G. Washington of the Smart Materials and Structures Laboratory at The Ohio State University. I would also like to thank Hwansik Y oon for his valuable help in understanding mechanical finite element analysis and for writing the FEM unit of the diffraction synthesis code and Dr. Teh-Hong Lee, Dr. Hsi-Tseng Chou and Prof P.H. Pathak for their help and support. This dissertation is dedicated to Heidi .    LIST OF FIGURES Figure 1. The subtended angle of the earth as seen from a geostationary satellite is approximately 17°. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 4 Figure 2. Geometry of the dual offset reflector antenna . ...... . . . . . .. . . . .... . 14 Figure 3. Geometry of Cassegrain dual offset reflector antenna . ... ... . __ . . . _.. 15 Figure 4. Perfectly conducting wedge for calculation of diffraction from subreflector edge ....... . ..... .. _.... . .. __ . . ___ . . . . . . . . 23 Figure 5 (a) Modified Jacobi polynomial for m=O... . ....... . .. . . ... .. . . .... 29 Figure 5 (b) Modified Jacobi polynomial for m=1. . . ..... _... .......... .. . .. 29 Figure 5 (c) Modified Jacobi polynomial for m=2 ..... .... .. . ... .. . . .. . ... .. 30 Figure 6. Co-polarized surface current density for a Cassegrain type dual offset reflector antenna ........... .. . ......... . .. . . . ...... . . .. 31 Figure 7. Far-field radiation pattern for the Cassegrain DOSR geometry Figure 8(a). Calculated far-field for a dual offset reflector antenna shown in figure 6 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 showing the subreflector edge diffraction effect for an oversized subreflector .... ... .. . ..... . ..... _ . . . . . . . . . . . . . . .. . .. .. .. . .. 33 Figure 8(b) . Sub reflector edge diffraction effect on the radiation pattern Figure 9. Diagram to determine sampling interval effect on the visible Figure 10. Mapping ofGB's onto the solid angle subtended at the feed Figure 11. Samples of coordinate systems used for launched beams showing of a dual offset reflector antenna .............. . ... _ .......... . .. 34 k-space spectrum . . _. . .... . . ..... . .. .. . ... .. ........... .. . ' 35 by the reflector rim . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 37 location of the real part of the saddle point (magenta circles) for a 10° offset angle from boresight going around in 36° increments ... . . 39 Figure 12. Projection showing unit circle used for surface series expansion Figure 13 (a) . Co-polarized far-field calculated using the developed Figure 13 (b). Cross-polarized far-field calculated using the developed of the subreflector in terms of the modified Jacobi polynomials ..... . . . 45 p-series code. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48    p-series code. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 Figure 14 (a). Co-polarized far-field calculated using OSU NECREF Version 3.0 . . 50 Figure 14 (b). Cross-polarized far-field calculated using OSU NECREF Version 3.0 .. .. . . . ..... . . .. .. .. . . .... . . . . ... . . . . .. .. . . 51 Figure 15 . Far-field calculated using PO and the GB technique for a front fed offset parabolic reflector shaped using the modified Jacobi polynomial expansion ... . . . . . ... .. . ... .. . ... . .. ... . .. . . .... 53 Figure 16. u-v-space test grid mapping onto geocentric surface. Test points Figure 17. Required main and subreflector surface deviation in 1mm contour Figure 18. Template used to calculate cost function during synthesis of the Figure 19. CONUS beam generated using combination ofgenetic and steepest are used to calculate the cost function during synthesis . . . . . . . . . . .. . 55 intervals for CONUS type contour beam . . . . . . . . . . . . . . . . .. . . . 62 CONUS beam . . . .. . . . .. . . ... . . .. .. .. . .. ... . . ... . .. . . . . . . . 63 gradient solvers in synthesis algoritlun . . . . . . . . . . . . . . . . . . . . . . . .. 63 Figure 20. Actuator positions projected on the Xs-Ys plane . . . . ..... . . .. . .. . .. 67 Figure 21. Showing individual stack showing clamshell configuration . . . . . . . . . . 68 Figure 22. Rainbow actuators in stacked clam configuration . . . . .. . . .. . . . . . . .. 69 Figure 23 . Required deviation from the initial hyperboloid surface in 2 mm contour intervals and the calculated co-polarized antenna radiation footprint for case 2 . . . . . . . . .. . .... . . . . . . . . .. . .. .. .. ... . . . . . 72 Figure 24. Required deviation from the initial hyperboloid surface in 2 mm contour intervals and the calculated co-polarized antenna radiation footprint for case 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 Figure 25. The achievable subreflector surface with no actuator adjustment and the resulting co-polarized radiation footprint .. . . . . .. . .. .. . . . . . . . 74 Figure 26. Mechanically achievable surface and the calculated co-polarized Figure 27. Mechanically achievable surface and the calculated co-polarized radiation pattern for case 2 .. . ... . . . . .. . . . . .. .. . . . . .. . . ... . .. 75 radiation pattern for case 4 . . . . . . . . . . . . . . . . . . . . . .. . ... . . . . . .. 76 Figure 28. FEM shell element geometry .. . .. . ...... . . . .. ... . . .. . .. .. . . .. 78 Figure 29. Sub reflector projection in the Xs - Ys plane showing the FEM node­   and element positions . . . . . . . . ... . .. .... .... ... . . ...... ..... 79 Figure 30. Sub reflector surface deviation due to displacement of actuator 66 by 10mm . ..... .. . . . . . ... . ... . ... . . . . . . . .. .... .. .... .. .. . . . 80 Figure 31 . Required surface deviation contours in 1 mm contour intervals for the subreflector surface with an unshaped main reflector giving a cost function of 59.5 units on an elliptical contour beam case .. ... . . .. . .. 81 Figure 32 (a) Surface deviation contours for 16 actuators arranged in a triangular pattern and bonded to different surface material thickness of 0.05", O.1" and 0.3" respectively . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 Figure 32 (b) Surface deviation contours for 22 actuators arranged in a triangular pattern and bonded to different surface material thickness of 0.05", 0.1 " and 0.3" respectively .. ..... .. .. .. . . .. .. . . . . ... .. .... 85 Figure 32 (c) Surface deviation contours for 38 actuators arranged in a triangular pattern and bonded to different surface material thickness of 0.05", 0.1" and 0.3" respectively . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 Figure 33 (a) Surface deviation contours for 15 actuators arranged in a rectangular pattern and bonded to different surface material thickness of 0.05", 0.1" and 0.3" respectively . . .. .. .. . . .. .. .. . .. .. .. . .. .. .. .. 87 Figure 3 3 (b) Surface deviation contours for 21 actuators arranged in a rectangular pattern and bonded to different surface material thickness of 0.05", 0.1 " and 0.3" respectively. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 88 Figure 33 (c) Surface deviation contours for 40 actuators arranged in a rectangular pattern and bonded to different surface material thickness of 0.05", 0.1" and 0.3" respectively . .. . . . .. . .. .. . .. . ... ..... . .. .. . ' 89 Figure 34 (a) Surface deviation contours for 14 actuators arranged in a radial pattern and bonded to different surface material thickness of 0.05", 0.1" and 0.3" respectively . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 Figure 34 (b) Surface deviation contours for 21 actuators arranged in a radial pattern and bonded to different surface material thickness of 0.05", 0.1" and 0.3" respectively . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 Figure 34 (c) Surface deviation contours for 39 actuators arranged in a radial pattern and bonded to different surface material thickness of 0.05",    OJ" and 0.3" respectively . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 92 Figure 38. Synthesized subreflector surface and Brazilian co-polarized Figure 39. Synthesized subreflector surface and Southern Mrica co-polarized Figure 40. Synthesized subreflector surface and Australian co-polarized Figure 35. Co-polarized far-field for the 0° elliptical beam case ............. . 94 Figure 36. Co-polarized far-field for the 45° elliptical beam case . . . . . . . . . . . . . 95 Figure 37. Co-polarized far-field for the 90° elliptical beam case . . ..... . . . .... 96 radiation pattern footprint . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 98 radiation pattern footprint. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 99 radiation pattern footprint. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. 100    

Reconfigurable contour beam synthesis using a mechanical FEM surface description of dual offset reflector antenna surfaces

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Reconfigurable contour beam synthesis using a mechanical FEM surface description of dual offset reflector antenna surfaces

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