7 I I . I4 DTIC ~4Z~ELECTE U OFB PLANAR ARRAY ANTENNA DESIGN ANALYSIS VOLUME I THESIS Bradley P. Chrisman Captain, USAF AFIT/GE/ENG/89D-4 DEPARTMENT OF THE AIR FORCE AIR UNIVERSITY AIR FORCE INSTITUTE OF TECHNOLOGY _ _ _ _ M_ O_ M _ _x Wright-Patterson Air Force Base, Ohio 89 12 o84 18 _____-J,-__,M,-.,. Ib. * U_,. ! AFIT/GE/ENG/89D-4 PLANAR ARRAY ANTENNA DESIGN ANALYSIS VOLUME I THESIS Presented to the Faculty of the School of Engineering of the Air Forc Tnq itut- of T-rhn(o'cgy Air University In Partial Fulfillment of the Requirements for the Degree of Master of Science in Electrical Engineering Bradley P. Chrisman, B.S. Captain, USAF December 1989 Approved for public release; distribution unlimited most important, I thank my wife Brenda and my daughter Andrea for their patience, understanding, and perseverance during those many hours I spent away studying or working on my thesis. Their encouragement is greatly appreciated, especially toward the end of the program where it counted the most. Bradley P. Chrisman iii Table of Contents Volume I Page Preface ......... ...................... ii List of Figures ........... .................. vii List of Tables ....... .................. xiii Abstract ............ ..................... xiv I. Introduction ..... ...... ................ 1 Background ......... .............. 1 Problem ..... ...... ................ 3 Scope ........... ................. 4 Assumptions/Limitations .............. 4 Review of the Literature ............. 6 Major Definitions ... ........... .11 Approach ..... ............... 15 II. Array Antenna Fundamentals .. ......... 18 Preliminaries .... ............. 19 Radiation Pattern ... ........... .21 Linear Arrays .... ............. 25 Arrays of Discrete, Identical Elements ......... 26 Linear Arrays - Fundamental Considerations ............... 29 Uniformly Excited Broadside Array .. ......... 30 Broadside Arrays with Tapered Excitation ......... 33 Scanned Linear Array ....... 34 Pattern Synthesis . ........ 36 Dolph-Chebyshev Linear Array Method 36 Discretized Taylor R-Parame ter Linear Array Method . 39 Planar Arrays .... ............. 45 Summary ..... ................ 48 III. The Effects of Random Errors on the Array Pattern ..... ................ 49 Sources of Errors Affecting Array Performance ... ........... .49 Reduction of Errors to Pure Ampiitude ann Phase Errors . . . . 51 iv Page Statistics of the Apparent Amplitude Error ..... 51 Statistics of the Apparent Phase Error ........ 53 Power Pattern .... ............. 56 Random Error Effects on Array Directivity ... ........... 61 Summary ...... ................ 65 IV. Program Mechanics .... .............. 67 Program Layout ... ............ 67 Program Development .. .......... 70 Part 1 - Data Entry and Element Excitation Routines . ....... 70 Part 2 - Radiation Pattern Calculations ... ........... 73 Part 3 - Design and Expected Beamwidth Calculations ........ 6 Part 4 - Directivity Calculations ... ........... 82 Part 5 - Output Routine and Recalculation .. .......... 85 Summary ...... ................ 90 V. Program Validation .... ............. 92 Validation of the Excitation and Pattern Routines ..... ............... .... 92 Validation of the Beamwidth and Directivity Calculation Routines . . 113 Beamwidth Validation ........ 113 Directivity Validation ...... 114 Error Validation ... ........... 115 Summary ...... ................ 131 VI. Conclusions and Recommendations ........ 136 Appendix A: Development of the Finite Length Dipole Element Factor .... ............ 139 Appendix B: Program List .... ............. 143 Appendix C: User's Guide .... ............. 144 Bibliography ........ ................... 155 Vita .......... ....................... 158 v Volume II Page Abstract.............. ............. ..... .. ....... I. Introduction................ ..... .. ....... Planar Array Antenna Design Analysis Code .......................... Program Names and Descriptions . . . .1 Appendix.................................5 PARRAY.FOR.......................6 AVERP.FOR......................21 BINOML. FOR.....................26 CHEBY.FOR.....................27 CI.FOR.......................29 DBWDTH.FOR.....................30 DESDIR.FOR.....................33 DESRP.FOR.....................36 DIPDIR.FOR.....................41 EBWDTH.FOR.....................42 ELDATA.FOR.....................45 ELEFEA.FOR.....................47 ELFAC.FOR.....................48 ERDATA.FOR.....................49 ERGFAL.FOR.....................52 ERPFEA.FOR.....................54 EXPDIR.FOR...................56 EXPRPF.FOR...................57 FACTRL. FOR.......................58 OUTPUT.FOR.....................59 PARFAC.FOR.....................62 PARFEA.FOR.......................63 REGFAL. FOR.....................64 ROMBER.FOR.......................66 SI.FOR.......................67 TAYLOR.FOR...................68 UNIFRM.FOR.....................72 USRDEF. FOR.....................73 vi List cf Figures Figure Page Half-Power Beamwidths for a Conical Beam -. Oriented Toward 6 = 6o, . ..0. ............. .. 14 2. Radiation Geometry ..... ............... . 22 3. Positional Notation for Array Elements ..... 27 4. Coordinate System for an (a) Even Number and (b) an Odd Number of Array Elements . . . . 31 5. Radiation Pattern for a Six Element, Uniformly Excited Linear Array with k Wavelength Interelement Spacing .... .............. 32 6. Radiation Pattern for a Five Element, Uniformly Excited Linear Array with Wavelength Interelement Spacing .... .............. 32 7. Radiation Pattern for a Five Element, Uniformly Excited Linear Array with One Wavelength Inter- element Spacing Showing the Grating Lobe at Theta = 90 ° ......... .. ............... 33 8. Radiation Pattern for an 11 Element Linear Array with a Binomial Current Distribution and Wavelength Interelement Spacing . ....... 35 9. Radiation Pattern for a 10 Element Linear Array with a Binomial Current Distribution and k Wavelenqth Interelement Spacing . ........ 35 10. Radiation Pattern for a Uniformly Excited, 12 Element Linear Array with Wavelength Inter- element Spacing, Scanned at 40° From Broadside 37 11. Radiation Pattern for a 10 Element, Dolph- Chebyshev Synthesized Linear Array with Wave- length Interelement Spacing Showing a -26 dB Side Lobe Level ...... ................ 40 12. Radiation Pattern for a 12 Element, Dolph- Chebyshev Synthesized Linear Array with Wave- length Interelement Spacing Showing a -35 dB Side Lobe Level ...... ................ 40 vii Figure Page 13. Radiation Pattern for a 19 Element, Taylor Synthesized (ni=6) Linear Array with 0.7 Wave- length Interelement Spacing and a -20 dB Design Side Lobe Level ...... ................ 44 14. Radiation Pattern for a 41 Element, Taylor Synthesized (i=6) Linear Array with ' Wavelength Interelement Spacing and a -25 dB Design Side Lobe Level ....... .................. 44 15. Planar Array Geometry .... ............. 46 16. Geometry for Beamwidth Calculations ...... 78 17. Coordinate Translation Steps for Beamwidth Calculations .... ............. . 79 18. Sample Output From PARRAY.EXE .. ......... 87 19. Radiation Pattern for a 10 Element, Dolph-Cheby- shev Synthesized Array with ), Spacing Showing a -26 dB Side Lobe Level ... ............ 95 20. Radiation Pattern for a 15 Element, Dolph-Cheby- shev Synthesized Array with x Spacing Showing a -35 dB Side Lobe Level ... ............ 95 21. Radiation Pattern for a 19 Element, Taylor Synthesized (h=6) Array with 0.7A Interelement Spacing and a -20 dB Side Lobe Level using Null Matching Weights ...... ................ 97 22. Radiation Pattern for a 19 Element, Taylor Synthesized (fi=6) Array with 0.7A Iinterelement Spacing and a -20 dB Side Lobe Level using Aperture Sampling Weights ... ........... 97 23. Radiation Pattern for a 21 Element, Taylor Synthesized (fi=7) Array with x Interelement Spacing and a -30 dB Side Lobe Level ...... . 99 24. Radiation Pattern for a 22 Element, Taylor Synthesized (i=8) Array with A Interelement Spacing and a -35 dB Side Lobe Level ...... . 99 25. Radiation Pattern for a 10 Element Array with a Binomial Current Distribution and %X Interelement Spacing .... .............. 101 viii Figure Page 26. Radiation Pattern for a 10 Element Array with a Binomial Current Distribution and kA Interelement Spacing .... .............. 101 27. Radiation Pattern for a 10 Element, Uniformly Excited Array with -A Interelement Spacing . . . 102 28. Radiation Pattern for a 16 Element, Uniformly Excited Array with 'A Interelement Spacing . . . 102 29. Radiation Pattern for a 5 Element Array iLh an Inverse-Triangular Current Distribution and -A Spacing ...... ................. 104 30. Radiation Pattern for a 5 Element Array with a Triangular Current Distribution with 'A Spacing ....... ................... 104 31. Radiation Pattern for a Half-Wavelength Dipole 106 32. Radiation Pattern for a Full-Wavelength Dipole 106 33. Radiation Pattern Overlay of a kA Dipole and a 10 Element, Dolph-Chebyshev Synthesized Array with X Interelement Spacing and -25 dB Side Lobe Level ...... .................. 107 34. XZ-Plane Radiation Pattern for a 10 Element, -25 dB Dolph-Chebyshev Synthesized Array with 'A Spacing ?nd X-Aligned Dipoles as Elements 107 35. Overlay of Radiation Patterns for a 1A Dipole and a 10 Element, -25 dB Dolph-Chebyshev Synthesized Array with -', Interelement Spacing 109 36. XZ-Plane Radiation Pattern of a 10 Element, -25 dB Dolph-Chebyshev Synthesized Array with -A Interelement Spacing and X-Aligned 1A Dipoles as Elements ....... .................. 109 37. Radiation Patterns for a 1x Dipole and a 10 Element, Dolph-Chebyshev Synthesized Array with A Interelement Spacing and a -25 dB Design Side Lobe Level Scanned at 30 ° From Broadside 110 38. Radiation Pattern of a 10 Element, Dolph- Chebyshev Synthesized Array with x Inter- element Spacing Showing a -25 dB Side Lobe Level Scanned at 30° Off Broadside with %A Dipoles as Elements ....... .............. 110 ix Figure Page 39. Radiation Patterns for a 1A Dipole and a 10 Element, Dolph-Chebyshev Synthesized Array with A Interelement Spacing Showing a -25 dB Design Side Lobe Level, Scanned at 30' Off Broadside ...... ................... 1 40. Radiation Pattern for a 10 Element, Dolph- Chebyshev Synthesized Array with 1 Inter- element Spacing and a -25 dB Design Side Lobe Level, and with IA Dipoles as Elements iI 41. No-Error Expected Radiation Pattern for a 10x15 Element, Dolph-Chebyshev Synthesized Array with A/2 Spacing and a -26 dB Design Side Lobe Level in Both Directions ........ .. 117 42. Expected and Design Radiation Patterns (xz-plane) for a 10xlO Element, Dolph-Cheby- shev Synthesized Array with X/2 Spacing and a -25 dB Design Side Lobe Level . ........ 120 43. Expected and Design Radiation Patterns (xz-plane) for a 10xl0 Element, Dolph-Cheby- shev Synthesized Array with A/2 Spacing and a -30 dB Design Side Lobe Level . ........ 120 44. Expected and Design Radiation Patterns (xz-plane) for a lOxlO Element, Dolph-Cheby- shev Synthesized Array with A/2 Spacing and a -35 dB Design Side Lobe Level .. ......... 121 45. Expected and Design Radiation Patterns (xz-plane) for a lOxlO Element, Dolph-Cheby- shev Synthesized Array with A/2 Spacing and a -40 dB Design Side Lobe Level .. ......... 121 46. Expected and Design Radiation Patterns (xz-plane) for a lOxlO Element, Dolph-Cheby- shev Synthesized Array with A/2 Spacing and a -30 dB Design Side Lobe Level .. ......... 123 47. Expected and Design Radiation Patterns (xz-plane) for a 12x12 Element, Dolph-Cheby- shev Synthesized Array with A/2 Spacing and a -30 dB Design Side Lobe Level .. ......... 123 48. Expected and Design Radiation Patterns (xz-plane) for a 15x15 Element, Dolph-Cheby- shev Synthesized Array with A/2 Spacing and a -30 dB Design Side Lobe Level .. ......... 124 x