Planar Array Antenna Design Analysis. Volume 1

176 Pages·2012·5.3 MB·English

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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
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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