VHF-UHF Phased Array Tec:hniqvles

120 Pages·2007·10.33 MB·English

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UPIR 3084 I
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PART I
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VHF-UHF Phased Array Tec:hniqvles
PART L CALCOMP Studies of Linear Arrays with
Non-Uniformly Spaced Isotropic: Elemc!nts
JOHN A. M. LYON, PHILIP H. FISKE,
MOHAMED A. HIDAYET, and JESS B. SCOTT
November 1973
Technical Report AFAL-TR-73-39'9, PART 1:
Distribution limited to 1I.S. Government Agencies only r
Test and Evaluation Data: November 1973. Other requlasts
for this document must be referred to AFAL/TEM.
Air Force Avionics Laboratory
Air Force Systems Command
Wright-Patterson Air Force Base, Ohio
NOTICE
When Government drawings, specifications, or other data are used for any purpose
other than in connection with a definitely related Government procurement operation,
the United States Government thereby incurs no responsibility nor any obligation
whatsoever; and the fact that the government may have formulated, furnished, or in
any way supplied the said drawings, specifications, or other data, is not to be regarded
by implication or otherwise as in any manner licensing the holder or any other person
or corporation, or conveying any rights orpermission to manpfacture, use, or sell any
patented invention that may in any way be related thereto.
Copies of this report should not be returned unless return is required by security
considerations, contractual obligations, or notice on a specific document.
VHF-UHF PHASED ARRAY TECHNIQUES
PART I: C:ALCOMP STUDIES OF LINEAR ARRAYS WITH NON-
UNIFORMLY SPACED ISOTROPIC ELEMENTS
John A. M. Lyon
Philip H. Fiske
Mohamed A. Hidayet
Jess B. Scott
Distribution limited to U. S. Government Agencies only; Test. a.nd
.
Evaluation Date; November 1973 Other requests for this doc~mlent
must be referred to AFALITEM.
FORE WORD
This report describes research performed LV The University of Michigan
Radiation I,aboratory, 2455 Hayward Street, Ann 'irbor, Michigan 48105 and
constitutes the first of two interim reports required under USAF Contract F33615-
71-6-1495, Task 05, Project 6099, "VHF-UHF Phased Array Techniques''. The
work was sponsored by the Electronic Technology Division, Air Force Avionics
Laboratory and the Technical Monitor was Mr. Harold E. Weber, AFAL~TEM-3.
The original work statement for this contract was quite different from the
modified work statement which was made available on 13 October 1972. The
present report covers items which were in the original work statement. A second
interim report will give coverage primarily to the amended work statement of 13
October 1972.
This report covers the time period 5 March 1971 through 30 June 1973 and
was prepared by John A. M. Lyon, Philip H. Fiske, Mohamed A. Hidayet and Jess B.
Scott; Professor Lyon also served as the Princip.il Investigator. The report has
been designated Radiation Laboratory Report Number 004970- 1-T for internal
control purposes. It was submitted for sponsor approval on 3 October 1973.
ABSTRACT
This report contains information obtained by numerous computer studies
of linear arrays of isotropic elements. A large range of numbers of elements
were used, Various formulations were used to provide control on the degree of
nc-kn-uniformity of spacing. Provision was made so as to provide a gradation in
the illumination of the various elements used. It was found that a simple expo-
nential relation provided illumination corresponding simultaneously to a l'cbebyscheff
t) pe radiation pattern.
It was decided that for practical purposes some restraint should be provided
011 the grading of the slot illumination from the center slot to either extreme end
slot. Therefore, in some of the studies utilizing an exponential variation of
illumination, an arbitrary limit was imposed which required the illumina1;ion on
the end slat to be either 9 or 12 dB below that of the center slot.
Considerable worlk was done on an optimization process, which has been
classified as the method of steepest descent. In the steepest descent method
a change in spacing is made in the direction that causes the most rapid rate of
change (reduction) in the difference between a prescribed radiation pattern and
the obtained radiation pattern. In other words, the change to be made was always
in the direction so as to decrease the error or difference between the two patterns
most rapidly, ln applying this optimization procedure it was decided that it was
appropriate to start with an array already reasonably well designed. For instance,
if a broadside Tchebyscheff array was selected, the optimization process would
be applied ancl changes would be made in the spacings of the elements so that the
sillelobe levels would be reduced.
iii

TABLE OF COhTENTS
Page
I INTRODUCTION
I1 USE OF COMPU'TER IN ARRAY PATTERN STUDY
2.0 Linear Array Formulation
2.1 Linear Array Program
2.2 Major Steps in Using CALCOMP
2 . Physical Constraints on Array
2.4 Random Errors in Arrays
2. 5 25-Element Arrays with Uniform Illumination but
Varied Spacings
2. 6 Studies on Variation of Tapered Illumination
2. 7 Studies Illustrating the Grating Lobe
2.8 Computer Simulations of Tschebyscheff Arrays
2.9 Optimization in the Presence of Power Constraints
2. 10 Optimization by Steepest Descent Technique
UI DISCUSSION ANT) CONCLUSIONS
REFERENCES
LIST OF ILLUSTRATIONS
Figure Page
Linear Array of Elements, Consisting of N Isotropic
Elements, where N is Odd. 7
Determination of fl's for Linear Array of Elements 7
Determination of Field Strength F for Linear Array
of Elements 10
Linear Array of Elements, Consisting of N Isotropic
Radiators, where N is Even. 10
-
Study A-1. 25 Elements Uniform Illumination and
Uniform Spacing of 0.331 X. 18
-
Study A-2. 25 Elements Uniform Illumination; Range
of Spacing 0.333X to 0.371 X. 19
-
Study A-3. 25 Elements Uniform Illumination; Range
of Spacing 0.333X to 0.414X. 20
-
Study A -4. 2 5 Elements Uniform Illumination; Range
of Spacing 0.333 X to 0. 513 A. 2 1
-
Study A-5. 25 Elements Uniform Illumination and
Uniform Spacing of 0.400h. 22
Study A-6. 25 Elements - Uniform Illumination; Range
of Spacing 0.40OX to 0.498 X. 23
-
Study A -7. 25 Elements Uniform Illumination and
Uniform Spacing of 0.500 A. 24
-
Study A-8. 2 5 Elements Uniform Illumination; Range
of Spacing 0. 500X to 0.558 A. 2 5
-
Study A-9. 25 Elements Uniform Illumination; Range
of Spacing O.500X to 0. S22h. 2 6
Study B-1. 150 Elements with Sn iform Spacing of 0.500 X.
.
Taper Factor CA 1 = 0.500 x 10 Each Abscissa Scale
Unit is 18'. 30
Study B-2. 150 Elements with Uniform Spacing of 0.500X.
5 .
Taper Factor CA 1 = 0.100 x 10 Each Abscissa Scale
Unit is 18'. 3 1
Study B-3. 150 Elements with Uniform Spacing of O.500X.
4
Taper Factor CA 1 = 0.500 x 10 . Each Abscissa Scale
Unit is 18'. 32
LIST OF ILLUSTRATIONS
(continued)
Fi gure Page
Study 13-4. 150 Elements with Uniform Spacing of 0.500X.
T a p r Factor. CA 1 = 0.200 x lo4. Each Abscissa Scale
Unit is: 18'- 33
Study 13-5. 150 Elements with Uniform Spacing of 0.500 X.
Taper Factor CA 1 = 0. 1.00 x lo4. Each Abscissa Scale
0
Unit is 18 34
Study B-6. 150 Elements with Uniform Spacing of 0. 500X
Taper Factor. (:A 1 = 0.800 x lo3. Each Abscissa Scale
Unit is; 18'. 35
Study 13-7. 150 Elements with Uniform Spacing of 0.500X
3 .
Taper Factor. CA 1 = 0.600 x 10 Each Abscissa Scale
Unit is; 18'. 36
Study 13-8. 150 Elements with Uniform Spacing of 0.500 X.
Taper Factor CA 1 = 0. 500 x lo3. Each Abscissa Scale
0 .
IJnit is' 18 37
Study 13-9. 250 Elements with Uniform Spacing of 0.500 X.
Taper Factor (;A 1 = 0.100 x lo5. Each Abscissa Scale
Unit is 18'. 3 8
Study 13-10. 250 Elements with Uniform Spacing of 0. 500X.
Taper Factor (>A 1 = 0.500 x 104 . Each Abscissa Sca.le
Unit is 18'. 39
Study 13-11. 250 Elements with Uniform Spacing of 0. 500 X.
4 .
Taper Factor CA 1 = 0.200 x 10 Each Abscissa Scale
Unit is 18'. 4 0
Study 13-12. 250 Elements with Uniform Spacing of 0. 500 X.
4
Taper Factor CA 1 = 0.180 x 10 . Each Abscissa Scale
Unit is 18'. 4 1
Study 13-13. 250 Elements with Uniform Spacing of 0.500X.
4 .
Taper :Factor CA 1 = 0.150 x 10 Each Abscissa Scale
Unit is 18'. 4 2
Stud,y B-14. 250 Elements with Uniform Spacing of 0. 500X.
Taper Factor CA 1 = 0.120 x 104 . Each Abscissa Scale
Unit is 18'. 4 3
Study B-15. 250 Elements with Uniform Spacing of 0. 500X.
4 .
Taper Factor (:A 1 = 0.100 x 10 Each Abscissa Scale
Unit is 18'. 44
LIST OF ILLUSTRATIONS
Figure (continued) Page
Study B-16. 250 Elements with Uniform Spacing of O.500X.
3
Taper Factor CA 1 = 0.800 x 19 . Each Akscissa Scale
Unit is 18'. 45
Study 6-1 on Grating Lobes. 250 Elements with Uniform
Spacing of 0.600X~T aper Factor CA 1 = 0.100 x 105 .
Each Abscissa Scale Unit is 18'. 47
Study C-2 on Grating Lobes. 250 Elements with Uniform
Spacing of 0.60Qh. Taper Factor CA 1 = 0.500 x lo4.
Each Abscissa Scale Unit is 18'. 48
Study C-3 on Grating Lobes. 250 Elements with Uniform
Spacing of 0.6OOX. Taper Factor CAI 10.100 x lo4.
Each Abscissa. Scale lJnit is 18'. 49
Study C-4 on Grating Lobes. 250 Elements with Uniform
Spacing of O.750h. Taper Factor CA 1 = 0.100 x lo5.
Each Absei.ssa Scale Unit is 18'. 50
Study C-5 on Grating Lobes. 250 Elements with Uniform
Spacing of 0.750X. Taper Factor CA 1 = 0.500 x lo4.
Each Abscissa Scale Unit is 18'. 5 1
Study C-6 on Grating Lobes. 250 Elements with Unid o rm
.
Spacing of 0.750A. Taper Factor CA 1 = 0.100 x 10
Each Abscissa Scale Unit is 180 . 52
Study D-1 on Tschebyscheff Simulation. 25 Elements with
Uniform Spacing of 0.500J . Taper Factor CA 1 = 0.550 x
10. Each Abscissa Scale Unit is 7.' 54
Study D-2 on Tschebyscheff Simulation. 25 Elements with
Uniform Spacing of O.500X. Taper Factor CA 1 = 0.140 x
lo2.
Each Abscissa Scale Unit is 18'. 55
Study D-3 on Tschebyscheff Simulation. 200 Elements
with Uniform Spacing of O.500X. Taper Factor CA 1 =
0.100 x lo4. Each Abscissa Scale Unit is 0.6 0 . 56
Study D-4 on Tschebyscheff Simulation. 280 Elements
with Uniform Spacing of 0.500 A. Taper Factor CA 1 =
0.180 x lo4. Each Abscissa Scale Unit is 10 . 57
Study D-5 on Tschebyscheff Simulation. 200 Elements
with Uniform Spacing of O.500h Taper Factor CA 1 =
0.700 x lo3. Each Abscissa Scale Unit is 0.6 0 . 58