EXPERIMENTAL INVESTIGATION OF THE MODIFICATION
OF THE BACKSCATTE‘RING CROSS SECTIONS OF
METALLIC OBJECTS

Thesis for the Degree of Ph. D.-
MICHIGAN STATE UNIVERSITY
MERVIN Ce VINCENT

1957 ’

 

    
      

LIBRARY

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INN-t. O in State
University

[Habits

This is to certify that the

thesis entitled
EXPERIMENTAL INVESTIGATION OF THE
MODIFICATION OF THE BACKSCATTERING

CROSS SECTIONS OF METALLIC OBJECTS
presented by

Mervin C. Vincent

has been accepted towards fulfillment

of the requirements for ' -
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fill.— degree mm

Mser C as;

F Major professor

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Date 11-16-67

0-169

EXPERIMENTAL INVESTIGATION OF THE MODIFICATION
OF THE BACKSCATTERING CROSS SECTIONS

OF METALLIC OBJECTS

BY

Me rvin C . Vinc ent

AN ABSTRACT OF A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOC TOR OF PHILOSOPHY

Department of Electrical Engineering

1967

 

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ABSTRACT

EXPERIMENTAL INVESTIGATION OF THE MODIFICATION
OF THE BACKSCATTERING CROSS SECTIONS
OF METALLIC OBJECTS

by Mervin C. Vincent

An experimental investigation on the backscattering cross
sections of the metallic objects of various shapes are presented.
The metallic scatterers are assumed to be illuminated by a plane
electromagnetic wave at normal incidence. The modification of
the backseattered fields of these targets are accomplished by
employing the impedance loading method or the compensation
method. The impedance loading method is to add some impedances
on the object surface and the compensation method consists of
attaching some impedance loaded wires to the target object.

The backscattering cross section of a sphere is modified
by the addition of two vertical cylinders loaded with appropriate
impedances. Both theory and experiment yield results which are
in good agreement. The backscattering cross sections of loops,
either circular or rectangular, are modified by loading the loop
with a pair of impedances positioned symmetrically on opposite
sides of the loop. The backscattering of a plate is modified by
placing an impedance loaded loop in front of the plate. Similarly,
the scattered field of a thick cylinder is modified by placing a thin
loaded cylinder adjacent to it. In all these schemes, a coaxial line

(or cavity) has been used as the loading impedance in the experiment.

 

methods cn‘
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MER VIN C . VINC ENT

The bandwidths of the impedance loading and the compensation
methods employed for modifying the backscatters of the above objects
are improved by either using a coaxial line (or cavity) with a high
characteristic impedance or adding a resistive component to the

impedance loading.

EXPERIMENTAL INVESTIGATION OF THE MODIFICATION
OF THE BACKSCATTERING CROSS SECTIONS

OF METALLIC OBJECTS

BY

Mervin C . Vincent

A THESIS

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY

Department of Electrical Engineering

1967

 

'Ihe a
professc-r Dr
the course (1'
of his guidam
and Dr. P. PI

Nyquist for c

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Appreciatit
Hef-fman of th

reported in :E

Research Lab

ACKNOWLEDGMENTS

The author wishes to express his indebtedness to his major
professor Dr. K. M. Chen for his guidance and encouragement in
the course of this research. He also wishes to thank the members
of his guidance committee, Dr. L. W. Von Tersch, Dr. B. Ho,
and Dr. P. K. Wong for reading the thesis and Dr. Dennis P.
Nyquist for correcting the manuscript and valuable suggestions.
Appreciation is also expressed for the help extended by Mr. J. W.
Hoffman of the Division of Engineering Research. The research
reported in this thesis was supported by the Air Force Cambridge

Research Laboratories under contract AF l9(628)-5732.

ii

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ACKNOWLED
LIST OF FIG'L

I. INTRODCC

1.1. INIuIi‘.
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1.2. Defin:
1.3. Backs
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TABLE OF CONTENTS

Page
ACKNOWLEDGMENTS ..................... ii
LIST OF FIGURES . . . ............... . . . . . iv
I. INTRODUCTION . .......... . . . . . . . . . . . 1

1.1. Motivation and History of Radar Back-

scattering Measurements. . . . . . . . . . . . . . . 1

l. 2. Definition of Radar Backseattering Cross Section . . 3
1.3. Backscatter Measurement Techniques . . . . . . . . 5
1.4. Outline of Research Objectives. . . . . . . . . . . . 6
II. EXPERIMENTAL ARRANGEMENT . . . . . ..... . . 10
2.1. Measurement Apparatus . . . . ..... . . . . . . 10
2.2. Experimental Techniques. . . . . . . . . . . . . . . 20
2.2.1. SWR Method . . . . . ........ . . 21

2.2.2. The Cancellation Method. . . . ..... . . 27

III. MODIFICATION OF BACKSCATTERING FROM
A SPHER E O O C O O O O O O O O O O O O O O O O O O O O O O 3 Z

3 1 Theory 0 O O O O O O I I O O O C O O O O O O O O O O O 32

3 0 2. EXPeriment O O O O O O O O O O O O O O ........ 40

3 3 Comparison of Theory and Experiment ....... 44
IV. MODIFICATION OF BACKSCATTERING FROM

METALLIC LOOPS . . ...... . . . . . . . ..... 53

4.1. Circular Loop ....... . . . . . ..... . . . 53

4.2. Rectangular Loop . . . . . . . . . . . ...... . . 56
V. MODIFICATION OF BACKSCATTERING FROM

A CONDUCTING PLATE ........ . . . . . ..... 73

5 1 Round Plate and Loop ............ . . . . . 73

5.2. Rectangular Plate and Loop ..... . . . . . . . . 96
VI. MODIFICATION OF BACKSCATTERING FROM

CYLINDERS . O O O O O O O O O O O O O O O O O ...... 106

6.1. Solid and Loaded Cylinders. . . . . ........ 106

6.1.1. Solid or Unloaded Cylinder . . . ...... 106

6.1.2. Impedance Loaded Cylinder . . . . . . . . . 108
6. 2. Thick Cylinder With a Parallel, Impedance
Loaded Thin Cylinder ....... . . . . . . . . . . 110

VII. TECHNIQUES FOR BANDWIDTH IMPROVEMENT . . . 124

7.1. Resistive Loading. . . . . . . . ..... . . . . . . 124
7. 2. Reactive Loading Using a Coaxial Cavity with
High Characteristic Impedance. . . . . . . . . . . . 128

REFERENCES . . ...... . . . . . ............ 132

iii

 

 

 

Figure

LIST OF FIGURES

Figure Page
1.1. Geometry of problem of sphere . . . . . . . . . . . . 7
1.2. Geometry of problem ofaloop . . . . . . . . . . . . 7
1.3. Circular plate witha loaded loop . . . . . . . . . . . 8

1.4. Thick cylinder with loaded thin cylinder . . . . . . . 8

2.1. Anechoic chamber showing access from rear . . . . 12
2. 2. Anechoic chamber with a scattering target

and the transmitting horn . . . . . . . . . . . . . . . 13
2.3. Layout of ground plane ............. . . . 15
2.4. Description of detector probe mount . . . . . . . . . 18
2.5. Structure of the probe carriage . . . . . . . . . . . . 19

2.6. Physical description of the SWR method . . . . . . . 23
2. 7. Experimental arrangement of the SWR method . . . . 24
2. 8. SWR of the empty anechoic chamber as a function

of the distance of probe from the transmitting
horn (f = Z. 0 GHZ) O O I O I O O O O O O O O O O O O O O 26

2. 9. Experimental arrangement of the cancellation

methOd O O I O O O O I O O O O O O O O O O O O O O O O O 29
3.1. Geometry of problem of sphere with loaded wires . . 33
3. 2. Geometry of reduced problem of sphere with

loaded Wires O O O O I I O O O O O O O O O O O O O O O O 33
3. 3. Optimum loading impedance for zero broadside

backseatter from sphere with loaded wires as a

function of electrical length of wires . . . . . . . . . 39

3.4. A sphere with loaded wires . . . . . . . . . . . . . . 41
3. 5. Backseattering cross section of a sphere with

loaded wires as a function of loading impedance
of loaded wires (a = 5.71 cm, h = 3.5 cm) . . . . . . 45

iv

 

Figure

3.6.

3.7.

3.8.

3.10.

3.12.

In

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Figure

3.6.

3.7.

3.8.

3.9.

3.10.

3.11.

3.12.

4.1.

4. 2.

4.3.

4.6.

4. 70

LIST OF FIGURES (continued)

Backscattering cross section of a sphere with
loaded wires as a function of loading impedance
of loaded wires (a = 5.71 cm, h = 6.1 cm) . . .

Backscattering cross section of a sphere with
loaded wires as a function of loading impedance
of loaded wires (a = 5.71 cm, h = 6.7 cm) . . .

Backscattering cross section of a sphere with
loaded wires as a function of loading impedance
of loaded wires (a = 5.71 cm, h = 8.4 cm) . . .

Backscattering cross section of a sphere with
loaded wires as a function of loading impedance
of loaded wires (a = 5.71 cm, h = 10.5 cm) . .

Maximum and minimum backseatters from a
sphere with loaded wires as a function of
electrical length of wires . . . . . . . . . . . .

Optimum reactance for minimum backscatter
from a sphere with loaded wires as a function
of electrical length of wires . . . . . . . . . .

Optimum reactance for maximum backseatter from

a sphere with loaded wires as a function of
electrical length of wires . . . . . . . . . . . .

Loaded, circular wire loop . . . . . . . . . . .
Loaded square wire loop . . . . . . . . . . . .

Backscattering cross section of a loaded loop
as a function of loading impedance (f = 1. 61 GHz

Backscattering cross section of a loaded 100p as
a function of loading impedance (f = 1. 7 GHz) .

Backscattering cross section of a loaded 100p as
a function of loading impedance (f = 1. 75 GHz) .

Backscattering cross section of a loaded loop as
a function of loading impedance (f = 1. 8 GHz) .

Backscattering cross section of a loaded 100p as
a function of loading impedance (f = l. 9 GHz)

)

Page

46

47

48

49

50

51

52
54

57

60

61

62

63

64

 

 

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4. 8.

4.15.

5.1.

5. 2.

5.3.

5. 4.

5. 5.

5.6.

LIST OF FIGURES (continued)

Backscattering cross section of a loaded loop as
a function of loading impedance (f = 2. 0 GHz) . .

Backscattering cross section of a loaded loop as
a function of loading impedance (f = 2.1 GHz) . .

Backscattering cross section of a loaded loop as
a function of loading impedance (f = 2. 2 GHz) . .

Backscattering cross section of a loaded loop as
a function of loading impedance (f = 2. 3 GHz) . .

Backscattering cross section of a loaded loop as
a function of loading impedance (f = 2. 4 GHz) . .

Backscattering cross section of a loaded loop as
a function of loading impedance (f = 2. 5 GHz) . .

Optimum reactive impedance for minimum
backscattering from a loaded loop illuminated
by a plane wave at normal incidence . . . . . . .

Optimum reactive impedance for maximum
backscattering from a loaded 100p illuminated
by a plane wave at normal incidence . . . . . . .

Circular plate and loaded loop . . . . . . . . . .
Backscatter of the small circular plate with a
loaded loop as a function of loop loading

(f=1.9GHz)...................

Backscatter of the small circular plate with a
loaded loop as a function of loop loading

(f = 1.97 GHz) ....................

Backscatter of the small circular plate with a
loaded 100p as a function of loop loading
(f : 2. 1 GHZ) O O O 00000000000000 O O

Backscatter of the small circular plate with a
loaded loop as a function of 100p loading

(f=2.2GHz) .......... ...........

Backscatter of the small circular plate with a
loaded loop as a function of loop loading
(f : 2. 78 GHZ) O O O O O O 0 O O O O O O O O O O 0

vi

Page

65

66

67

68

69

7O

71

72

74

76

77

78

79

80

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5.7.

5. 8.

5. 9.

5.10.

5.11.

5.12.

5.13.

5.14.

5.15.

5.16.

5.17.

5.18.

LIST OF FIGURES (continued)

Backscatter of the medium circular plate with
a loaded loop as a function of loop loading
(f : 2O 1 GHZ) O O O O O ..... O O O O O O O O

Backscatter of the medium circular plate with
a loaded loop as a function of loop loading
(f : 2O 2 GHZ) O O O O O O O O O ..... O O O O

Backscatter of the medium circular plate with
a loaded loop as a function of loop loading
(f = 2O 3 GHZ) O O O ..... O O O O O O O O O O

Backscatter of the medium circular plate with
a loaded loop as a function of loop loading

(f=2.4GHz)....................

Backscatter of the medium circular plate with
a loaded loop as a function of loop loading
(f = 2O 5 GHZ) O O O O O O O O O O O O O O O O O O

Backscatter of the medium circular plate with
a loaded loop as a function of loop loading
(f : 2O 7 GHZ) O O O O O O O O O O O O O O O O O O

Backscatter of the medium circular plate with
a loaded loop as a function of loop loading

(f=2.9GHz)...... ..............

Backscatter of the medium circular plate with
a loaded 100p as a function of loop loading

(f=3.04GHz) .. . . . ..............

Backscatter of a large circular plate with a
loaded loop as a function of loop loading

(f=1.9GHz).. ............. .....

Backscatter of a large circular plate with a
loaded loop as a function of loop loading

(f = 1.97 GHz) ......... . .........

Backscatter of a large circular plate with a
loaded loop as a function of 100p loading
(f : ZOl GHZ) O O O O O O O O OOOOO O O O O O

Backscatter of a large circular plate with a
loaded loop as a function of loop loading

(f = 2.3 GHz) ....................

vii

Page

81

82

83

84

85

86

87

88

89

90

91

92

 

   

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5.19.

5.20.

5.21.

5.22.

5.23.

5. 24.

5.25.

5.26.

5.27.

5.28.

LIST OF FIGURES (continued)

Backscatter of a large circular plate with a

loaded loop as a function of loop loading
(f = 2O 5 GHZ) O O O O O O O O O O O O O O O O O O O O O

Backscatter of a large circular plate with a
loaded loop as a function of loop loading
(f = 2O 78 GHZ) O O O O O O O O O O O O O O O O O O O O

Optimum impedance for minimum backscattering
from a circular plate with a loaded circular loop. .

Rectangular plate and loaded loop . . . . . . . . . .

Backscatter of the small rectangular plate with
a loaded loop as a function of loop loading
(f : 1O 72 GHZ) O O O O O O O O O O O O O O O O O O O O

Backscatter of the small rectangular plate with
a loaded loop as a function of loop loading
(f : 1O 8 GHZ) O O O O O O O O O O O O O O O O O O O O O

Backscatter of the small rectangular plate with
a loaded loop as a function of loop loading
(f : 1O 97 GHZ) O O O O O O O O O O O O O O O O O O O O

Backscatter from a large rectangular plate with
a loaded loop as a function of loop loading
(f : 1O 72 GHZ) O O O O O O O O O O O O O O O O O O O O

Backscatter from a large rectangular plate with
a loaded loop as a function of loop loading
(f : 1O 8 GHZ) O O O O O O O O O O O O O O O O OOOOO

Backscatter from a large rectangular plate with
a loaded loop as a function of loop loading

(f=l.97GHz)....................

Backscattering cross sections of solid cylinders
as a function of cylinder half-length h .......

Physical description of cylinders . . . ...... .
Thick cylinder with a loaded thin cylinder . . . . .
Backscattering cross section of a thick with a
loaded thin cylinder as a function of loading

impedance of thin cylinder (h1 = 2. 5 cm,
hZ : 2O 7 Cm) O O O O O O O O O O O O O O O O O O O O O

viii

Page

93

94

95
98

100

101

102

103

104

105

107
109

112

114

LIST OF FIGURES (continued)

Figure Page

6. 5. Backscattering cross section of a thick with a
loaded thin cylinder as a function of loading
impedance of thin cylinder (h1 = 3. 8 cm,
h2=12.9cm)...................... 115

6. 6. Backscattering cross section of a thick with a
loaded thin cylinder as a function of loading
impedance of thin cylinder (h1 = 12. 8 cm,
h2=15.2cm)...................... 116

6. 7. Maximum and minimum backscatters from a
thick with a loaded thin cylinder as a function
of thin cylinder half-length h2 (h1 = 2.5 cm) . . . . . 117

6. 8. Maximum and minimum backscatters from a
thick with a loaded thin cylinder as a function
of thin cylinder half-length h2 (h1 = 3. 8 cm) . . . . . 118

6. 9. Maximum and minimum backscatters from a
thick with a loaded thin cylinder as a function
of thin cylinder half-length h2 (h1 = 5.0 cm) . . . . . 119

6. 10. Maximum and minimum backscatters from a
thick with a loaded thin cylinder as a function
of thin cylinder half-length h2 (h1 = 10.1 cm) . . . . 120

6. 11. Maximum and minimum backscatters from a
thick with a loaded thin cylinder as a function
of thin cylinder half-length h2 (h1 = 11.6 cm) . . . . 121

6. 12. Maximum and minimum backscatters from a
thick with a loaded thin cylinder as a function
of thin cylinder half-length h2 (h1 = 12.8 cm) . . . . 122

6.13. Maximum and minimum backscatters from a
thick with a loaded thin cylinder as a function of
thin cylinder half-length h2 (h1 = 15. 0 cm). . . . . . 123

7.1. Backscattering cross section of a cylinder loaded
with reactive and resistive elements as a function

of reactive loading impedance (h : 2.7 cm) . . . . . . 125

7. 2. Backscattering cross sections of solid and loaded
cylinders as a function of frequency (h = 3. 5 cm) . . . 127

ix

 

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LIST OF FIGURES (continued)

Page

Backscattering cross sections of solid and loaded
cylinders as a function of frequency (h = 3. 5 cm) . . . 129

Backscattering cross sections of sphere and sphere
with loaded wires as a function of frequency
(a=5.71cm,h=3.4cm)............... 130

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CHAPTER I

INTR ODUC TION

Since the first experiments with radio waves by Hertz, there
has been qualitative observations that radio waves are scattered
and reflected by almost everything. The only interest at that time
was in modifying these reflections and scatterings from the supporting
towers of broadcast antennas and surrounding structures. However,
the interest in scattering of radio waves has increased exponentially
since the invention of radar in World War II. In recent years, radar
has been used to detect the space vehicles in addition to many
conventional aircrafts. As the result, intensive research on radar
measurements has improved its detecting efficiency tremendously
and consequently has generated great interest in methods of radar

camouflage as a counter measure to this advance.

1.1. Motivation and History of Radar Backscattering Measurements

 

A great number of the investigations performed thus far in
the area associated with the radar backscattering cross sections of
metallic bodies have been concerned with theoretical problems. The
value of experimental investigations of scattered fields is quite obvious,
however, when one realizes that there are very few bodies for which
exact solutions for the scattering is possible, although there are,
of course, excellent approximate solutions for a small number of
simple shapes. Much dependence is placed upon approximate solutions

in theoretical backscattering studies, and experimental results have

 

 

been very important in helping to develop such solutions and in
justifying their validities.

There are many metallic bodies which are far too complex
to allow either exact or approximate solutions for the scattered
fields. The backscattering cross sections of most space vehicles,
trucks, ships, and similar objects must always be determined
experimentally, although approximate formulas have been developed
for some which permit fairly accurate calculations of the scattering
patterns. It is the comparison with experimental data which has
made it possible to prove the reliability of these theoretical
techniques.

It is believed that the first comprehensive backscattering
cross section measurements, using models, were those performed
at Ohio State Lniversity around 1945. The principle objective was
to obtain the backscattering cross sections of aircrafts for use in
the design of decoys as radar-confusing devices. Since that time,
many advancements have been made in the techniques for measuring
scattering cross sections. Several of these methods are described
by King and Wu, 1 and Blacksmith, Hiatt, and Mack. 2

In recent years, the modification of the backscattered fields
of metallic cylinders has been studied with success by Chen and
Liepa, 3 -5 where the scattering cross sections were controlled by
either central loading of the cylinder or double loading at two
symmetric points along its axis. Liepa and Senior6 have reduced
the backscattering cross section of a metallic sphere by installing

a circumferential slot backed by an impedance on the spheric surface.

 

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An investigation was also made on the modification of the backscattering
cross section of a conducting plate by the techniques of cutting resonant
slots or installing a cavity-backed aperture on the plate. 7 Recently,
there has been some successful theoretical work performed on the
modification of the scattering cross section of a conducting wire loop.
This was also accomplished by the technique of loading the loop at

two symmetrical points with a pair of identical impedances. 8 In

most cases, however, the theoretical work is neither extensive nor
exact, which again stimulates an interest in the experimental aspect

of the problem.

1. 2. Definition of Radar Backscattering_Cross Section

 

In the study of the backscattering problem, where the fraction
of incident energy which is scattered or reflected by an object in a
given direction is desired, a scattering cross section for the object

is usually defined. This scattering cross section 0' is defined as

2 lsj<e.¢)l
6(9,¢,9..<I>.) = lim 4wR . (1.1)
1 1 R-m IS‘(ei.¢i)I

 

where R, 9 , <1), are spherical coordinates with the scattering
object fixed at their origin, Si is the time-average Poynting vector
of a plane wave incident upon the object from the direction 91, (Pi,
and S: is the time-average radial component of the Poynting vector,
corresponding to the scattering in a direction 9 , (I) at a far-field
distance R from the object. When 0‘ is evaluated in the direction
of the incident wave, it is called the backscattering cross section;

in any other direction it is referred to as the bistatic cross section.

.u .6 I. .I .t 11 PL
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It is the backscattering cross section which will be of interest through-
out this research.

In the radiation zone or far-zone of the object the scattered
wave is spherical, the radiation field components are transverse,
and the Poynting vector has only a radial component with a time-

average value given by

s:(e,¢)=1§Re1‘~- (ESXEST) (1.2)
E8 and H8 are the scattered electric and magnetic fields, and i"

is a unit vector in the radial direction. Additionally, the illuminating
field at the scatterer is nearly a plane wave. Since it is known that
the electric and magnetic fields are mutually orthogonal to one

another in the far-zone and are related by

as 9 x ES

H = —— (l. 3)
where Q is the characteristic wave impedance of the media, the

Poynting vector for the scattered field can be written as

s _ 1 jES(e,¢)1Z
Sr(es¢) — 2— g (1.4)

The Poynting vector for the incident field can be found in a similar
manner. The backscattering or radar cross section of an object
then becomes
2 stw «1112
o(9,¢) : lim 411R 4i 3 2 (1.5)
R-wo IE (9.4»!
where Es(9 , (P) is the component of the scattered field at the receiver,

in the direction (9 , Cb) , which is polarized parallel to the incident

F:

 

 

 

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plane wave field ERG , 4)) which illuminates the object from the
same direction (9 , <13) as that in which the scattered field is
measured.

In this research a ground plane measuring range has been
used. The incident and scattered fields are vertically polarized
with reference to the ground plane, and the illuminating field is
incident broadside (9 = 00) to all the scattering models which are
studied. Off-broadside angles were not considered in this research
since the image-type scattering range utilized is not suitable for
such measurements.

Dimensionally, (r is an area which is usually specified in
square meters, but can be expressed in decibels referred to some

standard backscattering cross section 00.

1.3. Backscatter Measurement Techniques

 

Procedures or methods for measuring 0' are quite easily
deduced from the definition of cr in terms of the incident and
scattered fields. Although many measurement methods have been
developed, only two of these are utilized in this research; they are
the SWR (standing wave ratio) and the cancellation methods. The
SWR method is analogous to transmission line measurement
techniques, in that the absolute value of 0' can be determined
from measurements of the standing waves caused by interference
of the incident field and the scattered field due to the scattering
model. The cancellation method provides a way of measuring the
relative value of 0' by cancelling out the detected incident signal

at the measuring probe and measuring only the reflected signal.

 

I

I?

 

back

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13 : it
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5.110

Of these two techniques for measuring 0' , the latter has a much
faster data rate and provides adequate information in most cases,
although a standard reference model, usually a sphere, is needed
for absolute measurements of o . The cancellation method is

used almost exclusively for the models studied in this research.

1. 4. Outline of Research Objectives

 

Both experimental and theoretical investigations of the
backscattering cross section of a sphere are carried out in this
research, as well as experimental studies of backscattering from
a plate, round and square loops, and cylinders. Further, both
minimization and enhancement of the backscattering cross sections
of these objects are studied, although minimization is studied more
extensively. The radar cross section of a sphere is modified by
attaching two thin, loaded cylinders symmetrically to it as shown
in Figure 1.1. The total backscattering of the composite of sphere
and cylinder can be controlled by adjusting the impedance which
loads the cylinder. To modify the backscattering cross section
of the loop, it is loaded symmetrically with a pair of identical
impedances as shown in Figure 1. 2. Again the backscattering can
be controlled by adjusting the impedance loading on the loop. This
is done successfully for both the square and the round loops. By
a technique similar to that for the sphere, the backscattering from
a plate can be modified by means of a composite structure. The
scheme of this method is to place a loaded loop directly in front of
the plate and parallel to it as shown in Figure 1. 3 so that the total

backscatter of the plate and loop can be controlled by adjusting the

sphere

  
  
 
 

loading

/impe danc e

L
”III/IA

thin c ylinde r

Figure 1.1. Geometry of problem of sphere.

 

 

2a

 

 

loading impedance

Figure 1. 2. Geometry of problem of a loop.

 

 

 

 

 

large plate (1 = 12. 7 cm
medium plate (1 = 10. 2 cm
small plate d = 7.6 cm
1
d
E
t

 

 

1111

Figure 1. 3. Circular plate with a loaded loop.

 

loading impedanc e

 

 

 

Figure 1. 4. Thick cylinder with loaded thin cylinder.

loading impedance. The backscatter from a thick cylinder can be
modified in a similar way as that for the plate. A thin loaded
cylinder is placed in the plane containing the large cylinder and
transverse to the incident field as shown in Figure 1. 4. The thin
cylinder can be placed a small distance on either side of the thick
cylinder since the cylinder has azimuthal symmetry. By adjusting
the impedance, the total backscatter of the two cylinders can be
controlled.

As a further investigation on the modification of the back-
scattering cross sections of these objects, the bandwidth
characteristics are studied. In all of the above models, only
reactive loading was considered, which in most cases was sufficient
to minimize the backscattering of these models. Addition of
resistive components and careful design of a reactive loading have

been tried and have been found to improve the bandwidth.

CHAPTER II

EXPERIMENTAL ARRANGEMENT

Backscattering measurements logically would be performed
out-of-doors since the ultimate purpose of these measurements is
its use on full-scale objects such as space vehicles. In most cases
these full-scale measurements are both too expensive and
inconvenient. This readily suggests scaled model measurements
which can be done indoors. Since free space conditions can easily
be simulated indoors, measurement variables involved may be

scaled without loss of generality.

2.1. Measurement Apparatus

 

The experimental arrangement consists basically of an
anechoic chamber constructed on an aluminum image or ground
plane. It is in this anechoic chamber that all the experimental
measurements are made. The purpose of this chamber is to
simulate a free space environment, which is the usual electro-
magnetic medium upon which actual radar systems depend for
their operation. Furthermore, the measurements can be performed
above the ground plane with only a detecting probe placed inside the
chamber. This reduces the possibility of extraneous reflections
from monitoring devices. The dimensions of the anechoic chamber
are adjusted so that the measuring devices are in the radiation zone
of both the source antenna and the scattering body. A simultaneous
requirement is that the scattererbe in the radiation field of the

transmitting antenna such that the incident wave approximates a

10

ll

plane wave field. These conditions require that the distances of
concern be of the order of 10 wavelengths. At a frequency of
2 GHz, the distance requirement for the radiation zone is therefore
approximately 150 cm or about 60 inches.

The anechoic chamber is constructed as shown in Figures
2.1 and 2. 2. It consists of a tapered wooden structure with the
dimensions of 3.65 meters (12 feet) in length, 3. 05 meters (10
feet) and . 915 meters (3 feet) respectively in width at the two ends,
and 1. 22 meters (4 feet) in height. The narrow end of the chamber
is left Open. This chamber structure then is located above a
rectangular aluminum ground plane erected 1. 02 meters (40 inches)
above the floor. The dimensions of the ground plane are 3. 65
meters in length, 3. 05 meters in width, and .635 cm thick. The
wooden table supporting the ground plane has dimensions of 3. 65
meters in length, 3. 05 meters in width, and l. 02 meters in height.
No metallic parts are used in the construction of the anechoic
chamber. All measurement and monitoring apparatus are located
beneath the conducting image plane. The shielding effect of the
ground plane thus eliminates the possibility of spurious reflections
from the equipment or its operator. The walls of the chamber are
secured with glue and wooden dowels to avoid any possibility of
unnecessary stray reflections. The three wooden walls and tOp
are covered with B. F. Goodrich type VHF-8 microwave absorbers.
This R. F. absorber is effective, over the range of frequencies
used (1. 7 - 4.1 GHz), in reducing the reflected power by at least

20 dB. It is felt that any interaction of the reflected fields with the

12

I I. l\ _ _l I

 

Figure 2.1. Anechoic chamber showing access from rear.

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incident and scatter fields is entirely negligible. This topic is
discussed in greater detail in the description of the SWR method.

The narrow open end of the tapered anechoic chamber is
used as the location for the transmitting antenna which provides
the incident traveling wave, while the scattering models being
studied are positioned at its wide end. For convenience of access
to the rear of the chamber, a square hole is cut in its rear wall
with the dimensions of .61 meters (2 feet) on a side, exactly the
size of a piece of microwave absorber. Thus a removable door
with a section of absorber provides the required access whenever
a change of scattering models is necessary.

The construction of the ground plane is as indicated in
Figure 2. 3. Field measurements in the chamber are facilitated
by a . 318 cm (0.125 inch) wide slot which is cut in the ground
plane and through which a detecting probe protrudes. The slot
starts approximately 1. 52 meters (5 feet) from the front of the
plate and terminates . 915 meters (3 feet) from the opposite end.
It is centered in the transverse dimension of the image plane. A
transmitting horn is placed approximately 80 cm from the front of
the slot and the models under study are placed essentially 23 cm
from its terminal end. The separation between the transmitting
horn and scattering element is of the order of 15 wavelengths,
which easily allows a detecting probe to be properly located between
the spherical wave source and scatterer such that it is in the far
zone field of either element. It should be noted that the ground plane

has dimensions of the order of 20 wavelengths by 24 wavelengths

15

 

 

I

 

ground

plane \

 

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ting horn

slot

 

 

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4
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A
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A
4
A

9 in.
T@\ scattering

element

 

A 10ft

 

 

Figure 2. 3. Layout of ground plane.

 

i1 2 ft

 

 

16

which surrounded by absorbers Will essentially eliminate the edge
effects, characteristic of a non-infinite image plane. Further,
since the microwave absorber terminates against the ground plane
along most of the chamber extremities, particularly along the side
walls where they rest on the ground plane, the surface wave fields
at the plate edges (and hence the reflections) are negligible.

A pyramidal transmitting horn (Scientific Atlantic Standard
gain horn, model 12-1. 7) is utilized with a lower cutoff frequency
of 1. 7 GHz. The horn is driven by a General Radio microwave
oscillator (GR 1360B) having a frequency range from 1.7 to 4.1 GHz.
A 50 ohm coaxial (RG58) transmission line is used to couple the
microwave energy from the generator to the transmitting horn. The
horn is placed directly upon. the ground plane such that the radiated
field is imaged continuously to form the total transmitted wave.
Since the radial distance between the horn and scattering element
is of the order of 15 wavelengths, then the wave incident upon the
scatterer may be assumed to consist of a plane wave field provided
its height is small compared with the above radial separation.
Furthermore, since the horn is assumed to radiate a spherical
traveling wave, the amplitude of the electric: and magnetic fields
must decay as l/R where R denotes the d1 stance from the horn.
It is indicated in a later description (section 2. 2.1) of the SWR
method that this assumption is approximately valid. The signal
amplitude therefore becomes quite small at large radial distances,
and limits the allowable separations between horn, scatterer, and

detecting probe.

 

DA-

.-!

 

 

 

 

The movable detecting probe structuri- and carriage is indicated
in Figures 2. 4 and Z. 5 respectively. This probe has the freedom to
traverse the full length of the four foot longitudinal slot in the ground
plane. The thin-wire probe structure (Central Res.Lab. MX-lOl9/u)
illustrated in Figure 2. 4 is mounted in the carriage of Figure 2. 5.

This probe carriage is supported by two 1. 22 meters (4 feet) steel

rods .127 cm (0. 50inch) diameter which are secured to the under

 

side of the ground plane. The carriage configuration makes use of
roller bearings which ride on the steel supporting rods. The probe
is centered in the longitudinal seat to prevent electric contact with
the conducting image plane, which would short the signal detected
by the monopole probe. Additionally the probe maintains a constant
height while traversing the length of the slot. To provide a means
of moving the probe when in front of the ground plane, a pully system
is constructed with a large pully secured at the front of the table
which can be rotated manually to locate the probe at any point along
the slot. For convenience in measuring relative positions of the
probe, a steel measuring tape, sLaled in centimeters, is used in
place of string or wire in the pully s "stem. By measuring the
physical distance between probe and scatterer or horn and noting
the centimeter reading on the tape for a given position of the probe,
these physical distances are known for all other probe locations.

The detecting probe utilizes a self-contained stub tuner to
provide optimum tuning of the receiving monopole or detecting probe
to the coaxial line (RG58-50 ohm line) which couples it to the measuring

apparatus. For all frequenm es utilized, it is easily tuned to provide an

 

18

/detector probe

 

 

 

7L1fIIIfL/Jlllil1

III/TIIfIIIJlI

 

—

1 C

 

 

to measuring
device

 

 

/

!

 

 

\

ground
plane

‘ "' coaxial line

\adjustable short

 

adjustable screw for
altering the length of

the probe

Figure 2. 4. Description of detector probe mount.

l9

 

_ ___ _ I
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- __/_. ________ _ ’J r
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/ 4 ft. long
/
L’
2. 5ir: ~

 

 

 

 

Figure 2. 5. Structure of the probe carriage.

20

adequate maximum signal. At the base of the probe structure is an
adjustment screw which varies the height of the probe above the
ground plane. The probe height can be adjusted from 1. 7 cm to 3. 8
cm. An Optimum height is that which provides a signal of satisfac-
torily large amplitude with minimum protrusion above the ground
plane. A probe of minimum length is necessary to avoid reradiation
from the probe which might subsequently interact with the transmitted
signal or, more importantly, with the scattered field from the metallic
object being investigated. It is felt that the power reradiated from the

probe is negligible over the range of frequencies used.

2. 2. Experimental Techniflues

 

The experimental techniques used for the investigation of
backscattering cross sections of metallic objects are the SWR and
cancellation methods. These are the only methods applicable with
the experimental setup of section 2.1 since the anechoic chamber
is based upon a ground plane. Due to the presence of the detecting
probe above the ground plane, only the broadSIde backscatter (9:00)
can be measured. It is felt that the broadside backscatter is of
sufficiently greater importance than the oblique or offubroadside
backscatter that the experimental results presented here contribute
significantly to the state of the art knowledge in this area of study.
The induced current due to oblique incidence upon a scatterer is
significantly smaller in amplitude than that for normal incidence
(the case being investigated in this research). Consequently, the
off broadside scatter field is smaller and in many cases can be

neglected c ompletely.

21

2. 2.1. SWR Method

 

The first of the techniques utilized for measuring the back-
scatter fields of metallic objects is designated as the SWR method.
In accordance with the above discussion of normal incidence of the
illuminating plane wave upon the scatterer, it is observed that the
probe is excited by both the incident E-field from the horn and the
scattered electric field from the metallic object. These incident
and scatter fields interfere to produce a spacially distributed
standing wave between horn and scatterer which is analogous to
the one produced by incident and reflected waves on a transmission
line.

The backscattering cross section of a metallic object can be
determined uniquely from measurements of the standing wave it sets
up in space, just as the terminal impedance of a transmission line
can be determined from probe measurements of the standing wave
pattern on the line. Since the total field which excites the probe is
measured in the radiation zones of the transmitting horn and
scattering obstacle, the incident and reflected fields are both
spherically diverging waves; consequently the l/R Variation in
amplitude must be considered. The usual definition of standing-wave

ratio (SWR) in terms of incident and scatter fields is

i s
Emax(wl) : E(W1)+E (W1) (2.1)

Emin (W2) Ei (W2) - ES(WZ)

 

SWR =

 

where W1 is the distance from the model to a maximum and W2

the distance to an adjacent minimum of the standing wave.

 

 

ata

and t

C€Ilfl

 

77

C305

teChp

‘chlo

22

Let the separation between the transmitter and the scattering
obstacle be designated as L and E0 as the incident field strength at
the obstacle. Suppose that the movable detecting probe is located
at a distance W from the scatterer along a line joining the scatterer
and transmitter. An electric field reflection coefficient 1" may be
defined as the ratio of the scattered field ES(L) at the transmitter
to the incident field E0 at the scatterer as I" = ES(L)/Eo. The

fields at the probe are then (see Figure 2.6)

EL EII‘IL
S O

i
E(W) = . E (W) = W (3.2)

 

 

By substitution of equation 2. 2 into equation 2.1, the amplitude of

the reflection coefficient can be found as

 

 

 

 

SWR - W2 -w1
W2 1+ L-WZ
IPI= (2.3)
L‘WZ SWR+ W {W
1_ 2W 1
I— 2 —4

 

 

Finally, from the definition of I" and 0‘ , the broadside backscattering
cross section“ of the reflecting obstacle is obtained as

2 Z
0' = lim 41rL [r] (2.4)
L—-oo

The experimental arrangement for the SWR measurement
technique is indicated in Figure 2. 7. The microwave oscillator
described previously in conjunction with the arrangement of

section 2. l is utilized with amplitude modulation provided by an

 

 

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external 1 kHz modulator built in for convenience, which was used
as the external 1 kHz source. The modulated R. F. signal is used
to excite the transmitting horn, which provides a spherical traveling
wave in its radiation or far-zone. The incident and scattered fields
excite the mon0pole probe located between the transmitter and
scatterer. An amplitude modulated received R. F. signal is
processed through a detecter or demodulator (General Radio
874-VQL detecting tee), which utilizes a microwave crystal diode
(Sylvania IN23B) as a square law detecting device. A 1 kHz band-
pass standing-wave-ratio indicator (HP415B) is used to monitor the
1 kHz detected signal. By adjusting the position of the receiving
probe along the longitudinally slotted ground plane, the SWR can
be experimentally determined from the indicator readings.

The principle advantages of this technique are that: (i) it
is self-normalizing, thus requiring no standard scattering model
for comparison; (ii) the equipment is very simple; (iii) no special
components are required; (iv) and the measurements are relatively
insensitive to small changes in frequency or amplitude of the
incident wave. Its principle disadvantage is the slow data rate,
since the standing wave pattern must be measured at each scattering
model aspect for which 0' is desired. This method is particularly
adaptable to use with a ground plane boxed anechoic chamber.

With use of the SWR technique, the effectiveness of the
anechoic chamber in suppressing spurious reflections can be
measured. Figure 2. 8 displays the standing wave pattern of the

empty chamber in the absence of a scattering model. By direct

26

 

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observation it is noted that the SWR is less than 1.1 for all positions
of the probe. Furthermore, the rate of decay is nearly the desired
l/R rate mentioned previously. According to comparison with
measurements by King1 and Sletten, 9 it is felt that this SWR is
sufficiently small for an empty anechoic chamber. The non-zero
SWR can be attributed to reflections from the edges of the ground

plane, the chamber walls, and objects outside of the chamber.

2. Z. 2. The Cancellation Method

 

A second technique for experimentally determining the back-
scattering cross sections of metallic objects is known as the
cancellation method. For this technique, a stationary detecting
probe is placed at a position d between the transmitter and the
scattering object in the far -field of each and on a line joining the
transmitter and scattering object. Just as for the SWR method,
it is noted that both incident and scatter fields excite the probe.

Correspondingly, the total signal from the probe can be written as

_ _ -j(91-wt) J'(92+WI)
Vtotal - Viqi-Vs " V1e +V2e (2-4)

where V1 and V2 are the magnitudes of voltages due to the incident
and scattered fields. The essential mechanism of this method is to
cancel the probe signal excited by the incident wave, obtained with
the scattering object absent from the anechoic chamber, by mixing

it with a reference signal from the microwave oscillator which has
the same amplitude but is exactly 1 800 out of phase with the probe

signal. Mathematically, this reference signal is

 

.PM

.3:

 

.V\ "A -J

CV

28

V : V e-j(91-wt+w) : _ V e--j(91--u)t)

ref 1 1

When the scattering object is replaced, the probe signal measured
is directly proportional to only the reflected field since
Vtotal + Vref : Vs '

The experimental arrangement for the cancellation method
is indicated in Figure 2. 9. A reference signal is obtained from
the same oscillator which drives the transmitting horn. The
detected and reference signals are then mixed by processing them
through a directional coupler. This also serves to isolate the
reference signal from the detecting probe, which in turn avoids
spurious radiation of the reference signal from the probe. The
phase of the reference signal is varied by means of a line section
of adjustable length (GR 874-LK20L), while its amplitude is adjusted
by means of a variable ZOdB attenuator (ARRA 2414-20). Phase and
amplitude of the reference voltage are then adjusted until the mixed

signal is zero. All R. F. connections are with RG58 coaxial lines

having a characteristic resistance of 50 ohms.

The mixed signal can be monitored by either of two procedures:

(i) 1 kHz modulation and amplitude detection, or (ii) hetrodyne
detection. The first technique is identical to that used for the SWR
method (section 2. 2.1) where the R. F. signal is amplitude -modulated
by a 1 kHz square-wave source and subsequently demodulated by a
crystal detector. A 1 kHz bandpass SWR indication may then be used
to monitor the mixed and processed signal. The meter scale is

calibrated in both a linear scale of volts, which is proportional to

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30

the electric field, and decibels. Since the dB or decibel reading
is a relative measurement of power, it produces directly the
desired relative measurements for 0' in decibels.

A second technique for measuring the mixed R. F. signals
at the output of the directional coupler involves hetrodyning this
signal with another having a frequency slightly higher or lower
than the measurement frequency in such a way as to produce a
signal of difference frequency low enough to amplify easily. The
I. F. or intermediate frequency amplifier (General Radio 1216A)
used in this research has a passband centered at 30 MHz, which
requires the hetrodyning frequency to be fS i 30 MHz to produce
the desired I. F. frequency of 30 MHz. Again, the meter scale is
calibrated either linearily in volts or in decibels. The same
measurements may therefore be made with this hetrodyning
technique as with the 1 kHz amplitude modulation method.

The principle advantage of the cancellation over the SWR
method is the rapid data rate. A decided disadvantage of the
cancellation methjd is its extreme sensitivity to small changes
in the frequency or amplitude of the incident wave. This problem
may be minimized by requiring the time period of data-taking
to be short. It is this method which has proved to be most valuable
in the present investigation, primarily because of the rapid data
rate.

An advantage of the hetrodyning method is its low noise
level, although that of the 1 kHz modulation method is generally

sufficiently small. The hetrodyning method is felt to be too sensitive

 

to extrane
persons in
there are t
even great<
Inodulation

cons equentl

 

 

 

31

to extraneous reflections, particularly when there is movement of
persons in the vicinity of the anechoic chamber. Further, since
there are two mixing signals involved in this method, there is
even greater sensitivity to small changes in frequency. The 1 kHz
modulation method, applied to the cancellation technique, is

consequently utilized almost exclusively throughout this research.

 

 

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CHAPTER III

MODIFICATION OF BACKSCATTERING FROM A SPHERE

Since the object of this research is to study the modification
of the backscatters of metallic objects, several shapes of conducting
bodies are considered; the solid conducting sphere being the first
configuration to be investigated. A new technique for modifying the
radar cross section of a metallic sphere is investigated experimentally
and theoretically. This method consists of attaching two thin, loaded
wires symmetrically to the sphere in the manner indicated in Figure
3.1. When the sphere and the loaded wires are illuminated by an
electromagnetic wave, currents are induced on the sphere and the
wires. The amplitude and phase of the induced current on the wire
can be controlled by adjusting the loading impedance in such a way
that the total scattered field from the sphere and wires can be
reduced (or enhanced). This method has the practical advantage

of simplicity, and should prove valuable in radar camouflage.

3.1. Theory

Let the sphere with loaded wires be illuminated by a plane
wave at a distance R from the transmitting horn as indicated in
Figure 3.1. The incident field at the center of the sphere and

cylinders is then
E1 : EOe-JBOR (3.1)
where E0 is a constant electric field amplitude, and (30 is the

32

 

transm;
horn

 

Figure

Figure

33

     

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horn h /1mpedance
2.

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Figure 3.1. Geometry of problem of sphere with loaded wires.

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(9 : 00) lS CO
fOrm a tW0 El:
the two Cylind

 

‘0 Yield an ex:

The 801

34

free space wave number.

Since an exact solution to this problem is far too complicated
to obtain, because the coupling between the sphere and the loaded
wires is difficult to account for, the superposition principle is
employed for this complex structure. The Sphere with the loaded
wires can be approximated by two separate structures, the solid
conducting sphere and two loaded wires which are attached to a
pair of infinite ground planes separated by the sphere diameter 2a
(see Figure 3. 2). It is assumed that the scatterer is in the far field
of the source (i. e. , R >> h, x , a) and that the wire radius is small
compared to the wavelength such that [30b << 1 .

This reduced problem may now be solved easily by considering
the backscattered fields from the sphere and from the two imaged,
monopole, cylindrical scatterers. Since only the backscatter field
(9 = 00) is considered in this research, the two imaged cylinders
form a two element colinear array and the total scattered field by
the two cylinders is twice that of a single cylinder. The backscattered
fields of the sphere and the loaded cylinders can then be superposed
to yield an expression for the total backscattered field.

The solution for the backscatter from a solid conducting sphere
is well known, and detailed numerical results have been tabulated by
M. E. Bechtel. 10 Given the incident field described above, the back-

scatter field of the Sphere is,

E8 — E i e'jzfiom'alo (3.2)

s 02R

 

 

where

the Hankel :‘
space wave
indicates th.
Hankel funct
function. It ‘
approximate:

As in
field of the 1
11693.3 Wit}

I
tar-zone bac E:

 

Where

{n
E1
CL

35

where

 

 

. -j2[3 a m J (B a) [[3 aJ ([3 all"
G =—E3‘L% o E (-1)n(2n+1) n o o n o ' (3.3)
o

Hflzlwom [ooaHff’moan

n=l

and Jn((30a) is the Bessel function of order n while Hfhfloa) is
the Hankel function of the second kind and order n. (30 is the free-
space wave number and a is the radius of the sphere. The prime
indicates the first derivative of the quantity containing the Bessel or
Hankel function, in either case, with respect to the argument of that
function. It is of interest to note here that G is a complex number
approximately equal to one for all arguments [30a .

As in the case for the sphere, the solution for the backscattered
field of the loaded cylinder has been obtained theoretically by Chen and
Liepa. 3 With the assumption of a plane wave illuminating field, 'the

far-zone backscatter field from the central loaded cylindersis

 

 

 

s -4 -j2(30R
E3C=(—---B R) e g (3.4)
o
where
_ M(sin (30h - [30h cos (30h) + N(l - cos Bob) (3 5)
g — cos (3 h - M T - N T '
0 ca sa
and
1
M = T (1- cos B h) (3.6)
0
cd
-Z sinB h(1-cosB h)2
N = L z 0 0 (3.7)
TCd ZL Sin Boh - JéOTCdTSd cos Boh

 

T .
Tcd’ Sd I

numericali

Wterethe kg

The radius 0:.

the Cylindel' “-

the Cylinder.
SinCe t

bYeXpresSicn

"i )1
«GAO of the Sp?-

 

36

T T T , and Tsa are integrals which must be computed

cd’ sd’ ca

numerically and are given as follows

h
_ I _ I I
TCd — 5‘ (cos [302 cos (30h)Kd(0, z ) dz
-h
h
_ ' I I I
Tsd _S smso(h-|z|)Kd(o,z)dz
-h
h
_ I _ I I
Tca — 5 (cos fioz cos Boh) Ka(h’ z ) dz
-h
h
_ - _ I I I
Tsa -5 smsom Izl)Ka(h,z)dz

where the kernels are,

Kd(z,z') = Ka(z,z') -Ka(h,z')

 

and

-ij ~/(z..z')2 + b2

 

 

(3. 8)

(3.9)

(3.10)

(3.11)

(3.12)

(3.13)

The radius of the cylinder is taken as b, 2 denotes position along

the cylinder with origin at its center, and 2h is the total length of

the cylinder .

Since the backscattering of the sphere and cylindersare given

by expressions (3. Z) and (3. 4), respectively, then the total backscatter

field of the sphere with loaded wires must be,

m
n

m
+
m

e-jZBOR s a

 

'26 a
= 4 _ 0 J -
It is the objective here to find the optimum impedance [ ZL] 0 which

will result in zero broadside backscattering from the composite
structure. The backscattered field BS is therefore equated to zero

to yield

M(sin Bob - [30h cos 60h) + N(1 - cos (30h)

 

: Gl(cos (30h - MTca - NTsa) (3.15)
where G1 is defined by
B a .
G1 = :3 elzfioa G (3.16)

It is observed from equations (3.6) and (3.7) that only N is dependent

upon Z , so expression (3.15) may therefore be solved for N = No

L

(at zero backscatter) and later equated to the right hand side of equation

(3.7) as

N _ G1 cos (30h - M(sin (30h - [30h cos (30h + G1 Tea) (3 17)
o — 1 - cos {3 h + G T °
0 1 sa

 

By solving for Z from (3.7) in terms of N = No’ the optimum

L

loading impedance for zero broadside backscatter is obtained as

38

[z] _ jNO6OTCdTSdcosBOh
L°_ T '2 h+' hl h2 (3.18)
NO cd Sin (30 8111 [30( -cos (30)

 

where NO has been defined in (3.17).

Figure 3. 3 indicates the optimum loading impedance [ ZL] o

as a function of electrical length of the wires. The real part of the
optimum impedance R2 is represented by a solid curve, while the
imaginary part X2 is represented by a dashed line curve. For this
research, [30a is chosen to be approximately 2. 0, since this is
near the first resonant peak of the backscatter from a sphere.

It is noted that a negative resistance is required to produce
zero broadside backscatter from the composite structure for nearly
all lengths of h, which is very difficult to achieve in practice.
Consequently, to simplify this problem, a purely reactive loading
is investigated as a means for modifying the backscatter from a
sphere with loaded wires. By substituting Z : jX

into (3.14)

L L

and finding an Optimum reactance [ X to minimize this expression,

L]o

the backscattered field is effectively minimized. Likewise, the
optimum reactance for enhancement of the backscatter from this
structure can be obtained.

It is therefore desired to minimize the right hand side of

(3.14), which subsequently implies that

A : G -g (3.19)

be minimized, where G and g are defined by (3.16) and (3. 5)

l

with Z replaced by jX

L L' Substituting G1 and g and then

optimum loading impedance [ ZL] 0 = R2 + jXZ

(ohms)

1600-

1400‘

1200.

1000‘

800 -

600‘

400 -(

200-

 

-200-
-4oo~
-600(
-800-

-1000-

-1200-

-1400-

-1600‘

 

 

39

 

 

 

 

Figure 3. 3. Optimum loading impedance for zero broadside
backscatter from sphere with loaded wires as a

 

40

simplifying, (3.19) can then be written as

. 2
(1 -cos(30h+Gl Tsa)XL31n(30h(l -cos(30h)

 

Gl(cos[30h-MTca)-M(sinBOh-Bohcos(30h)+ T (x .2 h 60T h)
cd LSln Bo - sdcosfio

 

ADCL) : . 2
XL Tsa Sln (30h(1-cos 00h)

TCd(X

 

(cosBOh-MTa)+ 2
C sin (30h - 60 Ts cos (30h)

L d

(3.20)

where M is defined in(3.6) and the integrals T , T , T , and
cd sd ca

Tsa are defined in (3. 9) to (3.11). The optimum reactances [XL] 0

for minimum or maximum backscatters are obtained directly from the

plots of A(XL) as a function of load reactance X Figures 3. 5 to

L O
3. 9 indicate these plots and will be discussed in section 3. 3, which is
concerned with the comparison of theory with experiment. In these

Figures, the theoretical results are represented by circular data

points.

3 . 2. Experiment

 

The compensation technique for modifying the backscattering
cross section of a conducting sphere is studied experimentally in this
research and excellent results are obtained. Part of these research
results have already been published. 11 Experimentally, it is observed
that the radar backscattering cross section of a conducting sphere
(Boa ~ 2 where 60 is the free-space wave number and a the
sphere's radius) can be practically e31§minated by attaching two

0

reactively loaded wires (h = -6— to :12 where h is the wire length

and BC the free-space wavelength) as shown in Figure 3. 4. The

41

 

I?! _.

E
loading loading

impedance (ZL) ‘ '[impedance (ZL)
l“'—— h ——--b 4
wire
a
sphere

 

(geometry of sphere and loaded wire)

 

 

 

(wire
hollow ajust-
sphere "" / able
1: short
‘- coaxial line

 

 

 

L“.

(experimental model)

Figure 3. 4. A sphere with loaded wires.

42

wires are loaded at the surface of the sphere by purely reactive
impedances which are realized in practice by adjusting coaxial
cavities. Measurement of the backscattered field is accomplished
as described in section 2. 2. 2. A frequency of l. 72 GHz is utilized
in the experiment.

Results of this experiment are indicated in Figures 3. 5 to
3.12. In Figures 3. 5 to 3.10, the backscattering cross section of
a sphere (a = 5. 71 cm = 0.328 K0) is represented by a solid straight
line and that of a sphere with solid wires (zero loading) by straight
dashed lines. In Figure 3. 5 the cross section of the combination of
the sphere (a : 5. 71 cm) with the loaded wires (h = 3. 5 cm) is plotted
as a function of the reactive loading of the wires, and is represented
by a solid curve. It is observed in Figure 3. 5 that if the length of
the coaxial cavity (or the value of the loading reactance) is properly
chosen, the total backscatter produced by the sphere and the loaded
wires can be reduced by 8 dB. It is also observed in Figure 3. 5
that, by varying the loading reactance, the backscatter of the sphere
can be enhanced. Figure 3. 6 demonstrates the case of a sphere
(a = 5. 71 cm) with loaded wires of greater length (h = 6.1 cm). In
this case, the backscattering of the sphere can be minimized to the
system noise level. At this condition, the sphere becomes invisible
to a radar detecting system. For the same wire length, by adjusting
the loading reactance, the backscatter of the sphere can also be
enhanced by approximately 7 dB. Thus, by simple adjustment of

the loading of the wires, the backscatter of a sphere can be varied

43

over a 14 dB range. Figures 3.7 and 3. 8 indicate the cases of a sphere
(a = 5. 71 cm) with loaded wires of still greater length (h = 6.7 cm and
h = 8. 4 cm).

Using longer loaded wires, the radar cross section of a sphere
can be similarly minimized to the system noise level. The minimum
peak, however, is very sharp compared with the cases of Figures
3. 5 to 3. 8. This implies that the bandwidth associated with this
minimization techique is Optimized by using shorter loaded wires,
as is discussed in greater detail in Chapter VII. Figure 3. 9 indicates
a similar case of the same sphere (a = 5. 71 cm) with longer loaded
wires (h = 10. 5 cm). Similar phenomena are again observed. The
backscattering cross section of the sphere may be minimized to the
system noise level, but the minimum peak is quite sharp. It is also
observed that the maximum peak is less sharp for longer wires
while the backscatter is nearly constant for a wide range of loading
impedances.

Various other excitation frequencies are used with similar
success. At a frequency of l. 72 GHz, various lengths of wires are
utilized and the maximum and minimum backscatters of the composite
structure are plotted as a function of the electrical length of the
wires (see Figure 3.10). The maximum backscatter of the sphere
with loaded wires is represented by a dashed line curve and the
minimum backscattering cross section is represented by a solid
curve. It is observed that minimization is very successful for
80h = 0.16 to 0. 5. The optimum reactances for minimum and

maximum backscatters from a sphere with loaded wires are indicated

44

in Figures 3.11 and 3.12, which are also plotted as a function of the
electrical length of the loaded wires. Stray capacitance which
exists at the terminal end of the coaxial cavity is taken into account

when calculating the effective load reactance XL .

3.3. Comparison of Theory and Experiment

 

For the case where f = l. 72 GHz and the sphere radius is
a = 5. 71 cm, the comparison of experiment with theory is quite
favorable. It is observed in Figures 3. 5 to 3. 9 that the maximum
peaks of the theoretical results are much sharper than the
experimental results. This is most likely due to the finite
conductivity of the sphere and wires, which attenuates the induced
currents on the sphere and wires in the resonant cases. The
minimum peaks however, compare quite well.

The comparison of theory with experiment of the optimum
impedances for minimum and maximum backscatters of the
composite sphere-loaded wire structure is presented in Figures
3. 11 and 3.12. There is an additional discontinuity in the optimum
theoretical minimizing reactance at Bob = 1r which the experiment
does disclose. Excluding this point, the comparison for both the

optimum minimizing and maximizing reactances is excellent.

45

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ll

 

(db)

N
1

O
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-2-I

-4-1

Optimum backscattering cross sections (IJ'B)o

-8-I

50

(maximum) sphere
with loaded wires

 

 

 

-10

0 ’~
. - ’ a ’ .
/" 16' ""0 o
p
/
I
/
sphere
(minimum) sphere
with loaded wireS‘I-
o
= l. 72 GHz
a = 5.71 cm

 

 

noise level

I’

 

 

1 2 3 4 5
(60h) electrical length of the wires

Figure 3. 10. Maximum and minimum backscatters from a

sphere with loaded wires as a function of

(ohms)

optimum minimizing reactance [ XL] 0

800‘

6004

400‘

51

experiment —-

theory 0 O O

 

 

 

 

 

200‘
o + i
l 5
O
-200"
O f = 1.72GHz
“£001 a = 5.71 cm
-600- E
I. if;
// /// /
O ”////l. 2; if /
-800"

 

Figure 3.11.

 

Optimum reactance for minimum backscatter from
a sphere with loaded wires as a function of electrical
length of wires.

Optimum maximizing reactance [XL] 0

52

 

 

 

(ohms)
800- T—
E h l
n L» It.“
/ // /
600 a //////l7I 2g4V/
f = 1.72 GHz
a = 5.71 cm 0
400 "‘

200

-200

-400

-600

-800

 

 

O
7 O
O
I . 3: 4
1 5
ooh O
H O

expe r iment "-

theory 0 O O

l

 

 

Figure 3.12.. Optimum reactance for maximum backscatter fr om

a sphere with loaded wires as a function of electrical
length of wires.

CHAPTER IV

MODIFICATION OF BACKSCATTERING FROM METALLIC LOOPS

The results of an experimental investigation on the backscatter
of a thin-wire, metallic loop, either circular or rectangular, are
presented here. In a recent paper,12 an experimental study on the
resonances of loops was reported. It was shown that the resonant
scattering cross sections of wire 100ps are dependent upon their
shape and periferal dimensions. As an extension to this study,
modification of the backscattering cross section of a loop by the
impedance loading technique is investigated. Some results of this

13
study has already been published elsewhere.

4.1. Circular Loop

 

The impedance loading technique is applied successfully to
modify the backscattered field of a circular, metallic loop. It is
observed that, with an Optimum impedance loading located at
apprOpriate points on the loop, the amplitude and phase of the
induced current can be controlled in such a. way that the backscattered
field maintained by the indu: ed current. is substantially modified. In
this investigation, both minimization and enhancement on the back-
scatter are studied.

Figure 4.1 indicates the geometry of the impedance loaded,
circular loop. An experimental model of this conducting loop
(diameter = 5.15 cm) is constructed of cylindrical copper wire

having a radius of 0.1 cm. In the experiment, the circular loop

54

 

 

2a

)alf of circular loop

g r ound plane

 

 

f/A ////////////// //

4— coaxial lines

 

 

 

 

 

 

 

 

 

 

adjustable shorts

 

 

(expe rimental model)

 

 

 

 

ML
\

ml

Figure 4.1. Loaded, circular wire loop.

is illuminated by a plane wave at normal incidence and at various
frequencies. The cancellation technique described in section 2. 2. 2
is again employed to measure the backscattered field from the loops.
The loop is symmetrically doubly loaded with a pair of identical
purely reactive impedances which are realized experimentally by
two adjustable coaxial cavities located beneath the ground plane.

In Figures 4. 3 to 4.13, the backscattering cross section of
the circular loop is plotted as a function of loading impedance for
various specified frequencies (1. 6 GHz - 2. 5 GHz). A solid curve
represents the cross section of the loaded IOOp while a solid straight
line represents that Of the solid one. It is observed that if the
loading impedance (or the length of the coaxial cavity) is properly
adjusted, the backscattered field of the loop can be minimized to
the noise level of the measurement system. Similarly, the back-
scattered field of the loop can be maximized or enhanced considerably
with another properly selected reactance loading. With the optimum
minimizing reactance, up to 15 db reduction in the backscattering
cross section is observed at each excitation frequency investigated.

For each specified frequency, an Optimum minimizing or
maximizing reactive loading impedance is obtained. These Optimum
impedances for a circular loop are plotted in Figures 4.14 and 4.15
as a function of the electrical loop circumference Bob, where b is
the radius of the 100p and BC is the free space wave number. The
solid curve in each of the two figures represents the optimum
minimizing impedance and the optimum enhancing impedance

respectively for the loaded circular loop. For each of the optimum

56

reactive impedances obtained, the stray capacitance which exists
at the terminal zone of the coaxial line or lOOp lOading point is

taken int 0 ac c ount .

4. 2. Rectangular Log)

 

The impedance loading technique is also applied successfully
to modify the backscattered field of a rectangular, thin-wire loop.
As observed for the case of a circular lOOp, proper choice of an
optimum impedance loading located at appropriate points on the
loop will control the amplitude and phase of the induced current in
such a way that the backscattered field of the loop is significantly
modified. A wide range of minimization or enhancement can be
achieved by a suitable choice of loading impedance.

In Figure 4. Z, the geometry of an impedance loaded,
rectangular lOOp is indicated. Cylindrical copper wire of 0.1 cm
radius is utilized in construction of the experimental rectangular
loop model which has dimensions of 4.15 cm on each side. A plane
wave at normal incidence and of various frequencies is employed
to illuminate the rectangular wire loop. Measurement of the back-
scattered field is accomplished through use of the cancellation
method (see section 2. 2.. Z). The loop is loaded symmetrically with
a pair of purely reactive impedances.

The backscattering cross section of the rectangular loop
for various frequencies (1. 6 GHz - 2. 5 GHz) is plotted in Figures
4. 3 to 4.13 as a function of the loading impedance. A dashed line

curve represents the cross section of a loaded square loop while

57

s—
U

 

 

half of square loop

:1. /
23—0-1 n.— I

E I b/Z /ground plane

1
7///// //////// ///////

‘---—- coaxial lines

 

 

 

 

 

 

 

 

 

adjustable shorts

 

 

 

 

i—u—i.

 

(experimental model)

2a

 

 

 

 

 

 

 

Figure 4. 2. Loaded square wire loop.

58

a dashed straight line represents that of a solid one. Proper adjust-
ment of the loading impedance will minimize the backscattered field
to the noise level of the measuring system. It is also observed that
another appropriate choice of loading impedance results in
maximization of the backscatter by up to 12 dB. The optimum
minimization impedance reduces the backscatter up to 15 dB at

each particular frequency.

As for the case of a circular loop, an optimum minimizing
or maximizing reactive impedance is obtained at each specified
frequency. These optimum impedances for the loaded square loop
are plotted in Figures 4.14 and 4.15 as a function of the electrical
length (30b, where b is the side length of the loop and (30 is the
free space wave number. The dashed line plots in the two figures
represent the Optimum minimizing impedance and the optimum
enhancing impedance respectively of the loaded square loop. These
impedances are obtained with account taken for the stray capacitance
existing at the input end of the coaxial cavity.

From Figures 4. 3 to 4.13, it is observed for each specified
frequency that the backscattering from a solid square loop is usually
less than that Of the solid circular loop (also observed by Lin and
Chen”), although the maximum cross section above the noise level
remains nearly the same for both loop shapes. This observation
readily indicates that the backscattering cross section of a circular
100p may be reduced more than that of a square loop, where as for
enhancement the opposite is true since the cross section of the square

loop can be maximized more.

59

As a further comparison of the two loop shapes, the optimum
reactive impedance for minimum and maximum backscatter indicated
in Figures 4.14 and 4.15 may be compared. It is observed that the
Optimum minimizing reactances for the two 100ps as a function of
loop sizes are positive, although those for the loaded square loop
are about three times larger for Bob/2 equal to 0. 94 and 1. 05.

For the optimum maximizing reactance of the circular and square
loops, the values are mainly negative and small, although those

for the circular loop of which Bob/2 is less than 0. 95 are positive.
The Optimum reactance for the maximum enhancement of the back-
scatter of a square loop has a fairly sharp peak at Bob/2 equal
1.275 where the reactive impedance is about xL = - 550 ohms. A
similar peak is seen for optimum maximizing reactance of the
circular loop although of a much less magnitude. This observation
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cross section as a function of coaxial line length I of the loaded
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coaxial cavity vary rapidly for small variations in 1 . The rapid
change in the cross sections as a function of I of both loop shapes
near the point of optimum minimization for bob/2 equal 1. 25 to
1.4 may be explained in a like manner since the reactance is large

there.

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CHAPTER V

MODIFICATION OF BACKSCATTERING FROM A CONDUCTING PLATE

In this chapter the modification of the backscattering cross
section of another fundamental shape, the metallic plate, is studied.
This shape has not been studied extensively. The only known methods
of controlling the backscatter of a plate are to cut a resonant slot
on the plate, 7 or install a cavity-backed aperture on the plate. These
methods can reduce the backscatter of the plate by not more than
15 dB and have the disadvantage of a requirement for cutting the
plate. The method presented in this research offers a more effective
means for backscatter reduction without the inherent disadvantages
mentioned above. In some cases a reduction of about 25 dB is
obtainable by this method. Part of this research has already been
published elsewhere. 14 Subsequently this method should have

important practical applications.

5.1. Round Plate and Loop

 

The basic scheme of this method is to place a loaded circular
loop directly in front of a round plate and parallel to it as indicated
in Figure 5. l. The amplitude and phase of the induced current on
the loop is controlled by a loading impedance in such a way that the
backscatter produced by the loop cancels fully or partly the back-
scatter due to the induced currents on the plate. Thus the total back-
scatter produced by the composite plate and the loop structure is
minimized. In a similar manner, the backscatter field from the

composite structure may be enhanced.

73

74

large plate d : 12. 7 cm
medium plate d : 10.2. cm
small plate d = 7.6 cm

 

 

 

 

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Figure 5.1. Circular plate and loaded loop.

75

In the experimental arrangement, a circular wire loop loaded
symmetrically with a pair of identical reactive impedances, as
described previously in section 4.1, is placed 0. 5 cm in front of
and parallel to a solid circular metallic plate. The plate and loop
are illuminated by a plane wave at normal incidence. The experi-
ment is performed at various frequencies and with circular plates
of various diameters. Throughout the experiment, the diameter
of the wire loop (diameter = 5.15 cm with wire radius = 0.1 cm)
is held constant.

The experimental results are presented in Figures 5. 2 to
5.20. In Figures 5. 2 to 5.6 the backscattering cross sections of
the small plate (diameter = 7. 6 cm) and loaded circular loop are plotted
as a function of the impedance loading of the loop. The backscatters
of the medium plate (diameter : lO. 2 cm) and loaded loop are
indicated in Figures 5.7 to 5.14, while those of the large plate
(diameter = 12. 7 cm) and loaded loop are presented in Figures 5.15
to 5. 20, all as a function of the loop loading impedance. In each
Figure, the cross section of the plate alone is represented by a
solid straight line and that of the plate and a solid circular loop by
a dashed straight line. The cross sections of the loaded loop alone
as a function of its loading impedance are indicated by dashed curves.

It is observed that the backscattered field of a circular
conducting plate can be reduced by approximately 25 dB in some cases
if the loading impedances (i. e. , the length of the coaxial lines) are
properly adjusted. On the other hand, another appropriate impedance

can, in some cases, enhance the radar cross sections of the plate

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Figure 5. 21. Optimum impedance for minimum backscattering
from a circular plate with a loaded circular loop.

96

by up to 5 dB. It is readily obvious that this technique for modifying
the backscatter from metallic plates is much more effective for
minimization of the backscatter of a circular plate than for its
enhancement. In fact, is is noted that for certain of the frequencies
utilized, the backscatter from the plate-loaded 100p structure can
be reduced to the noise level of the measuring system.

In the experiment, there were more frequencies used than
mentioned above. These experimental results tend to indicate that
there exists an optimum relation between the plate diameter d and
loop diameter b for a maximum reduction of the backscatter field.
For example, to obtain the maximum backscatter reduction at the
frequencies of 1.97 GHz, 2.1 GHz, and Z. 5 GHz, the optimum ratio
d/b should be 1. 47, l. 98, and 2. 47, respectively.

Another interesting observation from the Figures is that the
optimum reactive impedances for minimum backscatter for the three
variations in round plate -loaded loop structures are nearly the same
at each specified frequency. This Optimum reactance for minimum
radar cross section of the composite structure is plotted in Figure
5. 21 as a function of electrical loop circumference Bob/2, where
b is the loop diameter and [30 is the free space wave number. As
in section 4.1,the stray capacitance at the terminal end of the coaxial

line is c onsidered.

5. 2.. Rectangular Plate and Loop

 

A technique similar to that employed in section 5. l for modifying

the backscatter from a metallic plate is applied here for the case of

 

97

a conducting rectangular plate. The scheme of this method is to
place a slightly larger loaded rectangular loop in the same plane
with the plate, as indicated in Figure 5. 22. Again, as in the case
of the circular plate, the amplitude and phase of the induced current
on the loop is controlled by a loading impedance in such a way that
the backscatter field produced by the loop may either partially cancel
or enhance the backscatter field due to the induced currents on the
plate. Either minimization or enhancement of the backscattering
cross section of the rectangular plate may therefore be achieved,
depending upon which of the two appropriate loading impedances is
selected.
In the experiment, various sizes of rectangular plates and
correspondingly larger rectangular loops (wire radius = 0.1 cm)
are used. Each plate and corresponding loop are placed in the
same plane and are illuminated by a plane wave at normal incidence.
The wire loops are loaded symmetrically with a pair of identical
reactive impedances, obtained experimentally by means of adjustable
shorted coaxial line sections beneath the ground plane. Throughout
the experiment, the width (b = 5.15 cm) of the loops is held constant.
The results of this experiment are presented in Figures 5. 23
to 5. 28. Figures 5. 23 to 5. 25 indicate the backscattering cross
sections of the small rectangular plate (h = 2. 8 cm) and loaded loop
as a function of the loop loading impedance. The backscatters of
the large rectangular plate (h = 5.6 cm) and loaded 100p are given
in Figures 5. 26 to 5. 28, plotted also as a function of the loop loading

impedance. In each Figure, the cross section of the rectangular

 

98

5.15 cm
I. 0.2 cm

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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Figure 5. 22. Rectangular plate and loaded loop.

99

plate alone is represented by a solid straight line and that of the
rectangular plate and solid loop by a dashed straight line. Additionally,
the radar cross sections of the loaded loop alone are designated by
dashed curves, which are also plotted as a function of its loading
impedances.

It is observed that the backscatter from a rectangular metallic
plate can be reduced by about 11 dB in certain cases if the loading
impedances (i. e. , the length of the coaxial lines) are properly
adjusted. Correspondingly, enhancement is even more successful
since the cross sections of the rectangular plate can be enhanced by
nearly 10 dB in many cases. In most cases, furthermore, the
magnitude of enhancement is larger than that of the reduction.

In the experiment, there are various other sizes of rectangular
plates and frequencies utilized, but with much less success. These
experimental results seem to indicate that this technique has limited
applications since modification of the backscatter field of rectangular
plates of certain sizes is small. For this reason, the Optimum
reactance for either minimization or enhancement is not given,
although it can be obtained in exactly the same manner as those for

the circular plate and loaded loop.

 

100

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CHAPTER VI

’MODIFICATION OF BACKSCATTERING FROM CYLINDERS

The backscattering of a circular cylinder has been studied
rather conclusively by theoretical techniques.3 As an extension,
Chen15 studied the backscatter fr om the combination of a thick
cylinder and a parallel, impedance loaded thin-wire element.
Experimental investigations of the backscattering cross sections
of a single cylinder and combinations of parallel cylinders are
performed to demonstrate the reliability of these techniques, and
to study new problems which are much too complex for theoretical

study.

6.1. Solid and Loaded Cylinders

 

For comparison purposes, the backscattering cross section
of cylinders, both thick and thin, are studied here. The scattered
field from an unloaded cylinder, as well as loaded cylinder, is

inve stigated experimentally.

 

6.1.1. Solid or Unloaded CLIinder

. The relative backscattering cross section of the solid cylinder
(zero loading) is experimentally determined by use of the cancellation
technique described in section 2. 2. 2. The 1 kHz amplitude modulation
technique is used here for detection. For each cylinder thickness
(diameter = 2a), the relative radar cross section is determined as
a function of electrical cylinder half-length h/XO (see Figure 6.1).

The backscattering cross section of the thick cylinder is represented

106

backscattering cross section (63)

107

(db)
0..
2a 2 2.14 cm
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(h/X) electrical length of cylinder

Figure 6.1. Backscattering cross sections of solid cylinders as a
function of cylinder half-length h.

108

by a solid curve, the medium one by a dashed line, and the thin
cylinder by a dotted line. This experiment is performed at a
frequency of 2 GHz. Three different thicknesses are used: 2a 2
2.14 cm, 2a = 0.64cm, and 2a = 0.32 cm. Physical dimensions
of two of these cylinders (2a 2 2.14 cm and 2a = 0.32 cm) are
described in Figure 6. 2. It is observed from Figure 6.1 that the
backscatter from the thick cylinder is approximately 5 dB greater
than the two thinner cylinders. Furthermore, the resonant peaks
of the thick cylinder are not as distinct, since there is only about
2 dB variation between the resonant and antiresonant points.

6.1. 2. Impedance Loaded Cylinder

 

As a means of modifying the scattering cross sections of the
above mentioned thin cylinder (2a 2 0. 32 cm), the cylinder is loaded
at its center by a lumped impedance. In general, both resistive and
reactive impedance components are required to produce a maximum
variation of the radar backscattering. The problem becomes very
complex when the required resistance is negative. To simplify this
problem, only reactive loading is considered. This is accomplished
by means of a coaxial cavity located beneath the ground plane
(Microline adjustable coaxial shorted line). As before, the
cancellation method is employed for measurement of the radar
cross section of the loaded cylinder.

The experimental results for several lengths of thin cylinders
are indicated in Figures 6. 4 to 6. 6. In each of these. Figures, the

scattering cross section of a thin, loaded cylinder, represented by

109

thin cylinder (2a = 0. 32 cm)

 

"lull".

thick cylinder (2a : 2.14 cm)

Figure 6. 2. Physical description of cylinders.

110

dashed lines, is plotted as a function of the loading impedance of the
cylinder. A coaxial cavity is utilized as the loading device, there-
fore providing a purely reactive impedance. The approximate
impedance of the coaxial cavity can be calculated from the expression
ZL = j ZC tan 001 where ~Zc is the characteristic impedance of the
coaxial cavity, 00 is the wave number, and 1 is its length.

In most cases above, both minimization and enhancement can
be achieved to some degree for particular values of loading reactance.
The minimization of the scattering should have direct application to
space vehicle radar camouflage. It is observed that the radar cross
section of the cylinder can be minimized to the noise level for each
case, (up to 15 dB). [Enhancement is also observed for most cylinder
lengths, with the exception of resonant lengths, but generally to a
much lesser degree. It is a noteworthy observation that scattering
from antiresonant cylinders can be enhanced to the greatest extent;

this plays a significant role in the compensation method discussed

in the following section.

 

6.2. 'Thick Cylinder With a Parallel, Impedance Loaded Thin Cylinder
The method considered thus far for modifying the backscattering

of a metallic object utilizes an impedance loading technique. Other

conventional methods include the techniques of employing radar

absorbing materials and of reshaping the body. In some cases none

of these techniques are permissible for mechanical reasons. A

relatively new technique, the compensation method, is investigated

for possible use on those metallic bodies for which an impedance

111

loading technique cannot be applied.

The compensation method consists of adding a small metallic
body, such as a thin wire loaded with appropriate impedances, to
the main metallic body. When the main body and added thin wires
are illuminated by an electromagnetic wave, currents are induced
on either element. If the amplitude and phase of the induced current
on the thin wire can be properly adjusted by means of an appropriate
impedance loading, it can cancel or add to the radiation field due to
the induced current on the main body; thus the total backscatter
field from the main body and thin wire is modified.

The experiment involves a solid cylinder and a thin, center-
loaded wire placed parallel to one another, with a plane electro-
magnetic wave assumed to be incident broadside upon them, as
indicated in Figure 6. 3. 'Minimization of the radar cross section
of this combination is the primary goal of the research, although
enhancement is considered as well.

The experimental results are shown in‘Figures 6. 4 to 6. 6.
Solid lines represent scattering from the thick cylinder ( a = 1. 07 cm)
combined with the loaded, thin cylinder (b = 0.16 cm), for which the
scattering cross sections are plotted as functions of the cylinder
loading impedance. _A frequency of l. 72 GHz is used for the
experiment of Figures 6. 4 to 6. 6, although various other frequencies
are considered in this research. Various combinations of cylinder
lengths 2h are utilized for this study. It is observed that certain
combinations of lengths produce more minimizations or enhancement

than others. Figures 6. 7 to 6.13 indicate the maximum and minimum

112

2.14 cm

 

ml

0. 32 cm-"

 

thic k cylinde r

ZL\

loading impedanc e

 

V thin cylinder

 

 

 

 

 

 

 

 

\

g round plane

\ c oaxial line

 

 

 

 

 

H \adjustable short

(experimental model)

Figure 6. 3. Thick cylinder with a loaded thin cylinder.

113

backscatters from each combination of thick with optimum loaded thin
cylinders, plotted as functions of the thin cylinder half-length hZ . In
each figure the length of the thick cylinder h1 is held constant while

hZ is varied. The backscatter of the thick cylinder only is represented
by a solid straight line, while the minimum and maximum backscatters
of the combined thick with loaded thin cylinders are represented by
solid and dashed line curves, respectively.

It is noted that the largest variation in the backscatters occur
when the thin cylinder is considerably longer than the thick cylinder,
and also when the length of the thick cylinder is small compared with
the wavelength. Addition of resistive components, both positive

and negative, to the reactive loading should make the application of

this technique more successful.

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CHA PT ER VII

TECHNIQUES FOR BANDWIDTH IMPROVEMENT

It is observed from the preceding chapters that there is, in
connection with the compensation method, a need for bandwidth
improvement. Such improvements would be desirable for these
impedance loading techniques, as applied to metallic objects, to
have extensive success in radar camouflage applications. The
objective of this segment of the research is to improve the band-
width of these impedance loading techniques, which are utilized
to modify the backscattering cross sections of various shapes of
conducting bodies. Two approaches, (1) resistive loading and
(2) reactive loading using a coaxial cavity of high characteristic

impedance, have been evaluated with some success.

7.1. Resistive Loading

 

The introduction of a resistive component in the loading
impedance tends to somewhat improve the bandwidth. It is very
difficult at the frequencies utilized in this study to obtain a lumped
impedance with the correct frequency characteristics and physical
dimensions small enough to be placed on the models under study.
Consequently, high frequency devices, such as coaxial cavities,
are sought. A 50 ohm termination (GR 874-5011) is placed in
parallel with an adjustable shorted coaxial line section to produce
a loading with both reactive and resistive impedance components.

In Figure 7.1, the backscattering cross section of a cylinder

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126

(h = 2. 7 cm) loaded with such an impedance element is plotted as
a function of the coaxial cavity length. The backscatter of a solid
cylinder is indicated by a solid straight line and that of a cylinder
with a purely reactive loading by a solid curve. A dashed line
curve represents the backscatter from a cylinder loaded with an
element having both reactive and resistive impedance components.

Comparison of the backscatters from the cylinder with the
two different loading impedances indicates that the resistive
component increases the bandwidth of minimization somewhat,
since the minimum peak is not as sharp when the resistive component
is present and the backscatter is over 7 dB lower than the solid
cylinders for all values of reactance. The latter observation
suggests that the resistive element dissipates a fraction of power
incident upon the cylinder which might otherwise be scattered at
resonance, thus reducing the b.ai.:kscattered field.

For a more pertinent comparison of the two loading devices,
actual bandwidth measurements are obtained as shown in Figure 7. 2.
The backscatter from the resonant cylinder (h = 3. 5 cm) with pure
reactive loading is represented by a broken solid curve and that
from the cylinder with reactive and resistive loading by a solid
curve. A dashed line curve represents the backscattering cross
section of the solid cylinder {h : 3. 5 cm). All are plotted as a
function of frequency. Direct observation indicates that the intro-
duction of a resistive component does improve the bandwidth slightly.
Even better results can be obtained if a coaxial line with a higher

characteristic impedance is employed.

(

backscattering cross section (0B)

127

 

 

 

 

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Figure 7. Z. Backscattering cross sections of solid and loaded
cylinders as a function of frequency (h = 3. 5 cm).

 

12,8

7. 2. Reactive Loading Using a Coax1al Cav1ty with High Characteristic
Impedance

 

 

As suggested in the last section, a far better bandwidth improve-
ment result is obtained by loading the metallic object by a coaxial line
(or cavity) with 240 ohm characteristic impedance. With this coaxial
cavity loading, the backscatter of the cylinder is minimized over
quite a broad range of frequencies (1. 7 to 2. 3 CHz). With a conven-

tional 50 ohm coaxial cavity, the minimization of scattering can be F“-‘

 

achieved only over a much narrower frequency range (1. 9 to 2.1 GHz).
The experimental measurements on the backscatters from a solid
cylinder, a cylinder loaded with a 50 ohm coaxial cavity, and a
cylinder loaded with a 240 ohm coaxial cavity are presented in Figure
7. 3 as a function of frequency. The backscattering cross sections of
the 50 ohm loaded and 240 ohm loaded cylinders (h = 3. S cm) are
represented by thin and thick solid curves, respectively, and that of
the solid cylinder (h = 3. 5 cm) by a dashed line curve. This band-
width improvement by the technique of employing a high characteristic
impedance coaxial line can easily be explained, since this coaxial line
can provide a high impedance without operating about its antiresonant
length, where a slight change in frequency can cause a large change
in reactance.

The 240 ohm characteristic impedance coaxial line is also
applied as the loading impedance for the sphere with loaded wires,
as described in section 3.2. As in the case of the cylinder, this
technique for bandwidth improvement is quite successful for the
sphere (a = 5. 71 cm). In Figure 7. 4, the backscatters of the solid

sphere (dotted line), sphere with solid wires (dashed line), sphere

129

 

 

 

 

 

(db)
-44
.9 ‘\ coaxial
O/ ’ ~\\ llne
/ / \ \
_2 , // solid cylinder \ \
/ (h = 3. 5 cm) , \
/ ‘\
/~ ‘\ .
/ \
/ ‘\
O . / ' \
o \o\ o
0/ ' \\
/ ‘\
\
A I
0
3m 2 it I, o
c:
.2 I
*5 I
3% I,
3’: 4. I
° I
s.
U I
2" 7
'L‘ I
3 / cylinder (h = 3. 5 cm) loaded
"’ with 50 ohm coaxial line
g 6 II I, ‘ /
2*: - I - .
g /
/ o
81 J o o
/
I
' o
o
O O O
10i ‘
noise level cylinder (h = 3. 5 cm) loaded with 240 ohm coaxial
line
12 1 r
1.7 1.8 1.9 2.0 2.1 2.2 2.3

frequency (GHz)

Figure 7. 3. Backscattering cross sections of solid and loaded cylinders
as a function of frequency (h = 3. 5 cm).

(db)

4 a

Z ..

0 ..

Am -2 ‘
3
G
.9.
Ti
0
(D

m -4 -
m
0
H
O
on
.5
33

t} -6 4
rd
0
m
.1
U
(U
,0

-3 J

-10 "

' /

 

-12

130

 

 

u—J '
E h
171 I H a = 5.71 cm
'5 h = 3.4 cm
Ire—2a /
/
0/
sphere with // X
solidwires \ /
/ x
/ o
/ o
./
‘ /
sphere /’
\ / '
I,” ~.\ /
I, \‘\\ o/
x I, . \\/
o \
I X ‘\
/ _ \ .
I, / \\ g X
I Q ‘
l \\
:1, O / ‘\
\
/ O O ‘\ ’1’
\ ,I’
, \\ x ”I.
o /O \\ ’1’
o / \““.. ’I‘I
/ -
/ c
/ x 0
o 0
O /O O x O

a. .

sphere with /
loaded wires
(240 n coaxial line)

sphere with
loaded wires
(50 n. coaxial line)

 

/

noise level

 

f r W

l. 9 Z. O 2.1 2. 2
frequency (GHz)

1.7 1.8

Figure 7. 4. Backscattering cross sections of sphere and sphere
with loaded wires as a function of frequency (a = 5. 71 cm,

h = 3.4 cm).

with loaded wires {thin solid line? using coaxial line with 50 ohm
characteristic impedance, azzd ‘rhe sphere with loaded wires using
coaxial cavity of 240 ohm :haracteristic impedance (thick solid

line) are plotted as a function of frequency. There are two inter-
locking reasons for the bandwidth improvement using this technique.
The first is that the -: oaxial cavi‘hg; can provide high impedances with-
out operating about ;ts art‘resonant length, as explained above, and

the second is that for this size sphere (a = 5. ”.71 cm) length of wires

 

(h = 3. 5 cm), and center fr equencv {2. 0 CH2), the required impedance
for minimum backscatter is very small, which makes the use of a
coaxial line very effective.

Bandwidth improvement in the backscattering enhancement
of metallic objects can be .3_.':';1:eved by similar techniques. In
particular, the maximization of the backscatter from a sphere can
be made quite broadband by the use of longer wires. It is observed
in section 3. 2, Figure 3.10, chit the scattering from a sphere
(a = 5. 71 cm) with loaded Wires .Zh : 12. 9115- nearly independent
of loading impedance and maintained a level about 5 dB above the

cross section of the sphere.

 

10.

11.

REFERENCES

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of Waves, Harvard University Press, Cambridge, Mass.

(1959).

 

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133

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