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Optimization and engineering of microwave absorbers

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The Pennsylvania State University
The Graduate School
Department o f Engineering Science and Mechanics
OPTIMIZATION AND ENGINEERING OF
MICROWAVE ABSORBERS
A Thesis in
Engineering Science and Mechanics
by
Kuo-Liang Chen
©1998 Kuo-Liang Chen
Submitted in Partial Fulfillment
o f the Requirements
for the Degree o f
Doctor of Philosophy
May 1998
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We approve the thesis of Kuo-Liang Chen
Date o f Signature
^kr~d
(>, I W
Vijay Kr Varadan
Distinguished Alumni Professor o f Engineering
Science and Mechanics and Electrical Engineering
Thesis Co-Advisor
Co-Chair of Committee
Vasundara V. Varadan
Distinguished Alumni Professor o f Engineering
Science and Mechanics and Electrical Engineering
Thesis Co-Advisor
Co-Chair o f Committee
& I ^ *7¥
Sabih I. Hayek
/
Distinguished Professor of Engineering
Mechanics
l(K .
K . Kirt Shung
C ---Professor o f Bioengineering
f e ? ■ /.------ ^
B. L. "Lee
■J ~
j
y
Associate Professor of Engineering Science
and Mechanics
-T n J ?
"Richard P. McNitT
Professor of Engineering Science and Mechanics
Head of the Department of Engineering Science
and Mechanics
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<Tj 1 9 9 ?
ABSTRACT
In this thesis, a concerted effort has been made to study and evaluate the individual
electromagnetic properties o f the absorbing components including carbon black,
conducting fibers, metal flakes, magnetic materials such as carbonyl iron, ferrite and the
chiral type of micro-carbon coil.
The study o f the electromagnetic properties covers
functions such as dielectric dissipation, random scattering effect at low and high
frequencies, magnetic dissipation at high frequencies and also the effect o f chirality for
different angles o f incidence. The results o f these studies have been used in the design,
engineering and optimization o f the microwave absorbers.
The objective o f this thesis is to identify the absorption mechanism o f each of
various type of fillers and to study the synergic effect arising from a combination o f these
in a non-metallic host medium.
This will help us in producing microwave absorbers
suitable for broad band application with the advantages of light weight, having high
strength and possessing good chemical resistance.
The results from experimental
measurements of various material combinations have been greatly influenced by the
theoretical understanding o f the absorption mechanism.
Design o f microwave absorbers is governed by the requirement of the users as well
as the characteristics o f the objects (targets) inferred by theoretical understanding and
experimental data to arrive at the right formula.
Finally a detailed quality control program has to be charted out reflecting both the
electromagnetic as well as mechanical properties. This is done by carrying out the tests
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systematically on small samples and then proceeding to practical absorbers making use o f
the data compiled earlier on smaller samples.
In this thesis, to modify all dielectric absorbing components including micro-carbon
chirals to reduce the sensitivity o f absorption for different incident angles is
unprecedented topic.
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V
TABLE OF CONTENTS
LIST OF FIGURE............................................................................................VII
LIST OF TABLES............................................................................................ XI
ACKNOWLEGEMENTS.............................................................................. XII
Chapter 1 INTORDUCTION...........................................................................1
1.1 History....................................................................................... 1
1.2 Thesis objective and organization.......................................... 5
1.3 Electromagnetic theory.............................................................7
1.4 Absorbing components............................................................ 12
1.5 Measurement.............................................................................15
1.6 Optimization and engineering o f microwave absorbers.......16
Chapter 2 MECHANISMS OF ABSORPTION............................................18
2.1 Introduction.................................................................................18
2.2 Electromagnetic waves propagation.........................................18
2.3 Electromagnetic waves reflection............................................ 23
2.4 EM waves in lossy media...........................................................30
2.5 Metal backed absorbers..............................................................33
2.6 Random scattering effects & attenuations.............................. 35
2.7 Normal incidence scattering o f multilayer structure.............39
Chapter 3 SCATTERING AND ABSORPTION CHARACTERICS
OF PARTICULATE FILLERS..................................................44
3.1 Introduction............................................................................. 44
3.2 Metal flakes............................................................................... 44
3.3 Conducting fibers......................................................................59
3.4 Carbon black...............................................................................71
3.5 Conducting chirals......................................................................86
3.6 Magnetic materials: Carbonyl iron and ferrites.................. 110
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vi
Chapter 4 MEASUREMENT......................................................................... 121
4.1 Introduction.............................................................................. 121
4.2 Reflection and transmission measures.................................. 122
4.3 Time domain method................................................................127
Chapter 5 ENGINEERING OF MICROWAVE ABSORBERS............... 136
5.1 Introduction................................................................................136
5.2 The optimization o f absorber's formula................................137
5.3 The thickness criterion for EM wave absorbers................. 144
5.3.1 Optimized thickness o f metal backed single layer
absorbers..........................................................................144
5.3.2 The thickness o f multilayer absorbers......................... 149
5.4 Manufacturing methods o f microwave absorbers............... 155
5.4.1 Spraying.............................................................................155
5.4.2 Lamination........................................................................ 157
5.4.3 Preform molding...............................................................160
Chapter 6 CONCLUSION AND FUTHER STUDY..................................162
6.1 Conclusion................................................................................162
6.2 Further study............................................................................. 164
APPENDIX: Tested samples..........................................................................166
REFERENCES................................................................................................. 168
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LIST OF FIGURES
Figure 2.3-1 A plane EM wave travels through a semi-infinite dielectric slab.................24
Figure 2.3-2 A multilayer system , on which a uniform plane wave is normally
incidence from the left...................................................................................25
Figure 2.3-3 The “ Salisbury Screen “ absorber...................................................................27
Figure 2.3-4 Performance o f multiple resistive sh e e ts....................................................... 30
Figure 2.5-1 Single layer on metal surface........................................................................... 33
Figure 2.6-1 The attenuation due to the scattering cross section o f dielectric materials..37
Figure 2.7-1 A Plane wave normally incidence a m ultilayer............................................... 39
Figure 2.7-2 The propagation mechanism of resistive sheet sandwiched between two
dielectric layers.................................................................................................. 40
Figure 3.2-1 The spherical geometry......................................................................................45
Figure 3.2-2 The RCS o f conducting sphere over the three scattering regimes................ 48
Figure 3.2-3 The “ creeping wave “ o f a conducting sp h ere...............................................49
Figure 3.2-4 Geometry o f d is c ................................................................................................51
Figure 3.2-5 The random scattering cross section o f conducting disc and comparison
with same electric circumference o f conducting sphere...............................53
Figure 3.2-6 (a) The return loss o f same volume fraction for copper spheres and
aluminum flakes......................................................................................... 55
Figure 3.2-6 (b) The return loss o f 1.4% ( volume fraction) for both copper spheres
and aluminum fla k e s..................................................................................55
Figure 3.2-6 ( c ) The return loss o f 2.8% ( volume fraction) for both copper spheres
and aluminum flake....................................................................................56
Figure 3.2-6 (d) The return loss o f 5.6% (volume fraction) forboth copper spheres
and aluminum fla k e s ............................................................................... 56
Figure 3.2-7 The return loss o f 4.5% volume fraction o f aluminum flakes.................... 58
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Figure 3.3-1 The wire geom etry......................................................................................... 61
Figure 3.3-2 The normalized average scattering cross section vs. electric length o f
conducting fiber.............................................................................................64
Figure 3.3-3 The normalized scattering cross section vs. wave circumference o f
conducting sphere........................................................................................ 65
Figure 3.3-4 (a) The measured return loss of RAM in which included 0.7% o f
copper spheres and 0.007% o f carbon fibers...................................... 6 8
Figure 3.3-4 (b) The return loss o f 1.4% copper spheres and 0.014% carbon fibers.. . 6 8
Figure 3.3-4 (c) The return loss o f 2.8% copper spheres and 0.028% carbon fibers. .69
Figure 3.3-4 (d) The return loss o f 5.6% copper spheres and 0.056% carbon fibers...69
Figure 3.3-5 The return loss o f optimized volume fraction o f carbon fiber 0.022%...70
Figure 3.4-1 The shape and its impedance o f pyramidal PU foam s................................ 73
Figure 3.4-2 The return loss o f a pyramidal PU foam absorber loading carbon black.,74
Figure 3.4-3 The impedance profiles o f a stepped loading distribution o f carbon
black absorber...............................................................................................74
Figure 3.4-4 A double layer carbon black loading absorber..............................................75
Figure 3.4-5 The absorbent performance o f a double layer metal backed absorber
which is loaded carbon black only.........................
80
Figure 3.4-6 The return loss o f a double layer absorber in which loaded modified
dielectric absorbing components............................................................... 83
Figure 3.4-7 The dependence o f return loss and operating temperature for modified
dielectric RA M ........................................................................................... 84
Figure 3.4-8 The dependence o f return loss and operating temperature for
carbon system absorbing components.....................................................85
Figure 3.5-1 The 3-D traveling diagram of EM wave and the shape o f LCP & RCP
chirals.............................................................................................................. 87
Figure 3.5-2 The mechanism o f micro-coiled carbon fiber’s production..................... 89
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Figure 3.5-3 The normally incident plane wave passed through a double layer slab...93
Figure 3.5-4 (a) The return losses o f 0.75%copper chirals , 0.42 aluminum flakes,
0.036% carbon fibers, and their three com bination.........................101
Figure 3.5-4 (b) The return losses o f individual components with same volume
fractio n ................................................................................................... 1 0 1
Figure 3.5-5 The measured return loss of optimized volume fraction
composite................................................................................................... 104
Figure 3.5-6 The return loss o f same volume fraction o f carbon fibers and
aluminum flakes ( without copper chirals )............................................ 105
Figure 3.5-7 The return loss o f different volume fraction o f micro-carbon chirals... 106
Figure 3.5-8 The return loss o f 0.2 mm and 0.5 mm length microcarbon chirals.... 108
Figure 3.5-9 The signal property o f microcarbon chirals , less sensitive
for different incident an g le......................................................................109
Figure 3.6-1 A B-H hystersis lo o p s............................................................................. I l l
Figure 3.6-2 The general profile o f the electromagnetic parameter spectra for
magnetic materials..................................................................................114
Figure 3.6-3 The measured return loss of RAM which used one ferrite.................. 119
Figure 3.6-4 The measured return loss of three ferrites............................................. 120
Figure 4.2-1 The S-parameter & vector network analyzer test set in CEEM...........123
Figure 4.2-2 The signal flow o f the two port network analyzer................................ 124
Figure 4.2-3 The return loss measurement of metal backed sample in different
incident a n g le ......................................................................................... 125
Figure 4.3-1 One dimension “ time domain “ m easurem ent.................................... 128
Figure 4.3-2 The definition o f resolution for time domain measurement...............130
Figure 4.3-3 The geometry about correction of phase errors................................... 133
Figure 4.3-4 The correction diagram o f measurement...............................................134
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Figure 5.2-1 The measured return loss o f an optimized two-layer RAM.................. 140
Figure 5.2-2 A modified dielectric materials Em absorber after balance o f
component’s attenuation showing the broadband absorption............... 143
Figure 5.3.1-1 Single layer on metal surface.................................................................145
Figure 5.3.2-2 The thickness o f medium layer in multilayer system...........................150
Figure 5.3.2-3 Special case in theory but very common in practical application..... 152
Figure 5.4-1 The special spraying equipment which can spray the resin mixing
paste and chopped fibers instantaneously................................................ 157
Figure 6.1-1 The return loss and temperature dependence of magnetic R A M ..........163
Figure 6.1-2 The return loss and temperature dependence of dielectric R A M ..........164
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LIST OF TABLES
Table 1.3-1 The return loss comparing the wave energy loss in detection......................12
Table 3.2-1 Normalized random scattering cross section vs. different g and <pl ......... 51
Table 3.5-1 The relationship between different pitches o f copper wire spring
and absorptions at same inclusion volume fraction..................................... 1 0 2
Table 3.5-2 The absorption o f composites with different scattering com ponents....... 103
Appendix Tested samples..................................................................................................... 166
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ACKNOWLEDGEMENTS
I would like to thank my thesis advisors, Professor Vijay K. Varadan and
Professor Vasundara V. Varadan for their guidance and support for this thesis. Sincere
thanks are also due to Professor Sabih Hayek, Professor B. L. Lee and Professor K. Kirk
Shung for their valuable suggestions and corrections to this thesis.
I would also like to thank researchers in the Center for Engineering o f Electronic
and Acoustic Materials for their help and cooperation in the conduct o f this research.
Finally, this thesis would not have been completed but for my wife and children
and their patience and never ending love during my graduate school years at Penn State.
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1
CHAPTER 1
INTRODUCTION
Many engineering requirements demand a total elimination or a reduction of
electromagnetic wave reflection, diffraction, and refraction or scattering as they distort
radio communication, create ghost images in television transmissions, or reveal the
location o f targets to enemy. Under these circumstances, an ideal solution is to apply
microwave absorbers on certain objects or areas to eliminate or reduce the above
deterrents.
Furthermore, for indoor electromagnetic wave measurement, an anechoic
chamber, o f which the interior is usually covered with microwave absorbers, is used to
provide an interference free space environment. Here these microwave absorbers fulfill
the purpose o f simulating the free space in a confined space.
Being coated with
electromagnetic absorbing materials to minimize the electromagnetic interference
problem can enhance the performance o f many surveillance radar systems. Especially for
those at sea where they are subjected to very strong return signals from nearby objects
such as masts, high buildings, bridges, electrical cables, metal wires etc.
1.1 History
Since the mid 1930’s, both theoretical and experimental work has been done on
electromagnetic wave absorber [1]. The first absorber was a quartz resonance type at 2
GHz. It was designed and fabricated at the Namaalooze Vennootschap Machinereen in
Holland [2]. However the first patented electromagnetic wave absorber was carbon black
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2
type. In order to obtain higher dissipation at a reduced thickness, T iO , was added to
increase its high dielectric constant. This type o f absorber was used to cover the back
side o f an antenna to reduce EM diffraction and creeping waves from front to the back. It
was only during the Second World War that the need was felt to design and to develop an
electromagnetic wave absorber covering a wider bandwidth as well as having good
absorption qualities. This was necessitated mainly because of the increased use o f radar in
battlefield. During this period both USA and Germany launched projects to implement
the EM wave absorber ideas emerging from research through development and design test
and field evaluation for use in a limited number o f defense applications. While Germany
was interested in EM wave absorbers for radio camouflage, the effort in USA was
primarily directed toward developing absorbers that would enhance the radar performance
by reducing interfering reflections from nearby objects [3].
Between 1941 and 1945, a coating material called “HARP” (Halpem Anti-Radar
Paint) was developed in M.I.T. Radiation Laboratory under the leadership of Mr.Halpem
[5]. Although the HARP coating was only 0.6 mm thick, it achieved a return loss o f -15
dB to -2 0 dB in X-band range
(8
to 12 GHz). This material was suitable for aircraft
application because o f its small thickness.
Small thickness was a tribute to the
development o f an artificial high dielectric constant material such as barium titanate. of
which the real part o f the relative dielectric constant is about 150 at 10 GHz, the center
frequency o f X band. The main components o f HARP were carbon black, disc shaped
aluminum flakes, and barium titanate in a rubber matrix. Besides HARP coating, M.I.T.
Radiation Laboratory also successfully developed the now well-known “Salisbury” screen
absorber. This screen absorber showed zero reflection when a 377 ohms (impedance)
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3
resistive sheet was placed in front of a metal plate at a quarter wave length distance.
Although Salisbury absorbers were effective only for normal incident waves, its
absorbing mechanism
motivated scientists to continue the development o f EM wave
absorbers.
During the war years, the quality o f anechoic chambers became more and more
important to obtain accurate indoor measurements. Apart from the test equipment, a
perfect free space environment was required for precise measurement. Therefore, wide
bandwidth and high absorption performance o f EM wave absorbers are required. The
long pyramidal polymer foams loaded with carbon black were developed as EM wave
absorbers to cover the walls o f a rectangular room so as to achieve an artificial free space
environment [6 ].
From the absorbing mechanisms o f pyramidal foam absorbers, broadband absorber
was developed by gradually tailoring the effective EM properties near that o f free space at
the front surface to those o f a dissipative medium at the back surface. From 1945 to
1950, these broadband absorbers satisfied most o f the requirements for anechoic
chambers. The broadband absorbers had been developed from the knowledge of the
previous art of “dummy load“ design that inspired the scientists and engineers to develop
a lot o f typical “ dummy load materials”.
Other dissipative components such as metal and graphite powders, iron oxide, metal
wires, and steel wool had also been experimented in the development o f aborbers.
Subsequently, lots o f experimental work has been conducted on various surface
geometries including pyramids, cones, hemispheres and wedges. Mr. R.W. Wright, a
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scientist o f the U.S. Naval Research Laboratory, has been the most successful worker in
this field.
In the early 1950’s, Emerson of U.S. Naval Research Laboratory showed an effective
broad-band absorber which could be made by dipping or spraying tiny conducting
powders such as carbon black onto a bat o f loosely spun animal hair. Lightweight and
easy-to-make were the advantages o f this kind o f absorbers.
The Sponge Products
Company produced the first commercial product, “Spongex”, in 1951. A 2 inch thick
Spongex material offered a return loss o f about -20dB for normal incidence at the
frequency range from 2.4 to 10 GHz.
In the late 1950’s, Emerson & Cuming Inc. produced absorbers for anechoic chamber,
which provided over -40 dB return loss at a wide frequency range.
In the 1960’s, Mr. R .E. Hiatt, Head o f the Radiation Laboratory, University of
Michigan, Ann Arbor, demonstrated significant absorber thickness reduction using
magnetic ferrites as under layers. His work was sponsored by NASA. As they happened
to be the days o f satellite projects, the anechoic chambers had to be useful for making
many types o f measurements for multi-purposes. The 100 MHz to 400 MHz frequency
region was important for tracking and telemetry. It is known that at lower frequency it is
more difficult to obtain high absorbing performance.
High permeability and high
permittivity magnetic materials contribute for a high refraction index at low frequency
regions and hence reduce the thickness o f absorbers. This new development made it
possible to obtain - 40 dB return loss from 100 MHz to 1 GHz.
In the 1970’s, the Japanese used magnetic ferrites to make EM wave absorbing paint
and applied it on the outside wall o f high buildings to reduce the ghost images on
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5
television screen. The Plessy company in UK, a renowned manufacturer o f EM wave
absorbers, developed a new generation o f EM wave absorbers to satisfy the requirements
o f the British Navy including camouflage and minimizing electromagnetic interference
(EMI).
All these efforts have resulted in the development of “Stealth Material” by several
countries which will play a significant role in the development o f Advanced Bomber and
Fighter Aircrafts as well as the deployment o f RAM (Radar wave Absorbing Materials)
on Naval Vessels.
These developments have been achieved based on a synergistic
approach. The reduction in the radar cross section (RCS) o f a target has been obtained by
a number o f methods such as adjusting geometrical shapes to reduce the reflection at
certain sensitive angles and applying the RAM onto the target surface [7].
1.2 Thesis objective and organization
From the development history o f microwave absorber, we know that many problems
have to be overcome in making an “ideal absorber” especially for military applications.
Light loading, high temperature resistance, high strength, small thickness, very broad­
band absorption, and high absorbing performance are the essential requirements to satisfy
the fast growing electronic warfare.
In this thesis, the EM properties o f different types of absorbing materials were firstly
discussed.
These materials include metal flakes, conducting fibers, carbon black,
conducting chirals, and magnetic materials such as carbonyl iron, ferrites, etc. These
components have different EM wave absorbing properties such as random scattering
effects, dielectric and magnetic dissipation, and chirality.
Although each individual
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6
component has its own drawbacks, it is possible to optimize the absorbing performance
by a combination o f the above materials with appropriate scattering geometry. The main
objective o f this thesis is to make an absorber with the required performances such as
broader frequency absorption, lighter loading, smaller thickness, and high return loss.
This can only be achieved by an optimal combination o f the individual component.
The thesis is organized as follows:
In chapter 2, a general discussion o f EM theory for absorbing mechanisms is
presented. These include Maxwell’s equations, constitutive equations, wave equation,
the relationship between random scattering cross section and attenuation, Poynting power
density, the reflection due to impedance mismatch, Salisbury Screen effect, and magnetic
hystersis effect and dissipation.
In chapter 3, EM properties o f absorbing components and their physical & chemical
advantages and disadvantages are discussed.
These include EM wave absorbing
performance at certain frequency, density, chemical corrosion, mechanical strength,
temperature resistance, and the feasibility o f processing etc. A comparison o f analogous
materials to those studied in this thesis is presented. The methodology o f optimizing the
formulation is also presented.
In chapter 4, measurements on the absorbers are presented.
This is the most
important step to optimize the formula and to qualify the products. Different approaches
have been made to measure the chiral media and explore the special application o f the
new type o f chiral material: micro-carbon coil.
In chapter 5, based on the previous knowledge we have studied how to design and
find the optimized formula o f absorbers for practical applications.
After the design
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7
issues, we discussed the manufacture o f
microwave absorbers for mass production.
Finally, quality control was discussed, especially for practical targets.
In chapter 6, conclusion and suggested future research in this area are given.
1.3 Electromagnetic theory
The propagation and energy transfigurations o f electromagnetic waves are governed
by the well-known "Maxwell's equations" [8 ][9]. In differential form they are as follows:
Faraday’s Law o f Induction:
SB
V XE = --------dt
(1 .3 -1 )
Ampere Law :
3 D
V X H = ------- + J
dt
(1.3-2 )
Gauss's Law o f Magnetic Field:
V• B= 0
(1.3-3 )
Gauss's Law o f Electric Field:
V• D=p
(1.3-4 )
-
Where E is the electric field intensity in [V/m], H is the magnetic field intensity in unit
[A/m], B is the magnetic flux density in [W b/m 2 ], D is the electric flux density in unit
[C /m 2 ], J is the electric current density with unit [A/m 2 ], and p is the electric charge
density with unit [C/m 3 ].
The electromagnetic aspects o f microwave absorber design focus principally on
the synthesis of an arrangement o f dielectric or magnetic materials that provide a
specified impedance profile to an incident wave.
The study o f the evolution of
microwave absorber design is the study o f the materials and techniques employed to
achieve desirable impedance properties and, hence a good absorbing characteristics over
increasing bandwidths.
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The electric and magnetic properties of a dielectric material are characterized by the
A
A
complex permittivity, s , and permeability, j i :
A
A
£=s'-jE "
and
/y= p'-jp"
For lossy media, imaginary parts o f the complex permittivity and permeability are
nonzero. Generally these imaginary parts represents the absorbing performance.
The
actual absorption not only depends on the electric or magnetic losses but also the random
scattering effect and chirality effect o f the conducting chirals.
When an alternating electric field is applied across a dielectric slab (or layer ), an
alternating displacement current is observed which results from the oscillation of
the electric dipoles within the field.
Applying the Gauss's Law o f Electric Field: V •
layer, possesses an alternating conductivity.
D
= p, the dielectric slab or
It is independent o f other direct
displacement current that resulted from the migration o f free charge carriers. The total
dielectric loss o f the material has a relationship with the total conductivity that is due to
the summation o f the above two kinds o f displacement current. This is s" = cr / co,
where co is the angular frequency o f the applied field.
In magnetic materials, the magnetic tangent loss is due to the hysteresis phenomenon.
These loss tangents can be summarized as follows:
u
Magnetic loss tangent : tan | 5 m | = —r
M
£
Dielectric loss tangent : tan | 5 d | = —
s
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From the loss tangents we also can calculate the attenuation constants a o f the absorbers.
For dielectric materials,
co.
)y[M£
V2
[yll + {a/a>£)2
-1
] 1/2
(1.3-5)
For magnetic materials,
am=
Aa>2 . . .
.
. x
—— i e j u + £ M )
4n
(1-3-6)
Apart from the study o f the above lossy effects, we also discussed the attenuations
due to random scattering effects and chirality. When we use the conducting reflectors
whose sizes are smaller than the wavelength, the creeping waves and refraction will
occur. These factors create waves o f different phase and different direction.
The
interaction o f these waves causes attenuation.
In the three-dimensional case, the differential scattering cross section is defined by
<x(0,0) = lim
|£ * |2
\E‘\
The total scattering cross section <
j t is defined by the ratio o f time averaged total
scattered power to the time averaged incident Poynting vector, and is related to the
bistatic cross section by the equation
When scatters are used to make EM wave absorbers, the attenuation due to the random
scattering effect is
a s = p a r /2
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(1-3-7)
10
Where a s is the attenuation due to the random scattering effect, c is the scattering cross
section o f each scatterer, p is the number density o f flake per unit volume. The total
attenuation should be
a r = a , + a m + a d + a ch
(1.3-8)
Where a r is the total attenuation of composite
a m is the attenuation due to magnetic tangent losses
a d is the attenuation due to dissipation
a ch is the attenuation due to chiral media
The time-average Poynting vector power density o f a normally incident plane wave is
In lossy media the power o f EM wave is attenuated along the distance z and becomes
A
e -2^
2
= t — IE
77
|2
e ~2°t: = p
0
exp-2ar z
2/7
where r| is intrinsic impedance.
Except for the attenuation, the front-face reflection of absorbers depends strongly on the
total field impedance and intrinsic impedance o f the absorber. They have the following
relationship:
The intrinsic wave impedance:
7 = CE /
H
] = [^/s]w
Substitute the complex permittivity
IP]
A
O’
e = s -j —
into the above equation to get
co
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11
h
=[ H
1 1/2 / [ 1+ ( ^
s
) 2 ] 1/4
e *'m
’
[O]
(1.3-9)
The intrinsic impedance o f materials is independent of thickness and location. The total
field impedance of materials is
Z (*)=
h,
=
n
[n ]
(1.3-10)
i-r(z )
A
Where T(z) is the reflection coefficient at location z.
f (z)= f ( Z ) ~ f Z)
Z (z ) + T](z)
(1.3-11)
A very useful expression is the equation that enables finding reflection ratio at any
location:
f (z')= f (z> e w " '
O-3' 12)
The return loss is defined as
A
Return loss (dB) = 1 0 log p
2
The net time-average power flux passing through some normal open surface area A is
PIv = Pov * A
and
P ;=
p ^ ' A
Where positive and negative signs represent the incident and reflected wave powers.
Combining the previous return loss definition we obtain
|;H
Return loss (dB) = 10 log
= 10 log | T | 2
(1.3-13)
LP+
ov
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Following the definition o f the return loss, the return wave energies o f a target without
RAM compared with that o f with RAM are listed as follows:
Table 1.3-1 The return loss comparing the wave energy loss in detection.
Return loss (-dB)
Return wave energy (%)
-3 dB
- 5 dB
-10 dB
-20 dB
-30 dB
-40 dB
Wave energy loss for detection (%)
50%
30%
10%
1%
0 . 1%
0 .0 1 %
50%
70%
90%
99%
99.9%
99.99%
1.4 Absorbing components
During the 50’s and 60’s, magnetic media was considered as the main absorbing
component [10-12]. Ferrite which is one o f the magnetic materials has a wide range of
electrical and magnetic properties. The most common class, the spinel ferrite, has a cubic
crystal structure and can be represented by the general formula, M F e , O 4 . Where M is
usually a divalent transition metal ion, a combination of two or more such ions or other
combination such as mono- and trivalent ions that maintains overall electrical neutrality.
M nFe 2 0 4 , N ix Zn,_x F e, 0
4
and L ix Cr,_xFe, 0
4
are very common examples of
spinel ferrites. The hexagonal ferrites have absorbing resonant peaks in higher frequency
region. Using appropriate doping methods, it is easy to control the resonance frequency of
hexagonal ferrites.
Although the hexagonal ferrites are expensive and have poor
chemical resistance, it is the only way to obtain a very thin layer (below
high absorption (over -20 dB) at X band
(8
1
mm) with very
to 12 GHz).
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13
Electronic technology has been greatly developed in recent years, commercial and
military applications require high performance absorbing materials with light weight,
high strength over broad frequency band. This can be achieved if we could design and
optimize a combination o f different components based on their dielectric properties and
random scattering effects due to their respective geometry.
The conductive chirals can play a main role in electromagnetic wave absorbent
materials. If absorbers contained the chiral media only, the material might not satisfy the
above critical conditions. During the early history o f the study of chiral materials, metal
wires were used to make chiral shaped coils. The drawbacks of these metal wire chirals
are heavy weight, poor chemical resistance, poor EM wave absorption and high cost.
Recently, chemists have produced coiled chiral carbon fibers using acetylene as carbon
source and fine metal powder (0.03-12 pm) as catalysts.
pm in diameter and
20
Carbon chiral fibers with 2-3
pm in length have been produced.
This tiny conductive carbon chirals have many advantages over the original metal
wire chirals such as lower density, excellent chemical resistance, and higher temperature
stability. Furthermore, the spring fiber shapes are the reinforcing factors to make the
composites stronger.
Carbon black is the most popular raw material in microwave absorbers. In this thesis,
carbon black is dispersed in the binder (resin) to increase the dissipation o f the matrix. It
is necessary to maintain a proper ratio o f carbon black to the resin. Too high a ratio may
make the matrix into a good reflector.
Straight carbon fiber was also used as a waveguide and a random scattering reflector.
It is important to select proper fiber length and concentration to achieve high
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14
conductivity.
Homogeneous dispersion o f the carbon fibers in the matrix is also an
important issue in the manufacture o f EM wave absorbers.
Aluminum flake has played an important role in the history of microwave absorbers
acting as a random scattering reflector. Its tiny size and disc shape makes its dispersion
in matrix easier.
In this thesis, polyurethane elastomer is used as binder (matrix), because its dielectric
constant is 9, much higher than that o f other resins such as PE, PP, PTFE, and PVC with
dielectric constant is about 2 to 3. High dielectric constant (permittivity) means high
refractive index that improve the performance o f random scattering and reduce the
wavelength (or reduce the thickness o f the absorbing layer) in composite absorbers. Also
polyurethane elastomer has excellent fatigue resistance, very good flexibility, and good
chemical resistance.
Air is usually used for the impedance matching and reducing the density o f absorbers,
therefore, sponges or foams are commonly used. Blowing agents such as Freon 12 is
generally used. To our experience, this method makes it difficult to control the product
quality, especially in the distribution o f some anisotropic absorbing components such as
conducting fibers and metal flakes. Moreover, the sponge EM wave absorbers have very
poor physical strength. For practical application, it had serious limitations for absorbers
in anechoic chamber application.
Microballoon is the panacea o f this problem.
Ceramic microballoons offer
homogeneous distribution o f absorbing components and uniform size o f air bubbles. On
the other hand, sponge absorbers showed poor compressive strength due to the open cells.
Under high humidity surroundings, these opening bubbles easily absorb the moisture
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15
which in turn causes an increased loading and EM wave reflection, especially in the X
band. The ceramic microballoons have an inorganic cell. Generally they can stand 500psi
to 3000psi compressive pressure. Using different sizes o f microballoons at an optimal
volume fraction we can make the composites having enough compressive strength at
lowest density.
For low frequency, magnetic absorbing materials are always suitable for RAM due to
their high permeabilities and permittivities. Similarly reason for high dielectric constant
materials such as barium titanate or strontium titanate which are used in RAM to reduce
the thickness despite the high density.
Other materials such as glass fibers and glass flakes have also been used. Although
they have no absorbent effect for EM wave, they play an important role in reinforcing the
material (glass fibers) and protect the absorber from chemical corrosions (glass flakes)
[13].
1.5 Measurement
In the Research Center o f Engineering Electronic & Acoustic Materials of The
Pennsylvania State University, we have a free space measurement system. It is composed
o f HP 8510 B Vector Network Analyzer, HP 8340B Synthesizer sweeper, HP 8516A Sparameter, and series o f lens horn antenna.
The computing system including certain
software installed in personal computer and anechoic chamber are also used in
measurement.
Generally, return loss o f the metal backed absorbing materials mainly
measured. The transmission of the absorbers also needs to be evaluated in some cases.
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16
For chiral media, it is necessary to measure the reflection and transmission for different
rotation angles.
For small samples, the free space measuring equipment instead o f anechoic chamber
is used. Since it is more convenient than the traditional anechoic chamber set up [14]. In
free space set up, lens hom antenna is used to avoid end refraction effects.
1.6 The optimization and engineering o f microwave absorbers
After evaluating the EM properties o f all absorbing components, we have summarized
how to optimize the composition o f the absorbers for different frequency regions and
different environmental requirements. Furthermore, mechanical strengths and chemical
resistance were also considered in designing EM absorbers. Proper fillers were necessary
to reinforce the mechanical strength, such as glass fibers, glass flakes, and barium titanate
powder. Although these materials are almost transparent in frequency region below 18
GHz, their different dielectric constants also make some kinds o f reflection from front
face o f RAM due to mismatch o f impedance.
To obtain the broader frequency region of absorption multilayer processing of
different density o f absorbing components is essential. Impedance matching o f each layer
is the main topic o f optimization and engineering of absorber [15].
Finally for the purposes o f practical engineering, pratical experience is needed in the
manufacturing process o f absorbers. Working with these materials in the factory is not
easy because of their complex shapes. All polymer composite processing are adopted in
the manufacture o f RAM such as lamination, spraying, and preform molding. Quality
control is the final step and also is the most important process. Series measurements and
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17
corrections are required to guarantee that all qualities for good EM wave absorption such
as mechanical properties, chemical resistance, and conductivity etc. are to be satisfied.
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18
Chapter 2
MECHANISMS OF ABSORPTION
2.1 Introduction
In this chapter, wave-material interaction is discussed.
The basic equations are
Maxwell’s equations, constitutive equations, Helmholtz wave equations, definition of
impedance, and modified Bom’s equations for chirality. These equations enable us to
understand the absorbing mechanisms o f RAM [8 ] [9] [16].
2.2 Electromagnetic waves propagation
The propagation and energy transfigurations o f electromagnetic waves are governed
by Maxwell’s equations in differential forms:
Faraday’s Law of Induction:
-
/?
R
VXE = -----------------------d t
(2.2-1)
(2.2-2)
Gauss's Law o f Magnetic Field:
V• B= 0
(2.2-3)
Gauss's Law o f Electric Field:
V• D= p
(2.2-4)
-
✓9 r)
V X H = -------- 1- J
d t
Ampere Law:
Where E is the electric field intensity in [V/m], H is the magnetic field intensity in unit
[A/m], B is the magnetic flux density in [W b/m 2 ], D is the electric flux density in unit
[C/m 2 ], J is the electric current density with unit [A/m 2 ] and p is the electric charge
density with unit [C/m 3 ].
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19
Combining Ampere Law (2.2-2) and Gauss's Law (2.2-4), the continuity equation
which expresses the conservation of electric charge can be obtained:
V .J = ~ ^ £
d t
between D , E , and
The relationships
(2.2-5)
B , H are:
D =e E
where e is the permittivity.
B = p. H
where p is the permeability.
The electric and magnetic properties o f a dielectric material are characterized by the
a
a
complex permittivity, e , and the complex permeability, / / :
A
A
s
=
s' - j e"
n
and
= p ' - j ji"
a
a
The relative permittivity, s r , and relative permeability, fj. r , have the following
relationships:
A
A
£ r ~ £■ / S 0 — £ r “ j £ r
V
Where S 0 and
r =
M
I Vo
=
Hr
- j
H r-
f i 0 are the permittivity and the permeability o f free space respectively.
If C is the velocity o f electromagnetic propagation in free space, they have the following
relationship:
c =
1/
O
0
S 0]
1/2
[m/sec]
where S 0 is 8.854 X 10 " l2 [F/m], and p 0 is 4 n X 10 ' 7
[H/m]. Thus the resulted
velocity of electromagnetic propagation in free space c is 3 X 1 0 8 m/sec.
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20
The real part o f the permittivity or permeability is a measurement o f the region to that the
material would be polarized or magnetized by that electric or magnetic applied field.
The imaginary part is a measurement o f the energy losses resulting from the
rearrangement o f the alignment o f the electric or magnetic dipoles in an applied field.
From M axwell’s equation:
V•
D
=
p v ,
where D is electric displacement,
p v
is electric charge density per unit volume.
When an alternating electric field is applied across a dielectric slab (or layer ), an
alternating displacement current is resulted from the oscillation of the electric dipoles
with the field.
Therefore, the dielectric slab or layer possesses an alternating
conductivity. It is independent other kinds o f direct displacement current that resulted
from the migration o f free charge carriers. The total dielectric loss o f the material relates
to the total conductivity due to the summation o f above displacement currents, i.e.:
8 "
=
a
/
CD,
where CO is the angular frequency o f the applied field.
When a plane electromagnetic wave propagates through a dielectric slab along z
direction, its electric and magnetic field can be represented by:
E
H =
= E m exp (jcot - yZ)
[v/m]
H m exp(j© t-yZ )
[A/m]
where y is the propagation constant:
y = jco [ p ( e - j a/co)]
1/2
= j k [ 1 /m]
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21
Where k is called wave number, y can be separated into real and imaginary parts:
y = a + j p
where
[ 1 /m]
( 2 .2 -6 )
a is the attenuation, and P is the phase constant. Explicit expressions for a and P
are obtained by replacing y with a + jP , squaring both sides to remove the radical and
equating the real part and imaginary parts of the result. For non-magnetic materials, the
expressions o f a and P are as follows. The expressions o f a and P for magnetic system
will be discussed chapter 3 section 5.
1 [V l + { a l ( o e f
03
[ y/l + i a / ojs)2
- 1 ] ,/2
+ l
] l/2
[NP/m]
= 2n/X
The dissipation angle vanishes for a lossless region.
(2.2-7)
[rad/m]
(2.2-8)
Its tangent, the loss tangent or
dissipation factor, is defined by
tan|5J= — = 4
(O S
(2.2-9)
£
From this equation we can predict that the higher the conductivity of a dielectric media,
the better EM wave absorption we can obtain.
In EM wave absorbers, carbon black is usually dispersed in resin binder.
The
conductivity o f carbon black will seriously affect the performance o f absorbers. It is
feasible to control the concentration o f carbon black in a matrix to match the intrinsic
impedance for a multi-layer absorber.
The intrinsic wave impedance is defined as:
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22
A
rj
= [ E
/
H
Substitute the complex permittivity
n = [ M
A
] = [ v / e V 2 [Q]
A
O
•
e =
8
-J —
co
into above equation:
] ,,2 / [ i + ( £ r ) 2] 1'4 «
£
[O]
(2.2-10)
To explain the mechanism o f absorption in the dielectric materials, we may take a
simple example that a plane EM wave is propagating through a dielectric material. As
shown in Fig.2-1, the dielectric material is a semi-infinite slab. Part o f incident energy is
reflected at the interface and other part is transmitted, let
E l l( z ) = E + mxle ~r':
. E : 2(Z) = E ^ 2 e ”
. £-(z)= £^,e
are the incident, reflective, and transmitted electric fields respectively.
Where the total electric field o f medium 1 is E xX(z )= E *, (z) + E
(z).
In Fig. 2.3-
1, medium 2, the total electric field of semi-infinite slab is E l 2 (z) = E *2(z ) *
in
A
region 2 the reflection o f wave is zero, therefore E ~2 = 0.
e
Similarly,
,
H ;2 = H +
my2 e ~r*
are the
incident, reflected, and transmitted magnetic fields. For total magnetic field in medium
A
A
A
A
A
1, and medium 2 are H yl = H *yl + H y~l , H y2= H y2
Where H ; ,=
E ^ e
r,‘ / rj , and
H ^ E ^ e
/ ~ tj ,
The boundary conditions at z =0 interface of two media are as follows:
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23
£,,(0)= £;, + £;, = £ =
« A °) =
»;,+
HZ, = H -
EA
= H A
0)
0
)
2.3 Electromagnetic waves reflection
A
The electric field reflection coefficient, p , is defined by
a
~
By substituting above relationships we obtain
EmxI
At interface, z = 0 +
a
—
E m x\
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24
1 st
layer
(air)
2 nd
(eo ho )
layer
( S 2 H 2 C 7 ,)
A
F *
C xl
0
Fig.2.3-1 A plane EM wave travels through a semi-infinite dielectric slab
From the above equations we can obtain the complex amplitude o f the reflection as
A
E'^=
[(7
A
i-n , ) U n
2+
n
,)]
(2.3-1)
Similarly, the transmitted wave has the amplitude
E *mxi ~ E ^
[ 2 TJ , /
(7 7
2+
7
,) ]
(2.3-2)
From equation (2.3-1), we can see that the reflection approaches zero if
7
z =T1 \ •
Matching the impedance o f each relative layer is very important to enhance EM wave
absorption inbetween the layers.
In practical applications, broadband metal-backed absorbers instead of semi-infinite
backing are generally required. For metal-backing, single layer can not satisfy broadband
absorbent requirements.
Multilayer absorber with good impedance match between
interfaces offer good absorption at broad frequency region.
Figure 2.3-2 shows a
multilayer system, on which a uniform plane wave is normally incident from the left.
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25
region 1 :
(SlfilCTl)
A
E
A
Motion
A A
3
( S3|I3 CT3)
2
(S2 |I2 CT,)
u
4
{ &4fl4 (T4)
u
5
( £5 fl5 CT5 )
t >
u
A
A
h
*; t
A
A
,t
; 5 = e :s
J
t
,
A
A
H yi —E x\/~ 7 i
Fig. 2.3-2 A multilayer system, on which a uniform plane wave is normally
incident from the left.
The system of Fig.2.3-2 is generalized into 5 regions.
incident, time-harmonic wave, E
and H
Excited by the normally
in region 1. Each region acquires that, in
the sinusoidal steady state, the forward and backward traveling fields appear, except last
region 5. The total electric field for each region becomes
A
A
E,(z)=£;«
A
u*
A
- + E - „ e - = E '.e
—Y*
^
'[l + T W ]
Similarly,
Em
— ----
e
-F
A +
Em
A total- field impedance
% (z) is defined at any location z by the ratio o f the total
electric field to the total magnetic field.
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26
[Q]
(2.3-3)
From the above equations, the reflection ratio can be obtained
A
A
(2-3-4)
Z (z) + 77(z)
A very important and useful expression is the equation that enables finding reflection
ratio at any location. It can be written as
f (Z’) = f
Cz)
e rt
(2.3-5)
Equation (2.3-5) showed that the EM wave reflection loss varies with the depth of
incident dielectric layer. This is the reason why we increase the thickness o f some layers
that cannot increase the reflection loss. Increasing thickness, especially the top layer,
always makes the absorption peak move to a lower frequency range, and it always shows
poor performance at certain frequency regions.
Based on above equations, first, we discuss the most popular absorbent type, the
“Salisbury screen “ absorber as shown in Fig. 2.3-3. This classic absorbent mechanism
actually is a kind of resonance.
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27
region
1 2
3
resistive sheet
air
4
metal
/
/
/
/
/
/
✓
/
/
/
/
air
incident
EM wave
d2
ds= 1/4 X
Fig.2.3-3 The “Salisbury screen “ absorber.
The reflection mechanism begins from the surface o f region 4. Because region
4
is
metal, we can assume the conductivity o f metal is infinite o = oo, therefore the impedance
A
o f region 4 is zero Q. On the surface o f metal
The impedance o f region 3 (air) is 377
f.(<t.)=
=
z .w .j+ s ,
^
A
3
(d
3
)=
77 4
= 0 [Q ]
[Q ]. The reflection ratio
0 -3 7 7
= -i
0 + 3 77
Because region 3 is air and is lossless, its y 3 = jP 3 = jP 0 =j 2nJX 3 , therefore
r
3
(°)= r
3
( d 3 ) exp 2y 3 (0- d 3 ) = -1 • exp j( 47 c/X3 ) (-X3/4)
= -1* exp -j7t = 1
The total-field impedance at the starting point o f region 3 becomes
Z 3(0 ) = 7
i + r 3(0) _ -
1+ 1
i-n(O)
1 -1
=
00
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28
By the continuity relation across the interface:
Z 2(di ) = Z
j ( ° ) = 00
It makes the reflection coefficient at z = d 2
f
=<<», )-
=
i
Z i ( d 2) + T]2
Since f ' 2 (0) = p , ( d , ) exp 2y, (0- d , ), and
z m - i ' - l L M = Z , ( 0 ) , such that Z ,(0)
l _ r 2(0)
''
/X
A
l + e x p - 2 y 2^
2
A
' /vx_ ^ i ( 0 ) - 7 .
a
7 , ta n h (y -,^ ,)- 7 .
^ i ( 0 ) ——---------— , we can obtain r i ( 0 ) = ^ --------- — -----—
2 i( 0 )+ 7 ,
7 2 tanh(y 2 d 2) + 7 ,
A
From equation (2.3-6) we can find that if
7
( 2 .3 - 6 )
A
, ->
7
, , and the thickness o f resistant sheet is
small, we will obtain the minimum reflection. The return loss is defined as
A
Return loss (dB) = 10 log p
2
(2.3-7)
Basically, the “Salisbury screen” can be understood in terms o f a standing wave
pattern which is set up in the space in front o f the metal plate (perfect conductor) due to
the interaction o f the incident and reflected traveling waves. In electromagnetic point of
view, the maximum o f the electric field standing wave occurs at a plane one quarter o f the
wavelength in front o f the metal, it happens where the lossy dielectric material is located.
The maximum o f the magnetic field standing wave occurs at the metal boundary, it may
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29
be expected that a magnetic analogue o f the “Salisbury screen” could be constructed by
locating a thin lossy magnetic element on the metal.
Although the “Salisbury screen“ effect offers mono-frequency absorption, multilayer
absorbers have been developed based on this effect.
Broadband absorbers consist of
multiple resonant layers. A two-layer absorber with two loss peaks can be arranged either
to overlap, giving one wider absorption band, or to cover two totally separated narrow
frequency bands. Further improvements can be obtained with three or more layers. Fig
.2.3-4 shows the performance o f multilayer resistive sheet called “Jaumann Absorber”
[17].
“Jaumann absorber” consists o f a collection o f resistive sheets stacked one above
the other. Optimum performance is obtained when the spacing between sheets is fixed at
1/4 wavelength and the sheet resistivity varies from a high value at the outer sheet to a
low value at the inner sheet. It also means that the inner sheet has better conductivity
than the outer sheet. The absorption performance in Fig.2.3-4 results from four sheets
multilayer absorbers which have much broader frequency region.
However, large
thickness (about 3 cm) limits its application, especially in aerodynamic vehicles
applications. Too thicker absorbers will result in serious physical problems in high speed
flying or heat transfer gradient problems for army vehicles.
Although " Jaumann absorbers " are not very good EM wave absorbers, especially in
military application, their broader frequency absorbing mechanisms let engineers to make
good sense in design of other broadband absorbers. This issue will be covered latter.
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30
1 SHEET
2 SHEETS
3 SHEETS
4 SHEETS
_m -1 0
-2 0
_i
* -3 0 -
-4 0
FREQUENCY (GHz)
Fig. 2.3-4. Performance o f multiple resistive sheets.[17]
In some practical applications, very broad frequency region absorption are not
needed, but their thickness or physical properties are essential.
Generally, engineers
would like to design a single layer (because too many layers will cause some kind
difficulties o f processing and quality controlling), which can cover a medial frequency
region likes X band (
8
GHz to 12 G H z) or C band ( 4 GHz to
8
G H z).
2.4 EM waves in lossy media
For
l
dissipation lossy region ( a * 0), the reflection and impedance may be a
A
A
complex variable :T = Tr + j T, and rj = rjr + j
tj,
= [ ijr 2 + rji
2 ] l/2
e J0 = r \ e j 6.
The net time-average Poynting power density produced by the combined reflected and
incident fields at any point is:
Re[£ X H ' \
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31
A +
= - Re { E m e"* e " //k ( 1 + f ) a* X a y [ ^
e ' “ e -'* (1 - T)]*}
7
2
Where £ m • (£m ) * = ( E *
) 2
= 1 , also rj • rj = rj1 .
and e ' y/t • e
R e [ ( l + r ) ( 1 - f )• e' * ] = R e [ ( l + r r + j r , ) ( i - r r + j r t ) e j6 ]
= R e[( i + r r + j r , - r r - r r 2- j r r r , +j r, + j r r r , - r ,
2
)(cose+jsine)]
= Re [ ( 1- I r 12) cos 0 + j 2 r , cos e + j sin e ( 1 - 1r 12 ) - 2 r , sin e ]
= (
1 - 1r
| 2 ) cos
0
-
2
T, sin 0
Substitute into Poynting time-average power vector in above equation
a
+
2r]
e~2a: [( 1- I T | 2 ) cos 0 - 2 T, sin 0 ]
Where 0 is defined as:
0 =
(2.4-1)
—ta n _1 ( — )
2
as
Equation (2.4-1) shows the total Poynting time-average power density vector at any point.
If consider only the incident wave on the absorber’s surface p
,
A
let T , ( 0 ) =
0
we can obtain p m + as
Em
p „ +
\ Re { E m e - «
2
a x X a y [------—
A
7
e '* e '* ] }
Where Re [ — ] = Re [ —e jd ] = Re [ — ( cos 0 + j s i n 0 ) ] = — cos 0
* * 7
7
7
Substitute into previous equation become
p
A f a t
,
+ = a z -— — e
27
cos 0
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32
Similarly, consider only the reflected wave, and region 1 is lossless (air), equation (2.4-1)
havs no T, term and can be simplified as:
2rj
e -2“ c o se [
1
- m 2]
a+
Since p av = & „ * + & „ ' . The result is p m ' = - az - E- ^ e ' 2ar cos 0 | T
27
The net time-average power flux passing through a normal open surface area A is
p Iv =
and
P'a v = p av' A
Return loss (dB) = 10 log
= 10 log | T
[2
(2.4-2)
pav
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|2
33
2.5 Metal backed absorbers
For practical applications, absorbers are used to cover a reflector, usually a perfect
conductor. A single layer absorber is shown in Fig. 2.5-1. A homogeneous lossy layer
backed by a metallic plate is called "Dallenbach layer".
absorber metal
A
A
si
air
n 2
a —>oo
^ 0 M’O
E *
motion
0
, o2
0
A
E~x,
xl
J
d,
Fig. 2.5-1 Single layer on metal surface.
Fig. 2.5-1, in region 3 on the surface, Z 3 (0) = 0 = 7
A
(perfect conductor)
A
n z = [m 2/£2 ]
reflection ratio T , (cb) = [ ( Z
f j (0 ) =
3
r
2
3
1/2.
(0 )-
7
3) / ( Z
3
(0 ) +
7
3) ] = -1
(d2 ) exp 2 y , ( 0 -d2 )
(2.5-1)
Where y 2 — c t, + j |3 , —j a)^ju2e 2 = j k, where k , is the wave number.
r
2 (0
) = T , (d 2 ) exp- 2 y 2 d 2 =
-1
exp - 2 y 2 d 2
(2.5-2)
The total-impedance o f top layer surface in air region is
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34
7
4
, rw2 (V )
A
Tj 2
l + r 2(0) _ "
A
^ 2
1 _ r , (0)
Z , (0) = Zi ( 0) =
7 2 121111
l + e x p -2 ^ 2^ 2
1
1 “ exp_
O
*
J
e x p y 2 d-, - e x p - ^ ,^ - ,
=Lj ='
2«2
eXP / 2«2 + eXP“ X 2
^ 2^2
2
(2.5-3)
and reflection ratio o f surface is
r , (0 ) = ( Z
,
(0) -
tj
o
) / (Z
,
(0) +
Combine (2.5-3) become T , (0 ) =
rj 0
V
)
,
where
tj 0
= 111 [Q]
.
— tanh(/ 2d 2) - 1
----------------
(2.5-4)
^ j ^ t a n h ( x 2d 2) + l
Where n r, s r is relative permeability and relative permittivity respectively.
From above analysis, we know the reflection ratio is dependent on the total
impedance o f the surface o f absorbent layer, and the intrinsic impedance o f the absorbent
layer and its thickness. To obtain a high reflection loss, the absorbent layer must match
the free space impedance (377 Q) and metal impedance (0 Q). It is very difficult for a
single layer to match their impedances. Therefore, in order to obtain broader frequency
region o f absorption and high reflection loss materials, the use o f multilayer will be ideal.
Multilayer absorbent mechanisms are the same as above statement, as in Fig.2.3-2,
besides the reflection o f region 5 is -1 for metal back system.
The disadvantage of
multilayer absorbers is its difficulty for quality control, especially for complex object
processing. To set up the processing mechanism o f targets before the mass production is
absolutely necessary.
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35
2.6 Random scattering effects and attenuations
The scattering o f reflection and transmission occurs when an incident wave induces
currents at a material interface. These currents in turn produce a scattered wave that
radiates energy in various directions. For wave energy balance:
jjT o ta l
j j
_
£ incident
Total _
_j_
g sa c tte red
incident
j j
scattered
The total field is the sum o f an incident part and a scattered part. The boundary
conditions are on the total field. These boundary conditions may be represented as
equivalent source currents, which then become the source o f the scattered field.
In the three-dimensional case, the differential scattering cross section is defined by
cr(0,^) = lim
r-» o o
, |£ 5 f
-r~ r
(2-6-1)
£ '
The total scattering cross section crr is defined by the ratio o f time averaged total
scattered power to the time averaged incident Poynting vector, and is related to the
bistatic cross section by the equation
a T = — f T <j(d,<p)smdd6d<f>
4?=o «V=o
(2.6-2)
For practical applications, RAMs are expected not sensitive to incident angles and
have broader frequency absorption.
attenuation in materials.
The effective way is to increase the energy
If the attenuation constant is very large, from equations of
previous section, we will find that the reflection loss is high and it is hardly affected by
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phases. This means that the frequencies affect the absorption in a very small way. This is
very important for designing the broader frequency absorbers.
The attenuation o f absorbers include dissipation loss (or called dielectric tangent
loss), random scattering loss, magnetic tangent loss, and chiral media attenuation. It can
be written as
(2.6-3)
Where a , is the attenuation due to the random scattering effects,
a m is the attenuation due to magnetic tangent losses,
a d is the attenuation due to dissipation.
a ch is the attenuation due to chiral media.
The modified absorbent materials always have more than two kinds o f above losses to
achieve the high attenuation. The magnetic materials have different type o f permeabilities
(always are complex parameters) and their absorbing mechanisms will be discussed in
chapter 3. The microwave absorbing properties of chirals will be discussed in chapter 3
section 5.
A
For a plane wave, the electric field E * = E ^ exp -az • exp -jfiz and its conjugate
complex variable E * ’ = E ^ exp -az • exp jpz.
The time-average Poynting vector power density o f a normally incident plane wave is
#>-= \ R * [ £ X H - ]
A
(2.6-4)
A
E*
* _
Er
*
where H * = —— , H = - —- , H ' is the complex conjugate o f H .
n
n
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37
Substitute above relationships into time-average Poynting power vector
-2 cc
__
= — | E | 2 e 2cc ~ p o exp -2otz
(2.6-5)
Supposing the total attenuation o f absorbent slab is a , and this attenuation is due to the
random scattering of reflectors in the absorber. Fig. 2.6-1 shows the attenuation due to
the scattering cross section o f dielectric materials
Hz
Fig. 2.6-1 The attenuation due to the scattering cross section o f dielectric materials.
If the scattering cross section o f each reflector is o r . and the number density o f flake
per unit volume is p then we assume the attenuation o f total random scattering cross
section is due to the factor p o r . From energy balance of Fig. 2.6-1, we can derive the
equation as:
d p / d z = - pa T p ,
or
dp/p=-
p a r dz.
Integrating both sides from original point z = 0 to any point z to the according average
Poynting power, we obtain
or
In p m - l n ^ 0 = - p < r r z
P a v = P oexP-
PCTr z
( 2 .6- 6)
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38
Comparing equation (2.6-5) with (2.6-6), we can find that the relationship between a s ,
p, and cr r is
a s = p a r /2
(2.6-7)
This result is suitable for all attenuations due to random scattering effects. About chiral
media attenuation and magnetic loss tangent etch, and ctM, which will be explained in
sections 3.5 and 3.6.
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[
39
2.7 Normal incidence scattering o f multilayer structure
The reflection o f a normally incident plane wave from an infinite flat multilayer
structure involves the practical applications of boundary conditions derived from
Maxwell's equations to the general solution for both electric and magnetic fields in each
layer. The basic geometry is a finite number of dielectric layers stacked against a
metallic plate, as shown in Fig. 2.7-1. Each layer must have the same EM properties.
an
N+ 1
N
• •
m
n
• •
►
wave motion
metallic plate
r*—
X,
I
Fig. 2.7-1 A plane wave normally incidence on a multilayer absorber
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40
To explain the scattering mechanism between two dielectric layers, we assume that
an impedance sheet o f zero thickness may be sandwiched between the two dielectric
layers as shown in Fig. 2.7-2. The sheet can be characterized by a resistance R ohms per
square, or by a conductance, G mhos per square, where G = 1/R = R "1. It provides a
complex impedance, resistance R may be replaced by impedance Z or conductance G
replaced by admittance Y. Because the thickness o f layer we assume is assumed to be
very thin , approaching zero for infinite layers, the total field surface impedance Z is
equal to intrinsic impedance q , and so do G and Y.
G
m-layer
n-th layer
Fig. 2.7-2 The propagation mechanism o f resistive sheet
sandwiched between two dielectric layers.
In Fig. 2.7-2, the approach used to analyze the scattering is to postulate the form o f
the magnetic and electric fields in the dielectric layers on either side o f the resistive sheet
and to specify the boundary conditions that the fields must satisfy. The electric and
magnetic fields o f the plane wave in a given layer are
E = Enl+ e-jkx + E m-eikx
(2.7-1)
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41
H = Y (Em+e'jlcx - Em* e3*)
(2.7-2)
Where k is the wave number, k = corpus . Em+ and Em' represent the amplitudes of
forward and backward propagating waves, Enun+ is the amplitude of forward propagating
wave o f m-th layer, Emm' is the amplitude o f backward propagating wave o f n-th layer,
and so far forth. Following the definitions o f Y, G, R the boundary conditions to be
satisfied at the interface are
G E+ = G E’ = J
(2.7-3)
H* - FT = J
(2.7-4)
Where J is the current flowing in the sheet. If x„ is the location o f resistive sheet
between n and m layers, as shown in Fig.2.6-1. We can obtain the following equations
from (2.7-1) to (2.7-4)
+Emm Qjk^- = E mm+e ' ;*”x'
Emm+e
Y„ ( E l e-* *
(2.7-5)
- E l t * ' ) = ( G + Y„ ) E 1 e + ( G
- Y. ) E l e * *
(2.7-6)
From above two equations we can obtain
E l = ^ [ H : (
Y.
+ Y . t G ) e * ' t E „ ( Y , . Y , t O ) e A- '] (2 .6 -7 )
m
e~jkmX"
E l = - T f — [ E l (Y .
•Y ,.0 )t* 't E . ( Y .
+ Y , + G ) e ^ ] (2.6-8)
m
For the metallic plate backing, the total electric field should be eliminated, therefore
A
r i (0) = - 1 , and E~, = - E *, at x = 0. I f there is no metallic backing, the reflection o f
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42
the first layer should be zero , E “, = 0 . The same computation as previous section stated.
The sequence is iterated until the N + 1 layer is reached, which is air in practical
application. The reflection on the surface of multilayer absorber is
f ,v +i (0) =
(2.7-9)
mjV+l
The minimum reflection at the condition
E ^ , = 0. For the simple case of the
Salisbury screen , substituting in equation (2.7-8) we obtain,
e -JH
E»v„ = E ; 2 = —
[ - G e - '“ - ( 2 - G ) e '“ ]
(2.7-10)
^Ltc
For free space Y , = Y , = 1 , the resistance o f air is 377 Q/sq, and k 2 = k 0 = — . If
A
we want E “ , = 0 , only under the condition that the bracket is 0. Such that the equal
amplitude requirement forces G = 1. Thus the case become
-jkd
And
_
e 1 cos
=0
which requires
or
A
or
cos
A71d
..
- 0.
= ( — + n ) n, where n = 0, 1,2, 3,.
A
d =*+!!±
4
2
(2 .7 -H)
Therefore a Salisbury screen with a 377 Q /sq. resistance sheet set at an odd multiple
of electric quarter-wavelength in front o f a metallic plate will enable us to obtain zero
reflection on the surface o f the absorber. In practical application, high dielectric constant
filler may be used as spacer, but with a little reduction in bandwidth, because its k is
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43
larger than k 0 from equation (2.7-10) we can find if the source frequency change will
cause a large change in E
than that o f e r = I spacer.
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44
Chapter 3
SCATTERING AND ABSORPTION CHARACTERISTICS
OF PARTICULATE FILLERS
3.1 Introduction
In this chapter, the scattering and absorbing characteristics o f absorbing components in
this thesis will be discussed. These components include metal disc, conducting fibers,
carbon black, conducting chirals, magnetic ferrites and carbonyl iron. These absorbing
components have different absorbing properties such as dielectric loss tangent, magnetic
loss tangent [10][12], random scattering effects [18], and chirality [19-25].
These
absorbing properties play an important role in the absorbing behavior o f absorbers.
3.2 Metal flakes
Although metals are perfect conductors and totally reflect the EM waves, metal flakes
can be used as an absorbing component in a microwave absorber. In 1940’s, Halpem at
M.I.T. Radiation Laboratory produced a paint material known as “HARP” (Halpem-antiradar-paint)[3], which is rubber based composite material. With thickness o f only 0.025
inch (0.635 mm), the paint offered -15 dB to -20 dB absorption at X band with resonance.
Its thickness is a tribute to the successful development of an artificial dielectric (such as
barium titanate) with a dielectric constant o f about 150 at center frequency of X band, 10
GHz. The high dielectric constant was achieved through the use o f a high concentration
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45
and high degree o f alignment o f disc shaped aluminum flakes. Furthermore, carbon black
provided a proper loss tangent in this thin absorbent layer.
Metal flakes offer random scattering effects, which makes the waves to cancel each
other with different phases and directions due to random scattering.
Before discussing about metal flakes, the scattering o f metal spheres will be discussed
first. The spherical polar coordinates (r , 0 , <j>) shown in Fig.3.2-1, which are related to
the rectangular Cartesian coordinates (x , y , z) by the transformation
x = r sin 0 cos
y = r sin 0 sin <{>
z = r cos 0
z
wave
motion
x
Fig. 3.2-1 The spherical geometry.
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46
Where 0 < r< oo, 0 < 0 < n, 0 < <p < 2n. The coordinate surfaces, r = constant, are
concentric spheres intersected by meridian planes, <(>= constant, and a family o f cones,
A
A
A
0 = constant. The z-axis is the polar axis. The unit vectors r , 0 , and <p are shown in the
direction o f increasing r, 0 and <j»to constitute a right hand base system.
For a plane wave incident in the direction o f the negative z-axis, such that
i
A
E ' = x exp -ikz,
A
J
H = - y Y exp -ikz
where Y = —
z
Maxwell's equations for time harmonic waves in a source-free region, which show that a
time change E is the source for H, and that a time-changing H is the source for E, we can
rewrite the wave equations as follows:
V 2E + k 2E = 0
For spherical coordinate system, the associated Legendre polynomials are the
functions to generate the solution. By asymptotic expansion o f separation o f variables,
the solution o f wave equation for total field is
E' + E : =-
^
0 ) ‘
2 ( - / ) " ( 2 « + l ) [ ^ ( f a - ) - 6 .C ( * r ) ] ^ '( c o s S )
^
e ; + e ; = ^ £ ( - o - ^ - [ { y . ( f r ) - a . c ' m ) p '^
el +
kr "
n(n + 1)
sin#
' « ¥ , < . k r ) - K ? ? { k r ) } P'A ™ 9)-]
oQ
K
+e;=-
kr
n(n + 1)
dO
+
sind
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47
Where P J, (cosG) is the associated Legendre function o f order n and degree 1. The general
function is defined as
( i - x 2r /2 c/n+n,(x2- i r
2 nn\
dx'
hence , the first three orders o f P J, (cosG) have the values of
Po'(cos0) = 0
P,1(cos 0) = sin 9
P:'(cos0) = -^sin 20
The coefficients a „n 7, b n„ are
•t =
./„(*»)
/*\
5 and
h ? \k a )
bn =
where h(nl)(x) = j„(x) + iyn( x ) , in which
kaJ ^ ka^ ~ nJn^ka)
k a h " \(ka )- nh ^(ka)
j n(x) and
y„{x) are the first and second
kinds spherical Bessel functions respectively.
In the backscattering direction, E f becomes zero and the radar cross section (RCS) is
a =
xK
(3 .2 - 1 )
This is a famous expression, its diagram showed an important phenomenon as in Fig.3.22
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48
CM
CO
t=
D
.01
RAYLEIGH
REGION
.001
4
RESONANCE
I
REGION
“ |
O PTIC S
REGION
100
Fig. 3.2-2 The RCS o f conducting sphere over the three scattering regimes.[26]
Fig. 3.2-2 shows that in order to obtain the precise RCS o f the conducting sphere, the
circumference should be larger than 10 times wavelength. If the circumference or size o f
conducting sphere is not large enough, the "creeping wave return " will happen, as shown
in Fig. 3.2-3.
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specular
return
creepmg wave
return
Fig. 3.2-3 The "creeping wave" return when the electric circumference of
metal sphere ( k a ) is in Resonance and Rayleigh region, refer
to Fig. 3.1-2 [27].
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50
This is the reason that missile guide radars always use Ku band or higher frequency. In
EM absorber measurement, small samples have the same problem. The solution o f this
issue is to use the lens hom antenna to focus the wave so as to reduce the diffraction or
creep return.
In practical applications, EM wave absorbers consist o f conducting particles with
much smaller sizes than EM wavelength. Generally we select the size of particles in such
a way that it can pass through 64 mesh to 200 mesh screen filters ranging from 0.05 mm
to 0. 3 mm. Because the 0.3 mm diameter spheres (or discs) are much smaller than
wavelength o f microwave, therefore we used the low frequency approximations. In this
kind small circumference (in wavelengths) the curve o f scattering cross section vs.
circumference (in wavelengths) is suitable in “Rayleigh region “. Let r = a, the radius o f
spheres, following “ Electromagnetic and acoustic scattering by simple shapes “, chapter
10. The total random scattering cross sections may be obtained [18]:
1 0 / ;
\4ri
^
7 ,
= — (&*)4[1 + — ( t o ) '
m3
25
° Y
2137
4 56689.,
— O ) - 77777 0 ) 1
94500
56700
„
(3.2-2)
We will compare the total random scattering cross section with that for a disc in Fig. 3.22. Referring to the book “Electromagnetic and acoustic scattering by simple shapes”
chapter 10. The electric vector o f an incident plane wave has unit amplitude and makes
an angle <|>' with the plane o f incidence (z , x). The direction o f plane wave propagation
makes an angle C, with the positive z-axis, as shown in Fig. 3.2-4 [39].
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51
x
E
H
Fig.3.2-4 Geometry of disc .
“Electromagnetic and Acoustic Scattering by Simple Shapes”, chapter 14, equation (14270), about the disc shape which has a computed formula for “The normalized total
scattering cross section” that is :
a T/2nn2 = —
27;r‘ |cos£|
+ (-^sin2<J>' - 1) sin2^ + ^ c 2 [(22-5sin2 £ )
4
25
x c o s2 C, co s2 <j)' + —(88-54 sin 2 £ - 5 sin 4 C )sin 2 <f>' ]}
4
(3.2-3)
Where c is the product o f wave number and semi-focal distance, for disc shape is ka. In
which k is wave number, a is radius o f flake. In the random scattering phenomena, there
may be different C, , and <|>. We took C=0, 10, 20, 30, 50, 60, 70, 80, 90 each and
computed the average a r values.
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f
52
Table 3.2-1 The normalized random scattering cross section vs. different C, and <f>' .
or r /2na2
G
♦'
0
90
0.4803 c 4 + 0 c 6
10
80
0.4905 c 4 + 0.4638 c ‘
20
70
0.5167 c 4 + 0.4132 c 6
30
60
0.5456 c 4 + 0.4329 c 6
40
50
0.5576 c 4 + 0.5740 c 6
50
40
0.5514 c 4 + 0.8366 c 6
60
30
0.4650 c 4 + 0.1217 c 6
70
20
0.3444 c 4 + 0.1676 c 6
80
10
0.1836 c 4 + 0.0810 c 6
Above a T/2na2 values we took the average. Thus it became
<jr /2na2 (av) = 0 .4 5 9 4 c4 + 0 . 3 4 3 4 c 6
(3.2-4)
For different frequencies (or different wave numbers), different values o f can be
obtained.
Substituting the above parameter into a normalized scattering cross section
equation, we can obtain variation for a T!2na2 (ov) vs. c and then compare this with an
aluminum sphere (same radius), and c = ka. For the purpose of comparing the scattering
cross sections o f sphere and disc, the ratio of equation (3.2-2) becomes:
a r /27ia2 = 0.6667 c 4 + 0 . 1 6 c 6 - 0 . 0 1 5 c 8 -0.6665 c 10
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(3.2-5)
53
The variation of a r /2na2
vs. circumference c ( = ka ) for spheres and discs are shown
in Fig.3.2-5
-7
10
• o
-10
-12
Fig. 3.2-5 The random scattering cross section o f conducting disc and
comparison with same electric circumference o f conducting
sphere. Where o is disc’s trace, # is spherical trace.
From the volume fraction vs. scattering cross section if we
use the same volume fraction o f conducting flakes to replace
spheres we can obtain 27 times absorption performance in RAM.
From fig.3.2-5, we can find that the normalized total scattering cross section of
spheres is about 1.68 times higher than that o f disc. The occupied volume o f metal
sphere should be 45 times (for 0.5pm thickness disc) o f that o f the disc. For the same
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54
volume, we can pack a number of disc which is 45 times o f the number o f sphere,
although the spherical scattering cross section is 1.67 times o f that o f disc. We obtain 27
times the absorption performance when we use the disc. This is the main reason why we
use metal disc as the random scattering material in microwave absorbers. Furthermore,
Fig.3.2-5 shows that the scattering cross section in high frequency is larger than that at
low frequency.
Metal backed single layer absorbers consist of PU elastomer blending with
microballoons as matrix and same amount o f copper spheres and aluminum flakes as
absorbing components. The details of the composition are as follows:
Conducting spheres: Copper spheres, 325 mesh, about 40 microns diameter, density 8.96
g per cubic cm, each sphere volume 3.35 x 10~8 c m 3 .
Aluminum flakes: Aluminum disc, 0.1 mm diameter, 0.5 micron thickness, density is 2.7
g per cubic cm, volume o f each disc ( aluminum part ) is 3.9 X I 0 “9 c m 3. All the
comparing samples have the thickness 1.5 mm.
Fig. 3.2-6 (a), (b), (c) and (d) present the measured return loss of samples with
different concentrations. First comparison, same volume fractions o f copper spheres and
aluminum flakes are 5.6 %, 2.8 %, 1.4 % and 0.7 %. The average of 4 samples is
spresented.
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55
OdB
Return loss
-5dB
-lOdB
-15dB
8
10
12
16
18
Frequency (GHz)
Fig.3.2-6 (a) The measured return loss o f same volume fraction for copper spheres
and aluminum flakes absorbers is signally different even at 0.7
volume fraction. Solid line showed the return loss o f aluminum
flakes absorber, dash line showed that of copper spheres absorber.
The thicknesses of sample are same 1.5 mm. The density of
copper is 4 times that o f aluminum.
OdB
Return loss
-5dB
-lOdB
-15dB
8
10
12
16
18
Frequency (GHz)
Fig.3.2-6 (b)The measured return loss increases with increasing the volume
concentration. This is the return loss o f 1.4 % volume fraction
for both copper spheres and aluminum discs, 1.5 mm thickness.
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56
OdB
Return loss
-5dB
-lOdB
-15dB
8
10
12
16
18
Frequency (GHz)
Fig.3.2-6 (c) The measured return loss o f volume fraction 2.8 % for both copper spheres
and aluminum flakes absorbers showed the bigger difference in higher
volume fraction. Solid line showed the return loss o f aluminum flakes
absorber, dash line showed that o f copper spheres absorber.
OdB
Return loss
-5dB
-lOdB
-15dB
8
10
12
16
18
Frequency (GHz)
Fig.3.2-6 (d) The measured return loss o f copper spheres and aluminum flakes
absorbers at volume fraction 5.6 % showed the different tendency.
Because the geometry o f conducting discs have higher effective electric
“Percolation" , too high volume density makes “ connectivity o f
conducting particles. The result is increasing reflection in some
frequency regions.
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In Fig. 3.2-6 (d), the return loss o f aluminum flakes shows increasing reflection at
high frequency because the impedance o f the front-face decreases with the increase of
volume fraction of aluminum flakes. From equation (2.5-2),
—1 tanh(y
1
(2.5-2)
r , (0 ) =
— tanh(y,i/2)+ 1
the reflection from front-face can be written as
(3.2-6)
72r+l
From Eqn (2.6-3), higher volume concentration o f conducting random scattering
components will improve the attenuation, but also decrease the impedance o f absorbing
layer. From eq.(3.2-6), if this layer is face to face with air (top layer), the front-face
reflection will be increased.
The high concentration o f conducting components makes the “Percolation^
phenomenon. Except the random scattering effects, the effective “connectivity” o f
conducting particles increased with increasing volume fraction that cause decreasing the
A
impedance. In equation (3.2-6), when J]2r is less than 1, the relative impedance o f free
space
7
0, the reflection o f front face will be increased. Therefore, the absorbers have a
higher reflection at high frequency and have resonance at a lower but narrower frequency
region. This phenomenon is not desired for EM wave absorber designers. Therefore the
volume concentration o f conducting absorbing components including random scattering
reflectors and carbon blacks need an optimization. For example, in previous case the
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58
optimized volume fraction o f aluminum flakes is less than 5.6 % but larger than 2.8 %.
After conducting a series o f trial and error fabrication and measurements, it can be shown
that the optimum volume fraction will be about 4.5 %. The return loss curve just has the
tendency to improve the reflection at high frequency region at 4.5 % volume fraction.
Fig. 3.2-7 shows the measured return loss and the comparison with copper spheres
composite with the same volume fraction o f 4.5 %.
Return loss
OdE
-5dB
-lOdB
-15dB
8
10
12
16
18
Frequency (GHz)
Fig. 3.2-7 The optimized volume fraction o f aluminum flakes composite
in which the 4.5% volume concentration of aluminum flakes
makes good attenuation but its effective connectivity o f conducting
particles properly match the impedance with air that makes
no worse return loss in the whole frequency region .
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59
3.3 Conducting fibers
The idea o f using o f conducting fibers as component for EM wave absorbers was old.
In 1950’s, Emerson o f the US Naval Research Laboratory demonstrated that an effective
broad-band absorber could be made by dipping or spraying carbon black onto a bat of
loosely spun animal hair which was used in upholstering and packing in that time. The
material chosen for production was the so-called “Hair” absorber [I].
Commonly, conducting fibers used as component o f EM wave absorber fibero-chaff
and carbon fiber (or graphite fiber). The fibero-chaff is fabricated by vacuum deposition
o f metal onto the surface o f glass fibers [28-29], The thickness o f metallic coating is
about 0.3 micrometer.
The diameter o f hollow glass fiber is about 10 micrometers.
Normally, chaff was used to support electronic warfare. For example, when aircraft
encountered and locked on an enemy radar, especially fire-control radar, they release the
proper length (0.48 wavelength) o f fibro-chafif (automatic measure and cutting system) to
give a false target for enemy, because fibro-chaff can reflect or random scatter
incident EM wave.
the
A proper quantity and length o f fibro-chaff will give a good
scattering cross section, or it means that fibro-chaff can be a component o f a absorber.
The fibro-chaff has a very good advantage as an absorbent component o f EM wave
absorber because it is very easy to be dispersed homogeneously in PU matrix due to the
poor attractive force between fibro-chaffs, unlike that o f carbon fibers. But metal coated
glass fibers have the disadvantages as other metal products. They have poor chemical
resistance except those that used some expensive metals such as gold or titanium.
Therefore, today engineers avoid the use o f fibro-chafif as component for EM wave
absorbers.
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60
Carbon fibers (some grades o f carbon fibers are called “graphite fibers44) have
excellent chemical resistance and high temperature durability. Furthermore, carbon fibers
have very stable conductivity compared with fibro-chaff.
Because o f the failure of
vacuum deposited processing, fibro-chaff is unstable as far as its conductivity properties
are concerned.
But carbon fibers have a disadvantage that they are difficult to be
dispersed homogeneously in PU matrix due to the interacting force resulting from their
surface treatment agent. When looking through a microscope, small carbon fiber bundle
can be always found in the absorber. To prevent this, we used high viscosity resins to
blend the chopped carbon fibers properly.
The conductivity of carbon fiber plays an important role in EM wave absorbent. The
higher the conductivity, the larger the scattering cross section is. Generally, the higher
the modulus, the higher the conductivity.
For instance, UHMCF (ultrahigh modulus
carbon fiber) has conductivity over 3,000 mho/cm, HMCF (high modulus carbon fiber)
has conductivity of 1,000 mho/cm, and for common GPCF (graphite carbon fiber), its
conductivity is only about 200 mho/cm. In EM wave absorbent material, we always use
high modulus carbon fibers with conductivity about 2000 mho/cm.
For the mathematical inference o f scattering cross section o f carbon fiber, we referred
the book 44 Electromagnetic and acoustic scattering by simple shapes”, chapter 12, about
perfectly conducting 44wires”. The geometrical shape corresponding to a thin wire is a
finite circular cylinder, especially carbon fibers for absorber’s application, whose cross
section is small compared with its length and the wavelength. Generally, we use chopped
carbon fibers with 5 pm in diameter and 6 mm in length for X band ( wave length about 3
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61
cm). The contribution to the scattered field from the end surfaces o f the cylinder is
assumed to be negligible.
The geometry o f the wire and the orientation o f the incident plane EM wave are
shown in Fig. 3.3-1.
v
'y *
nz)
Fig.3.3-1 The wire geometry.
The incident wave is linearly polarized with the electric field vector in the plane o f the
direction of propagation and the wire axis: this is no limitation since only the component
o f the electric field parallel to the wire contributes to the far field scattering.
The following notation will be used throughout this section:
1
7d
L = - k l = j ,
(3.3-1)
For a plane incident wave o f unit amplitude
Eg = exp { - ikr(sin 0 sin#0 + cos 0 cos 0O)}
the scattered far field is written as
e'kr
E I (r, 0,0O) = — S(0 ,0 O).
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62
The average scattering cross section has been calculated by Chu [29] by assuming a
simple current distribution along the wire and determining its magnitude by equating the
real power calculated at the wire surface to that in the far field.
For practical application, we use chopped carbon fiber with 6 mm in length, L < 0.3.
In this length region, the normalized average scattering cross section has been obtained by
Van Vleck et al [29] by m eans o f the integral equation method. The result is
%
= -----------% --------4 5 * - { lo g ( - ) - l} :
a
(3.3-2)
The diameter o f carbon fiber is 5 pm and length is 6 mm. From eq. (3.3-2), by
substituting above values, we can obtain the variation of normalized scattering cross
section vs. L as shown in Fig.3.3-2. The average normalized scattering cross section of
carbon fibers at center frequency o f X band (10 GHz) is
r^ c 0 .0 0 6 Nfi
\
0.03 .
- f --------------SO006-------7 =1-51x10-=
4
^ 0.0000025}
and the average scattering cross section is
f ^ c 0.006 V
CTflv = (° -° 3 )-
J
I 0.03
----------------2 ^ 0 0 6 --------- 7 = 1 - 3 6 x 1 0 -
[ m- ]
45' r{1° g ( ao55oo2'5) - 1}‘
For random scattering cross section o f the same volume fraction o f conducting spheres,
the volume of sphere is
Vr = ^n a i =V/ =
( 2 .5 x 1 0 ^ ) 2 (0.006) = 1.178xl0-13
[ m 3]
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63
where V r and V f are the volume o f sphere and fiber respectively. The radius o f sphere
“a” can be obtained from above equation: a = 0.0000304 m. W ave circumference c is
_
c - ka
2na
2 70:3.04x1 O'5
— - ------ ——------ = 0.00637, corresponding to the spherical average
A
(J.l/3
normalized scattering cross section [18]
f j r - » ( W 4[ 1 -
( 3
J
- 3 )
The comparison o f average normalized scattering cross section o f conducting sphere is
shown in Fig. 3.3-3.
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/I
Fig. 3.3-2 The normalized average scattering cross section vs. electric length
o f conducting fiber.
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65
10-7
10 -8
o ’™ /27ra2
10
10
-9
-10
1 0 -11
10
-1 2
)•
5
10
ka = 2izaJX
15
20 ( x 10 “3 )
Fig. 3.3-3 The normalized scattering cross section vs. wave circumference
of conducting spheres by equation (3.3-3).
By substituting values into eq. (3.3-3) it should be written as
- = 1.48x10 -8
iT ta '
or
<r„ = 2/rx(3.04xl0~5) 2x l . 4 8 x l 0 ' 8 = 8.594xl0"17
[ m 2]
Comparing the scattering cross section o f a conducting sphere with that o f a carbon fiber,
it can be shown that the absorption performance of perfectly conducting fiber is several
ten thousand times that o f conducting sphere. Although the carbon fiber is actually a kind
o f semi-conductor, practical experimental results still show that it offers about several
thousand times more absorbing performance than that of metal flakes.
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66
Conducting fibers with high random scattering cross section have an important
property that their very long geometries easily results in “Electric connectivity”. This
phenomenon will cause partial or total wave energy reflection. On the other hand, the
proper “connectivity” will improve with a lower frequency EM wave absorption. This
has been confirmed by a series test results.
Therefore when we design the formula
(decide the volume fraction of conducting absorbing components, it is very important to
check the absorber conductivity and balance it with different frequency region
attenuations.
We used 5 microns diameter carbon fibers, and chopped them as 6 mm length to
blend with PU elastomer and ceramic microballoon matrix paste, and mixed the chopped
fibers distribution in matrix homogeneously. The thickness o f each piece is 2 mm. The
volume fractions o f carbon fibers in absorbers are one hundred times that o f copper
spheres in absorbers, i.e. 0.007%, 0.014%, 0.028% and 0.056%. The density o f carbon
fibers are 2.3 g/cm3 and volume v =7tr2d, where r is the radius o f fiber 2.5 pm. Each fiber
volume is v = n ( 2.5 X I O ^ X 0.6 = 1.17 x 10"7cm3, times its density 2.3 g/cm3, we can
find the weight o f each fiber is as 2.48 x l0 ‘7 g. We control these tiny quantity volume
fraction ( or weight ) by dilution method. We blend several grams o f chopped carbon
fibers in the 500 gram matrix paste for example, then mix it homogeneously. Each gram
o f mixing paste will contain many chopped fibers and then it has to be studied and
verified that was the correct number o f chopped fibers in one gram o f mixing paste. This
high concentration paste will be used as the fiber source to mix with non-fiber paste so
that it become a very low volume fraction working paste. In mass production, dilution
method is unnecessary, because the commercial weight scales are sensitive enough to
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67
weight the conducting fibers precisely. Figs.3.3-4 (a), (b), (c), and (d) show the measured
return loss o f these metal backed sample. Each result o f volume fraction tested sample is
the average o f 4 times tests. These diagrams show the experimental results o f comparison
in return loss vs. different volume fractions.
From Figs.3.3-4 (a), (b), (c), and (d), we can find that increasing the volume fraction
will also increase the return loss. But over certain value, partial energy will be reflected
at high frequency region. The peaks o f absorption move to the lower frequency region as
shown in Fig.3.3-4 (d). If we add top layer with lower density of absorbing components,
this phenomenon will occur again. That is to say that a mismatch o f layer impedance
exists. Fig.3.3-5 shows a straight return loss line. Adding top layer (lower density o f
absorbing components) will increase the bandwidth o f the return loss. Therefore this may
be the optimized volume fraction. The following figures show the measured return loss
for different volume fractions o f conducting spheres and other absorbing components.
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68
OdB
Return loss
-5dB
-lOdB
-15dB
8
10
16
12
18
Frequency (GHz)
Fig. 3.3-4 ( a ) The measured return loss o f copper spheres (dash lin e ) with 0.7 %
volume fraction. Where the solid line represented the return loss o f
carbon fibers ( 6 mm len g th ) with 0.007% volume fraction ( l / l 00
that o f copper spheres ) in matrix.
OdB
Return loss
-5dB
-lOdB
-15dB
8
10
12
16
18
Frequency (GHz)
Fig.3.3-4(b) The measured return loss o f copper spheres and carbon fibers.
Where dash line showed the return loss of 1.4% volume fraction
o f copper spheres and solid line showed the return loss o f 0.014%
volume fraction o f carbon fibers ( 6 mm length). In this volume
concentration has no percolation o f electric connectivity happen.
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69
OdB
Return loss
-5dB
-lOdB
-15dB
8
10
12
16
18
Frequency (GHz)
Fig. 3.3-4(c) The measured return loss o f 2.8% volume fraction o f copper spheres
( dash line ) and 0.028 % volume fraction of carbon fibers, 6 mm
length( solid line). In this volume concentration the conducting fibers
we can find that they have some kind of electric connectivity happen.
This phenomenon makes some high frequency regions reflect the wave
energy.
OdB
Return loss
-5dB
-lOdB
-15dB
8
10
12
16
Frequency (GHz)
18
Fig.3.3-4 (d) The measured return loss o f 5.6% volume fraction o f copper spheres
(dash line), and 0.056% volume fraction of carbon fibers (solid line).
In this volume fraction the effective electric connectivity become more
obvious that makes signal reflection in many frequency regions.
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I
70
From Fig.3.3-4 (a), (b) we can find that conducting fibers have a very good EM wave
absorbing performance when comparing volume fraction vs. absorption. But due to its
geometry, conducting fiber can very easily connect with each other to become a reflector.
So its volume concentration should be controlled carefully. Fig.3.3-4(c) shows the high
volume concentration o f carbon fibers makes some kinds o f electric connectivity which
change the impedance. This percolation phenomenon results in high EM wave reflection
at some frequency regions. To optimize the volume fraction o f conducting fibers, it is
necessary to have different types o f layed absorbers (single layer or multilayer). Fig.3.3-5
shows the optimized volume fraction o f carbon fibers
volume concentration.
(6
mm length) with
%
Its return loss curve is almost a straight line over the whole
frequency region.
OdB
Return loss
-5dB
-lOdB
-15dB
8
0 .0 2 2
10
12
Frequency (GHz)
16
18
Fig. 3.3-5 The measured return loss o f the optimized volume fraction o f carbon
fiber 0.022%. This optimized ratio makes return loss curve near the
straight line.
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71
3.4 Carbon black
Carbon black was the first raw material used as microwave absorbers. During World
War H, German engineers conducted a project known by a code o f “Schomsteinfeger”
which in German meant “Chimney sweep”. The material used in the absorber was carbon
black blended with rubber in proper proportions to make. This EM wave absorber was
used as a radar camouflage layer in submarine snorkels and periscopes [ 1 ].
The most important feature o f carbon black acting as an EM wave absorber is its
dissipation loss. The microstructure o f carbon black is the same as that o f graphite [10],
but the carbon layers are less ordered than those o f graphite, especially at the core o f the
particle. As a result, carbon black is classified as an intrinsic semi-conductor. The degree
to which carbon black renders a resistive polymer electrically conductive is influenced by
its physical and chemical properties.
Electrons flow through a carbon black polymer
composite is achieved when the carbon black forms a conductive network within the
polymer. Basically, electron flow occurs when the carbon black aggregates are in contact
or separated by very small distances. In separated case, electrons tunnel through the
resistive polymer from aggregate to aggregate. The more aggregates that are in contact or
close enough for tunneling to occur, the greater the electrical conductivity o f composite.
In Maxwell’s equations, conductive materials can be classified with reference to the
A
magnitude o f the conduction current density term <r E relative to the displacement
A
current density term jcoeE has the following relation:
VXH =
crE + jcoeE = j o ( e - j —)
co
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72
The complex permittivity can be defined as
e
The angle
6
. <J
= s -j —
co
d is called the dissipation angle, which vanishes for a lossless region. Its
tangent defined by: tan 15 d | =
cos
is called the loss tangent or dissipation factor. The
importance o f the loss tangent is recognized from its appearance in the attenuation
A
constant a , phase constant P and intrinsic impedance
semiconductive material.
7
.
Carbon is classified as a
The conductivity o f carbon black is almost the same as
graphite. Generally, the conductivity o f commercial products of carbon black is about
100 to 1000 mhos/cm depending on the purity and the particle size. But in practical
applications, we need binders such as polyurethane elastomer or rubbers to blend with
carbon black to obtain a continuous matrix. The conductivity of the binder polymer is
very low. Therefore the actual conductivity o f the matrix is determined by the volume
fraction o f carbon black. Carbon black is the highest oil (generally, use Dibutyl Phthalate
as test oil.) absorption filler o f non-porous materials. 100 g carbon black absorbs over 300
g Dibutyl Phthalate oil. For Ti02, oil absorption is only just 25 g oil per 100 g Ti02. Oil
absorption is an index that indicates how difficult to obtain the perfect dispersion of
fillers in resins. Carbon black has the maximum oil absorption. It is possible to achieve a
homogeneous mixture of carbon black and resin. It is the high volume ratio o f carbon
black that makes the mixture a rigid matrix. This will reduce the fatigue resistance of
absorbers. Therefore, manufactures o f EM wave absorbers always use high conductivity
carbon black to reduce its volume fraction while maintaining the same conductivity.
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73
The most popular application o f carbon black in an EM wave absorber is the
manufacturing o f pyramidal polyurethane (PU) foams. Polyurethane resin is m ixed with
proper quantity o f carbon black and blowing agent in a pyramidal mold, then heat or react
with some curing agents to fill the pyramidal mold. This PU foam absorbers was used to
be the wall o f anechoic chamber. Fig. 3.4-1 shows the shape o f pyramidal PU foam
[31-33].
Depth
Fig.3.4-1 The shape of pyramidal PU foams, (a) Right side is rear wall
absorber, (a) Left side is a squinted version designed for
side wall applications, (b) Impedance profiles, as functions
o f depth, where q 0 = 377 Cl.
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74
The absorbing performance o f pyramidal PU foam loaded with carbon black has very
broad frequency region and very high absorption if the depth was enough.
Fig 3.4-2
shows its absorption spectrum.
OdB
Return
-lOdB
loss
-20dB
-30dB
-40dB
-50dB
-60dB
2
4
6
8
10
12
Frequency (G H z )
14
16
18
20
Fig.3.4-2 The return loss spectrum o f a pyramidal absorber in carbon black
loading PU foam with pyramid depth o f 65 mm.
Depth
Fig.3.4-3 Impedance profiles o f a stepped, loading
distribution o f carbon black absorber.
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75
Based on the impedance matching rule, we apply the first layer on the metal surface
which has higher carbon black concentration then apply the second layer whose
concentration is less than the first and so on. At the top layer we let the impedance
approximate with that o f air 377 Q. This approach is called matching layer approach and
the impedance profile is shown in Fig.3.4-3.
region 1 (air)
2
3
4 (metal)
►
incident plane wave
Fig. 3.4-4 A double layer CB loading absorber
A double layers stepped loading absorber, a practical case, is shown in Fig. 3.4-4,
which encounters a normally incident plane wave.
sample is as follows.
The preparation o f the absorber
The first layer with conductivity o f 12 mho/m is prepared by
dispersing certain amount o f carbon black into a PU elastomer, which already has blended
with microballoons. The frequency o f incident EM wave is 10 GHz.
The dielectric
constant o f (real part o f permittivity) matrix is 3.4 for each layer. The conductivity o f the
second layer was controlled to be
1 .2
mho/m by reducing concentration o f carbon black to
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76
3% volume fraction. The thickness o f each layer is physically a quarter-wave length.
The absorbent mechanism is as follows:
The loss tangent — = ---- —— —----------- — = 6.35
cos
2^x10 x3.4x8.84j:10
J33 = " ^ y 3- [J l + ( V2
V
^ — )2
+ 1]
1/2
for region 3 (first layer)
3
= 744.26 rad/m
^3*3
the wave length in region 3
2it
X, = — = 0.008445 m = 8.445 mm.
&
The thickness o f the first layer is d , = — =2.11 mm
3
4
the intrinsic impedance o f the first layer is rj3 =
i ^3
[ i+ ( - ) 2 ] l/4
cos
—
a )
expj• -1 .tan ( —
2
cos
Substituting the values o f region 3, we obtain rj3 = 80.64 expj 40.50
Assuming the conductivity o f metal plate infinite, therefore the impedance o f region 4 is
A
zero, Z 3 (d 3 ) = 0. The reflection at the interface between metal plate and the first layer is
Zi(jd3) +r j 3
and
f 3 ( 0 ) = f 3 ( d , ) e x p 2 ( a , + j / ? j X 0 - r f 3)
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77
= -1 exp -2(636.23X0.00211) exp -J2(— X— )
A3 4
= 0.068
Z 3 ( 0) =
A l + fsfO)
- - An ; =92.7 expj 40.50
l - r 3(0)
73
at the interface between the first and second layer Z 3 (0) = Z 2( d , )
A
and
A
T 2( d 2) =
= 0.244 exp j l 6 8 0
Z 2( d 2) + rj2
r 2(0)= r i ( 0 ) = r 2 (tf2) exp -2 ( or, + / / ? 2 ) ^ 2
For the second layer:
^
loss tangent
12
— = ---------------------------------- -- 0.635
(oe
2 ^ 1 0 X'3.4Ar8.84AT0~12
Similarly, for region 2 we can obtain a 2 = 50.4 Np/m and /?, = 403.6 rad/m.
7
, = 187.8 expj 16.2° . / l 2 =
=0.0155 m = 15.5 mm. d , = 3.875 mm.
P
2
Substitute above values into surface reflection
r 2 (0) = r , (0) = 0 .2 4 4 exp j 1680 [ e x p -2(50.4X0.0155/4)] [exp -j 2 ( 2 n ! X 2){X2/ 4 )]
= -0.167 expj 168°
For a dissipation loss region ( <y * 0 ), the reflection and impedance may be a complex
variable:f = Tr + j T, and
7
= rjr + j
7
, = [7
,2
+
7
,
2 ] l/2
e jB = r \ e j e . The net
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78
time-average Poynting power density produced by the combined reflected and incident
fields at any point should be:
„ - i R e [ £ X H ']
0
A +
= ^ Re { E m e -~ e -y/t (
1
+ f ) a* X a y [
e -az e~J/t (1 - O f }
7
Where E m • ( E n )* —( E * ) 2
Re[( 1 + f" )(1 - f )*
e J0
a n d e~J/k • e y/t =
1
, also rj • rj =
.
tj2
] = Re [ ( 1 + r r + j T , ) ( l - r r + j r , ) e ^ ]
= Re [ ( i + r r + j r , . r r - r r 2 - j r r r, + j r , + j r r r, - r , 2 ) ( cos
0
+ j sin 0 ) ]
= Re [ ( 1 - 1r | 2) cos 9 + j 2 T, cos 0 + j sin 0 ( 1 - | T | 2) - 2 T, sin 0 ]
= ( 1 - 1r | 2 ) cos 9 - 2 T, sin 0
Substitute into Poynting time-average power vector become:
a
P o v = ^-
^
+
~ ~ ~ e 2a= [( 1- I r | 2) cos 0 - 2 T, sin 0 ]
27
Where 0 is:
0
(3.4-1)
= —tan -1 ( — )
2
COE
Equation (3.4-1) shows the total Poynting time-average power density vector at any point.
If we just consider the incident wave on the absorber surface p
, let
A
T , (0 ) =
0
we can obtain p m + as
P m-+ = \ Re { E n e -ar e " y*
Z
f^m}
a x X a y [ -----— e -0= e J/k ] }
A
7
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A
p
Substitute into previous equation
( E+)
* = a- -— — e~2<= co s 0
2 /;
Similarly, consider only the reflected wave, since region 1 is lossless (air), equation (3.41) has no T, term. It can be simplified as
P av=
27
e ~2<g c o s 9 [
1
- i n 2j
A
Since p m = p m + + p m ' . The result is p
=-az
2rj
e ' 2<c cos 9 \ T \ 2
The net time-average power flux passing through a normal open surface area A is
p Iv =
Pov+ A
and
Pm = p m ~ A
\ P ~ \
= 10 log | T |2
Return loss (dB) = 10 log
l^av j
The return loss can be calculated for the previous example as
Return loss (dB) = 10 log (0.1672 ) = - 15.5 dB .
Fig.3.4-5 shows the measured result of this double layer carbon black loading absorber.
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80
OdB
Return loss
-5dB
-lOdB
-15dB
-20dB
-25dB
8
9
10
11
Frequency (GHz)
12
Fig.3.4-5 The absorbent performance of a double layer metal backed
absorber which is loading carbon black.
From Fig 3.4-5, if carbon black is the only absorbent component, the performance o f
EM wave absorption is not sufficient, although it is easy to handle and process.
improve its performance, adding three dielectric materials such as
alum inum
To
flake,
carbon fiber and carbon black modifies the absorber. The matrix is the same as previous
case, but in first layer we added 12 % volume fraction of
aluminum
flake and 0.036 %
carbon fiber. In second layer (top layer) we added 2% aluminum flake and 0.0018 %
carbon fiber. The conductivity o f the absorber is almost the same as that o f previous
case, because the aluminum flakes are enclosed by insulation polymer and the carbon
A
fibers are in very small concentration. Therefore p, r) , and thickness d , , d 3 are all the
same except a.
The attenuation a is due to random scattering o f EM waves in the absorber. The
random scattering effects include aluminum flakes and carbon fiber.
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81
a = af +a c +a d
Where a / is attenuation due to aluminum flakes random scattering effect,
a c is attenuation due to carbon fibers random scattering effect.
a d is attenuation due to dissipation.
Following section A, B the a f , <xc are half o f the product o f number density and total
scattering section o f each item. Therefore in region 3 (first layer ) they are:
a /3
= ^ p a r , = ^ ( 3 . 5 6 x 1 0 13 ) x 7.5x10 " I3 = 13.35
ac3 =
( 2 x 1 0 8 ) x 6 . 2 x 10_s =6200
Np/m
Np/m
From above results people maybe tempted to ask why aluminum flakes are used when
its attenuation effect is lower than that o f carbon fibers. From practical experience, it has
been found that aluminum flakes play an important role in making the dispersion o f
carbon fibers homogeneous.
This effect is more important than its random scattering
effect in absorbent mechanism.
The total attenuation in region 3 is the summation o f three kinds of attenuation:
a 3 = a f + a c + a rf =6200 + 13.35 + 636.23 = 6850
Np/m
In region 2 ( second layer), similarly we can calculate each attenuation constant
af ,
= ^ p < j,= |
(5.93 X 1 0 12 ) (7.5 X 10 -13 ) = 2.224
a c , = | ( 10 7 ) ( 6 . 2 X 10"5) = 310
Np/m
Np/m
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82
a, = af
2
+ a c
2
+ ard2 =2.224 + 310 + 50.4= 362.64
Np/m
Similarly, the reflection at interface o f metal plate and the first layer is
+(<1,)=
=-i
Z 3 (d 3 ) +
and
7 3
f j ( 0 ) =r 3 (d 3 ) exp 2 ( a 3 + j / ? 3 ) ( 0 - d 3 )
= -1 exp -2(6850X0.00211) exp -j2( — X— )
23 4
= 1.24X10
a
z 3 (0) =
7 3
-2 9
i + r 3( 0 '»
----s
i-rj(0)
a
73
= 80.64 exp j 4 0 .5 0
A
A
at interface between first layer and second layer Z 3 ( 0 ) = Z 2 ( d , )
and
Z 2 (</, ) + 77,
80 64
y’4 0 i +1 81 8 eXP
71
62
T 2 ( 0 )= f 1(0) = f 2 (i/2) exp-2( a , + jj3 2)d2
= 0.452 exp j 1570 exp -2 ( 362.64X 0.0155/4 ) [exp -j 2( 2w/ Z 2)(A 2 /4)]
= -0.0272 expj 157°
The return loss on the surface referred previous statement is
IP '
Return loss (dB) = 10 log
\P.av
= 10 log | T | 2 = -31.3 dB.
Consequently when we analyze the reflection, especially at the interface o f the first layer
and second layer, we can find that the reflection is almost independent o f phase due to
very large attenuation [35], which means that the affect o f frequency on absorption is
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83
very small. This point is very important for the design of wide band absorbers. Fig. 3.4-6
shows the measured reflection properties against frequency.
OdB
Return loss
-lOdB
-20dB
-30dB
8
9
10
11
12
Frequency (GHz)
Fig.3.4-6 The double layer absorber showed the broader frequency absorption
due to using modified dielectric materials . The solid line is HH
polarization , and dotted line is W polarization .
From Fig. 3.4-6, we can find that the HH and W
difference.
polarization have a small
This is an important feature for using anisotropic dielectric materials as
absorbent component. Because in processing it is impossible to guarantee all the carbon
fibers are under uniform distribution. This is why we use multilayer processing even
though theoretically it is unnecessary.
The attenuation o f aluminum flake is mush smaller than that o f carbon fibers. This is
due to the fact that the calculation is focussed on center frequency o f 10 GHz. Actually
aluminum flakes play an important role in high frequency.
Except high frequency
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84
absorption, due to its different geometry and high volume density feasibility, aluminum
flakes are also essential component in formula.
Dielectric components, such as carbon fibers, carbon black are all semi-conductors.
The higher operating temperature, the higher conductivity they have. But for metal, such
as aluminum flakes, the higher operating temperature the lower their conductivity. The
addition o f aluminum flakes will reduce the difference between return loss due to
different operating temperature, although this phenomenon is reversible, i.e., when
temperature decreases, the return loss will be same as shown in Fig. 3.4-7.
OdB
Return
-5 dB
loss
-10 dB
-15 dB
-20 dB
-25 dB
-30 dB
-35 dB
2
3.6
5.2
6 .8
8.4
10
11.6
13.2
14.8
16.4
18
Frequency ( G H z )
Fig. 3.4-7 The dependence o f return loss and operating temperature for dielectric RAM
in which included carbon fibers, carbon black, aluminum flakes. Since
higher temperature make semi-conductive materials such as carbon fibers,
carbon black have higher conductivity. High electric connectivity makes
a little bit reflection in high frequency, but it is reversible.
---------- 25 °C
100 °C
....... 200 °C
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85
If carbon is the only absorbing component, since its conductivity increase with
increasing temperature, in high temperature condition, the high conductivity causes the
high frequency wave partially reflect and the lower frequency wave has more dissipation.
Refer to Fig. 3.4-8, the RAM consists o f PU elastomer and microballoon as matrix with
carbon black and carbon fibers as absorbing components.
OdB
Return
dB
loss
-10 dB
-15 dB
-20 dB
-25 dB
-30 dB
-35 dB
2
3.6
5.2
6 .8
8.4
10
11.6
13.2
14.8
16.4 18
Frequency ( G H z )
2 5 °C ------------- 100°C.... ..
200°C
Fig. 3.4-8 The temperature dependence o f carbon system RAM.
Since carbon materials are semiconductors, their conductivity
increase with increasing temperature, which makes high
frequency wave partially reflect, and lower frequency wave
has more dissipation.
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86
3.5
Conducting chirals
A chiral medium is one whose electric and magnetic fields are cross-coupled. The
characteristic aspect o f such materials is the intrinsic handedness, right or left, present in
their physical structure.
One o f the aspects characterizing chiral media is the
phenomenon o f optical activity. Optical activity is a polarization behavior o f a light when
it illuminating a material. Actually, the property of optically active media is that the
linear polarization plane o f EM wave (light) rotates as it passes through the medium.
Natural chiral structures include a diverse array o f sugars, DNA and so on. In EM wave
applications, man-made chirals include metal helix, spring shape copper wires., etc. A
random suspension o f conductive helical springs in a dielectric host constitutes a typical
electromagnetic chiral medium. When EM wave is incident on this kind o f matrix, equal
quantities o f left-circularity polarization (LCP) and right- circularity polarization (RCP)
interfere with the EM wave and result in an energy attenuation. Fig. 3.4-2. (a) shows EM
wave displayed along z at t=0 and its real-time projection below. The upper part showing
its 3-D circularity Crank counterclockwise simulating time increases in exp jco t. When
an EM wave travels with a complex phasor which has a negative image part, the direction
is right-circulatory polarization, and when it travels with a positive image part the
direction is left-circularity polarization [25]. For example, EM wave traveling vector,
A
A
A
A
a* + j a y has clockwise circular polarization or LCP, and a x - j a y has counterwise
circular polarization or RLP. Fig. 3.5-1 (b) shows the shape o f the LCP and RCP chirals.
In electromagnetic field, we just discuss the conducting chirals.
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87
2r
£jr*.0-Re[£S(zj«r'“‘]
Left-handed
Right-handed
Fig.3 .5-1 (a) The 3-D traveling diagram o f EM wave with complex phasor and its real
time projection, (b) The shape o f LCP and RCP chirals.
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88
Even though for many years scientists know that conductive chirals have EM wave
absorbent qualities, it also occurred to them that man- made metal chirals will also have
many problems for practical applications. First o f all, the size o f the man-made metal
chirals is too large to apply in a resin or ceramic matrix. Secondly, the cost o f mass
production is too high and the process is slow. Lastly the corrosion o f metal is a point o f
concern. Because the density o f copper chirals is 4 times that o f the resin, metal chirals
tend to settle on the lower layer before gelation o f the polymer binder.
Recently, a new fabrication process has been developed to produce micro-coiled
carbon fibers. The size o f the carbon coils is only about several micrometers. Excellent
chemical resistance and high temperature stability are ensured and these micro-coiled
carbon fibers will replace the traditional machine-made metal chirals in the future.
Coiled carbon fibers (or whiskers) can be obtained by catalytic pyrolysis of acetylene
at about 5000 C using N i crystal powders as catalyst. Different crystal structures o f Ni
catalyst result in different growth mechanisms o f coiled carbon fibers.
Carbon fiber
grows in opposite directions on the each side o f the Ni crystal. On one side, it is a righthanded helix and on the other side it is a left-handed helix. Using this process, we can
obtain micro-coiled carbon fibers having a coil radius about 5 pm, length about 50 pm to
100
pm, pitch about 2 pm, and the radius o f carbon fiber is about
1
pm.
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89
LCP
RCP
Ni crystal
Fig. 3.5—2 The mechanism o f micro-coiled carbon fiber production
Chiral materials are described in electromagnetics by one set o f constitutive equation
[19] [20] [25].
D = eE + p s V X E
(3.5-1)
B = |iH + P p V X H
(3.5-2)
Where s is the permittivity and p is the permeability o f the chiral materials. (5 is the
chirality parameter. The complex Maxwell’ equations in frequency domain are
V X E = j to B
(3.4-3)
V X H = -j coD + J
(3.4-4)
V• D = p
(3.4-5)
V • B = 0
(3.4-6)
The equation o f continuity
V • J = j to p
(3.5-7)
Since the vector identity has the following relationship
V2 A
= V (V* A ) - V X ( V X A )
(3-4-8)
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90
Using (3.5-8), the Maxwell’s equations can become the vector Helmholtz equation
V2 E + k 2 E = ^
-jcopJ
V 2 H + k 2H = - V X J
(3.5-9)
(3.5-10)
In a source- free region occupied by an isotropic chiral medium, E, H, D and B fields are
divergenceless by using (3.5-5) and (3.5-6) with constitutive equation.
From (3.5-3) and (3.5-4) combining with constitutive relations we obtained
E
E
V X
H
—
(3.5-11)
M
-
H
—
where K is the matrix given by
k 2p
j ©p
K=
(3.5 -12)
_-j cd s
k 2f i _
in which k = a ^ J is is the wavenumber.
Taking the curl of both sides of (3.5-11) and following eqn. (3.5-8), a wave equation can
be obtained:
E
V2
E
=
+ K2
H
0
(3.5-13)
H
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For chiral system, C.F. Bohren in 1974 [20] proposed
a transformation o f the
electromagnetic field by
E
Ql ~
=
(3.5-14)
M
H
Qr
such that
k LQL
~Q l “
+
V2
Qr
=
0
(3.5-15)
k rQ r
Where k L (LCP), kR (RCP) are wave numbers and QL, Q R are left and right circularity
polarized respectively. By substituting eqn. (3.5-14) into wave equation (3.5-13), then
comparing with (3.5-15), the wavenumbers can be simplified as:
co
ki =
1 P eople
l-k/3
a>y[jus
k
-
kR =
(3.5-16)
(3.5-17)
In a chiral medium, the LCP and RCP fields propagate in general with different complex
propagation constants. Since these must be positive hence its limit | kP|< 1 . This choice
will also ensure that the real and imaginary parts of the impedance is positive. From eqn.
(3.5-14) we obtained
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92
M
(3.5-18)
=
ai
I
in which
(3.5-19)
LCP and RCP fields have different complex wavenumbers, which result from the
chirality parameter p. It makes the rotation o f the plane o f the polarization and circular
dichrom. The QL, QR fields can be shown to satisfy the auxiliary condition
K
Ql
Ql
V X
(3.5-20)
kR
qr
and
0
~ Q l~
V«
“
(3.5-21)
=
_ Q r_
Qr
_0 _
Thus the EM fields are given by
E = Q l + ** Q*
(3.5-22)
H = a L Ql + Qr
(3.5-23)
LCP is along the direction o f a x + j a y, and RCP is along the direction o f a x - j a y .
To find the reflection and transmission in a double layer chiral sample, we have to
determine the three unknowns, kL, kR and the impedance o f chiral composite rj. Then
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93
using these data we can calculate the wave number
k,
the
permittivity
e, the
permeability p, and the chirality parameter P [34].
The procedure of sample preparation is as follows: The first layer consists o f PU
elastomer and microballoon as matrix with certain volume fraction o f micro-carbon
chirals. The second layer consists only matrix without any lossy component as shown in
Fig. 3.5-3
region 1
air
region 2
chirals medium
Mo
------------- ►
Incident wave
region 3
region 4
PU + microballoon
air
Mm
SchMcH P
RCP
LCP RCP+LCP
*0
*0
Mo
RCP + LCP
_
*
transmitted wave
z " " "
LCP
RCP + LCP — *
*
RCP RCP+LCP
«— |
reflected wave
d,
d.
Fig. 3.5-3 The normally incident plane wave is passing through a double layer slab
in which one layer is blended with chiral medium and the other layer is
PU elastomer blended with microballoon.
In region 2 (chiral medium), the RCP and LCP waves propagate with different
wavenumbers, while for other region (achiral media), RCP LCP wavenumbers are the
same. Generally, for a normal incident plane wave
A
A
A
Et = ( A H a x + A E a y ) exp j k 0 z
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94
A
2
Hi=
A
Where the coefficients A £ * 0, A H = 0
A„
A
— (A H a y - A
Ho
e
a x ) expj
k0 z
a TEpolarized planewave. A E = 0,
refer to
* 0 denotean incident TM polarized
field. Reflection and transmission
characteristics for circularity polarized plane waves can also be defined as A H = j A E for
LCP, similarly, A H = - j A E for RCP waves.
In region 2, the field has to be expressed in terms o f positive and negative
propagating LCP and RCP plane waves. The corresponding field along with Snell’s laws
in the chiral medium are given by
A
Ql
A
A
a y - j a* ) expj k £ z
=A , (
A
A
A
Qr = C , ( a y + j a z ) e x p j k * z
Where A ,
A
+ A , ( a y + j a x) exp - j k £ z
(3.5-24)
A
+ C , ( a y - j a* ) e x p - j k * z
(3.5-25)
, A 2 , C , , C , are constants to be determined.
The E field and H field in chiral medium from (3.4-22) and (3.4-23) become
A
A
A
E cA = A , ( a y - j a x ) exp j k £ z + A , ( a y
A
a*
A
A
= a i A,
A
+ C,
A
(ay
C,
A
+ j a ,) e x p - j k £
+j a x
) expj k £
A
A
+j a x
) expj k £
A
( a y + j a x ) expj k R z + C 2(
A
+ a £A , ( a y - j a x) e x p - j k Lz
z
A
+
+ a £C : ( a y -j a x ) e x p - j k* z
z
A
(ay
z
A
a y - j a x ) exp - j k R z
(3.5-27)
In region 3, PU elastomer blending with microballoon matrix, the E field and H field
are also expressed in terms o f circularity polarized waves as follows:
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(3.5-26)
95
E m = [ ( A 3 + C 3 ) a y + j ( C 3 - A 3 ) a x ] expj k n z +
[ ( A 4 + C 4 ) a y + j ( A 4 - C 4 ) a x ] e x p - j k mz
= —- { [ ( C 3 - A
nm
3
) a y - j (A
3
(3.5-28)
+ C 3 ) a x ] expj k m z +
[ ( A 4 - C 4 ) a y + j ( A 4 + C 4 ) flx] e x p - j k m z }
Where
rjm
(3.5-29)
, k m are impedance and wavenumber in region 3, matrix. Constants A 3,
C 3, A 4 , C 4 are to be determined.
In region 4, air, the transmitted E field and H field traveling along z direction. They
are given by
E r = [ ( T i + T* ) a y + j (T* - T t ) f l x ] expj k 0 z
(3.5-30)
H , = — { [ ( T i - T fi ) a y - j ( T t +T/J ) a x ] expj k 0 z
Ho
(3.5-31)
The reflection E field and H field in region 1, air, propagating along with -z axis are
E r =
[( r t
+
rR)
a y
+j
( ^
-
T/J
) flx ]
exp - j k 0 z
= — { [ ( Ei - T* ) a y + j (T t + r R ) ax ] e x p - j k 0 z
n0
(3.5-32)
(3.5-33)
Where T i , T R, T L, T R are transmitted and reflected coefficients that need to be
determined from the following boundary conditions.
At z= 0 for dielectric / dielectric interface
a z X [ E , + E r - E ch ] = 0
(3.5-34)
az X [ H , + H r - H cA ] = 0
(3.5-35)
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96
At z= d | , the interface between chiral medium and pure matrix
a - X [ E m - E rt ] = 0
(3.5-36)
A
a - X [ H m - H cA ] = 0
(3.5-37)
At z —d , , the interface between matrix and air
Qz X [ E m - E , ] = 0
(3.5-38)
A
(3.5-39)
The above 12 equations for A series and C series coefficients, T series and T series, in
general, must be solved by numerical method. The result will be shown that A , , A 4,
C , , C 3 , T R, and Tt vanish for a normally incident LCP plane wave. This implies that
A
A
only the waves polarized along a y - j a x direction can propagate in either the positive or
negative z direction. Similarly, for a normally incident RCP wave, A , , A 3 , C , , C 4,
A
A
T L, Tfi vanish, which implies that only waves polarized along a y + j a* direction can
propagate along either positive or negative z direction. It can be found that if there is no
mode conversion, RCP and LCP waves will propagate in each medium without
interfering with each other. Thus the reflection can be obtained by impedances for all
normally incident RCP or LCP waves.
According to the results o f Ruyen Ro 1992 [19], who used numerical method to solve
the above 12 equations, for a normally incident linearly polarized wave upon the chiral
medium sample, the chirality parameter P , wave numbers k R, kL, the permittivity e, the
permeability p, impedance rj, and k can be determined from following equations:
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97
k = - -------
1
0
r
(3.5-40)
1
1 ,
[ rR' K ]
< 3 -5 - 4 1 )
krj
p= —
co
(3.5-42)
k
e= —
(3.5-43)
COT]
The above EM parameters can be used topredict the propagating mechanism o f EM
wave in a chiral medium.
Subsequently we used our S-parameter, vector network
analyzer, and synthesizer sweeper system (refer to Fig. 3.4-6) to obtain the copolarized
reflection coefficients o f LCP and RCL which are expressed as S , u , S u/? respectively.
The power reflection is
— ,
f
| ~
T [S ui S lu + S
S nfi ] = T
(3.5-44)
j flv j
We measured the reflection and transmission fields with two copolarized antennas
and obtained the values o f S , lco and S 2lco. We also measured the transmission fields by
rotating the receiving antenna 90° and 0 from its copolarized position to obtain the
values o f S 2IcmtI and S 2W. Hence, linearly polarized waves have been mathematically
decomposed into coherent RCP and LCP waves of the same magnitude. Therefore, the
following relationships exist:
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98
(3.5-45)
2 1e m u
(3.5-46)
(3.5-47)
S 21 e m
^210
u
*^21 co C O S 0
sin #
(3.5-48)
The resultant transmitted wave o f these two circularly polarized waves is an
elliptically polarized wave and their polarization directions are rotated from that o f the
incident waves.
After computing the above values, we can determine the power transmission
coefficient T:
The power absorption coefficient A, for energy balance is given as
A + T+ T =
l
or
A = 1- T - T
(3.5-50)
From equation (3.5-50) o f chiral absorbent performance, it is clear that for a pure
chiral medium, the reflection and transmission with non-metal backed sample can be
obtained. The coefficients obtained with Free Space test equipment are shown in Fig.
5.4-1. Referring to chapter 2, we m ay obtain the attenuation o f chiral composite with
known thickness from its absorption. From equation (2.6-5)
1 E *
- —• E
2 rj
A = 1-
e
= 1 - ex p -2 az
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(2.6-5)
99
L e tz is the thickness d, then attenuation o f chiral medium composites a ch becomes
= ^l a 7 [ h l71 —
^ 7A ]
(3 -5' 5 1 >
From equation (3.5-51) after obtaining the absorption of chiral component, we can note
the attenuation o f chirals and combine it with other attenuations to make the total
attenuation similar to equation (2.6-5).
In the following experiments, we used copper wire springs and micro-carbon chirals
as main
absorbing component and checked their optimized volume
fraction.
Subsequently we mixed these chiral composites with other scattering components such as
aluminum flakes, carbon fibers to check their interaction
due to their different
geometries.
The first test sample consists o f copper wire springs with 0.1 mm in diameter (d),
which are coated with insulated polymer, ployimide. Copoper wire is coiled by a coiling
machine to become a spring with length (L) o f 2.5 mm (average), pitch (P) o f 0.15 mm,
and diameter o f helix (D) 1.2 mm. The density o f copper is 8.96 gram per c m 3 .
the geometry o f this copper spring we can calculate its inclusion volume:
= /r(—) (/rD)— = rc(05X 10
2'
'P
) (7rX 1.2 X10"3)
' v
7 0.15
= 4.93 XIO-10 m 3 = 4.93 X 10“4 c m 3
The occupied volume is
v «c =
^ ( ~ ) 2 L = tc( 0.6 XIO-3) 2 X2.5X10"3
= 2.83 X 1 0 '9 m 3 = 2.83 X 10 "3 c m 3
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From
100
The first sample has the maximum volume density with inclusion volume fraction of
12.4%.
The return loss is low for high frequency (X and Ku band) since the metal
packing is so dense that the impedance cannot match well. After the series test, we used
0.75 % inclusion volume fraction to compare the interaction with other scattering
components. We added aluminum flakes with 0.42% volume fraction into the original
matrix paste (included copper wire springs V mc- 0.75% already). In the same process we
added carbon fibers (volume fraction o f 0.036 %) into the matrix and in the final sample
we added both (aluminum flakes and carbon fibers, volume fraction 0.42%, 0.036%
respectively) into the matrix paste. The other series tests used the same volume fraction
o f aluminum flakes and carbon fibers to make the RAM sample individually without the
cooper wire springs. This comparison will enable us to study the effect o f chirals. Their
return losses are shown in Fig. 3.5-4 (a) and (b).
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101
OdB
Return -5dB
loss
(dB)
-lOdB
-!5dB
-20dB
9
8
10
Frequency (GHz)
11
12
Fig. 3.5-4 (a)The measured return losses o f RAM in which copper wire springs keep
as constant (inclusion volume fraction 0.75%) combined with aluminum
flakes (inclusion volume fraction 0.42 %), carbon fibers (volume fraction
0.036%), and three combination.
trace o f copper wire springs
----------------------- trace o f aluminum flakes
----------------------- trace o f carbon fibers
■ ■
trace o f three components combination
OdB
Return -5dB
loss
(dB)
-lOdB
-15dB
-20dB
8
9
10
11
12
Frequency (GHz)
Fig. 3.5-4 (b) The measured return losses o f individual aluminum flakes (dash line)
and carbon fibers (solid line ) with volume fraction 0 .4 2 % and
0.036 % respectively.
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102
From Fig. 3.5-4 (a, copper wire springs (dotted line) offer a poor absorbing
performance by itself. Thus other scattering components are necessary to be combined.
The combined results are significantly better by comparing Fig.3.5-4 (a) with (b). In
Fig.3.5-4 (a), the return loss o f three combination (broader solid line) become poor
because the conducting components density is too high. Therefore, the optimization of
volume fraction for each conducting component is necessary.
To obtain the optimum concentration o f the three absorbing components, we have to
reduce the reflection factor.
Using copper wire chirals with smaller pitch at higher
volume concentration can do this. We found that the copper wires with 0.15 mm pitch
are too small and by increasing the pitch to 0.5 mm we can obtain better absorption
results.
The tests showed the relationship between return losses (metal backed) and
different pitches at same volume concentration, 0.32% copper wire spring, 0.02% carbon
fiber and 0.24% aluminum flake.
Table 3.5-1 The relationship between different pitches o f copper wire springs
and absorptions at same inclusion volume concentration.
(0.32% copper spring, 0.02% carbon fiber, 0.24% aluminum flake)
pitch
(copper spring)
0.12 mm
0.25 mm
0.5 mm
1.0 mm
2. mm
8 GHz
- 3.2
- 5.8
-10.5
-11.2
-12.0
dB
dB
dB
dB
dB
return loss
10 GHz
-4.5
-6.7
-18.4
-14.3
- 8.3
dB
dB
dB
dB
dB
12 GHz
-8.6 dB
-12.5 dB
-17.8 dB
- 8.4 dB
- 6.9 dB
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103
From table 3.5-1, we find that the optimum pitch o f copper wire spring for 1.2 mm
diameter o f helix is 0.5 mm in X band absorption to combine with the carbon fibers and
aluminum flakes. Too high a pitch makes the copper wire spring seem like a conducting
fiber, which improves the low frequency absorption but reduces the high frequency
absorption.
A fter extension o f the copper wire spring, the occupied volume fraction
becomes 5.66 X I 0~3cm for each spring. We then reduced the concentration o f the three
1
components to — o f the previous value and subsequently we increased every component
by 30% to compare the absorption. Table 3.5-2 shows the test results.
Table 3.5-2 The absorption of composites with different scattering components
volume fraction
copper wire spring
carbon fiber
0. 25%
0. 32%
0. 32%
0. 32%
0. 32%
0. 32%
0.012%
0.015%
0.015%
0.02%
0.026%
0.032%
( inclusion)
aluminum flake
0.14%
0.18%
0.24%
0.24%
0.32%
0.4%
return loss at
frequency
8 GHz
10 GHz
12 GHz
-4,5
-6.9
-8.1
-10.5
-12.4
-13.1
dB
dB
dB
dB
dB
dB
-6.2 dB
-9.3 dB
-12.3 dB
-18.4 dB
-14.2 dB
-12.8dB
-8.4 dB
-12.2 dB
-18.6 dB
-17.8 dB
-13.2 dB
-10.9 dB
From Table 3.5-2, we can find that the optimum results were obtained in the fourth
test where the concentration is also high. Here the volume fraction o f copper wire spring,
carbon fiber, aluminum flake are 0.32 % 0.02 %, and 0.24% respectively. In this testing
process, we increased the copper wire spring volume fraction and then we adjusted the
volume concentrations o f carbon fiber and aluminum flake separately by referring to the
previously discussed result o f section 3.2 and 3.3 in which we observed that aluminum
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104
flakes improve the high frequency absorption and carbon fibers improve low frequency
absorption. After increasing the pitch o f copper wire spring, at higher concentration,
copper wire springs start twining with each other during the mixing process, therefore,
0.32 % inclusion volume fraction may be the maximum limit.
Too high a volume
fraction will result in uneven distribution o f the conducting springs. The measured return
loss o f the optimum concentration is shown in Fig. 3.5-5.
OdB
Return -5dB
loss
(dB)
-lOdB
-15dB
-20dB
8
9
10
11
12
Frequency (GHz)
Fig. 3.5-5 The measured return loss o f optimized volume fraction composite.
The volume fraction o f copper wire spring, carbon fiber,
and aluminum flake is 0.32 % , 0.02 % , and 0.24 %
respectively. The pitch o f copper wire springs are 0.5 mm
average.
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105
OdB
Return -5dB
loss
(dB)
-lOdB
-15dB
-20dB
8
9
10
Frequency (GHz)
11
12
Fig.3.5-6 The measured return loss o f same volume fraction o f carbon fibers
and aluminum flakes (0.02%, 0.24% respectively) as Fig. 3.5-5
composite, except without any copper wire spring.
Similarly, micro-carbon chiral has its optimum volume fraction. From the geometry
o f carbon chiral we can caculate its inclusion volume and occupied volume:
The diameter o f carbon coil (d) is 0.5 micron, the length (L) is 0.2 mm, the diameter of
helix (D) is 2.5 microns, pitch (P) is 12 microns. By using these values we may define the
inclusion volume o f each micro-carbon chiral as
d
L
/
V « = * (j)-(* D )-p - ;r(0.25xl0
, 02x10 '3
) («2Arl<>-‘ ) f ^ r
= 2.57X10 "l5m 3 = 2.57X 10 -’ e m 3
The stretched length is about 13 mm.
The occupied volume is
V^c =
fl-(y)2 L = tc( 1.25X10-*)2X 0.2X 10"3
- 1 0 ___ 3
= 9.82 X10"16 m 3 = 9.82 X 10-10
cm
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The density o f carbon chiral is 2.3 gram per c m 3 . We can easily obtain the number
density o f micro-carbon chiral in the matrix. We mix PU & microballoon matrix with
micro-carbon chiral at inclusion volume fraction o f 0.015%, 0.03 % , 0.06 % , and 0.12%.
The measured return losses is shown in Fig. 3.5-7
OdB
Return -5dB loss
(dB)
-lOdB
r
-15dB
8
9
10
11
12
Frequency (GHz)
Fig. 3.5-7 The variation o f measured return losses o f RAM in which are included
different inclusion volume fractions o f micro-carbon chiral.
______________ trace of inclusion volume fraction 0. 015%
_______________trace o f inclusion volume fraction 0. 03 %
_______________trace of inclusion volume fraction 0. 06 %
_______________trace of inclusion volume fraction 0. 12 %
From Fig.3.5-7 we can conclude that the optimized inclusion volume fraction of
carbon chiral is near 0.06 %. In the last sample, 0.12 % volume fraction is too high. The
electrical effective “conductivity” o f conducting chirals causes mismatch o f impedance.
Basically, the absorbing performance o f chiral medium composites is affected by the
length c f the micro-carbon chirals. But in practical operation, micro-carbon chirals over
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107
0.2 mm long tend to entangle each other and are difficult to be uniformly dispersed in the
binder (resin paste).
When strong power and high speed mixer is used to blend the
mixing paste, the chirals are partially broken and still had non-homogeneous distribution.
This limitation leads to the use o f shorter micro-carbon chirals (shorter than 0.2 mm)
which justified their absorbing performance in high frequency, as shown in Fig. 3.5-8.
The dotted line is showing the return loss o f RAM in which was included 0.08
%
inclusion volume fraction o f micro-carbon chiral RAM as primer layer, 0.012 % as top
layer. The micro-carbon chiral has 0.2 mm in length, 2.5 microns diameter of helix, 0.5
micron diameter of fiber and 1.2 micron pitch. Solid line shows a different return loss o f
0.5 mm long microcarbon chirals with the same volume fractions o f other components.
But for the latter sample we had to waste over 8 hours to separate the entwined longer
than (0.5 mm) micro-carbon chirals, and its distribution still was not perfect.
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108
OdB
Return -5dB
loss
(dB)
-lOdB
-15dB
-20dB
8
10
12
14
16
18
Frequency (GHz)
Fig. 3.5-8 Dash line showed the return loss o f 0.2 mm length micro-carbon chirals
medium in PU elastomer & microballoons matrix.
Solid line showed the return loss o f same composites but with 0.5 mm
length microcarbon chirals.( Both cases are metal backed)
On the other hand, micro-carbon chirals fibers have a special characteristic that RAM
containing chirals component will make the composite becomes less sensitive in terms of
return loss for different incident angles. Fig. 3.5-9 shows the difference between RAM
having and not having micro-carbon chiral. The two samples compared were made by
two different absorbing layers in which they had the same volume fraction o f aluminum
flakes, carbon black, carbon fibers except micro-carbon chirals. From Fig. 3.5-9 (b), we
can say that the optimum formula have excellent normal incidence absorption and less
sensitive return loss for o ff normal incident angles.
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109
OdB
off normal 0
-5dB
Return
loss
(dB)
o ff normal 15
off normal 30
-lOdB
-15dB
(a)
-20dB
-25dB
8
OdB
10
12
14
16
18
off normal 0
-5dB
Return
loss
(dB)
o ff normal 15
o ff normal 30
-lOdB
-15dB
(b)
-20dB
-25dB
8
10
12
14
16
18
Frequency (GHz)
Fig. 3.5-9 The signal property o f micro-carbon chirals except their absorption
performance is that they make RAM become less sensitive for different incident angles,
(a) shows the return loss o f RAM for different incident angles in which has no carbon
chirals. (b) shows the return loss o f same formula RAM except addition o f carbon chirals
(0.2 mm length), primer layer with 0.036 % volume fraction, top layer with 0.012 %
volume fraction.
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110
3.6 Magnetic Materials: Carbonyl Iron and Ferrites
Apart from carbon black, carbonyl iron powder was the earliest raw material for EM
wave absorbers. During World War II, it was known as the “Wesch Material”, and has
resonant at about 3 GHz. It was made in the form of a semi-flexible rubber sheet, which
was loaded with about 30 % volume fraction (70% wt. fraction, due to 5 times density o f
rubber.) o f carbonyl iron powder. Its thickness was about 0.3 inches. Its front surface
was extended out into a “waffle” geometry to improve bandwidth. In Japan, the Audio
tape manufacturer, TDK used ferrites made EM absorber having thickness 0.8 mm
showing - 20 dB return loss at X band in 1970’s.
Both carbonyl iron and ferrites are magnetic materials. The magnetic components o f
EM wave explain the absorbent mechanisms with its magnetic loss tangent. For magnetic
material, we must consider the permeability as a complex variable [10].
and permittivity
£ = £ - } £
A
rj = r| e ,e =
the intrinsic impedance
—
By substituting the complex permittivity and permeability into the intrinsic impedance, it
A
becomes
where
rj = [
rv
1
(e'fi + £ / j )2 + (£ •> ’ ~ g > ' ) 2 j i / 4e ,*
0 = — tan
2
- I
r
[
S
U
—r~ ,
-
£
U
r ~
£//+£//
]
(3.6-1)
(3.6-2)
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Ill
Similarly, magnetic and dielectric loss tangent are:
magnetic loss tangent : tan | 8 m | =
r
M
s
dielectric loss tangent : tan | 5 d | = —
E
The magnetic tangent loss is due to the hysteresis phenomenon when magnetic materials
encounter the external magnetic fields as shown in Fig. 3.6-1 [36].
B
(BH)m
applied magnetic field
Fig. 3.6-1 When a ferromagnetic material encounter an external magnetic field
a B-H hystersis loops happens. Where B I is saturation value o f
magnetic flux density, H c is coercive magnetic field intensity.
The propagation constant is y = j cosj^e - a + j p. By substituting the complex
permittivity and permeability it becomes
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112
y = j k = j co V(/*' - j f t X e - j e ) = a + j p
(3.6-3)
Where k is the wave number k = coy fx s
(3.6-4)
The index o f refraction n =
(3.6-5)
Comparing the real and imaginary part o f the above equation (3.6-3), we can obtain the
following constants:
The attenuation constant for a transversal EM wave is:
Xa>2
. .
. .
a = —— ( s j u + s n )
4K
(3.6-6)
The phase factor is:
p.
X
=m[iLajz££i X {
2
1+ Jl +
£ /X + £ fX
} ] 1/2
(3.6-7)
\ S fj. + £ fX J
For magnetic and dielectric materials, the constitutive equations are:
D = £ 0 E + P = £ 0 ( l + yjf£ ) E = £ r s 0 E
(3.6-8)
where X e is the electric susceptibility.
B = /t0 H + M =
fiQ
( 1+ x u ) H =
fxr
/xQ H
(3.6-9)
where X m is the magnetic susceptibility.
Carbonyl iron is iron with proper quantity o f carbon and oxygen. It is produced by
reacting CO gas with iron under high pressure (about 10 times o f atmospheric pressure)
and high temperature (150° C to 200 °C). Manufacturers used chemical processing to
decompose it and make it into many tiny powder particles.
After reducing volume
processing, phosphoric surface treatment is necessary to improve its corrosive resistance
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113
and insulation. Basically, carbonyl iron powder is a non-conductive material and that
makes it very useful in high frequency magnetic devices. It also has low attenuation in
high frequency region [37].
Carbonyl iron powder used as absorbing component generally has the size o f about 1
to 5 pm. For example, German BASF product, the HFQ system has particle size o f one
micrometer, and EW system is 5 micrometer. The smaller the particle size the easier it is
to handle the quality due to high density o f carbonyl iron. Nowadays people seldom use
carbonyl iron as EM wave absorber because o f two reasons, they are too heavy (density is
five times that o f resin or rubber matrix), and they have poor chemical resistance. The
only advantage for EM wave absorbent application is its high Curie temperature, about
550 0 C, that let this component to be used in EM absorbent coating applied on SR-71
thirty years ago [1].
Most o f its application is in microwave shielding materials, especially as electrical
cable o f automobiles (loading high voltage & ac current) due to its good electric
insulation. The price o f carbonyl iron always used EW system is 1/6 that o f the HFQ
system. The other usage is in the field o f magnetic recording materials, but it is limited to
HFQ system, the size is only one micrometer.
The magnetic properties o f carbonyl iron are close to pure iron. Its relative initial
permeability is the permeability when B field start from zero //, =
lim — >
B -* 0
is
H
about 3,000, the maximum permeability n m is 20,000 (to / / 0), coercive force H c is 6.4
(A/m), remnant Br is 2.2 (wb/m2 ).
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114
The general profile o f the relative permittivity and permeability spectra for carbonyl
iron and ferrites are shown in Fig. 3.6-2:
Material
parameters
/uXf
0.1 f r
fr
Frequency
Fig. 3.6-2 The general profile of the electromagnetic parameter spectra
for magnetic materials.
Ferrites cover a very wide range o f substituted iron oxides which have a wide range o f
electrical and magnetic properties. Generally, the spinel ferrites have a cubic crystal
structure and can be represented by the general formula, M F e, O 4 , where M is a divalent
transition metal ion, a combination o f two or more ions or alternatively a combination of
mono-and trivalent ions that maintain overall electrical neutrality. Most popular spinel
ferrites used in EM wave absorber are L ix Cr,_x M Fe, 0 4 , N i x Zn,_x M F e , 0 4, and
M nM Fe, O 4 . Because ferrites have the ability to obtain high packing densities, to resist
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115
oxidation to a nonmagnetic form, and to allow synthesis of properties through appropriate
doping make ferrites widely used in magnetic RAM than carbonyl iron. Especially for
hexagonal ferrites, in which the frequency at which / i r and /ur peaks can be controlled
by doping, such as C o +2, and Ti*4
to replace the F e+3 ions. This doping method can
achieve impedance matching layers over different frequency ranges [38].
In Fig. 3.6-2, the real part o f the permeability o f ferrites and carbonyl iron, fuXf, falls
in a frequency region extending over about 2 decades. Half o f this reduction occurs at the
mid-point o f this region, f r . It also has a peak o f magnetic loss. This phenomenon is the
result o f the progressive failure o f magnetization to follow the oscillation o f the applied
field as frequency is increased. In Fig. 3.6-2, we also find that ferrites exhibit a slight rise
in the real part o f the permeability at low frequency end o f the dispersion region and at
the high frequency end it has a dip.
This is similar to the magnetic resonance and
relaxation.
Furthermore, the magnetic loss often shows a second peak which seems to be
smaller or broader. At high frequency region, the relaxation dispersion can make a small
upper frequency extension o f useful frequency band. The real and imaginary parts of
complex permeability for magnetic material are related to each other.
A typical spinel ferrite with f i xf in the range o f 10 to 1,000. Its f r is in the region o f
5 to 500 MHz. Snoek [32] found these two parameters are dependent each other. The
Snoek’s empirical formula is:
juXf f r s constant = 5600 MHz
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116
This relation may be used when operating frequency is under 1 GHz. The spinel ferrites
commonly used in low frequency absorbers inclusde MnFe 2 O 4 , Ni F e , O 4 , Mg
Fe 2 O 4 , and Cu Fe 2 O 4 .
For higher frequency, the hexagonal ferrites have slightly lower /uxf and higher f r .
The Snoek’s formula becomes [32]:
HXf f r = constant = 15 to 30 GHz
These hedagonal ferrites include Ba F e 120 ]9 , Pb F e I20 I9, and rare earth group
Er 3 Fe s O I2. Basically, hexagonal ferrites are about 10 times more expensive than spinel
ferrites. However, its resonance frequency is always at X and Ku bands, the military
bands. For radar camouflage system o f aircraft, some doping hexagonal ferrites are the
most favored material due to the smaller thickness (less than 1 mm ) of this magnetic
RAM. Narrow absorption frequency is one o f its drawbacks.
The permittivities o f magnetic materials are found to change with frequency and
also the permeability o f the magnetic materials changes with applied magnetic field.
Lack o f correlation between dielectric and magnetic materials is the reason that they can
not cover a broadband frequency with a small thickness.
So when we use magnetic
materials as the component for EM wave absorbers, we must consider many variables and
for different frequencies we encountered totally different parameters.
Moreover, the
permeability changes with field strength even if the frequency is the same. These factors
made it difficult for engineers to predict the return loss. In practical application, we first
checked the magnetic and dielectric properties shown in Fig. 3.6-2 and to find f r
(corresponding to the 1 / 2 ( n xf -1)) satisfying the requirements. From a selected f r , we
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117
can obtain all the corresponding parameters from general form as Fig. 3.6-2. Parameters,
fj.r , fj.r , s r and e r
are used to calculate a, (3, and rj. Same procedure should be
adopted as previous section. If the materials source can not provide enough data, then a
series test and practical measurements are needed.
Actually, the permeability also
changes with temperature, and some ferrites are very sensitive even at 50 to 100° C.
Practical experience is important to use magnetic materials as the absorbent component.
Trial and error is the best method and the fastest (and some times the only way) to obtain
the answers.
Magnetic materials have a narrow band o f EM wave absorption, its
absorbent bandwidth is only ju st about 1.5 GHz (over -15dB ). It is necessary to modify
the magnetic materials using other dielectric materials.
The most important advantage o f magnetic materials, especially, spinel ferrites is
the absorbent component, the thickness of absorbers will be one tenth that of dielectric
components in low frequency region (below 1.7 GHz). Although magnetic EM absorbers
tend to be heavy, their merit lies in the ability to provide extended low-frequency
performances with smaller material thicknesses. For example, at a frequency of 100 MHz
where an ordinary dielectric absorber will have to be many inches thick to achieve such a
low-frequency coverage,
however
magnetic
materials
can
achieve
comparable
performance with much less than one tenth o f thickness. We can check this merit from
an example. For sintered Nickel Zinc Ferrite, its four parameters at different frequencies
are as follows: At 100 MHz s r = 27, £ r = 54, f i r = 15, / / r = 45. At 1 GHz £ r = 20,
£ r = 9, i i r = 1.2, fxr = 12. A t 10 GHz £ r = 15, £ r = 6.3, f i r = 0.1, fur = 0.32.
For 100MHz the index o f refraction n following (3.6-6)
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118
n = |V^77| = |V(15 —/4 5 )(2 7 -/5 4 )| = |(20_5 - /49.4)| = *J(205)2 + (49.4)2 = 53.48 .
we may obtain the reflection o f single layer. The front-face reflection becomes
j— tanh(/
|r,(0)| = V
) -1
/— ta n h (y ,i/,)+ 1
pr
J - - 1
= V g'
J ^
pr
+1
/ ( -5 y 4 5 ) - l
= V( 27- yS4)
= , -0.116-y0.0628
i
+l
^ 4 - y 0 .0 6 2 8
(2 7 -/5 4 )
= [ (-0.0604)2 + ( -0.0353)2 ] 1/2 = 0.06996 =0.07.
Surface (air surrounding) return loss = 10 log (0.07)2 = -23.1 dB.
Dielectric absorbing materials with this return loss require a thickness o f about 75 cm.
Similarly, we can obtain other frequencies at 1 GHz and 10 GHz, they have front surface
return loss -10.3 dB, -2.3 dB respectively with same electrical thickness. Their refraction
indexes are 16.3 and 2.3 at 1 GHz and 10 GHz. From the above result we can find that
spinel ferrite has good absorption performance at low frequency (100 MHz) but has poor
absorption performance at high frequency (10 GHz). In practical applications, "Hybrid
RAM" is always used for broadband absorbing.
Hybrid RAM is an EM absorbing
composite, which combines two or more different absorber designs. For example, we use
spinel ferrites absorber as the first layer (contact metal objects), then apply dielectric
absorbing layer as the second layer (or upper multi-layers), we can obtain an EM wave
absorber with broader bandwidth and thinner thickness. We will discuss this in chapter 5.
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!
119
Figs. 3.6-3 and 3.6-4 show measured return losses o f a single ferrite RAM
(P b F e ,,0 I9 doping with Co*2) and triple-layer RAM (doping PbFe,2O l9, BaFeI2O l9,
and E r3Fe 5O l2) respectively. Two samples have same thickness o f 3 mm.
0 dB
Return
-5 dB
loss
-10 dB
-15 dB
-20 dB
-25 dB
-30 dB
-35 dB
8
10
Frequency (GHz)
12
Fig. 3.6-3 The measured return loss o f RAM which used one ferrite PbFe I20 19
(doping with Co *2) showing the narrow absorbing band.
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120
0 dB
Return
-5 dB
loss
-10 dB
-15 dB
-20 dB
-25 dB
-30 dB
-35 dB
8
10
12
Frequency (GHz)
Fig. 3.6-4 The measured return loss o f triple-layer RAM which included three ferrites
(PbFe,, O I9, BaFe 12O I9, and Er 3Fe 5O ,,) showing the broadband absorption.
In Fig. 3.6-4, three ferrites have different frequency resonance.
The wideband
absorption can be obtained by carefully matching the impedance o f each layer.
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121
Chapter 4
MEASUREMENT
4.1 Introduction
The development o f EM wave absorbers requires an incorporation o f the
electromagnetic properties o f each component.
These EM properties are permittivity,
permeability, attenuation, phase constant and chirality parameter in the chiral medium.
After all the components are mixed together in the designed manner, the absorption
performance is tested. Usually, a series o f corrections are made for the
optimum
results.
The measurement o f reflection and transmission is to determine and study the EM
properties. Subsequently the absorbing performance of products in simple shape can be
tested [46].
In the practical engineering o f microwave absorbers, the design parameters are
influenced by targets with invariable complex shapes and the specific purposes o f
absorbers.
For example the absorption performance required for aircraft cockpit,
reflection o f radome, leading edges, rudder edges are totally different and the design o f
the absorber in each case cited above needs to be addressed differently.
In the case of ships, the areas of concern are the diffraction o f comers, low frequency
absorption, EMI issues o f masts, the effect o f reflection and scattering on the deck ...
etc.
These phenomena can not be observed by the simple test o f reflection and
transmission. Therefore, microwave imaging o f practical targets for 2-dimension and
even 3-dimension is necessary. From time domain (range measurement) diagrams we can
know if the location o f complex target is defective (high reflection) and what causes the
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122
creeping return or end diffraction, and scattering. Corrections will be compensated after
checking these microwave image pictures [48] [50],
4.2 Reflection and transmission measurement
The free space equipment in the Research Center for Engineering Electronic and
Acoustic Materials is used for the reflection and transmission measurement. It includes a
HP 8510 B vector network analyzer, HP 8340B synthesized sweeper, HP 8516A Sparameter and a series of lens hom antenna, and coaxial waveguides. Shown in Fig. 4.2-1
is the free-space set up.
It is very important to carry out proper calibration in order to obtain precise results.
During the calibration, a series o f known devices or standards are connected.
The
systematic effects o f these are determined to find out the difference between the measured
and known response o f the standards.
Once this is characterized, the errors can be
mathematically related by solving a signal flow graph.
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123
Synthesizer Sweeper
0.01 -40 GHz
I
HP 8510B
HP
Plotter
Network Analyzer
I
Test Set
HP
Printer
0.045 - 40 GHz
Port 1
Port 2
Coaxial
Cable
Coaxial
Cable
Sample Holder
Mode
Transitions
Mode
Transitions
Receiving Antenna
Fig.4.2-1 The S-parameter & vector network analyzer test set in Center for the
Engineering Electronic & Acoustic Materials o f Engineering Science
& Mechanics Department in The Penn State University.
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124
The reflection o f the sample can be obtained from S ,, or S „ , and the transmission is
S | 2 or S 2I after proper calibration. Because the summation of reflection, transmission,
and absorption is
1
in non-metal backed cases, we can compute any coefficient from two
o f them. In metal backed cases, the return loss was obtained directly from S ,, or S „ for
normally incident EM waves, which is explained in Fig. 4.2-2.
a,
S 2,
--------
>
1-------
*---------j t-------*------
1f
i
S„
b,
b2
S 22
s12
a2
Fig.4.2-2 The signal flow o f the two port network analyzer.
If we put the sample in the comer o f the circular orbit on the aluminum table and let
antennas (transmitter and receiver) locate the angle (face to sample) properly, we can
obtain reflections from different incident angles from S 12 or S ;1 • This is a bistation
measurement, the receiver and the transmitter are separated as shown in Fig.4.2-3.
Although the bistation measurement data can not be used directly in practical
engineering, different incident angle reflection will be a good reference to predict the
reflection and scattering o f complex shaped objects.
These measurements are good
guidelines for studying the different incident angles o f reflection and the scattering effect
of complex shaped objects.
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125
test sample
circle orbit
to port
to port 2
1
transmitter
receiver
Fig. 4.2-3 The return loss measurement of metal backed sample in different
incident angle.
Free-space method using spot focusing antennas providing plane wave illumination,
the samples don’t have to meet strict tolerances on size and shape. A wide variety of
ambient conditions may be used during the measurement by using a suitable means of
holding the sample between the antennas. Because the antennas are focused to the center
o f sample, there are no edge diffractions to affect the test result. From the measured EM
parameters, we can predict the propagating mechanism o f EM wave in different media.
S-parameter, vector network analyzer, and synthesized sweeper system in Fig.4.2-1 are
used to obtain the copolarized reflection coefficients in chiral medium composites. The
LCP and RCL reflections are S Ui , S 11/? respectively [14].
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126
The power o f the reflection is
We have measured the reflection and transmission fields with two circularly
antennas and obtained S Uco and S 2Xco. We also measured transmission fields by rotating
the receiving antenna 9 0 0 and 0 from its copolarized position to obtain the values S 1)crasi
and S , 1(?.
The linearly polarized waves have been mathematically decomposed into
coherent RCP and LCP waves o f the same magnitude as shown below [19-21]:
S uco —
( S a t + S llfi ) —S ut - S nR
(4.2-2)
S -]r ~ S 2Ico + j
(4.2-3)
S 2 1 i —S 21CO ~ j S 21crou
(4-2-4)
s
(4.2-5)
sin 0
The resultant transmitted wave of these two circularly polarized waves is an
elliptically polarized wave and their polarization directions are rotated from that o f the
incident waves.
After computing the above values, we can determine the power transmission
coefficient T:
T = ? 7 = \ <Sjli s “
+ S : '” s ; " , = S ! I “ s ; , “ + s ='"“ s ='"”“
(4-2‘6)
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127
The power absorption coefficient A, for energy balance can be designed as
A + T + T = l
or
A = l - T - T
(4.2-7)
Although we can not use power absorption coefficient A to predict the practical
metal backed cases we can observe the chiral absorbent mechanism for the pure chiral
medium. Above coefficients can be obtained with our Free Space test equipment, as
shown in Fig. 4.1-1. Referring to chapter 2, about EM theories, we may obtain the
attenuation o f chiral media composites from their absorption with known thicknesses.
From equation (2.5-3)
A
(2.5-3)
A = 1- p
p o = 1 - exp -2az
Let z is the thickness d, then attenuation o f chiral medium composites a ch was obtained
from equation (4.2-8).
4.3 Time domain method
The most basic method o f microwave imaging involves the range determination [27]
[48], which is accomplished by measuring the round trip delay of the transferred signal
and computing the distance using the propagation velocity. This is known as the "Time
domain method" [56]. The time delay between a distinct feature, which is presented in a
transmitted waveform and recognizable in the received waveform, is measured by
electronic circuits. The time delay, which maximizes the correction between transmitted
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128
and received waveform corresponding to the
2 -way
range, is the fundamental
measurement o f the correction process. The most popular system for range measurement
is the pulse radar which provides inherent tim e marks by the leading and trailing edges o f
the pulse. Fig. 4.3-1 shows a one -dimension time domain range measurement.
O
antennas
target
(a)
specular
return
amplitude
of
reflection
wave
creep ing
ave ret urn
-4
3
1
1
-2
0
nano-second ( or each scale 15 cm .)
(b)
2
Fig. 4.3-1 One dim ension" time domain " measurement, (a) showed the location
o f each component, (b) showed the result of range measurement in which
included specular return and creeping wave return.
Fig.4.3-1 (a) shows the location of RF antennas and object, and d is the distance
between antennas and object.
The one-dimension time domain range measured and
shown in result (b), which shows the time delay o f return wave, w hich actually means the
distance between antennas and object. Since the velocity o f EM wave in free space is 3 X
10 10 cm per second, each nano-second (1 0 -9 second) delay means 15 cm distance.
Conducting object has a high amplitude reflection and for low frequency response
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129
generally has a creeping wave (or end diffraction) behind the specular reflection. These
phenomena can not be analyzed by RCS measurement, therefore microwave imaging
becomes a very powerful tool to check the absorbing performance o f complex targets
[54].
The fundamental requirement for microwave image is to get the reflection (backward
wave including scattering, creeping wave and diffraction) response which is a function of
body location. This is done by causing the relative phase to change in both down and
cross range. The change o f cross range is accomplished by rotating the body, and the
change of down range phase variation is accomplished experimentally by sweeping the
frequency that changes the relative down range position or phase o f the scattering centers.
In electromagnetic point of view, we stretch the body in time delay (phase) so that we
can reconstruct the wave scattering locations by the Furrier Transform.
In modem
computing method it is called "Fast Furrier Transform" or FFT. In practical experiments,
the only way to move scattering centers down range is to vary the number o f wavelengths
in a down ranges.
The resolution o f radar wave image increases with bandwidth, as
shown in Fig.4.3-2.
Resolution = AR = —— = -----------2A /
2 (4 /7 /)
(4.3-1)
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130
RESOLUTION
CELL
ANTENNA
R A0
•
CROSSLANGE
DIMENSION
BEAMWIDTH
RADAR
RANGE DIMENSION
Fig.4.3-2 The definition o f resolution for time domain measurements [26].
In Fig. 4.3-2, the resolution cell is defined by the range dimension AR of radiated
waveform and the cross-range dimension RAG o f the beam. The beam width A0 s —,
L
where X is the wavelength o f radiated energy and L is the size of antenna.
The
fundamental advantage offered by the wide radar bandwidth is its increased information
about the present location and identity of targets such as ships, aircrafts, and even the
earth's surface features.
Such increased information is produced by the additional,
independent target reflectivity data that can be collected. For the design of RAM, the first
step should be measuring the absorbing performance in an indoor facility, because that is
the easiest condition to control. For this reason modem radar is always operated over a
wide frequency band, by changing the transmitter frequency from pulse to pulse,
collecting target reflectivity data in
2
dimensions , reflectivity versus frequency and
viewing angle. This is also the reason why we must design the broadband frequency EM
wave absorbers [58].
From equation (4.3-1) we can find that a 10% bandwidth yields approximately a five
wavelength resolution, which is satisfactory at X band
(8
GHz to 12 GHz). But at low
frequencies such as VHF or L bands the resolution are poor. Cross range resolution is
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131
increased by increasing the angular extent over which the model (or target) is rotated. If
the angle o f cross range is small such that cosG =
1
, and sinG = 0 , the resolution will be
poor. On the other hand, increasing the angle will cause the image defocus. For practical
targets, 150 to 3 0 0 maybe the optimized angle range.
In the engineering o f microwave absorbers, the most important issue in quality
control is what frequency range will be used to measure the primary processing in which
we build up the mechanism from the small model o f practical targets (complex objects o f
course). For example, building up F-16 requires use ten times frequency 80 GHz to 120
GHz to obtain the reliable reference from the 1/10 model imaging measurements [43], if
we focus at X band
(8
GHz to 12 GHz), the so called "military band", for practical
application.
Basically, the wave circumference o f targets ( for sphere c = ka, cylinder c = ^ kd, a
is radius o f sphere, d is the length o f cylinder ) must be the same. Now the problems will
be the reflection from leading edge, rudder edge, and tailing edge for aircrafts. Because
these parts of the aircraft model maybe just have 1 to 3 mm thickness. If we want to
obtain the precise measurement results we should use higher than 100 GHz frequency to
measure the front face (face to leading edges or rudder edges) or other sharp comer
scatterings.
Even so, when we apply these RAM onto the amplified (or practical) targets we need
correction for these differences.
Therefore it is necessary to set up the processing
mechanism. Firstly, we use contracted model with corresponding frequency (same wave
circumference) to predict the processing. Secondly, we use the same mechanism to apply
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132
the RAM materials onto target with the same size and shape, which is made by wood or
plaster with metal foil (thickness over 5 times o f its minimum skin depth) cover. The last
step is to find the correction factors for practical target comparison with wood made (or
plaster) prototype. Generally, because the practical targets or prototypes are too heavy,
we can not use the foam plastic support column. String supports (hanging method) may
be the good way to isolate the targets.
The economical way for large target measurement is using sky as anechoic chamber.
The sky is the biggest anechoic chamber except for the weather constraints.
essential conditions exist in using the hanging method for target support.
Two
Firstl, the
hanging ropes must have no EM wave reflection (below 40 GHz), generally nylon or
Kevlar ropes are used. Secondly the gain o f antennas should be large enough to cover the
whole target in any rotated angle and small enough not to cover the string supports,
because most string supports are made o f
steel and have
100%
reflection for all
frequency.
If the direction o f EM waves is along the ground, "clear zone" surroundings are
necessary.
To prevent the interference from the reflection o ff the ground,
some
"microwave fences" are necessary [50].
For outdoor measurement, far field measuring results are obtained, because far field
measurement is closer to the practical application. However, the formal definition o f
RCS is that the distance between the radar and target must be infinite:
a = l i m 4 *ft 2
R-><a
\ES\2
L
(4.3-2)
\E \
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Equation (4.3-2) defines such limitation for eliminating any distance dependence in the
RCS measurement. It is assumed that the target is illuminated by a plane wave. But for
practical situations, the incident waves are nearly spherical waves. N ow we may make
the reasonable approximations to solve these problems.
First we assume that the radar is a point source and examine the deviation of the
incident phase fronts from perfectly uniform wave over an aperture having the same
width as the target. Fig. 4.3-3 shows the geometry o f this situation.
* h
—
Fig. 4.3-3 The geometry about correction o f phase errors.
Referring to Fig.4.3-3, we can use the elementary geometry to express h in terms of
R and d in following equation:
h = R - [ R ; -( i
] ' " = R - R [ l - ( ^ - ) : ] l,:
Z
(4.3-3)
ZK
where we assume a reasonable restriction that R » d for far field conditions. Based on
this approach, we can simplify equation (4.3-3)
h
s
R - R [ I - -( 2^ S )2_ ] = _d 1
(4.3-4)
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134
Fig.4.3-4 shows the relationship between frequency, distance, and size o f target.
The RCS test community has adopted an acceptable phase error o f 22.5 degree. The
analysis below suggests that common error is less than one dB. 22.5 degree equal to —,
8
27 th
TV
TV
and for wave distance k h = ------ isrestricted to be smaller than —. It will become — >
/I
8
8
2^
k h. By substituting k h =
relationship into the previous equation, it will be
X
h <—
16
(4.3-5)
v
We combine the equations (4.2-4) and (4.2-5) to obtain the R:
R > —
X
(4.3-6)
Equation (4.3-6) is the famous far-field criterion to ensure that RCS test data are accurate
to 1 dB or better due to the finite range from the radar to the target. For example, a tank
with minimum size o f 3 m, the measuring frequency is 10 GHz (wavelength 3 cm)
following equation (4.3-6), the minimum distance between the target and radar should be
longer than 600 meters [27].
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135
d ( size)
radar-*-
distance R
f, GHz
target
R, kft
100 x
d, ft
T 100
1000
3 0 ■■
100
10 Jj
•> 3 0
: : 10
10
1
0.1
0.3 ■■
■*•
0.1 J-
0 .0 1
3
Fig. 4.3-4 The correction diagram o f measurement showed the relationship
between frequency, distance, and size o f targets [27].
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136
Chapter 5
ENGINEERING OF MICROWAVE ABSORBERS
5.1 Introduction
In the engineering o f microwave absorbers, many property aspects apart from the EM
wave absorbing performance have to be considered. For example, physical strengths
including tensile strength, bending strength, shear strength, compressive strength, and
fatigue strength, temperature resistance, chemical resistance, and processing feasibility.
Processing feasibility includes lamination, complex objects processing, and preform
molding.
These processing methods depend on the shapes, sizes o f objects and
requirements of users.
The m ost important issue in the manufacture o f microwave
absorbers is quality control (QC).
Quality control of EM wave absorbent materials
includes absorbing performance, mechanical properties, and chemical resistances. [49].
An engineer must have the comprehension to receive and overcome the difference
between the QC method deployed in the laboratory and that required for practical
applications, especially in the area o f microwave absorbing performance. Because the
RCS measurement is different if the testing sample is not large enough (over ten times of
wavelength) even though same absorbing materials are applied onto surfaces with same
shape but different size. End diffractions and creeping waves o f small objects or sharp
edges always interfere with the precision o f RCS measurement.
For mechanical
properties, the leading edge or tips o f targets are the problems need to be considered. The
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137
chemical resistance is always encountered in practical situations. We will discuss these
issues at the end of this chapter.
5.2 The optimization o f absorber formula
For manufacturing, the most important step is to design an optimized formula o f
material. The first consideration o f formula design is how to obtain a high performance
absorber, which can cover certain frequency region. The absorbing performance depends
on absorbing components. The reinforced components may be considered after that of
absorbing components, because reinforced components have no effects (or said very
small) on absorption performance in normally operating frequency 2 GHz to 18 GHz.
If
the operating frequency is higher than 40 GHz, we must consider the EM properties o f
binder and reinforced materials, polymers and aramid fibers (such as Kevlar 49), because
for the frequency higher than 40 GHz these components have the absorption peaks.
In chapter 2, we have discussed that the performance of a good absorber should not
be sensitive to different incidence angle and frequency.
Some absorbers carry out
absorption function by their different (or converse) phases navigating the incident wave.
These absorbers are very sensitive to varied incident angles and different frequencies.
Because these shifts (changes o f incident angles and frequencies) will sabotage the
resonance phenomenon. Following equation (2.3-4), "How to improve the attenuation"
is the key point for EM wave absorber designers.
Form chapter 3, we can find all the absorbing components have their advantages and
disadvantages for EM wave absorbent performance. For example, metal flakes have good
random scattering effect at high frequency region, but poor performance at low frequency.
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138
However, carbon fibers with an optimal length o f
6
mm offer excellent absorbent
performance at lower frequency, but its absorbent performance is poor at higher
frequency region. We modified these two random scattering materials and improved the
dissipation effect by adding proper quantity of carbon black to matching the impedance o f
each layer.
The modifications result in very good absorbent performance including
broadband and stronger absorption. Besides EM wave absorption, micro-carbon chirals
offer significant improvement in their ability to reduce the difference o f return loss for
different incident angle which truly is an important revolution [4 5 ].
From our series test results, wave interactions are resulted from multiple random
scatterings o f absorbing components with different shapes. The random scattering of EM
waves improves the absorbent performance in absorbers. This led to the use of two
different geometrically shaped dielectric materials in the absorbers.
Before we design an optimized formula, EM parameters o f raw materials must be
measured.
For broadband frequency, it is impossible to measure permittivities and
permeabilities o f all the components from
their modifications.
8
GHz to 18 GHz to predict the absorption of
An easier way is to balance the attenuation o f some essential
absorbing components such as metal flakes, conducting fibers and carbon chirals. In
order to obtain an broader frequency absorption, the first step is to achieve an absorbing
performance not changing with frequency at required frequency region. After balancing
the attenuation o f all absorbing components, especially conducting materials, we must
check the conductivity o f new formula. In chapter 3, section 2 , 3 , and 5 in which tables
3.2-1, 3.3-1, and 3.5-1 showed the typical ways to obtain the optimized formula. We
always list the volume fraction and different frequency vs. their return loss to check if the
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139
impedance o f each layer properly matches that o f other layers and the environment.
According to the property o f each component, proper impedance matching can be
achieved by adjusting its volume fraction. Similar analysis has been presented in chapter
3.
Different components perform differently as frequency changes.
However, a
composite consisting o f these components offer an absorbing performance not changing
with frequency at the required frequency region.
In chapter 2, we discussed the classification o f attenuations
a = <*, + a m + a d + a CH
(2.6-3)
where a J is the attenuation due to the random scattering effects, a m is the attenuation
due to magnetic tangent losses, a d is the attenuation due to dissipation, and a CH is the
attenuation due to chirality o f micro-carbon chirals.
For different random scattering
components, such as conducting fibers, metal flakes, since their attenuations depend on
frequency, we denote their attenuation are a Sl, and a S2 respectively at certain frequency
region. In the case o f a balanced attenuation, a sx = a S2 at certain frequency region. For
example, X band
(8
GHz to 12 GHz), its center frequency is 10 GHz. We check then-
random scattering cross section values crTX, a T2 at 10 GHz, then substitute into the
equation
a s = par r / 2
(2.6-7)
We obtain the balance equation
« s, =
= ««
<S-2-D
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140
From ( 5.2-1 ) we easily obtain the relationship o f number densities per unit volume of
both components p x, and p 2. Once one o f them is decided, the other is fixed.
An optimized two-layer EM wave absorber for X band and Ku band (from
8
GHz to
18 GHz) consists of aluminum flakes, carbon fibers, carbon black, micro-carbon chirals
(0.2mm length) with different volume fractions. Its measured return loss is shown in Fig.
5.2-1.
OdB
-5dB
Return
loss
(dB)
-lOdB
-15dB
-20dB
-25 dB
12
14
16
18
Frequency (GHz)
Fig. 5.2-1 The measured return loss of an optimized two-layer RAM.
8
10
After the balance of all the attenuations o f absorbing components, we need to check
the electric connectivity. The processes are the same as in chapter 3 section 2,3, and 5.
To table all the volume fractions o f absorbing components and their coordinating return
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141
losses to obtain the optimized formula is the powerful and direct way. The realization of
EM properties o f each absorbing material is the first step and essential requirement.
Magnetic components are used only in special cases because o f their high density, and
poor chemical resistance.
In "Hybrid RAM" (frequency region from 100 MHz to 18
GHz) we put spinel ferrites layers, the magnetic layer, on the metal surface and add
dielectric layer on the magnetic layer.
The dielectric layer contains carbon black,
conducting fibers metal flakes, and micro-carbon coils. The absorbing performance of
hybrid RAM was discussed in chapter 3 section 6 .
In chapter 3 section 3, we observed that carbon black plays an insignificant role when
compared to the attenuations o f conducting fibers and metal flakes, and it is easy to
realize impedance match by graded concentration for broader frequency region.
Therefore, in practical applications, we just balance the attenuation o f conducting fibers
and metal flakes, then blend with binders such as polyurethane elastomer, microballoon,
chopped glass fibers etc.
Normally the physical properties o f composites follow the rule o f mixture: If we
assume V / , V m are the volume fractions o f fillers and matrix respectively, and X c , X f ,
X m are the physical properties o f composites, fillers, and matrixes respectively, we can
use following formula [1 1][63]:
Young's modulus: E c = V / E / + V m E m
Tensile or other strengths: S c = V / S r + V m S m
Conductivity: a c = V f crf + V m a m
Traditional permittivity: e c =W f s f + V m s m
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142
Recent empirical results confirmed the practical values o f the permittivity of
composites, which can better be approximated by using empirical formula:
log \ec \ = V f l o g l ^ | + V m lo g \ s j
Where \ s c \ , \ e f |, \em\ are the magnitudes o f the complex permittivity o f composite,
fillers, and matrix respectively.
For phase angle: S c = V f S f + V m S m
Although it is known that the strength o f the orientational filler composites is better
than that o f unidirectional or bi-directional (random distribution) composites, random
type is preferred because of the big difference in the polarization o f EM wave due to the
orientational arrangement of scattering reflectors.
Generally, the reinforced components such as PU elastomer, microballoon, and glass
fiber have very small effects on EM properties in the frequency region below 20 GHz.
But their existence will make the concentrations o f original absorbing components
become dilute following the above mixing rules.
By using above physical properties, we can easily control all the parameters and
match impedance from air (377 Q) to metal base (0 Q) and obtain a very broad frequency
absorbers. Fig. 5.2-2 shows the measured return loss of a balanced sample. Its absorbing
performance covered frequency over 10 GHz with -20 dB return loss for -20 dB. The
thickness o f this sample is 6 mm, filler loading is 1.5 kg per sq. meter, and is processed in
a two-layer processing.
elastomer,
The sample contains reinforced components such as PU
microballoon, and glass fibers, and absorbing components such as fibers,
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143
aluminum flakes and carbon black. Their concentrations have gradually decreased from
rear layer (metal backed) to front face layer (face to air) [15].
OdB
Return loss
-lOdB
-20dB
-30dB
8
10
12
16
Frequency (GHz)
18
Fig. 5.2-2 A modified dielectric materials EM absorber
after the balance o f component's attenuation
showing the broad band absorption.
Magnetic attenuation a m, will be used independently as bottom layer for "Hybrid
RAM", or as front-face layer with their high and
r | = \/ur\ (It makes | rjr | = 1 to match
the impedance o f air.) EM properties. Because longer fibers entangle with each other,
shorter microcarbon chirals with average length o f 0.2 mm are used. They have other
special EM properties due to their chiralities. In this thesis we use micro-carbon chiral
fibers as assistant absorbing additive.
In this attenuation balance process, the
consideration of frequency effect is not required.
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144
5. 3 The thickness criterion for EM wave absorbers
In the engineering o f absorbers, to control the thickness o f applied material is an
important topic for quality control. From chapter 2 we know that thickness plays an
important role in the absorbing mechanisms and by increasing only the thickness the
absorption can not increase. On the other hand, increasing thickness will cause serious
physical problems for some objects, especially for high-speed vehicles. Loading is the
other problem for aircraft. Reduction o f the thickness and loading (involving density) are
the main responsibilities in manufacturing the EM wave absorbers [42].
5.3.1 The optimized thickness o f metal backed single layer absorbers
In many circumstances, narrow band absorption is enough, especially X band,
8
GHz
to 12 GHz for fire control radar system. Either dielectric system or magnetic component
can cover this band with -15 dB return loss requirement by a single layer. This single
layer processing is easier to control and has few physical problems. Usually, thickness is
the only parameter to control after the composition is fixed, and smaller thickness has
fewer physical problems.
For most o f practical applications, absorbers are used to cover a reflector, a perfect
electric conductor. If the backed materials is not a perfect conductor, for example "Fiber
glass reinforced plastic" or other dielectric materials, the EM wave absorbing
mechanisms are different. In our experience, these cases are easier to treat than that of
metallic objects, since the non-total reflection background gives us more space to absorb
EM wave energy.
In the case o f single layer thickness, consider the metal backed diagram in Fig. 5.3.1-1.
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145
absorber metal
A
air
A
SI
// 2
C7—>00
EoHo
motion
0
02
rO
A
XI
E~X2
J
d,
Fig.5.3.1-1 Single layer on metal surface.
First, in region 3 the surface o f metal, Z 3 (0) = 0 = 77
A
and the intrinsic impedance o f absorber is
reflection ratio
f
2
(d2) = [ ( Z
r , (0 ) = T
I
Where Y2 = a
2
+ j P 2= j
2
A
3
(0 )-
7 3
7
A
3
(perfect conductor)
A
2 = [ fj. , / e 2 ]
) / ( Z 3 (0 ) +
7
,
3) ] = -1
(d2 ) exp 2y 2 ( 0 -d2 )
(5.3.1-1)
A
5-2
=j
(5.3.1-2)
^2
and k 2 is the "wave number ". From above equation we know k
f
Where y 2 = a
2 (0
) = T 2 (d2 ) exp- 2 y 2 d2 =
-1
exp - 2 y , d2
A
2
+ j P 2, fornon-magnetic materials //
(5.3.1-3)
2
2
k
= 1, and p 2 = —
Z2
A,
If the single layer thickness is d , = —s such that
4
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146
r
2
(®) = ' l ex p -2 o r 2 d 2 « e x p -2 (— )(— ) = e x p - 2 a 2 d 2
A., 4
A
from equation (5.3.1-4), we find that when d 2 = - j A
completely (- rt). This phenomenon states that the —
4
(5.3.1-4)
the phase of reflection changes
thickness of non-magnetic RAM
makes the phase o f reflection become a total interruption phase to the incident wave.
It
should be the optimized thickness o f the RAM.
The total-impedance o f top layer surface in air region is
z , ( 0 ) = z 2(0)=
7 , [ ( 1 + f 2( 0 ) ) / ( i - r 2(0))]
and the reflection ratio o f surface is
r , (0 ) = ( Z , (0) -
7
o ) / ( Z , (0) +
7 0
) , where
7 0
= 377 [ Q ] .
A
For magnetic absorbing components, //
I
A
A
2
* 1, generally /j.
2
is the complex
A
parameter, y 2 = j co-\j^2 £ 2 = j k 2 . Similar process is following until (5.3.1-3), the totalimpedance o f top layer surface in air region is
7
/m
Z , (0) =
A
7
,
l + r 2(0 ) _ l + e x p -2
expy,d,-exp-y^d-,
-------- ------- 7 , ----------------- =-^=- = 7 , — - - ~------- -— ~
l - f \ (0)
* 1 “ eXP“
2^2
* eXP r 2 ^ 2 + eXP~ Y 2d 2
Z 2 ( 0)= Zi ( 0 ) =
7 2
tanh y 2</2
(5.3.1-5)
Equation (5.3.1-5) is also called short circuit measurement o f impedance.
The reflection ratio o f surface is
T , (0 ) = ( Z , (0) -
7
o ) / ( Z , (0) +
7
0), where
7 0
= 377 [Q].
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147
For magnetic absorbing component, the permeability is a complex variable having
A
real and image parts.
We define
A
n r ,£ r
the relative complex
permeability
permittivity respectively.
*
LI
Mr =
Mo
■
= O r
a
~ JMr )
^
£ r = -------= & r ~ j S r " s )
£0
where / / 0, s 0 are the permeability and permittivity in free space.
tanh(y , * / , ) - 1
£r
Combining (5.3-5), f , (0 ) =
(5.3.1-6)
anfo(y 2d 2) + \
£r
Maximum absorption at
T = 0 or
t a n h( j ^
S r
d, )=
1,
A
,
. 2 /r . 2 n F* ~
where y 2 = j — = j — yjMr £ '
A
-)
/V Q
In practical application, d , « X, when w «
Such that
1, tanhw s w.
nr
I n I* *
H
2n ,
— (J - T ^ H r S r d , ) = 1.
~ (J — d 2 ) = U ° r
*r
^
1
•' 2 n
Simplified to be j /ur — d , =
1
2n
By substituting /ur into above equation, we obtain j — d 2 ( f i r - j/ur) = 1.
2 -n
2n , . .
° r
y
d 2 (j
•,
Mr + M r )
,
= 1-
(5.3.1-7)
An
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and
148
In practical application, we use magnetic component with / / r »
fi r. From (5.3.1-
7), when the thickness d 2 = —
} a minimum reflection in magnetic media composites
2nHr
will be resulted.
From the above two mathematical analysis, we can conclude that a quarterwavelength thickness is the optimum for dielectric absorbers; for magnetic absorbers, the
required thickness may even exceed a half-wavelength for a minimum reflection.
It is common to use a single layer metal backed microwave absorbent material. It can
be tuned for maximum performance by applying a quarter-wavelength thick layer. But
for magnetic absorbers, it is different as shown in equation (5.3.1-6). Eugene F. Knott
made a mathematical approximations in his paper "The Thickness Criterion for SingleLayer Radar Absorbers "[42]. The magneti absorbers have the maximum absorption at
near half-wavelength thickness, and for materials with \jur\ = | f r |, the return loss
A
increases with increasing thickness.
A
Because its front-face impedance, Z i( 0 ) = ^ , =
, makes face reflection
A
A
Zi(0)-7,
A
—» 0.
This means all wave energy incidences into the
Zi(0)+77,
material, and its absorption performance just depends on the lossy depth.
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149
5.3.2 The thickness o f multi-layer absorbers
From the above mathematical analysis, we know that the reflection ratio depends on
the total impedance o f the surface o f the absorbent layer, and it also depends on the
intrinsic impedance o f absorbent layer and its thickness.
In order to obtain a high
reflection loss, the absorbent layer must match the free space impedance (377 Q) and
metal impedance (0 Q) for a broad frequency band. It is very difficult to use single layer
to match such a big difference o f impedance.
Therefore, multi-layer type of high
reflection loss absorbers offer broadband absorption [45] [48].
It is common to put the low impedance layer as the first layer to match zero
impedance object, usually a metal.
The dielectric absorber layer contains higher
concentration of dielectric components such as carbon black, conducting fibers, metal
flakes and /or micro-carbon chirals.
Material with impedance o f nearly 377 Q
(impedance o f air) is used as the front layer facing air. The middle layers have impedance
between metal (0 Q) and air 377 (0 Q).
Fig. 5.3.2-2 shows a multilayer system
represented by a three-region situation. The lossy layers are assumed good enough due to
their high attenuation constants except for the first layer which is backed by a metal. The
reflection o f region 3 can be neglected. This approximation is valid in the frequency
region from
8
to 18 GHz, and 5% correction is required in practical engineering.
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150
region
region
1
f*\ ?^1 5O'I
157
motion
region 3
2
^ 2, £ 2,ar2, y 1,T]2
0
metal
Fig. 5.3.2-2 The thickness o f medium layer in multilayer system.
From point 0 , , consider the continuity condition, the total field impedance on the surface
(region 1 ) should be
^ (0)
I'm - Z
^ 2(0)
r m - t]2
n l + ra2 (°) Z\
1
1
tj2
- T 2 (0 )
1
+ r- ^ ) e x p - 2 y 2d
1 -r:(rf)e x
p - 2 y 2d
where
f !(d )
=
Z z ( d ) + tj2
A
A
A
Since at the interface between region 2 and region 3, Zz(d) = Z 3 ( 0 ) = rj2,
A
A
f , « o - 71 ~ -'h A
A
>73+ >72
A
A
l + Hl
A
A
>73+ >72
Z\(0) = rj2
1
A
A
>73
>72
A
A
A
*
A
(>73 + >72 ) + (>73 — V2
( 7 3+ > 7 2 ) - ( 7 3 - 7 2 ) e '2r3rf
>73+ >72
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151
A (73+
= n2
17^)^rid + ( 7 i - n->)e~
rid
—
( 5 .3 .2-i)
( r } 3 + r j 2 ) e r 'd - ( t j 2 - T)2 ) e ' r '-d
e 0 + e~ e
If we use the hyperbolic cosine and sine function defined by cosh = -----
and
,
e* + e'*
sinh = ------------ , equation (5.3.2-1) becomes
1
^ . ( 0 ) = 772
T l ^
+ d-^-d ) + Tj2{e^d - e ~ ^ d)
rj 2 ( e r '-d
- e ~ r'-d )+T1^ e r'-d +e~r'd)
--------------------------------------------------
A n, coshr,*/-f- n , sinhy,<i
n 2 a ------7 s------ —
7 3 sin h y 2d + rj2 coshy 2d
(5.3.2-2)
The minimum reflection will be obtained if we know the EM parameters, and control the
optimized thickness d. I f region 1 is air, and the permittivities and permeabilities are
I
known, let
y
A
2 = jeo-\j^i2
A
s 2=j
2n
A
A
— , Zi(0) = rj „ = 377 Q , and
X
A
rj 2
can be obtained from
,
measurement, then substitute these parameters into equation (5.3.2-2), an optimized
thickness d will be obtained.
In some cases, the objects are not metal backed directly, for example, the fiber glass
reinforced plastics (FRP) as shown in Fig.5.3.2-3, The non-conducting, and nonmagnetic
composites are lossless from 2 GHz to 18 GHz.
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152
motion
Fig. 53.2-3 Special case in theory but very common in practical application,
where part a is the lossless reinforced or protecting lay er, part b
is the R A M , part c is the non-metal structure region such as FRP
part d maybe is the space or other honeycomb regions , and part
e is the metal region such as engine , electronic system.
The lossless region a in Fig. 5.3.2-3 can be considered as region 2 in Fig. 5.3.2-2 with
thickness o f a quarter-wavelength thickness, — .
4
2
k
y 2 = a 2 + y'/?, = j/32 = / —
and
77,
( lossless a 2 = 0 ),
=rj2 = — is pure real. ( s2 is 2 to 3.5 for common FRP.)
V £■>
Such that y 2d = j f i 2d =
=
= 1, e
= -1.
Then equation (5.2.2-2) can be rewritten as
(n> +n2)eJ*12 +(>73_
Z i(U )- rj2 —------------------------------(;J]i+n2)ejzi:1 -(.ri^-Ti2)e-J*n
^ _
_
j i n i rj2
+nJ-K—
v i --------------nz)
--------j(rj3+ rj2) + 7(73“ ^ 2 )
_________
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153
(5.3.2-3)
y'2^3
In Fig. 5.3.2-2, region 1 is air or upper layer, region 2 is medium layer, and region 3 is
lower layer. In Fig. 5.3.2-3 upper, medium and lower layers are air, region a and b
respectively. Generally, the impedance o f medium layer is:
(5.3.2-4)
where
is the intrinsic impedance o f middle, upper, and lower layer.
For a two-layer absorber, its impedance o f first layer is 42 Q, and that o f air is 377 Q.
Therefore we make the second layer (or part a, protecting layer in Fig. 5.3.2-3) a quarterwave thickness and having the impedance o f
[(42 ) (3 7 7 )]
=126 Q .
Then we can obtain highest reflection loss. Due to the loading reduction o f the flying
vehicles, FRP composites are frequently used as structure. If the reinforced fibers are
glass fibers or Kevlar 49, equation (5.3.2-4) can be used in the FRP backed areas. But for
conducting fibers such as carbon fibers (or graphite fibers), boron whiskers, reinforced
composites we can not used this equation, because they are good reflectors for EM wave.
In practical applications, the thickness for dielectric components does not exceed a
quarter-wavelength. If the dielectric constant o f layer is e , then the wavelength in this
region is
. Therefore in order to reduce thickness we added some high dielectric
constant materials to the matrix such as BaTiC>3 or SrTiC>3 . The drawbacks due to the
addition o f these high dielectric constant materials are that the tensile strength of
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154
composites will be decreased and the density will be increased. It is absolutely necessary
to conduct proper control while adding high dielectric constant materials into the matrix.
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155
5.4 Manufacturing methods o f microwave absorbers
The processing difference between microwave absorbers and FRP composites is that
EM properties o f the materials must be considered as well as their mechanical strengths.
This is the greatest challenge for engineers who design RAM. For example, the outside
layer facing air should have impedance near that o f air 377 Q. In normal practice, raw
materials with impedance near 377 are filled with air bubbles or magnetic powder to
match the air impedance. The magnetic powder has high density, high permeability, high
permittivity, and | pr | = | Sr I •
The bubble-filled composites have poor compressive
strength and other mechanical properties.
The high concentration magnetic powder
composites have poor fatigue resistance and low flexibility. Generally, the surface layer
should posses the best mechanical properties such as high compressive strength, shear
strength, tensile strength, and very good flexibility. The solutions are to use different
methods in processing and optimization o f formulas. In Section 5.2.3, we studied the
special case o f a lossless layer and non-metal backed system, which is a practical
requirement for aircraft RAM coverage.
Kevlar 49 cloth reinforced epoxy layer is a
lossless and non-metal backed material having high strength coverage.
If we don't
consider the optimization o f thickness, we will end up with a worse absorbing
performance composites although this layer is " lossless ".
5.4.1 Spraying
Spraying is the most common and the easiest way to apply materials onto the
object surface. This process is always used with magnetic RAM, and their thicknesses
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156
are very thin, less than 1 mm. Proper dispersion o f a spraying solution is very important
because of the big difference in density between polymer resin (binder) and magnetic
powders (absorbing components). Proper viscosity will also control the bagging flow
when objects are vertically processed. There are two kinds o f spraying, air spraying and
airless high pressure spraying. In air spraying, the material paste material is sprayed with
about 150 psi compressive air, the viscosity o f the paste should be low, therefore the solid
concentration is low also. A 0.5 mm thickr dried layer needs 10 times of air spraying
processes as a minimum requirement. In airless high pressure spraying, the paste at very
high pressure (over 1000 psi) is directly applied onto the material surface through a
nozzle, a spray gun.
In airless high pressure spraying, we can use high solid
concentration paste. A 0.5 mm thick layer can be obtained by spraying twice. Too much
solvent often causes the separation of powders with different densities in the paste.
Therefore when we use airless high pressure spraying process we always ensure that the
selected absorbing magnetic components have relatively small difference in density. In
air spraying, except for very thin thickness, it has the drawback o f causing serious air
pollution.
For dielectric absorbers, the spraying process is always used for applying the top
protecting layer on the RAM finished objects. The thickness is about 0.01-0.03 mm only.
For complex shape objects or large and vertical targets, traditional spraying always
has problems pertaining to bagging flow and uniformity.
Furthermore, pure small
particulate fillers such as magnetic powders, or small metal flakes in matrix can not
increase tensile strength, blending strength, or fatigue resistance. The solution for the
above problems is to add glass fibers (or Kevlar fibers) in the spraying process. Fig. 5.4-
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157
1 is a special spraying equipment which can cut fibers and spray the resin mixing paste
instantaneously.
M
Fig.5.4-1 The special spraying equipment which can spray the resin
mixing paste and chopped fibers instantaneously [63].
The spraying process is such that it is impossible that it will have bagging flow
during the processing. Even when spraying the mixing paste onto the vertical surface o f
large targets, the spraying layer (wet) yet is stable and fixed. Also the homogeneous
distribution of chopped glass fibers will improve the tensile strength, blending strength
and fatigue resistance significantly. The spraying method shown in Fig. 5.4-1 was also
used in preform molding process as first step.
5.4.2 Lamination
For dielectric EM wave absorbing materials, lamination is the simplest and the oldest
processing.
It has an advantage o f easy control o f EM properties and mechanical
strength, especially for small samples and sharp edges. To setup a processing mechanism
is a complicated and important step for complex objects. Lamination in step by step
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158
progress to build up the mechanism is the only way for mass production o f practical
complex targets in RAM engineering.
In traditional composite processing, we always use fabric or mat, cloth saturated with
liquid resin in such a way that the lay-up was made by building layer upon layer to obtain
the desired thickness. This kind o f composites has very high mechanical strengths due to
their high volume fraction o f orientational reinforcement. But for EM wave absorbers,
especially containing anisotropic random
scattering reflectors, the orientational
arrangement o f absorbing components will cause a big difference between different
polarizations.
This phenomenon is not desirable.
Random distribution o f absorbing
components makes perfect return loss for different incident angles. Chopped fibers are
good option for this reason. Multilayer processing even for same formula material is also
done for the same reason. The direction o f scrape should be converse for different layers
to prevent the orientation o f anisotropic absorbing components [13].
The length of reinforced chopped fibers needs optimization also.
Basically the
tensile strength is proportional to the length o f reinforced fibers. The problem arises
when we use too long chopped fibers, the difficulty o f process increases. 6 mm length
and 60% volume fraction combined with 2.8 mm length and 40% volume fraction is the
optimization according to the results o f our experimental observations.
When we use one component PU elastomer (thermal plastic) as the binder, we
don't need to worry about plot-life issue o f resin. The solvent o f PU elastomer is the
combination o f Methyl ethyl ketone (M.E.K.) 85% and Dimethyl formamide (D.M.F.)
15%. In the processing, while the working paste dried we just added M.E.K. to control its
viscosity, because M.E.K. is the highly volatilized solvent, easy to escape at room
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159
temperature. D.M.F. is o f low volatilization and is also toxic for human body. Therefore
the manufacturing plants should be should have good ventilation system. [33].
Before lamination, a thin protecting layer is applied onto the surface of targets,
especially metallic surface. This will improve the adhesion between RAM and objects
surface. Epoxy resin is a good option. RAM is applied after drying o f the primary layer.
After drying o f each layer, we need to check the absorption level o f material. If the
target is a complex object, it is necessary to conduct image measurement from different
perspectives. In general, each target needs at least two hundred image pictures to confirm
o f the EM wave absorption quality. Defects always exist at leading edge, rudder edge,
cockpit, and inlet or nozzle.
Except for RAM, these defects need RAS (radar wave
absorbing structure) to overcome the creep return wave and scattering o f sharp edges.
The final layer (face to air) should be polished after surface drying.
Therefore,
excess thickness o f the top layer is required. Generally, 0.25 mm to 0.5 mm for small
objects or flat plates, 0.5 mm to 1 mm for large targets or sharp edges are polished. In
polishing process, RCS measurement or image measurement at any time is necessary.
Over polish at edges are very popular defects.
Before next layer is processed, the applied layer on surface must be dried out
completely, because the solvent o f inside layer will be more difficult to escape after upper
layer is applied. Organic solvents, such as M.E.K. and D.M.F. have partially reflecting at
10 GHz to 16 GHz. They will interfere with the return loss test and thus confuse the
mechanism of processing if they remain in RAM while measuring.
Normally one
component resin is dried at room temperature, but sometimes forced drying is necessary.
Far infrared lamps (thermal radiation heaters) combining with electric fans (forced
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160
convection) are frequently used to accelerate the drying o f applied materials. Organic
solvents are flammable and should be processed in open air or in surroundings which
have forced convection.
5.4.3 Preform molding
For mass production o f practical targets or large objects and removable RAM,
preform molding is the best way. For example, it is not easy to hang the target and then
carry out the microwave imaging for an aircraft or even a bomber although it is possible.
For a warship, it is impossible to hang the target and to rotate it to obtain the radar image,
as the weight o f the target will be in the region of about three thousand tons. Preform
molding is the solution [13].
In preform molding, the molds are prepared in the approximate shapes as separated
parts o f the large targets or complex objects. Before the preform molding, we spray the
release agents such as silicone emulsion onto the mold surface for easily separating the
RAM and molds after curing. Next, we preform the RAM by applying the mixture of
reinforcements and absorbing components blending with resin binder onto the surface of
molds. After drying and separation we assemble these different parts and adhere them
onto the practical targets with proper adhesives. The other method is to make the nonmetal backed RAM by previous processes and install the reinforced plastic connectors.
For example, short glass fibers reinforced nylon is mass produced by injection molding.
Therefore, RAM connects with each other and the target surface becomes a removable
RAM system. These removable RAMs are very convenient for naval application or large
complex objects.
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161
Theoreticaly, preform molding can be manufactured by extrusion and injection
molding.
Because the operational paste contains microballoons, these high pressure
processings are not preferred. For very low frequency (below 1.7 GHz) layer, generally
we don't use microballoons.
To reduce the propagating wavelength to obtain thin
absorbing layers, high dielectric constant powders are used to replace the microballoons.
This absorbing layer in hybrid RAMs plays an important role and is always installed at
the bottom layer. Extrusion and injection molding can be used in manufacture [63].
The removable RAM systems are generally used in naval fields or movable army
facilities. The design o f this RAM must be considered in such a way that total weight o f
each separated part is not over 20 kg in order to be delivered and installed by a single
person or by two as in some cases as a matter o f convenience. In order to enclose the
targets tightly with RAM, for some objects hooks are added on the surface o f targets.
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162
CHAPTER 6
CONCLUSION AND FURTHER STUDY
6.1 Conclusion
Current commercial electromagnetic wave absorbers satisfy most o f the
requirements, because their mechanical strengths, thickness, loading, and even
environmental conditions are not considered seriously.
However, for military
application, there are many problems to be overcome. The first problem is loading,
especially for aircrafts and missiles. These targets are very sensitive for their weights
due to dynamic balance and energy potential. The second problem is the thickness.
Even the targets have enough energy potential and adaptive balance, too high
thickness will cause physical problems. For example, the gradient o f shear strengths
along the depth will increase with increasing thickness. This problem will cause the
distortion of the RAM after certain period o f usage, and finally separate with target
body. The third problem is the frequency region. Modem electronic technology has
developed advanced detectors (or sensors) that operate at frequencies much broader
than that of the former. New fighters have automatically jumped pulse radar to check
targets o f the enemy in the frequency region from 2 GHz to 18 GHz in one
equipment. Such a broadband EM wave absorbing performance is very difficult to
achieve, especially for more than -20dB return loss over the whole frequency region
with a light, high strengths and thin RAM.
The fourth problem is temperature
durability.
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163
For magnetic absorbing components, especially X band absorbing ferrites, the
hexagonal ferrites, have very low Curie temperature, about 150° C or lower.
If the
operational temperature is over their Curie temperatures there will be irreversible changes
(always reductions) o f the absorbing performance.
Fig. 6.1-1 is the return loss of
multilayer (3 layers) magnetic RAM, which was composed o f different doping
concentration o f C o +2 onto the hexagonal ferrite P b F e ,,0 I9. Their Curie temperatures
are about 145 °C .
When the operational temperature reached 200 °C , the return loss
changes even after cooling down.
It losses the absorption as shown in the previous
condition for the same temperature.
Return 0 dB
loss
-5 dB
-10 dB
-15 dB
-20 dB
-25 dB
-30 dB _
-35 dB
2
3.6
5.2
6.8
8.4
10
11.6
Frequency (GHz)
13.2
14.8
16.4
18
Fig. 6.1-1 The return loss and temperature dependence of magnetic RAM. ( Doping
C o+2 hexagonal ferrite P b F e ,,0 19, its Curie temperature is 145 0 C .) Solid
line showed the return loss at room temperature , dashed-dot line showed the
return loss at 200 0 C. This absorption change is irreversible!
------------- room temperature (250 C)
—
2000C
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164
0 dB
Return
dB
loss
-10 dB
-15 dB
-20 dB
-25 dB
-30 dB
-35 dB
2
3.6
5.2
6.8
8.4
10
Frequency (GHz)
11.6
13.2
14.8
16.4
18
Fig. 6.1-2 The return loss and temperature dependence o f dielectric RAM.
The absorbing components are carbon black, aluminum flakes, carbon fibers.
This absorption change is reversible, when temperature cool down the return
loss will go back! The solid line showed the return loss at room temperaturer
The dash-dotted line showed the return loss at 200 0 C.
--------------
room temperature (2 5 0 C)
------
— 200 °C
Fig. 6.1-2 shows the return losses at room temperature and high temperature
(2000 C).
Except for the small difference in return loss, the change o f absorption is
reversible.
So in high temperature or unstable temperature environments, dielectric
RAMs are good option if the thickness is not critical.
6.2 Further study
At low temperature, PU elastomer matrix RAMs have good mechanical strength due
to their very high flexibility below glass transition temperature. But at high temperature
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165
(over 2 000 C) PU elastomer will lose their tensile modulus and compressive strength.
When the flying vehicles fly at an altitude below 10.000 ft with super sonic velocity, their
surface temperature (especially at leading edges) will rise up to 200 °C or higher.
Furthermore, high flying speed o f new missiles, which is higher than 5 times o f the sonic
velocity, causes their surface temperature to rise up to 1000 °C. At high temperature,
ceramic matrix reinforced by silicon nitride fibers composites is a good option to replace
the PU elastomer reinforced with glass fibers. But the weight and fatigue resistance will
be the new problems of ceramic matrix. Tile ceramic RAM is one o f the solutions, but
adhesive strength for super sonic vehicles also needs to be improved.
In some cases, -20dB return loss is not enough, such as in a dog-fight situation. The
fire control radar in short distance are very sensitive.
necessary.
Over -40 dB return loss is
Dynamically adaptive RAM combining with the passive RAM is a good
suggestion in improving the absorption in fire control frequency.
Above problems and suggestions will be the topics o f study and research for the
future. Better sintering facilities o f ceramic and some corresponding equipment for the
development o f polymers for dynamically adaptive impedance matching will be required.
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166
APPENDIX
Tested samples
Summary Result
Absorbing
Component
Aluminum flakes
# o f Samples Absorbing Return Loss Thickness Purpose
Average
Frequency
(mm)
(-dB)
(GHz)
6
8-12
5 - 10
2
find opt.
vol. fraction
Carbon fibers
8
8-18
6-20
4
find opt.
vol. fraction
Carbon black
6
8-18
3 - 15
6
find opt.
vol. fraction
Microcarbon chirals
4
8-18
3 - 20
3
find opt.
vol. fraction
Ferrites (hexagonal)
4
8-12
15-25
3
practical use
Copper wire spring
6
8-12
3 - 12
3
find opt. pitch
Copper wire spring
Aluminum flakes
Carbon fibers
4
8-12
5-20
4
find opt.
vol. fraction
Aluminum flakes
Carbon fibers
4
8-12
7-15
3
comparison
Copper spheres
4
8-12
2 -7
1.5
comparison
Copper spheres
Carbon fibers
Aluminum flakes
4
8-12
3-10
1.5
comparison
Aluminum flakes
Carbon fibers
Carbon black
12
8-18
15-25
6
practical use
6
8-18
20-28
Aluminum flakes
Carbon fibers
Carbon black
Microcarbon chirals
6
practical use
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167
Aluminum flakes
Carbon fibers
Carbon black
Aluminum flakes
Carbon fibers
Carbon black
Barium titanate
Carbon black
Carbon fibers
3
4
3
2-18
15-30
25
practical use
8-18
17-25
2.5
practical use
4
temperature
resistance
tests
8-18
10-24
* The matrixes o f above samples all are PU elastomer blended with ceramic
microballoons and reinforcing materials are chopped glass fibers.
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168
References
[1] “Electromagnetic Wave Absorbers and Anechoic Chambers Through the years” by
William H. Emerson. IEEE Transactions on antenna and propagation , vol. ap-21 no. 4,
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[2] “Schomsteinfeger“ by H. A. Scade. U.S. Tech. Mission Europe, Tech. Rep. 90-45
AD-47746, May 1945.
[3] “Broadband absorbing materials for use in darkrooms" by R. W. Wright and W. H.
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[4] “Method and means for minimizing reflection high frequency radio waves" by O.
Halpren, U.S. Patent 2 923 934.
[5] “Absorbent body for electromagnetic waves“ by w. w. Salisbury , U.S. Patent 2 599
944, June 10 , 1952.
[6] “Anechoic chamber for microwaves" by A. Simmons and W. Emeson. Tele-Tech, vol.
12, no. 7, July 1953.
[7] “Stealth Bomber" by Bill Sweetman, Airlife England, 1989.
[8] “Engineering Electromagnetic Fields and Waves" by Carl T. A. Johnk second edition,
John Wiley & Sons, 1988.
[9] “Elements o f Electromagnetics" second edtion by Matthew N. O. Sadiku. Oxford
University Press, 1995.
[10]“Dielectric Materials and Applications" by Arthur von Hippel ,Artech house. 1954.
[1 l]“Microwave Materials44 by V R K Murthy, Springer-Verlag, 1994.
[12]“Dielectrics and Waves44by Arthur von Hippel, Artech house, 1954.
[13]“Fundamentals o f Composites Manufacturing44 by Dr. A. Brent Strong, Society
Manufacturing Engineering, Dearborn, Michigan 48121, 1989.
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VITA
The author was bom in Taiwan in Dec. 1949.
He obtained his BS degree of
Chemical Engineering from Chung Yung University, Taiwan, and his MS degree of
Chemical Engineering from National Center University, Taiwan.
He had been an
instructor in Haw-Shang Institute o f Technology, Taipei. He left college and worked in
chemical industry in 1982, and had been an engineer, chief engineer, head o f R & D
department, factory manager, and general manager o f several companies. He had full
working experience in polymer composites field.
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