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Resistively-loaded antenna designs for ultra-wideband confocal microwave imaging of breast cancer

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Resistively-Loaded A n t e n n a Designs for
Ultra-Wideband Confocal Microwave
Imaging of Breast Cancer
Houssam
Kanj
^ l i l yp
JL# ILif
Department of Electrical & Computer Engineering
McGill University,
Montreal, Quebec H3A 2A7, Canada
December 2007
A thesis submitted to McGill University in partial fulfillment of the requirements for
the degree of Doctor of Philosophy.
© 2007 Houssam Kanj
2007/12/10
1*1
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1
Abstract
Confocal microwave imaging (CMI) has recently been suggested as a screening method for
early detection of cancerous breast tumors. This recently proposed detection and imaging
method relies on the dielectric properties differences between malignant and healthy breast
tissue at microwave frequencies (1-10 GHz). A pulsed signal is launched by a transmitting
antenna on the skin surface to penetrate into the underlying tissues. As the pulse encounters
the tumor, it reflects off the malignant lesion and the reflection can be collected by a
receiving antenna on the skin surface. The narrower the pulse signal used, the smaller
the detectable tumor would be by such a method. However, as the narrow pulse contains
a wide frequency range, the trans-receiving antenna must exhibit a broadband behavior.
Further, it was recently demonstrated that a higher-resolution image can be obtained if
a single antenna-element is replaced by a suitable antenna array. In addition, research
indicates that further improvement of microwave breast cancer detection systems is possible
by sensing the cross-polarized backscatter reflections from the malignant lesion. For this
application, a compact broadband antenna design is a fundamental element of the system.
Such a design will enable the development of the desired array with a large number of
cross-polarized antennas.
Motivated by this application and many other similar applications, such as biological sensing, through-wall imaging, ground-penetrating radars and fixed surveillance, this
dissertation focuses on the design of an ultra-wideband (UWB) ultra-compact low-profile
resistively-loaded antenna easily manufactured by standard printed circuit board (PCB)
means with embedded passives. First, a planar antenna design, named "Dark Eyes", is
presented. The antenna takes advantage of constant resistive loading in combination with
favorable antenna geometry to achieve its broadband behavior. Second, the antenna is
miniaturized to centimeter size while maintaining a comparable performance to that of the
original one. Third, a complete microstrip-feed for the miniaturized "Dark Eyes" antenna is
presented. Then, the antenna is studied in a cross-polarized arrangement for tumor detection and the advantage of this approach is demonstrated. Finally, a novel antenna design
with an extremely broadband behavior and a very compact size is presented. This new
design is simpler than the "Dark Eyes" antenna with an order of magnitude improved performance. Such a design is a key element in developing the multistatic microwave imaging
system with a large number of cross-polarized antenna-elements.
11
Sommaire
L'imagerie micro-onde confocale (CMI) a ete recemment suggeree comme methode de depistage
pour la detection de tumeurs cancereuses de sein. Cette methode recemment proposee pour la
detection et formation image se fonde sur les differences de proprietes dielectriques entre tissu
malin et sain mammaire aux frequences micro-onde (1-10 GHz). Un signal pulse est lance par une
antenne de transmission sur la surface de la peau pour penetrer dans les tissus sous-jacent. Quand
Pimpulsion rencontre la tumeur, elle se reflete sur la lesion maligne et la reflexion peut etre captee
par une antenne de reception sur la surface de peau. Le plus etroit le signal d'impulsion utilize,
le plus petit la tumeur discernable serait par une telle methode. Cependant, comme la pulsation
etroite contient une large gamme de frequence, l'antenne de la trans-reception doit exposer un
comportement a bande large. De plus, on a recemment demontre qu'une image a haute resolution
peut etre obtenue si une antenne-element seule est remplacee par un reseau d'antennes approprie.
En outre, la recherche indique que l'amelioration supplemental des systemes de detection de
cancer du sein par micro-onde est possible en exploitant les reflexions de polarisation orthogonale
de la lesion maligne. Pour cette application, une conception d'antenne compacte a bande large est
un element fondamental du systeme. Une telle conception permettra le developpement du reseau
desiree avec un grand nombre d'antennes a polarisation croisee.
Motive par cette application et beaucoup d'autres applications semblables, telles que la sensation biologique, la formation image a travers mur, les radars penetrant GPR et la surveillance
fixee, cette dissertation se concentre sur la conception d'une antenne ultralarge bande (UWB)
ultra-compacte et discrete facilement construite par des moyens standard de la carte de circuit
imprime (PCB) avec des passives incorpores. Premierement, une conception d'antenne planaire,
nommee "Dark Eyes", est presentee. L'antenne profite du chargement resistif constant en combination avec la geometrie d'antenne favorable pour realiser son comportement a bande large.
Deuxieme, l'antenne est miniaturisee a la taille de centimetre tout en maintenant une performance comparable a celle de l'originale. Troisiemement, un complet microruban-alimente pour
l'antenne miniaturisee "Dark Eyes" est presente. Puis, l'antenne est etudiee dans un arrangement
croix-polarises pour la detection de tumeur et l'avantage de cette approche est demontre. Finalement, une conception originale d'antenne avec un comportement extremement a bande large
et une dimension tres compacte est presentee. Cette nouvelle conception est plus simple que
l'antenne "Dark Eyes" avec ordre de magnitude de performance amelioree. Une telle conception
est un element cle en developpant le systeme multistatique de formation image de micro-onde
avec un grand nombre d'antenne-elements orthogonale.
iii
To the memory of Damon Hartung for his brave fight with leukemia.
/-"
IV
Biography
Houssam Kanj received his B.Sc. in Computer and Communication Engineering from The
American University of Beirut in 1999, and the M.Sc. in Electrical Engineering from North
Carolina State University in 2003. His Masters research was in the fields of analog circuit
design and computer-aided modeling of nonlinear circuits including electro-thermal and
lasers. His research interests include numerical methods in electromagnetics and antenna
design.
V
Acknowledgments
I would like to express sincere gratitude to my adviser, Dr. Milica Popovic, for her guidance
throughout my Ph.D. program. I would also like to express my great appreciation to Dr.
Dennis Giannacopoulos and Dr. Ioannis Psaromiligkos for their interest in my research
and for serving on my committee. Finally, I must thank my family and friends for all their
support and encouragement.
VI
Preface
Concerning the Format of This Thesis
This thesis was prepared in the manuscript-format in the form of five self-contained research
papers designated Chapters 3, 4, 5, 6, and 7.
Chapter 3, entitled "Microwave-Range Broadband 'Dark Eyes' Antenna: Detailed Analysis and Design", and Chapter 5, entitled "Microstrip-Fed 'Dark Eyes' Antenna for NearField Microwave Sensing", were published in the IEEE Antennas and Wireless Propagation
Letters journal. Chapter 4, entitled "Strategic miniaturization of the broadband 'Dark
Eyes' antenna for biological sensing", was published in the conference proceedings of the
International Symposium on Antenna Technology and Applied Electromagnetics. Chapter 6, "Two-Element T-Array for Cross-Polarized Breast Tumor Detection" and Chapter 7,
"A Novel Ultra-Compact Broadband Antenna for Microwave Breast Tumor Detection" are
to be submitted for publication.
Three more chapters are added to the above papers to develop a coherent dissertation.
Chapter 1 and 2 are the thesis introduction and comprehensive literature review, while
Chapter 8 provides the summary and conclusion of the dissertation. In addition, five short
single paragraphs are added as a preface and bridging materials to each of the paper-based
chapters.
Contributions of Authors
The applicant, Houssam Kanj, is the primary author of each chapter in this Thesis. Prof.
Milica Popovic has contributed to this work by initiating the initial idea of this research, and
by providing suggestions, guidance and insightful discussions, manuscript editing, support,
and extraordinary supervision through out the work on this thesis. The design development
Vll
and progress, and the interpretation and reporting of the research were primarily performed
by the candidate. Mr. Qingsheng Han, who is a co-author on the paper of chapter 4, was
generous in providing computational resources to run the simulations needed for this study.
Guidelines Concerning a Manuscript-Format Thesis Preparation
According to the Guidelines Concerning Thesis Preparation published by the Faculty of
Graduate Studies and Research at McGill University, a Thesis can be prepared in the
format of published or to-be-published papers. The following excerpts are taken from the
guidelines:
Candidates have the option of including, as part of the thesis, the text of one
or more papers submitted or to be submitted for publication, or the clearlyduplicated text of one or more published papers. These texts must be bound
together as an integral part of the thesis.
The thesis must be more than a collection of manuscripts. All components must
be integrated into a cohesive unit with a logical progression from one chapter to
the next by connecting texts that provide logical bridges between the different
papers.
The thesis must conform to all other requirements of the Guidelines for Thesis
Preparation. The thesis must include: a table of contents; an abstract in English
and French; an introduction which clearly states the rational and objectives of
the research; a comprehensive review of the literature; and a final conclusion
and summary. Additional material must be provided where appropriate, (e.g.,
in appendices) and in sufficient detail to allow a clear and precise judgment to
be made of the importance and original of the research reported in the thesis.
In the case of manuscripts co-authored by the candidate and others, the candidate is required to make an explicit statement in the thesis as to who contributed to such work and to what extent. This statement should appear in a
single section entitled " Contribution of Authors" as a preface to the thesis. The
supervisor must attest to the accuracy of this statement at the doctoral oral
defense. Since the task of the examiner is made more difficult in these cases,
it is in the candidate's interest to clearly specify the responsibilities of all the
authors of the co-authored papers.
Contents
1 Introduction
1.1 UWB Microwave Radar Imaging of Breast Cancer
1.2 Research Objectives
1.3 Dissertation Overview
1.4 Original Contributions
1
2
5
5
7
2 Literature Review
2.1 Introduction
2.2 Broadband Loaded Antennas
9
9
9
2.2.1 The Concept of Loading, The Wu-King Profile
2.2.2 Loading with Purely Capacitive Elements
2.2.3 Antennas Characterizations for Pulse Radiation
2.3 Survey of Broadband Loaded Antennas
2.3.1 Monopoles and Dipoles
2.3.2 Vee Dipoles
2.3.3 Conical and Bow-Tie Antennas
2.3.4 TEM Horn Antenna
2.4 Antennas for UWB Microwave Breast Imaging
2.5
2.4.1 Definition of Antenna Profile
2.4.2 Proposed Non-planar Antennas
2.4.3 Planar Antennas with a Surface Profile
2.4.4 Planar Antennas with a Line Profile
Theory of the Finite-Difference Time-Domain Method
2.5.1 FDTD Theory
10
15
17
21
21
24
25
26
27
28
30
31
33
34
34
Contents
2.6
2.7
ix
2.5.2 Stability of the FDTD Method
Simulation Tools
Summary
3 Microwave-Range Broadband "Dark Eyes" Antenna
3.1 Introduction
3.2 Antenna Geometry and Simulation Tools
3.3 Results and Discussion
3.3.1 Return Loss
3.3.2 Efficiency
3.3.3 Fidelity
3.3.4 Radiation Pattern
3.4
4
Conclusion
Strategic Miniaturization of "Dark Eyes" Antenna
4.1 Introduction and Background
4.2 Methodology
4.2.1
4.2.2
4.3
4.4
Numerical Tools
Antenna Geometry and Parameters
Results
Conclusion
36
36
36
40
41
41
42
42
44
45
46
48
50
50
51
51
51
53
55
5 Miniaturized Microstrip-Fed "Dark Eyes" Antenna
5.1 Introduction
5.2 Design Geometry
5.3 Results and Discussion
5.3.1 Return Loss and Efficiency in the Dielectric Medium
59
60
60
62
62
5.3.2 Near-field Radiation and Fidelity
5.3.3 Return Loss and Far-field Radiation In Air
Conclusion
64
68
70
5.4
6 Two-Element Cross-Polarized T-Array
6.1 Introduction
6.2 Geometry and Characterization of the Two-Antenna T-arrangement . . . .
72
73
73
Contents
x
6.3
6.4
6.5
75
78
81
Layered Tissue Model and Near-Field Radiation
Tumor Response Study of the T-arrangement
Conclusion
7 Novel Ultra-Compact Broadband Antenna
7.1 Introduction
7.2 Antenna Design
7.2.1 Characteristic Impedance of CPS and APS lines
7.2.2 Evolution Steps
7.2.3 Design rules guideline for the TWTLTLA antenna:
85
86
86
90
96
103
7.3
Antenna Characteristics in the UWB range
105
7.4
7.5
7.3.1 Efficiency
7.3.2 Near-field Radiation and Antenna Fidelity
Balun Design
Conclusion
106
106
110
116
8 Conclusion
8.1 Summary and Discussion
8.1.1 The "Dark Eyes" Antenna
8.1.2 The Cross-polarized Card Array Arrangement
8.1.3 The TWTLTLA Antenna
8.2 Future Work
117
117
118
119
119
120
Appendix
121
A Antenna Manufacturing
121
A.l Ohmega Technologies
A.2 The Etching Process
121
122
References
124
XI
List of Figures
1.1
1.2
1.3
1.4
(a) UWB Gaussian modulated sine-wave pulse centered at 6 GHz. (b) Its
normalized spectrum
Illustration of the basic concept of microwave imaging, (a) Transmitted
waves in the absence of a tumor, (b) Transmitted and scattered waves in
the presence of a tumor
Multistatic array configuration suggested in [1]
Multistatic array configuration with: (a) cross-polarized colocated antenna
elements, and (b) cross-polarized adjacent antenna elements
3
3
4
6
2.1 Wu-King resistive profile
2.2 Efficiency of the non-reflecting dipole antenna computed with the "Wu-King"
approximation theory [2]
19
2.3
2.4
2.5
2.6
2.7
2.8
2.9
22
24
24
25
26
27
28
Single element of resistively tapered dipole probe. Adopted from [3]
Resistively loaded quadratic V-antenna [4]
Resistively loaded modified V-antenna [5]
Resistively loaded conical antenna
Photograph of the RC-loaded bow-tie antenna [6]
TEM horn antenna
Horn antenna
2.10 Slot antenna in a finite ground plane
2.11 Tapered slot antenna
2.12 Yee's one-dimensional scheme for updating E and H fields in space and time.
After [7]
15
29
29
35
List of Figures
3.1
3.2
3.3
4.1
(a) Geometry of the resistively loaded "Dark Eyes" antenna. The dimensions are (in mm): a=5, c=5, and <i=35. (b) Illustration of the antenna
orientation in polar coordinates
for (a) Rs = 100n/D, (b) Ra = 200O/D, and (c) Rs = 400O/D
Simulation results for far-field radiation patterns at 3 GHz (a) and (b), 6
GHz (c) and (d), and 9 GHz (e) and (f). Results are shown for both HFSS
and SEMCAD for Ra = 100Q/D
43
47
(a) Sketch of the resistively loaded "Dark Eyes" antenna. In addition to
its role in the overall design, the bowtie-shaped metallic segment facilitates
easier connection with the generator. The tapered resistive section has a
surface resistance of Rs = lOOfi/D. (b) One-half of the antenna sketched in
52
Calculated |T| of the original antenna design (1.1) and its miniaturized versions, where every parameter of Figure 4.1(b) is scaled down by a factor of 2
(antenna 1.2 of Table 4.1) and 4 (antenna 1.3 of Table 4.1). The thin dashed
line shows the normalized spectrum of the input pulse
4.3 Calculated |T| of the original antenna design (1.1) and its strategically (nonuniformly) miniaturized versions. With reference to Figure 4.1(b), parameter
c is kept at the value of the reference antenna (1.1). Parameters a and d are
scaled down by a factor of 2 (antenna II. 1 of Table 4.1) or 4 (antenna II.2
of Table 4.1). The thin dashed line shows the normalized spectrum of the
input pulse
4.4
42
Antenna's return loss Sn in the range 1 to 14 GHz computed assuming a
feed line with Rref = 100R Results are shown for both HFSS and SEMCAD
(a), indicating the dimensions used as design parameters
4.2
xii
Calculated |r| of the original antenna design (1.1) and its strategically (nonuniformly) miniaturized versions. With reference to Figure 4.1(b), parameter
c is kept at the value of the reference antenna (1.1). Result for antenna II. 1
already presented in Figure 4.3 is graphed here for comparison. For antenna
II.3, parameter a is scaled down by a factor of 1.66 and d by a factor of 4.37.
The thin dashed line shows the normalized spectrum of the input pulse. . .
53
54
56
List of Figures
xiii
5.1
Geometry of the microstrip-fed resistively loaded "Dark Eyes" antenna. The
dimensions are (in mm): W\ = W% = W4 = 0.75, W2 = 1.5, W$ = S\ =
S2 = 0.375, Li = U = 1.5, L2 = L3 = 3.75, L4 = 5.625, L6 = L7 = 2.25,
L 8 = 4.5, L 9 = 8, L10 = 6, L = 20, W = 12.75, and * = 0.65. The dielectric
substrate has er — 10.2. The noted coordinate system is centered at the
apex of the antenna
61
5.2
Antenna's return loss S\\ in the 1-llGHz range, computed for a feedline of
Rref = 50fi. The antenna is immersed in a dielectric medium of er = 9.
Results are shown for Rs = 25ft/D,50ftyD, 100O/D and 250fi/D
62
Maximum magnitude of the radiated electric field and its fidelity versus
polar angles at a 3-cm radial distance from the antenna apex: (a), (c) in
the H-plane and (b), (d) in the E-plane. Plots are shown for all four values
of surface resistivity Rs. The antenna was excited with the 1-V pulse. The
data were obtained from the time-domain computations
65
Maximum magnitude of the radiated electric field and its fidelity versus
polar angles at a 3-cm radial distance from the antenna apex: (a), (c) in
the H-plane and (b), (d) in the E-plane. Plots are shown for all three values
of the coplanar stripline section Lg with Rs = 5 0 0 / • . The antenna was
excited with the 1-V pulse. The data were obtained from the time-domain
computations
67
5.3
5.4
5.5
5.6
Antenna's return loss Sn (in air) in the 1-llGHz range, computed for a
feedline of Rref = 50fi, for Rs = 50O/n and L 8 = 9.0mm. Two simulation
tools were used for validation. The discretization with the two methods is
not identical which can explain the small discrepancy in the results
Antenna's co- and cross-polarization patterns in the (a) H- and the (b) Eplane at 6GHz. The maximum cross-polarization in the H- and the E-plane
is -15.9dB and -17.4dB, respectively.
68
69
List of Figures
6.1
6.2
6.3
6.4
(a) Geometry of the microstrip-fed resistively loaded "Dark Eyes" antenna.
L — 20 mm, W = 25 mm, and t = 0.65 mm. The dielectric substrate has
relative permittivity er = 10.2. The resistive loading and the resistive layer
both have surface resistivity of 5 0 0 / • . Full description and analysis of the
antenna can be found in [8]. (b) Proposed cross-polarized T-arrangement
of the microwave sensing array unit, with "Dark Eyes" antenna from Figure 6.1(a) as its main element [9]
74
Simulated S-parameters for the T-arrangement of Figure 6.1(b). (a) Input return loss characteristic Sn. (b) Mutual coupling Si2- The entire
T-arrangement unit is considered to be immersed in a lossless dielectric
medium of er = 10.2, for the purpose of dielectric medium matching with
the fatty breast tissue. Results are shown for SEMCAD (FDTD-based) and
HFSS (FEM-based) simulation tools for comparison and verification. . . .
76
Layered model of the breast showing the T-arrangement, the matching medium,
skin layer, fat, and 9 of the 25 simulated tumor locations
77
Electric field magnitude at a radial distance of 30 mm from the antenna apex
in the layered model of Figure 6.3 at: (a) 3 GHz, (b) 6 GHz, (c) 9 GHz.
The parameters of the fat layer containing the points for which the field is
plotted are as follows: er(3GHz) = 9.95 and <r(3GHz) = 0.21S/m, er(6GHz)
= 9.8 and a(6GHz) = 0.4S/m, er(9GHz) = 9.6 and a(9GHz) = 0.66S/m. .
6.5
7.1
xiv
79
The co-polarized and cross-polarized tumor response (dB) for the different
tumor shapes/orientations. The tumor was considered to be either a sphere
(D=5 mm) or a cylinder with a (D=2.75 mm, H=5.5 mm). The cylinder
is either oriented in parallel with Antenna-1, when we refer to it as CoCylinder, or it is oriented in parallel with Antenna-2, when it is called XCylinder. Results for: (a) and (b) Sphere, (c) and (d) Co-Cylinder, and (e)
and (f) X-Cylinder
82
The original "Dark Eyes" antenna design with its CPS transmission line
feed and the left arm of the evolved TWTLTLA final antenna design showing
parameterization curves and points. Total width of the original "Dark Eyes"
antenna, I'-to-I' (left point of the left arm to right point of the right arm),
is 20mm
88
List of Figures
7.2
7.3
7.4
7.5
7.6
7.7
7.8
7.9
7.10
Return loss Su of the original "Dark Eyes" antenna in the l-35GHz range,
computed for a reference feedline with Rref = 500. The antenna is immersed
in a dielectric medium of er = 10.2. The return loss is below -lOdB in the
3.12-22.48 GHz range
xv
88
Initial idea to combine the CPS line feed and the initial metallic section of
the original "Dark Eyes" antenna to form a single tapered transmission line
section. Two ellipses E\ with semimajor axis a and semiminor axis b, and
E2 with semimajor axis a' and semiminor axis b are used to form the tapered
transmission line section. E\ passes through point A and N' and it is tangent
to line section NT. E2 is a shifted version of E\ that passes through point C
and scaled along its major axis to pass through point M'
Coplanar stripline (CPS) configuration
Characteristic impedance versus frequency for a CPS line printed on a dielectric board with a dielectric constant of ers = 10.2 and immersed in a
background medium of dielectric constant erb — 10.2. The CPS dimensions
are: w = 375/wn, s = 375/im, and t = 70/im. The board thickness is
89
91
h = 0.635mm
91
Characteristic impedance versus frequency for a CPS line printed on a dielectric board with a dielectric constant of ers = 10.2 and immersed in a
background medium of dielectric constant erb = 10.2. The CPS dimensions
are: w = 375/im, s = 200//m, and t = 70/im. The board thickness is
h = 0.635mm
92
Antipodal stripline (APS) configuration with even strip edges
Antipodal stripline (APS) configuration with separated strip edges
Antipodal stripline (APS) configuration with overlaping strip edges
Characteristic impedance versus frequency for an APS line with overlaping
strip edges. The APS line is printed on a dielectric board with a dielectric
constant of ers = 10.2 and immersed in a background medium of dielectric
constant erb — 10.2. The APS dimensions are: w = 375/xm, s = 100/um, and
94
94
95
t = 70/im. The board thickness is h = 0.635mm
95
List of Figures
xvi
7.11 First evolved design. Resistive area is the same as the one used in the
"Dark Eyes" antenna and the total antenna width I'-to-I' is still 20mm.
However, in this design, the CPS feedline and the initial metallic section of
the "Dark Eyes" antenna are merged to form a tapered elliptical transmission
line defined by the ellipses shown in Fig. 7.3. This design shows an improved
return loss at higher frequencies, but a relatively degraded performance in the
lower frequency range. This could be explained by the strong discontinuity
that exist at point M' where both the material and the geometric form change. 98
7.12 Return loss Sn of the first evolved design in the l-35GHz range, computed
for a reference feedline with Rref = 50fi. The antenna is immersed in a
dielectric medium of er = 10.2. This design has a return loss below -lOdB
in the 4.43-28.65 GHz range
7.13 Second evolved design. Here, the line M'N' (border between different material) is pushed back toward the transmission line origin and form the HG
line. The behavior of this antenna improves significantly, however, the resistive area is now quite large which implies lower antenna efficiency. The
antenna width, I'-to-I', remains to be 20mm
98
99
7.14 Return loss Sn of the second evolved design in the l-35GHz range, computed
for a reference feedline with Rrej = 50JT2. The antenna is immersed in a
dielectric medium of er = 10.2. This design has a return loss below -lOdB
in the 1.78-35 GHz range
7.15 Third evolved design. Here, an attempt to reduce the effect of the discontinuity at point M' is executed by pushing it further away on the CI curve
up to point M and making the lossy path that the current has to travel
longer before it intercepts the discontinuity. Then, the total antenna width
is reduced by first pushing point N' slightly back to point N, and second by
extending the line at point N in a tangent direction to intercept the line MI'
at point I". In this manner, the lossy resistive area is reduced. The total
antenna width, I"-to-I", is also reduced to 16mm
99
100
7.16 Return loss Sn of the third evolved design in the l-35GHz range, computed
for a reference feedline with Rref = 50O. The antenna is immersed in a
dielectric medium of er = 10.2. This design has a return loss below -lOdB
in the 1.84-35 GHz range
100
List of Figures
xvii
7.17 The final design. First, the discontinuity at point M is removed by simply
extending the elliptic curve to point I where it is intercepted by another
elliptical curve NI. In this manner, all discontinuities are removed and the
antenna total width, I-to-I, is further reduced to only 14mm
7.18 Return loss Su of the final antenna design in the l-35GHz range, computed
for a reference feedline with Rref = 50fi. The antenna is immersed in a
dielectric medium of er = 10.2. The results computed with SEMCAD show
a return loss below -lOdB in the 1.94-35 GHz range. For HFSS, the computed
results show a return loss below -lOdB in the 1.73-34.37 GHz range
101
7.19 Return loss Su of the final antenna design in the l-35GHz range computed
with HFSS. The solid line curve is for the antenna with a separation s =
375/im and referenced to a 50fi feedline while the dashed line curve is for
the same antenna when referenced to a 60fi feedline. On the other hand,
the dash-dot line curve is for the antenna with a separation s = 200/im
and referenced to a 50fi feedline. The antenna is immersed in a dielectric
medium of er = 10.2
102
7.20 Return loss Su of the final antenna design when developed from an antipodal
stripline APS with overlaping strip edges of s = 100/^m. The results are
shown in the l-35GHz range and referenced to a 50il feedline. The results
computed with SEMCAD show that the minimum lower operating frequency
of -lOdB return loss is equal to 2.14GHz while for results computed with
HFSS it is equal to 1.87GHz
102
101
7.21 Detailed antenna geometry and electrical dimensions associated with a matching medium of dielectric constant er and designed for a specific minimum
lower operating frequency fa = c/(Ay/e^)
104
7.22 Waveform of the Gaussian modulated sine described by Eqn. 7.1
7.23 Antenna orientation in polar coordinates
7.24 Radiated electric field waveform computed at 3cm radial distance from the
antenna apex in the H-plane and as a function of the polar angle <>
/
7.25 Radiated electric field waveform computed at 3cm radial distance from the
antenna apex in the E-plane and as a function of the polar angle 9
105
106
107
107
List of Figures
xviii
7.26 Antenna near E-field magnitude computed at 3cm radial distance from the
antenna apex in the H-plane at three selected frequencies: 3GHz, 6GHz, and
9GHz
109
7.27 Antenna near E-field magnitude computed at 3cm radial distance from the
antenna apex in the E-plane at three selected frequencies: 3GHz, 6GHz, and
9GHz
109
7.28 Antenna board view. Coordinate dimensions are in mm
Ill
7.29 Antenna's top plane art work (top view). Coordinate dimensions are in mm. 112
7.30 Antenna's bottom plane art work (top view). Coordinate dimensions are in
mm
7.31 Detailed antenna geometry and absolute physical dimensions derived from
elliptical shapes and including the tapered feed/balun
7.32 Geometry of the SMA connector used in the HFSS simulations: (a) Crosssection in the x-y plane, (b) Cross-section in the y-z plane. SMA dimensions
(in mm): a=1.25, 6=4.2, c=0.5, and d=2. The attached tab has a thickness
of 0.5mm. The SMA connector was assumed to be filled with Teflon with a
dielectric constant er = 2.1
112
113
114
7.33 The radiating elements of the antenna are immersed in a matching medium
of er = 10.2. The tapered feed/balun is kept in free space
7.34 Return loss Su of the final antenna design with the microstrip balun/feed
simulated using both SEMCAD and HFSS but without the SMA connector.
The results are shown in the l-35GHz range and referenced to a 50f2 feedline. The results computed with SEMCAD show that the minimum lower
operating frequency of-lOdB return loss is equal to 2.18GHz while for results
computed with HFSS it is equal to 1.97GHz
114
115
7.35 Return loss Sn of the final antenna design with the microstrip balun/feed
and the SMA connector simulated with HFSS. The results are shown in the
l-20GHz range and referenced to a 50fi feedline. As we can see from the plot,
the antenna has a broad operating bandwidth of -lOdB return loss ranging
from 1.9GHz to 16.0GHz. The high frequency operation becomes limited by
the SMA to microstrip transition
A.l OHMEGA-PLY® laminate [10]
115
122
List of Figures
A.2 Summary of the etching steps in manufacturing the TWTLTLA antenna
with the RCM Ohmega laminates, (a) First etch: etching excessive copper
material, (b) Second etch: etching excessive resistive material, (c) Third
etch: etching excessive copper where the resistive material is to be kept.
The third etch is considered to be the most critical one
xix
123
XX
List of Tables
2.1
Input energy distribution and radiation efficiency of loaded monopoles [11]
23
2.2
General comparison of the FDTD and the FEM methods
37
2.3
Summary of different antennas proposed for microwave breast imaging
. .
38
3.1
Percentage distribution of the total incident energy from a feed with Rref =
lOOfi
Radiated electric field fidelity F at selected polar angles
44
46
4.2
Miniaturized versions of the "Dark Eye" antenna obtained by variation of
parameters indicated in Figure 4.1(b)
Values of the reflection coefficient within the 3dB and lOdB power range. .
52
55
5.1
Percentage distribution of the total incident energy from a feedline with
3.2
4.1
Rref = 500
63
6.1
6.2
Material properties of the debye dispersive model
Tumor response summary
78
81
7.1
Percentage distribution of the total incident energy from a feedline with
Rref = 500
Radiated electric field fidelity F at selected polar angles
7.2
106
108
1
Chapter 1
Introduction
Breast cancer is considered to be one of the highest health risks to women. In 2006, it
was estimated that 22,300 Canadian women will be diagnosed with and 5,300 will die from
breast cancer [12]. Globally, the International Agency for Research on Cancer estimated
that, in 2002, the disease was diagnosed in approximately 1.15 million patients and was
the cause of 411,000 deaths. These figures underscore the importance of new detection
technologies and therapies targeting breast cancer.
The key to successful breast tumor treatment is the diagnosis of the disease in its early
stages. In developed regions, women are counseled to perform self-examinations and to
regularly schedule mammograms. Recommended frequency of screening is dependent on
factors such as age, lifestyle and family history [13,14]. Frequent screening is crucial in
detection of early-stage tumors. Five year survival rates are 100% at "stage 0", 98% at
"stage 1", 88% and 76% for "stage 2a/b" [15]. Unfortunately, many women do not choose
to undergo screening due to various reasons, including high costs, discomfort and accessibility of screening devices. 39% of Canadian women over the age of 35 have never had a
mammogram. Even for the women over 50, who are expected to undergo routine breast
screenings, the exam rates vary with education level and family income [16]. The Canadian Cancer Society estimates that, if 70% of the diseased women of age 50-69 underwent
frequent screenings, nearly 25% of breast cancer deaths could be prevented.
The current "gold standard" for breast cancer screening is X-ray mammography. During
the exam, the breast is compressed firmly between two plastic plates and an X-ray image is
formed. The compression is necessary to spread the glandular tissue and make the image
2007/12/10
1 Introduction
2
clear. However, X-ray mammography has several drawbacks. First, it causes an extreme
patient discomfort and exposes the tissue to ionizing radiation. In addition, it has a high
percentage of false positives leading to a continued anxiety until further tests are conducted.
Finally and most importantly, it has a low detection rate at early tumor stages.
Other imaging methods such as Ultrasound and Magnetic Resonance Imaging (MRI)
are also commonly used. Because of the acoustic impedance difference between solid and
fluid, Ultrasound is usually used to determine if a detected lump is a solid mass or just a
cyst, a fluid-filled mass that is not considered a health threat. On the other hand, MRI
yields high-resolution images, but it is time-consuming and expensive. Its use is currently
limited to screening for additional cancers once one has been diagnosed.
With the lack of an inexpensive and fast screening tool for early detection of breast
cancer, several imaging and screening modalities have been proposed [17]. One promising
method that has the potential to detect early stage millimeter tumors is UWB Microwave
Radar Imaging. In addition, it has the advantage of avoiding breast compression and
ionizing radiation. Its principle is discussed next.
1.1 U W B Microwave Radar Imaging of Breast Cancer
The basic concept of microwave imaging relies on the difference in electrical properties
between healthy tissue and cancerous tissue. These dielectric properties (conductivity and
permittivity) determine the level and nature of tissue interaction with radiation, and are
dependent on the frequency of the radiating wave [18]. At microwave frequencies (GHz
range), due to the high water content of the cancerous tissue, there is a notable contrast in
electrical properties of breast tumors with respect to the healthy surrounding tissue [19,20].
This significant contrast makes the tumor "visible" to a microwave signal. Thus, if an UWB
pulse similar to the one shown in Fig. 1.1 is launched from skin surface, it penetrates through
the healthy tissue until it encounters the tumor. Due to high tumor-tissue electrical contrast
that it "sees", part of the microwave signal scatters back to the skin surface as illustrated in
Fig. 1.2. It is this backscattered signal that can be detected by a sensor element on the skin
surface and can yield information on the presence of cancer embedded within the healthy
tissue. Several investigations of this method reports that small early-stage breast tumors
could be resolved [19,21,22]. Most of these systems relies on a synthetically generated
array using a monostatic or a bistatic system mechanically scanning the breast. In the
1 Introduction
1.5
Time (ns)
(a)
10
Frequency (GHz)
(b)
Fig. 1.1 (a) UWB Gaussian modulated sine-wave pulse centered at 6 GHz.
(b) Its normalized spectrum.
(a)
(b)
Fig. 1.2 Illustration of the basic concept of microwave imaging, (a) Transmitted waves in the absence of a tumor, (b) Transmitted and scattered waves
in the presence of a tumor.
1 Introduction
4
monostatic case, a single trans-receiving antenna is used to transmit the pulse and receive
the backscatter signal, while in the bistatic case, a pair of antennas (one transmitting and
one receiving) is used.
Mulistatic systems have also been proposed [1,23,24]. In this case, a real aperture array
with several transmitting and receiving antennas is used, where each transmitting antenna
takes turns to transmit the pulse while all receiving antennas receive the backscatter signals. The transmitting and/or the receiving antennas could also be used as trans-receiving
antennas, however, only one antenna is active at a time (one-transmit, multi-receive). This
is actually a special case of the multiple-input multiple-output (MIMO) UWB radar with
one of the multiple transmitted waveforms being the UWB pulse and the others are zeros.
Fig. 1.3
Multistatic array configuration suggested in [1].
Fig. 1.3 shows the multistatic microwave imaging system recently proposed by Xie et al [1].
The system was studied numerically and the antennas were modeled as point sources (illustrated by short dipole antennas in Fig. 1.3). While not realistic, the imaging method
has demonstrated a notable improvement over the monostatic and bistatic case. This im-
1 Introduction
5
proved performance of the multistatic system is attributed to exploiting both transmitter
and receiver spatial diversity. That is, the additional information yield about the tumor is
achieved by simultaneously recording multiple received signals that travel along different
paths throughout of the breast.
1.2 Research Objectives
Recent work in the signal processing algorithms of mulistatic microwave imaging systems [24,25] holds high promise for the development of an inexpensive and fast screening
tool for the early-stage detection of breast cancer. However, these systems rely on a real
aperture array of N elements where N is usually over 40. The lack of a small enough
antenna to form a real aperture array of this order will prevent any further development,
experimental work and implementation until such a design is reached.
On the other hand, it was also demonstrated that the tumor detection process will
benefit from recording both the co-polarized and the cross-polarized tumor backscatter [26,
27]. For example, and as shown in Fig. 1.4, the multistatic system proposed in [1] could
be expanded with cross-polarized colocated or adjacent antenna elements to achieve this
purpose. However, this will push further the requirements of the array-element design.
With the aim to enable the realization of UWB multistatic confocal microwave imaging
(CMI) systems, in addition to other similar applications such as hand-held through-wall
imaging systems and ground penetrating radars, the main objective of this dissertation is
the development of an UWB, ultra-compact, and low profile antenna designs for the use in
a planar or a spherical cross-polarized array imaging systems.
1.3 Dissertation Overview
Chapter 2 presents a theoretical review and a literature survey of traveling-wave broadband
loaded antennas. In addition, it provides a review section on antenna designs suggested for
UWB microwave imaging of breast cancer. Chapter 3 introduces the first antenna design
named "Dark Eyes" antenna. This design illustrates the concept of using a particular
antenna geometry with constant resistive loading to achieve the broadband behavior. Since
the "Dark Eyes" antenna is relatively large for the application of breast cancer detection,
Chapter 4 describes a miniaturization study performed to achieve a reduced antenna design
6
1 Introduction
Antenna array
Breast
Cross-polarized
colocated elements
(a)
Antenna array
Breast
Cross-polarized
adjacent elements
(b)
Fig. 1.4 Multistatic array configuration with: (a) cross-polarized colocated
antenna elements, and (b) cross-polarized adjacent antenna elements.
1 Introduction
7
with similar characteristic to the original design. Chapter 5 presents a complete microstipfed design of the miniaturized "Dark Eyes" antenna. In addition, a detailed study of the
near-field antenna characteristics is presented and the results show good performance for use
in pulsed biological sensing. Chapter 6 demonstrates the use of the "Dark Eyes" antenna
in a card array to detect both the co-polarized and cross-polarized tumor backscatter. A
computational study of the tumor response for different tumor shapes and orientations
is executed with two adjacent cross-polarized antennas and the benefits of recording the
cross-polarized tumor backscatter is confirmed. Chapter 7 introduces the second antenna
design, the traveling wave tapered and loaded transmission line antenna (TWTLTLA). The
antenna is an evolution of the "Dark Eyes" design, though, it is a unique and novel design
in many aspects. The antenna is uniplanar making it much easier to manufacture. In
addition, the antenna is ultra-broadband and ultra-compact with a very low line profile.
This makes it an excellent candidate for a cross-polarized card array of several elements.
Finally, the dissertation is concluded by Chapter 8 with a brief summary of the main
contributions of the work and discussions for future research directions.
1.4 Original Contributions
This thesis presents the following original contributions:
• A detailed parametric analysis of the "Dark Eyes" antenna previously proposed by
Prof. Popovic. This analysis identified the effects of the surface resistive loading on
the antenna bandwidth, efficiency, and fidelity.
• Miniaturization of the "Dark Eyes" antenna design through strategic optimization of
its geometric parameters. In addition, the result of this study helped in identifying
the strong relation between the geometric parameters of the two different antenna
sections, metallic and resistive, and the antenna characteristics such as bandwidth
and center frequency of operation.
• A planar broadband microstrip-to-CPS feed is developed for the miniaturized "Dark
Eyes" antenna. The complete antenna design was investigated in detail and the
antenna was optimized for pulse radiation.
1 Introduction
8
• A cross-polarized card array of adjacent antenna elements was proposed for the detection of cross polarized tumor backscatter. Through numerical simulations, a tumor
detection study of different tumor shapes and orientations was performed to demonstrate the advantages of this detection method.
• Development of the novel miniaturized TWTLTLA antenna design. Through a unique
geometry, the design combines the advantages of tapered transmission line antennas
with the concept of resistive loading to achieve an Ultra Broadband and compact
planar structure with a very low profile. The antenna is easily manufactured since it
employs only thin film technology with a constant surface resistivity. In addition, the
manufacturing repeatability of highly accurate designs for antenna arrays is easily
achievable.
• Establishing a set of design rules and guidelines for the development of the TWTLTLA
antenna operating in different frequency range and background medium, and with
different feed designs.
• A provisional patent was filed based on the TWTLTLA antenna design and its use
in a cross-polarized card array arrangement for microwave imaging of breast cancer.
9
Chapter 2
Literature Review
2.1 Introduction
This chapter is a theoretical review and a literature survey of the main research areas of this
dissertation, which includes the traveling-wave broadband loaded antennas. In addition,
this chapter provides a review section on antenna designs suggested for the application of
microwave imaging of breast cancer. While this chapter is not aimed to be comprehensive
to cover all the antenna designs in these two fields, it does cover the theoretical basis,
original work, and most important key references reported on both subjects. Further, this
chapter introduces in brief the theory of the finite-difference time-domain method (FDTD),
the main tool used to model the antennas proposed in this thesis.
2.2 Broadband Loaded Antennas
The current wave along a short metallic linear antenna exhibits a standing wave distribution. This results in a large variation of antenna parameters such as input impedance
and radiation patterns with frequency. In contrast, a traveling-wave antenna has relatively
constant parameters that are independent of frequency. In 1961, Altshuler [28] was the
first to report on a traveling-wave linear dipole antenna. He achieved this traveling-wave
behavior by placing an optimum resistive load a quarter-wavelength from the antenna ends.
Although the location of the resistors is not critical, this traveling-wave current distribution vanishes as the frequency is changed. Later on, Wu and King [29] proved theoretically
that a traveling-wave dipole antenna can be realized by continuous resistive loading, were
2007/12/10
2 Literature Review
10
the internal resistance per unit length is an increasing function of position along the antenna. In this way, the current attenuates rapidly as it travels toward the antenna ends
and a pure outward traveling-wave antenna is realized. However, the obvious disadvantage of this increased resistive loading technique is the reduced efficiency of the antenna.
On the other hand, several authors studied the possibility of increasing the bandwidth of
the linear antenna by loading it with purely reactive components. Much earlier than Altshuler, Mushiake and Tai [30] reported that a linear antenna could be broadbanded to a
certain extent by loading it with equal capacitive elements at equal intervals. Furthermore,
Hallen [31] was able to obtain a broadband antenna with a 3:1 impedance bandwidth by
increasing the values of the capacitive elements. In parallel to this work, Nyquist and
Chen [32] demonstrated a traveling-wave dipole by inserting a pair of reactive elements at
an optimum distance from the antenna ends. However, this optimum location was a function of frequency and again, the traveling-wave nature of the antenna was not maintained.
Finally, Rao et al [33] were able to obtain a broadband antenna using an exponentially
increasing capacitive loading. This antenna achieved a 3:1 radiation pattern bandwidth
and up to 10:1 impedance bandwidth.
2.2.1 The Concept of Loading, The Wu-King Profile
The Differential Equation and its Solution
Following the work presented in [2,29], let a thin cylindrical antenna of length 2h oriented
along the z — axis be driven at its center by a delta-function generator 5(z) with emf V0e, has
an internal impedance per unit length zl(z), and carry a total axial current I{z). Then, the
axial component of the vector potential Az(z) on its surface satisfies the one dimensional
wave equation:
(I? + f c ° 2 ) M z ) = i!r W*'W - v°5{z)}
(2 1}
-
wherefco= Wy/Hoeo is the free space wavenumber and assuming a time dependence of the
form e?wt. For a circular tube of constant radius a, the internal impedance per unit length
zl(z) can be expressed as a function of the axial coordinate z as follows
zUz) =
\
(2.2)
2 Literature Review
11
where a and d are the conductivity and wall thickness respectively. They are assumed to be
a function of z in order to be able to vary the internal impedance zl (z) along the antenna.
Then, the vector potential on the surface of the antenna is
^(*)
= r
T W)K{z,z')dz'
(2.3)
J —fi
where
p-jk0r
K(z,z')
= -
(2.4)
r
with
r = y/{z-z')2
+ a?.
(2.5)
In the above Eqns. (2.3) and (2.4), //Q and eo a r e the free space permeability and permittivity
respectively.
Now, let the "expansion parameter" ^(z) be the quantity which is related to the ratio
of the vector potential to the current at any cross section along the antenna. It is defined
as
V(z) =
A-K^1YJ$-
fov-h<z<h
(2.6)
and it is shown to be essentially constant along the major extent of the cylinder [34]. Then,
it is possible to set
/
Iz(z')K(z,
z')dz' = A^^Az{z)
= Iz{z)H>
(2.7)
J-h
where ^ is the magnitude of &(z) where the current Iz(z) has a maximum.
From Eqns. (2.3)-(2.7) and with the intrinsic impedance (0 = y/^/eQ, it follows that
{& + k%) **tfM*) = ^
[*W(*) - Vf8(z)]
(2.8)
which can be approximated as
{& + hl ~jkof{z))Iz{z)
= J
~ i^rv°es{z)
(2 9)
-
12
2 Literature Review
where
M = £«')
P.10)
Except at the driving point z — 0, the current must satisfy the differential equation
£
fc
+
o-J'W)^)
=0
(2.11)
By direct substitution in Eqn. (2.11), it is verified that when
f(z) = T - ^ - T
h — \z\
(2.12)
Eqn. (2.11) becomes
( & , ,2
J2fc0
Va*»+*-iR^'-<'>-0
P.13)
and a solution is
Ix(z) = C(h - \z\)e-jk°W
(2.14)
It is specifically important to note that a solution of the form eJ'fc°'*' does not satisfy
Eqn. (2.13), and Eqn. (2.14) represents a current wave traveling in the direction of increasing
\z\ toward the antenna ends. The usual backward reflected wave does not exist.
The Impedance and Expansion Parameter
From the current wave solution given by Eqn. (2.14), the vector potential follows as
Az(z) = ^C(h
- \z\)e-ik°M
(2.15)
47T
and the scalar potential 4>(z) must satisfy the Lorentz condition
^z)
=J
M~dz-
Also, by symmetry, 4>(—z) = <p(z). Then, for z > 0
(2 16)
-
2 Literature Review
13
0W
nz) ==
-§B^Ce~jkoz
[_1 - jk°{h -z)]
(2 17)
-
and
0(0+) = -r^-^C
47rweo
Now, if the driving voltage is defined by
[1 + jk0h]
(2.18)
V$ = 0(0+) - 0(0-) = 20(0+)
(2.19)
it follows that
32nwe0Vf
=
{
*(l + jk0h)
'
Hence,
2lrV
T(z) -
0
{Z)
-tMl-3/koh)\l
(l _ \A\ e-Jko\z\
h)e
(o 2V\
{2 21)
-
The input impedance of the dipole is then
Zo = Ro~ j/wCo = ~ ( l - j/k0h)
= 60* - j/we0h
(2.22)
and R0 ^> 1/WCQ when k0h ;» 1. This result indicates that the input impedance of the
antenna is primarily large and resistive if koh >• 1 and a function of * which is relatively
constant.
It is desirable to derive an approximate value of the the expansion parameter * which
from Eqns. (2.7) and (2.14) can be rewritten as
/ > *(z) = —
z')e-^'
' ,u
-ikr\
V1
\ -u
,
kr
e-i
JL A
-
2
dz'
(2-23)
where r\ = y/(z' — z)2 + a2 and r 2 = y/(z' + z)2 + a2
Since I(z) and A(z) both have maximum amplitudes at z — 0, it is best to derive * at
2 = 0. That is, let
14
2 Literature Review
h
, ,p-Jkr°
-y-3kz-— dz'
r0
z'
# = |#(0)| = 2 / (i o
h
(2.24)
where
r0 = Vz'2 + a2
(2.25)
Eqn. (2.24) can be simplified by setting kz' = kr0 in the exponent in the first integral and
r 0 = z' in the second integral. This is mainly due to the fact that k0a <C 1 and a <^i h.
Then,
h
*
p -j2fe 0 ro
2 /
o
O
,
dz7 - =- I
h
?"o
e-j2koZdz'
(2.26)
0
and with A = ka, it follows that
*
sinh~l-
- C(2A, 2kh) - jS(2A, 2kh)
+
i(i-«-^)
(2.27)
where C(a, x) and 5(a, x) are the generalized sine and cosine integrals:
:xl-cosjy
6(a,x)= /
—
du &
rrx 11
^(0, x) = / —
sin W
w
du
(2.28)
and
W={u2
+ a2)1/2
(2.29)
Then, the continuously varying optimum internal-impedance loading of the antenna
l
z (z) is expressed as follows
z\z) =
Co*
60*
27r h — \z\
h — \z\
(2.30)
Eqn. (2.30) describes the well known Wu-King profile and it is plotted in Fig. 2.1. It
is important to note that the expansion parameter ^ in Eqn. (2.30) is real and constant.
However, in general, the expansion parameter * is complex and frequency dependent. This
will lead to a complex internal impedance zl(z) that is also frequency dependent. It can
be shown that *& exhibits weak frequency dependence, at least at low frequencies and for
practical antennas, the complex internal impedance of Eqn. (2.30) is usually approximated
2 Literature Review
15
Asymptotic
toward °o
Wu-King
Profil
Dipole Arm
->z
Fig. 2.1 Wu-King resistive profile.
by a purely resistive internal impedance rl{z) [35]:
r \z) —
Co^o
2TT
1
h — \z\
60*o
h — \z\
(2-31)
where *o is the magnitude of the zero frequency value of ~^{z).
2.2.2 Loading with Purely Capacitive Elements
In the previous section, the theoretical basis of resistively loading a linear antenna to
achieve broadband behavior was presented. The main disadvantage of resistive loading is
the lowered antenna efficiency as a radiator. This has lead many researchers to study the
effect of antenna loading with purely capacitive components. In this section, and following
the work presented in [33], the approximate current distribution for an antenna loaded
with purely capacitive elements is derived. This shows that the current decays rapidly as
it travels toward the antenna ends and it is not frequency sensitive when sufficiently large
capacitive load is used. Again, let zl(z) be the internal impedance loading per unit length
of the antenna and let I(z) be the total axial current along the antenna which is driven at
z = 0 by a delta function generator with emf VQ. Then from Eqn. (2.8), the current I(z)
satisfies the one dimensional wave equation
2 Literature Review
(S
16
+ kl I{Z) =
)
^ F M ^ W - W*)]
(2-32)
Here, we are interested in capacitive loading and it is assumed to be exponentially
increasing given by
z\z) = -jB(eaz
- 1)
(2.33)
where B and a are arbitrary constants which depend on the required taper profile. Then,
except at the driving point z = 0, the current must satisfy the differential equation
(J? + *° + k°h ~ kokieaZ)
/(z) =
°'
(2 34)
-
where
fci = ^ ? Co*
(2-35)
Equation (2.34) can be solved by letting
j2v^re0a/2
a
which reduces to a familiar differential equation
(2.36)
a =
d2
1 d
k20 + fepfc! .
^T+
„x22,o
(9a;2 + Z
xdx
a2 + 1 M ( ^ ) = 0,
(2-37)
the solution of which are Bessel functions I±iV(v), and where
I> = — ix,
&
i/ = —-—
.
(2.38)
a
It is important to note that these functions are complex since both their orders and
their arguments are imaginary. However, the solution of Eqn. (2.37) which satisfies the
boundary condition 1(h) = 0 (h being the length of the antenna) can also be expressed by
two real functions F„(v) and Gv(v) [36] as
I{z) = Fu(vh)Gv{v)
- Gu(vh)Fv(v),
(2.39)
2 Literature Review
17
where v^ is given by
vh = 2V§Eec*/2_
(2.40)
a
When the order v is large and positive, these functions are given by the following asymptotic
series [36],
7T \ l / 2
F»{v)
shun
+
\2v/
7T\V2
GM~e-(£)
4u2 + l 2
•
l\(8v)
+
Av2 + l2
1+ l!(8u)
..^ , +
(2.41)
(2.42)
When k2 <C A:0fci over the frequency range of interest, it is clear from Eqn. (2.38) that
v = vo = 2^k0ki/a
and v is always greater than v for 2 > 0 and specifically -u^ » z^.
Then, only the first term in the solution given by Eqn. (2.39) is dominant and from the
asymptotic series given by Eqns. (2.41) and (2.42), the current decreases rapidly toward
the antenna ends as
I(z)
-voe
az/2
vW a 2 / 2
(2.43)
In addition, since the reactance of a capacitor C decreases directly with the increase in
frequency (Xc — —1/wC = —B(eaz — 1)), and since k% <C k0k\ over the frequency range of
interest, then v and v (and as a result, the current distribution I(z)) become independent
of frequency. However, for high frequencies, it is more appropriate to take the skin effect
(Sskindepth oc l / / 1 / 2 ) into consideration. Then, the capacitive reactance decreases directly
with Z - 1 / 2 , indicating that v and v increase as the / _ 1 / 4 . Hence, at high frequencies, the
current I(z) on a capacitively loaded antenna decays rapidly toward the antenna ends and
it is not very sensitive to frequency change, provided k% <C k0ki, which implies a large
capacitive load.
2.2.3 Antennas Characterizations for Pulse Radiation
In the previous sections, the concept of loading antennas to achieve a traveling wave broadband behavior was presented. This section discuss the most important characteristics and
measures of antennas for pulse radiation. These parameters are the input reflection coeffi-
2 Literature Review
18
cient, radiation efficiency, gain, and fidelity.
Reflection Coefficient
The input reflection coefficient |r(«;)| is defined as
^--W^t,
(244)
-
where Z^iyS) is the antenna input impedance and Zref is the reference impedance. In
general, an antenna is classified as broadband if its input impedance and radiation pattern
do not change significantly over an octave {fu/JL = 2, fu and fi are the upper and lower
frequencies respectively) or more of frequency [37]. For pulse radiation, it is desirable that
the Reflection Coefficient does not change over the major span of the pulse spectrum to
be radiated. In addition, it is important for the Reflection Coefficient to be as small as
possible for the specific chosen reference impedance Zrej.
Radiation Efficiency
The radiation efficiency er of the antenna is defined as the ratio of the energy radiated over
the energy accepted by the antenna. In time domain, it is defined as follows [38]:
Energy Radiated
er = — ^ —
Energy Accepted
. JN. .
(2.45a)
-^—r sin 9 dt d6 dg>
=oJe=0Jt=^
TTo
(245b)
The energy radiated is calculated by integrating the transmitted fields on a closed
surface surrounding the antenna and over time. The energy accepted is calculated by integrating over time the instantaneous power Pinput(t) at the input terminals of the antenna.
In addition, it is important to note that the instantaneous power Pinput{t) is computed from
the product Vinput(t)Iinput(t) and not \Vinput(t)\2/ZA, since ZA is a function of frequency.
However, if the antenna is connected to a transmission line with a constant characteristic
impedance Z c , then the accepted energy by the antenna could also be computed from the
2 Literature Review
19
difference between the energy incident from the source minus the energy reflected at the
input terminals of the antenna [11]:
"'J V r e f^
Energy Accepted = f°° ^ ^
dt
(2.46)
where V(t) is the incident voltage from the source and Vref(t) is the reflected voltage in
the transmission line.
At this point, it might be interesting to look at the theoretical efficiency of the "WuKing" dipole antenna. Only the results are presented here. The theoretical derivations can
be found in [2].
Fig. 2.2 shows the radiation efficiency of the "Wu-King" non-reflecting dipole with
ka = 0.021, where k is the wave number and a is the radius of the circular tube that
constituts the antenna. The efficiency is plotted for kh ranging from ir/2 to 407T, where 2/i
is the total length of the dipole. For example, for a A/2 dipole, kh = ir/2 and the efficiency
is around 9%, while for a 2A dipole, kh — 2n and the efficiency is around 25%. As it can
be clearly seen, the efficiency of a short "Wu-King" dipole antenna is very low.
50
^
j
n
27T
,
,
,
j.
20-7T
407T
40
UJ
£ 20
u_
LU
10
7l72
67T 107T
kh
Fig. 2.2 Efficiency of the non-reflecting dipole antenna computed with the
"Wu-King" approximation theory [2].
Finally, for pulse radiation, the percentage of energy radiated may be a more meaningful
-^"^
2 Literature Review
20
measure than the radiation efficiency since it takes into account losses due to mismatch as
well as losses due to dissipation in the antenna. It can be easily computed from the ratio
of the radiated energy over the total energy from the source.
Gain
For pulse performance, the direction in which the antenna radiates the pulse is very important. For the far-field region, this is usually quantified by the antenna gain and it is
independent of the radial distance r. In time domain, it is defined as [38]:
\Etrans(r,e,(/),t)\2
0(9, 0) = 4 7 r r 2 ^
9°
(2.47)
/
'input\t)-Linput\t) <*£
J — oo
On the other hand, it is customary to look at the intensity of the radiated electric field
as a measure of the antenna radiation in the near-field region. That is, \Etrans(r, 9, 0, w)\
in frequency domain, or max\Etrans(r, 9,0, t)\ in time domain.
Fidelity
For pulse radiating antennas, the shape of the radiated pulse is usually the most important
factor. It is quantified by the fidelity parameter F which is defined in general for two
signals s\(t) and s2(t) as [39]:
F = max / r(t)s2(t + r)dt
(2.48)
r(t) = L[Sl(t)]
(2.49)
where
x
(t) = —
+00
I
r(t)
K 2
- ~-TE
\r(t)\2dt
1 L
I
(2-50)
2 Literature Review
21
S2(t)
s2(t) -
' "
/
1/2
(2-51)
2
\s2{t)\ dt
and L[»] is a linear operator that operates on the signal Si(t).
Since r(t) and s2(t) are normalized with respect to their energies, fidelity varies between
0 < F < 1 with F = 1 indicating a perfect match between the output waveform s2{t) and
the template of the input signal L[si(t)}. However, it is important to note that fidelity F
is dependent not only on the input signal Si(i), but also on the linear operator £[•].
With respect to antenna systems, fidelity is defined as the maximum normalized crosscorrelation between the antenna's received response and the incident waveform for antennas in receiving mode, or between the transmitted waveform and the time derivative of
the input signal for transmitting antennas [38]. That is, for receiving antennas, the input
signal is the j t h component of the incident electric field S\{t) = E3inc{r — 0,9,cf),t), the
linear operator L[»] = 1 (that is L[si(t)} — S\{t)), and the output signal s2(t) = Vrec(t).
For transmitting antennas, s\(t) = Vsource(t), L[»] = d/dt (that is L[s-[(t)] — ;§Si(£)),
and s2(t) = E3trans(r, 9,4>, t). This difference in the definition of fidelity between transmitting and receiving antennas is mainly due to the antenna reciprocity relation in time
domain [40-44]. A clear derivation of this reciprocity relation and the "derivative relation"
for transmission and reception is presented in a recent paper by Smith [45].
2.3 Survey of Broadband Loaded Antennas
Sec. 2.2 presented the fundamentals and the initial work reported on traveling wave and
broadband loaded antennas. In this section, a survey of several proposed designs for broadband antennas is reviewed. These broadband antennas and sensors are designed using
different profiles of continuous resistive and/or discrete capacitive loading. Most of these
designs where either suggested as E-field sensors or for ground penetrating radars (GPR).
They are described next.
2.3.1 Monopoles and Dipoles
As the original work on antenna loading was for linear dipoles and monopoles, several
authors continued to study them both theoretically and experimentally. Specifically, Kanda
22
2 Literature Review
has extensively studied the linear antenna with resistive and capacitive loading [46,47].
However, his focus was directed toward field measurements [48-52] and the antennas were
mainly studied as probes in the receiving mode. A resistively loaded monopole antenna
can be made for example by depositing a thin-film resistive alloy with a linearly tapered
thickness on a glass rod [48].
Alternatively, the dipole can be made planar and the resistive loading can be achieved
by tapering the dipole width as shown in Fig. 2.3.
O M t S«ntflng
Pidi (Gold)
Nicftrome
Rttistinct Un*« '
FtittdQuirU
Sub»lr»le
.Output Sending
Fig. 2.3 Single element of resistively tapered dipole probe. Adopted from [3].
In addition, several researchers were concerned with resistively loaded monopole designs
for pulse radiation [35,53]. Reference [11] presented a comparative study of five broad-band
loaded monopoles in addition to the perfectly loaded one. The broad-band designs were:
a. Resistive, Wu-King profile [29,35] with the continuous resistive loading per unit length
R(z/h) = R0(l — z/h)~l where RQ = (r)o^fo)/(27rh). Here, z/h is the relative position
along the antenna, r]0 = yjio/^o and ^o is the magnitude of the zero frequency value
of the expansion parameter ty.
b. Resistive-capacitive, Wu-King profile [47] with the continuous resistive and reactive
loading per unit length are R(z/h) = R0(l — z/h)~l and X(z/h) = X0(l — z/h)~l
respectively. However, here R0 = (r]o\Re(iif)\)/(27rh) and X0 = — (rj0\Im(ty)\)/(2irh)
23
2 Literature Review
c. Resistive-capacitive, empirical [53]. This design combines continuous resistive loading
and discrete capacitive loadings that were empirically optimized to give a 3:1 bandwidth with an approximately real input impedance. It consisted of four sections of
constant resistance separated by three capacitive gaps. The first section was metal,
and the following sections were of fixed length with increasing resistance. The capacitances were implemented as gaps in the wire and they decreased in value toward the
open end. A compensation inductor was also placed in parallel at the feed to tune
out the capacitive reactance of the antenna input impedance.
d. Capacitive, exponential profile [33] of the form C(z/h)
discussed in Sec. 2.2.2
= Co[exp(az/h) — 1] _ 1 as
e. Capacitive, linear profile [31] of the form C(z/h) — C 0 (l — z/h). This profile that
was first proposed by Hallen is actually similar to the Wu-King reactive profile.
Table 2.1 Input energy distribution and radiation efficiency of loaded
monopoles [11]
Antenna type
a.
b.
c.
d.
e.
Resistive, Wu-King Profile
Resistive-Capacitive, Wu-King Profile
Resistive-Capacitive, Emperical
Capacitive, Exponential Profile
Capacitive, Linear Profile
Reflected
Energy
21.5%
20%
10.5%
17%
20%
Dissipated
Energy
55%
48.5%
35.5%
0%
0%
Radiated
Energy
23.5%
31.5%
54%
83%
80%
Radiation
Efficiency
29.5%
39.5%
60%
100%
100%
The conclusion was that the designs that incorporate some resistive loading were best
able to minimize the reflected voltage at the feed and to radiate a signal similar to the input
pulse (a-c), and the designs using a "Wu-King" profile performed best (a-b). However, this
comes at the expense of lower radiated energy of these antennas as shown in Table 2.1. In
addition, it is interesting to note that by using an initial metallic section on the monopole as
in design (c) allows more energy to couple onto the antenna, increasing the initial radiated
pulse and reducing the reflected voltage at the input feed point.
24
2 Literature Review
2.3.2 Vee Dipoles
A Vee dipole is another simple and commonly used antenna for several applications. Its
main difference with respect to the straight dipole antenna is in its directive radiation
pattern. It is usually constructed from two linear arms in the V shape. Fig. 2.4 shows the
conventional Vee antenna with linear arms and a modified quadratic version [4] that have
been resistively loaded for the application of GPR systems. In this recent work, the voltage
standing wave ratio (VSWR), gain, and front-to-back ratio of the resistively loaded Vee
dipole (RVD) was improved by curving the arms and using a modified "Wu-King" loading
profile.
L=17.15cm
V-antenna
Modified
V-antenna
Fig. 2.4 Resistively loaded quadratic V-antenna [4].
Fig. 2.5 shows another RVD antenna developed for land mine detection system [5]. In
this design, a constant resistive sheet was used with a linearly tapered geometry given by
W{s/h) = WQ{1 — s/h) to implement the resistive "Wu-King" profile.
Fig. 2.5 Resistively loaded modified V-antenna [5].
2 Literature Review
25
Several other authors have also studied the Vee dipole antenna. In references [54,55],
the Vee dipole was successfully used as a sensor for very short electromagnetic pulses, while
reference [56] studied the current distribution analytically on a resistive loaded thin-wire
Vee antenna. However, all of these antennas are relatively large (several centimeters).
2.3.3 Conical and Bow-Tie Antennas
Another very popular standard transmitting antenna is the conical antenna. Its planar
counterpart, the Bow-Tie antenna has also been extensively used as a pulse radiating
antenna. These antennas where first investigated experimentally by Brown and Woodward [57]. Their study showed that these antennas have broader bandwidth than the
cylindrical dipole antenna. Actually, the infinitely long biconical antenna is a frequencyindependent structure [58]. However, the transients in a finite length biconical antenna are
not ideal [59].
Fig. 2.6 shows a resistively loaded conical antenna that has been proposed and studied
in [60]. The results of this study showed that this antenna is capable of radiating temporally
short wide-bandwidth pulses that meet the requirements of subsurface ground penetrating radars. The antenna radiation efficiency is 86% and it is considered very good when
compared to the resistively loaded "Wu-King" dipole, however, the antenna is relatively
large.
RESISTIVE SHEET
Ai
METTALIC SHEET
Fig. 2.6 Resistively loaded conical antenna.
2 Literature Review
26
Fig. 2.7 Photograph of the RC-loaded bow-tie antenna [6].
Resistively and resistor-loaded bow-tie antennas were also studied for pulse radiation.
In reference [61], a bow-tie antenna was optimized for pulse radiation using the "Wu-King"
resistive profile. For this antenna, the radiation efficiency was about 47%. Because of the
manufacturing difficulty of the resistive profile, several authors designed bow-tie antennas
loaded with discrete resistors and even with microwave absorbers. In reference [62] two
discrete resistors were effectively added at the end of the bow-tie antenna to suppress the
signal ringing. In addition, since the entire antenna structure is lossless, the radiation efficiency of such an antenna is considered to be good. Fig. 2.7 shows a recently proposed
RC-loaded circular bow-tie antenna [6]. In this design, a linear capacitive loading was implemented by etching concentric slots on the antenna surface. A resistive load is added by
covering the conducting side of the antenna with volumetric microwave absorbers. Radiation happens then through the dielectric substrate of the antenna. The antenna has good
radiation efficiency and allows the transmission of short transient pulses with very small
late-time ringing.
2.3.4 TEM Horn Antenna
Another type of broadband antenna that has been used to radiate and receive pulsed signals
is the TEM horn [63]. Broadband behavior of such an antenna is usually further improved
by either tapering the shape of the triangular plates [64] or by resistively loading them [65].
27
2 Literature Review
Fig. 2.8 TEM horn antenna.
Fig. 2.8 shows a typical TEM horn antenna. A detailed analysis of both the shape
tapered TEM horn and the resistively loaded one was carried in [66]. While these designs
are usually good in terms of the fidelity of the radiated pulse, they mainly suffer (in view
of the application presented in this thesis) from their relatively large size.
2.4 Antennas for U W B Microwave Breast Imaging
Most of the antennas shown in the previous section are large structures that have been
developed as standards for antenna measurements or for GPR systems. A direct scale
down of these antennas to the low microwave frequency range (~lGHz) will not result
in designs that are compact enough to be used for microwave breast imaging. In this
section, we focus our attention on antennas that have been developed specifically for UWB
microwave breast imaging. The discussion here will include the antenna performance, and
in addition, the antenna size, 3D or 2D, its profile as defined next, and if it is possible to
use the antenna for co- and cross-polarized sensing of the tumor backscatter.
The antenna profile as defined next is a key element and restriction on the antennas
developed in this dissertation. The reason for this restriction is the primary objective of
2 Literature R e v i e w
28
using these antennas in either a totally electronic mono-static system or a multi-static one
as discussed in Chapter 1.
2.4.1 Definition of A n t e n n a Profile
The antenna profile is a "loose" engineering term that is used to describe the antenna
size and how compact it is in a certain dimension. For example, a low profile monopole
antenna above a ground plane would be relatively short when compared to a conventional
monopole, while maintaining a similar performance. In this dissertation, and to provide
a better measure of different antenna designs, the antenna profile is strictly defined. This
will also further clarify the ultimate objective of this dissertation.
For a non-planar antenna, the antenna profile Sp is the surface defined by the smallest
rectangle that encompasses the intersection of the antenna structure with the plane perpendicular to the direction of radiation. It is important to note t h a t in the above definition,
the antenna profile is not the surface defined by the intersection, but rather the smallest
rectangle that encompasses it. This is mainly due to the fact t h a t when an antenna of an
irregular shape is used as an element in an array, the elements are usually arranged in the
same orientation. Fig. 2.9 shows a typical pyramidal horn antenna and its profile.
^
(
I
i
y
k:
I
I
I
I
I
LFig. 2.9
Antenna profile
surface Sp
Z
Direction of radiation
Horn antenna.
For a planar antenna with its radiation vector perpendicular to its structure, the antenna
profile is the surface Sp defined by the smallest rectangle that encompass the antenna
2 Literature Review
29
structure. An example of such an antenna is a patch over a ground plane or a slot antenna
in a finite ground plane. Fig. 2.10 shows a typical slot antenna and its profile Sp.
/
Antenna profile
surface S„
/
/
/
/
/
/
/
Ground plane
Fig. 2.10
Direction of radiation
Slot antenna in a finite ground plane.
Finally, for a planar antenna with its radiation vector parallel to its structure, the
antenna profile is the line Lp defined by the intersection of the antenna structure with the
plane perpendicular to the direction of radiation. An example of such an antenna is the
tapered slot antenna (TSA) shown in Fig. 2.11.
Antenna profile
line LD
Tapered Slot
> X
Direction of
radiation
Ground plane
Fig. 2.11
Tapered slot antenna.
From the above definition and in face with the surface available to arrange the large
2 Literature Review
30
number of antennas needed around the breast, it is clear that an antenna with a very low
profile is needed (a compact antenna with a very short line profile Lp).
2.4.2 Proposed Non-planar Antennas
Ridged Pyramidal Horn
In reference [67], Li et al. proposed an UWB ridged pyramidal horn antenna for pulse
radiation. The antenna has a curved launching plane that is loaded at its end with two
discrete chip resistors of 100 O. The antenna demonstrates a very broadband behavior with
a voltage standing wave ratio (VSWR) less than or equal to 1.5 in the range 1 to 11 GHz
and a very high fidelity (> 0.92). However, the antenna is non-planar with a surface profile
Sp = 25 mm x 20 mm.
Wideband Bow-tie Antenna
A wideband bow-tie antenna with a coplanar stripline feed was proposed by Bindu et al.
in [68]. The antenna has a 2:1 VSWR bandwidth of 1.575 GHz operating in the band 1.853.425 GHz. The antenna size is 4 cm x 4 cm mounted horizontally over an image plane at a
2 cm distance. The image plane extends 2 cm over the antenna edges and gives the antenna
a unidirectional radiation pattern. The antenna is lossless with low cross-polarization and
reduced back radiation, however, the antenna profile is large and equal to the size of the
image plane (Sp ~ 8 cm x 8 cm).
Slotline Bow-tie Hybrid Antenna
Another UWB antenna design for breast cancer detection was explored by Shannon et al. [69].
The antenna is a modification of the slotline bow-tie hybrid (SBH) proposed in [70]. The
bow-tie structure in this design is actually folded to become similar in structure to a TEM
horn. To miniaturize and match the antenna for breast cancer detection, the folded bowtie structure was filled with a dielectric material similar to those of the breast tissue. The
antenna has a return loss greater than lOdB in the 2.5-10 GHz band and has one of the
smallest surface profiles reported to date Sp = 16 mm x 12 mm.
2 Literature Review
31
Cross-polarized Bow-tie Antenna
The compact cross-polarized bow-tie antenna [27,71] is the only antenna design proposed
specifically to sense the cross-polarized reflection of the tumor. The antenna consists of
two crossed bow-tie elements backed by an octagonal cavity and attached to it a metal
flange. The octagonal cavity behind the antenna, which purpose is to block the waves
radiated away from the breast, is filled with an epoxy of dielectric constant er = 10 and
the antenna is immersed in a matching medium with dielectric properties similar to fatty
tissue (er = 9, a = 0.2 S/m). The antenna return loss is less than —10 dB from 2.0 GHz
to 4.4 GHz and the antenna can record the cross-polarized reflections from the tumor in
the breast. However, the antenna profile is relatively large Sp = 6.25 cm x 6.25 cm, and it
is intended for use in radar-based microwave scanning systems.
Magnetic Slot Antenna
Several of the antennas proposed for microwave breast imaging were adopted from designs
developed for UWB communication applications. Many of these designs have the form
of either a slot antenna, or a folded monopole into the ground plane, or finally a folded
monopole on the edge of the ground plane. Mosquera and Isasa modified an UWB magnetic
slot antenna for breast tumor detection [72]. The antenna consisted originally of two leafshaped slots connected at their stem in a flat ground plane. In their configuration, the
ground plane was bent to form a V shaped slot antenna. Each slot (slot-arm) has a length
of A0 and a maximum width of A0/2. In addition, absorber sheets were placed in the
back side to suppress sidelobes and back radiation. The antenna was designed at a center
frequency of 6 GHz and was well match to 50fi impedance over the entire frequency band
3-9 GHz. The antenna profile is dependent on the ground plane size and its bending angle.
For the proposed design, Sp ~ 4.8 cm x 5.0 cm.
2.4.3 Planar Antennas with a Surface Profile
Ultralow Reverberation Bow-tie
The wideband resistively loaded bow-tie antenna is the first proposed design for pulsed
microwave system for breast cancer detection [73]. The bow-tie has a 53° flare angle and it
is loaded with the "Wu-King" resistive profile along its axial distance. When the antenna
2 Literature Review
32
is immersed in a fat-like tissue which er = 9 and a = 0.4 S/m, the antenna return loss
bandwidth is in the 2-8 GHz range. In addition, when the antenna is excited with a
Gaussian modulated sine pulse centered at 6 GHz, the reflections from the antenna ends
is seen to be around -106 dB relative to the exciting pulse. This reverberation range is
sufficiently small to allow monostatic sensing of a tumor several centimeters below the skin
surface even without calibration. However, the "Wu-King" resistive loading of the antenna
makes it difficult for manufacturing. In addition, the antenna profile is relatively large,
Sp = 8.0 cm x 4.0 cm.
Eccentric Annular Slot
A second UWB design that has been adopted for breast cancer detection is the eccentric
annular slot antenna [74]. The antenna has —10 dB return loss bandwidth in air in the
range 3-7 GHz. Again, the antenna is planar, however, its radiation pattern results in an
antenna surface profile Sp ss 5.0 cm x 5.0 cm.
U W B Slot Antenna
Another antenna developed for both UWB communications and for UWB imaging systems
is presented in [75]. The antenna consists of a disc-sector tuning stub centered in a radiating
slot of a similar shape. The tuning stub is tapered at its base to improve the impedance
match and electromagnetic radiation of the antenna. In general, the antenna is similar in
form to the disc monopole folded into the ground plane presented in [76]. The antenna has
a return loss less that —10 dB from 3.1 to 10.0 GHz when immersed in a biological medium
(pork fat). When two antennas are placed side by side with 5 mm separation to form an
array, the mutual coupling S21 between the two antennas is below —19.5 dB over the entire
UWB range. Finally, the antenna surface profile is Sp — 20 mm x 22 mm.
CPW-fed U W B Monopole
An antenna design for microwave imaging for breast cancer was adopted from recently
reported coplanar waveguide (CPW) fed UWB communication antennas [77]. The antenna
is a folded monopole on the edge of the ground plane. In addition, the antenna is compact
and easy to manufacture with good performance characteristics. The antenna has a return
loss is below —9.6 dB from 3.4 GHz to 9.9 GHz when placed in a biological medium e.g.,
2 Literature Review
33
(pork fat), and its near-field radiation patterns are relatively uniform across the UWB
frequency range. This will make it possible to construct prototype imaging arrays for
UWB radar-based or microwave tomographic systems. However, the antenna profile is
Sp = 26 mm x 30 mm, which makes it difficult to arrange a large number of antennas to
achieve a totally electronic or a multi-static system.
2.4.4 Planar Antennas with a Line Profile
Ultra-Broadband V-Antenna
A resistively loaded V-wire antenna was designed and optimized using genetic algorithms
(GA) for detecting breast tumors in [78]. The antenna has arms of length 6.4 mm and
an interior angle of 47°. Each antenna arm was discretized into 16 segments and discrete
resistors were used to form the resistive load profile. The GA algorithm was used to obtain
the values of the resistors that achieve the best broadband performance over the 0-25 GHz
range. The optimized antenna has a small line profile Lp = 5.1 mm and shows an improved
performance when compared to the theoretical "Wu-King" V-antenna. However, the lower
frequency limit of the antenna bandwidth is >5 GHz.
Cross-Vivaldi Antenna
A Cross-Vivaldi antenna capable of measuring the cross-polarized tumor backscatter is
proposed in [79]. The antenna is formed by arranging two Vivaldi antennas in a symmetric
crossed position. The antenna is designed and investigated when immersed in a matching
dielectric material similar to normal breast tissue (er = 10, a = 0.4 S/m). Simulation
results show that the —10 dB bandwidth of the antenna is in the 1 to 9 GHz range.
In addition, the antenna is capable of detecting tumors of different size and at different
locations by recording the difference in cross-polarization. The Cross-Vivaldi has a surface
profile Sp = 3.7 cm x 3.7 cm. However, it is also possible to use only one Vivaldi antenna
to record only the co-polarized reflections. Then, the antenna would have a line profile
Lp = 3.7 cm.
34
2 Literature Review
2.5 Theory of the Finite-Difference Time-Domain Method
This section introduces the Finite-Difference Time-Domain method (FDTD), a simple but
versatile technique that is used to solve Maxwell's equations. The method has been successfully applied to numerous electromagnetic problems such as microstrip circuits, antenna design, and in the field of bio-electromagnetics. This technique was first proposed
by K. S. Yee in 1966 [80]. The explanation of the FDTD technique will be carried in the
next section through the one-dimensional free space formulation. Detailed explanation of
the three dimensional formulation and several other aspects and development of the theory
is presented in [81]. Practical implementation of the method can be found in [7].
2.5.1 F D T D Theory
The Finite-Difference Time-Domain method is a direct solution to Maxwell's equations in
time domain. The idea is to simply discretized the equations both in space and time with
the central difference approximations. This will result in a second order accurate solution
to the electromagnetic problem. To better clarify the theory of the method, we will consider
the one-dimensional problem in free space following the development in [7]. In this case,
Maxwell's equations can be written as:
^ = -VxH
dt
e0
(2.52)
^ = _ J_v x E
(2.53)
dt
no
where E and H are the electric and magnetic fields respectively. In one dimension, they
can be rewritten as:
amx
dE
dt
»u y
1i dH
e0 dz
dHy
dt
1 dEx
/i 0 dz
(2.54)
which represents a plane wave traveling in the z direction.
Yee's scheme consists in taking the central difference approximation of both the space
and time derivatives. In this way, the electric and magnetic fields Ex and Hy are considered
2 Literature R e v i e w
35
to be shifted in space by half a cell and in time by half a time step . Thus, equations (2.54)
and (2.55) can be written as:
Enx+l/2{k)
1/2
- £T
(fc) _
1 H-(k + 1/2) - H-(k - 1/2)
At
Hp\k
e0
Az
1 Enx+l/\k
+ 1/2) - H-(k + 1/2)
At
+ 1) -
IJLQ
^ '
'
^ '
'
Enx+l/\k)
Az
In the above two equations, the superscript n means a time t = n At and the index k
means a distance z = k Az.
The 1/2 increment in both space and time is to indicate the
fact that the Ex and Hy fileds are interleaved both in space and in time. This is illustrated
in Fig. 2.12.
Ex
Time:(n-1/2)A
T
T
k-2
k-1\
//
//
\\
\
Hy
•*;
T
T
T
k
k+1
;«•'•
T i m e : (n) A
T
k-3/2
k-1/2
\\
\
Ex
,.
T
T
k+1/2
k+3/2
/
//
^
p
,.
Time: (n+1/2) A
t
t
t
t
k-2
k-1
k
k+1
,.
Fig. 2.12 Yee's one-dimensional scheme for updating E and H fields in space
and time. After [7].
Equations (2.56) and (2.57) can be rearranged to form an iterative time marching algorithm in a "leap-frog" manner:
Enx^2(k)
Hny+\k
= Enx-^{k)
- -^-z\Hny{k
+ 1/2) = Hny{k + 1/2) - ^z[E:+i'2{k
+ 1/2) - H^(k - 1/2)]
+ 1) - E^^(k)].
These are the explicit one-dimensional F D T D update equations in free space.
(2.58)
(2.59)
For
2 Literature Review
36
example, in equation (2.58), the new value of Ex is calculated from the previous value of
Ex (one time step in the past) and the most recent values of Hy (one half time step in the
past).
2.5.2 Stability of the F D T D Method
Two important parameters when modeling electromagnetic problems with FDTD are the
choice of the space and time discretization, Az and At respectively. Usually, the space discretization is set first and it is determined in general by Az < A/10 which has been verified
to be necessary to ensure correct representation of the geometry [81]. Second, the time
discretization is set based on the minimum space discretization. Since an electromagnetic
wave propagating in free space cannot go faster than the speed of light CQ, a minimum time
of At = AX/CQ is required for the wave to propagate one cell. In general, to guarantee
numerical stability in three-dimensional simulations, the time step should be bounded as:
A
• [
At < mm < — - ^ ^ ^ = = = = =
(2.60)
(, Y (A**)2 + (AW)2 ^ (A^) 2
which is the well known "Courant Condition" [81,82].
2.6 Simulation Tools
In this thesis, modeling of the antennas was primarily conducted with SEMCAD [83], a
three dimensional FDTD solver. For further verification, the antenna was also simulated
with HFSS [84], a three-dimensional finite-element (FEM) solver [85]. A detailed description of the FEM method is beyond the scope of this thesis, however, Table 2.2 presents a
general comparison between between the FDTD and the FEM methods.
2.7 Summary
This chapter introduced the concept of traveling wave loaded broadband antennas. The
mathematical fundamentals of both resistively and capacitively loaded straight wire antennas were reviewed. Definitions of key antenna characteristics that are important for
pulse radiation were also presented. These parameters are: reflection coefficient, radiation
2 Literature Review
Table 2.2
37
General comparison of the FDTD and the FEM methods
Computational requirements
Conformal modeling
Modeling of inhomogeneous (biological) materials
Modeling of waveguides and connectors
Computation of wideband response
FDTD
low
not in general
easy
difficult
easy
FEM
high
yes
difficult
easy
difficult
efficiency, gain, and fidelity. Then, a survey of several proposed designs of loaded antennas
was presented. Most of these designs were developed for GPR systems and are relatively
large and non-planar. A survey of most proposed antenna designs for microwave breast
cancer imaging was also presented. Some of these designs were resistively- or resistorloaded designs. A large number of these antennas were adopted and modified from UWB
communication designs. They have the advantage of being planar, relatively compact and
easy to manufacture. However, a problem with most of them is their radiation pattern that
is usually directed perpendicularly to their ground plane regardless of their shape. This
will result in a relatively large antenna surface profile Sp that is approximately equal to
their ground plane. Since the intended application is the development of a completely electronic monostatic or multistatic microwave imaging system that requires a large number
of backscatter signals, an antenna design with an extremely low line profile Lp is desirable.
Table 2.3 summarized the characteristics of all the antennas presented in the survey. The
only two antennas that have a line profile are the Ultra-Broadband V-Antenna and the Vivaldi design. However, the V-antenna operates in the high frequency range and the Vivaldi
profile is still quite large for the intended application. Finally, this chapter introduced in
short the FDTD method and the simulation tools used to model the antennas in this thesis.
Bandwidth
1-11 GHz
1.85-3.425 GHz
2.5-10 GHz
2.0-4.4 GHz
3-9 GHz
2-8 GHz
3-7 GHz
3.1-10 GHz
3.4-9.9 GHz
6-25 GHz
1-9 GHz
Resist ively Loaded
yes
no
no
no
no
yes
no
no
no
yes
no
Polarization
Co-pol
Co-pol
Co-pol
Cross-pol
Co-pol
Co-pol
Co-pol
Co-pol
Co-pol
Co-pol
Cross-pol
Profile
Sp = 25 mm x 20 mm
Sp ~ 8 cm x 8 cm
Sp = 16 mm x 12 mm
Sp = 6.25 cm x 6.25 cm
Sp ~ 4.8 cm x 5.0 cm
Sp = 8.0 cm x 4.0 cm
Sp ~ 5.0 cm x 5.0 cm
Sp = 20 mm x 22 mm
Sp = 26 mm x 30 mm
Lp = 5.1 mm
Sp = 3.7 cm x 3.7 cm
Summary of different antennas proposed for microwave breast imaging
Antenna type
Ridged Pyramidal Horn
Wideband Bow-tie
Slotline Bow-tie Hybrid
Cross-polarized Bow-tie
Magnetic Slot
Ultralow Reverberation Bow-tie
Eccentric Annular Slot
UWB Slot Antenna
CPW-fed UWB Monopole
Ultra-Broadband V Antenna
Cross-Vivaldi
Table 2.3
)
2 Literature Review
39
Preface to Chapter 3:
Microwave-Range Broadband "Dark Eyes" Antenna: Detailed
Analysis and Design
The following chapter is included as a paper published in the IEEE Antennas and
Wireless Propagation Letters journal. It presents our first antenna designed to illustrate the
concept of using a favorable antenna geometry with constant resistive loading to achieve the
broadband antenna behavior. While the antenna is still physically large for the application
of breast cancer detection, it has excellent properties and can be used for other applications
such as through-wall imaging and ground penetrating radars.
40
Chapter 3
Microwave-Range B r o a d b a n d "Dark
Eyes" Antenna: Detailed Analysis
and Design
Houssam Kanj and Milica Popovic
Department of Electrical & Computer Engineering
McGill University
Montreal, Quebec H3A 2A7, Canada
houssam.kanj@mail.mcgill.ca
Abstract: In this work, we present a broadband antenna designed for microwave-range
applications. The antenna is planar and the combination of its geometry with resistive loading results in its broadband behavior. For several values of surface resistive loading under
investigation, we calculate the return loss, percentage distribution of the total incident
energy and the radiated electric field fidelity. Finally, we discuss criteria for choosing the
optimal surface resistivity and plot the corresponding radiation pattern.
Index Terms: Broadband antennas, resistively loaded antennas, pulse radiation, microwave.
1
Reprinted, with permission, from reference [86], © 2005 IEEE.
2007/12/10
3 Microwave-Range Broadband "Dark Eyes" Antenna
41
3.1 Introduction
The idea of achieving broadband behavior of antennas by applying resistive loading has
been extensively reported in the literature to date [3,29,35]. Variable resistive loading has
been suggested as a part of the broadband design, however, this technique implies challenges
and potential cost increase in the antenna fabrication. Here, we choose to limit our design
technique to constant surface resistive loading for cost-effectiveness and practicality, and
aim to achieve broadband behavior by favorable antenna geometry. Although our work
is motivated by the possibility of applying such design for pulsed microwave biological
probing [26], the proposed design can be used for a wide range of applications, e.g. for
impulse radar or a pulsed-field probe.
3.2 Antenna Geometry and Simulation Tools
Figure 3.1 shows the antenna geometry. The proposed design is symmetrical with respect
to the feeding point. Each side of the antenna consists of two sections. The first is a
metallic bowtie-like, located at the apex of the antenna. The second section is tapered and
of constant surface resistive loading Rs. It is this section that is used to minimize the signal
reflections off the antenna ends and hence improve its broadband behavior. With reference
to Figure 3.1(a), the antenna dimensions are: a=5mm, c=5mm, d=35mm and its thickness
was 70/im. In the preceding papers published on this topic, the authors nicknamed the
design as " Dark Eyes" antenna, as the described geometry was reminiscent of the eye shape.
The antenna was characterized by SEMCAD [83], a three-dimensional finite-difference
time-domain (FDTD) solver. In the simulations, a nonuniform staircase mesh was used with
a minimum and maximum grid resolution of 35/im and 1mm, respectively. The metallic
section of the antenna was modeled as perfect electric conductor (PEC), while the resistive
sections was modeled as a dielectric with the appropriate conductivity a to achieve the
required surface resistivity. For example, In this work, the antenna was considered to be
70/im thick. For a surface resistivity Rs = 5 0 0 / • , the required conductivity is then a =
285.7S/m. The antenna was fed at its center with a 1-V, 50-fi resistive gap source and the
grid domain was terminated with an 8-cell PML absorbing boundary. For verification and
comparison of calculated parameters and radiation pattern, the antenna was also simulated
with HFSS [84], a three-dimensional finite-element (FEM) solver.
42
3 M i c r o w a v e - R a n g e B r o a d b a n d "Dark Eyes" A n t e n n a
Constant
resistive
loading Rs
Antenna
aDex
\
Bowtie-like
metallic
Section
A.
_
^
(a)
A
*•>•
(b)
Fig. 3.1 (a) Geometry of the resistively loaded "Dark Eyes" antenna. The
dimensions are (in mm): a—5, c=5, and d=35. (b) Illustration of the antenna
orientation in polar coordinates.
3.3 Results and Discussion
3.3.1 R e t u r n Loss
The antenna can be characterized in the frequency domain by observing its input reflection
coefficient Sn- The Sn parameter is computed assuming a feed line with a characteristic
impedance of Rref = 1000. This reference is commonly used for antennas with high input
impedance [87]. Sn parameter is computed for three different surface resistivity values Rs
(lOOfi/D, 200O/D and 400O/D) and plotted in the 0.1GHz - 14GHz range. The choice of
surface resistivity range is based upon previously reported work [88,89]. Results graphed
in figure 3.2 show a return loss of -lOdB in the range of 3.8GHz to 8.5GHz for the antenna
with Rs = 100O/D and a single resonant frequency around 6GHz for all Rs values under
investigation. The antennas with Rs = 2 0 0 0 / • and Rs = 4 0 0 0 / • demonstrate a slight
3 Microwave-Range B r o a d b a n d " D a r k Eyes" A n t e n n a
o
---
SEMCAD
HFSS
-5
-10
m
V15
A
/
A. /
Rs = 100fi/n
-20
-25
4
-30 (
6
8
10
Frequency (GHz)
12
14
(a)
°r
- - - SEMCAD
HFSS
-5
-10
S
•D
X-15
in"
-20
R , = 200J1/D
-25
If
-30-
4
6
8
10
Frequency (GHz)
12
14
12
14
(b)
2
4
6
8
10
Frequency (GHz)
(c)
Fig. 3.2 Antenna's return loss Sn in the range 1 to 14 GHz computed
assuming a feed line with Rref = 100J7. Results are shown for both HFSS and
SEMCAD for (a) Rs = lOOft/D, (b) Rs = 200ft/a, and (c) Rs = 400fi/D.
43
3 Microwave-Range Broadband "Dark Eyes" Antenna
44
degradation in broadband behavior on the lower side of the spectrum. Finally, we note the
close match of simulation results obtained with both SEMCAD and HFSS tools.
3.3.2 Efficiency
A key characteristic of resistively loaded antennas is their efficiency. Table 3.1 shows the
percentage distribution of the total energy of the incident pulse in the feedline for several
values of surface resistivity Rs. For the antenna with Rs = OO, the "resistive" section
is considered existent but non-dissipative. In contrast, for the antenna with Rs = oo/O,
no signal propagates to the "resistive" section, and it is therefore perceived by the signal
as practically non-existent. The results in Table 3.1 are computed from the time-domain
simulations. It is important to note that they are dependent on the pulse excitation shape
and its spectral content. The excitation waveform used in the simulations was a Gaussian
modulated sinusoidal pulse mathematically described by:
V(t) = sin[27r/o(t - to)} exp[-(t - t0)2/2r2}
(3.1)
with /o = 6GHz, r = 80ps, and t0 = 5r. This pulse shape and its parameters follow from
the intended application of the antenna for breast cancer detection [26].
Table 3.1 Percentage distribution of the total incident energy from a feed
with Rref = 100a
Antenna Surface
Resistivity
Ra = 0 0 / •
Rs = 500/ •
RB = 100O/D
Rs = 200O/D
R9 = 400O/D
Ra = 8000/ •
Rs = ooO/D
Reflected
Energy
17.5%
4.7%
4.3%
4.7%
7%
12.4%
51.2%
Dissipated
Energy
0%
56.3%
61.2%
63.9%
62.6%
56%
0%
Radiated
Energy
82.5%
39%
34.5%
31.4%
30.4%
31.6%
48.8%
Radiation
Efficiency
100%
41%
36%
33%
32.7%
36.1%
100%
The first column of Table 3.1 presents the values for the percentage of the reflected
energy at the feed, computed from the magnitude of the reflection coefficient Sn. As
3 Microwave-Range Broadband "Dark Eyes" Antenna
45
can be observed, the antenna with Rs = 100O/D demonstrates the smallest percentage
of reflected energy. However, we point out that this does not necessarily translate into
maximum radiated energy due to the lossy nature of the antenna.
Table 3.1 further gives the following energy quantities: the percentage of radiated energy
and the radiation efficiency, defined as the ratio of the energy radiated over the energy
accepted by the antenna. The radiated energy is calculated by integrating the fields on a
closed surface around the antenna, while the dissipated energy is computed as the difference
between the radiated energy and the reflected one. For pulse radiation, the percentage of
radiated energy is a more meaningful measure than the radiation efficiency as it takes also
into account the losses due to mismatch in the feed line. As we can see in Table 3.1,
both effectively lossless antennas (Rs — 0 0 / • and Rs = ooO/D) have the highest radiated
energy. This comes at the expense of degraded fidelity, as will be discussed next. Other
antenna designs, with Rs of value between the two above-mentioned extremes, are lossy
and have lower radiated energy, with the minimum for the antenna with Rs — 4 0 0 0 / • .
This result may initially seem counter-intuitive, but a careful further analysis leads to it as
follows. As mentioned before, when Rs increases from zero to infinity, the antenna resistive
section behavior changes from lossless to lossy, and then practically to non-existent, leaving
the whole radiation task up to the bow-tie metallic section. Thus, the radiated energy
is expected to have a minimum for a value of Rs that lies somewhere between the two
extremes. Finally, we note that for all resistively loaded antennas considered, the one with
Rs = 5 0 0 / • has the highest radiated energy.
3.3.3 Fidelity
For pulse performance, the
parameter. This could be
similarity between the time
field Sg(t). Mathematically,
and £g(t) as such [40]:
shape of the radiated pulse by the antenna is an important
quantified by the antenna fidelity F, which is a measure of
derivative of the exciting pulse V(t) and the radiated electric
this is defined as the maximum cross-correlation between f(t)
+oo
F = max / r(t)£rg(t + r)dt,
—oo
(3.2)
3 Microwave-Range Broadband "Dark Eyes" Antenna
46
Table 3.2 Radiated electric field fidelity F at selected polar angles
Antenna Surface
Resistivity
Rs = 00/D
Rs = 500/D
Rs = 100O/D
Ra = 2 0 0 0 / •
Rs = 4 0 0 0 / •
R8 = 800O/D
R8 = ooO/D
0 = 90°
0 = 0°
0.6348
0.9774
0.9868
0.9917
0.9863
0.9676
0.8554
0 = 90°
0 = 45°
0.5617
0.9684
0.9845
0.9908
0.9852
0.9656
0.8511
0 = 90°
0 = 90°
0.6225
0.9678
0.9802
0.9892
0.9875
0.9714
0.8628
0 = 45°
6 = 5°
0 = 0°
0 = 0°
0.9383
0.9816
0.9877
0.9894
0.9815
0.9611
0.8459
0.9173
0.9937
0.9944
0.9970
0.9967
0.9854
0.8915
where f(t) = dV(t)/dt and Sg(t) are normalized to their respective energies. Table 3.2 shows
the antenna fidelity computed at a 7-cm radial distance from the antenna apex in the Eand H-plane at selected polar angels. The E-plane considered for fidelity computation is
the one perpendicular to the antenna plane itself, shown in the illustration (Figure 3.1b)
as the x-z plane. It is also important to note that the antenna fidelity is dependent on the
exciting pulse (3.1), therefore, the results should be interpreted in this context.
From the results presented in Table 3.2, we first conclude that antennas with the minimal
and maximal surface resistivity value (Rs = 0 0 / • and Rs = ooO/D) show a degraded
fidelity in most directions. Note that the effectively shorter antenna (Rs = ooO/D) has
a better fidelity in general, as expected. Further, antennas of all other Rs values under
investigation show an excellent antenna fidelity exceeding 0.96, with the antenna with
Rs = 2 0 0 0 / • having the highest fidelity values. Finally, it is worthwhile noting that as
surface resistivity increases from 0 0 / • to ooO/D, the antenna fidelity in all directions
increases up to a peak value and experiences subsequent drop-off.
3.3.4 Radiation Pattern
From the results presented in Table 3.1 and Table 3.2, we observe that the highest radiated
energy occurs for Rs = 5 0 0 / • , while the maximum fidelity value is reached for Rs =
200O/D, as noted before. We hence choose the surface resistivity value of Rs = 100O/D
as a compromise for plotting the radiation pattern. Figure 3.3 graphs the E- and H-plane
3 Microwave-Range B r o a d b a n d "Dark Eyes" A n t e n n a
(a) E-plane
(b) H-plane
(c) E-plane
(d) H-plane
(e) E-plane
(f) H-plane
Fig. 3.3 Simulation results for far-field radiation patterns at 3 GHz (a) and
(b), 6 GHz (c) and (d), and 9 GHz (e) and (f). Results are shown for both
HFSS and SEMCAD for Ra = 100ft/n.
47
3 Microwave-Range Broadband "Dark Eyes" Antenna
48
radiation pattern for 3GHz (3.3a and 3.3b), 6GHz (3.3c and 3.3d), and 9GHz (3.3e and
3.3f). Each plot shows data obtained with both SEMCAD and HFSS for validation. A
close match between the results can clearly be seen. With the frequency increase, the main
beam in the E-plane broadens with multiple peaks appearing at different polar angles, but
no side-lobes appear over the entire spectrum. In addition, we note that, in the H-plane,
antenna shows higher radiation level along the x-axis (Figure 3.1b).
3.4 Conclusion
This paper summarized design and analyis of the broadband "Dark Eyes" antenna structure, intended for pulse probing in the microwave range. The antenna is a symmetric
structure, comprising of a short, bow-tie metallic part, and a longer, tapered section of
surface resistivity Rs. We draw several conclusions. First, the return loss analysis showed
that the largest bandwidth is achieved for lower values of surface resistivity. Second, the
antenna with lower Rs values of those considered demonstrates higher efficiency. Third, antenna fidelity was computed and showed a maximum value for Rs = 200f2/D. Finally, the
radiation pattern for the antenna with Rs = 100fi/D was presented for 3GHz, 6GHz and
9GHz, suggesting a single-beam radiation of the designed antenna over the entire spectrum
of interest.
3 Microwave-Range Broadband "Dark Eyes" Antenna
49
Preface to Chapter 4:
Strategic Miniaturization of the Broadband "Dark Eyes"
Antenna
The following chapter is included as a paper published in the conference proceedings of
the International Symposium on Antenna Technology and Applied Electromagnetics. The
purpose of the work presented in this study, from the perspective of the goal of this thesis,
is to arrive to a compact antenna design based on the "Dark Eyes" antenna of Chapter 3
while maintaining the desired performance characteristics.
50
r^.
Chapter 4
Strategic Miniaturization of the
Broadband "Dark Eyes" Antenna
Houssam Kanj, Qingsheng Han, and Milica Popovic
Department of Electrical & Computer Engineering
McGill University
Montreal, Quebec H3A 2A7, Canada
houssam.kanj©mail.mcgill.ca
4.1 Introduction and Background
The general motivation behind the work presented in the paper is the need for broadband
antennas for pulsed biological sensing centered in the microwave range [26,88]. We continue
our study of a particular antenna design ("inverse bowtie" or the "Dark Eyes" antenna)
which takes advantage of constant resistive loading in combination with favorable antenna
geometry to minimize reflections from antenna ends [3,88,89].
1
Reprinted, with permission, from reference [90], © 2004 ANTEM.
2007/12/10
4 Strategic Miniaturization of "Dark Eyes" Antenna
51
4.2 Methodology
4.2.1 Numerical Tools
All antenna simulations were performed with SEMCAD [83] (three dimensional finite difference time-domain (FDTD) solver). A non-uniform staircase mesh was used with a maximum cell size of 1mm in all simulations. The minimum cell size varied between 0.0625mm
and 0.25mm for different antenna sizes under investigation, with the ratio of the smallest
dimension to the minimum cell size kept constant. Similar to Chapter 3, the metallic section of the antenna was modeled as perfect electric conductor (PEC), while the resistive
sections was modeled as a dielectric with the appropriate conductivity a to achieve the required surface resistivity. The antenna was fed with a 1-volt resistive source. PML (8-cell)
was used as the absorbing boundary condition. Finally, the magnitude of the reflection
coefficient T for each antenna was computed assuming a 50fi feed impedance and plotted
over the normalized spectrum of the input pulse.
4.2.2 Antenna Geometry and Parameters
Figure 4.1(a) shows the overall structure of the symmetric, resistively loaded "Dark Eyes"
antenna. Antenna feed connects to a bowtie-like metallic section, which continues into a
resistive tapered section [88,89] of surface resistance Rs = lOOft/D. Antenna thickness
throughout this study was kept at 1mm. Figure 4.1(b) depicts one-half of the antenna,
indicating longitudinal dimensions c and d, and the transverse dimension a, which were
used as the design parameters for our study.
Table 4.1 lists antenna types under investigation obtained by variation of the geometric
parameters as indicated in Figure 1(b). Type I antennas (1.1, 1.2 and 1.3) conform to
the shape of the originally investigated "Dark Eyes" antenna (I.I., the reference antenna).
Antennas 1.2 and 1.3 are versions of 1.1, scaled-down by factors of 2 and 4, respectively.
Type II antennas (II. 1, II.2 and II.3) all retain the same length c of the metallic section,
but vary in the transverse dimension a and the longitudinal dimension of the resistive part
d, thus departing from the shape defined by the original antenna structure (Type I).
4 Strategic Miniaturization of "Dark Eyes" Antenna
Constant
resistive
loading Rs
Antenna
Feed
Bowtie-like
metallic
Section
(a)
t-
«*--
(b)
Fig. 4.1 (a) Sketch of the resistively loaded "Dark Eyes" antenna. In addition to its role in the overall design, the bowtie-shaped metallic segment
facilitates easier connection with the generator. The tapered resistive section
has a surface resistance of Rs = 100f2/D. (b) One-half of the antenna sketched
in (a), indicating the dimensions used as design parameters.
Table 4.1 Miniaturized versions of the "Dark Eye" antenna obtained by
variation of parameters indicated in Figure 4.1(b).
Antenna type
Parameter a (mm)
Parameter c(mm)
Parameter rf(mm)
1.1 / Reference Antenna
5
2.5
35
1.2
5
2.5
17.5
1.3
1.25
1.25
8.75
II.l
2.5
5
17.5
II.2
1.25
5
8.75
II.3
3
5
8
4 Strategic Miniaturization of "Dark Eyes" Antenna
53
4.3 Results
In order to estimate the effect of geometric parameter variation on the bandwidth and the
central frequency of the antenna, we choose to observe the reflection coefficient T in the
frequency band around the frequency of interest (6 GHz). Selected results are plotted in
Figures 4.2, 4.3, and 4.4. The reflection coefficient of the reference antenna 1.1 is graphed in
each figure for comparison. For reference, together with the calculated data, the normalized
spectrum of the input pulse is also displayed in each of the figures.
5
10
15
Frequency (GHz)
Fig. 4.2 Calculated |T| of the original antenna design (1.1) and its miniaturized versions, where every parameter of Figure 4.1(b) is scaled down by a
factor of 2 (antenna 1.2 of Table 4.1) and 4 (antenna 1.3 of Table 4.1). The
thin dashed line shows the normalized spectrum of the input pulse.
Figure 4.2 depicts F for the Type I antennas of Table 4.1. As the original antenna
(1.1) experiences the size reduction by factors 2 (1.2) and 4 (1.3), while maintaining its
overall shape, we observe the central frequency shift from 6 GHz to around 10 GHz and 16
4 Strategic Miniaturization of "Dark Eyes" Antenna
54
GHz, respectively. This result steers our study in the direction of strategic, non-uniform
reduction of the individual parameters noted in Figure 4.1(b).
Next, we consider keeping the longitudinal dimension of the metallic section c unchanged, while varying the transverse dimension a and the length of the resistive section d
(antennas of type II, Table 4.1).
Figure 4.3 graphs the calculated T for antennas with a and d reduction by factors of
2 (II. 1) and 4 (II.2). As these parameters are decreased, the shift of the center frequency
and the bandwidth is far less pronounced than in the previous case (Figure 4.2). However,
we note the unfavorable increase of the reflection coefficient F.
1
•W"-....
I
I
•••
••'
l\
1
1
i
1.1
0.9
—- n.i n.2
0.8
"
\
\
0.7
\
0.6
\
/
'"',-
\
\ x\
V
*•
\
|r| 0.5
\
\ ***
\
h
V
\<^rs^
'
0.4
0.3
\
{
0.2
0.1
...--'*
1
1
4
!
i
6
8
Frequency (GHz)
i
--M---
10
12
14
F i g . 4 . 3 Calculated |T| of the original antenna design (1.1) and its strategically (non-uniformly) miniaturized versions. W i t h reference to Figure 4.1(b),
parameter c is kept at the value of the reference antenna (1.1). Parameters a
and d are scaled down by a factor of 2 (antenna II.1 of Table 4.1) or 4 (antenna
II.2 of Table 4.1). T h e thin dashed line shows the normalized spectrum of the
input pulse.
4 Strategic Miniaturization of "Dark Eyes" Antenna
55
Figure 4.4 graphs T for 1.1 and II.1, and, in addition, for antenna II.3 of Table 4.1,
where a different reduction factor was applied (with respect to 1.1) to each of the design
parameters: c = 5mm (no reduction), a = 3mm (reduction by a factor of 1.66), d = 8mm
(reduction by a factor of 4.37). We note that non-uniform parameter reduction resulted in
a physically smaller antenna with T, central frequency and the bandwidth close to those of
the original design (1.1). This was not the case with the previously mentioned miniaturized
antenna structures (1.2, 1.3, II. 1 and II.2). For comparison, we present numerical values of
interest for antennas 1.1 and II.3 in Table 4.2, within the 3dB and lOdB range around the
peak of the normalized input pulse spectrum.
Table 4.2
range.
Values of the reflection coefficient within the 3dB and lOdB power
Antenna type
1.1
II.3
3dB Power range
r | < 0.47
r <0.46
lOdB Power range
0.44 < T| < 0.61
0.49 < |r < 0.77
Results of Figures 4.2, 4.3, and 4.4 suggest that the length c of the metallic, bowtielike section of the "Dark Eyes" antenna is the key parameter for controlling the central
frequency of the antenna. The longitudinal dimension of the resistive section d can be
used to improve the bandwidth around the central frequency. In comparison with the
effect of these two parameters, the variation of the transverse dimension a yields a less
pronounced variation in the antenna properties. Nevertheless, reduction of a contributes
to the undesirable shift of central frequency and a higher |r|.
4.4 Conclusion
In this work, we presented further investigations of the broadband "Dark Eyes" antenna.
Motivated by the potential use of this design in an array configuration, we observed the
miniaturization effect by strategic change of several design parameters.
We draw two key conclusions from our study. First, the parameters of the metallic,
bowtie-like part of the antenna play a key role in maintaining the desired center frequency
(6 GHz). Second, the geometric parameters of the resistive section have dominant effect on
the antenna bandwidth. These observations have helped us achieve antenna performance
4 Strategic Miniaturization of "Dark Eyes" Antenna
1
0.9
A\ ' A
\
0.8
\
\
0.7
0.6
i
1
LI
— - H.1 "
— H.3
\
\ i
>
;
• \v
|r| o.s
i
56
iV
;
-
\
A_„-"
\
"i
2**—-
1 \<A
0.4
0.3
0.2
0.1
. . - - '
i
i
i
6
1
1
"—\—.
8
to
12
14
Frequency (GHz)
Fig. 4.4 Calculated |T| of the original antenna design (1.1) and its strategically (non-uniformly) miniaturized versions. With reference to Figure 4.1(b),
parameter c is kept at the value of the reference antenna (1.1). Result for
antenna II. 1 already presented in Figure 4.3 is graphed here for comparison.
For antenna II.3, parameter a is scaled down by a factor of 1.66 and d by a
factor of 4.37. The thin dashed line shows the normalized spectrum of the
input pulse.
4 Strategic Miniaturization of "Dark Eyes" Antenna
57
comparable to that of the original design, but with a structure three times smaller in the
longitudinal direction.
Future work includes further optimization of the antenna and consideration of constraints imposed by array theory of co-located cross-polarized elements
4 Strategic Miniaturization of "Dark Eyes" Antenna
58
Preface to Chapter 5:
Miniaturized Microstrip-Fed "Dark Eyes" Antenna for
Near-Field Microwave Sensing
The following chapter is included as a paper published in the IEEE Antennas and
Wireless Propagation Letters journal. It presents the complete design of the miniaturized
microstrip-fed "Dark Eyes" antenna. A detailed study of the antenna near-field radiation
pattern, fidelity, and efficiency is carried out. In addition, the antenna is analyzed in free
space and its return loss and radiation patterns are presented.
59
Chapter 5
Miniaturized Microstrip-Fed "Dark
Eyes" A n t e n n a for Near-Field
Microwave Sensing 1
Houssam Kanj and Milica Popovic
Department of Electrical & Computer Engineering
McGill University
Montreal, Quebec H3A 2A7, Canada
houssam.kanj@mail.mcgill.ca
Abstract: This paper presents a parametric study of a miniaturized, microstrip-fed
"Dark Eyes" antenna for pulsed biological sensing. The antenna is considered to be in
a medium with dielectric properties similar to those of biological materials. The planar
antenna can be easily manufactured using PCB technology with thin-film resistive layers.
Analysis indicates fidelity above 0.92 and broadband characteristics. The simulated efficiency, return loss, radiation patterns and the near-field electric-field vector magnitude are
also presented.
1
Reprinted, with permission, from reference [8], © 2005 IEEE.
2007/12/10
5 Miniaturized Microstrip-Fed "Dark Eyes" Antenna
60
Index Terms: Resistively loaded antennas, pulse radiation, microwave, breast cancer,
imaging.
5.1 Introduction
Pulsed microwave biological imaging can benefit from improved compact broadband antenna designs. Antennas used for the mentioned applications have been investigated in
the past. Several broadband designs that have been proposed [69] [67] have a compact,
but non-planar structure. [26] reports on a planar, bowtie structure where the broadband
operation is achieved through variable surface resistive loading. In this work, we present a
miniaturized design of the planar "Dark Eyes" antenna [86] that employs constant surface
resistive loading. Finally, electrically-small planar structures can be used to implement
arrays of cross-polarized antennas for versatile breast tumor imaging systems.
5.2 Design Geometry
The proposed design of the miniaturized "Dark Eyes" antenna is shown in Figure 5.1. The
antenna is to be printed on Rogers Duroid 6010 laminates coated with resistive materials
(Ohmega technologies [10]). The dielectric constant of this substrate is er = 10.2. This er
is close to the real part of relative permittivity of the biological material to be irradiated
(e.g. for fat, er = 9 at 6GHz). 6GHz is chosen as the center frequency of the 1-llGHz
band suggested for pulsed breast cancer imaging [26]. In the media-matching sense, this
choice of dielectric substrate favors our goal of imaging biological materials in the near
field. Hence, in the near-field studies, the antenna is considered to be completely immersed
in a dielectric medium of relative permittivity er = 10.2.
The dimensions of the microstrip feed [91] are also given in Figure 5.1. A resistive parasitic cover is introduced over the top dielectric layer to reduce the radiation of the feed. The
ground plane is placed on the outer surface of the bottom dielectric layer. With practical
manufacturing requirements in mind, the antenna is studied for four different commercially
available surface resistivities [10]: 25Q/D, 50O/D, lOOfi/D, and 250Q/D. Finally, the dimension of the overall structure is 22.25mmx20mmx 1.3mm. This corresponds to electrical
dimension in the dielectric medium of 0.05A2 and 6.2A2 at 1 GHz and 11GHz, respectively.
5 Miniaturized Microstrip-Fed "Dark Eyes" Antenna
Resistive Loading
Dielectric substrate of
thickness f and relative
permittivity €r
Fig. 5.1 Geometry of the microstrip-fed resistively loaded "Dark Eyes" antenna. The dimensions are (in mm): W\ = W3 = W4 = 0.75, W% = 1.5,
W5 = Si = S2 = 0.375, Lx = L5 = 1.5, L2 = L3 = 3.75, L 4 = 5.625,
L6 = L7 = 2.25, L8 = 4.5, L 9 = 8, L1Q = 6, L = 20, W = 12.75, and
t = 0.65. The dielectric substrate has er = 10.2. The noted coordinate system
is centered at the apex of the antenna.
61
5 Miniaturized Microstrip-Fed "Dark Eyes" Antenna
62
5.3 Results and Discussion
The antenna is simulated with SEMCAD [83] (three-dimensional finite-difference timedomain (FDTD) solver), which allows for easy inclusion of the complex human anatomy,
planned as near-future work. Details of the antenna modeling are identical to those in
Chapter 3. The pulse response is more easily analyzed in time domain, but HFSS [84]
(three-dimensional finite-element (FEM) solver) was used to validate Sn and antenna characterization in air. In all simulations, each layer containing conductive or resistive elements
is 70-fim thick.
Frequency (GHz)
Fig. 5.2 Antenna's return loss Sn in the 1-llGHz range, computed for a
feedline of Rref = 50S1. The antenna is immersed in a dielectric medium of
er = 9. Results are shown for Rs = 25Q/D, 50n/D, lOOfi/D and 250fi/D.
5.3.1 Return Loss and Efficiency in the Dielectric Medium
Figure 5.2 presents the antenna's Su parameter in the range 1-11 GHz for all four considered
surface resistivity values. We note that the 2:1 VSWR bandwidth calculated here is between
5 Miniaturized Microstrip-Fed "Dark Eyes" Antenna
63
2.7-9.7 GHz for all Rs values under investigation.
Table 5.1 Percentage distribution of the total incident energy from a feedline
with Rref — 50f2
Antenna Surface
Resistivity
Rs = 2 5 0 / •
Rs = 5 0 0 / •
Rs = ioon/a
Rs = 250fi/D
Reflected
Energy
4.9%
4.6%
4.5%
5.1%
Dissipated
Energy
67.0%
67.1%
62.6%
50.1%
Radiated
Energy
28.1%
28.3%
32.9%
44.8%
Radiation
Efficiency
29.5%
29.6%
34.5%
47.2%
An important parameter of resistively loaded antennas is efficiency. Table 5.1 presents
the calculated radiation efficiency and the percentage distribution of the total energy of the
incident pulse from the feedline. It is important to note that these results are dependent on
the form of the exciting pulse and its spectral content. In this case, excitation is a Gaussian
modulated continuous waveform mathematically described by:
V(t) = sm[2irf0(t - t0)] exp[-(* - t0)2/2r2}
(5.1)
with /o = 6GHz, r = 80ps, and t0 = 5r.
The first column in Table 5.1 shows the percentage of the incident energy reflected
from the feed, computed from the magnitude of the reflection coefficient Sn- As can be
estimated from Figure 5.2, it is a small percentage for all values of Rs. The second and the
third column present the values of the percentage of the dissipated and radiated energy,
respectively. The radiated energy is calculated by integrating the fields on a closed surface
around the antenna, while the dissipated energy is computed as the difference between the
radiated and reflected energy. It is interesting to note the large increase of efficiency for
larger values of surface resistivity Rs. This seemingly counter-intuitive result is explained as
follows. As Rs increases from zero to infinity, the antenna resistive section behavior changes
from lossless to lossy, and then practically to non-existent, leaving the whole radiation task
up to the bow-tie metallic section. Thus, the radiated energy is expected to have a minimum
value between value for a lossless and that of an infinitely lossy tapered section. The fourth
column shows the radiation efficiency defined as the ratio of the energy radiated over energy
5 Miniaturized Microstrip-Fed "Dark Eyes" Antenna
64
accepted by the antenna.
5.3.2 Near-field Radiation and Fidelity
The antenna is intended for use in the near-field microwave imaging applications (e.g.
breast cancer detection). With reference to Figure 5.1, the E-plane (y-z plane) defines the
origin of the polar coordinate (0 = 0). The ground and the resistive planes, parallel to the
y-z plane, are at x=-0.65mm and x=+0.65mm, respectively.
Figures 5.3(a) and 5.3(b) show the maximum magnitude of the radiated electric field in
the E- and H-plane obtained from the time-domain computations. First, the results suggest
that the radiation of the antenna is directed to its forward region (0° < 6 < 180°, —90° <
0 < 90°). Second, for different values of surface resistivity Rs used in the simulations, we
note that the intensity of the radiated electric field decreases for lower values of Rs, and
we observe a small difference in the values for Rs — 2 5 0 / • and Rs = 50O/n. Finally,
the near-field radiation pattern in the E-plane shows the radiation maxima to be directed
in the 0 = —60° and 0 = 60° with a local minimum at 0 — 0°. This can be explained
as follows. The radiating element (the "Dark Eyes" antenna) itself exhibits maximum
radiation at 0 = —90° and 0 = 90°, as was found in the initial numerical investigations.
However, the ground plane acts as a reflector element and the total structure (the radiating
element, the feed and the ground plane) radiates as shown in Figure 5.3(a). Similarly, the
maximum radiation in the H-plane is directed at 6 = 60°, as shown in Figure 5.3(b), where
the asymmetry in the radiation pattern results from the presence of the feeding structure
in the vicinity of the radiating element.
In addition, an important parameter for pulse-radiating antennas is the shape of
radiated pulse and how close it resembles the source pulse or the ideal output of
antenna. This could be measured by the antenna fidelity F, defined as the peak of
cross-correlation function between the time derivative of the exciting pulse V(t) and
radiated electric field Sre(t). Mathematically, this is defined as [40]:
the
the
the
the
+ 0O
F = max / r(t)£re(t + r)dt,
(5.2)
—oo
where r(t) = dV(t)/dt and £g(t) are normalized to their respective energies.
Figures 5.3(c) and 5.3(d) show the antenna fidelity computed at a 3-cm radial distance
5 Miniaturized Microstrip-Fed "Dark Eyes" Antenna
65
<t> = 0 °
9 = 90°
7.0
5.5
R8 = 25il/n
— Rs = 50WD
--• Rs = l(xm/n
6.5
6.0
i /i\ i
: ».
\:
: .'
\;
5.0 .....;
•— Rl = 250Q/D
/
4.5
5.5
5.0
4.0
£ 4.5
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•
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Rs = '25il/n
--• Rs = iwn/n
— Rs = 50fi7D •
:\\
s : %
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: ^*
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-60
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<>
l (deg)
60
90
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:
1.0
120
30
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120
150
180
210
0.99
•••'•" & = S M f f i
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--• i£ = l00sVn.
0.97
•• R. = '25il/n
— Ra = 50Q.7 •
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. — R, = 250fi/D
•— Rs-
U.0-94
..&0.93
90
6 (deg)
:0°
9 = 90°
•
0.96 - --• RS = ioon/a
250ft/D
:
:
:
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120
,
135
,
150
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U.0.94
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-
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nil
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30 , / ' - -45
,
60
,
75
,
90
105
,
,
9 (deg)
(d)
F i g . 5.3 Maximum magnitude of the radiated electric field and its fidelity
versus polar angles at a 3-cm radial distance from the antenna apex: (a), (c)
in the H-plane and (b), (d) in the E-plane. Plots are shown for all four values
of surface resistivity Rs. The antenna was excited with the 1-V pulse. The
d a t a were obtained from the time-domain computations.
\\\~
5 Miniaturized Microstrip-Fed "Dark Eyes" Antenna
66
from the antenna apex in the E- and H-plane as a function of the polar angels. It is important to note that the antenna fidelity is dependent on the exciting pulse (5.1), therefore,
the results should be interpreted in this context. The results of fidelity are plotted in the
range of interest (20° < 0 < 160°, -90° < (p < 90°). First, we note that the antenna fidelity
changes greatly with polar angles both in the H- and E-plane. This is mainly due to the
effect of the feed, as the initial simulations showed that the "Dark Eyes" antenna itself has
good values of fidelity in all directions [86]. The results suggest that the antenna fidelity
improves for decreasing values of surface resistivity Rs. This follows from the rationale
and discussion on the radiated energy dependence on Rs given at the end of the previous
section. Best results are achieved for antennas with Rs — 25f2/D and Rs = 5 0 0 / • . However, fidelity does not appear to be satisfactory for all values of Rs. In particular, in the
center of the region of interest (0 = 90°, 4> < 0°) further improvement is needed. In the
attempt to minimize the effect of the microstrip feed radiation on the antenna fidelity, the
coplanar strip (CPS) line length (Lg) was extended so that the radiating element is further
away from the complex feed structure. The chosen surface resistivity was Rs = 50O/D
and the simulations were repeated for two additional CPS line lengths (L$ = 6.75mm and
L8 = 9.0mm).
Figures 5.4(a) and 5.4(b) show the maximum magnitude of the radiated electric field in
the E- and H-plane at a 3-cm radial distance from the antenna apex. For the E-plane and
for longer CPS, the radiation in forward region is reduced and, in contrast, the radiation
in the backward region is increased. It is important to note that in the forward region (the
region of interest), the radiation pattern is similar for all three antennas with a minimum
at <f> = 0° between two maxima at (f) = —60° and (p = 90°. In the E-plane, the antennas
have very similar pattern as expected.
However, the effect of the length of the CPS line is much more pronounced on antenna
fidelity. Figures 5.4(c) and 5.4(d) show the antenna fidelity computed at a 3-cm radial
distance from the antenna apex in the E- and H-plane as a function of the polar angles.
First, as shown in Figure 5.4(c), the antenna fidelity shows a large improvement in the
H-plane with the increase of CPS length in the region of interest, but for a narrower
beamwidth (F > 0.92 for -75° < 0 < 58° with L 8 = 9.0mm). Outside this region, the
fidelity degrades and this could be attributed mainly to radiation from the longer CPS
line. It is also interesting to note that the increase in the CPS length results in the antenna
fidelity improvement in the E-plane. This is presented in Figure 5.4(d) and for the antenna
5 Miniaturized Microstrip-Fed "Dark Eyes" Antenna
) = 0°
8 = 90°
7.0
\
;
5.5
— L8 = 9.0mm
— Lg = 6.75mm
— Ls = 4.5mm
6.5
6.0
67
;
— L$ = 9.0mm
•-•- L$ = 6.75mm.
— L§ — 4.5mm
5.0
4.5
5.5
4.0
5.0
' " • • • /
.
/
\
"
\
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>
:
>
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90
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1.0
-30
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30
(a)
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60
90
120
9 (deg)
150
180
210
(b)
<|) = 0o
9 = 90°
0.99-
1
1
!
— L$ = 9.0mm
—- Ls = 6.75mm
— Lg = 4.5mm
0.98
0.970.96 ....;
t
• *¥
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2.0
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0.94
—
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: !
i
0.88
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0.86--80
1
^y
i
-60
-40
-20
0
20
* (deg)
(c)
40
i
i
60
80
v
30
45
60
75
90
105
e(deg)
120
(d)
Fig. 5.4 Maximum magnitude of the radiated electric field and its fidelity
versus polar angles at a 3-cm radial distance from the antenna apex: (a),
(c) in the H-plane and (b), (d) in the E-plane. Plots are shown for all three
values of the coplanar stripline section Ls with Rs = 50fi/D. The antenna
was excited with the 1-V pulse. The data were obtained from the time-domain
computations.
135
150
-
68
5 Miniaturized Microstrip-Fed "Dark Eyes" Antenna
with L8 - 9.0mm, fidelity F > 0.92 for 15° < 6 < 135°.
Finally, the computed efficiency for antenna with L 8 = 9.0mm is 30.25%. The reflected
energy, dissipated energy, and radiated energy are 4.72%, 66.46%, and 28.82% respectively.
The radiated energy is comparable, but slightly higher with respect to that of the antenna
with L8 = 4.5mm. This could be attributed to the radiation from the longer non-lossy
CPS line.
5.3.3 Return Loss and Far-field Radiation In Air
For completeness, the antenna was also characterized in air. Figure 5.5 shows the calculated
return loss. At the lower end of the frequency range of interest, the return loss degrades
in air, which is expected as the antenna's electrical length becomes smaller. The antenna
is linearly polarized and from Figure 5.6 the maximum cross-polarization levels in the Hand E-plane are -15.9dB and -17.4dB, respectively.
i
y
1
2
i
3
i
4
i
i
i
5
6
7
8
Frequency (GHz)
i
i
9
i
10
I
11
Fig. 5.5 Antenna's return loss Su (in air) in the 1-11 GHz range, computed
for a feedline of Rref = 50f2, for Rs = 50JT2/D and L§ = 9.0mm, Two simulation tools were used for validation. The discretization with the two methods
is not identical which can explain the small discrepancy in the results.
5 Miniaturized Microstrip-Fed "Dark Eyes" Antenna
21 Q
180
150
300
270
240
210
180
150
(b)
Fig. 5.6 Antenna's co- and cross-polarization patterns in the (a) H- and
the (b) E-plane at 6GHz. The maximum cross-polarization in the H- and the
E-plane is -15.9dB and -17.4dB, respectively.
69
5 Miniaturized Microstrip-Fed "Dark Eyes" A n t e n n a
70
5.4 Conclusion
A compact broadband trans-receiving antenna design is proposed for use in the near-field of
pulsed biological sensing. The antenna is a dual-layer planar structure, with the radiating
element and the microstrip feed embedded between two dielectric layers. The antenna
return loss demonstrated that it is not very sensitive to the choice of the surface resistivity
Rs, and it is less than -lOdB over the entire UWB range. For all values of surface resistivity
tested in the antenna design, the antenna with Rs = 5 0 0 / • and extended CPS feed has
demonstrated pulse transmission with fidelity exceeding 0.92 within angles of 133° in the
H-plane and 120° in the E-plane. Our ongoing work is in the direction of experimental
verification of the antenna design. In addition, the compact antenna will be studied in an
array configuration for near-field imaging applications.
5 Miniaturized Microstrip-Fed "Dark Eyes" Antenna
71
Preface to Chapter 6:
Two-Element T-Array for Cross-Polarized Breast Tumor
Detection
The following chapter is included as a manuscript in preparation for submission. Its
role in the thesis is to demonstrate the use of the "Dark Eyes" antenna in a card array
to detect both the co-polarized and cross-polarized tumor backscatter. Two antennas are
used in a T-arrangement and the tumor scans of different tumor shapes and orientations
in a layered tissue model are presented. Most important, the results show the benefits of
recording the cross-polarized tumor backscatter even when using adjacent cross-polarized
elements.
72
Chapter 6
Two-Element T-Array for
Cross-Polarized Breast Tumor
Detection
Houssam Kanj and Milica Popovic
Department of Electrical & Computer Engineering
McGill University
Montreal, Quebec H3A 2A7, Canada
houssam.kanj@mail.mcgill.ca
Abstract: This paper reports on a computational study of a 2-element cross-polarized
antenna array for breast cancer detection. The "Dark Eyes" antenna is used in a Tarrangement to form the array. The antenna return loss is below -lOdB in the range 2.3-10.3
GHz and the cross-polarized mutual coupling is less than -30dB for frequencies over 2.4
GHz. Using the finite-difference time-domain (FDTD) method, an ultra-wideband (UWB)
pulse is transmitted in the numerical breast phantom and the co- and cross-polarized backscatter response is recorded from tumors at different locations. The breast phantom was
modeled as a simple layered medium of skin and fat. The dispersive properties of layers
were introduces through a Debye model. Simulation results for a spherical and a cylindrical
tumor of different orientations are presented and discussed.
2007/12/10
6 Two-Element Cross-Polarized T-Array
73
Index Terms: Resistively loaded antennas, microwave imaging, cross-polarized array,
breast cancer detection.
6.1 Introduction
Microwave imaging techniques are currently being studied as an effective low-cost screening
tool for breast cancer detection systems [19,92]. Furthermore, polarimetric radar-base
imaging is thought to improve the imaging technique. For this application, several antennas
have been suggested [26,27]. However, most of these antennas are either large or nonplanar
and thus difficult for use in an antenna array.
In a previous work, we have proposed an ultra-wideband (UWB) compact planar antenna design [8] that is easily fabricated using the standard printed circuit board (PCB)
process with embedded resistive technology. The antenna can be manufactured on Rogers
Duroid 6010 high frequency substrates [93] laminated with a resistive conductive material
(RCM) available from Ohmega Technologies [10]. The key advantage of this antenna is
its forward-region radiation pattern. This makes the antenna a perfect candidate for a
cross-polarized card-array arrangement as suggested in [9]. In our work presented here, we
extend our study [94] of the T-arrangement to be used as a sub-array unit for radar-based
polarimetric breast cancer detection system.
The paper is organized as follows. Section 6.2 focuses on the geometry and characterization of T-arrangement for two "Dark Eyes" antennas in a homogeneous lossless medium. In
Section 6.3, we present a layered tissue model to assess near-field radiation characteristics
of the antenna arrangement of Section 6.2. Section 6.4 offers a detailed study on the tumor
detection levels as a function of the tumor shape and orientation (spherical, cylindrical —
oriented in the cross- or co-polarized manner) and discusses the reported results. Finally,
we make the concluding remarks and comment on our near-future work in Section 6.5.
6.2 Geometry and Characterization of the Two-Antenna
T-arrangement
Figure 6.1(a) shows the miniaturized "Dark Eyes" antenna reported in [8]. Figure 6.1(b)
illustrates the proposed T-arrangement of two of these antennas in a cross-polarized configuration [9]. As the antenna is aimed to serve for microwave breast cancer detection, in
6 Two-Element Cross-Polarized T-Array
Ground Plane
Resistive Layer
74
Dielectric substrate of
thickness f and relative
permittivity er
Antenna Apex
Resistive Loading
(a)
Antenna-1
Antenna-2
(b)
Fig. 6.1 (a) Geometry of the microstrip-fed resistively loaded "Dark Eyes"
antenna. L = 20 mm, W — 25 mm, and t = 0.65 mm. The dielectric
substrate has relative permittivity er = 10.2. The resistive loading and the
resistive layer both have surface resistivity of 50S7/D. Full description and
analysis of the antenna can be found in [8]. (b) Proposed cross-polarized Tarrangement of the microwave sensing array unit, with "Dark Eyes" antenna
from Figure 6.1(a) as its main element [9].
6 Two-Element Cross-Polarized T-Array
75
our study, it is immersed in a lossless medium of relative permittivity er = 10.2 which is
dielectrically close to that of the fatty breast tissue at the center of the frequency range
under investigation. The structure was simulated with SEMCAD [83] (three-dimensional
finite-difference time-domain (FDTD) solver). Details of the antenna modeling are identical to those in Chapter 3. The return loss Sn and mutual coupling 5i 2 results were also
verified with HFSS [84] (three-dimensional finite-element (FEM) solver).
We here report on the return loss and mutual coupling of the T-arrangement unit.
The structure exhibits asymmetry and should be described by all three S-parameter values
—
Sn, S12, and S22, where the indices correlate with antenna numeration indicated in
Figure 6.1(b). Figure 6.2(a) shows that the Antenna-1 return loss Sn in the 2.3-10.3GHz
range and does not exceed -lOdB. Nearly identical results (not shown here) are obtained for
S22 (Antenna-2 return loss). Another important parameter for array design is the mutual
coupling. This is quantified by the Su parameter graphed in Figure 6.2(b). As can be
observed, although the antennas were placed with only 11mm center-to-center spacing, the
£>i2 is less than -30dB in the 2.4-llGHz range. These results suggest broadband behavior
(low return loss and negligible mutual coupling) of the T-arrangement unit within the
microwave range of interest for the intended application.
6.3 Layered Tissue Model and Near-Field Radiation of the
T-arrangement Unit
Figure 6.3 presents the simple layered tissue model of the breast. It consists of a matching
medium, a 1-rnm skin layer, and a fat medium. The T-arrangement is immersed in the
matching medium which has a dielectric constant of er = 10.2. The skin, fat, and tumor
tissue are modeled with a single-pole Debye dispersive medium defined as follows:
4H
= er(w)-j4{w)
= e0O + ^ ^ - j ^ -
(6.1)
where e^ is the relative permittivity at infinite frequency, es is the static relative permittivity, as is the static conductivity, and r is the relaxation time constant. Specific material
properties for each tissue are presented in Table 6.1 [95].
Figure 6.3 shows 9 of the 25 simulated tumor locations alphabetically labeled 'a', 'b',
... 'i'. These locations, in addition to the other 16 not shown in the sketch, are evenly dis-
6 Two-Element Cross-Polarized T-Array
0
-5
/s I | |
-10
\
-15
I M
~-20
SEMCAD
- - • HFSS
:
:
> * *
HfW^r\ fx K
%/' A i
\\
CD
76
\
r
:*
T-
en
-25
>
-30
"
:
-35
;
-40.
1
: I
:"'|1
: ,1
:
1
\....\
•
!
!
4
!
i
!
5
6
7
Frequency (GHz)
1
|
i
8
10
11
8
10
11
(a)
4
5
6
7
Frequency (GHz)
(b)
Fig. 6.2 Simulated S-parameters for the T-arrangement of Figure 6.1(b).
(a) Input return loss characteristic S\\. (b) Mutual coupling Syi- The entire T-arrangement unit is considered to be immersed in a lossless dielectric
medium of er = 10.2, for the purpose of dielectric medium matching with the
fatty breast tissue. Results are shown for SEMCAD (FDTD-based) and HFSS
(FEM-based) simulation tools for comparison and verification.
6 Two-Element Cross-Polarized T - A r r a y
Fig. 6.3 Layered model of the breast showing the T-arrangement, the matching medium, skin layer, fat, and 9 of the 25 simulated tumor locations.
77
6 Two-Element Cross-Polarized T-Array
Table 6.1
78
Material properties of the debye dispersive model
Tissue
^oo
Skin
Tumor
Fat
4.00
3.99
7.00
Parameters
<rs(S/m)
es
37.00
1.10
54.00
0.70
10.00
0.15
r(ps)
7.23
7.0
7.0
tributed on the portion of the sphere centered at Antenna-1 apex. Therefore, the 25 points
find themselves distributed along a "bowl-like" surface beneath Antenna-1. The choice of
sampling field points over such a surface (as opposed to, e.g., a plane) was motivated by the
fact that we are investigating near-field radiation, where the wave has not yet acquired the
plane-front of propagation. In all the simulations, the distance between the antenna apex
and the skin is 5 mm. The tumor locations are also measured radially from the antenna
apex with a radial distance of 3 cm.
Figure 6.4 shows near-field plots on the portion of the sphere inside the layered model.
The plots are computed with HFSS and shown for three frequencies: (a) 3 GHz, (b) 6 GHz,
and (c) 9 GHz. In these simulations, both antennas are present, however, only Antenna-2
is active, while Antenna-1 is passive. As we can see from the plots, the maximum intensity
of the radiated electric field shifts toward the left side as the frequency increases. However,
it is important to note that the range of the field magnitudes at all three frequencies is
similar, approximately (2.5-5.5 V/m).
6.4 Tumor Response Study of the T-arrangement
In this section, the antenna array is used to study the co-polarized and cross-polarized
response of different tumor shapes and orientations at various locations, summarized in
Table 6.2. The antenna array was simulated using SEMCAD X [83]. The tumor was
considered to be either a sphere of diameter D = 5 mm or a cylinder with a base diameter
D = 2.75 mm and height H = 5.5 mm. The chosen cylinder has its height equal to twice
of its diameter (H — 2D), and it has the same volume as the chosen sphere. Finally, the
cylinder is either oriented in parallel with Antenna-1, when we refer to it as Co-Cylinder,
or it is oriented in parallel with Antenna-2, when it is called X-Cylinder. In this study,
6 Two-Element Cross-Polarized T-Array
79
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, 1 7S85
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1.8S86
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1,8305
3.7892
3.5623
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2.9608
2. 7828
2.8162
2.1596
2.3123
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(b)
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2.7270
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1,1783
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.93
imm
>(,
WSm
Ijjll
Bill
!C
m
d
1C
|||S
Sii
(c)
F i g . 6.4 Electric field magnitude at a radial distance of 30 m m from the
antenna apex in the layered model of Figure 6.3 at: (a) 3 GHz, (b) 6 GHz,
(c) 9 GHz. T h e parameters of the fat layer containing the points for which
the field is plotted are as follows: e r (3GHz) = 9.95 and cr(3GHz) = 0.21S/m,
e r (6GHz) = 9.8 and CT(6GHZ) = 0.4S/m, e r (9GHz) = 9.6 and CT(9GHZ) =
0.66S/m.
80
6 Two-Element Cross-Polarized T-Array
a tumor is placed in the layered model at one of the 25 locations evenly distributed on
the portion of a sphere shown in Figure 6.3, and SEMCAD is used to compute the tumor
response. Antenna-1 is excited with a Gaussian modulated sinusoidal pulse described by
V(t) = sin[27r/o(t-t 0 )]exp
(t - t0f
2r 2
(6.2)
with /o = 6GHz, T = 80ps, and t0 = 5r, while Antenna-2 is kept passive. To compute
the tumor response for each tumor location, two simulations are performed to obtain the
voltage at the antenna feed: one with, and one without the tumor. By subtracting one
simulated response from the other, skin reflection and early-time artifacts could be removed,
providing the response of the tumor only. This is done for both antennas, Antenna-1 and
Antenna-2, to compute the co-polarized and cross-polarized tumor response, respectively.
Figure 6.5 shows the co-polarized and cross-polarized tumor response for the different
tumor shapes/orientations considered within the spherical surface defined in Figure 6.3.
The presented results are the linear interpolation of the computed tumor response at the
25 simulated locations for each case. First, from Figure 6.5 (a) and the computed data, we
can see that the co-polarized tumor response for the sphere ranges from -88.6dB to -81.5dB
(7.1dB). Our study confirms that the tumor response plot in this specific case correlates
with the near-field radiation pattern of the "Dark Eyes" antenna. For the Co-Cylinder
case shown in Figure 6.5 (c), the co-polarized tumor response ranges from -90.2dB to 83.2dB (7.0dB), while for the X-Cylinder case shown in Figure 6.5 (e), the co-polarized
tumor response ranges from -94.8dB to -86.5dB (8.3dB). We note that the co-polarized
tumor response spatial variation is approximately 7dB to 8dB for all three cases, however,
the co-polarized tumor response for the Sphere and the Co-Cylinder is approximately 4dB
higher than that of the co-polarized X-Cylinder tumor response.
Second, Figures 6.5 (b), (d), and (f) show the cross-polarized tumor response for all
three of the previously noted cases. Figure 6.5 (b) shows the cross-polarized tumor response
for the Sphere, ranging from -105.OdB to -88.7dB (16.3dB). Then, for the Co-Cylinder case
shown in Figure 6.5 (d), the cross-polarized tumor response ranges from -104.OdB to -91.8dB
(12.2dB). Finally, the X-Cylinder case is shown in Figure 6.5 (f) with its cross-polarized
tumor response ranging from -101.3dB to -89.3dB (12.OdB).
When we compare results in graphs Figure 6.5 (b), (d), and (f) with Figure 6.5 (a), (c),
and (e), we can note that the co-polarized tumor response is always higher than that of the
6 Two-Element Cross-Polarized T-Array
81
cross-polarized tumor response for the case of the Sphere and the Co-Cylinder. However,
this is not the case for the X-Cylinder where the approximate 5.5dB overlap in the range
of the co-polarized tumor response [-94.8dB to -86.5dB] and that of the cross-polarized
tumor response [-101.3dB to -89.3dB] implies that having both co- and cross-polarization
measurement may be advantageous for the overall detection process. Table 6.2 presents a
summary of the tumor response study for all three cases under investigation.
Table 6.2 Tumor response summary
Tumor shape and orientation
Sphere
Size (mm)
Co-pol response range (dB)
Cross-pol response range (dB)
Diameter D = 5
max = —81.5
min = —88.6
delta = 7.1
max = —88.7
min = —105.0
delta = 16.3
Base Diameter D = 2.75
Height H = 5.5
max = —83.2
min = —90.2
delta = 7.0
max = —91.8
min = —104.0
delta = 12.2
Base Diameter D = 2.75
Height H = 5.5
max = —86.5
min = —94.8
delta = 8.3
max = —89.3
min = —101.3
delta = 12.0
Antenna-2 axis fc
V-ss.
Antenna-1 axis
©••-*
Co-cylinder
Antenna-2 axis ft
**
•• — ( T ^ >
Antenna-1 axis
— - »
Cross-cylinder
Antenna-2 axis ^
£\
Antenna-1 axis
6.5 Conclusion
This work presented an array arrangement of the "Dark Eyes" antenna for breast cancer
detection. The antennas are arranged in a cross-polarized card array and exhibit low
return loss (-10dB from 2.3GHz to 10.3GHz) and low mutual coupling (-30dB from 2.4GHz
to 11 GHz) even when placed in the very proximity of each other. The near-field radiation
patterns at 3GHz, 6GHz, and 9GHz were also presented and the results show that the
radiated energy is better directed to the forward region of the antenna at the lower frequency
range. Further, a computational study of the tumor response for different tumor shapes
and orientations was executed in a simple layered breast model. Both, the co-polarized and
the cross-polarized backscatter was recorded from the tumor placed at different locations
in the forward region of the antenna array. The initial results indicate that when looking
at the co-polarized response, it is the Sphere and the Co-Cylinder that provided higher-
6 Two-Element Cross-Polarized T-Array
(a) co-polarized response
•<&>
82
(b) cross-polarized response
fr
•100
i
•102
•104
(c) co-polarized response
(d) cross-polarized response
•90
-92
-94
•96
•98
•100
9
•102
-95
•104
(e) co-polarized response
(f) cross-polarized response
F i g . 6.5 T h e co-polarized and cross-polarized t u m o r response (dB) for the
different tumor shapes/orientations. T h e tumor was considered to be either
a sphere ( D = 5 mm) or a cylinder with a (D=2.75 m m , H = 5 . 5 m m ) . The
cylinder is either oriented in parallel with Antenna-1, when we refer to it as
Co-Cylinder, or it is oriented in parallel with Antenna-2, when it is called
X-Cylinder. Results for: (a) and (b) Sphere, (c) and (d) Co-Cylinder, and (e)
and (f) X-Cylinder.
6 Two-Element Cross-Polarized T-Array
83
amplitude response. On the other hand, when looking at the cross-polarized response,
it is the X-Cylinder that provided the higher-amplitude response. Thus, for extracting
maximum information about the tumor, and since the tumor shape and orientation are
unknown, there is an advantage in using the cross-polarized array arrangement.
6 Two-Element Cross-Polarized T-Array
84
Preface to Chapter 7:
A Novel Ultra-Compact Broadband Antenna for Microwave
Breast Tumor Detection
The following chapter is included as a paper in preparation. It presents a novel antenna
design for microwave imaging applications. The antenna has a similar structure to the
"Dark Eyes" antenna as it is planar and resistively loaded with a constant surface resistive
material. However, the antenna is uniplanar making it much easier to manufacture. In
addition, the antenna is ultra-compact ultra-broadband with a strong forward radiation
pattern. Its low profile makes it an excellent candidate for a cross-polarized card array
arrangement of several elements.
85
Chapter 7
A Novel Ultra-Compact B r o a d b a n d
A n t e n n a for Microwave Breast
Tumor Detection
Houssam Kanj and Milica Popovic
Department of Electrical & Computer Engineering
McGill University
Montreal, Quebec H3A 2A7, Canada
houssam.kanj @mail.mcgill.ca
Abstract: This paper presents a novel resistively loaded antenna design for microwave
breast cancer detection. The antenna is planar and ultra-compact, and can be easily
manufactured using PCB technology with embedded thin-film resistive layers. Through
numerical simulations, the antenna demonstrates a return loss below -10 dB over a wide
frequency range from 2 to 35 GHz. For pulse radiation in the ultra-wideband (UWB)
range in a biological medium, the antenna shows an excellent fidelity above 0.95 and a
relatively high radiation efficiency of 39.21% in comparison to resistively loaded antennas.
In addition, a design rule guideline is presented for designing the antenna to radiate in
a specific background medium and with a given lower operating frequency. Finally, a
complete microstrip feed design is presented for the antenna operating in the UWB range.
2007/12/10
7 Novel Ultra-Compact Broadband Antenna
86
Index Terms: Broadband antennas, resistively loaded antennas, microwave imaging,
breast cancer detection.
7.1 Introduction
Confocal microwave imaging techniques (CMI) are currently being studied as an effective
low-cost screening tool for breast cancer detection systems [19,21,22]. In this method, a single trans-receiving antenna or a couple of antennas is used to scan the breast mechanically
and synthetically generate the antenna array. On the other hand, recent work [1,23,24] has
demonstrated that multistatic systems with a real aperture array offer a notable improvement for the imaging technique. Although several antennas have been suggested [27,67] for
use with CMI breast tumor detection, most of these antennas are either large or nonplanar
and thus difficult for use as a base for an antenna array of several elements.
In a previous work, we have suggested an ultra-wideband (UWB) compact planar antenna design [8] that is easily fabricated using the standard printed circuit board (PCB)
process with embedded resistive technology. In this work, a new antenna design with a very
wide-band behavior and an ultra-compact size is presented. This new design is simpler than
the "Dark Eyes" antenna with an order of magnitude of improved performance. The antenna can be manufactured on Rogers Duroid 6010 high-frequency substrates [93] laminated
with resistive conductive material (RCM) available from Ohmega Technologies [10]. In addition, the key advantage of this antenna is its strong forward-region radiation pattern.
This makes the antenna a perfect candidate for a cross-polarized card-array arrangement
as suggested in [9]. This new design will be a key element in developing the radar-based
multistatic polarimetric breast cancer detection system.
7.2 Antenna Design
The new proposed design named the Traveling Wave Tapered and Loaded Transmission Line Antenna (TWTLTLA) has evolved from the coplanar-strip fed miniaturized
"Dark Eyes" antenna through several design modifications with the main objective to
improve the antenna lower operating frequency and to further miniaturize it at the same
time. The idea started by re-thinking about what is exactly an antenna.
According to the IEEE Standard Definitions of Terms for Antennas [96], the antenna
7 Novel Ultra-Compact Broadband Antenna
87
is a mean to radiate or receive radio waves. In other words, it is a transitional structure
between free-space and a guiding device [97]. It could also be interpreted as a mode
transformer that transforms a guided wave in a transmission line or a waveguide structure
into a plane wave propagating in free-space [98]. This usually happens under matched
condition and it is a key idea in developing traveling wave antennas. Furthermore, for
broadband antennas, this matched condition should be satisfied within a broad range of
frequencies. In addition, the above definition equally applies for radiating waves in a
different background medium than free-space.
For a matched condition to happen, reflections should be minimized at the joint location
of the transmission line guiding the wave and the antenna. In addition, the antenna itself
should have a traveling wave nature. This led to the idea of merging the "Dark Eyes"
antenna with its coplanar-strip feed to form one smooth tapered and resistively loaded
structure that will guide the wave and radiate it into the background medium.
The evolution steps that transformed the "Dark Eyes" antenna into the TWTLTLA
antenna are summarized next, but first we will present the initial development idea.
The antenna was simulated with SEMCAD [83], three-dimentional finite-difference
(FDTD) solver, and with high-frequency structure simulator (HFSS) [84]. In all simulations, the antenna was assumed to be printed on a dielectric board of dielectric constant
er = 10.2 and immersed in a background medium of the same dielectric constant er = 10.2.
The antenna conductive and resistive layers were assumed to be 70-^m thick, and the
resistive material has a surface resistivity Rs = 50£2/n.
Fig. 7.1 show the original miniaturized "Dark Eyes" antenna with its CPS line feed
and Fig. 7.2 present the return loss Su computed with SEMCAD in the range l-35GHz.
Although the antenna has a broad operating bandwidth, the return loss degrades below
3.12GHz. With the objective of further miniaturizing the antenna and improve its lower
operating frequency, new ideas were thought. One such idea is the use of the CPS line
length to radiate the wave in a similar manner to the operating mechanism of tapered slot
antennas (TSAs). This idea of combining a tapered transmission line with a resistively
loaded section proves to be novel and does not suffer from the size limitation of typical
traveling wave TSAs (length L > 2A and width W > A/2) [98]. For example, the final
TWTLTLA antenna can achieve a traveling behavior with a width much smaller than A/2.
Fig. 7.3 presents the initial idea developed using elliptical curves.
88
7 Novel Ultra-Compact Broadband Antenna
Resistive Material
Copper
A
C
Fig. 7.1 The original "Dark Eyes" antenna design with its CPS transmission
line feed and the left arm of the evolved TWTLTLA final antenna design
showing parameterization curves and points. Total width of the original "Dark
Eyes" antenna, I'-to-F (left point of the left arm to right point of the right
arm), is 20mm.
-10
-15
m
T3
-20
V)
-25
-30
-35
-40
YfV]
10
15
20
Frequency (GHz)
25
30
35
Fig. 7.2 Return loss Su of the original "Dark Eyes" antenna in the l-35GHz
range, computed for a reference feedline with i? r e / = 50£1 The antenna is
immersed in a dielectric medium of er = 10.2. The return loss is below -lOdB
in the 3.12-22.48 GHz range.
7 Novel Ultra-Compact Broadband Antenna
Fig. 7.3 Initial idea to combine the CPS line feed and the initial metallic
section of the original "Dark Eyes" antenna to form a single tapered transmission line section. Two ellipses E\ with semimajor axis a and semiminor axis
b, and E-i with semimajor axis a' and semiminor axis b are used to form the
tapered transmission line section. E\ passes through point A and N' and it is
tangent to line section NT. E2 is a shifted version of E\ that passes through
point C and scaled along its major axis to pass through point M'.
89
7 Novel Ultra-Compact Broadband Antenna
90
7.2.1 Characteristic Impedance of CPS and A P S lines
Since the TWTLTLA antenna is formed by tapering a transmission line, either a CPS line
or an APS line, the design process starts by developing a transmission line with a desired
characteristic impedance ZQ. In this section, we assume that the desired characteristic
impedance is Z0 = 50O. However, the design process of a TWTLTLA antenna that is
matched to any given reasonable ZQ is identical.
Figure 7.4 shows a CPS structure. The characteristic impedance Z 0 of such a structure
depends on the following parameters: the relative permittivity of the dielectric substrate
ers, The relative permittivity of the background material er&, dielectric substrate height h,
conducting strip width w, conducting strip thickness t, and the conducting strip separation s.
Two CPS line were designed on a substrate with ers = 10.2 and assumed to be immersed
in the same background medium with erb = 10.2. The first one has the following dimensions: w = 375/xm, s = 375/im, t = 70/um, and h = 0.635mm. Using a two dimensional
finite difference code, the characteristic impedance was computed to be Z0 — 61.80. The
characteristic impedance versus frequency was also computed using SEMCAD and HFSS
in the l-20GHz range and it is shown in Fig. 7.5. HFSS result, Z0(lGHz) = 620, is in
close agreement with the finite difference code, while SEMCAD predicted a slightly lower
value of Z0(lGHz) = 520.
A second CPS was designed which has the same dimensions as the first one except
for the separation s = 200/nm. The characteristic impedance computed using the two
dimensional finite difference code was found to be Z0 = 49.30. Simulation results using
SEMCAD and HFSS are presented in Fig. 7.6. Again, HFSS result, Z0(lGHz) = 510, is in
close agreement with the finite difference code, while SEMCAD predicted a slightly lower
value of Z0(lGHz) = 430.
7 Novel Ultra-Compact Broadband Antenna
91
Dielectric Substrate
£ = £„£„
Conducting Strips
Background Dielectric
e = e.e.
Fig. 7.4
Coplanar stripline (CPS) configuration.
70
60
r
g 50
~ ~
_i_
T3
| 40
.o
(fl
30
I10
HFSS
- - - SEMCAD
10
Frequency (GHz)
15
20
Fig. 7.5 Characteristic impedance versus frequency for a CPS line printed
on a dielectric board with a dielectric constant of e rs = 10.2 and immersed in
a background medium of dielectric constant erb = 10.2. The CPS dimensions
are: w = 375/Ltm, s = 375/xm, and t = 70/um. The board thickness is h =
0.635mm.
7 Novel U l t r a - C o m p a c t B r o a d b a n d A n t e n n a
92
60
50
I 40
v
a.
E
o 30
*3
</>
"C
§ 20
re
£
o
10
1
HFSS
- - - SEMCAD
5
10
Frequency (GHz)
15
20
Fig. 7.6 Characteristic impedance versus frequency for a CPS line printed
on a dielectric board with a dielectric constant of ers = 10.2 and immersed in
a background medium of dielectric constant erb = 10.2. The CPS dimensions
are: w — 375jum, s = 200/um, and t = 70/j.m. The board thickness is h =
0.635mm.
7 Novel Ultra-Compact Broadband Antenna
93
An important step in the design of a broadband antenna is the choice of a suitable
feeding technique. In order to open the possibility of using a direct microstrip feed in a
similar manner to the microstrip fed antipodal Vivaldi antenna [99], APS line was also
designed and used to develop the TWTLTLA antenna.
Fig. 7.7-7.9 show the three possible configurations of an APS line. Depending on the
background medium (er&) and the substrate characteristics (ers, h and r), one configuration
might be more suitable than the others to achieve a given characteristic impedance Z0.
With the objective of designing an APS line with a characteristic impedance as close
to 50O as possible but with similar dimensions to the CPS line presented above, an APS
line with overlapping strip edges with the following dimensions was designed: w = 375//m,
s = 10(tyim, t = 70/rni, and h = 0.635mm. The dielectric constant of the background
medium and the board was also considered to be 10.2.
Using the two dimensional finite difference code, the characteristic impedance was computed to be ZQ = 65.20. Simulation results using HFSS and SEMCAD are also plotted
in Fig. 7.10. HFSS result, Z0(lGHz) = 670, are again in close agreement with the finite
difference code, while SEMCAD predicted a slightly lower value of Z0(lGHz) = 620 and
further decreases a higher frequency.
As we can see, the characteristic impedance of the APS line is slightly higher than the
desired value of 50O, however, simulation results in the following section will show that
this will have a minor effect on the input return loss of the antipodal TWTLTLA antenna
design.
7 Novel Ultra-Compact Broadband Antenna
Dielectric Substrate
Fig. 7.7
Fig. 7.8
Antipodal stripline (APS) configuration with even strip edges.
Antipodal stripline (APS) configuration with separated strip edges.
7 Novel Ultra-Compact Broadband Antenna
Dielectric Substrate
Conducting Strips
Background Dielectric
Fig. 7.9
Antipodal stripline (APS) configuration with overlaping strip edges.
70
60
- — — — —_
"* •*•—
u 50
-.
" " " " • - " • - .
-- -
c
IS
T3
<U
a
40
E
30
o
re 20
x:
O
10
I
HFSS
I - - - SEMCAD
10
Frequency (GHz)
15
20
Fig. 7.10 Characteristic impedance versus frequency for an APS line with
overlaping strip edges. The APS line is printed on a dielectric board with
a dielectric constant of ers = 10.2 and immersed in a background medium
of dielectric constant er(, = 10.2. The APS dimensions are: w — 375//m,
s = 100/Ltm, and t = 70^im. The board thickness is h = 0.635mm.
7 Novel Ultra-Compact Broadband Antenna
96
7.2.2 Evolution Steps
Figures 7.11-7.17 depict the sequence of modifications and rationale that resulted in transforming the "Dark Eyes" antenna into the TWTLTLA antenna with a large improved
performance. Unless otherwise stated, the return loss Sn of each evolved design is computed using SEMCAD and plotted for a reference impedance Rref — 50£1
Fig. 7.11 presents the first evolved design. It is formed from the ellipses defined in
Fig. 7.3. This design has an improved higher frequency performance, however, its lower
frequency limit is rather high (//, = 4.43GHz).
To improve the lower frequency operation of the antenna, the resistive area was increased
by pushing back the border line between the different material toward the transmission line
origin. In addition, this will eliminate the geometric discontinuity at the border line of the
material. This constitute the second evolved design shown in Fig. 7.13. The antenna has a
very large bandwidth with a lower frequency limit fL = 1.78GHz. However, the increased
size of the resistive area will further reduce the antenna efficiency.
Fig. 7.15 presents the third evolved design. Here, the objective was to reduce the size of
the resistive and the total antenna length while keeping the improved performance of the
second evolved design. This was achieved through the geometrical modification explained
step-by-step in the figure caption. This design has a total width of 16mm and a lower
frequency limit of JL = 1.84GHz.
Fig. 7.17 presents the final design. In this design, all discontinuities are removed and the
geometric taper of both antenna sections (conductive and resistive) is formed from smooth
curves only (from the origin of the transmission line to the antenna ends). The figure
caption explains in further detail how to construct the antenna taper. In this design, the
total antenna width is further reduced to only 14mm. For this design, the antenna return
loss Sn was computed using both SEMCAD and HFSS for comparison and verification. The
results computed with SEMCAD show a return loss below -lOdB in the 1.94-35 GHz range.
For HFSS, the computed results show a return loss below -lOdB in the 1.73-34.37 GHz
range. Simulation results for both SEMCAD and HFSS are in close agreement as can be
seen in Fig. 7.18.
The above discussion summarized the steps that have led to the development of the
TWTLTLA. In addition, and through numerous numerical analysis, a design methodology
and guideline for developing antipodal and coplanar TWTLTLA will be presented in the
7 Novel Ultra-Compact Broadband Antenna
97
following section. However, an important point that was observed and need to be stressed
here is the fact that the antenna input impedance "takes on" the characteristic impedance
of the original transmission line. Fig. 7.19 presents HFSS simulation results for the final
antenna design of Fig. 7.17 referenced to both 50fi and 60fl As we can see, since HFSS
predicts a characteristic impedance of 60J1 for the CPS line with separation s = 375/im
(as shown in Fig. 7.5), the antenna return loss improves when referenced to Rrej = 6017.
Fig. 7.19 also presents the HFSS simulation results for the final antenna design when
developed from an identical CPS line but with a separation s = 200/im. As we can see again,
since HFSS predicts a characteristic impedance of 50fi for the CPS line with separation
s = 200^m (as shown in Fig. 7.6), this antenna is rather matched to Rref = 50(1
Finally, Fig. 7.20 shows the results for the TWTLTLA developed from the APS line
of Fig. 7.10. When referenced to 50fi, the results computed with SEMCAD show that
the minimum lower operating frequency of -lOdB return loss is equal to 2.14GHz while for
results computed with HFSS it is equal to 1.97GHz. As we can see, the antipodal design
has similar performance to the coplanar version. Again, simulation results have shown that
the antenna input impedance is rather matched to 60O and not 50f2. This is explained by
the fact that the APS used to develop the antenna has a characteristic impedance slightly
higher than 50O (as shown in Fig. 7.10).
7 Novel Ultra-Compact Broadband Antenna
98
>*
Fig. 7.11 First evolved design. Resistive area is the same as the one used
in the "Dark Eyes" antenna and the total antenna width I'-to-I' is still 20mm.
However, in this design, the CPS feedline and the initial metallic section of
the "Dark Eyes" antenna are merged to form a tapered elliptical transmission
line defined by the ellipses shown in Fig. 7.3. This design shows an improved
return loss at higher frequencies, but a relatively degraded performance in the
lower frequency range. This could be explained by the strong discontinuity
that exist at point M' where both the material and the geometric form change.
0
-5
-10
-15
S
-20
-25
-30
\
-35
-40
10
15
20
Frequency (GHz)
\
25
30
35
Fig. 7.12 Return loss S\\ of the first evolved design in the l-35GHz range,
computed for a reference feedline with Rref = 50S7. The antenna is immersed
in a dielectric medium of er = 10.2. This design has a return loss below -lOdB
in the 4.43-28.65 GHz range.
7 Novel Ultra-Compact Broadband Antenna
99
IW
Fig. 7.13 Second evolved design. Here, the line M'N' (border between different material) is pushed back toward the transmission line origin and form
the HG line. The behavior of this antenna improves significantly, however, the
resistive area is now quite large which implies lower antenna efficiency. The
antenna width, I'-to-I', remains to be 20mm.
o
1
1
r
i
~r
—
-5
-10
-15
\
-20
-25
-30
-35
"1
5
10
15
20
Frequency (GHz)
25
30
35
Fig. 7.14 Return loss S\\ of the second evolved design in the l-35GHz range,
computed for a reference feedline with Rref = 50f2. The antenna is immersed
in a dielectric medium of er = 10.2. This design has a return loss below -lOdB
in the 1.78-35 GHz range.
7 Novel Ultra-Compact Broadband Antenna
100
Fig. 7.15 Third evolved design. Here, an attempt to reduce the effect of
the discontinuity at point M' is executed by pushing it further away on the
CI curve up to point M and making the lossy path that the current has to
travel longer before it intercepts the discontinuity. Then, the total antenna
width is reduced by first pushing point N' slightly back to point N, and second
by extending the line at point N in a tangent direction to intercept the line
MI' at point I". In this manner, the lossy resistive area is reduced. The total
antenna width, I"-to-I", is also reduced to 16mm.
0
i
!
5
10
i
!
r
r
25
30
-5
-10
-15
ST
-25
-30
-35
"1
15
20
Frequency (GHz)
35
Fig. 7.16 Return loss Su of the third evolved design in the l-35GHz range,
computed for a reference feedline with Rref — 50fi. The antenna is immersed
in a dielectric medium of e r = 10.2. This design has a return loss below -lOdB
in the 1.84-35 GHz range.
7 Novel Ultra-Compact Broadband Antenna
101
+C
Fig. 7.17 The final design. First, the discontinuity at point M is removed
by simply extending the elliptic curve to point I where it is intercepted by
another elliptical curve NI. In this manner, all discontinuities are removed
and the antenna total width, I-to-I, is further reduced to only 14mm.
0
I
!
>
SEMCAD
- - - HFSS
-5 A
-10
-15
m
S
c/f
_20
n
n
:
\
\ 'A' f\ » /'
if
'W
-25
-30
ll
1
'
i|
-
/A
A
V//'
\V 7 ""\"v7,-
v/
\ V'
1,»
...l . 1 :
l'f
>
1
II
10
15
20
Frequency (GHz)
-35 r
-40
25
30
35
Fig. 7.18 Return loss S u of the final antenna design in the l-35GHz range,
computed for a reference feedline with Rrej = 50fL The antenna is immersed
in a dielectric medium of er = 10.2. The results computed with SEMCAD
show a return loss below -lOdB in the 1.94-35 GHz range. For HFSS, the
computed results show a return loss below -lOdB in the 1.73-34.37 GHz range.
102
7 Novel Ultra-Compact Broadband Antenna
— s=0.375mm, R =50£2
ref
. - - s=0.375mm, R =60Si
ref
. . . s=0.2mm, R ,=50fi
'
ref
m
•o
tn
10
15
20
Frequency (GHz)
25
35
Fig. 7.19 Return loss 5 n of the final antenna design in the l-35GHz range
computed with HFSS. The solid line curve is for the antenna with a separation
s = 375/im and referenced to a 50O feedline while the dashed line curve is for
the same antenna when referenced to a 60fi feedline. On the other hand,
the dash-dot line curve is for the antenna with a separation s = 200^m and
referenced to a 50O feedline. The antenna is immersed in a dielectric medium
of er = 10.2.
15
20
Frequency (GHz)
Fig. 7.20 Return loss 5 n of the final antenna design when developed from
an antipodal stripline APS with overlaping strip edges of s = 100/um. The
results are shown in the l-35GHz range and referenced to a 50f2 feedline. The
results computed with SEMCAD show that the minimum lower operating
frequency of -lOdB return loss is equal to 2.14GHz while for results computed
with HFSS it is equal to 1.87GHz.
7 Novel Ultra-Compact Broadband Antenna
103
7.2.3 Design rules guideline for the TWTLTLA antenna:
1- Depending whether it is desired for the antenna to be coplanar or antipodal, begin by
designing a CPS or an APS transmission line with the desired characteristic impedance ZQ
(the final antenna design will have an input impedance matched to Z0).
Note: Antipodal antennas have usually higher cross-polarization radiation than their
planar counterpart, however it is easier to design a broadband matching feed for the antipodal structure.
2- Once the CPS or the APS is designed (in a specific background medium that the antenna
is supposed to radiate in), taper every conducting strip of the CPS or the APS following the
geometric dimensions given in Figure 7.21. This will lead to an almost optimal TWTLTLA
antenna design.
a. Path "AC" corresponds to the conducting strip width w.
b . The resistive material should have a surface resistivity Rs. A good choice for Rs is
50O/D, however, the optimal Rs value for a specific medium should be determined
through simulations and experiments.
c. A is the wavelength in the radiating medium corresponding to the lower operating
frequency fL of the antenna.
d. Path "CHMI" is elliptical, but it could also be exponential, or any function of a
similar form. However, it is advisable to keep all curves smooth, which is to have
a continuous second order derivative at any joining point. The same holds for path
"AGN" and path "NI".
e. Points H and G are used to further optimize the antenna. They are also dependent
on the available surface resistivity Rs.
f. Conducting strip separation s at the origin of the antenna design should be the same
as in the CPS or the APS design. In fact, a transverse plane cut at the origin of
the antenna should be identical to any transverse plane cut in the CPS or the APS
design.
7 Novel Ultra-Compact Broadband Antenna
X = wavelength in the radiating medium
for the antenna lower cutoff frequency
Points H & G are "floating"
Path "CHMI" is elliptical, but it could
be exponential or any function of a
similar form
The same is true for path "AGN" and path "Nl"
Fig. 7.21 Detailed antenna geometry and electrical dimensions associated
with a matching medium of dielectric constant er and designed for a specific
minimum lower operating frequency /z, = c/(Xy/e^).
104
7 Novel Ultra-Compact Broadband Antenna
105
7.3 Antenna Characteristics in the U W B range
Since the antenna is intended for use in confocal microwave imaging of breast cancer and
similar near-field sensing applications, it is important to characterize its pulse radiation
performance in the UWB range and in the near-field.
The antenna was simulated with SEMCAD as it is easier to analyze the pulse response
in time domain. The excitation pulse is shown in Fig. 7.22. It consists of a Gaussian
modulated sinusoidal waveform mathematically described by:
V(t) = sin[27r/0(t - to)] exp[-(t -
t0)2/2r2}
(7.1)
with /o = 6GHz, r = 80ps, and t0 = 5r. This pulse has a temporal width of 0.19 ns (full
width at half maximum-FWHM). Its is centered at 6GHz with a spectral width of 4.4 GHz
(FWHM) and no dc content.
Simulation results for the antenna efficiency, near-field radiation and fidelity are presented next.
1
0.8
0.6
0.4
£
0.2
c
(0
S -0.2
-0.4
-0.6
4—
-0.8
0.5
Fig. 7.22
1
Time (ns)
1.5
Waveform of the Gaussian modulated sine described by Eqn. 7.1.
7 Novel Ultra-Compact Broadband Antenna
106
7.3.1 Efficiency
Table 7.1 presents the calculated antenna efficiency and the percentage distribution of the
total energy of the pulse incident from the feedline. As we can see, the antenna efficiency is
relatively high when compared to typical resistively loaded antennas presented in Table 2.1.
However, it important to note these results are dependent on the excitation waveform and
its spectral content.
Table 7.1 Percentage distribution of the total incident energy from a feedline
with Rref = 50O.
Antenna Surface
Resistivity
Rs = 5 0 0 / •
Reflected
Energy
2.82%
Dissipated
Energy
59.08%
Radiated
Energy
38.1%
Radiation
Efficiency
39.21%
7.3.2 Near-field Radiation and Antenna Fidelity
6>
+ J>
-wmpc
0
Fig. 7.23 Antenna orientation in polar coordinates.
The antenna pulse performance in the UWB range can be characterized by fidelity (F)
of the radiated field in time domain. It is a measure of distortion in the radiated waveform
as it propagates away from the antenna and it is defined as the maximum cross-correlation
107
7 Novel Ultra-Compact Broadband Antenna
\ 135 Jr
45
1
1.4
1
1.4
/
-180°—
3.2
0.6
1
1.4
Fig. 7.24 Radiated electric field waveform computed at 3cm radial distance
from the antenna apex in the H-plane and as a function of the polar angle </>.
\
9°
135
1
1.4
1
1.4
/
45°
-180°—
.2
0.6
Fig. 7.25 Radiated electric field waveform computed at 3cm radial distance
from the antenna apex in the E-plane and as a function of the polar angle 9.
7 Novel Ultra-Compact Broadband Antenna
108
between the time derivative of the exciting pulse V(t) and the radiated electric field Sre{t)
as such [40]:
+00
F-max
/ r(t)8re{t + T)dt,
(7.2)
—oo
where r(t) = dV(t)/dt and ££(*) are normalized to their respective energies. With this
definition, the fidelity ranges from 0 to 1 with F=l indicating a perfect match between f(t)
and £g{t).
Since we are interested in sensing applications in the near-field, the antenna fidelity was
computed at 3cm radial distance from the antenna apex in the E- and H-plane. Fig. 7.24
and 7.25 present the transient radiated electric field waveform ££(£) in a 180° span in the
forward region. By visual inspection, it is possible to observe that the radiated waveform
is approximately the time derivative of the exciting signal given by Eqn. 7.1. For a quantitative measure, Table 7.2 presents the computed fidelity at several observation angle in
the E- and H-plane. As we can see, except for fidelity at 90° angles off boresight in the
H-plane, the antenna fidelity is excellent and it is over 0.95.
Table 7.2
Radiated electric field fidelity F at selected polar angles
"——^___^^ Polar angles: 9 or <j)
0°
Radiation
~~~——-____^^
Plane
-—_____^
0.821
H-plane (d = 90°)
0.959
E-plane (<p = 90°)
22.5°
45°
67.5°
90°
0.958
0.977
0.989
0.986
0.996
0.993
0.997
0.997
Finaly, the antenna near-field radiation patterns computed at 3cm radial distance from
the antenna apex are presented. Fig. 7.26 and 7.27 give the magnitude of the radiated
electric field in the H-plane and E-plane at three selected frequencies across the UWB
span: 3GHz, 6GHz, and 9GHz. As we can see, the antenna near-field radiation is relatively
uniform in the H-plane with a half-power beamwidth of 183.20°, 124.96°, and 99.68° at
3GHz, 6GHz, and 9GHz respectively. In the E-plane, the near-filed radiated intensity
varies slightly, however, the -3dB beamwidth it is still wide and equal to 101.81°, 78.30°,
and 77.73° at 3GHz, 6GHz, and 9GHz respectively.
7 Novel Ultra-Compact Broadband Antenna
109
r
i
^\
/
-5
/
x
v
-\\—
s
V
..._...,„
-::.-:.-,. r-
•\ '~'\~v^
/
i
\
i
/.,.
/
/
V '*"'«.
\\ : x sx
\
\
'l
\
i
i
•i= - 1 5 h i
i
V
:
\\
-20;i
- - 3 GHz
- - - 6 GHz
9 GHz
-25
-30
0
20
40
60
V
A
UJ
CO
0>
"
80
100
t> (deg)
120
V
140
'
160
180
Fig. 7.26 Antenna near E-field magnitude computed at 3cm radial distance
from the antenna apex in the H-plane at three selected frequencies: 3GHz,
6GHz, and 9GHz.
1
-^~~*-^
v
\
\
t
/
I-
4
h
•
/ \
/ \
•
/
s
/
•
•
•
/
/
^s'
y
y
\
•
\
\
>
\
\
y
• — 3 GHz
- - - 6 GHz
9 GHz
y
0
\
's^
y
y
-10
\
1
y
1 -8
\
•
^ „ '
UJ
\
4
y
f
\
\
\
y
20
40
60
80
100
6 (deg)
120
140
160
180
Fig. 7.27 Antenna near E-field magnitude computed at 3cm radial distance
from the antenna apex in the E-plane at three selected frequencies: 3GHz,
6GHz, and 9GHz.
7 Novel Ultra-Compact Broadband Antenna
110
7.4 Balun Design
Figure 7.28 shows the antenna design with the balun/feed as it will be manufactured on a
printed circuit board. It consists of a top layer, a dielectric substrate, and a bottom layer.
The detailed dimensions of the top layer are shown in Figure 7.29. First, a copper
section consisting of a linearly tapered microstrip feed connected to the elliptical radiating
element. Second, the elliptical tapered resistive section serving as a partially radiating
partially dissipating element. Figure 7.30 shows the detailed dimensions of the bottom
layer. The first section consists of an elliptical tapered copper section forming the ground
plane/balun. It is the idea of opening the possibility to use a tapered ground plane as a
balun that have led to the development of the TWTLTLA in its both versions, coplanar
and antipodal. In this way, the balun design is not limited to only coplanar structures. The
second and the third sections form the radiating/dissipating elements of this layer and they
are identical to the one of the top layer. Finally Figure 7.31 presents the ellipses dimensions
and orientation used to define both the radiating elements and the tapered balun.
To verify the performance of the antenna design with the tapered ground plane feed,
it was simulated using both HFSS and SEMCAD. In addition, a subminiature version A
(SMA) connector was designed to simulate the complete antenna structure. The SMA
connector was simulated as a co-axial termination with a rectangular tab connected to its
center conductor. The SMA is shown in Figure 7.32. Its dimensions and characteristics are
close to commercially available ones [100].
Figure 7.33 presents the simulation setting of the antenna. As it can be seen, the antenna
is designed in such a way to be partially inserted as a card in a slot of some dielectric
matching medium. The SMA connector and the microstrip/balun feed are supposed to be
kept in free space. Only the radiating element of the antenna is immersed in the matching
medium.
Figure 7.34 presents the return loss Sn of the final antenna design with the microstrip
balun/feed but without the SMA connector. The results are shown in the l-35GHz range
and referenced to a 50O feedline. As we can see, the results are similar to those computed
for the radiator only with a return loss below -lOdB starting from around 2GHz to almost
30GHz. On the other hand, when the SMA is present, the higher limit of the return loss of
the antenna bandwidth is limited to 16GHz. This is mainly due to the coax-to-microstrip
transition.
x-^.
7 Novel Ultra-Compact Broadband Antenna
111
r
/
1
/
,
'
y
i
i
i
o
g
ft!'
•r-
n
£*
^'
LO
1
§yx
3
\\
/
iI'
\
\ s.
*-
S
/
/
*--
/
^
,'
\I 4 '- . .
>
"~~ — ^
"~ ~" —
*
•D&E
*1§1§:
\
\
\
""*--.«.
?.
CO
o
at
- i
Q.
Microstrip Feed
N
A (0,0.375,0)
B (0,0.05,0.635)
C (0,0,0)
D (0,-0.325,0)
E (0,-0.325,0.635)
\
Groud Plane/Balun
Fig. 7.28
Antenna board view. Coordinate dimensions are in mm.
7 Novel Ultra-Compact Broadband Antenna
%—®
B (0,0.05,0.635)
E (0,-0.325,0.635)
J (-4,0.175,0.635)
K (-6,0.175,0.635)
L (-6,-0.325,0.635)
Fig. 7.29 Antenna's top plane art work (top view). Coordinate dimensions
are in mm.
Fig. 7.30 Antenna's bottom plane art work (top view). Coordinate dimensions are in mm.
112
7 Novel Ultra-Compact Broadband Antenna
Fig. 7.31 Detailed antenna geometry and absolute physical dimensions derived from elliptical shapes and including the tapered feed/balun.
113
7 Novel Ultra-Compact Broadband Antenna
•
\
c
y
<->
114
!
Jab
!
!
_
!
. JI , ®
6—•
I •
I
f
y
y
®—•
Z
--—X a
K—
X
(a)
(b)
Fig. 7.32 Geometry of the SMA connector used in the HFSS simulations:
(a) Cross-section in the x-y plane, (b) Cross-section in the y-z plane. SMA
dimensions (in mm): a=1.25, 6=4.2, c=0.5, and d=2. The attached tab has a
thickness of 0.5mm. The SMA connector was assumed to be filled with Teflon
with a dielectric constant er = 2.1.
Fig. 7.33 The radiating elements of the antenna are immersed in a matching
medium of er = 10.2. The tapered feed/balun is kept in free space.
7 Novel Ultra-Compact Broadband Antenna
;l
,
1
_,
5
,
10
115
,
15
20
Frequency (GHz)
,
,
1
25
30
35
Fig. 7.34 Return loss S\i of the final antenna design with the microstrip
balun/feed simulated using both SEMCAD and HFSS but without the SMA
connector. The results are shown in the l-35GHz range and referenced to a
50Q feedline. The results computed with SEMCAD show that the minimum
lower operating frequency of -lOdB return loss is equal to 2.18GHz while for
results computed with HFSS it is equal to 1.97GHz.
0|
1
I
1
!
<ri~
!
!
!
!
1
!
\ ;/ ; ; \: A :
-20
i\ /
;
;•• X
-25 - • - - i
-30'
1
!
1
1
1
!
!
!
!
/ ;
\ V I
i I/ ; ;V ;
'
'
'
'
;....:....
'
'
'
'
'
'
'
'
3
4
5
6
7
8
9 10 11 12 13 14 15 16 17 18 19 20
1
'
'
i
'
2
'
Freauencv (GHz)
Fig. 7.35 Return loss Su of the final antenna design with the microstrip
balun/feed and the SMA connector simulated with HFSS. The results are
shown in the l-20GHz range and referenced to a 50f2 feedline. As we can see
from the plot, the antenna has a broad operating bandwidth of -lOdB return
loss ranging from 1.9GHz to 16.0GHz. The high frequency operation becomes
limited by the SMA to microstrip transition.
7 Novel Ultra-Compact Broadband Antenna
116
7.5 Conclusion
In this paper, a novel ultra-compact and ultra-broadband antenna design, named the
TWTLTLA antenna, is proposed for pulse radiation in the near-field. The antenna derives its name from its design procedure and its operation mechanism. The antenna has a
return loss below -lOdB in the range of 1.9GHz to 35.0GHz. The antenna was also studied
for pulse radiation in the UWB range. Its radiation efficiency is 39.21%. In the forward
region, the computed fidelity at 3 cm radial distance from the antenna apex is over 0.95
within a span of 180° angles in the E-plane and a span of 135° angles in the H-plane.
The antenna has a planar structure and a line profile of only Lp = 14 mm. With this
dimension, the antenna is the smallest of all reported designs up to date for the application of UWB microwave imaging of breast cancer. This antenna will be a key element in
developing a multistatic microwave imaging system with a large number of cross-polarized
antenna-elements.
117
Chapter 8
Conclusion
8.1 Summary and Discussion
This thesis details the development of broadband planar antenna designs for pulse radiation. These antennas find applications in several areas such as biological sensing, through
wall imaging, and ground penetrating radars. Of the most important characteristic of pulse
radiating antennas is their ability to radiate and receive pulses with high fidelity. In addition, a compact and low profile antenna is highly desirable when the antenna is intended
for use in an antenna array system such as the multistatic UWB microwave imaging of
breast cancer.
Variable resistive loading is an approach extensively used in the design of pulse radiating
antennas, however, the manufacturing process of these antennas is usually complex. In this
work, a novel alternative design concept is suggested. Constant surface resistive loading
is employed instead and combined with a favorable antenna geometry to achieve the same
objective. This design methodology did not only simplify the manufacturing process, but it
has also demonstrated that the design of ultra-compact and ultra-broadband pulse radiating
antennas is possible. Further, based on the developed antenna designs, this thesis suggests
the use of a multistatic card-array of cross-polarized elements for the detection of breast
tumors. The card array design allows the arrangement of a large number of antennas
around a small volume such as the breast, while the cross-polarized elements improve the
detection capabilities of the imaging system.
2007/12/10
8 Conclusion
118
8.1.1 The "Dark Eyes" Antenna
The "Dark Eyes" antenna described in Chapter 3 presents the first attempt to achieve a
broadband antenna design through the effective combination of favorable antenna geometry and a constant surface resistive load. The antenna structure is a dipole-like form of
uneven diamond-shaped arms. Each arm consists of two triangles, one conductive and one
resistive, connected back-to-back. The linearly tapered resistive section was chosen since
it is equivalent to the "Wu-King" resistive profile in the longitudinal direction.
Detailed numerical analysis of the antenna demonstrated a clear traveling-wave behavior. When a surface resistivity of Rs = 1 0 0 0 / • is used, the antenna has a center frequency
of 6GHz with an impedance bandwidth better than -lOdB in the range of 3.8GHz to 8.5GHz.
Furthermore, the antenna provides a dipole-like radiation pattern with a single-beam of radiation over the entire spectrum of interest from 3GHz to 9GHz. On the other hand, and
for pulse radiation, the antenna has excellent fidelity of over 0.98 in all radiation direction.
In addition, the antenna efficiency is 36% compared to only about 24% for a "Wu-King"
dipole of the same length operating at 6Ghz.
Since the antenna was relatively large for the intended application, the multistatic
antenna array for imaging of breast cancer, the next step presented was antenna miniaturization. Again, numerical simulations were conducted to understand the effect of different
geometric parameters on the antenna performance. Then, by a strategic scale-down of
the antenna width and the length of conductive and resistive sections, a new design with
a comparable performance to that of the original one was achieved, but with a structure
three times smaller in the longitudinal direction.
The final step in the development process was the design of a broadband feed for
the miniaturized antenna and the study of its impact on the antenna design. Chapter 5
describes a parametric study of a complete microstrip-fed "Dark Eyes" antenna radiating
in a biological medium. The optimal design has a surface resistivity Rs = 5 0 0 / • . This
design showed a 2:1 VSWR bandwidth in the 2.7-9.7GHz range and a radiation efficiency
of 30.25%. For near field pulse radiation, the antenna exhibits good performace in the
forwared region, the intended direction of radiation, with fidelity exceeding 0.92. Finally,
the antenna has a line profile of only Lp = 20 mm.
8 Conclusion
119
8.1.2 The Cross-polarized Card Array Arrangement
After establishing the antenna design, the main objective was to demonstrate the antenna
tumor detection capability. For this, a cross-polarized antenna array of two adjacent elements was used in a computational study of the tumor response. In this study, the breast
model consisted of a matching medium layer, a 1-mm skin layer, and a fat layer, while
the tumor model consisted of either a sphere or a cylinder oriented in two different crosspolarized orientations.
Through numerical simulations, results showed that the two antennas exhibit low mutual coupling with a smooth near-field radiation pattern. In addition, the range of the
tumor responses recorded by the antenna is equal to the reported values by several other
researchers using different antenna designs. Most importantly, for different tumor shapes
and orientations, the study showed that, for tumor detection, there is an advantage in
recording both the co-polarized and the cross-polarized tumor backscatter.
8.1.3 The TWTLTLA Antenna
The TWTLTLA antenna was developed from several insights and collected knowledge
gained throughout the work on the "Dark Eyes" antenna and through extensive numerical
simulation, the result is the summarizing steps that transformed the "Dark Eyes" into the
TWTLTLA presented in Chapter 7. In addition, a design methodology is presented for
developing TWTLTLA radiating in a specific dielectric medium and with a given minimum
lower frequency of operation fi- Most important, the final design has a line profile that is
only equal to one-fourth of the wavelength in the radiating medium (Lp = Aj,/4). For the
UWB multistatic CMI system, the antenna designed has an impedance bandwidth better
than -lOdB in the range of 1.9GHz to 35.0GHz, and a radiation efficiency of 39.21%. In
addition, for pulse radiation in the near field, the antenna exhibits good performace in the
forwared region with fidelity better than 0.95. Finally, the antenna has a line profile of only
Lp = 14 mm. On the other hand, the complete antenna design with the tapered feed/balun
and the SMA connector has an impedance bandwidth better than -lOdB in the range of
1.9GHz to 16.0GHz.
8 Conclusion
120
8.2 Future Work
Based on the research developed in this thesis, several future directions could be suggested:
• For the TWTLTLA design, the value of surface resistivity Rs — 5 0 0 / • was based
on insights gained through the work on the "Dark Eyes" antenna. However, this is
not necessarily the optimum choice. Parametric simulations could be performed to
identify the optimum surface resistivity value with respect to antenna fidelity and its
radiation efficiency.
• The TWTLTLA antenna have used an elliptical profile for its tapered geometry, however, other curved profiles are possible and interesting to study such as exponential,
quadratic, and so on.
• Further miniaturization of the TWTLTLA antenna to achieve even a lower profile
through general optimization techniques.
• Modification of the antenna design may include capacitive loads in addition to resistive loads using the loading technique described in [6].
• A study of antenna loading with a slot would point to the effect of this method on
different antenna parameters and its possible advantages.
• Development of a feed design that allows for placement of two cross-polarized colocated TWTLTLA antenna elements (instead of adjacent elements) for the crosspolarized arrangement would offer new possibilities for the overall antenna-array layout.
121
Appendix A
Antenna Manufacturing
As it has been presented before, the traveling wave tapered and loaded transmission line
antenna (TWTLTLA) is a planar antenna loaded with resistive material. Usually, manufacturing resistively loaded antenna present a technical difficulty, especially for antennas with
variable resistive loading. However, this is not the case for the TWTLTLA antenna as it
relies on favorable geometrical shape with constant surface resistivity to achieve its broadband behavior. This opens the possibility to manufacture the antenna with OHMEGAPLY® laminate. These laminates are usually provided directly from Ohmega Technologies [10] on simple FR4 dielectric substrates, or on high frequency laminates available from
Rogers Corporation [93], and they can be processed easily by many standard printed circuit
board (PCB) prototyping shops [101,102]. The following sections discuss briefly Ohmega
Technologies materials and the manufacturing process of the TWTLTLA antenna.
A . l Ohmega Technologies
OHMEGA-PLY® material is a thin film nickel alloy of constant thickness electrodeposited onto copper foil [10]. This product, which is called OHMEGA-PLY® RESISTORCONDUCTOR MATERIAL (RCM), is then laminated to a dielectric material as shown
in Figure A.l and subtractively processed to produce planar resistors. Because of its thin
film nature of constant thickness (usually 0.1-0.4 /im), the resistive material will have a
constant surface resistivity of Rs — 25 — 2 5 0 0 / • and it can be buried within layers without increasing the thickness of the printed circuit board. In addition, the manufacturing
repeatability of highly accurate designs for antenna arrays is easily achievable.
2007/12/10
A Antenna Manufacturing
122
copper
fELECTROPLATING 1
OHMEGA-PLYRCM
copper
resistive material
OHMEGA-PLY
LAMINATE
copper
resistive material • M p p N H H p a M M p i p
ielectric substrate ww§mffimlfe
>'/:••
-,fWJ^M^^ 'aSMWM--'-^
copper
Fig. A.l
t LAMINATION J
OHMEGA-PLY® laminate [10].
A.2 The Etching Process
The manufacturing of board designs with OHMEGA-PLY® laminates could be summarized by the following three etching steps shown in Figure A.2. The first step is etching
the copper that covers the excess resistive materials (Figure A.2 (a)). This step is identical
to any standard copper etching process carried by many PCB prototyping shops. The
second etch (Figure A.2 (b)) consists of etching the excess resistive Ohmega materials.
This is done with a solution containing 250 grams per liter of copper sulfate pentahydrate
(CuS04-5H 2 0) and 2 milliliters of concentrated sulfuric acid (H2SO4) per liter maintained
at a temperature over 90° C. Finally, the third etch is carried by etching the copper where
to keep the underneath resistive material (Figure A.2 (c)). This step is a very critical
one because the copper material should be etched away but the process should make sure
that the etch solution will not attack the Nickel Alloy thin film resistive material and thus
increase its surface resistivity.
This final step could be done in one of two ways: by either using Copper Ammonium
Chloride (Cu(NH3)sCl2) in a process available from many PCB prototyping shops, or by using Chromic Acid (Cr0 3 ), a 300g/L of Cr0 3 with 30ml/L of sulfuric acid (H 2 S0 4 ) at 50°C
Detailed description of this process is available from Ohmega Technologies website [10].
A Antenna Manufacturing
123
•
•
Copper
Resistive Material
Dielectric Substrate
(a)
Y-Y
(b)
Y-Y
(c)
Fig. A.2 Summary of the etching steps in manufacturing the TWTLTLA
antenna with the RCM Ohmega laminates, (a) First etch: etching excessive copper material, (b) Second etch: etching excessive resistive material, (c)
Third etch: etching excessive copper where the resistive material is to be kept.
The third etch is considered to be the most critical one.
124
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