loizos thesis dec8 - texas a&m...
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A NON-PYRAMIDAL RECTANGULAR-TO-TROUGH WAVEGUIDE
TRANSITION AND PATTERN RECONFIGURABLE TROUGH WAVEGUIDE
ANTENNA
A Thesis
by
LOIZOS LOIZOU
Submitted to the Office of Graduate Studies of Texas A&M University
in partial fulfillment of the requirements for the degree of
MASTER OF SCIENCE
December 2010
Major Subject: Electrical Engineering
A Non-Pyramidal Rectangular-to-Trough Waveguide Transition and Pattern
Reconfigurable Trough Waveguide Antenna
Copyright 2010 Loizos Loizou
A NON-PYRAMIDAL RECTANGULAR-TO-TROUGH WAVEGUIDE
TRANSITION AND PATTERN RECONFIGURABLE TROUGH WAVEGUIDE
ANTENNA
A Thesis
by
LOIZOS LOIZOU
Submitted to the Office of Graduate Studies of Texas A&M University
in partial fulfillment of the requirements for the degree of
MASTER OF SCIENCE
Approved by:
Co-Chairs of Committee, Gregory H. Huff Robert D. Nevels Committee Members, Henry Pfister Othon Rediniotis Head of Department, Costas N. Georgiades
December 2010
Major Subject: Electrical Engineering
iii
ABSTRACT
A Non-Pyramidal Rectangular-to-Trough Waveguide Transition and Pattern
Reconfigurable Trough Waveguide Antenna. (December 2010)
Loizos Loizou, Diploma, National Technical University of Athens
Co-Chairs of Advisory Committee: Dr. Gregory. Huff
Dr. Robert D. Nevels
Trough waveguides (TWG) have been utilized in a variety of radio frequency
(RF) and other related applications including radar, the treatment of hypothermia and in
the generation of plasmas. Perturbing the guided wave in these structures with blocks,
rods, dielectrics, and other structures can create reconfigurable periodic line sources.
These trough waveguide antennas (TWA) are then capable of providing both fixed-
frequency and frequency-dependent beam steering. This was originally performed using
electro-mechanical “cam-and-gear” mechanisms. Previous work related to the excitation
of TWG and the performance of TWA topologies are limited when compared to more
common antenna designs, yet they possess many desirable features that can be exploited
in a modern system.
This thesis will examines an S-band rectangular-to-trough waveguide transition
and trough guide antenna that has been designed for broadband reconfigurable antenna
applications considering as well the airflow characteristics for sensing applications. The
design, fabrication, and electromagnetic performance (mode conversion, impedance
iv
matching, and antenna performance) are discussed, including the use of metallic
cantilever perturbations placed along the troughguide sidewalls that are designed to
provide improved impedance matching when steering the beam from the backward
quadrant through broadside, towards the forward quadrant. Impedance matching
techniques such as use of circular holes at the edge of each actuated cantilever are used
to reduce power reflections and provide a low voltage standing wave ratio (VSWR)
along the S-band. Finite element simulations will provide a demonstration of the airflow
and turbulence characteristics throughout the entire structure, where the metallic
cantilevers are used to manipulate the flow of air, to distribute it across the surfaces of
the structure better and improve its potential for sensing operations.
v
ACKNOWLEDGEMENTS
I would like to thank my committee co-chairs, Dr. Gregory Huff and Dr. Robert
Nevels, and my committee members, Dr. Othon Rediniotis and Dr. Henry Pfister, for
their guidance and support throughout the course of my research.
Thanks also go to my friends and colleagues and the department faculty and staff
for making my time at Texas A&M University a great experience. Special thanks to S.
A. Long, F. J. Drummond and S. A. Goldberger for their help and useful remarks during
this procedure.
Finally, thanks to my mother and father for their encouragement and support.
vi
NOMENCLATURE
TWA Trough Wave Antenna
TWG Trough Wave Guide
RWG Rectangular Wave Guide
P Pressure
T Time
TEM Transverse Electromagnetic
TE Transverse Electric
TM Transverse Magnetic
EM Electromagnetics
VSWR Voltage Standing Wave Ratio
RF Radio Frequency
DUT Device Under Test
UAV Unmanned Aerial Vehicle
PIFA Planar Inverted F-Antenna
GPS Global Position System
WSN Wireless Sensor Network
PDA Personal Digital Assistant
BAN Body Area Network
LWA Leaky Wave Antenna
vii
TABLE OF CONTENTS
Page
ABSTRACT ..................................................................................................................... iii
ACKNOWLEDGEMENTS ............................................................................................... v
NOMENCLATURE .......................................................................................................... vi
TABLE OF CONTENTS ................................................................................................. vii
LIST OF FIGURES............................................................................................................ix
CHAPTER
I INTRODUCTION .............................................................................................. 1
II BACKGROUND ................................................................................................ 4
A. S-Parameters ............................................................................................. 4
B. The ABCD Matrix .................................................................................... 7
C. Waveguides ............................................................................................... 9
D. Leaky-Wave Antennas (LWA) ............................................................... 11
E. Uniform Leaky-Wave Antennas ............................................................. 12
F. Periodic Leaky-Wave Antennas .............................................................. 14
G. Phase Accumulation ............................................................................... 14
H. Trough Waveguide Antennas (TWA) .................................................... 16
I. Antenna Measurements ............................................................................ 19
J. Aerodynamic Concepts ............................................................................ 20
III A NON-PYRAMIDAL RECTANGULAR-TO-TROUGH WAVEGUIDE
TRANSITION .................................................................................................. 21
A. Introduction ............................................................................................ 21
B. Transition Topology and Operation ........................................................ 22
C. Fabricated Transition and Results .......................................................... 25
D. Aerodynamic Performance ..................................................................... 29
viii
CHAPTER Page
IV A PATTERN RECONFIGURABLE TROUGH WAVEGUIDE
ANTENNA ....................................................................................................... 34
A. Introduction ............................................................................................ 34
B. Simulated Designs .................................................................................. 34
C. Holes in the Center ................................................................................. 38
D. Holes at the Edge .................................................................................... 40
E. Cantilevers with Two Holes ................................................................... 42
F. Different Matching Geometries .............................................................. 44
G. Fabrication of the TWA ......................................................................... 45
H. Experimental Setup I .............................................................................. 49
I. Experimental Setup II .............................................................................. 52
J. Experimental setup III - Pattern Reconfigurable Design ......................... 59
K. Aerodynamic Performance of the TWA with Cantilever
Perturbations ................................................................................................ 74
V FUTURE WORK ............................................................................................. 76
VI CONCLUSIONS ............................................................................................. 77
REFERENCES ................................................................................................................. 78
APPENDIX A .................................................................................................................. 81
VITA…………………………………………………………………………………….84
ix
LIST OF FIGURES Page
Fig. 1. An N port network showing the incident and reflected voltages and currents. .... 4 Fig. 2. A 2-port network representation of a leaky wave structure. ................................. 6 Fig. 3. An ABCD matrix representation of a 2-port network. ......................................... 7 Fig. 4. Casketed 2-port networks. .................................................................................... 8 Fig. 5. A deembeded 2-port cascaded network. ............................................................... 8 Fig. 6. A rectangular waveguide showing the fundamental mode. .................................. 9 Fig. 7. A RWG with a radiating slit on the side ( from [2] ). ......................................... 11 Fig. 8. A rectangular dielectric rod with an array of metal strips ( from [2] ). .............. 12 Fig. 9. Reflection from cascaded transmission line sections. ......................................... 15 Fig. 10. TWA with arrays of holes and teeth ( from [3] ). ............................................. 16 Fig. 11. TWA with vertical and horizontal rods on the center fin ( from [4] ). ............. 17 Fig. 12. An equivalent transmission line circuit of the TWG. ....................................... 18 Fig. 13. A continuously asymmetric trough and a periodically antisymmetric trough ( from [5] ). ........................................................................................... 19 Fig. 14. CAD model of the non-pyramidal rectangular-to-trough waveguide transition. .......................................................................................................... 22 Fig. 15. Distribution of the electric field within the trough waveguide (left), transition (middle) and rectangular waveguide (right). ..................................... 23 Fig. 16. The trough waveguide (left) as an equivalent rectangular waveguide (right). . 24 Fig. 17. Real part of the impedance with respect to transition's length. ......................... 25 Fig. 18. Average VSWR and 2:1 VSWR bandwidth with respect to the transition length. ............................................................................................... 26 Fig. 19. The end-on views of the transition. ................................................................... 27
x
Page
Fig. 20. Two fabricated S-band transitions in back-to-back arrangement. .................... 27 Fig. 21. A cut of the three dimensional drawing of the transition. ................................. 27 Fig. 22. Measured and simulated results for the back-to-back transition....................... 28 Fig. 23. Measured and simulated results for a single transition. .................................... 29 Fig. 24. Aerodynamic performance at the inlet and outlet of a 320 mm (left) and a 160 mm (right) transition with an inlet velocity of 0.1 m/s. .................... 30 Fig. 25. Aerodynamic performance at the inlet and outlet of a 320 mm (left) and 160 mm (right) long transition with an inlet velocity of 1 m/s. ................. 30 Fig. 26. Aerodynamic performance at the inlet and outlet of a 320 mm (left) and a 160 mm (right) long transition with an inlet velocity of 10 m/s. ............. 30 Fig. 27. Aerodynamic performance at the inlet and outlet of a 320 mm (left) and a 160 mm (right) long transitions with an inlet velocity of 25 m/s. ........... 31 Fig. 28. Aerodynamic performance at the inlet and outlet of a 320 mm (left) and a 160 mm (right) long transition with an inlet velocity of 44.5 m/s. .......... 31 Fig. 29. Aerodynamic performance at the inlet and outlet of a 320 mm (left) and a 160 mm (right) long transition with an inlet velocity of 61 m/s. ............. 31 Fig. 30. Vorticity field at the outlet of 320 mm and 160 mm long transitions. .............. 32 Fig. 31. Streamline plots of the vorticity for a 160 mm and a 320 mm long transition. 33 Fig. 32. Cantilever actuated from the center fin (case 1) and from the sidewall (case 2). ............................................................................................................. 35 Fig. 33. Insertion loss with respect to the perturbation angle, for cantilevers of different width and placement in the trough. ................................................ 36 Fig. 34. TWA with cantilever perturbations. ................................................................. 37 Fig. 35. VSWR (left) and (right) along the S-band. ................................................... 38 Fig. 36. Radiations patterns, with fixed perturbation angle at 30° and a frequency sweep. .................................................................................... 38
xi
Page Fig. 37. Currents excited on a cantilever with a hole in the center. ............................... 39 Fig. 38. VSWR (left) and (right) for cantilevers with a 6 mm radius hole on the center. .................................................................................................... 40 Fig. 39. VSWR (left) and (right) for cantilevers with a 10 mm radius hole on the center. .................................................................................................... 40 Fig. 40. Currents excited on a cantilever with a hole at the edge. .................................. 41 Fig. 41. VSWR (left) and (right) for cantilevers with a 6 mm radius hole at the edge. ........................................................................................................ 41 Fig. 42. VSWR (left) and (right) for cantilevers with 10 mm radius hole at the edge. ........................................................................................................ 41 Fig. 43. VSWR (left) and (right) for cantilevers with edge and center holes with a 30° angle. ............................................................................................... 42 Fig. 44. TWA with two holes on each cantilever. .......................................................... 43 Fig. 45. VSWR (left) and (right) for cantilevers with 6 mm and 8 mm radius holes and 30° perturbation angle. ..................................................................... 43 Fig. 46. Radiation patterns for a TWA with cantilevers with two holes of 6 mm, 8 mm and 10 mm. ............................................................................................. 43 Fig. 47. TWA with two triangular or rectangular holes. ................................................ 44 Fig. 48. VSWR of the TWA with two holes of circular, triangular and rectangular geometries. .................................................................................... 45 Fig. 49. CAD design of the trough wave guide. ............................................................. 46 Fig. 50. CAD drawing of the bottom plate of the troughguide (upper) and the custom made flange (lower). ............................................................... 47 Fig. 51. CAD drawings of the troughguide. .................................................................... 48 Fig. 52. Fabricated version of cantilevers for broadside radiation using copper sheets (upper left), Copper cantilevers placed in the TWG (lower left), measured and simulated VSWR. ....................................................................... 50
xii
Page Fig. 53. Radiation patterns at 2.6 GHz, 3 GHz, and 3.9 GHz at the co-polarization and cross-polarization planes. .......................................................................... 51 Fig. 54. Fabricated cantilevers in the TWG (left), λ/2 paper cantilever with one hole (upper right), λ/2 paper cantilever with no hole (lower right). ........... 52 Fig. 55. Measured and simulated insertion loss (left), VSWR (right). .......................... 54 Fig. 56. Co- and cross-polarization plane radiation patterns of the TWA with cantilevers. ........................................................................................................ 55 Fig. 57. Measured and simulated VSWR (left) and insertion loss (right). ..................... 56 Fig. 58. Experimental setup for measuring radiation patterns in the anechoic chamber. ............................................................................................................ 57 Fig. 59. Radiation patterns for the half wavelength cantilevers with a hole. ................. 58 Fig. 60. Tapering perturbation angle for 12 cantilevers form one end to the middle of a TWG. ............................................................................................. 59 Fig. 61. Quarter wavelength long cantilevers. ............................................................... 61 Fig. 62. Measured and simulated VSWR (left) and S-parameters (right). ..................... 61 Fig. 63. Radiation patterns at the co-polarization and cross-polarization planes at 2.6 GHz, 3 GHz and 3.9 GHz. ........................................................................ 62 Fig. 64. Measured and simulated VSWR (left) and S-parameters (right). ..................... 63 Fig. 65. Radiation patterns at the co-polarization and cross-polarization planes at 2.6 GHz, 3 GHz and 3.9 GHz. .......................................................... 64 Fig. 66. Measured and simulated VSWR (left) and S-parameters (right). ..................... 65 Fig. 67. Radiation patterns at the co-polarization and cross-polarization planes at 2.6 GHz, 3 GHz and 3.9 GHz. .......................................................... 66 Fig. 68. Half wave long cantilever with two holes. ........................................................ 67 Fig. 69. Measured and simulated VSWR (left) and S-parameters (right). .................... 67 Fig. 70. Radiation patterns at the co-polarization and cross-polarization planes at 2.6 GHz, 3 GHz and 3.9 GHz. .......................................................... 68
xiii
Page
Fig. 71. Measured and simulated VSWR (left) and S-parameters (right). ..................... 69 Fig. 72. Radiation patterns at the co-polarization and cross-polarization planes at 2.6 GHz, 3 GHz and 3.9 GHz. .......................................................... 70 Fig. 73. Three quarter wave long cantilevers with and without holes in a TWG. .......... 71 Fig. 74. Measured and simulated VSWR (left) and S-parameters (right). ..................... 72 Fig. 75. The experimental setup used for measurements with the waveguide calibration kit, the network analyzer and the DUT. ......................................... 72 Fig. 76. Radiation patterns at the co-polarization and cross-polarization planes at 2.6 GHz, 3 GHz and 3.9 GHz. ......................................................... 73 Fig. 77. Beam steering by changing the length of the cantilevers.................................. 74 Fig. 78. Aerodynamic performance of the TWA with cantilevers. ................................ 75
1
This thesis follows the style of IEEE Transactions on Antennas and Propagation.
CHAPTER I
INTRODUCTION
Cell phones, electronic personal assistants (PDAs), global position systems
(GPS), wireless and satellite television represent just a few of the examples of the impact
wireless communication systems have made on everyday life. Wireless sensor networks,
a subset of wireless systems, have been developed to play an important role in personal
and public safety. Applications range from body area networks (BAN) for remotely
monitoring and treating a patient’s health to more environmentally oriented applications
such as temperature and humidity monitoring. Public safety applications include the
detection of biological and chemical threats, toxins and poisons in air, and smoke for
advanced fire safety and early warning measures. There are many other potential
applications.
Modern technology is driven toward constant miniaturization and integration of
systems and devices. Meeting the demands of the former may be limited by the size of
larger system components such as antennas, whose efficiency and performance is
predominantly dependent on their effective aperture size. Antenna designs such as
microstrip patches and planar inverted F-antennas (PIFAs) have led to conformal planar
topologies that help reduce their size, but there are still fundamental physical limits that
exist and certain applications will almost always require larger antennas with higher gain
and directivity. To this end, the structural and functional integration of several
subsystems can result in technologies that can support the demands of these systems.
2
Multifunctionality is a term describing this desire and the set of devices that can
efficiently and simultaneously perform more than one function or operational objective;
however, it can lead to a potentially complex integration process so the amalgamation of
function must be done diligently. This work seeks to do this by blending antenna
technologies amendable to the base stations of a wireless networks. These are commonly
placed atop a rooftop, which provides an opportunity to include sensing mechanisms for
measuring temperature, humidity in the air, and potentially the detection of smoke
and/or poisonous gases. Future applications may also include the structural integration of
these antennas into mobile platforms such as UAVS or even into high security buildings
to detect weapons, explosives, chemical agents, biological threats, and possibly to
perform imaging during sensing operations.
Trough waveguides (TWG) are open structures that offer 50% more bandwidth
than regular waveguides (RWG). Any perturbation inside the TWG can cause radiation
to leak out through the effective aperture (e.g., the open end of the structure) and create a
trough waveguide antenna (TWA). This process of facilitating radiation in the TWA can
be controlled, thereby making it possible to create a reconfigurable antenna from this
design. This kind of large aperture antenna based on leaky-wave structures can also
support multifunction operations in many microwave applications. It is well known that
most leaky-wave antennas have a main beam which is scanned by applying a frequency
sweep. Some of these structures can also been designed to provide beam steering for a
fixed frequency; this reduces the use of phase shifters and large feed networks in some
cases and minimizes the system losses. These losses are actually present in the other
3
elements of the electromechanical system but they are removed from the flow or
throughput of information that is the antennas primary function. By using an
electromagnetically (EM) transparent cover (e.g., one that does not dramatically alter the
performance of the antenna), the TWG structure can be sealed and pressurized fluids or
gasses can be passed through it. More specifically, pressurized air can be guided through
the TWA where sensors can be integrated inside the structure and passed to the antenna
to transmit the information across a long distance.
This thesis discusses the electromagnetic and aerodynamic co-design of a non-
pyramidal RWG-to-TWG transition and a fixed-frequency pattern reconfigurable TWA
providing many of the desirable characteristics required by a platform which integrates
reconfigurable antennas and sensing mechanisms into the same device. A review of the
TWA and their applications is followed by the design, analysis, fabrication and
evaluation procedures of an RWG-to-TWG transition examining both the
electromagnetic and aerodynamic performance of the structure. The use of cantilever
perturbations is then discussed for controlling the leaked power from the TWA for
broadside radiation and pattern reconfigurable antennas (e.g., fixed frequency beam
steering). An aerodynamic study of the structure investigates the airflow and turbulence
characteristics throughout the entire RWG-to-TWG transition and within the TWA. The
effect of the metallic cantilevers is also examined providing the means to control the
flow of air, to better distribute it across the surfaces of the structure and improve its
potential for sensing operations.
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CHAPTER I
ACKGROUN
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5
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applying a voltage jV to port j and getting a voltage iV out of port i. The excitation on
all the other ports is set to zero (also known as a matched termination condition) so Sij
gives the transmission coefficient from port j to port i. For reciprocal lossless networks,
the elements in the S-matrix have the property shown in (3).
1 111 12 1
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a transmission line topology, in which relatively large values of attenuation are due to
radiation. The propagation characteristics in these leaky-wave structures are given by the
complex propagation constant in (4), where α is the attenuation constant related to
dissipated power (including radiation losses) and β is the phase constant that describes
the propagation of EM energy within the structure. Each of these parameters is
controllable through the design of the radiating or guiding structure.
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j m m x n yE A e
k a a b
j m m x n yH A e
k a a b
j n m x n yH A e
k b a b
(11)
2 2 2 2 2( ) ( )c
m nk k k
a b
(12)
The attenuation constant α accounts for ohmic and radiation losses, so for most materials
(i.e. copper and aluminum) the ohmic losses are very small compared to radiation from
the guide. Hence, this work seeks to maximize the equivalent α. The wave impedance of
a waveguide is also an important quantity, and is given by (13), where 2 f with f as
the operational frequency, μ the permittivity and n the impedance of free space. The
characteristic impedance of the waveguide Z0 is given by (14), where B is a constant
depended on the b dimension of the guide [1]. Each mode in the waveguide has a cutoff
frequency fc,mn (15). Frequencies below fc,mn cannot propagate in the corresponding mn
mode. Frequencies below the lowest fc (typically the TE10 illustrated in Fig. 6) are in cut-
off and will not propagate. Typically, the waveguide's dimensions are selected to allow
operation within the band of interest (fc,10 < fband < higher order fc). The separation
between the lowest, or fundamental mode, and second lowest mode’s fc provide the
concept of bandwidth for the waveguide.
D.
(4)
com
on
sca
Fig
lev
Leaky-Wave
Leaky w
. The attenu
mbined with
frequency a
anned with fr
g. 7. A RWG
Taperin
vel often crea
(wZ
mncf
e Antennas (
wave structu
uation consta
h the effectiv
and is relate
frequency.
with a radiati
ng the effect
ating a narro
( ) xmn
y
ETE
E
2n
ck
(LWA)
ures are char
ant α is rela
ve aperture t
ed to the dire
ing slit on the
tive aperture
ow pencil be
1
0 wZ BZ
1(
2
racterized by
ated to the ra
to the beam
ection of the
side ( from [2
e of the stru
eam on the s
2,
c
nf
f
f
2( ) (m n
a b
y a complex
adiation effi
mwidth. The
e beam, so le
2] ).
ucture gives
scan plane. T
cf
2)
propagation
iciency of th
phase const
eaky wave a
control ove
The cross pla
(
(
(
n wave numb
he antenna a
tant β, depen
antennas can
er the side lo
ane radiation
11
13)
14)
15)
ber
and
nds
n be
obe
n is
a fa
and
ear
wa
ope
uni
fro
a p
bac
Fig
E.
and
fan shape bea
d even perm
rly designs
aveguide ante
Two ty
eration: peri
iform type h
m endfire cl
periodic geo
ckward and s
g. 8. A rectan
Uniform Lea
For an a
d β are deter
am. Techniq
mit 2-dimens
based on
enna, the gro
ypes of leak
iodic and un
has a uniform
lose to broad
ometry, whi
some of the
gular dielectr
aky-Wave An
antenna of e
rmined theor
ques exist in
ional scanni
waveguides
oove guide, t
ky wave an
niform. Each
m geometry
dside region,
ch is respon
forward qua
ric rod with an
ntennas
effective aper
retically or e
the literatur
ing. Many le
with long
the microstr
ntennas exi
h provides s
along its len
, with a cons
nsible for r
adrant.
n array of met
rture length
experimental
re for narrow
eaky wave s
slits. Such
rip line and o
st and diffe
some differe
ngth and can
stant beamw
radiation and
tal strips ( from
L, and depe
lly to functi
wing the cro
structures di
h devises a
others.
fer in both
ences in per
n scan in the
width. The pe
d can scan
m [2] ).
ending on the
onally descr
oss plane bea
iffer from th
are the trou
geometry a
rformance. T
e first quadr
eriodic type h
almost all
e application
ribe the desi
12
am,
heir
ugh
and
The
rant
has
the
n, α
gn.
13
The main beam’s direction is then given by (16) with a beamwidth from (17) using the
free-space wave number (18). The maximum angle of the beam from broadside direction
is m , with (19) a condition to ensure 90% of the input power is radiated.
sin mok
(16)
1
cos mo
L
(17)
2
oo
k
(18)
0.18
o
o
L
k
(19)
Scan angle m behavior depends on the topology of the uniform leaky wave
antenna. For an air filled guide the variation of scan angle with frequency is slower
compared with the partially dielectric- filled type of waveguide. The radiation pattern is
found by the Fourier transform of the aperture distribution and for an infinite antenna
length (20); tapering the amplitude of this distribution can reduce the sidelobe level.
2
2 2
cos( )
sino o
R
k k
(20)
14
F. Periodic Leaky-Wave Antennas
In contrast to the uniform LWA, the periodic LWA topologies are modulated in a
repetitive distribution along their length. The leakage mechanism is also different in a
sense that uniform antennas support a “fast” mode which radiates. On the other hand, the
dominate mode in a periodic structure needs to be introduced since it is a “slow”
structure. The introduction of a periodic array in the guide perturbs the bounded mode in
a manner that introduces an infinite number of space harmonics which are related to
each other by (21), where 1
o
df
is the period and o is the fundamental space
harmonic.
2n od d n (21)
If one of the space harmonics becomes fast, radiation is achieved. Since only one
beam is desirable, the integer n = -1 is chosen and for a frequency sweep this beam will
emerge from backfire and sweep through broadside towards the forward quadrant. The
resulting beam direction is determined by (22) with 1
2o d
and 1
o
df
.
1sin o om
o gk d
(22)
G. Phase Accumulation
The radiation mechanism previously described explains the "open stop band"
region which occurs in such periodic structures at a narrow region around broadside
where resonant lengths are required for broadside radiation. The system can be seen as a
cas
bro
lon
giv
sum
tota
ref
Fig
scaded circu
oadside whe
ng each trans
ven by (23).
m of the refl
al reflection
flected (givin
g. 9. Reflectio
it of transmi
re the eleme
smission line
This means
flections from
n coefficient
ng a high VS
on from cascad
1[ ] [ ]
c
1
0
totT T
jY
ission lines c
ents of the p
e is then λ/2
s that the tot
m reactive lo
t (24). Most
SWR) when
ded transmiss
2[ ]...[ ]
2cos
22
sin2
0 1 0
1 1
n
o
T T
Y
Y
connected to
periodic arra
2 long. The t
tal reflection
oads Y. Each
t of the pow
the beam sc
ion line sectio
cos
sin
2sin
2cos
2
1 0 1
0 1
o
o
l
jY l
jZ
Y
0tot
o similar loa
ay are exact
total transmi
n seen at the
h of these sh
wer delivere
cans through
ons.
sin
cos
1 02 .1
0 1...
1
ojZ l
l
Y
Y
ads and show
tly half a wa
ission of the
e input of the
hunt loads c
ed to the str
broadside.
1 0...
1
..
0
1
n
Y
wn in Fig. 9.
avelength (λ
system is th
e system is
contributes t
ructure will
(2
(2
15
At
λ/2)
hen
the
o a
be
23)
24)
H.
stu
Oli
the
stu
Fig
the
and
ant
unb
rod
ele
Trough Wav
Trough
udied in the
iner [3] wer
e center fin.
udies for ante
g. 10. TWA w
TWG a
ese perturbat
d came to a
tisymmetric
bound TEM
d combined
ement. A ser
veguide Ante
h waveguides
past as ante
re able to alt
An array of
enna scannin
with arrays of
are open stru
tions. Rotma
a series of u
obstacles in
M mode, and
with a vert
ries of perpe
ennas (TWA)
s have been
ennas, filters
ter the prop
f circular ho
ng and filteri
holes and teet
uctures but
an and Karas
useful concl
n TWA cou
symmetric
tical rod in
endicularly p
)
around for
s and other
agation char
oles and an a
ing applicati
th ( from [3] ).
they do not
s [4] introdu
lusions rega
uple energy b
obstacles ca
Fig. 11 (m
placed teeth
some time
microwave
racteristics o
array of teet
ions as seen
.
t radiate effi
uced some m
arding their
between the
an be used
middle) facili
on the cente
and have be
application
of the guide
th are the ba
at Fig.10.
iciently with
microwave a
functionality
e bound TE
for tuning.
itates a reso
er fin, Fig. 1
een extensiv
s. Rotman a
e by modifyi
asic geometr
hout the use
antenna desig
y; namely t
mode and
The horizon
onant radiat
11 (left) cau
16
vely
and
ing
ries
e of
gns
that
the
ntal
ing
uses
rad
tee
Fig
cha
wa
sec
the
fre
reg
If t
ang
the
on
diation as we
eth (Fig. 11, r
g. 11. TWA w
Rotman
anging the p
as based on
cond was to
e TW is mad
quency is g
gion), o is t
the TW is m
gle of the m
e perturbatio
a fixed setu
ell as a contin
right) make
with vertical an
n and Maest
phase velocit
the rotation
vary the hei
de continuo
given by (25
the free spac
made partial
main beam fo
n. In this pr
up and using
nuous asymm
the TWA a
nd horizontal
tri reported
ty in the gui
n of symmet
ight of an ar
usly asymm
5) where
ce wavelengt
lly asymmet
or a fixed fre
rior work the
g metallic b
metry on on
slow wave s
rods on the ce
a “scannabl
de. The first
trical structu
rray of teeth
metric the di
is the beam
th, and g is
sin o
g
tric near bro
equency is g
e beam is sc
blocks as per
ne side of the
structure.
enter fin ( from
le” array in
t method use
ures along t
h placed on t
irection of th
m angle (lim
the guided w
oadside radi
given by (26
canned by ap
rturbations w
e TWA. A se
m [4] ).
[5]; this wa
ed to achiev
the axis of t
the top of th
the main bea
mited to the
wavelength.
iation is ach
6), where l i
pplying a fre
with a varia
eries of verti
as achieved
ve this behav
the guide. T
he center fin
am for a fix
e near end f
(2
hieved and
is the length
equency swe
able height t
17
ical
by
vior
The
n. If
xed
fire
25)
the
h of
eep
that
cha
len
the
wa
rad
equ
ana
Fig
occ
In
rec
of
anges the g
ngth of the b
e length of ea
In a m
ave antennas
diation and
uivalent tran
alytical mod
g. 12. An equi
Further
curs at broad
a later wor
configurable
a W-band t
guided wave
locks chang
ach block is
ore extensiv
s based on
another m
nsmission li
del using the
ivalent transm
rmore to add
dside the use
rk Huff and
radiation us
trough wave
elength. By
ges, effective
seen to be h
sin
ve work, Ro
the TWA. O
made periodi
ine circuit
transverse r
mission line cir
dress the hi
e of tuning p
Long [7] s
sing cantilev
eguide anten
changing th
ely scanning
half free-spac
n2
o
g
otman and O
One made c
ically asym
is presented
esonance tec
rcuit of the TW
igh reflectio
osts, Fig. 13
studied the e
ver perturbati
nna. It was
he frequenc
the beam aw
ce waveleng
2o
l
Oliner [6] p
continuously
mmetric for
d as seen i
chnique.
WG.
ons due to p
3(right) on th
effect of the
ions for fixe
shown that
cy or height
way from br
gth.
present two
y asymmetr
broadside
in Fig. 12
phase accum
he center fin
e aperture d
ed frequency
tapering th
t the electri
roadside wh
(2
types of lea
ric for end-f
radiation.
along with
mulation wh
n was propos
distribution
y beam steeri
e shape of
18
ical
here
26)
aky
fire
An
an
hich
sed.
for
ing
the
can
lob
to s
Fig
I. A
ant
abs
set
a d
For
the
kno
ntilevers imp
be level at br
scan the bea
g. 13. A contin
Antenna Mea
The me
tenna is the
solute gains.
the DUT (e
distance R fr
r the second
e received po
own gain (G
proves the ra
roadside. Th
am.
nuously asym
asurements
ethod used i
Gain-Trans
. During this
e.g., the TWA
rom a standa
d measureme
ower (Ps) is
GT) the gain o
adiation beh
his work also
metric trough
in this work
sfer method
s procedure
A) is a recei
ard gain ant
ent the DUT
s again mea
of the DUT c
( )T sG dB G
havior away
o examined
h and a period
to measure
d. A standar
two sets of
iving antenn
tenna where
T is replaced
sured. Since
can be calcu
( ) (s TdB P d
from broad
the use of v
dically antisym
the radiatio
rd gain ante
f measureme
na that is pla
e the receive
d by another
e the standar
ulated using b
) ( )SdB P dB
dside but inc
variable-leng
mmetric troug
on pattern of
enna is used
ents are mad
aced on a rot
ed power is
standard ga
ard gain (GS)
by (27).
)
creases the s
gth perturbat
h ( from [5] ).
f the prototy
d to determ
de. For the fi
tating fixture
measured (P
ain antenna a
) antenna is
(2
19
ide
ion
ype
mine
first
e at
Pt).
and
s of
27)
20
J. Aerodynamic Concepts
The aerodynamic behavior of this structure is also of interest to this work. The
viscosity is an important parameter since it characterizes the internal resistance to flow
within the structure. It also plays a significant role along with the velocity of the airflow
and geometry confining the flow, which is described by two regimes – laminar and
turbulent. Laminar flow occurs when a fluid flows in parallel layers or sheets, with no
significant disruption between the layers. It is characterized by high momentum
diffusion and low momentum convention. Flow is this regime usually corresponds to
low Reynolds numbers (28); a dimensionless number that gives a measure of the ratio of
inertial forces ρV²L² to viscous forces µVL and quantifies the relative importance of
these two types of forces for given flow conditions. It is used to characterize flow regime
by linking the fluid density ρ, viscosity µ, velocity V, characteristic dimension L. For
rectangular pipes and structures, the characteristic dimension is given by the hydraulic
diameter DH (29) with A as the cross sectional area and P as the wetted perimeter.
Turbulent is then oppositely characterized by chaotic, stochastic property changes and
dominated by inertial forces which result to random eddies, vortices and other flow
instabilities. Turbulent flow is characterized by a high Reynolds number.
ReVL
(28)
4
H
AD
P (29)
21
CHAPTER III
A NON-PYRAMIDAL RECTANGULAR-TO-TROUGH WAVEGUIDE TRANSITION
A. Introduction
The TWAs in [3]-[4] have been utilized in a variety of antenna and other related
applications including radar, the treatment of hypothermia [8], and in the generation of
plasmas [9]. Excitation of the TWG from transmission line topologies like coaxial in [4]
and [10], and guiding structures like RWG [8] are common. The latter requires a
transition for broadband mode conversion and/or impedance transformation, which in-
turn presents a key challenge towards their effectiveness in many of these previous
applications.
A candidate rectangular-to-trough waveguide transition was designed to provide
the excitation to a TWG and a TWA with reconfigurable radiation characteristics. It was
also desired that air can flow through the TWA to be turbulent around perturbation for
their dual purpose in sensing operations. The proposed transition provides impedance
transformation and mode conversion across the full waveguide band (S-Band) for the
TWG antenna structure under consideration. This section first presents the transition and
discusses its operation as a mode converter and impedance transformer; a small degree
of physical insight into the design of the transition design is presented in an attempt to
provide a more comprehensive and useful discussion. The measured and simulated
results for an S-band design are presented next. A study of the aerodynamic performance
of
this
B.
len
per
b1
top
Ho
ma
or
RW
the
Fig
the structure
s transition u
Transition T
Fig. 14
ngth L and a
rimeter of th
and the TW
p and bottom
owever, flari
aintain a flat
top surface,
WG port to th
e bottom of t
g. 14. CAD m
e follows an
under differe
Topology and
shows the C
metal thickn
he transition
WG dimensio
m walls) rem
ing between
mounting su
, of the TW
he fin height
the structure
model of the no
nd results are
ent condition
d Operation
CAD model
ness t that re
provides a
ns 2b2 + t a
mains symme
n the heights
urface at the
WG). The sep
t s at the TW
.
on-pyramidal r
e shown and
ns.
of the propo
emains unifo
linear taper
and a2. Flarin
etric about th
s b1 and a2 (
e bottom of t
ptum tapers
WG port. It al
rectangular-to
d compared f
osed RWG-t
orm througho
between the
ng between
he center fin
(the side wa
the structure
linearly fro
lso occurs in
o-trough wave
for two defe
to-TWG tran
out the struc
e RWG dim
the widths a
n throughout
alls) is upw
e (with respe
om a height
n an upward
eguide transit
erent lengths
nsition. It ha
cture. The ou
mensions a1 a
a1 and 2b2 (
t the transiti
ward-directed
ect to open e
of zero at
d direction fr
tion.
22
s of
as a
uter
and
(the
on.
d to
nd,
the
om
trou
dim
rep
bot
Figrec
suf
(RW
sin
con
imp
can
Th
Fig. 15
ugh wavegu
mensions of
present the o
th the imped
g. 15. Distributangular wave
Observ
fficient evide
WG-to-TWG
ngle ridge w
nfidence in t
This co
pedances. O
n be placed
ese can eac
5 shows a c
uide (left), t
f the TWG
nly degrees
dances and fi
ution of the eleeguide (right)
ations [11] a
ence that the
G mode con
waveguide [1
this model bu
orroborates w
On the TWG
across the
ch be treated
conceptual v
transition (m
and RWG
of freedom
ield (mode) c
ectric field wit.
and prior wo
e tapered fin
nversion). T
16]-[17]. Th
ut trends rem
with the mo
side, the fin
guide to ap
d analyticall
view of the
middle), and
are fixed, th
in the design
configuratio
thin the trough
ork on linear
n in Fig. 1 ac
The transitio
he narrow fi
main similar
ore conceptu
n height can
pproximate e
ly as two w
electric fie
rectangular
the dimensio
n of the broa
ons must be t
h waveguide (
r and steppe
cts as a dual
on’s cross-se
in width t c
.
ual view of
be extended
each trough
waveguides
eld distribut
r waveguide
on L and it
adband trans
transitioned
(left), transitio
ed tapered se
-polarizer ro
ection resem
creates devi
f the transiti
d to a’ and a
as a closed
that suppor
tion within
e (right). If
ts taper prof
sition. As su
through it.
on (middle) an
eptums prov
otator [12]-[
mbles a flari
ation from
ion using po
a magnetic w
d structure [
rt quarter-wa
23
the
the
file
uch,
nd
vide
15]
ing
the
ort-
wall
[5].
ave
mo
acc
can
rec
δ r
and
ind
rec
Fig
res
app
the
odes, with a
curately pred
n be conside
ctangular wa
represents a
d their conn
dicate that t
ctangular wa
g. 16. The tro
Fig. 17
spect to its
proximated a
e simulated a
a TE10 cut-
dicting the T
ered in parall
aveguide as s
shift of the
nection throu
heir combin
aveguide.
ugh waveguid
7 represents
length at 3
as the rectan
and calculate
-off conditio
TWG cut-off
lel, Fig. 16 (
seen in Fig.
reference pl
ugh a plane
ned impedan
de (left) as an e
the real com
3GHz. At t
ngular waveg
ed results de
on approxim
f conditions
(left), from a
16(right) wit
lane due to
of electrical
nce can be
equivalent rec
mponent of
the TWG s
guide of Fig.
viate until th
mated by λc
this provide
an impedanc
th b=b2 and
fringing eff
l symmetry
approximat
ctangular wav
the impedan
side (L = 0
. 16 (right).
he model bre
c10 ~ 4a’.
es that each
ce point of v
a'=2(s+δ+t
fects [5]. Th
at the cente
te by the im
veguide (right)
nce for the
0 mm) the
Moving tow
eaks down in
In addition
of the troug
view formin
t). The varia
his arrangem
er of the TW
mpedance o
).
transition w
impedance
wards the cen
n the middle
24
to
ghs
ng a
able
ment
WG
f a
with
is
nter
e of
the
320
res
to t
Fig
C.
ele
pro
pro
pro
of
e structure w
0 mm) calcu
sults for a sm
the growing
g. 17. Real pa
Fabricated
The ch
ectromagneti
oviding larg
ovide turbule
ovides an av
2.33 GHz. F
where mode
ulations neg
mall distance
height of th
art of the impe
Transition a
hoice of th
ic and aerod
e Bandwidth
ence and air
erage VSWR
Fig. 19 show
conversion
lect the pres
into the gui
he septum.
edance with re
and Results
e length (L
dynamic perf
h and low a
r circulation
R less than 1
ws end-on v
and rotation
sence of the
ide before th
espect to trans
L) was bas
formance fro
average VSW
n was selecte
1.1 across th
views of the
n occurs. Sta
e center fin;
he structure o
sition's length
sed on simu
om which th
WR, (Fig. 1
ed to be 32
he S-Band an
resulting C
arting from R
this follows
of the fields
h.
ulations [11
he shortest p
18), and at
cm. This tr
nd a 2:1 VSW
CAD model
RWG side (
s the simula
is changed d
1]-[18] of
possible len
the same ti
ansition leng
WR Bandwi
for the S-ba
25
(L=
ated
due
the
gth
ime
gth
dth
and
tran
(top
me
3.4
Fig
and
hol
dra
bot
of t
nsition with
p-right), an
easurements
404 cm), (a2,
g. 18. Average
Each w
d mechanica
les for mac
awing where
ttom up to co
the structure
h the custom
nd the back
is shown in
, 2b2) = (9.3
e VSWR and
wall was mec
ally assemb
chine screws
e the center f
onnect it to t
e is seen with
m TWG ante
k-to-back a
Fig. 20. Th
cm, 4.8 cm)
2:1 VSWR ba
chanically m
led by peri
s. Fig. 21 s
fin along the
the bottom p
h an array of
nna flange (
arrangement
e transition’
), and L = 32
andwidth with
milled from a
odically dri
shows a cut
e length is se
plate. The cu
f screws and
(top-left) an
of fabrica
s parameter
2 cm.
h respect to th
an aluminum
illing and ta
t of the thr
een with scr
ustom flange
d 1/4 in. hole
nd circular W
ated transiti
rs are: (a1, b1
e transition le
m plate with
apping 3.45
ree dimensi
rew holes co
e attached on
es to connect
WR-284 flan
ions used
1) = (7.214 c
ength.
h t = 6.35 m
mm diame
onal transiti
oming from
n the outer s
t to the TWA
26
nge
for
cm,
mm,
eter
ion
the
ide
A.
Fig
Fig
Fig
g. 19. The end
g. 20. Two fab
g. 21. A cut of
d-on views of t
bricated S-ban
f the three dim
the transition.
nd transitions
mensional draw
.
in back-to-ba
wing of the tr
ack arrangem
ransition.
ment.
27
stru
ana
goo
the
tole
due
a s
me
net
and
Fig
The sim
ucture. Mea
alyzer which
od agreemen
e desired S-B
erances and
e to the shall
single transi
easured S-pa
twork. A M
d measured r
g. 22. Measur
mulated and
asurements
h was calibr
nt with simu
Band (2.6 GH
the connect
low height o
ition. The d
arameters to
atlab script
results are al
red and simula
measured r
were taken
ated using a
lated results
Hz to 3.95 G
tion of the f
of the fin. Fi
deembeddin
o ABCD-par
used for thi
lso in close a
ated results fo
results show
on an Ag
an S-Band w
s and show le
GHz). Major
fin to the gr
g. 23 shows
g procedure
rameters in
is purpose i
agreement fo
or the back-to-
wn in Fig. 22
gilent Techn
waveguide ca
ess than 0.5
deviations a
round where
s the simulat
e included
order to sp
is included i
or this.
-back transitio
2 are for th
nologies E8
alibration ki
dB of insert
are attributed
e screws wer
ted and meas
the transfor
plit into half
in Appendix
on.
e back-to-ba
361C netwo
it. These are
tion loss acr
d to fabricati
re not possi
sured results
rmation of
f the cascad
x A. Simula
28
ack
ork
e in
oss
ion
ible
s of
the
ded
ated
Fig
D.
dif
car
unm
Th
the
for
des
EM
des
g. 23. Measur
Aerodynami
The aer
fferent inlet v
r in an urban
manned aeri
e magnitude
e inlet and th
r air with
sign with L =
M performan
sign for diffe
red and simula
ic Performan
rodynamic p
velocities: a
n area at (V
ial vehicle (U
e of the velo
he outlet of
= 1.19 kg/m
= 320 mm (
nce (right). T
erent modali
ated results fo
nce
performance
a light breez
V = 10 m/s),
UAV) (V =
city, vorticit
the transitio
m3 and =
(left) and a s
The compari
ities in a mul
or a single tran
e of the stru
e (V = 0.1 m
, a car on a
45 m/s), and
ty and turbu
on for these
1.8e-5 Pa·s.
shorter trans
son in length
ltifunctional
nsition.
ucture was e
m/s), a stron
a freeway dr
d a category
ulent kinetic
scenarios in
These plot
ition with L
th is meant t
l structure.
examined [1
ng breeze at
riving at (V
y 4 hurricane
energy are s
n Figs. 24-29
s also show
L = 160 mm
to illustrate t
18] for seve
(V = 1 m/s)
V = 25 m/s),
e (V = 61 m
shown for b
9, respective
w the fabrica
and equival
the need to
29
eral
), a
an
/s).
oth
ely,
ated
lent
co-
Figtran
Figlon
Figlon
g. 24. Aerodynsition with a
g. 25. Aerodyg transition w
g. 26. Aerodyg transition w
namic performn inlet velocity
namic performwith an inlet ve
namic performwith an inlet ve
mance at the iy of 0.1 m/s.
mance at the ielocity of 1 m/
mance at the ielocity of 10 m
inlet and outle
inlet and outle/s.
inlet and outlem/s.
et of a 320 mm
et of a 320 mm
et of a 320 mm
m (left) and a 1
m (left) and 16
m (left) and a 1
160 mm (right
60 mm (right)
160 mm (right
30
t)
t)
Figlon
Figlon
Figlon
acr
Fig
g. 27. Aerodyg transitions w
g. 28. Aerodyg transition w
g. 29. Aerodyg transition w
The air
ross a wider
gs. 24-29. Th
namic performwith an inlet v
namic performwith an inlet ve
namic performwith an inlet ve
rflow from
range of inl
hese plots sh
mance at the ivelocity of 25 m
mance at the ielocity of 44.5
mance at the ielocity of 61 m
the RWG-to
let velocities
how that the
inlet and outlem/s.
inlet and outlem/s.
inlet and outlem/s.
o-TWG tran
s in the long
air vorticity
et of a 320 mm
et of a 320 mm
et of a 320 mm
nsition appe
g transition b
y and velocit
m (left) and a 1
m (left) and a 1
m (left) and a 1
ears to be m
by observing
ty are identic
160 mm (right
160 mm (right
160 mm (right
more consist
g the results
cal at the RW
31
t)
t)
t)
tent
s in
WG
inle
vor
and
and
vor
wil
cel
Fig
the
has
the
den
et of the tr
rticity and v
d air 'circula
d justifies th
rticity field
ll change fo
llular networ
g. 30. Vorticit
Fig. 31
e length of th
s the stream
e longer tran
nse, indicatin
ansition, bu
velocity plot
ation' in the a
he choice o
at the outlet
or different w
rks so the an
ty field at the
shows the t
he transition
lines which
nsition. In th
ng the prese
ut the TWG
ts indicate t
area between
of a longer
t of the trans
waveguide b
nalysis is vali
outlet of 320 m
hree dimens
n. It can be o
h are not sym
he long trans
ence of turbu
G outlet of t
that the long
n the center
transition. F
sition to hig
bands, but t
id for these r
mm and 160 m
sional stream
observed fro
mmetric arou
sition the vo
ulences in th
the structure
ger transitio
fin and the s
Fig. 30 pres
ghlight these
this design w
ranges of inl
mm long trans
mline plots o
om this plot
und the cen
orticity stream
he troughs an
e differs. Sp
n creates m
sidewalls. T
sents a com
differences
will function
let velocities
sitions.
f the vorticit
that in the s
nter fin and l
m lines are
nd better air
pecifically,
more turbulen
his is desira
mparison of
. This scena
n across ma
s.
ty vector do
short transiti
less dense th
symmetric a
r 'circulation
32
the
nce
able
the
ario
any
wn
ion
han
and
n' in
the
pro
fro
Fig
e channel be
oposed trans
m a multifun
g. 31. Streaml
etween the
ition is suita
nctional TW
line plots of th
center fin
able for appl
WG antenna i
he vorticity for
and the sid
ications whe
s desired.
r a 160 mm an
dewalls. The
ere broadban
nd a 320 mm l
ese results v
nd reconfigu
long transition
verify that
urable radiati
n.
33
the
ion
34
CHAPTER IV
A PATTERN RECONFIGURABLE TROUGH WAVEGUIDE ANTENNA
A. Introduction
Metallic blocks were used as perturbations in a TWA for both symmetric and
periodically asymmetric leaky-wave antenna designs. These were discussed in Ch. II
along with another design that examined the use of vertical and horizontal rods (with a
frequency depended length) that were placed atop the center fin to scanned the main
beam. This work proposes an alternative electromechanical design using cantilever
perturbations in the troughguide; they offer a series of advantages compared with the
blocks since they can be made much lighter, are easier to work, and can be
functionalized according to the application. They also offer several degrees of freedom
that include length for frequency scaling, width for tuning, and angle for amplitude
tapering and leakage from the antenna. Cantilevers can also come in racks as modular
component which makes them easily replaceable depending in the requirements of the
application. Additionally sensors and other devises can be integrated on the cantilevers
for multifunctional operations and potentially can be designed so they can control and be
control by air flow without their electromagnetic performance being affected.
B. Simulated Designs
The performance of different cantilever topologies was examined using [11] to
better understand the attenuation properties of the cantilever in the TWA. Fig. 32 shows
two
cen
wa
fun
ind
at t
esp
Fig
o different
nter fin and
all and the b
nction of ca
dicates that a
the junction
pecially for a
g. 32. Cantilev
configuratio
the bottom
bottom plate
antilever ang
a cantilever w
between th
angles aroun
ver actuated f
ons, one hav
plate (case
e (case 2).
gle (formed
with the sam
he sidewall a
nd 30°.
from the cente
ving the can
1) and the o
Fig. 33 sho
d by the ca
me width (24
and the botto
er fin (case 1)
ntilever plac
other placed
ows the inse
antilever and
4 mm) as th
om plate, le
and from the
ced at the j
at the junct
ertion loss p
d the bottom
he bottom pla
aks more po
sidewall (case
unction of
tion of the s
per meter a
m plate). T
ate, and plac
ower per me
e 2).
35
the
ide
s a
This
ced
eter
Figpla
tran
rad
sm
eff
(es
we
wa
g. 33. Insertioncement in the
It is kn
nsform of t
diation patte
moother trans
fect of taperi
specially awa
ere not actua
as designed f
n loss with restrough.
nown in ante
the aperture
ern and min
sition of the
ing in radiat
ay from bro
ated in this f
for a sinusoid
spect to the pe
enna theory
e distribution
nimizes the
fields throug
tion and sho
oadside by ta
fashion for th
dal taper wit
erturbation an
that the rad
n. Tapering
side lobe l
gh the struct
owed that im
apering the
he designs i
th a 1.2 m lo
ngle, for cantil
diation patte
g the apertu
levels, prov
ture. Previou
mproved radi
aperture dis
in this work
ong (10λ) eff
levers of diffe
ern is given
ure gives co
iding at the
us work [7]
iation pattern
stribution). T
, but the eff
fective apert
rent width an
by the Four
ontrol over
e same time
considered
ns are possi
The cantilev
fective apertu
ture at 3 GHz
36
nd
rier
the
e a
the
ible
vers
ure
z.
Fig
ang
can
can
VS
pow
rad
lea
at b
sho
per
g. 34. TWA w
Fig. 35
gles varying
ntilever pair
ntilevers tap
SWR has va
wer. The VS
diation only
aked). The hi
broadside wh
ows the sim
rturbation an
with cantilever
shows the s
from 20° to
r in the cen
pering accord
alues greater
SWR is less
provides <
igh VSWR c
here the can
mulated radi
ngle fixed at
r perturbation
simulated VS
o 70° with a
nter of the
ding to the
r of 2 indic
than 2 for an
< 5 dB/m at
close to 3 GH
ntilevers are h
iation patter
30°; note th
ns.
SWR and
10° step size
troughguide
sinusoidal d
ating more
ngles 60° an
t 3 GHz (e.g
Hz is a resul
half wavelen
rns at 2.6 G
hat the main b
per unit len
e; this refers
e with the
distribution)
than 10% r
nd 70° but as
g., less than
lt of phase a
ngth long (ex
GHz, 3 GH
beam scans
ngth (P.U.L.)
to the angle
bottom pla
. For angles
reflection of
s Fig. 35 (rig
33% of the
accumulation
xplained in
Hz and 3.9
as frequency
) for cantilev
e formed by
ate (with oth
s less than 5
f the deliver
ght) shows,
input power
n, which occ
Ch. II). Fig.
GHz with
y varies.
37
ver
the
her
50°
red
the
r is
urs
36
the
Fig
Fig C.
me
at b
per
GH
g. 35. VSWR
g. 36. Radiati
Holes in the
Arrays
ethods used i
broadside-w
riodic leaky-
Hz. Instead o
(left) and (r
ons patterns,
e Center
of holes, te
in the past to
where phase r
-wave anten
of altering th
right) along th
with fixed per
eeth and ver
o treat high r
reversal betw
nnas), which
he physical st
he S-band.
rturbation ang
rtical rods on
reflections d
ween succes
h happens in
tructure of th
gle at 30° and
n top of the
due to phase
ssive elemen
n this design
he troughgui
a frequency s
e center fin
accumulatio
nts is require
n in the neig
ide by makin
sweep.
are two of
on. This occ
ed (common
ghborhood o
ng holes on
38
the
urs
n to
of 3
the
fin
No
gui
suc
for
can
mis
for
sho
a V
loo
tha
sug
gen
Fig
or the wa
otionally, the
ided wave.
ccessive can
r this effect,
Circula
ntilever as sh
smatch from
r 6 mm and
owed improv
VSWR = 2.5
ok at the curr
at the current
ggests that th
nerate a high
g. 37. Curren
alls, holes w
e cantilevers
This creates
ntilevers. The
and are of in
ar holes of 6
hown in Fig.
m phase accu
10 mm rad
vement to th
(with hole t
rent distribu
ts are strong
he hole shou
her inductive
ts excited on a
were design
s inside the
s reflections
e circular ho
nterest to thi
mm and 10
. 37 to provid
umulation. Fi
dius holes, r
he VSWR –
to the center
ution produce
ger at the edg
uld be place
e loading.
a cantilever w
ned on the
TWG prese
s due to the
oles add a sh
s work.
mm diamet
de a compen
igs. 38 and 3
espectively,
bringing it f
r) – but a low
ed on the ca
ge of each c
d at the edg
ith a hole in th
center of
ent a shunt c
e cascaded i
hunt inducti
er were desi
nsating effec
39 show the
in the cent
from a VSW
wer VSWR i
antilevers in
cantilever co
ge where it c
he center.
each actua
capacitive re
impedance m
ive reactive
igned on the
ct and educe
VSWR (left
ter. Although
WR = 3.5 (wi
is required. T
Fig. 37, it ca
ompared to t
can perturb t
ated cantilev
eactance to
mismatch fr
to compens
e center of ea
the impedan
ft) and (rig
h both desig
ith no holes)
Taking a clo
an be observ
the center. T
the current a
39
ver.
the
om
sate
ach
nce
ght)
gns
) to
oser
ved
This
and
Fig
Fig
D.
eac
can
wit
Th
for
g. 38. VSWR
g. 39. VSWR
Holes at the
The des
ch cantilever
ntilever. Fig
th one hole o
ese plots ind
r a 30° pertur
(left) and (r
(left) and (r
e Edge
sign in Fig. 3
r (Fig. 40);
gs. 41 and 42
of radius of
dicate that th
rbation angle
right) for cant
right) for cant
37 was mod
this was ba
2 show the V
6 mm and 1
he VSWR w
e with more
tilevers with a
tilevers with a
ified so each
ased on that
VSWR (left)
10 mm at th
was reduced
than 50% o
a 6 mm radius
a 10 mm radiu
h hole move
observation
) and (righ
e edge of ea
below 2 (es
f the total po
hole on the ce
us hole on the c
ed beyond th
n of current
ht) for the m
ach cantileve
specially the
ower lost per
enter.
center.
he outer edge
density on
modified desi
er respective
e 6 mm radi
r meter.
40
e of
the
ign
ely.
ius)
Fig
Fig
Fig
can
imp
g. 40. Curren
g. 41. VSWR
g. 42. VSWR
Designs
ntilever are
provement i
ts excited on a
(left) and (r
(left) and (r
s with holes
compared
in VSWR w
a cantilever w
right) for cant
right) for cant
s of 6 mm an
in Fig. 43
when the ho
ith a hole at th
tilevers with a
tilevers with 1
nd 10 mm ra
for a pert
ole is moved
he edge.
a 6 mm radius
0 mm radius h
adius at the
turbation an
d towards t
hole at the ed
hole at the edg
center and t
ngle of 30°
the edge. Ca
dge.
ge.
the edge of
° showing
antilevers w
41
the
the
with
hol
com
ref
pro
Fig
E.
Fig
the
des
per
wh
dua
det
les at the ed
mpared to th
flection coe
operties of th
g. 43. VSWR
Cantilevers
A desig
g. 44. This w
e current an
signs with i
rturbation an
hen the holes
al-hole desig
terioration is
dge appear
he cantilever
fficient nea
he antenna ar
(left) and (r
with Two Ho
gn with two
was examine
nd its effect
dentical 6 m
ngle of 30°.
s have a rad
gn with 6 m
s apparent an
to be electr
rs without ho
ar the frequ
re not affect
right) for cant
Holes
holes on ea
ed to observe
on the VS
mm and 8 m
The VSWR
dius of 6 mm
mm, 8 mm a
nd the main b
rically longe
oles, but pha
uency with
ed, providin
tilevers with ed
ach cantileve
e the impact
SWR and ra
mm radii ho
R is lower t
m. Radiation
and 10 mm
beam points
er at the ope
ase accumula
h broadside
ng a narrow b
dge and cente
er (6 mm an
t of a more
adiation patt
oles are plot
than 1.5 for
n patterns as
holes (on ea
s towards nea
erating freq
ation does n
radiation.
beam at broa
er holes with a
nd 8 mm rad
significant p
terns. The r
tted in Fig.
perturbation
s shown in F
ach cantilev
ar broadside
quency (> λ0
ot cause a hi
The radiat
adside region
a 30° angle.
dii) is shown
perturbation
results for t
45 for a fix
n angle of 3
Fig. 46 for
ver); no patt
e.
42
0/2)
igh
ion
n.
n in
on
two
xed
30°
the
ern
Fig
Figper
Fig
g. 44. TWA w
g. 45. VSWR rturbation ang
g. 46. Radiati
with two holes
(left) and (rgle.
on patterns fo
on each cantil
right) for cant
or a TWA with
lever.
tilevers with 6
h cantilevers w
mm and 8 mm
with two holes
m radius hole
s of 6 mm, 8 m
es and 30°
mm and 10 mm
43
m.
F. D
for
Sim
mit
det
cha
wit
Fig All
rec
for
and
Different Ma
The eff
r two- and t
milar results
tigating the
teriorate sign
ange in the m
thout two ho
g. 47. TWA w
l three case
ctangular geo
r the circular
d showed an
atching Geo
fect of holes
three-hole de
s were obse
high reflec
nificantly at
main beam’s
oles on each
with two triang
es provided
ometries gen
r, triangular,
n even greate
ometries
with triangu
esigns (e.g.,
erved, show
ctions due to
the center o
s beam direc
cantilever) i
gular or rectan
in Fig. 48
nerally treat
rectangular
er effect towa
ular and rect
, holes per c
wing a redu
o phase acc
of the band (a
ction. The VS
is shown in F
ngular holes.
show a VS
the problem
topologies o
ards reducin
tangular geom
cantilever).
uction to th
cumulation.
as desired) a
SWR of all
Fig. 48 for a
SWR < 2; h
m more effec
on each cant
ng the VSWR
metries was
This is show
he VSWR a
Radiation p
and there is
three geome
a 30° perturb
however, th
ctively. Thre
tilever were
R
also examin
wn in Fig.
and effectiv
patterns do n
only a nomi
etries (with a
bation angle.
he circular a
ee–hole desig
also examin
44
ned
47.
vely
not
inal
and
and
gns
ned
Fig
G.
wa
dim
as
the
flan
the
CA
loc
g. 48. VSWR
Fabrication
Two pi
all was mille
mensions of
explained in
e milling ma
nges were a
e transitions
AD drawings
cated.
of the TWA w
n of the TWA
eces of TWA
ed and tapp
the structure
n Fig. 49. Ea
achine could
lso designed
and the fee
s of the parts
with two holes
A
A were fabr
ped accordin
e are b2=54.
ach piece w
d process pr
d and fabrica
ed connectio
s used to fab
of circular, tr
ricated from
ngly for con
35 mm, a2 =
as 75 cm lo
roviding an
ated to conn
ons to the tr
bricate the T
riangular and
m 1/4 inch thi
nstruction us
= 93 mm, t =
ong as it was
overall ape
nect the two
roughguide.
WG and sho
d rectangular g
ick aluminu
sing machin
= 6.35 mm,
s the maxim
erture 1.5 m
pieces toget
Figs. 50 an
own where s
geometries.
um plates. Ea
ne screws. T
and h=37 m
mum length t
m long. Cust
ther and mou
nd 51 show
screw holes
45
ach
The
mm
that
om
unt
the
are
Figg. 49. CAD deesign of the troough wave gu
ide.
46
Fig(low
g. 50. CAD drwer).
rawing of the bbottom plate o
of the troughgguide (upper) and the custo
om made flang
47
ge
Fig
g. 51. CAD drawings of the troughguide.
48
49
H. Experimental Setup I
Two sets of cantilevers were fabricated according to the previous results; these
were made from 0.6 mm thick copper sheets. Each set had four 60 cm long racks (due to
the dimensions of the metal sheets) giving a 1.2 m (10λ) long aperture. Each rack has a 2
mm base in order for mechanical stability at the bottom of the TWA. The width of the
cantilevers is 22 mm (e.g., 2mm less than the width of the trough) and each has the
length of 60 mm for broadside radiation near 3 GHz. The fabricated version without
holes can be seen on the left of Fig. 52. The transitions were placed into the TWA and
measured using an Agilent Technologies E8361C network analyzer that was calibrated
with an S-Band waveguide calibration kit. The VSWR is shown on the right side of Fig.
52, and Fig. 53 shows the radiation patterns for both the co-polarization and cross-
polarization patterns at 2.6 GHz, 3 GHz, and 3.9 GHz. Measured results are in no
agreement with the simulated results for this configuration. This deviation was due
primarily to fabrication errors in machining the cantilevers (not of all of the same exact
length and width). Some cantilevers were also forced into the structure and deformed.
This created air gaps between the troughguide walls and the cantilevers. A second set of
cantilevers was made with a hole at the edge but it was not tested.
FigCop
g. 52. Fabricapper cantileve
ated version ofers placed in t
f cantilevers fohe TWG (low
or broadside rwer left), measu
radiation usinured and simu
ng copper sheeulated VSWR
ets (upper left.
50
t),
Figpol
g. 53. Radiatiarization plan
on patterns atnes.
t 2.6 GHz, 3 G
GHz, and 3.9 GGHz at the co--polarization a
and cross-
51
I. E
dim
for
han
can
for
mm
tap
one
can
Figλ/2
Experimenta
The fa
mensions pro
r the same d
nd fabricatio
ntilever is no
r mechanical
m. An apertu
ped on paper
e with a sin
ntilevers insi
g. 54. Fabricapaper cantile
al Setup II
abrication d
ovided many
design using
on. The main
ow able to be
l support. Th
ure 120 cm
rboard. Two
ngle hole at
ide the troug
ated cantilevever with no ho
difficulties a
y lessons-le
copper tape
n deviation f
e 24 mm (th
he copper ta
(10λ) long
sets were m
the edge of
ghguide are s
rs in the TWGole (lower righ
and sensitiv
arned, so an
e on paper c
from the pre
he full width
ape also has
was formed
made, one w
f each cantil
shown in Fig
G (left), λ/2 paht).
vity of the
n alternative
antilevers. T
evious desig
h of the troug
thickness o
d using 20 a
without holes
lever (Fig. 5
g. 54.
aper cantileve
TWA to
e approach w
This gave m
gn is that the
gh) since no
of 0.025 mm
actuated cop
s (Fig. 54, lo
54, upper rig
er with one ho
the cantilev
was develop
more control
e width of ea
base is need
m instead of
pper cantilev
ower right) a
ght); the pap
ole (upper rig
52
ver
ped
for
ach
ded
0.6
vers
and
per
ght),
53
The paper cardstock was marked using a caliper and cut using a guillotine-style
paper cutter. A piece of copper tape was placed on each card. For better electrical
contact it was taped against the bottom wall of the troughguide (the tape has a
conductive adhesive). The angle of these paper cantilevers was tapered in a sinusoidal
manner starting from the center of the guide towards the ends. Small pieces of foam
were used to support the cantilevers to the right angle. After measuring the structure the
cantilevers were taken out and a hole, 12 mm in diameter, was cut on every one using a
razor blade.
1. λ/2 Cantilevers with No Holes
Half-wavelength cantilevers (at 3 GHz) were placed in the TWG and the
performance of the antenna was measured using a network analyzer. The VSWR plots in
Fig. 55 (left) show the spike in VSWR (due to phase accumulation) close to the
operating frequency at both simulated and measured results. Insertion loss plots in Fig.
55 (right) indicate that 90% power was attenuated via radiation through the aperture.
Radiation pattern measurements in the anechoic chamber also indicate agreement
between the simulated and measured results (co- and cross-polarization) at 2.6 GHz, 3
GHz and 3.9 GHz (Fig. 56). An antenna gain G near 14 dBi was achieved at broadside.
F
Fig. 55. Meassured and sim
ulated insertioon loss (left), VVSWR (right)).
54
Fig
g. 56. Co- andd cross-polarizzation plane r
adiation patteerns of the TWWA with canti
levers.
55
2. λ
by
rad
ape
sim
exp
can
asy
the
Th
Fig
trou
Fig
λ/2 Cantileve
Prior re
cutting hole
dius hole at t
erture. The
mulated data
pected, but t
ntilever wer
ymmetries. M
e design mak
e insertion lo
g. 57. Measur
In Fig.
ugh wavegu
g. 59 shows
ers with a H
esults showe
es at the edge
the edge we
VSWR wa
a as seen in
the peak wa
re not identi
Moreover, m
king the can
oss plotted a
red and simula
58 is a pictu
uide antenna
the radiation
Hole
ed that refle
e of each ca
ere placed in
as measured
n Fig. 57 (le
as shifted to
ical and we
most of the h
ntilever to ap
at Fig.57 (rig
ated VSWR (l
ure of the exp
a is mounted
n patterns fo
ctions due t
ntilever. Hal
n the TWG p
d and plotte
eft). It is se
the left (a l
ere roughed
holes were m
ppear longe
ght) appears
left) and insert
perimental s
d on a rotati
or the half w
to phase acc
lf-waveleng
providing a
ed against f
een that the
lower freque
out of the
measured to
er, which ex
also shifted
tion loss (righ
setup inside t
ing stand ac
wavelength c
cumulation c
gth cantilever
120 cm (10λ
frequency a
e VSWR wa
ency) as the
copper tap
o have a larg
xplains the fr
for the same
ht).
the anechoic
cross the sta
cantilevers w
can be reduc
rs with a 6 m
λ) long taper
along with
as lowered,
e holes on ea
pe, resulting
ger radius th
frequency sh
e reasons.
c chamber. T
andard anten
with one hole
56
ced
mm
red
the
as
ach
in
han
hift.
The
nna.
e at
the
Me
wit
sim
tap
Fig
e edge for b
easured and
th frequenc
mulation but
pered accurat
g. 58. Experim
both the co-
simulated r
y. Measure
t this is attr
tely and a re
mental setup f
- and cross
results are in
ed results s
ributed to fa
esult is the ap
for measuring
-polarization
n agreement
show much
abrication di
ppearance of
radiation pat
n at 2.6 GH
t and captur
h higher sid
ifficulties. T
f high level s
tterns in the a
Hz, 3 GHz
re the main
delobes com
The aperture
sidelobes.
anechoic cham
and 3.9 GH
beam steer
mpared to
e was also n
mber.
57
Hz.
ing
the
not
Fig
g. 59. Radiation patterns foor the half wav
velength cantiilevers with a hole.
58
J. E
thir
wit
can
(30
can
mid
ape
stro
len
tim
gro
per
wit
for
Fig
Experimenta
Reconf
rd setup usin
th copper ta
ntilevers we
0) about the
ntilever corr
ddle of the
erture of 14
ongest pertu
ngth and the
me in anti-sy
oups corres
rturbations. E
th cantilever
rm the backw
g. 60. Taperin
al setup III -
figuration of
ng quarter w
ape on car-st
re actuated
e center of
responding
troughguide
44 cm in to
urbations-big
direction of
ymmetric pa
sponded to
Experimenta
r perturbatio
ward quadran
ng perturbatio
Pattern Rec
f the radiation
wavelength lo
tock paper –
with a distr
the TWA.
to the amp
e. The angl
otal from on
gger angles.
f the beam,
airs. Each le
o one-quar
al and simul
ons can be
nt trough bro
on angle for 12
configurable
n pattern at
ong cantilev
– this was d
ribution give
Fig. 60 sh
litude distri
es are show
ne end to th
In order to
cantilevers w
ength (one, t
rter, one-ha
lated results
used for re
oadside to th
2 cantilevers f
Design
a fixed frequ
vers that wer
done both wi
en by a cos
hows the pe
ibution start
wn for 12 ca
he other, wi
consider the
were actuate
two, or thre
alf, and t
follow whi
configurable
he forward q
form one end t
uency was e
re simulated
ith and with
sine amplitu
erturbation
ting from o
antilevers, w
ith the midd
e effect of th
ed one, two,
ee at a time
three-quarte
ch illustrate
e beam stee
quadrant.
to the middle
evaluated in
and fabrica
hout holes. T
ude distribut
angle of ea
one end to
which form
dle having
he perturbat
, and three a
e) of cantilev
er wavelen
that the TW
ering, scann
of a TWG.
59
the
ated
The
ion
ach
the
an
the
ion
at a
ver
gth
WA
ing
60
1. λ/4 Cantilevers
A new set of cantilevers was made using copper tape and paper. Each cantilever
was 30 mm (λ/4) long 24 mm wide as represented at Fig. 61. The cantilevers were
placed in the trough waveguide as before taped on the sidewalls, tapered with a cosine
distribution given by (30) and supported by small pieces of foam (which are EM
transparent due to their electrical permittivity being near unity). In (30) N is the number
of cantilevers in half the trough and n corresponds to the index of the nth cantilever from
the center. Fig. 62 (left) shows the simulated and measured VSWR. The cantilevers are
not a half-wavelength so there is no phase accumulation problem. The measured and
simulated S-parameters are potted at Fig. 62 (right). The measured radiation patterns,
Fig. 63, show higher sidelobes compared to the simulated mainly because the tapering
was made approximately. At 3 GHz the main beam is 50° from broadside towards the
backward quadrant.
0.2 0.8cos( )n
AN
(30)
Fig
Fig
g. 61. Quarter
g. 62. Measur
r wavelength l
red and simula
long cantileve
ated VSWR (l
ers.
left) and S-parrameters (righht).
61
Figand
g. 63. Radiatiod 3.9 GHz.
on patterns at the co-polariz
zation and crooss-polarizatioon planes at 2
.6 GHz, 3 GH
62
Hz
2.
sho
pha
can
the
Fig
λ/4 Cantilev
An 8 m
ow the VSW
ase accumul
ntilevers wit
e main beam
g. 64. Measur
vers with a H
mm radius ho
WR (left) an
lation. Radi
th an 8 mm
pointing 50
red and simula
Hole
ole was mad
nd S-parame
ation pattern
radius hole.
0° away from
ated VSWR (l
de in each q
eters in dB
ns are displ
. At 3 GHZ
m broadside t
left) and S-par
quarter-wave
(right). The
layed at Fig
measured a
to the backw
rameters (righ
elength canti
e results do
g. 65 for th
and simulate
ward quadran
ht).
ilever. Figs.
not show a
he quarter lo
ed results sh
nt.
63
64
any
ong
how
Figand
g. 65. Radiatid 3.9 GHz.
on patterns att the co-polari
ization and crross-polarizatiion planes at 2
2.6 GHz, 3 GH
64
Hz
3.
per
wit
wit
goo
Fig
bro
hig
Sup
eno
λ/2 Cantilev
Two q
rturbation (e
th half-wave
th simulated
od agreemen
g. 66. Measur
The rad
oadside radia
gher sidelob
pporting the
ough to repro
vers
quarter-wave
each at the s
e long cantil
d results in F
nt, showing a
red and simula
diation patte
ation occurs
es due to fa
e cantilevers
oduce the de
e long cant
ame angle)
levers (no h
Fig. 66. Mea
a peak aroun
ated VSWR (l
erns are show
at 3 GHz. A
aults in the
s with foam
esire distribu
tilevers wer
to provide a
holes) was m
asured and s
nd to 2.9 GH
left) and S-par
wn in Fig. 6
As in the pre
placement o
m to create t
ution, but suf
re then act
a half wave
measured an
simulated V
Hz due to pha
rameters (righ
67 for this c
evious cases
of the canti
the tapering
fficient to ap
tuated toget
long cantile
nd results ar
VSWR (Fig.
ase accumul
ht).
configuratio
s, measured
ilevers in th
g angles wa
pproximate i
ther as sin
ever. The TW
e shown alo
66, left) are
lation.
n, where ne
results show
he troughgui
as not accur
it.
65
ngle
WA
ong
e in
ear-
wed
ide.
rate
Figand
g. 67. Radiatid 3.9 GHz.
on patterns att the co-polari
ization and cr
ross-polarizatiion planes at 2
2.6 GHz, 3 GH
66
Hz
4.
exa
lon
me
ver
me
Fig
Fig
λ/2 Cantilev
Two qu
amined next
ng cantilever
easured resul
rify that the
ethod and sti
g. 68. Half wa
g. 69. Measur
vers with Tw
uarter-wavel
t (Fig. 68) to
r can reduc
lts in Fig. 69
reflections
ll achieve br
ave long cantil
red and simul
wo Holes
length long
o verify tha
e the reflec
9 (left) dem
due to the p
roadside rad
lever with two
lated VSWR (
cantilevers
at holes plac
tions due to
onstrate this
phase accum
iation (Fig. 7
o holes.
left) and S-pa
(with two
ced along th
o phase acc
s through the
mulation can
70).
arameters (rig
8 mm radiu
he edge of h
cumulation.
e reduction
n be mitigate
ght).
us holes) w
half-wavelen
Simulated a
in VSWR, a
ed through t
67
were
gth
and
and
this
Figand
g. 70. Radiatid 3.9 GHz.
on patterns att the co-polari
ization and crross-polarizatiion planes at 2
2.6 GHz, 3 GH
68
Hz
5. 3
hol
for
me
ref
at 2
At
Fig
3λ/4 Cantile
Fig. 73
les that are
r this scenari
easured. A h
flections as it
2.6 GHz, 3 G
3 GHz the m
g. 71. Measur
vers
3 (lower righ
actuated tog
io are shown
high peak i
t also seen fr
GHz and 3.9
main beam p
red and simula
ht) shows th
gether at the
n in Fig. 71
s located at
from the S-p
9 GHz are sh
points 20° aw
ated VSWR (l
hree quarter
same angle
with good
t 3.6 GHz,
arameter plo
hown in Fig.
way from bro
left) and S-par
r-wavelength
e. The measu
agreement b
where the
ots of Fig. 71
72 for the c
oadside towa
rameters (righ
h long canti
ured and sim
between the
system suff
1(right). Rad
co- and cross
ards the forw
ht).
ilevers with
mulated resu
simulated a
fers from h
diation patte
s-polarizatio
ward quadran
69
out
ults
and
igh
erns
ons.
nt.
Figand
g. 72. Radiatid 3.9 GHz.
on patterns att the co-polari
ization and crross-polarizatiion planes at 22.6 GHz, 3 GH
70
Hz
6. 3
als
and
shi
rad
the
the
the
wa
Fig
3λ/4 Cantile
Three q
o examined
d S-paramete
ifted to the
diation patter
e forward qu
e TWA and
esis. The TW
aveguide ada
g. 73. Three q
vers with Th
quarter-wave
(shown in
ers are show
left as the
rns where at
uadrant. Fig.
S-Band wav
WA is conn
aptor and con
quarter wave l
hree Holes
elength long
Fig. 73, left
wn in Fig. 74
cantilevers
t 3 GHz, the
75 shows th
veguide cali
nected to th
nnected to th
long cantileve
g cantilevers
t). Simulated
4. A small pe
appear long
main beam
he network a
ibration kit
he transition
he network a
rs with and w
s (with three
d and measu
eak can still
ger with the
is located 2
analyzer on
used for all
n which is
analyzer thro
without holes in
e 8 mm rad
ured results
be detected
holes. Fig.
20° from bro
an optics tab
l the measur
connected
ough a coaxi
n a TWG.
dius holes w
of the VSW
d that is sligh
76 shows
adside towa
ble and next
rements in t
to a coax-
al cable.
71
were
WR
htly
the
ards
t to
this
-to-
Fig
Fignet
g. 74. Measur
g. 75. The expwork analyzer
red and simula
perimental setr and the DUT
ated VSWR (l
tup used for mT.
left) and S-par
measurements
rameters (righ
with the wave
ht).
eguide calibraation kit, the
72
Figand
g. 76. Radiatid 3.9 GHz.
ion patterns aat the co-polar
rization and crross-polarizattion planes at
2.6 GHz, 3 GH
73
Hz
can
bro
bea
suf
Fig
K. A
ant
TW
tran
Fin
Fig. 77
ntilever leng
oadside (λ/2)
am direction
fficiently by
g. 77. Beam st
Aerodynami
The tro
tennas and s
WG structur
nsparent cov
nite elements
7 summarize
gth. The ma
) towards the
n, which de
actuating di
teering by cha
ic Performan
ough wavegu
sensing mec
res can be
ver and usin
s simulation
es the reconf
ain beam can
e forward qu
emonstrates
ifferent sets
anging the len
nce of the TW
uide provide
chanisms int
exploited
ng the topolo
ns [18] were
figuration o
n steer from
uadrant (3λ/4
the concept
of cantilever
gth of the can
WA with Can
es a rigid p
to the same
by sealing
ogy for pres
employed t
f the radiati
m the backw
4). The VSW
t that the m
rs to create d
ntilevers.
ntilever Pert
platform that
device. The
g them wit
ssurized air-
to study the
ion pattern b
ward quadran
WR and atten
main beam
discretized le
turbations
t integrates
e internal vo
th an elect
-flow throug
aerodynami
by altering
nt (λ/4) trou
nuation of ea
can be alter
engths.
reconfigura
olume of th
tromagnetica
gh the anten
ic performan
74
the
ugh
ach
red
able
ese
ally
nna.
nce
and
an
in C
sid
airf
pot
stru
Fig
d characteris
extension o
Ch.3. It was
dewalls and
flow, creatin
tentially be p
ucture of the
g. 78. Aerody
stics of the t
f the aerody
also shown
the center
ng vortices
placed. Fig.
e velocity an
namic perform
trough wave
ynamic perfo
that air flow
fin. The pr
around the
78 shows cu
nd vorticity f
mance of the T
guide antenn
ormance of t
w through th
resence of c
cantilevers
ut planes alo
fields along w
TWA with can
na with the
the RWG-to-
he transition
cantilevers i
where sens
ong the lengt
with the vort
ntilevers.
cantilever p
-TWG trans
is channeliz
in the TWA
ors and oth
th inside the
ticity stream
perturbations
sition discuss
ed between
A perturbs
her devices c
e volume of
mlines.
75
s as
sed
the
the
can
the
76
CHAPTER V
FUTURE WORK
The foundations of developing a multifunctional device based on the troughguide
antenna and waveguide platform with integrated sensing capabilities has been discussed
in this thesis. Ongoing and future work will examine more TWA designs and evaluate
“better” self-matching networks in the cantilever (spiral slots, etc.) to better mitigate
phase accumulation. Further, a more extensive study of the aerodynamic performance
will be undertaken to explore different setups and conditions under which the structure
will perform (air tunnel tests, etc.). Finally, the development of sensor systems for
certain applications is of interest to this work.
77
CHAPTER VI
CONCLUSIONS
The electromagnetic and aerodynamic co-design of a non-pyramidal RWG-to-
TWG transition and fixed-frequency pattern reconfigurable TWA can provide many of
the desirable characteristics required by a platform which integrates reconfigurable
antennas and sensing mechanisms into the same device. An S-band design (2.6 GHZ to
3.95 GHz) of a non-pyramidal RWG-to-TWG transition was proposed for this.
Simulated and measured results for a fabricated device validated this thesis by designing
the structure to meet both its electromagnetic and aerodynamic performance
requirements. The resulting pattern reconfigurable TWA using cantilever perturbations
provided high gain and was also demonstrated using experimental and simulated results
that showed scanning from the backward quadrant (-50°) to the forward quadrant (20°)
can be achieved. Methods for treating high reflections due to phase accumulation
problem at broadside were also discussed and as results showed how the requirements
can be met.
78
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81
APPENDIX A
A. Matlab script for deembedding using ABCD-parameters
%----------------Deembedding the transitions----------------- % %----------------Loizos Loizou------------------------------- %----------------Texas A&M University------------------------ %----------------October 2010------------------------------- % %Convert the measured data from db to watts and into a complex form. %First column of the data is the frequency, second is the S11 in db and the %third is the phase of S11.Same applies for all S parameters. data = data; S_11=10.^((data(:,2))./10); S_21=10.^((data(:,4))./10); S_12=10.^((data(:,6))./10); S_22=10.^((data(:,8))./10); F=data(:,1).*1e-9; %In order to perform calculations using the build in functions s2abcd is %needed that the data are arranged into a 2x2xm matrix. n=20501; for i=1:n sparam(1,1,i)=S_11(i,1); sparam(1,2,i)=S_12(i,1); sparam(2,1,i)=S_21(i,1); sparam(2,2,i)=S_22(i,1); end; abcd_params = s2abcd(sparam,50); %s to abcd parameters %for solving the system for A,B,C,D parameters syms a b c d am bm cm dm [a b c d] = solve(a.^2+b.*c-am,a.*b+b.*d-bm,a.*c+c.*d-cm,b.*c+d.^2-dm,'a','b','c','d'); am = abcd_params(1,1,:); bm = abcd_params(1,2,:); cm = abcd_params(2,1,:); dm = abcd_params(2,2,:); a_m(1,:)=am; am=a_m; b_m(1,:)=bm; bm=b_m; c_m(1,:)=cm; cm=c_m;
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d_m(1,:)=dm; dm=d_m; a = eval(vectorize(a(1))); b = eval(vectorize(b(1))); c = eval(vectorize(c(1))); d = eval(vectorize(d(1))); %creat again a 2x2xm matrix with all the ABCD parameters and convert back %to S parameters. for i=1:n abcd(1,1,i)=a(1,i); abcd(1,2,i)=b(1,i); abcd(2,1,i)=c(1,i); abcd(2,2,i)=d(1,i); end; s_params = abcd2s(abcd,50); for i=1:n Single_connector_S_P(:,1)=F; Single_connector_S_P(i,2)=10.*log10(abs(s_params(1,1,i))); %Single_connector_S_P(i,3)=angle(s_params(1,1,i)); Single_connector_S_P(i,3)=10.*log10(abs(s_params(1,2,i))); %Single_connector_S_P(i,5)=angle(s_params(1,2,i)); Single_connector_S_P(i,4)=10.*log10(abs(s_params(2,1,i))); %Single_connector_S_P(i,7)=angle(s_params(2,1,i)); Single_connector_S_P(i,5)=10.*log10(abs(s_params(2,2,i))); %Single_connector_S_P(i,9)=angle(s_params(2,2,i)); end; figure plot(F,Single_connector_S_P(:,3)); title('S12');
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B. Matlab script of the transition impedance model
% Impedance Model of the Taper Transition ---- Rectangular WG model % %------------------Loizos Loizou--------------------------------- %------------------Texas A&M University-------------------------- %------------------October 2010--------------------------------- % %---------------------------------------------------------------- %This script reads the waveguide dimensions from an excel file, %calculates the cutoff frequency and the real part of the %characteristic impedance of the waveguide at 3GHz for both troughguide %and rectangular sides. close all; clear all; clc; data = xlsread('TransitionData_Chen2.xls'); no=120*pi; eo=8.854e-12; mo=pi*4e-7; c=3e8; h=data(:,4)./1000; a2=data(:,2)./1000; t=data(:,3)./1000; ext=data(:,8)./1000; b1=data(:,5); b2=data(:,6); a1=data(:,7)/1000; L=320; %f=2.5e9:0.46e8:4e9; f=3e9; %lamda=1000*c./f; x=0:10:L; x2=sort(x','descend'); fc1=1./(2.*a1'.*(eo*mo)^0.5); fc2 = 1./(2.*(2.*h+2.*ext+2*t).*(eo*mo)^0.5); Zo1=(no)./(sqrt(1-((fc1./f).^2))); Zo2=(no)./(sqrt(1-((fc2./f).^2))); Rrect= 0.58*(real(Zo1')); Rtrough = 0.255*real(Zo2); figure (1); plot(x2,Rrect,'red'); title('Resistance'); hold on plot(x2,Rtrough);
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VITA
Name: Loizos Loizou
Address: 214 Zachry Engineering Center, TAMU 3128, College Station, Texas 77843-3128
Email Address: [email protected] [email protected] Education: M.S., Electrical Engineering, Texas A&M University, 2010 Diploma in Electrical and Computer Engineering, National Technical University of Athens, 2008