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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2

2

cos sin

cos sin

sin cos

csin cos

cos sin

j zZ mn

j zx mn

c

j zy mn

c

j zx mn

c

j zy mn

c

m x n yH A e

a bj n m x n y

E A ek b a b

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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[26] L. Loizou, F. J. Drummond, G. H. Huff, "Electromagnetic and aerodynamic

performance of a rectangular-to-trough waveguide transition and troughguide

antenna with cantilever perturbations and high Reynolds number air flow," in

Proc. 2010 IEEE/URSI Int. Symp. Antennas and Propagation, Toronto, Canada,

July, ses.308.8, 2010.

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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: lloizos@gmail.com loizos@neo.tamu.edu Education: M.S., Electrical Engineering, Texas A&M University, 2010 Diploma in Electrical and Computer Engineering, National Technical University of Athens, 2008