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Microwave/millimeter-wave beam steering/shaping phased antenna arrays and planar imaging antenna arrays for plasma diagnostic application

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Microwave/Millimeter-Wave Beam Steering/Shaping
Phased Antenna Arrays and Planar Imaging Antenna
Arrays for Plasma Diagnostic Application
By
Lu Yang
B.S. (University of Science and Technology of China) 2003
M.S. (University of California, Davis) 2006
DISSERTATION
Submitted in partial satisfaction of the requirements for the degree of
DOCTOR OF PHILOSOPHY
In
Electrical and Computer Engineering
in the
OFFICE OF GRADUATE STUDIES
of the
UNIVERSITY OF CALIFORNIA
DAVIS
Approved:
P. H eritage^
Neville C. Luhmann, Jr. (Committee Chair)
Committee in Charge
2007
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To my family
I so love you all.
ii
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Acknowledgements
First of all, I would like to express my sincere appreciation to my advisor, Prof. Neville
C. Luhmann, Jr., who provided me with the opportunity and always supported me to do
this research. From him, I received motivation and encouragement during all my studies.
Without his invaluable support, guidance, and encouragement, this work would not have
been possible.
I would like to thank my parents in China, for their love, support, understanding, and
their faith in me. Without them, I could have never been able to go through the long path
of the PhD study in a foreign country, and I could have never been able to reach the point
that I have got today.
In addition, I would like to thank all my PhD committee members, Professor Jonathan
Heritage and Professor Anh-Vu Pham, for contributing their valuable time and advice in
this dissertation.
Furthermore, I would also like to thank Dr. Calvin Domier for his valuable comments
and assistance during this work; Mr. Mike, who fabricated the fixtures for antenna
measurement and contributed significant amount of time for teaching me how to use
mechanical machines. Special thanks go to Naoki Ito at Kyushu University who has
given me a lot of help with circuit fabrication and made the PAA system possible.
Former graduate students, Dr. Chiachan Chang and Dr. Zhenggang Xia had
participated in this PAA and substrate lens antenna work during their PhD studies. Without
their contribution, this work would not exist.
I would also like to acknowledge my sincere pleasure and gratitude to all the
iii
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members of UC Davis Microwave/Millimeter Wave lab for the valuable discussions and
kind assistance.
Finally, I would like to thank my husband, Long Pham, not only for his valuable
assistance and help from work, but also for his love, support, and encouragement in my
everyday life.
iv
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Microwave/Millimeter-Wave Beam Steering/Shaping
Phased Antenna Arrays and Planar Imaging Antenna
Arrays for Plasma Diagnostic Application
Abstract
by
Lu Yang
Doctor of Philosophy in Electrical and Computer Engineering
University of California, Davis; 2007
Professor Neville C. Luhmann, Jr., Chair
18 to 40 GHz 1 x 16-element beam shaping and 1 x 8-element beam steering phased
antenna arrays (PAAs) are realized on a single low cost PCB substrate. The system
consists of a wideband power divider with amplitude taper for sidelobe suppression,
wideband microstrip-to-slotline transition, a low-cost true time piezoelectric transducer
(PET)-controlled phase shifter, and wideband Fermi antennas with corrugations along the
sides. Coplanar stripline (CPS) is used under a PET-controlled phase shifter, which can
generate 50% more phase shift compared to the perturbation on microstrip line. The
systems are fabricated using Electro-Fine-Forming (EF2) micro-fabrication technology,
which is uniquely developed by Kyushu Hitachi Maxell. Measured VSWR is less than 2
within the designed frequency range for both the beam steering and beam shaping PAAs.
The beam shaping PAA has a 12° 3-dB and 18° 10-dB beamwidth broadening range. The
sidelobe levels are -27, -23 and -20 dB at 20, 30 and 40 GHz, respectively, without
perturbation. The sidelobe levels are -20, -16, and -15 dB at 20, 30 and 40 GHz with
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maximum perturbation. The beam steering PAA has 35° (-16° to +19°), 36° (-17° to +19°)
and 31° (-14° to +17°) beam scanning range measured at 20, 30 and 40 GHz.
An investigation of the receiving properties of a 1-D 13-element and a 2-D 8 x
4-element dual dipole antenna arrays on an elliptical MACOR lens from Q- to V-band is
presented next. The far-field radiation patterns are calculated using ray tracing and
integration methods and measured in an anechoic chamber. Theoretical and measured
results agree well for both the patterns and steering angles. Sensitivity and angular field
of views are measured from 38 to 75 GHz and theoretically calculated for comparison.
Different lens materials are compared at last.
The analytical and experimental results provide guidance toward the development
of new arrays for future use in MIR systems with significantly enhanced performance.
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Contents
Acknowledgment............................................................................................................... iii
Abstract............................................................................................................................... v
Chapter I Introduction
1.1
Motivation........................................................................................................... 1
1.1.1 Phased Array Antennas Review on Fundamentals............................. 2
1.1.2 The Need for True Time Delay Technologies.................................... 10
1.1.3 Substrate Lens Antenna Review on Fundamentals............................17
1.1.4 Introduction to Plasma Fusion Research............................................ 20
1.2 Dissertation Overview......................................................................................23
Chapter II
Introduction to Plasma Microwave Imaging Reflectometry
2.1
Basic Principle of Plasma Reflectometry.................................................... 32
2.2
The Need Imaging Technology..................................................................... 36
2.3
Microwave Imaging Reflectometry (MIR) Technology............................ 40
2.4
Theoretical Calculation of Plasma Cutoff Surfaces for TEXTOR and NSTX
Plasma Devices..................................................................................44
2.5
The Requirement for the Design of the Phased Antenna Array................ 51
2.5.1 Element Number Estimation................................................................ 51
2.5.2 Power Requirements............................................................................. 51
C h apter III B eam Steerin g/S h ap in g P hased A n ten n a A rray D esign B ased on
Piezoelectric Transducer Controlled Delay Line Technology
3.1
Phased Antenna Array Theory....................................................................... 57
3.2
Beam Shaping Theory................................................................................
3.3
Design of 16-way Unequal Power Divider..................................................68
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60
3.3.1 Design Principles.................................................................................69
3.3.2 Simulation Results.............................................................................. 70
3.4
Design of Wideband Microstrip to Slotline Baiun.................................... 72
3.5
Design of Fermi Tapered Slot Antenna.......................................................74
3.6
Design of Piezoelectric Transducer Controlled Delay Line on C PS
Chapter IV
80
Assembly and Testing of PAA System
4.1
Measurement of Wideband Microstrip Line to Slotline Baiun..................89
4.2
Antenna Array Measurement........................................................................92
4.2.1
UC-Davis Anechoic Chamber.........................................................92
4.2.2
Lab View Code Development for Instrument Control..................93
4.2.3
Beam Steering Demonstration........................................................94
4.3.4
Beam Shaping Demonstration......................................................100
Chapter V
Q- to V-Band 1-D/2-D Elliptical Lens Antenna Arrays
5.1
General Analysis and Design...................................................................... 107
5.2
MACOR Elliptical Lens Antenna Array Measurement...........................112
5.2.1 Sensitivity M easurement.................................................................. 112
5.2.2 Single Beam Measurement...............................................................116
5.2.3 Multiple-Beam Measurement.......................................................... 119
5.2.4 Angular Field of View M easurem ent............................................ 123
Chapter VI
Conclusions and Future Work
6.1
Conclusions..........................................
126
6.2
Future W ork................................................................. ............................... 128
6.2.1 Other True Time Delay Technologies........................................... 128
6.2.1.1 Distributed RF MEMS True TimeDelay Line....................129
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6.2.1.2 Liquid Crystal Beam Former............................................... 131
6.2.2 Multi-Frequency Illumination Source............................................. 133
6.2.3 Selection of Lens Material for Substrate Lens Antenna...............134
Appendix
A.
Villeneuve n Array Distribution Calculation............................................140
B.
Calculation of Far-Field Radiation Patterns of Dual-Dipole Antenna Array
on Elliptical Lens in MATLAB................................................................... 144
C.
Dynamic Range and Standard Gain Horn Measurements...........................150
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List of Figures
Fig. 1.1
Schematic representation of a phased antenna array
Fig. 1.2
Schematic of a beam shaping phased antenna array based on curved time
delay arrangement
Fig. 1.3
Schematics of lei scanning in Doppler Reflectomery using (a) single horn
and (b) multiple horns
Fig. 1.4
Schematics of (a) transmitting and (b) receiving systems in Imaging Doppler
Reflectometry by using beam steering PAA
Fig. 1.5
Switched type digital delay line
Fig. 1.6
Schematic of a 200 psec digital-type MEMS switched delay line
Fig. 1.7
AO-FDPC optical delay lines
Fig. 1.8
Liquid Crystal delay lines
Fig. 1.9
Nonlinear delay lines schematic
Fig. 1.10
Equivalent lumped circuit for varactor loaded transmission line
Fig. 1.11
(a) 5 GHz PAA using hybrid (b) 6-18 GHz PAA using monolithic NDLs
Fig. 1.12
Piezoelectric transducer controlled delay line
Fig. 1.13
Schematic of the substrate lens antenna
Fig. 1.14
Schematic representation of a tokamak, showing the principle of operation
Fig. 1.15
Schematic of MIR systems on NSTX plasma machine for detecting plasma
electron density profile
Fig. 2.1
ne
fluctuations
The principle of plasma reflectometry can be explained by the analogy with
a tapered waveguide
Fig. 2.2
Principle of plasma reflectometry (based on conventional systems)
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Fig. 2.3
Schematic of wave reflection in the Ionospheric plasma
Fig. 2.4
Comparison of (a) 1-D (with phase modulation) (b) 2-D reflectometry (with
both phase and amplitude modulations)
Fig. 2.5
Schematic representation of beam trajectories in the vicinity of the cutoff
layer
Fig. 2.6
Schematic representation of imaging technology to restore the phase front
from the cutoff layer
Fig. 2.7
Two separate paths for the MIR system
Fig. 2.8
Schematic representation of MIR system
Fig. 2.9
Fig. 2.10
Schematic of the test setup, showing the MIR and 1-D configuration
Photographs of the corrugated bicycle wheel used to model the plasma
surface fluctuations
Fig. 2.11
Test results from reflected target (a) 1-D system at 10 cm (b) 1-D system at
30 cm (c) MIR system at focus point =235 cm. The reflector has
corrugations of ke = 1.25 cm '1 and depth =1.7 mm
Fig 2.12
Two target plasma machines (a) National Spherical Torus Experiment
(NSTX) and (b) TEXTOR
Fig. 2.13
X-mode plasma cutoff surfaces of TEXTOR with (a) fixed magnetic field
and (b) fixed central electron density
Fig. 2.14
Combined ECEI/MIR Imaging System under development for TEXTOR
Fig 2.15
Elongation and tragularity effects to a normal circle
Fig. 2.16
NSTX plasma cutoff surfaces at two physical conditions
Fig. 2.17
PAA beam shaping concept
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Fig. 2.18
Schematic of MIR systems on the NSTX plasma device for detecting plasma
electron density profile ne fluctuations
Fig. 2.19
Schematic of transmitting system power
Fig. 3.1
Schematic of linear phased antenna array geometry
Fig. 3.2
Array factor patterns with and without amplitude taper
Fig. 3.3
Schematic of two subarrays for beam broadening
Fig. 3.4
Array factor patterns before and after beam bifurcation using the sub-array
concept
Fig. 3.5
Schematic of a beam shaping phased antenna array based on a curved time
delay arrangement
Fig. 3.6
Linear Arrays with quadratic phase excitation can be represented by
physically bent arc arrays
Fig. 3.7
Array factor patterns adding quadratic wavefronts (a) with and (b) without
amplitude taper
Fig. 3.8
(a) Wilkinson (b) rat race and (c) T-junction structures
Fig. 3.9
2-way unequal T-junction power divider structure
Fig. 3.10
Drawing of a 2-way unequal power divider in HFSS
Fig. 3.11
Layout of the 16-way unequal power divider
Fig. 3.12
Simulated insertion loss of 16-way unequal power divider in HFSS
Fig. 3.13
Back-back (a) balanced and (b) unbalanced microstrip to slotline transition
Fig. 3.14
Schematic and port field plot of the microstrip to slotline transition
Fig. 3.15
Simulated S-parameters of back-to-back the balanced and unbalanced
microstrip to slotline transition
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Fig. 3.16
TSA with different tapered profiles: (a) exponential, (b) tangential, (c)
parabolic, (d) linear, (e) linear-constant, (f) exponential-constant, (g)
step-constant, (h) broken-linear (the red part is the metal)
Fig. 3.17
Antipodal Vivaldi antenna structure
Fig. 3.18
Geometry of microstrip-fed Fermi tapered slot antenna
Fig. 3.19
Comparison of the E-plane far field radiation patterns (a) without
corrugation and (b) with corrugation
Fig. 3.20
Schematics of (a) Fermi (b) linear and (c) Vivaldi tapered slot antennas
Fig. 3.21
Comparison of (a) E- and (b) H-plane radiation patterns of three types of
TSAs
Fig. 3.22
Schematic of PET controlled phase shifter
Fig. 3.23
Schematic of the multilayer structure of the PET controlled phase shifter
Fig. 3.24
Different types of transmission lines (a) Microstrip Line (b) Coplanar
Waveguide (CPW) Line (c) Coplanar Waveguide with bottom ground plane
(CPWG) (d) Coplanar Stripline (CPS) (e) Slot Line
Fig. 3.25
Comparison of the differential phase shift generated by CPS (gap width g =
0.1 mm, line width = 0.2 mm), CPW (gap width g = 0.05 mm, line width =
0.25 mm) and microstrip line (line width = 0.238 mm).
Fig. 4.1
Photographs of back-to-back (a) balanced and (b) unbalanced microstrip to
slotline transition
Fig. 4.2
Measured S-parameters of back-to-back (a) balanced and (b) unbalanced
microstrip to slotline balun
Fig. 4.3
Photographs of (a) UC Davis anechoic chamber overview, (b) inside antenna
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mounting and (c) transmitting horn mounting
Fig. 4.4
Lab View code for antenna measurements
Fig. 4.5
Schematic of measurement setup
Fig. 4.6
(a) Schematic and (b) photograph of beam steering demonstration
Fig. 4.7
Measured return loss of beam steering PAA system
Fig. 4.8
Measured E-plane far field radiation patterns for 8-element PAA at (a)
20-, (b) 30- and (c) 40 GHz in beam steering demonstration
Fig.4.9
Measured H-plane far field radiation patterns at 30 GHz for 8-element PAA
Fig. 4.10
Measured E-plane far field radiation patterns at 20-, 30- and 40 GHz
Fig. 4.11
Measured return loss of beam shaping PAA system
Fig. 4.12
Measured E-plane far field radiation patterns at (a) 20-, (b) 30- and (c) 40
GHz in beam shaping demonstration
Fig. 4.13
Measured H-plane far field radiation patterns at 30 GHz for 16-element
PAA
Fig. 5.1
Schematic of an MIR receiving system
Fig. 5.2
The elliptical lens and the ray-tracing/field-integration technique
Fig. 5.3
Calculated 4-element antenna array patterns in (a) E-plane and (b) H-plane
Fig. 5.4
Experimental setup of substrate lens antenna measurement
Fig. 5.5
Sensitivity of antennas of different sizes
Fig. 5.6
(a) Calculated and (b) measured sensitivity (normalized)
Fig. 5.7
Calculated and measured (a) E- and (b) H-plane radiation patterns at 60
GHz
Fig. 5.8
Measured (a) Q band E-plane, (b) Q-band H-plane (c) V-band E-plane and
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(d) V-band H-plane far field radiation patterns
Fig. 5.9
Photographs of (a) 1-D 13-element dual-dipole array, (b) array mounted on
the lens and (c) elliptical MACOR lens mounted on a 2-D rotation stage
Fig. 5.10
Measured E-plane radiation patterns for the 1-D array
Fig. 5.11
Measured and calculated steering angles
Fig. 5.12
Photo of 8 x 4-element 2-D dual dipole array
Fig. 5.13
Measured (a) E- and (b) H-plane radiation patterns for 2-D array at 60 GHz
Fig. 5.14
Measured and calculated normalized peak responsivity for MACOR
elliptical lens measured at 60 GHz
Fig. 6.1
Extended tuning range MEMS varactor structure
Fig. 6.2
Photographs of the extended tuning range MEMS varactor structure
(courtesy of Y. Liang)
Fig. 6.3
3-D Drawing of 7-section MEMS delay line in HFSS (courtesy of Y. Liang)
Fig. 6.4
Structure of millimeter wave beam former using Liquid Crystal
Fig. 6.5
Measured radiation pattern at different frequencies in V-band
Fig. 6.6
Generation of multi-frequency illumination source for NSTX MIR system;
the modules are fabricated by Kyungpook National University
Fig. A. 1
VILLENEUVE n amplitude distribution for N = 8 , SLR = 35 dB and n = 4
Fig. A.2
VILLENEUVE fl amplitude distribution for A = 16 , SLR = 35 dB and
n=4
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List of Tables
TABLE 2.1 Power Losses and Output Powers of the PAA System at Various Frequencies
Assuming 100 mW Input Power
TABLE 2.2 Average Power Handling Capabilities of a 50-Q Microstrip Line
TABLE 3.1 Excitation Coefficient of 8-Element Array with n = 6 and SLR=30 dB
TABLE 3.2 Normalized Output Power Ratios
TABLE 3.3 Design Parameters for Fermi TSA
TABLE 5.1 Measured and Calculated Full 3-dB Beamwidth for E- and H-planes
TABLE 6.1 Comparisons of Si, Alumina, Quartz and MACOR Lens
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Chapter I
Introduction
1.1 Motivation
In this dissertation, an investigation into a number of innovative technologies was
performed in order to develop novel components for potential utilization in various high
frequency imaging and radar applications. In recent years, microwave and millimeter
wave radar and imaging systems have become increasingly important for numerous
commercial, environmental, medical, diagnostic and military applications [1-7]. The
transmitter and/or receiver technology is the heart of most of these systems, each of
which can be employed for a myriad of different functions. This dissertation research is
largely aimed at the development of such components.
The demand for phased array antennas (PAAs) has increased significantly during the
past decades. PAAs have the potential for a wide variety of applications ranging from
surveillance, tracking astronomy, and geodesy to wireless and satellite communications
[1-6]. Novel approaches to develop compact, high operating frequency, wide bandwidth,
low sidelobes, appropriate beamwidth and cost effective PAAs are needed in order to
implement these radar systems. In contrast to dish or slotted array antennas, which use
physical shape and direction to form and steer the beam, phased array antennas utilize the
interference between multiple radiating elements to achieve beam forming and beam
steering. In radar and communication systems, they are typically employed to
transmit/receive a signal or search/trace a target [1]. The potential for increased target
1
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handling capacity available in Track While Scan radars is limited by the requirement to
position the radar antenna mechanically [2], Existing mechanical scanning methods are
inherently slow and require large amounts of power in order to respond sufficiently
rapidly to deal with large numbers of high speed maneuvering targets. With mechanically
scanned systems, antenna inertia and inflexibility prevent employment of optimum radar
beam positioning patterns that can reduce reaction times and increase target capacity.
With electronic scanning, the radar beams are positioned almost instantaneously and
completely without the inertia, time lags, and vibration of mechanical systems [3].
High gain, high efficiency, multi-channel imaging arrays are required for active
radiometric imaging applications such as Microwave Imaging Reflectometry (MIR) [1618]. Planar imaging arrays can be employed to vastly improve system scanning and
detection capabilities, as well as provide low cost alternative to expensive arrays of all­
waveguide components. Clearly, there exists the need to develop and improve simple,
cost effective, and efficient imaging array systems.
1.1.1
Phased Antenna Array Review on Fundamentals
The fundamental principles underlying the concept of electronic beam steering are
derived from electromagnetic radiation theory employing constructive and destructive
interference. These principles can be stated as follows: The electromagnetic energy
received at a point in space from two or more closely spaced radiating elements is a
maximum when the energy from each radiating element arrives at the point in phase.
Controlling the phase through the many segments of the antenna system allows the beam
to be rapidly directed in different directions. Figure 1.1 shows a 4-element linear array of
2
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antennas with constant phase difference between neighboring phase shifters, where &0 is
the scan angle, vv, to w4 are amplitude weights, and d is the spacing between adjacent
antenna elements.
Antenna
Elements
Phase
Shifter
F E E D NETW ORK
Fig 1.1 Schematic representation of a phased antenna array
The scan angle 0o depends on the operating frequency, spacing between antenna
elements, and the phase offset between signals in the individual elements. The far-field
pattern of a phased antenna array is controlled by the relative phase and the amplitude
distribution of the microwave signals emitted by regularly spaced radiating elements [R.J.
Mailloux, 1993]. Since antenna characteristics are reciprocal, the phased antenna array
can also be used as a receiving system, as well as a transmitter. For a transmitter array, it
requires power amplifiers and upconverters combined into the system. For a receiver
array, additional components, such as low noise amplifiers, and downconverters or
sampling circuits, are required. In addition, low loss antenna system is crucial in order to
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provide required sensitivity. The operational frequency bandwidth of the PAA is
ultimately limited by the bandwidth of these elements.
Depending upon the particular application, the design of a PAA must meet a variety
of requirements, including the type of antenna, driving power and power-handling
capability, reciprocal or nonreciprocal operation, operating frequency and bandwidth,
sidelobe level, beamwidth, multi-beam capability and switching time, beam shaping
capability, polarization, physical size and weight, etc.
For mobile and personal wireless communications, the physical size and weight of
PAAs should be as small as possible. In contrast, in radio astronomy and space research,
a huge aperture is required to give the maximum coverage of the sky observation. For
instance, the world’s largest steerable telescope (Effelsberg), which is located in West
Germany, has 100-meter diameter and is nearly 40 stories high [4].
To overcome the huge loss encountered during the signal transmission, high power
gain is required for satellite communication applications. At the earth station, the
microwave signal is typically amplified by a klystron to the 5-10 kW level before it is
introduced into the antenna for the uplink [5]. Typically, a high gain parabolic dish
reflector is used as the station antenna based on its high power handling capability.
In airborne radar, low sidelobe levels become extremely important in order to cope
with ground clutter and noise jamming [1]. This feature is also desirable to reduce the
spacing in order to accommodate more satellites in orbit.
In principle, the antennas are reciprocal. However, in the transmission application,
high gain and high efficiency are most important while a large signal-to-noise ratio (SNR)
is more desirable in the reception application. The choice of antenna type is also
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dependent upon its purpose. Dipoles and helices are frequently used at VHF and UHF for
telemetry and tracking while parabolic dishes fed by horns are often installed in the
satellite [7].
Although scanning capability is the most common function, a phased antenna array
can also provide beam-shaping capability by appropriate arrangement of the feed signals.
This topic has been investigated by many researchers [7-11]. Recently, the so-called
FLAPS (Flat Parabolic Surface) reflector [11], which consists of an array of dipole
scatters and is spatially fed using a feed assembly as in a conventional reflector system,
has been employed to realize beam shaping and beam scanning functions by adjusting the
length of the dipoles so that the phase shift between the incident and reflected wave can
be controlled [10]. In this Ph.D work, 18- to 40 GHz beam steering/shaping PAAs based
on true-time delay (TTD) technology have been built for a plasma radar reflectometry
application [16-20], The use of TTD devices can overcome the frequency bandwidth
limitation suffered by many systems which rely upon frequency dependant phase shifting
elements. The system consists of a wideband power divider with amplitude taper for
sidelobe suppression, wideband microstrip-to-slotline transition, a low-cost true time
piezoelectric transducer (PET)-controlled phase shifter, and wideband Fermi antennas
with
corrugations
along
the
sides
[21-26].
A so-called
“Microwave
Imaging
Reflectometry” (MIR) system has been developed by the UC Davis plasma diagnostic
research group over the past several years for plasma fusion diagnostic studies [16-20].
Based on this particular application, the design of this beam shaping phased antenna array
also must meet a number of strict system requirements including the operation power
level, the focal position movement, etc., which posed some significant challenges in this
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work. A detailed discussion will be presented later in Chapt. III.
The study of beam shaping approaches was begun during World War II, a period
during which radar systems were rapidly developed. In many applications, a particular
beam shape is sometimes required. To generate a desired beam shape, the radiation
patterns can be synthesized by controlling the relative excitation of each array element,
including the amplitude distribution, phase distribution, and array spacing distribution. In
many cases, the excitation is configured with a tapered distribution. The maximum is
located at the center of the aperture while the field strength decreases toward the edges.
Usually, significant amplitude tapering is used to lower the sidelobe level. Phase taper
synthesis, on the other hand, broadens a transmitting beam [15].
The major objectives of beam shaping are to minimize pattern ripples, to reduce
sidelobe levels, change null positions, or control output power levels, etc. Recently, PAAs
with variable beamwidth have been receiving considerable attention for telemetry and
communication applications [7-11]. A radar system with variable beamwidth can produce
a wide beam for the acquisition of targets and a narrow beam for subsequent highprecision tracking [7-8]. Additionally, a broadcast satellite antenna with variable
beamwidth can achieve efficient coverage of irregularly shaped geographical service
areas based on the environment or a traffic condition, which is an important feature for
communication systems [7-8], To vary the antenna beamwidth, there are many methods
which may be employed. In this dissertation, phase-only adjustment is used to vary the
beamwidth. In [7], a “sub-array” concept was introduced to broaden the beam. However,
beam bifurcation occurs when the scan angles of the sub-arrays extend beyond some
value. The useful range for an application, which is just before beam bifurcation, is very
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limited. Adding a quadratic phase error on the array aperture moves the array’s phase
center and changes its focusing distance [7] (see Fig. 1.2). However, for a given size of
an array aperture, there is a limit to the movement of the phase center. Beyond a certain
value of phase taper across the array aperture, beam bifurcation on the plane of the linear
array occurs [7]. In addition, the sidelobe level of an array with equal power feeding
increases rapidly as the value of phase taper increases. In order to increase the useful
range and control the sidelobe level, a so-called Taylor N-bar [6] amplitude taper is
introduced across the array aperture in this design. Detailed discussion will be presented
later in Chapt. III.
N
Variation of the F ocu sin g
B eam Shaping PAA
D elay Tim e
Fig. 1.2 Schematic of a beam shaping phased antenna array based on curved time delay
arrangement
The beam steering/shaping PAAs also have great potential for use in several other
plasma imaging systems including imaging Doppler Reflectometry and Synthetic
Imaging systems [27-28]. Doppler Reflectometry is characterized by a finite tilt angle of
the probing microwave beam with respect to the normal onto the cutoff surface [27-28],
The principle of Dopper Reflectometry can be explained using the model of a reflection
grating with small sinusoidal corrugation characterized by a wave number
k-L
= 2tt/A_l
moving in the vacuum. For a diffraction pattern of order -1 to return to the monostatic
7
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antenna, the Bragg condition requires
kL = 2 k o s\n{0mi)
(1.1)
where ko is the wave vector of the microwave. By a variation of 0tiit, the k± -spectrum of
the density perturbation can be scanned [27]. The spectrum in k i - space selected by 0tjit
is transformed into a spectrum in frequency space. The frequency shift can alternatively
be described as the Doppler shift of a wave reflected from the moving target. This
frequency shift can be then detected by standard heterodyne detection [28], In order to
obtain a broad kx range, 0tiit needs to be varied. There are two conventional approaches to
vary
0tiit.
The first one uses a single transmitting horn antenna and by changing the
location of horn antenna,
0 tiit
can be changed (Fig. 1.3 (a)). However, only one tilt angle
can be measured at a given time. The second approach is to use multiple horn antennas at
different locations to collect the data from different tilt angles (Fig. 1.3(b)). However,
multiple horns occupy considerable space and multiple detector systems are needed in the
receiving system.
C ut off
8
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Cut off
Fig. 1.3 Schematics of k± scanning in Doppler Reflectomery using (a) single horn and (b)
multiple horns
We propose an Imaging Doppler Reflectometry technique in which a collimated
probe beam is incident on the plasma with an electronically-controlled tilt angle 0 (Fig.
1.4(a)). In the receiving system, scattered radiation from the plasma cutoff layer is
imaged onto a 2-D detector array, with each array element corresponding to a distinct
poloidal and toroidal scattering angle (Fig. 1.4(b)). Using this approach, simultaneous
multiple frequency illumination and detection allows a detailed 3-D mapping of the
localized density gratings to be acquired.
Launching
0 .8 -
Imaging lens
cutoff
0.4
“
0.0 es2/\g = s*
-0.4
window
Beam steering PAA
- 0 .8 -
-t.2
9
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1.2
Receiving
0.8 J
Imaging fens
rr> = o y
0.4
“
IM
(fc)
JA
Detector Array
0.0
- 0 .4 - 0 .8 -
JF and Vide
, Electronic?
i r i r - p i i l l ' j 11 i i i | i 'i 'i i | m
i [ i
| i I i i [ I I I r
Fig. 1.4 Schematics of (a) transmitting and (b) receiving systems in Imaging Doppler
Reflectometry by using beam steering PAA
1.1.2 The Need for True Time Delay Technologies
The bandwidth of a phased antenna array is affected by many factors, including
change of element input impedance with frequency, change of array spacing in
wavelengths that may allow grating lobes, change in element beamwidth, etc. When an
array is scanned with fixed values of phase shift, provided by phase shifters, there is also
a bandwidth limitation as the position of the main beam will change with frequency,
which is called beam squint [6]. This can be seen from Eqn. 1.2, where / is the operating
frequency, d is the antenna element spacing, n is the element number, and 0{)is the scan
angle. It is obvious that changing the frequency results in a change of the scan angle for
fixed element spacing. In contrast, when the array is scanned with true time delay, the
beam position is independent of frequency to first order (see Eqn. 1.3).
n -d
•sin(0o)
c
( 1.2 )
I(D=W,
(1.3)
10
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In recent years, a variety of approaches have been reported to realize TTD. Generally,
the available technologies fall into two categories: digital delay lines and analog delay
lines.
The digital delay lines usually utilize switching elements. Different lengths of
transmission lines can be switched into the signal paths to produce different delays. A 3bit switched type digital delay line is shown in Figure 1.5. The switched type delay line
has excellent performance over a wide bandwidth; however, the size of this device is a
major drawback [30]. Typically, this shortcoming is partially ameliorated by using folded
lines with meander or fractal shapes such that the effective length is reduced; however,
the performance is deteriorated [30]. The bandwidth is not limited by the dispersion in the
line, but rather by the quality of the switching device. Phase quantization lobes is a
common drawback associated with digital delay lines [6].
Microelectromechanical systems (MEMS) switches become good candidates to
generate the required time delay for microwave and millimeter applications based on
their numerous advantages including low cost fabrication, extremely high ON/OFF
contrast ratios, low insertion loss, high isolation, high linearity, and relatively high power
handling capability. Switches operating at frequencies up to 40 GHz with very low
insertion loss and high isolation have been successfully demonstrated [40].
Delay Section
RF Switch
Fig. 1.5 Switched type digital delay line
11
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The MEMS switch can be configured to generate phase shift by switching between
two different-length signal paths (digital-type) [41-42], or can be used as a distributed
capacitive switch to change the effective capacitance of the transmission line (analogtype) [40]. Figure 1.6 shows the digital-type MEMS switched delay line. The phase shift
is determined by the difference between the two path lengths, which is selectively
controlled by DC bias. It has been reported that multi-bridges (typically 2-8 bridges [40])
are used to create a single switch for good RF signal block.
Bias Pad
MEMS Switch
High Impedance
Bias Line
Bias Pad
RF
Output
RF
Input
96 ps Delay
48 p s Delay
24 ps Delay
12 p s Delay
6 ps Delay
3 ps Delay
Fig. 1.6 Schematic of a 200 psec digital-type MEMS switched delay line
The acousto-optic frequency-dependent phase compensated (AO-FDPC) heterodyne
technique has also been utilized to generate microwave delay lines [31-33]. The system
schematic is shown in Figure 1.7. In this approach, the signal from the laser source is
separated into two paths using a beam splitter. Subsequently, one of the signals is then
modulated by the m icrowave signal. The AO cell is used as a single sideband (SSB )
frequency modulator because at low RF power levels, the AO output light intensity is
linearly proportional to the RF amplitude. In addition, the AO cell will spatially separate
the modulated signal into composite frequencies, effectively performing a spatial Fourier
12
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Transform [34]. The lens after the AO cell is used to stop the angular spread from the AO
cell and to image the frequency components onto the rotating mirror. The mirror is
capable of both translation and rotation. Each frequency component experiences a
different delay due to the different optical path traversed. The path difference can be
varied by rotation and translation of the mirror. Since the heterodyne process preserves
phases, an RF phase shift equal to the optical phase shift results. This RF phase shift
varies linearly with frequency and in effect provides true time delay. This technique can
realize analog time delay; however, since the AO cell works as a frequency modulator
only at low RF power, the power rating of this system is low. Furthermore, the system is
complicated and expensive to be realized.
Laser D etector
LD
Signal O ut
Bragg Cell
Laser
^
j)
Beam Splitter
R otating M irror
Signal Input
Fig. 1.7 AO-FDPC optical delay lines [16]
The aforementioned types both use “space” to produce a change in the “time” while
the “velocity” is kept constant. In contrast, the distributed type delay lines take advantage
of the possibility of controlling the wave velocity, while keeping the length of the
propagation path constant. The liquid crystal phase shifter is one of the distributed types
of delay lines, and has drawn considerable attention recently [35-39]. The schematic of
13
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this approach is shown in Figure 1.8. In liquid crystal, the dielectric constant is
anisotropic, which means it is different in the direction along the director (molecule) from
the one in the direction perpendicular to it. This occurs when the charge distribution
along the molecule responds differently to the parallel component of the local electric
field than the distribution perpendicular to the length does to the perpendicular
component, thereby yielding a difference in dielectric constants. When an electric field is
applied, the molecule tends to rotate and align parallel or perpendicular to the electric
field which depends on whether the LC has positive or negative anisotropy. Consequently,
the dielectric constant can be changed and therefore the propagation constant can be
changed. The LC phase shifter is an easy, less expensive true time delay technology;
however, the modulation speed is low, which is on the order of several Hz.
s i " It can steer millimeterw ave beam
Electrode
(10 u m thick)
LL
.
w ave™ 1" '
(horizontally
polarized)
ifi Minr vf/
2 4 0 liquid crystal
and elec tro d e layers
(ap p rox. 2 5 m m )
Control
^ voltage
source
^
*
Fig. 1.8 Liquid Crystal delay lines [23]
Another distributed type of delay line is the variable capacitance delay line, which we
refer to as the nonlinear delay line. The nonlinear delay line (NDL) consists of a specially
designed coplanar waveguide (CPW) nonlinear transmission line (NLTL) loaded with
reverse biased Schottky varactor diodes together with a DC control circuit [19]. The
14
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schematic is shown Figure 1.9. A two-conductor transmission line can be described by
lumped parameters that are distributed throughout its length. By utilizing a first order
approximation,
this
high
impedance
interconnecting
transmission
line
can
be
approximated by L-C sections, as shown in Figure 1.10. The group velocity of this LC
network is given by:
y
= —= = = = = = = = =
-\] Lline
(C line +
^ Diode
(1.4)
M)
and the ladder-network cutoff frequency (Bragg frequency) is given as [M.J. Rodwell,
1991, 1994]:
(1.5)
When the operating frequency fo is far below the Bragg frequency (jo < 20% fBmgg)
[W.M. Zhang, 1996(b)], the varactor behaves like a linear element and the group velocity
of this nonlinear transmission line is essentially frequency independent, and only
dependent upon DC bias voltage. Therefore, the delay time generated by each section of
the NLTL is a function of interconnection transmission line length, varactor diode
capacitance and DC bias voltage. This method has been investigated in our group by
former students C. Liang and C. Chang and applied in the PAA systems [19-20]. The 5
GHz PAA system utilizing hybrid NDL and the 6-18 GHz PAA system utilizing
m onolithic N D L are shown in Figure 1.11 [20]. The main drawback o f this approach is
that the varactor must work in the small signal region in order to avoid nonlinear effects
such as pulse steepening (which occurs before breakdown); hence, its power handling
capability is low.
15
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Transmission line
Z.
r diode
""diode
■'diode
Fig. 1.9 Nonlinear delay lines schematic
....... §.r w
v - i ..
r
H ue
i
^line f
» ........... ....... _
1
"
Fdiod
L
_
_
«
—
.t
.1
L
Fig. 1.10 Equivalent lumped circuit for varactor loaded transmission line
W
.j« g a
■ 5 GHz
• 6 -1 8 G H z
* 22 sectio n s hybrid
• 80 sectio n s
monolithic NDL with
100 pg d ela y
CPWgroum
for :: delay
.2 -D 4 « 4 P & te
•1 -D 1 x 8 P M §
5 0 Q for
inr nti'u jtput
impedance
match
*±10° beam
steerin q
s
• ± 1 5 ° b e a m steerin g
!Mmii NDL
(a)
(b)
Fig. 1.11 (a) 5 GHz PAA using hybrid (b) 6-18 GHz PAA using monolithic NDLs [25-26]
The fourth type of the true time delay line, which is also the topic of this dissertation
work, is the piezoelectric transducer (PET) controlled delay line [21-22]. A schematic of
the concept is shown in Figure 1.12. A dielectric material used as a perturber is attached
16
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
with a piezoelectric bending element, which is placed above a microwave transmission
line (ex. Microstrip line). A voltage applied to the piezoelectric bender causes a vertical
deflection. Therefore, the air gap between the transmission line and perturber changes
when different DC bias levels are applied, which results in a change in the propagation
velocity on the transmission line [21-22]. This entire structure can be treated as a
multilayer transmission line for purposes of theoretical analysis. Since there is no solidstate device required in this delay line design, high power-handling capability can be
expected, which becomes the major benefit for the plasma radar reflectometric diagnostic
application described later.
DC B ia s
P iezoelectric translator
Dielectric Pertgrber
Microstrip Line
C hangeable Air Gap
S u b stra te
Fig. 1.12 Piezoelectric transducer controlled delay line
1.1.3
Substrate Lens Antenna Review on Fundamentals
Millimeter wave are becoming important in many scientific and military applications.
Both hybrid and monolithic integrated circuit receivers consisting of a planar antenna
integrated with a planar Schottky diode or an anti-parallel Schottky diode pairs have
many advantages over waveguide based receivers at millimeter-wave frequencies [43-53].
They are less expensive and more easily produced in large numbers for imaging
applications. Integrated antennas on thick dielectric substrates suffer from power loss into
substrate modes [49-50]. One way to avoid this problem is to integrate the antennas on a
17
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very thin substrate, typically less then 0.02Xd for dipoles and 0.04
for slot antennas.
However, the substrates become very thin and fragile at millimeter and submillimeterwave frequencies. An attractive method to eliminate the substrate modes is to place the
antenna on a dielectric lens (Fig. 1.13) [49-53]. The lens has the same dielectric constant
as the planar antenna substrate. The structure of the dielectric lens does not support
surface-waves. Antennas placed on dielectric side making the pattern unidirectional on
”3/9
high dielectric constant lens. The ratio of powers between the dielectric and air is er for
an elementary slot antenna and er for an elementary dipole antenna [51], where sr is the
relative dielectric constant of the lens. The dielectric lens is a very attractive solution
since it also provides mechanical rigidity and thermal stability.
The substrate dielectric lens shapes can be hemispherical, hyper-hemispherical or
ellipsoidal and researchers have placed various antennas on these lenses for receiver
applications [43-53]. An elliptical lens antenna is an ellipsoid cut off at a plane
perpendicular to its major axis at its second geometric focus, with a planar antenna
mounted on the flat surface. This results in a far-field pattern with a main beam that is
diffraction limited by the aperture of the elliptical lens. The elliptical lens is compatible
with a large f-number imaging system due to the potential of achieving very narrow beam
patterns. The elliptical lens couples well to a Gaussian-beam at its minimum waist, where
there is a planar equiphase front [51]. Most of the work reported thus far used highpermittivity low loss material hemispherical lenses, such as silicon and alumina lenses,
because higher dielectric constant yields a more exact geometrical approximation to an
elliptical lens and a wider multiple-beam coverage range [50-52] or low-permittivity low
loss plastic material elliptical lenses [53] because they are low cost and easily machinable
18
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with standard tools. In the present application, the dielectric constant of the lens material
needs to be chosen carefully. The lower the dielectric constant is, the longer the extension
length, which will increase the lens blockage and consequently decrease the multiplebeam coverage range resulting in a poor spatial resolution for plasma imaging
applications [16]. However, the local oscillator power received by the antenna from the
backside of the lens will decrease if the lens material has too high a dielectric constant
due to the fact that most of the power is radiated into the substrate lens side. In addition,
it is desirable that the lens material be low cost and relatively easy to be machined.
In this dissertation, the elliptical lens is made of a low cost machinable glass-ceramic
MACOR with dielectric constant around 5.62 [54-55]. The millimeter and sub-millimeter
wave dielectric parameters of this material have been investigated in [54]. The radiation
patterns of a 13-element 1-D dual dipole array and an 8 x 4 2-D array are calculated using
ray tracing and integration methods [15] and measured in an anechoic chamber.
Theoretical and measured results agree well for both the patterns and steering angles.
Sensitivity is measured from 38 GHz to 75 GHz for three different antenna sizes.
A ntenna S u b strate '
S u b strate L ens
A ntenna
Fig. 1.13 Schematic of the substrate lens antenna
19
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1.1.4 Introduction to Plasma Fusion Research
It is generally recognized that energy resources (ex. oil, coal, natural gas, etc.) are
limited in extent and are rapidly being depleted. Consequently, there has been intensive
international research activity aimed at the realization of a new energy source [25].
Although numerous reactions, including chemical, fission and fusion, can release energy,
fusion is generally recognized as one which can produce copious amounts of energy
minimal adverse effect on the environment. The fuel supply for fusion may be obtained
from sea water, and there are no carbon products and no greenhouse emissions and
relatively short-lived radioactive wastes.
Research in controlled nuclear fusion began in the 1950s and was initially classified
until the world community recognized both the complexity of the problem as well as its
importance to mankind. This plasma must be held together (confined) sufficiently long
that many fusion reactions occur. One of the approaches under active investigation for an
eventual energy source is to employ a magnetic field configuration to confine the plasma
(magnetic confinement). The most advanced of such magnetic fusion concepts is the socalled tokamak approach [55].
Figure 1.14 is a schematic of an early embodiment of the tokamak concept. The
donut-shaped plasma has a major radius R, and a minor radius a. The toroidal magnetic
field (B^) is generated by external coils, which are symmetrically distributed around the
torus, surrounding the vacuum vessel. Thus, from Ampere’s law, the toroidal magnetic
field strength has a 1/R dependence within the coils. The poloidal magnetic field (Be) is
generated by the plasma currents (I). The resultant total magnetic fields are helical, with
the field lines wrapping around the torus both toroidally and poloidally, forming nested
20
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magnetic surfaces within the vacuum vessel.
Toroidal Field Coils
Primary Windings
Plasm a
V
\
x\
Magnetic flux su rfaces forming
a se t of nested toroids
Magnetic field lines
^ and current lines lie
J in magnetic surfaces
Fig. 1.14 Schematic representation of a tokamak, showing the principle of operation
The dynamics of high temperature plasmas in toroidal devices is extremely complex.
Substantial progress towards this goal has been made over the past many decades, but
many challenges still remain and the technologies are not yet mature. To successfully
develop fusion energy in the future, scientists need to well understand the physical
reactions and theories through these plasma fusion devices [55-57].
The UC Davis Plasma Diagnostic Group has been a pioneer in this research area, both
demonstrating novel millimeter wave instruments on relevant magnetic fusion devices,
and obtaining important physics results with these diagnostics [16-18]. These provide
basic physics understanding and also contribute to the eventual realization of magnetic
fusion energy.
21
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Microwave reflectometry is a radar technique used to infer both the electron density
profile and associated density fluctuations by probing the density-dependent cutoff layer
in magnetized plasma [17-18]. In the presence of two-dimensional (2-D) radial and
poloidal density fluctuations, the reflected electromagnetic wave spectrum can be
distorted due to wave interference from multiple components of the reflected probing
beam, thus limiting the range of validity of the fluctuation measurement [18]. In order to
overcome this limitation, UC Davis has been involved in an extensive collaboration with
PPPL researchers Dr. E. Mazzucato, Prof. T. Munsat (University of Colorado, Boulder
currently), and H. K. Park together with researchers from the FOM Institute for Plasma
Physics Rijnhuizen in the Netherlands, to develop revolutionary 2-D and 3-D microwave
imaging reflectometer (MIR) systems for imaging electron density profile ne fluctuations
and profiles on the TEXTOR magnetic fusion device [16-18] and to extend the study to
another fusion device, NSTX, which is also the targeted plasma machine in this
dissertation. Figure 1.15 shows the schematic of MIR systems on NSTX plasma machine
with the proposed beam focusing/defocusing PAA in the transmitter system.
22
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Beam Splitter
2-D Imaging Array
J
Mjrror H
Mirror E
LO Source
Window
A
42 cm
*A
RF Source
X i L-=
« IL= r-
Vr
r -
Electronically controlled Beam
F ocusing/D efocusing A ntenna
Array
Figure 1.15 Schematic of MIR systems on NSTX plasma machine for detecting plasma
electron density profile ne fluctuations
1.2 Dissertation Overview
During the course of this PhD dissertation work, the author has worked on the design,
fabrication and testing of the transmitting and receiving antenna systems for the
application of Microwave Imaging Reflectometry on NSTX. Investigation into a number
of innovative technologies was performed in order to develop novel components for the
potential utilization in various high frequency imaging and radar applications. A novel 18
to 40 GHz PAA system has been developed in this dissertation research to address the
need for wideband,
low
sidelobe,
and low
cost,
electrically-controlled beam
shaping/steering PAA transmitter [58]. A low cost true time delay technology was used to
overcome the frequency bandwidth limitation suffered by many systems which rely upon
the frequency dependent phase shifting elements. In the receiving system, Q- to V-band
1-D and 2-D dual dipole imaging arrays on the back of an elliptical MACOR lens were
23
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investigated [59-60]. Detailed modeling and calculation of the receiving properties are
presented, which can be used to guide the future design. The organization of this thesis is
as follows:
Chapter II describes in detail the fundamental principles of plasma reflectometry
theory. The current measurement technologies and previous contributions are presented.
It is followed by a discussion of the need for these beam shaping PAAs in the transmitter
system, detailed beam shaping/steering theory, and the requirements for PAA design
based on NSTX’s specifications. Power issues are also presented here.
Chapter III presents the detailed design procedure for beam steering/shaping PAAs.
The beam shaping theory and technologies are also addressed. Antenna element designs
including array pattern simulation and calculations are also given in this chapter.
Chapter IV describes the detailed measurement procedure for the PAA system
including fixture design and fabrication, lab facilities calibration, LabView code
development including many new features and complete test data.
Chapter V will present the detailed design procedure for the substrate lens antenna
array. Theoretical analysis including pattern, sensitivity, angular field of view, steering
angles, losses and the measurement results will be compared and discussed. Lenses made
of different materials will be compared from many aspects, such as loss, off-axis
performance, cost, etc.
Chapter VI contains the results and conclusions of this dissertation. Future work
associated with this topic and other applications of this technique are suggested.
24
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ASDEX Upgrade Using Doppler Reflectometry”, IAED-CN-149, Chengdu 2006.
[29] Kim M., Hacker J.B., Mihailovich R.E., DeNatale J.F., “A DC-to-40GHz four-bit RF
MEMS true-time delay network”, IEEE Microw. and Wireless Let., vol. 11, no.2, 2001.
[30] http://www.amicom.info/OpenPlatform/index.php/Delav lines and phase shifters.
[31] William D. Jemison, “Analysis of the AO-FDPC Optical Heterodyne Technique for
Microwave Time Delay and Phased Array Beamsteering Applications”,IEEE Trans, on
Microwave Theory and Tech, vol.50, no.7, July, 2002.
[32] Edward N. Toughlian, Henry Zmuuda, “A Photonic Variable RF Delay Line for
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Phase Array Antennas”, Journal o f Lightwave Technology, vol.8, no. 12, 1990.
[33] Istvan Frigyes, A. J. Seeds, “Optically Generated True-Time Delay in PhasedArray Antennas”, IEEE Trans, on MTT, vol.43, no.9, 1995.
[34] William D. Jemison, “Analysis of the AO-FDPC Optical Heterodyne Technique for
Microwave Time Delay and Phased Array Beamsteering Applications”, IEEE Trans, on
Microwave Theory and Tech, vol.50, no.7, July, 2002.
[35] D. Dolfi, M. Labeyrie, P. Joffre, and J. P. Huignard, “Liquid Crystal Microwave
Phase Shifter”, Electronics Letters, 13th May 1993, vol. 29, no. 10.
[36] Frederic Guerin, Jean-Marc Chappe, Pascal Joffre and Daniel Dolei, “Modeling,
Synthesis and Characterization of a Millimeter-Wave Multilayer Microstrip Liquid
Crystal Phase shifter”, J. Appl. Phys. vol. 36(1997), pp.4409-4413.
[37] Hirokazu Kamoda, Takao Kuki, Hideo Fujikake and Toshihiro Nomoto, “Millimeterwave Beam Former Using Liquid Crystal”, 34th European Microwave Conference,
Amsterdam, 2004.
[38] http://www.elis.ugent.be/ELISgroups/lcd/lc/lc2.html.
[39] NHK STRL Annual Report 2002.
(http://www.nhk.or.ip/strl/results/annual2002/en/annual2002-rr32e.pdf)
[40] N. S. Barker and G.M. Rebeiz, “Distributed MEMS true-time delay phase shifters
and wide-band switches”, IEEE Trans, on Microwave Theory and Tech., vol.46, no. 11,
pp. 1881-90, Nov. 1998.
[41] A. Borgioli, Y. Liu, A.S. Nagra, and R.A. York, “Low-Loss Distributed MEMS
Phase Shifter”, IEEE Microwave Guided Wave Letters, vol.10, n o .l, pp.7-9, Jan. 2000.
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[42] Yu Liu, A. Borgioli, A. S. Nagra and Robert A. York, “K-Band 3-Bit Low-Loss
Distributed MEMS Phase Shifter”, IEEE Microwave and Guided Wave Letters., Vol. 10,
No. 10, Oct., 2000, p 415-417.
[43] Gidas Gauthier, “Low Noise Receivers, Micromachinged Antennas and Low loss
Transitions for Millimeter wave Applications” Ph.D dissertation, University of
Michigan, 1999.
[44] Sanjay Raman and Gabriel M. Rebeiz, “Single and Dual Polarized Slot Ring
Subharmonic Receivers”, IEEE MIT-S Digest, pp.565-568, 1997.
[45] Brain K. Kormanyos, Paul H. Ostdiek, William L. Bishop, Thomas W. Crowe, “A
Planar Wideband 80-200 GHz Subharmonic Receiver” , IEEE Trans. Microwave
Theory and Techniques, vol. 41, no.10, pp.1730-343, October, 1993.
[46] Steven S. Gearhart and Gabiel M. Rebeiz, “A Monolithic 250 GHz Schottky Diode
Receiver”, IEEE Trans, on Microwave Theory and Tech, vol. 42, no. 12, pp.2504-2511,
December, 1994.
[47] B.K. Kormanyos and G.M.Rebeiz, “A 30-180 GHz Harmonic Mixer Receiver”,
IEEE MIT-S Digest, pp.341-344, 1992.
[48] Paolo Focardi, William R. McGrath, “Design Guidelines for Terahertz Mixers and
Detectors, IEEE Trans, on Microw. Theory and Tech, vol.53, no.5, pp. 1653-1661, May,
2005.
[49] D. B. Rutledge, D. P. Neikirk and D. P. Kasilingam, “Integrated Circuit Antennas,”
IRMMW, vol. 10, K. J. Button, Ed., New York Academic Press, pp. 1-90, 1983.
[50] G. M. Rebeiz, “Millimeter-wave and terahertz integrated circuit antenna,” Proc.
IEEE, vol. 80, no. 11, pp.1748-1770, Nov. 1992.
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[51] D. F. Filipovic, S. S. Gearhart and G. M. Rebeiz, “Double-slot Antennas on Extended
Hemispherical and Elliptical Silicon Dielectric Lenses,” IEEE Trans, on Microwave
Theory and Tech, 41 (1993), no. 10, pp. 1738-1749.
[52] B. K. Kormanyos, R H. Ostdiek, W. L. Bishop and T. W. Crowe, “A Planar
Wideband 80-200 GHz Subharmonic Receiver”, IEEE Trans, on Microwave Theory and
Tech 41 (1993), no. 10, pp.1730-1737.
[53] X. Wu, G. V. Eleftheriades and T. E. v. Deventer-Perkins, “Design and
Characterization of Single and Multiple-Beam MM-wave Circularly Polarized Substrate
Lens Antennas for Wireless Communications”, IEEE Trans, on Microwave Theory and
Tech, 49(2001), no.3, pp.431-441.
[54] M. N. Asfar and K. J. Button, “Millimeter and submillimeter wave measurement of
complex optical and dielectric parameters of materials. Ii. 5 mm to 0.66 mm for coming
macor machinable glass ceramic,” Int. Journal o fIR and M M Waves 3 (1982), 319-329.
[55] http://hvperphysics.phv-astr.gsu.edu/hbase/nucene/fusmag.html
[56] *Edward V. Appleton, “The Ionosphere”, Nobel Lecture, 1947.
[57] E. Mazzucato, Rev. Sci. Instrum. 69 (1998), 2201.
[58] Lu Yang, N. Ito, C.W. Domier, N.C. Luhmann, Jr. and A. Mase, “20 GHz to 40 GHz
Beam Shaping/Steering Phased Antenna Array System Using Fermi Tapered Slot
Antenna”, IEEE M TTInt. Symp., Honolulu, June 2007.
[59] Lu Yang, C.W. Domier and N.C. Luhmann, Jr., “38 GHz to 75 GHz 1-D and 2-D
MACOR Elliptical Lens Antenna Arrays”, IEEE Antenna Propagat. Society Int. Symp.,
Honolulu, June 2007.
[60] Lu Yang, C.W. Domier and N.C. Luhmann, Jr., “Q-band to V-band 1-D and 2-D
30
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Elliptical Lens Antenna Arrays”, to be published on Microwave and Optical Technology
Letters, 2007.
31
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Chapter II
Introduction to Plasma Microwave Imaging
Reflectometry
2.1 Basic Principles of Plasma Reflectometry
Plasmas are dispersive media whose refractive index is a function of plasma density.
In reflectometry, an electromagnetic wave propagating through plasma is reflected from a
cutoff surface where the EM wave frequency is equal to the plasma cutoff frequency in
the case of O-mode (see below )[l]. As shown in Figure 2.1, the principle is readily
understood through the analogy with a slowly tapered rectangular waveguide, where the
local cutoff frequency is determined by the aperture dimensions.
Fig. 2.1 The principle of plasma reflectometry can be explained by the analogy with a
tapered waveguide
The electromagnetic waves perpendicular to the magnetic field B0can be classified as
ordinary wave (O-mode), in which the oscillating electric field E y is parallel to the
magnetic field B0 and extraordinary wave (X-mode), in which the oscillating electric
field E 1 is perpendicular to the magnetic field 6 0 [ 1]. The dispersion relations for O-
32
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mode and X-mode are shown in Eqn.2.1 and Eqn.2.2.
co —cop + c k
(O-mode)
(2.1)
c 2k 2
col co2 - col
— T = 1-----T — 2----- T (X-mode)
CO
CO CO —COh
(2.2)
In the above, co is the plasma frequency, which is given by Eqn. 2.3 [1],
co =
V
m d I sec
(2.3)
£ 0m e
where n0(r) is the equilibrium plasma electron density which is a function of the radial
location r . In addition, coh is the plasma upper hybrid frequency, which is given by Eqn.
2.4 [1],
(2-4)
l +a)c
where C0i is the electron cyclotron frequency
coc =
e-B
(2.5)
me
The cutoff frequencies can be obtained by setting k equal to zero in Eqn. 2.1 and Eqn.
2.2. The plasma cutoff frequencies for O-mode and X-mode are given in Eqn. 2.6 to Eqn.
2 .8.
C00 = COp (r) =
in (7*1 •a2
V
(O-mode)
(2.6)
£0 -me
C0r ~ ~[coc + (co/ + 4c o / Y 2] (Right-hand cutoff in X-mode)
(2.7)
coL = ^ \-c o c + (co/ + 4cop2) ^ ] (Left-hand cutoff in X-mode)
(2.8)
33
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Figure 2.2 is a simplified schematic showing the plasma reflectometry principle. The
phase difference between the launched and reflected wave (traveling in the r direction
and measured at the plasma edge) is given by 0 = 2k0 [ 4 e ■dr (apart from an additive
constant) where ko is the free-space wave number of the probing wave, £ = (ckjco) 2 is
the plasma permittivity, and rc is the position of the wave cutoff. Measurement of 0 thus
determines the location of rc. By sweeping the frequency of the probing wave and
recording the phase history from the beginning of the plasma discharge, the electron
density profile can be determined (or the B-field for the case of X-mode if the density is
known).
n
Cutoff layer
frequency
for
Transmitting Horn
+•
Receiving Horn
Fig. 2.2 Principle of plasma reflectometry (based on conventional systems)
The first application using a similar idea is the detection of the ionosphere, which
won Appleton the Nobel Prize in 1947 [2]. Such a situation is pictured in Figure 2.3. The
radio waves can travel from the sender to the receiver by two paths - one direct and one
indirect. When a radio wave reaches the ionosphere, the electric field in the wave forces
34
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the electrons in the ionosphere into oscillation at the same frequency as the radio wave.
Some of the radio wave energy is given up to this mechanical oscillation. The oscillating
electrons will then either be lost to recombination or will re-radiate the original wave
energy back downward again. At any given time, each ionospheric layer has a maximum
frequency at which radio waves can be transmitted vertically and reflected back to earth.
This frequency is known as the critical frequency. Radio waves transmitted at frequencies
higher then the critical frequency of a given layer will pass through the layer and be lost
in space; however, if they encounter a layer with higher critical frequency, they will be
refracted by a given degree of ionization [3].
Ionized Layer
Transit
Receiver
Antenna
Directed wave
#2^
m
m
m
m
m
m
m
,
Fig. 2.3 Schematic of wave reflection in the Ionospheric plasma
It is important to point out that the fluctuating phase of the reflected wave is
dominated by the change in permittivity close to the cutoff layer, which becom es very
large near the cutoff (as the group velocity approaches zero) [1]. The measurement of
fluctuating phase therefore represents a localized measurement of fluctuations near the
cutoff layer, rather than a combined measurement of modulation along the entire ray
35
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
trajectory. Indeed, this is one of the most valuable features of reflectometry as a
fluctuation diagnostic [4-12].
2.2 The Need for Imaging Technology
Conventional microwave reflectometry has proven to be an extremely useful and
sensitive tool for measuring small density fluctuations in some circumstances; however,
this technique has been shown to have limited viability for large amplitude, high
k e fluctuations and /or core measurements [4-12],
Figure 2.4 shows the comparison of the reflected wave-fronts for the cases of 1-D and
2-D fluctuations. For 1-D fluctuations, the reflection layer will move back and forth in
the radial direction, resulting in only phase changes in the reflected wave. The stratified
permittivity is £ = £0(r) + e(r) (with fluctuation components£(r) « 1). The fluctuating
component of the signal phase is given by the approximation of geometric optics [4]
(2.9)
By taking |kr|> l / L £ since we are interested in short-scale fluctuations, where k r is
the radial fluctuation wavenumber and Le is the scale length of the plasma permittivity at
the plasma cutoff rc and £0(r) ~ (rc - r ) / L e since most of the contribution to Q comes
from a narrow region near the cutoff, one obtains the power spectrum of ^ as a function
of the power spectrum of the density fluctuations [4]
36
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In the above, Ln is the scale length of the electron density n, r^(kr) is the power
spectrum of the m easured^, and T,,(kr) is the power spectrum of the relative plasma
density fluctuation n / n . Therefore, for 1-D turbulence, the power spectrum of density
fluctuations can be obtained from the power spectrum of the reflected signal phase
fluctuations.
Reflected Wavefront
Reflection layer
m oves back and
forth
(a) 1 -D Reflectom etry
(b) 2_D Ref|ectometry
(real plasm a surface)
Fig. 2.4 Comparison of (a) 1-D (with phase modulation) (b) 2-D reflectometry (with both
phase and amplitude modulations)
However, in the presence of two-dimensional (2-D) radial and poloidal density
fluctuations, the plasma permittivity fluctuates perpendicularly to the direction of
propagation of the probing wave and therefore, the spectral components of the reflected
field propagate in different directions resulting in a complicated interference pattern on
the detector plane, from which it is very difficult to extract any information about the
37
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
plasma fluctuations [4]. Unfortunately, this is precisely the case of interest in
magnetically confined plasmas, such as in Tokamaks. To better understand and quantify
this phenomenon, Mazzucato has performed a series of numerical simulations of
reflectometry in plasmas with 2-D fluctuations [4]. The numerical results demonstrate a
“virtual cutoff’ surface, located behind the actual cutoff surface and the spatial structure
of density fluctuations near the cutoff could be obtained from the measurement of the
phase fluctuation at the virtual cutoff <j)G [4]. Such a measurement can be done by
collecting the reflected waves with a sufficiently wide aperture antenna, and by imaging
the cut-off onto the detector plane taking the effect of the average plasma permittivity
into account [5], Figure 2.5 shows the beam trajectories in the vicinity of the cutoff layer.
Here, n, is labeled as the plasma boundary, rc is the cutoff location, and rmm is the location
of the “virtual cutoff’.
Plasm a Boundary: r=rb
/
Actual Cutoff U y e j f e lf P ■
B eam Trajectories
Virtual Cutoj
Fig. 2.5 Schematic representation of beam trajectories in the vicinity of the cutoff layer
38
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If the reflected rays are collected by a large-aperture optical system, the spatial
structure of the density fluctuations near the cutoff layer can be determined by a
reconstruction of the reflected wavefront at the image plane; phase fluctuations measured
at the image plane will directly correspond to density fluctuations at the cutoff layer.
Additionally, the use of imaging optics enables the simultaneous sampling of an extended
region of the cutoff layer by an extended array of detectors at the image plane. Therefore,
using optical technology to image the reflection waves will permit the restoration of the
phase front.
P la sm a Cut-off
Im aging Cut-off
O ptical L en s
Fig. 2.6 Schematic representation of imaging technology to restore the phase front from
the cutoff layer
In addition to classical large aperture optical type imaging, an alternative turbulence
imaging measurement approach, which has received increasing attention in recent years,
is the synthetic aperture imaging using either an array of poloidally an/or toroidally
displaced antennas, or a single antenna with rotating plasma and inverting the signal time
evolution to give the turbulence spatial (poloidal) structure [5-6]. The advantage of
synthetic imaging is that the image can be produced without the need of a large lens of
high optical quality, and each frequency that is launched can be independently imaged [5].
In rapidly rotating plasmas such as NSTX, the possibility of synthetic imaging may be
39
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
pursued as a low cost method for measuring the poloidal structure of density fluctuations
in the plasma [5]. However, as the ratio of the parallel to poloidal correction length
decreases, a poloidal array of receivers needs to be used to synthesize the image with
high accuracy [5].
2.3 Microwave Imaging Reflectometry Technology
The study of the effect of 2-D turbulence on reflectometer measurements led to the
development of the Microwave Imaging Reflectometry (MIR) concept. MIR is a
technique in which large aperture optics at the plasma edge are used to collect as much of
the scattered wave-front as possible and optically focus an image of the cutoff layer onto
an array of detectors, thus restoring the integrity of the phase measurement. The MIR
system consists of two parts. First, an RF source in the transmitting system launches the
microwave probe signal through the focusing mirrors to illuminate the plasma. The
curvature of the probe-beam is matched to that of the cut-off surfaces (toroidal and
poloidal). Subsequently, the reflected waves are imaged onto the detector array of the
receiving system through the same optical elements. The two paths are separated by a
beam splitter. Figure 2.7 shows the detailed schematics of these two separate paths.
40
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Illumination
magnetic
surface
cutoff
surface
microwave
source
Detection
magnetic
surface
cutoff
surface
image
plane
Fig. 2.7 Two separate paths for the MIR system
A schematic of the MIR system is shown in Figure 2.8. The RF source in the
transmitting system launches a microwave probe signal through the focusing mirrors to
illuminate the plasma. By moving the horn antenna, the curvature of the probe-beam is
matched to that of the cut-off surfaces (toroidal and poloidal). Subsequently, the reflected
waves are imaged onto the detector array of the receiving system through the same
optical elements. The reflected signal is separated from the probing beam by means of a
beam splitter.
41
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Different Cutoff Surfaces
11
ii/ 1\i
RF Source
Window
|
Mirror E
MIR RF Lens
MIR Beam Splitter
r
Mirror H
t
Plasma
Curved in vertical direction
U
s p in ie r
Beam spnner
V
-
t
i-u Detector Array
Imaging Lens
Fig. 2.8 Schematic representation of MIR system
The initial laboratory test of the MIR configuration compared with a conventional
reflectometer arrangement was performed by Munsat [8-11]. The laboratory arrangement
of the MIR and one-dimensional configurations are schematically shown in Figure 2.9.
The target reflectors were constructed from an inner wheel of 60 cm in diameter and 20
cm wide, with a sinusoidally corrugated flexible aluminum strip wrapped around the
circumference. The corrugation wavelength Xcorr and corrugation height hcorr were both
precisely imposed on the construction. Measurements were taken with each of the
reflectometer systems for a series of targets covering a range of k e and hcon, and for
geometries covering a range of distances from the instrument to the target surface. The
measurement results are shown in Figure 2.11 [8]. Clearly from the results, the 1-D
configuration produces a close match to the reference curve when the distance d is small.
However, when d increases, the 1-D measurement is quite distorted, no longer
42
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
representing the actual target surface. The MIR system represents the cleanest
measurement of the wheel surface, despite being physically the furthest removed from
the target [8]. Further experiment shows that within ±10 cm with respect to the focal
plane location, the MIR system can give a clean measurement. This 20 cm range
represents the distance over which multi-radial (multi-frequency) data could be collected
simultaneously with a fixed set of image optics [8-10],
(corrugation
w avelen gth )
2n!K
launching horn
collection mirror
receiving horn
(corrugation height)
launching horn
steerin g mirror
receiving horn
Fig. 2.9 Schematic of the test setup, showing the MIR and 1-D configuration [10]
Fig. 2.10 Photographs of the corrugated bicycle wheel used to model the plasma surface
fluctuations [8]
43
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■4
(a) 1-D System
2
(d=10cm )
£ o
■2
A
2
(b) 1-D System
(d=30cm )
~2
A
2
(c) Imaging System
1 O
(d at im age fo c u s = 2 3 5 cm )
-2
4
Signal
■e— R e fere n c e Signal
Fig. 2.11 Test results from reflected target (a) 1-D system at 10 cm (b) 1-D system at 30
cm (c) MIR system at focus point =235 cm. The reflector has corrugations of ke = 1.25
cm '1 and depth =1.7 mm [10]
The conclusion from these laboratory tests is that the critical distance for the 1-D
detection system is limited by the diffraction distance as predicted, which is most often
considerably shorter than the measurement distance in practice (due to plasma device
access constraints).
2.4 Theoretical Calculations of Plasma Cutoff Surfaces for TEXTOR
and NSTX Plasma Devices
The two plasma devices under investigation are the National Spherical Torus
Experiment (NSTX) [7-8] located at the Princeton Plasma Physics Laboratory (PPPL)
and the TEXTOR tokamak machine located in Germany [9-11] (Figure 2.12).
44
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For TEXTOR, the operating frequency has been fixed at a single frequency, 88 GHz,
for the initial proof-of-principle demonstration, but will eventually extend from 70 GHz
to 100 GHz. The shape and location of the plasma cutoff surfaces depend on two
parameters: the center electron density ne0 and the magnetic field B0 . Typically,
ne0changes from 3 x l0 19m~3to 6 x l 0 19m”3and B0changes from 2 .2 5 rto 2 .5 7 \ Figure
2.13 shows the contours of the X-mode plasma cutoff surfaces of TEXTOR.
(a)
45
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(b)
Fig. 2.12 Two target plasma machines (a) National Spherical Torus Experiment (NSTX)
and (b) TEXTOR
04
0.4
0.3
(3,3
0.2
£
- 0.1
-0.3
12
1.8
1.4
1 .6
mt
n'eO
Bq= 2,5T
1» . -5
: 6x10!V 3
1.8
RJml
6 i o i9/ / r 3
2
B0 = 2.25T
^, = 2457*
4 = 233T
4 = 2,57'
22
Fig. 2.13 X-mode plasma cutoff surfaces of TEXTOR with (a) fixed magnetic field and
(b) fixed central electron density
46
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
We see from the above plots that the plasma cutoff surfaces of TEXTOR are quite
circular and that when ne0 and/or B0change, the centers of these circular-shaped layers
remain at nearly the same locations. In other words, TEXTOR has nearly commoncentered cutoff surfaces. This fact results in the need to move the lens only over a very
short range to match different cutoff layers. Figure 2.14 shows the schematic drawing for
the combined ECEI/MIR system which was installed in December, 2003 [8].
Toroidal and Poloidal Mirrors
Fig. 2.14 Combined ECEI/MIR Imaging System under development for TEXTOR
However, for the National Spherical Torus Experiment (NSTX) plasma device, the
shapes of the cutoff surfaces are quite different from those of TEXTOR. In addition to
central electron density ne0 and magnetic field B0 , there are several other physical
parameters which control the shapes and locations of plasma cutoff layers. They are the
plasma elongation factor K and the plasma triangularity 8 . The plasma shape is defined
47
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
by [12]
R = R0 + a cos(# + £sin d)
(2.11)
Z = m s in 0
(2.12)
where a is the minor radius and Ro is the major radius. Figure 2.15 shows the effect of
adding k and 8 to a normal circle. Figure 2.16 shows the calculated cutoff layers for
NSTX under two physical conditions.
0.5
E_
N
- 0.5
0.5
R[m]
E
N
0.E
-0.5
E,
N
1
-0.5
0
0.5
1
-0.E-
-0.5
0.5
R[ m]
Fig. 2.15 Elongation and tragularity effects to a normal circle
48
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neo = 6 x 1019m “ 3 , f i 0 = 0.45T, K = 2.4, 6
=
0.55
*e0 = 4 x l0 19m~3, f i0 = 0.307, *•=1.8 ,8 = 0.75
0.6
0,4
0.2
0
0,2
■
■0.4
06
02
0.4
0.6
0.8
RM
1
1.2
0.2
1.4
0.4
0.6
0.8
1
1,2
R_curve(45G H z)=112.8cm
R_curve(45GHz)=30.7cm
FLcurve(50G Hz)=80,6cm
R_curve(50GHz)=24.9cm
R„curve(55G H z)=46.0cm
R_curve(55GHz)=17.8cm
1.4
Fig. 2.16 NSTX plasma cutoff surfaces at two physical conditions
Clearly from the above plots, the NSTX plasma cutoff surfaces are quite non-circular.
Consequently, the focal properties of the probing beam need to change considerably to
match these highly shaped plasma cutoff surfaces. Because of the large variation range of
the focal properties of the probing beam, and the fact that the frequency range of NSTX,
which is 38 GHz to 75 GHz, is very suitable for micro/millimeter wave applications, an
electronically controlled beam focusing/defocusing antenna array is proposed to take the
place of the horn antenna as the RF source. This concept is illustrated in Figure 2.17. A
multi-frequency illumination beam is sent out from the PAA. By programming the PAA
and giving it an appropriate time delay distribution, it can generate a convex or concave
wavefront and function like a controllable artificial “lens” whose focal properties can be
adjusted to the particular plasma cutoff surface. The initial “strawman” optical setup was
designed by Wang [16] and the schematic of the MIR system on NSTX employing a
49
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
beam shaping PAA is shown in Figure 2.18. Detailed design procedures for the beam
steering/shaping PAA system are provided in Chapter 3.
Multi-Frequency Illumination
Fig. 2.17 PAA beam shaping concept
Beam Splitter
2-D Imaging Array
j
Mirror H
1 ,/l
3
Mirror E
0
LO Source
Window
M
42 c n
A
30 cm'
RF Source
E lectronically controlled Beam
F ocusing/D efocusing A ntenna
Array
Fig. 2.18 Schematic of MIR systems on the NSTX plasma device for detecting plasma
electron density profile ne fluctuations
50
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2.5 Requirements for Phased Antenna Array Design
2.5.1 Element Number Estimation
Based on the primary optical design shown in Figure 2.17 and the NSTX plasma
cutoff surface properties, the beam waist radius of the probing beam w0 should be less
An
than 15 mm. From w0 = ------ ------ [7], where GUe is the asymptotic beam growth angle,
n tan01/e
0 886/1
we have 6Ue >1.2° and 0HPBW > 8 .5 °. From antenna theory [8], 0HPBW = —------- where
L
L = Nd (d is the antenna element spacing, N is the total number of antenna elements,
and ^ is the wavelength), we have 0HPB = 6.3°fo rA = 16.
In order to minimize the phase variation introduced by the probing beam itself and
power loss, it is desirable to launch as clean a Gaussian beam as possible, with minimal
sidelobes, and to maintain the clean beam through the focusing elements [9-10].
Therefore, a certain amount of amplitude taper is preferred to lower the sidelobe level
and to achieve wider beam broadening range. Therefore, 16-elements are chosen for the
PAA design.
2.5.2 Power Requirements
Because of the various losses in the system, to make sure that the receiver gets
enough signal power, there is a minimum power requirement for detection of the cutoff
surface. Using imaging technology, an important advantage is that we can collect as
much of the power as possible. Therefore, the major sources of the losses come from
cutoff surface mismatch, mixer noise, and Gaussian beam spillover through the optical
system. Also, the capacity of the digitizer at the last of receiving circuit restricts the
51
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minimum acceptable signal to noise ratio. The power of one channel on the plasma cutoff
surface i s
940
23296
of the power of all channels. Here, 940mm2 is the area of the spot size of
one channel and 23296mm2 is the area of the spot size of all channels. We assume there is
3dB loss due to mismatch to the cutoff surface and another 3dB loss due to the taper of
1(V)
the illumination beam. Assuming we use a 12 bit digitizer, then the L S B = —
2
= 0.24m V .
-1
The signal to noise ratio for field measurement should be greater than----- — - = 4167.
0.24x10
O
The noise temperature for the mixer is assumed to be 50,OOOC based on experimental
results. Consequently, the minimum power at the receiver that can be detectable is given
by
Prmin = ( S /N ) mmKTeB = 41672 x l .3 8 x l0 “23 x 50273x l.3 M = -1 8 dBm
In the above, 1.3 MHz is the bandwidth. Also assuming that 30% of the power is lost
on the way due to the finite dimensions of the optical components, then,
940
1
1
23296
2
2
Pin x70% x ----- — x - x - = -18(4Bm)
From the above, we obtain:
Pin = 3 .5 d B m (2mW)
Consequently, the minimum power emanating from the antenna array is about 2mW.
The PAA system is realized on a standard PCB substrate. The loss mainly comes from
the conductor loss (microstrip line, coplanar stripline, etc.), dielectric loss (loss tangent of
the substrate), radiation loss (CPS, etc.), and impedance mismatch. The first three types
of losses of microstrip line and CPS can be calculated from closed form expressions
considering the dispersion effect [17]. The impedance mismatch can be measured as Sn.
52
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Within the designed frequency range, Sn should be less than -10 dB. Consequently, -10
dB is used in the calculation as the worst case. Figure 2.19 shows the power flow chart of
the transmitting system. Table 2.1 lists the power loss and output power of the system at
various frequencies assuming 100 mW (20 dBm) input power.
Im pedance m ism atch + conductor
loss + dielectric loss + radiation loss
r
P E T co n tro lle d d elay lin e
P E T c o n tro lle d d elay lin e
Pin=100m W =
2 0 dBm
Wideband
Antenna
Array
■Pout
P E T co n tro lle d d elay lin e
P E T co n tro lle d d elay lin e
16-Way T-junction power divider
with amplitude taper
S LR = 30 dB, N -b a r = 6
Fig. 2.19 Schematic of transmitting system power
TABLE 2.1 Power Losses and Output Powers of the PAA System at Various Frequencies
Assuming 100 mW Input Power
Freq
20 GHz
30 GHz
40 GHz
50 GHz
60 GHz
75 GHz
Power Loss
7.1 dB
9.5 dB
11.6 dB
14.0 dB
16.0 dB
19.4 dB
Pout
12.9 dBm
10.5 dBm
8.4 dBm
6.0 dBm
4.0 dBm
0.6 dBm
As the frequency increases, the power loss increases. Below 60 GHz, 100 mW input
53
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power should be sufficient. Above 60 GHz, however, 100 mW input power might not be
enough to satisfy the system requirement. An input power of 200 mW is believed
necessary to satisfy the system power requirement up to 75 GHz. The power handling
capability of the transmission line is limited by heating caused by Ohmic and dielectric
losses and dielectric breakdown [17]. An increase in temperature due to conductor and
dielectric losses limits the average power of the microstrip line, while the breakdown
between the strip conductor and ground plane limits the peak power [17]. Copper’s
melting temperature is more than 1800° and the highest operating temperature of the
substrate Taconic RF-60A is 125°. Using the formula in [17], the calculated average
power handling capabilities at various frequencies for a 50 Q microstrip line are listed in
Table 2.2.
TABLE 2.2 Average Power Handling Capabilities of a 50-Q Microstrip Line
Freq
Power
20 GHz
32.0 W
30 GHz
23.8 W
40 GHz
18.8 W
50 GHz
15.4 W
60 GHz
12.9W
75 GHz
10.2W
Consequently, 200 mW should have no problem in being transmitted through the
system. Power levels on the order of Watt can be sent into the system without destroying
the performance.
In conclusion, the requirements for the PAA design are,
•
Frequency range is from 38 GHz to 75 GHz;
•
16 elements are needed;
•
Amplitude taper is necessary to lower the sidelobe level.
•
The output power from the PAA is at least 2 mW.
54
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References
[1] Francis F. Chen, “Introduction to Plasma Physics and Controlled Fusion, 2nd Edition”,
Plenum Press, 1983.
[2] *Edward V. Appleton, “The Ionosphere”, Nobel Lecture, 1947.
[3] http://www.tpub.com/neets/book 10/40e.htm
[4] E. Mazzucato, “Microwave Imaging Reflectometry for the Visualization of turbulence
in Tokamaks”, Nuclear Fusion, vol. 41, no. 2, pp. 203-213, 2001.
[5] Kramer G., Nazikian R. and Valeo E.J. 2004 Plasma Phys. Control. Fusion 46 695
[6] G.D. Conway 2006 Plasma Phys. Control. Fusion 46 665
[7] http://nstx.pppl.gov
[8] Tobin Munsat, “Microwave Imaging Reflectometry for fluctuation measurement on
NSTX”, presented at NSTX Research Forum, Sep. 12, 2002
[9] T. Munsat, et, al. “Microwave Imaging Relectometer for TEXTOR”, Review o f
Scientific Instrument, vol. 74, no. 3, 2003.
[10] T. Munsat, E. Mazzucato, H. Park, C.W. Domier, and N.C. Luhmann Jr., A.J. Donne
and M vab de Pol, “Laboratory Characterization of and Imaging Refelectometer System”,
Plasma Phys. Control. Fusion 45 (2003) 469-487.
[11] http://www.fz-iuelich.de/ief/ief-4//textor en/
[12] A. Costley, “Microwave Refelectometry”, Diagnostics fo r Contemporary Fusion
Experiments, ISPP-9 “Piero Caldirola”, pp. 113-134, 1991
[13] Paul F. Goldsmith, “Quasioptical Systems: Gaussian Beam Quasioptical Propagation
and Applications”, IEEE Press, 1998.
[14] R.C. Hansen, “Phased Array Antennas”, John Wiley & Sons, Inc, 1998.
55
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
[15] http://www.tpub.com/neets/bookl0/40e.htm.
[16] Jian Wang, “Microwave imaging reflectometry (MIR) system for plasma turbulence
studies”, Ph.D. Dissertation, UCD, 2005.
[17] K.C. Gupta et al., “Microstrip Lines and Slotlines”, Artech House, 1996.
[18] E. Mazzucato, “Density Fluctuations in the Adiabatic Toroidal Compressor”,
Bulletin o f The American Physical Society 20, pp.1241, 1975.
[19] C. Laviron, A.J.H. Donne, M.E. Manso, J. Sanchez, “Reflectometry Techniques for
Density Profile Measurements on Fusion Plasmas”, Plasma Physics and Controlled
Fusion, vol.38, IOP Publishing, p.905-36, July 1996.
[20] R. Nazikian, G.J. Kramer,and E. Valeo, “A Tutorial on the Basic Principles of
Microwave Reflectometry Applied to Fluctuation Measurements in Fusion Plasmas”,
Phys. o f Plasmas 8, p. 1840-1855, 2001.
56
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Chapter III
Beam Steering/Shaping Phased Antenna Array Design
Based on Piezoelectric Transducer Controlled Delay
Line Technology
3.1 Phased Antenna Array Theory
The basic principle describing how phased antenna array works is that the
electromagnetic energy received at a point in space from two or more closely spaced
radiating elements is a maximum when the energy from each radiating element arrives at
the point in phase [1].
Scan A ngle 9
E quiphase Front
Antenna
E lem ents
Phase S h ifte rs/
Tim e D elay D evices a Z
n =1
n =2
n=(N)
(An' M
d (Spacing)
Fig. 3.1 Schematic of linear phased antenna array geometry
57
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*- X
Figure 3.1 shows the one-dimensional linear array geometry. The excitation of the
array consists of specified amplitude and phase at each element. This discrete distribution
is often called an aperture distribution, where the discrete array is the aperture [1].
The analysis begins with a one-dimensional linear array comprised of lxN antenna
elements. It is straightforward to develop the two-dimensional rectangular array
characteristics based on a linear array by using superposition. We assume that a control
element is located behind each radiator/antenna element sitting in-plane with an
amplitude coefficient, A„, and phase taper, (j)n. The received signals from all radiators
would be combined in phase to produce a maximum response in the scan direction, 6q.
For phase scanning in one dimension, with a linear phase taper, and thus a constant phase
difference between adjacent radiators, each phase element would have the form [2]
(j)n = - n k d • sin(0o)
(3.1)
where n denotes that nth element of the array, d is the inter-element array spacing, and k is
the free space wave number (2n//1) at frequency fo. In the transmit mode, the signals add
in phase to produce a main beam in the direction of do.
The far field pattern of an array is the product of the far field pattern corresponding to
a single element and the array spatial factor and it is given by,
E A r ra y = E S in gle E A rra y _ f a c to r
^
2)
For a linear array in the X Z plane as shown in Figure 3.1, the spatial factor depends
on the excitation and angular position 6 . It is given by Eqn. 3.3
Ea(e) = ^ A n -ejkndisin0-sin^
n
58
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( 3 .3)
For a uniformly illuminated beam steering array, the array factor is simplified to:
sin[N n •— (sin Q- sin 0Q)]
e m
=
-d------------------
(3.4)
N •sin[;r •—(sin 0 - sin 00)]
X
For a uniformly illuminated linear array, the half-power beam-width (HPBW) is
given by,
0.88581
HPBW
~ , TJ
r.
Nd cos 80
In the above, X is the wavelength, N is the total number of antenna elements, d is the
spacing between each element, and 80 is the steering angle. Therefore, for an array with
fixed spacing and steering angle, the pattern becomes narrower as the frequency increases.
If the element spacing exceeds a critical dimension, grating lobes (GL) occur in the
array factor, which reduce the power in the main beam and consequently reduce the
antenna gain [2]. The equation for grating lobes is determined by Eqn. 3.6 [3],
d
X
n
sin 60 - sin 6
(3.6)
For half-wavelength spacing, a grating lobe appears at -90° for a beam scanned to
+90°. A spacing of one-wavelength allows grating lobes at ± 90° when the main beam is
broadside. Therefore, for applications requiring large scanning angle, half-wavelength or
a slightly larger spacing is usually chosen.
The bandwidth of an array is affected by many factors, including change of element
input impedances with frequency, change of array spacing in wavelengths that may allow
grating lobes, and change in element beam-width. [3]. When an array is scanned with
59
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fixed units of phase shift, provided by a phase shifter, there is also a bandwidth limitation
as the position of the main beam will change with frequency. This can be explained from
Eqn. 3.4. When <pn is fixed, changing the frequency will result in a change of the scan
angle. Using true time delay to provide the beam scanning, then the required amount of
delay time is given by [2]:
v , = ~ n ' d ' Si" W
c
(3.7)
In the above, T is a time delay constant representing the amount of progressive time
delay for each individual element. From Eqn. 3.7, we see that when the array is scanned
with true time delay, the beam position is independent of frequency to the first order.
3.2 Beam Shaping Theory
The fields radiated from a linear array are a superposition of the fields radiated by
each element in the presence of the other elements. Each element has an excitation
parameter, which is current for a dipole, voltage for a slot, and mode voltage for a multimode element [1]. For the “forced excitation” problem, the drive of each element is
individually adjusted so that the excitation is as desired. This adjustment of the drive
accommodates the mutual coupling among feeds which changes the element input
impedance. The excitation of each element includes amplitude and phase. The beam
shaping technology is used to reduce the sidelobe level and to realize narrow-beam and
shaped beam operation. It can be achieved either by amplitude distribution or phase
distribution.
60
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Low sidelobes, which might be roughly defined as -30 dB to -60 dB, are of interest
for several reasons: reduction of radar and communications intercept probability,
reduction of radar clutter and jammer vulnerability, and increasing spectrum congestion
in satellite transmissions. There are several pattern synthesis methods to reduce the
sidelobe level, including the Taylor one-parameter distribution, Hamming distribution,
Taylor n distribution, and Villeneuve n distribution (Taylorn distribution for small number
of elements) [1-2]. Among these methods, the Taylor n distribution gives the highest
directivity for a given sidelobe ratio and therefore, it is widely used [1]. The aperture
distribution is expressed in Eqn. 3.8 [1],
(3.8)
In the above, p is zero at the center and unity at the ends of the array. The coefficient
used in this formula is [1],
(3.9)
For an array with a small number of elements, Villeneuve (1984) developed an
elegant method for the design of the Taylor n distribution [1, 3], Detailed mathematical
expressions can be found in Appendix A. These expressions appear complex, but are
readily programmed for computer solution. From Sec. 2.6.1, 16 elements are necessary in
the array design. Considering the fabrication limitations, which will be described later in
this Chapter, a Taylor n distribution with sidelobe ratio (SLR) = 30 dB, and n = 6 is
61
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chosen as the amplitude taper. The first 8 normalized voltage and power coefficients are
shown in Table 3.1. The next 8 elements are a mirror of the first 8 because the desired
pattern is symmetrical with respect to the center of the array.
TABLE 3.1 Excitation Coefficient of 8-Element Array with n = 6 and SLR=30 dB
Port
Number
Normalized
Amplitude
Normalized
Power
1
2
3
4
5
6
7
8
0.2690
0.3247
0.4459
0.5988
0.7401
0.8612
0.9534
1
0.0724
0.1054
0.1988
0.3586
0.5477
0.7417
0.9090
1
Without Amplitude Taper
With Amplitude Taper
_
CO
' 10
T3,
I
-20
o
Q.
<D
J:
*
CD
cc
-30
-40
-50
-90
-60
-30
0
30
60
90
A ngle (d eg ree)
Fig. 3.2 Array factor patterns with and without amplitude taper
The array factor patterns for a 16-element array with and without Taylor n amplitude
distribution shown in Table 3.1 are plotted in Figure 3.2 assuming half-wavelength
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
spacing. We see that the sidelobe level is suppressed and the beamwidth is widened by
amplitude taper.
In addition to the amplitude distribution, the phase distribution can also be controlled
to generate the desired pattern. The technology surrounding phase shifter/time delay units
has become more mature in the past few decades [5-10]. However, phase-only control
could result in some distortion in the main beam as well as the sidelobes. Instead of
lowering the sidelobe level which is often the purpose of amplitude taper, phase tapering
cannot provide the low sidelobe level. Therefore, several approaches have lead to
different combinations of amplitude and phase distributions of the aperture excitation for
different beam shapes.
In [11], a “sub-array” concept was utilized to generate variable beamwidth. In this
approach, the entire antenna array elements were separated into two interleaved subarrays,
which point in different directions, so that the two main beams will overlap [11].
However, because the element spacing of the individual sub-arrays is twice that of the
aperture, further problems with grating lobes can be anticipated. Beam bifurcation is
another problem associated with this approach when the two beams’ pointing angles are
beyond a certain range, which limits the useful range for an application. Figure 3.4 shows
the array factor patterns calculated in MathCAD for a 1x16 antenna array using this sub­
array approach. We can clearly see the two large grating lobes appearing at about ± 65°
and beam bifurcation at the center.
Adding a quadratic phase error on the array aperture moves the array’s phase center
and changes the shape of the beam by changing its beamwidth [12] (see Figure 3.5). The
rays emanating from an aperture may be focused at a finite distance by introducing
63
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quadratic phase error at the radiating aperture. The same concept can be applied in an
array antenna, because an array behaves like an aperture with discrete distribution. The
focusing effect will shift the apparent phase center of a linear array along the axis of
symmetry because it gives the same effects as if the array is physically bent, as shown in
Figure 3.6. The focus distance reduces when the array is bent mechanically or electrically;
this produces a taper in far-field phase and as a result the phase center moves away from
the radiating aperture and shifts towards the caustics produced at some finite distance
[12], The variable focusing effect can be utilized to change the shape of radiated beam.
Fig. 3.3 Schematic of two subarrays for beam broadening
64
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10
0
GO
T3,
0
O
0.
0
-20
>
_0
0
-30
oc
-40
-50
-90
Before bifurcation
After bifurcation
-60
0
-30
30
60
90
A n g le (d e g r e e )
Fig. 3.4 Array factor patterns before and after beam bifurcation using the sub-array
concept
N
Variation of the Focusing
3
Beam Shaping PAA
Delay Time
Fig. 3.5 Schematic of a beam shaping phased antenna array based on a curved time delay
arrangement
65
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Fig. 3.6 Linear Arrays with quadratic phase excitation can be represented by physically
bent arc arrays
However, for a given size of the array aperture, there is a limit to the movement of the
array phase center because beam bifurcation is observed in the far field when the antenna
is focused at a closer range. Amplitude taper across the aperture can increase the useful
range before beam bifurcation and control the sidelobe level. Figure 3.7 shows the
calculated array factor patterns without and with amplitude taper after adding quadratic
wavefronts. We can clearly see that without amplitude taper, the sidelobe level increases
rapidly with increasing phase taper and bifurcation limits the useful range, while with
amplitude taper, the sidelobe level is controlled and the beamwidth is varied without
bifurcation.
66
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CD
;o
CD
5
0.
0
>
"■I—
'
o
JO
0
DC
no quadratic phase taper
with quadratic phase taper (after bifurcation)
with quadratic phase taper (before bifurcation)
-30
0
30
A n g le (d eg ree)
CD
T3,
CD
5
o
CL
0
>
4 —*
JO
0
CD
no quadratic phase taper
with larger quadratic phase taper
with quadratic phase taper
-30
0
30
A n gle (d egree)
Fig. 3.7 Array factor patterns adding quadratic wavefronts (a) with and (b) without
amplitude taper
67
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3.3 Design of 16-way Unequal Power Divider
To add an amplitude taper across the array aperture, a 16-way unequal power divider
is designed as the array feed network. Commonly used microstrip power dividers are
Wilkinson, Rat race, and T-junction power dividers [13]. Their structures are shown in
Figure 3.8.
3
(a)
d
d
(b)
(c)
Fig. 3.8 (a) Wilkinson (b) rat race and (c) T-junction structures
The Wilkinson power divider has excellent isolation between the output terminals by
adding a resistive element and has the advantage that its input and output power are not
consumed in the isolating resistor [13]; however, the losses become significant when the
incoming signals from the output ports are out of phase. Bending the quarter-wavelength
branches at high frequencies become more and more difficult when the wavelength
decreases to be on the same order as the transmission line width. In addition, the
resistor’s parasitic capacitance/inductance increases with increasing frequencies, which
decreases the performance. The rat race structure also has good isolation between outputs,
but the disadvantage is that radiation, ohmic, and dielectric losses are higher than the
losses in a T-junction. Another disadvantage of the rat race is the need for a matching
68
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resistor in the isolated port (port 4) that generates losses and makes the fabrication of the
structure more complicated and more expensive. The T-junction power divider has the
simplest structure and by designing the impedance ratio properly, it is easy to realize
unequal power division [13-14], In addition, the T-junction does not need high frequency
resistors. The disadvantage of the T-junction power divider is that it does not provide
good isolation between the output terminals [13].
3.3.1 Design Principles
To achieve the tapered power distribution of the corporate feed, the microstrip Tjunctions were designed using the lossless transmission line model as shown below.
P.
"
Zoi
Fig. 3.9 2-way unequal T-junction power divider structure
Since the lossless model is the one that is being used, the total output power
P out =
P 1+ P 2 = Pin-
Therefore, for an unequal power distribution
Pi =
KPm
,
,
Pi=(l-K)P„
0<K<\
(3.10)
The impedance at each side of the matching junction can be obtained as
7
= ^ 01
K
Z2 = ^
2 1- K
(3-11)
Thus, the total output impedance at the right side of the junction Z/HZ2 is equal to the
69
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input impedance and maintains the matched condition. Three-section wideband
Chebyshev impedance transformers are designed to match the transmission lines at the
outputs of the divider with characteristic impedance of the next stage to the desired
impedances at the junction. To reduce undesired reflection and radiation losses, optimal
miters have been employed [13].
3.3.2 Simulation Results
Simulation is performed in Ansoft HFSS. The impedances at each junction are
calculated from the power ratio shown in Table 3.1 and Eqn. 3.10 to Eqn. 3.11. The
power divider is designed on Taconic RF-60A substrate with thickness 6.5 mil and
dielectric constant 6.15. The center frequency is at 30 GHz. Figure 3.10 shows the
drawing of a 2-way unequal power divider with ports and boundary defined in HFSS. A
complete 16-way unequal power divider layout is shown in Figure 3.11. The
characteristic impedances on the three branches are 20 Cl, 30 Cl, and 40 Cl, respectively,
considering the fabrication limitation due to the multi-section impedance transformers
after each branch. The resulting narrowest line width is 35.8 pm, which is within
available fabrication limitations. The spacing of the output ports is 0.8Ao to decrease the
mutual coupling effect. The metal thickness is 10 pm.
Radiation
boundar
Port3 (w ave port)
Port2 (w ave port)
Fig. 3.10 Drawing of a 2-way unequal power divider in HFSS
70
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In
„
4 0 £2
t
\ I
C 1^
20
.....
f*\50 £2
>
I
Bottom metallization
Top metallization^ t
I
N
>
I
r W
28 0
8
7
6
5
4
3
V
2
1
Fig. 3.11 Layout of the 16-way unequal power divider
Simulated insertion losses at the
8
output terminals are shown in Figure 3.12. We can
see that the taper effect decreases with increasing frequency, which is primarily caused
by the dispersion and mutual coupling of the microstrip lines.
The normalized output power ratios at 20-, 30- and 40-GHz are read from simulation
data and they are compared with the calculated (ideal) result in Table 3.2. The sidelobe
levels of the antenna array can be calculated from the simulated amplitude taper. They
are -26 dB, -22 dB and -19 dB at 20-, 30- and 40 GHz, respectively.
P8
P7
P6
P5
P4
P3
P2
CO
~0
CD
CD
E
C
D
I -
-16
-20
20
25
30
35
40
F req (G H z)
Fig. 3.12 Simulated insertion loss of 16-way unequal power divider in HFSS
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
TABLE 3.2 Normalized Output Power Ratios
(Simulation vs. Calculation (Ideal))
P o rt No. C alculated 20 GHz
30 GHz
40 GHz
1
0.0724
0.1288
0.1995
2
3
4
5
6
7
8
0.1054
0.1988
0.3586
0.5477
0.7417
0.9090
0.1858
0.2924
0.4656
0.5272
0.7096
0.9660
0.2624
0.3598
0.4820
0.6324
0.7396
0.8395
0.3954
0.5395
0.5916
0.6266
0.6637
0.8472
0.9572
1
1
1
1
3.4 Design of Wideband Microstrip to Slotline Baiun
A microstrip to slotline balun is necessary in order to connect the power divider to the
antenna element. The balun is designed by first employing a symmetric, optimized Tjunction for signal combining/dividing and using optimal miters for the 90-degree
microstrip bends. Then, the CPS changes gradually to slotline by means of a tapered
section. Figure 3.13 shows the back-to-back balanced and unbalanced structures. The
microstrip line at the input port is assumed to have a characteristic impedance of 50 fl,
which matches the impedance of the 2.4 mm connector. The two branches have 56 Q
characteristic impedance. The 180 degrees phase delay is realized by adjusting Pi and P 2
so that Pi-P 2 = A,g/4, where Xg is the guide wavelength in the microstrip. By doing so, the
propagation mode in the coupled microstriplines will be dominantly the odd mode, which
can be easily transformed into the CPS mode after the ground plane is truncated [15]. In
addition, because this is essentially a true time delay section, wideband performance can
be expected using this approach. No via-hole is required, which makes it easier to
fabricate. To reduce undesired reflection and radiation losses at the 90-degree microstrip
72
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bends, optimal miters have been employed [15]. The taper angle 0 is optimized to be 60°
by using Ansoft HFSS. The dimensions of the structures are: W = 0.238 mm, W] = 0.305
mm, W 2 = 0.4 mm, W 3 = 0.52 mm, W 4 = 0.62 mm, L| = 1.113 mm, L 2 = 1.101 mm, L 3 =
1.057 mm, S = 0.2 mm, G = 0.1 mm, C = 0.3 mm. Figure 3.14 shows the schematic of the
back-to-back balanced structure in HFSS. The microstrip line port field is also plotted in
Figure 3.14. Figure 3.15 shows the simulated S-parameters from 20 to 40 GHz.
Top metallization
Bottom metallization
Fig. 3.13 Back-back (a) balanced and (b) unbalanced microstrip to slotline transition
Radiation
boundary
Fig. 3.14 Schematic and port field plot of the microstrip to slotline transition
73
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-10
-15
-20
-25
Q_
-30
-35
-40
20
S21
S11
S21
S11
(Balanced Structure)
(Balanced Structure)
(Unbalanced Structure)
(Unbalanced Structure)
25
30
35
40
F req (G H z)
Fig. 3.15 Simulated S-parameters of back-to-back the balanced and unbalanced
microstrip to slotline transition
3.5 Design of Fermi Tapered Slot Antenna
Tapered Slot Antennas (TSAs), also known as notch antennas, belong to the general
class of endfire traveling-wave antennas, and have been widely utilized in numerous
applications involving millimeter-wave integrated circuits over the last several decades
[16-33]. TSA has many advantages such as low profile, low weight, easy fabrication,
suitability for conformal installation, and compatibility with microwave integrated
circuits [16-33]. In addition, TSA has demonstrated multi-octave bandwidth, moderately
high gain (7-10 dB), and symmetrical E- and H-plane beam patterns [16-17]. A typical
TSA consists of a tapered slot cut in a thin film of metal, which is present on only one
side of a dielectric substrate. One end of the slot is narrowly tapered for coupling to
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
devices, and at the other end, the slot is tapered and a traveling wave propagates along the
slot in the end-fire direction with a phase velocity vph < c. The energy in the wave is
bound to the conductors in the region with small slotline separation and progressively
radiates into free space as the slot separation increases [3].
(a)
(c)
(b)
(g )
(d)
(h)
Fig. 3.16
TSA with different tapered profiles: (a) exponential, (b) tangential, (c)
parabolic, (d) linear, (e) linear-constant, (f) exponential-constant, (g) step-constant, (h)
broken-linear (the red part is the metal)
The antennas differ from each other only in the taper profile of the slot which
constitutes the radiating region of the antenna. A variety of taper profiles are illustrated in
Figure 3.15 [3]. Among them, the Vivaldi, linear, and linear-constant antennas, have been
w idely studied due to their sim ple structure, light weight, very broad bandwidth, high
efficiency, and high gain [16]. Much of the research has focused on a co-planar antenna
structure that exploits a slotline feed [16-18]. However, a subclass of these antennas is
known as antipodal tapered slot antennas. These were first suggested by Gazit in [23] and
75
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
utilize a balanced microstrip feed and a double-sided arrangement for the antenna. This
arrangement alleviates the difficulties of broadband coupling to slotline, through the
simple wideband balun that couples simple microstrip to balanced microstrip
transmission lines. Recently, a Vivaldi antenna of this sort was presented with an
operating bandwidth of
8
to 40 GHz [19, 24], However, the antipodal structure results in
higher cross-polarization because of the twisted E-field [25] (see Figure 3.16).
Bottom metallization
/
Dielectric
Top m etallization
Fig. 3.17 Antipodal Vivaldi antenna structure
In the formation of antenna arrays, small spacing between antennas is needed, as in
the case of mm-wave imaging arrays. Recently, Sugawara et al. [26] have proposed a
TSA called the “Fermi antenna”, which has a taper profile given by the Fermi-Dirac
function and a corrugation on the side of the substrate. The corrugation structure
effectively reduced the width of tapered slot antennas without degrading their antenna
patterns. They are suitable for building PAAs if the proper power feed network and phase
shifters are provided.
The geometry of the microstrip-fed Fermi tapered slot antenna with corrugations
along the sides is shown in Fig. 3.17. The antenna is designed on 6.5-mil-thick Taconic
RF-60A (sr = 6.15) substrate with 10 pm metallization on both sides. The top
76
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
metallization consists of the microstrip feed, a broadband microstrip to slotline balun, and
the Fermi antenna. The bottom metallization is a truncated microstrip ground*
cl
Bottom metallization
\
l l l l l l l l l l l .....................
W
Top metallization
Fig. 3.18 Geometry of microstrip-fed Fermi tapered slot antenna
The Fermi-Dirac taper is determined by the following equation [23]
/( * ) =
a
1
+ e
(3.12)
-b(x-c)
where a, b, and c are parameters to be determined to obtain the desired patterns. The
opening width W can be varied according to the spacing between the antenna elements.
In [26-27], it has been successfully demonstrated that the corrugations along the sides can
reduce the antenna width, improve the VSWR over a wide frequency range, and suppress
the side lobe levels. The length of the antenna is selected as
so that the taper section
exhibits traveling wave characteristics, where h) is the free spacing wavelength at 30
GHz. The dimensions of the corrugation with the width wc, the pitch dc and the length Lc
are listed in Table 3.3 [27]:
77
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TABLE 3.3 Design Parameters for Fermi TSA
Parameter X at 30 GHz
w
0.34 X
L
41
wc
L/100
Lc
0.13 X
The parameters a, b and c are determined as [27]:
a = 0.16A 0
2 .4
b = —j—
o
c = A0
(3.13)
The antenna is simulated in Ansoft HFSS. The E-plane far field radiation patterns of
two narrow-width Fermi antennas with and without corrugations along the side are
compared at 30 GHz (see Figure 3.18). The antennas have exactly the same dimensions
and utilize the same substrate. We can see the dramatic improvement in pattern with
corrugation. The surface current is plotted and shown in Figure 3.18. Without corrugation,
there are strong standing waves even at the edge of the taper. With corrugation, the
current at the edge is successfully suppressed and the antenna behaves like a traveling
wave antenna. Narrow-width linear TSA (LTSA) and Vivaldi antennas with corrugations
are also investigated and are compared with the Fermi TSA (FTSA). Figure 3.19 shows
the schematics of these three types. The corrugations, opening widths, and substrate are
the same for these three types. The simulated E- and H-plane radiation patterns shown in
Figure 3.20 show that the FTSA gives the best performance among the three. This is
because the curvature of the profile affects the beamwidth [12]. The FTSA opens out the
fastest while the Vivaldi opens out the most slowly and the LTSA is in the middle.
Consequently, the beamwidth is narrowest for the FTSA and widest for the Vivaldi. By
78
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
properly designing the parameters a, b, and c in Eqn. 3.13, the sidelobe level o f the Fermi
antenna can be optimized.
V. ’ is* , V-> «,■ ■.
' J
b
l
.SfrMj*. V .
18
12
6
CO
T3
0
•6
12
-90
E-plane
H-plane
■60
■30
E-plane
0
30
60
-2 0
90
-90
A n gle (degree)
H -p la n e
-60
-30
0
30
60
90
A n g le (degree)
(a)
(b)
Fig. 3.19 Comparison of the E-plane far field radiation patterns (a) without corrugation
and (b) with corrugation
LLUUL1LLI111I I I I I JULLUJJ.
w
86828412
(a)
(c)
Fig. 3.20 Schematics of (a) Fermi (b) linear and (c) Vivaldi tapered slot antennas
79
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
i
FTSA Eco
LTSA Eco
Vivaldi Eco
oo
LU
-10
-90
-60
-30
0
30
60
90
60
90
Angle (d egree)
30
20
o0
1
FTSA Hco
LTSA Hco
Vivaldi Hco
-10
-90
-60
-30
0
30
A ngle (d eg ree)
Fig. 3.21 Comparison of (a) E- and (b) H-plane radiation patterns of three types of TSAs
3.6 Design of Piezoelectric Transducer Controlled Delay Line on CPS
The concept of the Piezoelectric Transducer (PET) controlled delay line was first
developed and applied to a beam steering PAA system as a true time delay device by T.Y.
Yun and K. Chang [28-33]. In this approach, a piece of thick dielectric material is placed
80
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
above a transmission medium (such as microstrip line) separated by a small air gap. This
dielectric material is also attached to a DC voltage-driven piezoelectric transducer.
Applying different DC voltages will cause the transducer to move down or up (depending
upon the polarity of the bias voltage), and consequently change the air gap. The
schematic of this multilayer structure is shown in Figure 3.22. Different thicknesses of air
gap will result in different values of effective dielectric constant. Since the wave
propagation constant is dependent upon the effective dielectric constant, this will also be
changed. Therefore, a true-time delay type phase shift will be generated.
Up & Down
Supporter
Substrate
Test Fixture
CPS
Fig. 3.22 Schematic of PET controlled phase shifter
Figure 3.23 shows the multilayer structure of this type of perturbative true time
delay (TTD) line . The substrate has dielectric constant eri and thickness Hi. A piece of
dielectric material, which is used to perturb the EM field of the transmission line, has
dielectric constant £r3, thickness H3, and length L. The air gap between the substrate and
the perturbing piece is defined as H 2, which is variable. In this case, it is controlled by
the piezoelectric transducer. The effective dielectric constant can be changed by moving
81
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
the perturber up and/or down. The differential phase shift A0 caused by the perturbation
is given by Eqn. 3.14,
A 0 = Lp xA /3
(3.14)
In the above, Lp is the length of the microstrip line under perturbation and A/3 is the
difference between the unperturbed and perturbed propagation constant which is given by
Eqn. 3.15.
(3.15)
£r4 = 1
P ertu rb er
M W W b B
H2
^>2 — ^
■ B i l l B
H
m
s m
m
Fig. 3.23 Schematic of the multilayer structure of the PET controlled phase shifter
In the above, £eff( f ) is the effective dielectric constant before perturbation ( £ r3 = 1 )
and £eff ( / ) is the effective dielectric constant after perturbation ( £ r3 ^ 1). Consequently,
the delay time At generated by the perturbation is:
At ■
A(/)
360 /
(3.16)
There are many types of planar transmission line that can be used under the
perturber. Figure 3.24 shows five commonly utilized planar transmission structures,
including microstrip line, coplanar waveguide (CPW), coplanar waveguide with ground
plane (CPWG), coplanar stripline (CPS), and slot line. In [16] and [28-31], microstrip
82
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line was used as the transmission media because of the easy connection to the microstrip
power divider. However, because the field of the microstrip line is more confined within
the substrate as compared to that of CPS and CPW, it is less sensitive to the perturber
upon it and consequently, less differential phase shift is generated. It was successfully
demonstrated in [33] that CPW indeed can generate about 50% more phase shift than
microstrip line. In this design, CPS is selected not only because CPS can also generate
50% more phase shift than microstrip line, but also because the transition from CPS to a
slotline-feed antenna element is much simpler than from CPW.
(a) Microstrip Line
(b) Coplanar W aveguide
(CPW)
(c) Coplanar W aveguide with
Ground Plane (CPWG)
, E-Field Line
H-Field Line
(d) Coplanar Stripline (CPS)
(e) Slot Line
Figure 3.24 Different types of transmission lines (a) Microstrip Line (b) Coplanar
Waveguide (CPW) Line (c) Coplanar Waveguide with bottom ground plane (CPWG) (d)
Coplanar Stripline (CPS) (e) Slot Line
In Yun’s work [32], he summarized the general design rules for this piezoelectric
bender controlled delay line according to his experimental results. To maximize the
generated phase shift, several approaches can be used:
•
Higher permittivity of substrate and dielectric perturbing piece (£rj and £r3 )
•
Thicker perturbing piece (//?); at least twice that of the substrate thickness
(H3/ H i >2)
83
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In this dissertation design, Taconic RF-60A (er= 6.15) is chosen as the CPS substrate
so that the entire system can be fabricated on a single PCB. The perturber uses the same
material as the substrate with 20 mil thickness. Strong leaky waves at high frequencies
can be avoided by using the same materials for transmission line substrate and perturber
[32], The differential phase shift for microstrip line, CPW and CPS with 1 in length are
calculated using PCAAMT [34] and compared in Figure 3.25. The line width of the
microstrip line is 0.238 mm. The line width and gap width of the CPW are 0.25 mm and
0.05 mm. They both have 50 Q, characteristic impedances. The line width and gap width
of the CPS are 0.2 mm and 0.1 mm after optimizing the balun performance mentioned in
Sec. 3.4.
0
0
o>
a>
-o
-100
•200
sz
V)
<d -300
C/5
CO
_c
^ -400
CO
c
a>
0
Q
-500
CPS (s=0.2 mm g=0.1 mm)
CPW (s=0.25 mm g=0.05 mm)
Microstripline (w= 0.238mm)
-600
0.0
0.1
0.2
0.3
0.4
0.5
Air Gap Thickness (mm)
Fig. 3.25 Comparison of the differential phase shift generated by CPS (gap width g = 0.1
mm, line width = 0.2 mm), CPW (gap width g = 0.05 mm, line width = 0.25 mm) and
microstrip line (line width = 0.238 mm)
We can see that CPS can generate 50% more phase shift than microstrip line. This is
due to the fact that the electromagnetic field on a CPS is less confined than those on
microstrip lines, thereby making them more sensitive to perturbers placed above them.
84
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References
[1] R.C. Hansen, “Phased Array Antennas”, John Wiley & Sons, Inc, 1998.
[2] R. J. Mailloux, “Phased Array Antenna Handbook,” Artech House Inc., 1993.
[3] Lee, Kai Fong and Wei Chen, “Advances in Microstrip and Printed Antennas”, New
York, Wiley, 1997.
[4] Alfred T. Villeneuve, “Taylor Patterns for Discrete Arrays”, IEEE Trans. On
Antenna and Propagation, vol. AP-32, No. 10, pp. 1089-1093, Oct. 1984.
[5] Kim M., Hacker J.B., Mihailovich R.E., DeNatale J.F., “A DC-to-40GHz four-bit RF
MEMS true-time delay network”, IEEE Microw. and Wireless Let., v o l.ll, no.2, 2001.
[6 ] http://www.amicom.info/OpenPlatform/index.php/Delav lines and phase shifters.
[7] William D. Jemison, “Analysis of the AO-FDPC Optical Heterodyne Technique for
Microwave Time Delay and Phased Array Beamsteering Applications”, IEEE Trans.
MTT, vol.50, no.7, July, 2002.
[8 ] Edward N. Toughlian, Henry Zmuuda, “A Photonic Variable RF Delay Line for
Phase Array Antennas”, Journal o f Lightwave Technology, vol.8 , no.12, 1990.
[9] Istvan Frigyes, A. J. Seeds, “Optically Generated True-Time Delay in Phased-Array
Antennas”, IEEE Trans. MTT, vol.43, no.9, 1995.
[10] William D. Jemison, “Analysis of the AO-FDPC Optical Heterodyne Technique for
Microwave Time Delay and Phased Array Beamsteering Applications”, IEEE Trans.
MTT, vol.50, no.7, July, 2002.
[11] G.M. Shaw, et al., “Beam Broadening for Active Aperture Antennas”, IEEE Antenna
Propagat. Society Int. Symp., vol.l, pp. 26-30, June 1989.
85
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[12] J.U.I. Syed, “Beam Shaping by Moving the Phase Center of Array Antenna”, M TT
Proc. pp. 349-352, Aug. 1998.
[13] David M. Pozar, “Microwave Engineering”, 2nd edition, John Wiley & Sons, Inc,
1998.
[14] Mauricio Sanchez Barbetty, “Design and Implementation of a Transceiver and
Microstrip Cooperate for Solid State X-band Radar”, Master thesis, 2005.
[15] Yongxi Qian and Tatsuo Ito, “A Broadband Uniplanar Micorstrip-to-CPS transition”,
APMC, pp. 609-612,1997.
[16] P. J. Gibson, “The Vivaldi Aerial,” 9th Eur. Microwave Conf., Brighton, U.K.,
pp.101-105, 1979.
[17] L.R. Lewis, M. Fassett, and J. Hunt, “A Broadband Stripline Array Element”, IEEE
AP-S Int. Symp., Atlanta, GA, June 1974, pp. 335-337.
[18] D.H. Schaubert and J.A. Aas, “An Explanation of Some E-plane Scan Blindnesses
in Single-polarized Tapered Slot Arrays”, IEEE AP-S Int. Symp., Ann Arbor, MI, June
1993, pp. 1612-1615.
[19] Lu Yang, C.W. Domier and N.C. Luhmann, Jr., “Ka-Band E-plane Beam
Steering/Shaping Phased Array System Using Antipodal Elliptically-Tapered Slot
Antenna”, Int. Journal o f Infrared and Millimeter Waves, pp. 283-289, March, 2007.
[20] Lu Yang, N. Ito, C.W. Domier, N.C. Luhmann, Jr. and A. Mase, “20 GHz to 40 GHz
Beam Shaping/Steering Phased Antenna Array System Using Fermi Tapered Slot
Antenna”, IEEE M TT Int. Symp., Honolulu, June 2007.
86
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
[21] Kolberg, E.L., et al., “New Results on Tapered Slot Endfire Antennas on Dielectric
Substrate”, IEEE 8th Inter. Conf. on Infrared and Millimeter Waves, U.S.A., 1983, pp.
F3.6/1-2
[22] R. Janaswamy and D. H. Schaubert, “Analysis of the Tapered Slot Antenna”, IEEE
Trans. Antennas Propagat., vol. AP-35, pp. 1058-1064, Sept. 1987
[23] E. Gazit, "Improved Design of the Vivaldi Antenna," 1EE Proceedings, vol. 135, pt.
H, no. 2, Apr 1988.
[24] S. Kim and K. Chang, "Ultra Wideband Exponentially-Tapered Antipodal Vivaldi
Antennas," IEEE AP-S Int. Symp. Digest, Monterey, USA, pp. 2273-2276, Jun. 2004.
[25] J.D.S. Langley, et al., “Balanced Antipodal Vivaldi Antenna for Wide Bandwidth
Phased Arrays,” IEE Proceedings Microwave, Antenna and Propagat., vol. 143, pp. 97102, April 1996.
[26] Satoru Sugawara, Yutaka Maita, Kazuhiko Adachi, Koji Mori and Koji Mizuno, “A
mm-wave Tapered Slot Antenna with Improved Radiation Pattern”, IEEE MTT-S Digest,
pp. 959-962 1997.
[27] Hiroyasu Sato et al., “Broadband FDTD Analysis of Fermi Antenna with Narrow
Width Substrate”, IEEE Antenna & Propagat. Society Int. Symp., vol.l, pp. 261-264,
2003.
[28] T. Yun, and K. Chang, “A Low-Loss Time-Delay Phase Shifter Controlled by
Piezoelectric Transducer to Perturb Microstrip Line,” IEEE Microwave and Guided
Wave Letters, vol. 10, no. 3, pp.96-98, March 2000.
[29] T. Yun, and K. Chang, “A Low-Cost
Piezoelectric
8
to 26.5 GHz Phased Array Antenna Using a
Transducer Controlled Phase Shifter,” IEEE
Tran. Antenna
87
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and
Propagation, vol. 49, no. 9, pp. 1290-98, Step. 2001.
[30] K. Chang, M-Y Li and T.-Y. Yun “Novel Low-Cost Beam-Steering Technologies,”
IEEE Trans. Antennas and Propagation, vol. 50, No. 5, pp.618-27, May 2002.
[31] T.-Y. Yun, C. Wang P. Zepeda, C. T. Rodenbeck, M. R. Coutant, M-Y Li and K.
Chang, “A 10-to 21-GHz. Low-Cost, Multifrequency, and Full-Duplex Phased-Array
Antenna System”, IEEE Tran. On Antenna and Propagation, vol. 50, no. 5, pp.641-49,
May 2002
[32] T.-Y. Yun, “One-Dimensional Photonic Bandgap Structures and Piezoelectric
Transducer Controlled Devices for Microwave Applications,” PhD Dissertation, Texas
A&M University, 2001.
[33] San-Gyu Kim, Tae-Yeoul Yun and Kai Chang, “Time-delay phase shifter
controlled by Piezoelectric Transducer on coplanar waveguide”, IEEE Microwave and
Wireless Components Letters, vol. 13, no.l, pp. 19-20, 1993.
[34] N. K. Das and D.M. Pozar, “Personal computer aided analysis of multiplayer
transmission lines”, version 1.0, 1990.
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Chapter IV
Assembly and Testing of PAA System
The PAA system including power divider, true time delay line and Fermi antenna
array, is fabricated using the Electro-Fine-Forming (EF2) micro-fabrication technique,
developed by Kyushu Hitachi Maxell [1-2]. As the importance of millimeter-wave
imaging diagnostics increases, the fabrication of high performance millimeter-wave
planar components such as high-frequency planar antennas and filters becomes essential
[1]. In this technique, the adhesion of copper to the substrate is improved using surface
treatment of fluorine films by radiation-induced graft polymerization [2]. In addition, it
can provide excellent pattern without side edges [1-2]. High frequency planar antennas
and frequency selective filters with narrow line width on large printed circuit boards have
been successfully fabricated using this technique in a low cost [3-4].
4.1 Measurement of Wideband Microstrip Line to Slotline Baiun
The wideband microstrip line to slotline balun is measured using an HP 851 OB
network analyzer. Two 2.4 mm end launch connectors at the ends of the balun connect
the microstrip circuit to the coaxial cables. Figure 4.1 shows the photographs of the
fabricated back-to-back balanced and unbalanced structures.
89
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(b)
Fig. 4.1 Photographs of back-to-back (a) balanced and (b) unbalanced microstrip to
slotline transition
The measured S-parameters are plotted together with simulation results as shown in
Figure 4.2. We can see that the basic trend of the measured and simulated results agrees
quite well. It is believed that the deviations from predicted values are due primarily to the
extra transition from microstrip line to CPWG, which is required to connect the end
launch connectors to the circuit. This extra transition is not considered in the simulation.
90
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CD
T3
v_
0
1
0
?
11J
ill
E
0
i_
0
CL
CD
Simulated S
— Simulated S
Measured S
Measured S
40
Freq
CD
CD
E
-20
0
1—
0
CL
CD
-30
— Simulated S.
— Simulated S
— Measured S 2
— Measured SH
-40
20
30
25
35
40
F req (G H z)
Fig. 4.2 Measured S-parameters of back-to-back (a) balanced and (b) unbalanced
microstrip to slotline balun
91
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4.2 Antenna Array Measurement
4.2.1 UC Davis Anechoic Chamber
The antenna measurement facility at UC-Davis consists of an anechoic chamber
configured to serve as an indoor compact range. This chamber is realized by completely
covering all room surfaces with pyramidal shaped wave absorber to eliminate reflection
from various surfaces. This serves to provide a nonreflecting environment similar to free
space. However, the distance requirement is usually a limitation in simple indoor ranges.
Generally, anechoic chambers may be designed as rectangular or tapered in shape
depending on their purpose. The shape of the UC-Davis anechoic chamber is tapered
from the source, which results in a flatter taper, to reduce reflection from the walls [W.H.
Emerson, 1965], [W.H. Kummer, 1978]. The operating frequency range of the anechoic
chamber is directly indicated by the dimensions of the absorbers; the ECCOSORB @
VHP-4 pyramids absorbers used in the UC-Davis chamber can achieve at least -3 0 dB
maximum reflectivity above 3 GHz [W.H. Emerson, 1973][W.D. Burnside, 1987],
(a)
92
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission
(b)
(c)
Fig. 4.3 Photographs of (a) UC Davis anechoic chamber overview, (b) inside antenna
mounting and (c) transmitting horn mounting
4.2.2 LabView Code Development for Instruments Control
The far field radiation patterns of the PAA and substrate lens antenna (see Chapter V)
systems are both measured in the anechoic chamber. Different instruments are used to
perform the measurements. The antenna under test is mounted onto a 2-D rotation stage
inside the chamber. A new LabView code is developed to combine these two sets of
antenna measurement setups into one code. In addition, a sensitivity selector code is
written to select the optimum sensitivity range of the lock-in amplifier automatically in
the substrate lens antenna measurement so that the dynamic range is significantly
increased.
A real time plot function makes it easier to check errors during the
measurement. Figure 4.4 shows the code interface.
93
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
HP8510 Network Anglyjer 2
(by L /q itj)
j
P o sitio n N ow ( d e g r e e ) |l o . 0 0
S c a n High E nd (d e g r e e ) ^ 150.00
w
•
j
Total ste p s |141
S c a n L o w End (d e g re e )
R e so lu tio n ( d e o r e e )
]
Scan Angle
[
jiS l.Q O .
|
ccw
jjP W j
S y m m etric s c a n
( j HP8 5 1 D N e tw o rk A n alyzer
^
StatusliJi/Vaiting for someone to hit the 'go' button...
O V E R ID E
i6®/ W a i f o f f for* use)
Direction (t=cw ):
|
6 o /v V a it
Scan Direction
cw
M OTOR.
E - P la n e
D a ta Collection
Ooctods.
|
N um ber o f d e g r e e :
j j g W " ”’",]
S p e e d (m s p e r s te p ):
j
f l s .........1
(default = Sms/step)
Analyzer Initial Setup
P ow er O n / O f f
(s e t b e fo r e running..Pow er O n /O ff o f f + <3o /W oit on)
% .................................. d
Stimulus Mode (T :S in g le)|
0
§ )
i S t o u x t o , ]
Stop Freq (2 .G e a H z I
Single
C ontinual
Num of Points (2 :2 01)1
51 -p i
5 -o a ra m e te r ( 3 :5 2 2 ) 1
io i - h
201-p i
521-fe
512-p
401 - b
S2 2 - ^ l
Display Mode (4:Four Par S plit) j
Steoocooooo.oooD
SOI - f *
]»
! Imaginary
Channel (F :C h 1) |
H
E
C h an nel 2
C h an nel 1
1
Initial Sensitivity]
]
2 5 uV
_vj
y .
^
“1
j
f
M agnitude
|
,
V C fT ”
iC
y
0
Ui)
iPlot Frequency!
^ Mid Freq
Fig. 4.4 LabView code for antenna measurements
4.2.3 Beam Steering Demonstration
The beam steering PAA system consists of a wideband
8
-way equal power divider,
wideband microstrip to slotline transition, and Fermi tapered slot antenna with
corrugations. The spacing between each element is 0.66L> Three-section Chebyshev
impedance transformers are used to cover the wide bandwidth [3]. The input port has
characteristic impedance of 50 Q. to match the connector. Figure 4.5 shows the schematic
of the measurement setup. The antenna array is mounted onto a 2-D rotation stage inside
the chamber. 18- to 40 GHz LNAs from MITEQ [5] and Spacek Labs [6 ] before the horn
and after the PAA boost the signal power and increase the dynamic range. The far field
radiation patterns are measured using an HP 851 OB network analyzer. High frequency
94
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low loss cable from Insulated Wave [7] connects the amplifier output to the network
analyzer.
8510 Network A nalyzer
A nechoic C ham ber
A ntenna u n d er te s t
2-D rotation s ta g e
Low lo ss cable
C om puter
GPIB cable
Fig. 4.5 Schematic of measurement setup
Figure 4.6 shows the schematic and photograph of the beam steering PAA. The
system is fabricated on a single PCB Taconic RF-60A (er = 6.15, loss tangent = 0.0028)
with thickness 6.5 mil for easy integration and it avoids the extra loss caused by the
connection of different circuit pieces. The perturber uses the same material as the
substrate with thickness 20 mil to avoid strong leaky waves at high frequency [4], To
generate a linear wavefront in beam steering, the perturber is cut linearly from 35 mm on
the 1st CPS to 0 mm on the 8 th CPS as shown in Figure 4.6.
95
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1
2
3
4
5
6
7
8
Dielectric perturber
Fig. 4.6 (a) Schematic and (b) photograph of beam steering demonstration
When the DC bias voltage applied to the PET is 0 V, the perturber just touches the
transmission line, corresponding to the maximum perturbation. From previous
measurements [8 ], when the bias voltage exceeds 40 V, the perturbation effect is
negligible. Consequently, the variation range of the DC bias voltage is from 0 V to 40 V.
Figure 4.7 shows the measured return loss of the system. The VSWR is less than 2 in the
designed frequency range. E-plane far field radiation patterns are measured from 18- to
40 GHz as shown in Figure 4.8. The PAA shows a -16° to +19°, -17° to +19°, -14° to
96
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+17° beam scanning ranges at 20-, 30-, and 40 GHz. The measured H-plane radiation
pattern is plotted in Figure 4.9.
co
co
O
_i
c
-15
-t—'
CD -20
cr
-25
-30
20
30
25
35
40
Freq (GHz)
Fig. 4.7 Measured return loss of beam steering PAA system
97
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0
oc
No perturbation
Maximum perturbation left scan
Maximum perturbation right scan
-90
-60
-30
0
30
60
90
Angle (degree)
17 1+19
3 0 GHz
00
i—
o
£
o
Q_
0
>
_co
0
DC
N o perturbation
Maximum perturbation right sca n
Maximum perturbation left sca n
-30
Angle (degree)
98
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90
0
4 0 GHz
-10
m
CD
5
Q.
CD
o
>
-30
i3
0
DC
-40
-50
-90
No perturbation
Maximum perturbation right scan
Maximum perturbation left scan
-60
-30
0
30
60
90
A n g le (d e g r e e )
Fig. 4.8 Measured E-plane far field radiation patterns for 8 -element PAA at (a) 20-, (b)
30- and (c) 40 GHz in beam steering demonstration
0
30 GHz
•5
00
0
-10
o
CL
0
>
jo
-15
0
DC
-20
-25
-90
-60
-30
0
30
60
90
A n g le ( d e g r e e )
Fig. 4.9 Measured H-plane far field radiation patterns at 30 GHz for 8 -element PAA
99
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4.2.4 Beam Shaping Demonstration
The beam shaping system consists of a wideband 16-way unequal power divider,
wideband microstrip to slotline transition and Fermi antenna array. The spacing between
elements is 0.8A<). The perturber is cut according to a quadratic function to generate a
quadratic wavefront. The length of the perturber is 10 mm at the center and 0 mm at the
edge (see Figure 4.9). The minimum beamwidth is obtained when the phase distribution
across the antenna array aperture is uniform (no perturbation). The beamwidth increases
as the phase taper increases. Photographs of the beam shaping PAA are shown in Figure
4.10. The measured system return loss is shown in Figure 4.11. The VSWR is less than 2
in the designed frequency range. The measured beam broadening results are shown in
Figure 4.12. At 40 V bias voltage (no perturbation), the sidelobe levels are -27 dB, -23
dB, and -20 dB at 20-, 30-, and 40 GHz corresponding to the lowest sidelobe levels. The
results agree very well with simulation results in Sec. 3.3.2. The increase of the SLR at
high frequencies is attributed to the fact that the amplitude taper effect decreases and the
mutual coupling between antenna elements increases. The sidelobe increases as the
beamwidth increases. With the amplitude taper, the sidelobe level is controlled to be
below -15 dB at the widest beamwidth up to 40 GHz. The 3dB and lOdB beamwidths are
widened by about 12° and 18°, which satisfy the requirement for MIR system (See
chapter II). The measured H-plane radiation pattern is shown in Figure 4.13. Because
there is only one element in the H-plane, the pattern is much wider than that of the Eplane.
100
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1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16
D ie le c tr ic p ertu rb er
Fig. 4.10 M easured E-plane far field radiation patterns at 20, 30 and 40 GHz
101
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-15
c
-20
0
DC
-25
-30
35
30
25
20
40
F req (G H z)
Fig. 4.11 Measured return loss of beam shaping PAA system
0
26
GHz
-10
CO
33,
0
5
-20
o
CL
CD
> -30
CD
DC
-40
-50
-90
M axim um perturbation
N o perturbation
-60
-30
0
30
60
A n g le (d e g r e e )
102
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90
36 GHz
m
;u
CD
5
o
CL
<D
>
CD
cc
M a x im u m p e r tu r b a tio n
N o p e r tu r b a tio n
-30
0
30
A n g le (d e g r e e )
40GHz
> -30
-50
-90
M a x im u m p e r tu r b a tio n
N o p e r tu r b a tio n
-60
-30
0
30
60
90
A n g le (d e g r e e )
Fig. 4.12 Measured E-plane far field radiation patterns at (a) 20-, (b) 30- and (c) 40 GHz
in beam shaping demonstration
103
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30 GHz
co
|
-10
o
CL
CD
g
co
-15
CD
QC
-20
-25
-90
-60
-30
0
30
60
90
A n g le (d e g r e e )
Fig. 4.13 Measured H-plane far field radiation patterns at 30 GHz for 16-element PAA
104
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References
[1] Naoki Ito, Atsushi Mase, Noriaki Seko, Masao Tamada, Eiji Sakat and Yuichiro Kogi,
“Surface Treatment of Poly(tetrafluoroethylene) and Perfluoroethylene-propylene by
Radiation Grafting”, Japanese Journal o f Applied Physics, vol.45, no. 12, 2006, pp.92449246.
[2] Naoki Ito, Atsushi Mase, et al., “Advanced Fabrication Method of Planar Components
for Plasma Diagnostic”, Plasma and Fusion Research, vol.l, 2006.
[3] Lu Yang, Naoki Ito, C.W. Domier, N.C. Luhmann, Jr and A.Mase, “20 GHz to 40
GHz Beam Shaping/Steering Phased Antenna Array System Using Fermi Tapered Slot
Antenna”, IEEE M TT Int. Symp., Honolulu, June 2007.
[4] Z. Shen, N. Ito, E. Sakata, C.W. Domier, Y. Liang, N.C. Luhmann, Jr. and A. Mase,
“Frequency Selective Surface Notch Filter for Use in a Millimeter Wave Imaging
System”, IEEE AP-S Int. Symposium, June 2006, Albuquerque, NM.
[5] David M. Pozar, “Microwave Engineering”, 2nd edition, John Wiley & Sons, Inc,
1998.
[4] N.K.Das and D.M.Pozar, “Full-wave Spectral-domain Computation of Material,
Radiation, and Guided Wave Losses in Infinite Multiplayered Printed Transmission
Lines,” IEEE Trans. Microwave Theory and Tech., vol. 39, no. 1, pp.54-63, Jan. 1991.
[5] Model No.: JF-18004000-30-8P
[6 ] Model No.: SLKKa-30-6
[7] Cable Series: 150
[8 ] Chiachan Chang, “Microwave and Millimeter Wave Beam Steering/Shaping Phased
Antenna Arrays and Related Applications”, Ph.D dissertation, 2003.
105
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Chapter V
Q- to V-Band 1-D/2-D Elliptical Lens Antenna Arrays
The concept of quasi-optical beamforming by means of substrate-lens antenna
combinations is well established and extensively explored with a focus on applications in
radio astronomy and remote sensing at 100-150 GHz and above; see, for example [1-3].
Attempts have also been made to apply the substrate lens technique for wireless
communications at 30 GHz [4].
Quasi-optical planar antenna mixers offer an attractive advantage over wave-guide
based mixers at millimeter wave frequencies. They are smaller and lighter than wave­
guide systems and can be easily produced in large numbers for low cost applications such
as millimeter wave imaging systems. In the NSTX MIR system, a quasi-optical antenna
mixer system is employed as shown in Figure 5.1. It transforms a radio frequency (RF)
signal reflected from the plasma cutoff layers into an intermediate frequency (IF) signal
immediately after the antenna receives the spatially combined RF and the local oscillator
(LO) signals. The downconverted signal will then go to the IF electronic circuits for
further processing and detection [5].
In designing the focal plane imaging antenna array, there are a large number of
physical phenomena and practical considerations that need to be taken into account; they
include optimization of the antenna pattern, RF frequency bandwidth, local oscillator
coupling efficiency, and inter-array coupling. The specific goal of the dissertation work
106
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described in this chapter is developing a 2-D imaging receiving array for use in the
NSTX MIR system.
Mixer;
A n ten n a T
;iFA m p
l-Q M ix e r
F ilte r s
D A C s
V id e o A m p s i
P la s m a
Fig. 5.1 Schematic of an MIR receiving system
5.1 General Analysis and Design
As mentioned in Sec. 1.1.3, an elliptical lens antenna is an ellipsoid cut off at a plane
perpendicular to its major axis at its second geometric focus, with a planar antenna
mounted on the flat surface, resulting in a far-field pattern with a main beam that is
diffraction limited by the aperture of the elliptical lens. The diffraction-limited patterns
have been verified for log-periodic and spiral antennas [7], a simple dipole antenna [8 ], a
dual dipole antenna [9-10], a double slot antenna [1] and a bow tie antenna [16]. A dual­
dipole antenna is chosen as the feed antenna for the elliptical lens in order to realize a
simple and compact structure. Dual-dipole antennas have been previously used by A.
Skalare et al. in SIS receivers at 100 and 400 GHz [7]. Recently, S.V. Shitov et al. has
developed a 1-THz low noise SIS mixer with dual-dipole antenna on a hemispherical
single-crystal silicon (er = 11.7) coated with a 200-nm-thick Nb film on one side [10].
The lens also has an antireflection coating made of a 46-pm-thick layer of Stycast-1264
107
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(er = 2.9) epoxy compound [10]. This coating acts like a quarter-wavelength impedance
transformer at 960 GHz.
In this dissertation design, the elliptical lens is made of a low cost machinable glassceramic MACOR with dielectric constant 5.62. The reason to choose this material is
explained in Sec. 1.1.3. The millimeter and sub-millimeter wave dielectric parameters of
this material have been investigated in [6 ].
The schematic of the elliptical lens is shown in Figure 5.2. It is known from optics
that for a given index of refraction n, the eccentricity of the ellipse is
. . c l
eccentricity = —= —.
b n
(5.1)
where n is the index of refraction of the lens [ 1 1 ].
The defining equation for the ellipsoid is:
2
2
2
V ^ r + V i
a b a
(5-2)
From the above, we can derive that:
a
b—
(5.3)
(5.4)
n
In the above, a, b, and c are the minor radius, major radius and focal length of the
ellipsoid. er is the effective dielectric constant of the lens material.
The dual dipole antenna patterns are calculated assuming a sinusoidal electric-current
distribution on the wires and using an array factor in the H-plane direction. The dipole
lies in the x-z plane as shown in Figure 5.2. The normalized electric field radiated into the
dielectric by the dual dipole is [ 1 1 ],
108
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A
s in 0 [ c o s ( k e lc o s 0 ) - c o s k m l]
Ee =
-cos k e —sintfcosy?
V
( k ^ - k ^ C O S 2 0)
(5.5)
2
where km = 2 n /\m , Xm is the geometric mean wavelength given by
= XQ/ J i ~ ,
em =(i+er ) / 2 , ke = 2 jt/xdiel for the dielectric side, and ke = 27t/^air for the air side [1]. The
length and width of the antenna are / and d, respectively.
7
I = 0.375k
(d x ,d y ,d z )
d = 0.213A0 a
¥
a = 35 mm
b = 38.6 mm
c = 16.3 mm
Fig. 5.2 The elliptical lens and the ray-tracing/field-integration technique
The vector normal to the ellipsoid surface is given by
^ 2 x: s
2y s
2zs
(5.6)
V a 2 ’ ub 2 ’ a 2y
where (xs, ys, zs) are the surface coordinates.
The transmission coefficients for the perpendicular and parallel electric field
components are
2n cos0-
T± =
I
ncosGj + J l - n
2
.
sin
2
(5.7)
0j
109
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and
2ncos0-
T/ / =
1
2 .2
cosGj + n-Jl - n sin 0^
'
(5'8)
where 0; is the incident angle. The fields across the surface of the lens are
E = Tj_Ej_n + T //E //(sx h)
(5 .9 )
H = -(sxEt)
h
where s is the ray path vector outside the lens, E^ and
(5.10)
are the perpendicular and
parallel electric field components inside the ellipsoid. Once the electric and magnetic
fields have been found, the equivalent electric and magnetic current densities are
calculated just outside the spherical surface using
Js = n x H
(5.11)
Ms = - n x E
(5.12)
where n is the vector normal to the air/lens interface. In the far field, the transverse
electric field is equal to [ 1 1 ]:
E „ s - j ! ^ ( L t + n N ,)
(5.13)
(5 .1 4 )
Am
In the above, N and L are defined by:
N = \ \ J s e i k r 0 0 S ¥ ds
(5.15)
L = \\M s e ik rC 0 S y /ds
(5.16)
110
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I
I
where .v is the closed surface just outside then lens, r is the distance from the center of
the ellipsoid to the equivalent electric and magnetic currents, and r is the distance from
the origin to the far field point. The far field patterns can then be calculated using the
field equivalence principle [13]. The complete code is written in MATLAB and is
provided in Appendix B.
Figure 5.3 shows the calculated far field radiation patterns for a 4-element dual dipole
array in the E- and H-planes at 60 GHz. The distance from the center of the lens to the
antenna element is d. The dimensions of the antenna and lens are shown in Figure 5.2.
m
d=0
d = 80 mil
d = 160 mil
d = 2 4 0 mil
-10
CD
O
a.
-20
CD
>
33
CD
OC
-30
-40
60
80
100
120
A n g le (d e g r e e )
(a)
111
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d = 0 mil
d = 8 0 mil
00
T3,
d = 2 4 0 mil
-10
5—
CD
5
O
CL
-2 0
CD
>
jo
CD
K
-3 0
-4 0
60
80
100
120
A n g le (d e g r e e )
(b)
Fig. 5.3 Calculated 4-element antenna array patterns in (a) E-plane and (b) H-plane
5.2 MACOR Elliptical Lens Antenna Array Measurement
5.2.1 Sensitivity Measurement
The envelope of the high frequency signal can be detected by direct rectification of
the signal by nonlinear devices such as a Schottky diode. This detection scheme is
commonly known as video detection or direct detection [14]. Compared with heterodyne
detection, video detection has a lower sensitivity, but it is much simpler, which makes it
an inexpensive and attractive method for measuring power in many laboratory
experiments [15]. In this measurement, an Aeroflex flip chip Schottky diode [17] is
epoxy-attached at the center of the antenna on a coplanar stripline (CPS) to detect the
received signal power. The antenna far- field patterns are measured from 38 GHz to 75
GHz in an anechoic chamber at UC Davis. Figure 5.4 shows the schematic of the
112
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
measurement setup. The BWO source was modulated at 1 kHz and the output from the
diode was fed to a lock-in amplifier. The detected voltage is read from an HP 34410
multi-meter. A LabView code (see Sec. 4.2.2) is written to control the rotation stage
inside the chamber and record data.
The sensitivity is defined as the ratio of the diode output voltage to the signal
transmitted from the horn. Many factors can affect the received signal power, such as
reflection loss at the air/lens interface, MACOR absorption loss, the RF matching, and
diode junction/parasitic resistance/capacitance. The Schottky diode used to detect the
power in this experiment is purchased from
a commercial company,
so its
junction/parasitic resistance/capacitance are fixed. The sensitivity for a fixed lens
material then can be optimized by selecting the proper antenna dimensions. Dual-dipole
antennas of three different sizes are measured and compared. These antennas are
fabricated on 20 mil Taconic RF-60A (er = 6.15) so that the dielectric constant of the
substrate is similar to that of the lens material (sr = 5.62). Figure 5.5 shows the measured
results. The antenna having a length of 74 mil and width of 42 mil gives best sensitivity
performance from Q- to V-band.
113
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DC
Bias
Lock-In ___ ^ HP 34401A
Amplifier
multi-meter
Computer
V-band BWO *
4
Function
generator
Frequency
meter
HP436A
power meter
Fig. 5.4 Experimental setup of substrate lens antenna measurement
The RF and low frequency circuit analyses have been investigated in detail in [14-16]
to theoretically calculate the sensitivity. From the equivalent circuits [14-16], the
sensitivity is theoretically calculated from 38- to 75 GHz (see Figure 5.6 (a)). In the
calculation, the antenna parameters such as the input impedances are obtained from
HFSS simulation. The diode junction capacitance and resistance are obtained from
Aeroflex flip chip Schottky diode MGS801 datasheet. Figure 5.6 shows the calculated
and measured sensitivity from 38- to 75 GHz using the antenna of 74 mil length and 42
mil width. We can see that the basic trends agree very well although there are some
deviations. The sensitivity peak appears at almost the same frequency. The deviations
might be caused by various reasons, such as uncertainty in power-meter calibration
factors, system losses and the fact that two different horns were used for the Q- and V
114
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band measurements, so the beam characteristics (beamwidth, gain, etc.) are different. In
addition, MACOR absorption losses are different at different frequencies [6 ].
140
d = 42 mil l=74 mil
d = 49 mil l=62 mil
d = 49 mil l=74 mil
120
100
>
co
c
CD
CO
35
40
45
50
55
60
65
70
75
Freq (GHz)
Fig. 5.5 Measured sensitivity of antennas of different sizes
-10
-12
4
4.5
5
5.5
Freq
6
6.5
7
7.5
x 1010
(a)
115
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>>
>
-4—'
CO
c
a)
CO
■a
CD
N
-14
35
40
45
50
55
60
65
70
75
Freq (GHz)
(b)
Fig. 5.6 (a) Calculated and (b) measured sensitivity (normalized)
5.2.2 Single Beam Measurement
The single antenna far-field radiation patterns are measured from 38- to 75 GHz. The
antenna is located at the center of the lens. Measured results are compared with
theoretical calculation (see Figure 5.7) at 60 GHz. As can be seen, there are small
differences between theoretical and measured results. This is attributed primarily to the
mismatch of the dielectric constant between the antenna substrate and the lens material.
The coplanar strip line (CPS), which lies in the H-plane and is used to carry out the low
frequency signal, causes a small asymmetry in the H-plane. The center channel antenna
performances throughout Q-band and V-band were measured and the results are shown in
Figure 5.8. Table 5.1 lists the measured and calculated 3-dB beamwidth from 38- to 75
GHz for E- and H-plane. They agree very well.
116
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-•— Measured Eco
— Calculated Eco
-10
0Q
©
s
Q.
a)
-20
o
-
-30
-40
-30
-20
-10
A ngle (d egree)
* — Measured Hco
Calculated Hco
-10
co
I -20
o
Q.
©
- -30
ro
©
QL
-i—<
-40
-30
-20
-10
A ngle (d egree)
Fig. 5.7 Calculated and measured (a) E- and (b) H-plane radiation patterns at 60 GHz
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
38 GHz
45 GHz
50 GHz
o -20
££ -40
-40
-30
-20
-10
0
10
30
20
40
Angle (degree)
38 GHz
45 GHz
50 GHz
5, -10
o -20
£ -30
-40
-40
-30
-20
-1 0
0
10
30
20
40
A ngle (degree)
■— 55GHz
60GHz
•— 65GHz
> -- 70GHz
75GHz
% -2 0 -
-40
-30
-20
-1 0
0
10
20
30
40
Angle (degree)
ffl
55GHz
60GHz
65GHz
70GHz
75GHz
.10
% -2 0 -
<d -40-40
-30
-20
-10
0
10
20
30
40
A ngle (degree)
Fig. 5.8 Measured (a) Q band E-plane, (b) Q-band H-plane (c) V-band E-plane and (d) Vband H-plane far field radiation patterns
118
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TABLE 5.1
Measured and Calculated Full 3-dB Beamwidth for E- and H-planes
Freq (GHz)
38
45
50
55
60
65
70
75
Measurement
6.9°
5.8°
5.0°
4.6°
4.2°
4.0°
3.8°
3.6°
Calculation
7.0°
6.0°
5.2°
4.8°
4.4°
4.2°
4.0°
3.8°
Measurement
6.0°
5.6°
5.2°
4.4°
4.2°
4.0°
3.75°
3.5°
Calculation
6.2°
5.6°
5.0°
4.6°
4.3°
4.18°
CO
3.6°
E-plane
H-plane
o
00
5.2.3 Multiple-Beam Measurement
The off-center characteristics of the elliptical lens have been characterized by
measuring a 13-element 1-D array and an
8
x 4-element 2-D array. Figure 5.9 are the
photographs of the 1-D array. The spacing between each element is 80 mil. The stacked
rectangular structure has been chosen for compactness resulting in better spatial
resolution for the plasma imaging system application.
9
1
j r
11
.1 3
T r J L - ir
T 2 T 4
8
I
10 *12
’
(a)
119
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(b)
(c)
Fig. 5.9 Photographs of (a) 1-D 13-element dual-dipole array, (b) array mounted on the
lens and (c) elliptical MACOR lens mounted on a 2-D rotation stage
The measured E-plane radiation patterns are shown in Figure 5.10 with the numbers
labeled as shown in Figure 5.9 (a). Theoretical steering angles for off-axis antenna
elements can be calculated using the method described in Sec. 5.1. They are compared
with the measurement results in Figure 5.11. The difference increases for the channels
located further away from center. This is because an increased portion of the beam was
blocked by the side of the lens for elements far away from center.
. A 2-D 8 x 4 array was designed, fabricated on the same substrate, and tested (Figure
5.12). The elements are arranged in a rectangular stack so that the structure is more
compact and the signal is easily carried out by CPS to the following IF circuit [5]. The
distance between elements in the E- and H-planes is chosen to be 72 mil. The E-plane
and H-plane radiation patterns are measured and plotted in Figure 5.13 with the number
labeled as shown in Figure 5.12. The 2-D array launches 32 beams with 3-dB beamwidth
120
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overlapping between adjacent beams and 3-dB scan coverage of about 70° in the E-plane
and 20° in the H-plane.
,A .
-10
o5 -20
<— 10
12
co -30
-40
-40
-30
-20
-10
0
10
20
30
40
Angle (degree)
Fig. 5.10 Measured E-plane radiation patterns for the 1-D array
35
• M easured steerin g a n g le
■»— C alculated steerin g an gle
30
$ 25
O)
CD
2 20
CD
5CD 1 5
CD
CO
0
2
4
6
8
10
12
14
Distance from center (mm)
Fig. 5.11 Measured and calculated steering angles
121
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Fig. 5.12 Photo of 8 x 4-element 2-D dual dipole array
OQ -10
T3
\/
%-20
o
Q.
^ -30
-40
-30
-20
-10
Angle (degree)
co -10
"O
-20
*v
CL
a) -30
-40
-40
-30
-20
-10
0
10
20
30
40
Angle (degree)
Fig. 5.13 Measured (a) E- and (b) H-plane radiation patterns for 2-D array at 60 GHz
122
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5.2.4 Angular Field of View Measurement
In multi-channel measurements, the peak power of an antenna element decreases as
the element is located further away from the center of the lens. The angular field of view
determined from the half power points, is a figure-of-merit to decide the scanning range
of a substrate lens antenna [15]. The theoretical normalized peak responsivity can be
calculated using the approach described in Sec. 5.1. Figure 5.14 shows the measured and
calculated normalized peak responsivity for the MACOR elliptical lens at 60 GHz. The
deviations may be caused by the uncertainty in power-meter calibration factors, unstable
BWO output power, and other system losses. The full angular field of view determined
from the half power points is approximately 30°. Therefore, the scanning range of the
8
x
4 2-D antenna array is just within the angular field of view.
— M easured
<»— C a l c u l a t e d
o
>
0.8
V)
S
cn
0.6
CD
^
0.4
0.2
0.0
-12
8
4
0
4
8
12
A n te n n a p o sitio n (m m )
Fig. 5.14 Measured and calculated normalized peak responsivity for MACOR elliptical
lens measured at 60 GHz
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
References:
[1] D. F. Filipovic, S. S. Gearhart and G. M. Rebeiz, “Double-Slot Antennas on Extended
Hemispherical and Elliptical Silicon Dielectric Lenses”, IEEE Transaction on M TT 41
(1993), no. 10, 1738-1749.
[2] G. M. Rebeiz, “Millimeter-wave and Terahertz Integrated Circuit Antennas”, Proc o f
I E E E m (1992), no. 11, 1748-1770.
[2] B. K. Kormanyos, P. H. Ostdiek, W. L. Bishop and T. W. Crowe, “A Planar
Wideband 80-200 GHz Subharmonic Receiver”, IEEE Transaction on M TT 41 (1993),
no. 10, 1730-1737.
[4] X. Wu, G. V. Eleftheriades and T. E. v. Deventer-Perkins, “Design and
Characterization of Single and Multiple-beam mm-wave Circularly Polarized Substrate
Lens Antennas for Wireless Communications”, IEEE Transaction on M TT 49 (2001), no.
3, 431-441.
[5] C.W. Domier, Z.G. Xia, P. Zhang and N.C. Luhmann, Jr., “Upgrades to the TEXTOR
Electron Cyclotron Emission Imaging Diagnostic”, Review o f Scientific Instruments 77,
10E924, 2006.
[6 ] M. N. Asfar and K. J. Button, “Millimeter and Sub millimeter Wave Measurement of
Complex Optical and Dielectric Parameters of Materials. Ii. 5 mm to 0.66 mm for
corning macor machinable glass ceramic”, Int. J. o fIR and M M Waves 3 (1982), 319-329.
[7] H. van de Stadt, Th. de Graauw, A. Skalare, R.A. Panhuyzen, R. Zwiggelaar,
“Millimeter and Submillimeter Studies of Planar Antennas, ” First Int. Symp. on Space
Terahertz Technology, Ann Arbor, MI, pp. 235-255, Mar. 1990.
124
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
[8 ] C. J. Adler, C. R. Brewitt-Taylor, M. Dixon, R. D. Hodges, L. D. Irving, and H. D.
Rees, “Microwave and Millimeter-wave Receivers with Integral Antennas,” IEEE Proc.H, vol. 138, pp. 253-257, 1991.
[9] A. Skalare, H. van de Stadt, Th. De Graauw, R.A. Panhuyzen, and M.MT.M. Dierichs,
“Double-dipole Antenna SIS Receivers at 100 and 400 GHz”, Proc. 3rd Int. Conf. Space
Terahertz Technology, Ann Arbor, MI, pp. 222-233, March 1992.
[10] S.V. Shitov, A.V. Markov, B.D. Jackson, A.M. Baryshev, N.N. Iosad, J.R. Gao and
T.M. Klapwijk, “ 1-THz low-noise SIS mixer with a Double-dipole Antenna”, Technical
Physics, vol.47, no.9, 2002, pp. 1152-1157.
[11] E. Hecht, Optics, 2nd Edition, Reading, MA: Addison-Wesley, pp. 129-131, 1987.
[12] R.S. Elliott, Antenna Theory and Design, New Jersey: Prentice-Hall, Chap. 4, 1981.
[13] SILVER, S. (Ed): “Microwave Antenna Theory and Design”, IEE series on
Electromagnetic waves (Peter Peregrinus, 1984).
[14] A. Kreisker, M. Pyee and M. Redon, “Parameters Influencing for Infrared
Videodetection with Submicron-size Schottky Diode”, Int. J. o f Infrared and Millimeter
Waves, vol. 5, No. 4, pp. 559-584, 1984.
[15] Chung-en Zah, Dayalan Kasilingam, John Steven Smith and Davis Rutledge,
“Millimeter Wave Monolithic Schottky Diode Imaging Arrays”, Int. J. Infrared and
Millimeter Waves, vol.6 , no. 10, 1985.
[16] Li Xizhi and P.L. Richard, “SIS Quasiparticle Mixers With Bow-tie Antennas”, Int.
J. o f Infrared and Millimeter Waves, vol.9, no.2, 1988, pp.101-133.
[17] S. Dixon, T.R. AuCoin and R.L. Ross, “60 GHz Planar Doped Barrier Subharmonic
Mixer”, 8th Int. Conf. on Infrared and Millimeter Waves, T 6.9, 1983.
125
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Chapter VI
Conclusions and Future Work
6.1 Conclusions
In this dissertation, investigation into a number of innovative technologies was
performed in order to develop novel components for potential utilization in various high
frequency imaging and radar applications.
Wideband, variable beamwidth/scan angle beam shaping/steering PAAs are necessary
for many radar and communication systems. This dissertation has demonstrated an
inexpensive approach for producing such PAA systems using wideband, high gain Fermi
tapered slot antennas and piezoelectric true time delay phase shifters on CPS together
with amplitude taper across the antenna array. The systems are fabricated on a single low
cost PCB substrate using Electro Fine Form (EF2) micro-fabrication technology to avoid
the extra loss caused by connection of different circuit pieces and for easier integration
and simpler circuit structure [1-2]. By adding an amplitude taper across the array, not
only does the useful range of the beam broadening increase, but also the side lobe levels
are effectively suppressed. Using CPS under the PET-controlled phase shifter effectively
increases the progressive phase shift and the system has low return losses from 18 to 40
GHz with and without perturbation.
The
8
-element beam steering PAA shows -16° to +19°, -17° to +19°, -14° to +17°
beam scanning ranges at 20-, 30-, and 40 GHz. The measured beam scanning range is
about 4° less than the simulation results. This is attributed to the bender tile producing an
126
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uneven air gap between the dielectric perturber and antenna board, the eight outputs of
the power divider not being exactly the same causing unequal amplitude excitation to
each antenna element, the individual antenna element being imperfectly flat, and also
because of the mutual couplings between antenna elements. In the 16-element beam
shaping PAA system, the sidelobe levels are -27 dB, -23 dB, and -20 dB at 20-, 30-, and
40 GHz corresponding to the lowest sidelobe levels, which agree very well with
simulation results. The side lobe levels increase at high frequency. This is attributed to
the fact that the amplitude taper of the power divider decreases and the mutual coupling
between antenna elements increases at high frequencies. With the amplitude taper, the
sidelobe level is controlled to be below -15 dB at the widest beamwidth up to 40 GHz.
The 3-dB and 10-dB beamwidths are widened by about 12° and 18°, which satisfy the
requirements for the MIR system. The technology is inherently scalable to larger arrays
and higher frequencies using more advanced fabrication techniques and should have
wide-ranging applications.
In the receiving antenna system, 38 GHz to 75 GHz single-beam and multiple-beam
dipole antenna arrays on an elliptical lens were designed, implemented using low cost
MACOR, and experimentally characterized [10-11]. The single-beam antenna shows a
4.2° 3-dB full beamwidth and -16 dB side lobe ratio at 60 GHz. Theoretical and
measured beamwidths agree very well. In the multiple-beam demonstration, both 13element 1-D and
8
x 4-element 2-D antenna arrays are tested. Off-center characteristics
of the elliptical lens have been characterized and a stacked rectangular array has been
chosen for compactness resulting in better spatial resolution for the plasma imaging
system and the CPS can easily carry out the signal from each channel to the following IF
127
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circuits. The 2-D array launches 32 beams with 3-dB beamwidth overlapping between
adjacent beams and a 3-dB scan coverage of about 70° in the E-plane and 20° in the bi­
plane, which is required by the intended 2-D imaging reflectometric system. The
measurement results agree well with theoretical calculations for both the center and offcenter antennas. Sensitivity was measured for antennas of three different sizes and the
optimum one chosen for the final array design. Sensitivity was also theoretically
calculated and compared with experimental results. The angular field of view was
measured and theoretically analyzed to determine the scanning range of the lens. The
array will be used in an optical system for MIR application on the NSTX plasma device
to detect and image electron density fluctuations.
6.2 Future Work
6.2.1 Other True Time Delay Technologies
This work has successfully demonstrated the beam steering/shaping phased antenna
array design with sidelobe suppression, both theoretically and experimentally. This
wideband system is designed to operate from 18- to 40 GHz, in which the frequency is
close to, but still lower than, the frequency range of the MIR system intended for on
installation on the NSTX plasma device (38- to 52 GHz initially and eventually up to 75
GHz).
There are many advantages associated with the PET controlled line, such as wide
bandwidth, simple structure, low cost, high power handling capability, low power
consumption, and continuous phase control. [14]. Applications up to 40 GHz have been
demonstrated in several papers [1-8]. However, as the antenna element number increases
128
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and/or the scanning range increases, the required time delay increases. Because the time
delay is proportional to the transmission line length, the length increases and therefore the
system becomes relatively bulky. What is more, losses including dielectric loss,
conductor loss and radiation loss associated with planar transmission line all increase and
dispersion effects also degrade the performance of the PET controlled delay line at high
frequencies [9]. For future practical use in an actual MIR system, there exist many
possibilities which could be explored in terms of design improvements and adjustment.
6.2.1.1 Distributed RF MEMS True Time Delay Line
The distributed RF MEMS true time delay line [12] is a good candidate at high
frequencies to generate the required time delay due to its low loss, compact size,
relatively high modulation speed (ms), and high power-handling capacity. The main
advantages of MEMS capacitors are a high Q when using metal as a structural material,
a mechanical structure that isolates the control circuit from the signal circuit, and
mechanical inertia that prevents modulation of the capacitance value by the RF signal
[12]. Figure 6.1 shows the structure of an extended tuning range MEMS varactor. The
pull-in effect is the major limitation in MEMS varactor designs. It occurs when the DC
bias causes the air gap to decrease below 1/3 of the entire gap. At that time, the two
metal plates will quickly snap into contact. This effect will cause nonlinearity and
mechanical instability of the MEMS varactors. To prevent snap down, in older MEMS
varactor designs, the capacitance ratio Cmax/Cmin of the MEMS varactor had to be
limited to less than 1.5. By using the extended tuning range structure shown in Figure
5.2, if the distance di between the two signal electrodes Ei and E 2 is less than d 2/ 3 , the
129
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upper beam Ei is constrained to travel a maximum distance of di. As this is less than
the pull-in limit of d 2 / 3 , the pull-in effect will not occur and the theoretical capacitance
tuning range can go to infinity [13].
Fig. 6.1 Extended tuning range MEMS varactor structure
The prototype of a 28 GHz MEMS extended tuning range varactor is currently being
studied by fellow student Yaping Liang. The photographs of the fabricated delay line are
shown in Figure 6.2.
60 GHz MEMS extended tuning range varactor delay lines have been simulated in
Ansoft HFSS (see Figure 6.3) by Yaping Liang for future practical use in an actual MIR
system. The simulation results show that the 7-section delay line can generate 217.97°
phase shift at 60 GHz with 1.77 dB insertion loss. The length of each section is 160 pm.
130
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Fig. 6.2 Photographs of the extended tuning range MEMS varactor structure (courtesy of
Y. Liang)
%
Fig. 6.3 3-D Drawing of 7-section MEMS delay line in F1FSS (courtesy of Y. Liang)
6.2.1.2 Liquid Crystal Beam Former
In liquid crystal (LC) materials, the dielectric constant is anisotropic, which means it
is different in the direction along the director (molecule) from the one in the direction
131
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perpendicular to it. This occurs when the charge distribution along the molecule responds
differently to the parallel component of the local electric field than the distribution
perpendicular to the length does to the perpendicular component, yielding a difference in
dielectric constants. When an electric field is applied, the molecule tends to rotate and
align parallel or perpendicular to the electric field which depends on whether the LC has
positive or negative anisotropy. Therefore, the dielectric constant can be changed [7]. In
recent years, LC material has received increased attention. It has been investigated from
microwave to THz frequencies [14-19] and employed successfully in numerous
applications such as tunable capacitor [14], tunable-frequency antenna [15] and LC beam
former (LCBF) [16-18]. Because the frequency range of LCBF is well suited for the
MIR system on the NSTX plasma device, this is another possible beam shaping approach
for plasma imaging application.
In [16], a LC beam former (LCBF) has a structure consisting of LC layers and the
control electrodes alternately stacked (see Figure 6.4).
By controlling the voltage
between the electrodes, the orientation of the LC molecule can be changed so that the
permittivity of the layer can be changed. Experimental results show that the beam former
can generate 420° phase shift at 60 GHz when a 120 Vrms voltage is applied. The total
loss including dielectric loss and conductor loss is 8.5 dB at 0 Vrms and 6.4 dB at 120
Vrms. A V-band horn antenna attached to the LCBF has a ±13° beam scanning range (see
Figure 6.5). By controlling the applied voltages properly, the LCBF also has a beam
shaping function, which is particularly important in the application to the MIR system. In
addition, because this is essentially a true time delay technology, wideband operation is
expected and has been experimentally proved [16],
132
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it can steer millimeterwave beam
A- V l
Electrode
(10 ; , m thiCk)
I
Control
voltage
— - I source
M illim e te rw ave
(horizontally
polarized)
J 7
2 4 0 quid crystal
electrode
layers
a n d ele
c tro d e layers
(ap p ro x . 25 m m )
rL± d f f i i l ayer
(1 0 0 w m thick)
S tructure of liquid crystal millimeter-wave beam form er
Fig. 5.4 Structure of millimeter wave beam former using Liquid Crystal [10]
Fig. 5.5 Measured radiation pattern at different frequencies in Y-band [10]
6.2.2 Multi-Frequency Illumination Source
In the NSTX MIR system, a multi-frequency probe beam needs to be launched into
the plasma. In collaboration with Kyungpook National University, a 47- to 54 GHz
illumination source is currently being investigated by the UC Davis millimeter wave
group. Figure 5.6 shows the schematic of the transmitting system. Eight IF frequencies
from 2- to 9 GHz are first upconverted by a 45 GHz oscillator. The eight upconverted and
133
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filtered signals are combined into a multi-frequency signal and amplified by a U-band
power amplifier. The amplified signal is then sent to the antenna system. Fabricated
modules including a 45 GHz oscillator, mixer, power amplifier by Kyungpook National
University together with bean shaping PAA which are described in this dissertation are
also shown in Figure 5.6 [20-25].
A ntenna
Mixers W aveguide
I
Filter
Microstrip
Power
Combiner
U- B a n d \
Power Amplifier
Fig. 5.6 Generation of multi-frequency illumination source for NSTX MIR system; the
modules are fabricated by Kyungpook National University [25]
6.2.3 Selection of Lens Materials for Substrate Lens Antenna
MACOR has been chosen as the substrate lens material in this dissertation. There are
several other materials that have the potential to be used in the design, such as highresistivity Si, Alumina, and Quartz. Table 6.1 shows the comparison of these materials.
We see that MACOR has the highest absorption loss among them. Si has the widest
angular field-of-view and Quartz has the narrowest. The higher the dielectric constant of
the material, the wider the angular field-of-view is. Consequently, for large antenna array
134
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requiring wide scanning range, lens material with high dielectric constant is preferred.
The reflection loss at lens/air interface is due to the mismatch of the refractive index. Si
has the highest reflection loss because it has the highest refractive index. The use of a
matching cap might be necessary to reduce the power loss [25-27]. Another consideration
is the injection of the LO power. In the current design, LO power is injected from the
back of the lens onto the antenna. The ratio of powers between the dielectric and air is
s r3/2 for an elementary slot antenna and erfor an elementary dipole antenna [24], where er
is the relative dielectric constant of the lens. Therefore, it is difficult to get enough LO
power using high dielectric constant lens material if the LO is injected from the back of
the lens. However, if the LO power can be designed so that it is injected from the front or
side, high dielectric constant and low loss materials are good candidates because they can
provide wider scanning range than low dielectric constant materials, which is particularly
important for detecting a large number of channels in the plasma imaging application.
TABLE 6.1 Comparisons of Si, Alumina, Quartz and MACOR Lens
Material
Si
Alumina
Quartz
MACOR
Absorption loss
Good
Good
Very Good
Not good
(neper/cm)
(0.14)
(0.1)
(0.03)
(0.38)
Good
Good
Not good
Medium
(40°)
(38°)
(20°)
(30°)
Not good
Not good
Good
Medium
(1.52
(1.36)
(0.78)
(0.95)
Cost
Expensive
Expensive
Expensive
Cheap
LO from back
Bad
Bad
Good
Medium
Angular field of view
Reflection loss (dB)
135
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References:
[1] Lu Yang, N. Ito, C.W. Domier, N.C. Luhmann, Jr. and A. Mase, “20 GHz to 40 GHz
Beam Shaping/Steering Phased Antenna Array System Using Fermi Tapered Slot
Antenna”, IEEE M TT Int. Symp., Honolulu, June 2007.
[2] Lu Yang, C.W. Domier and N.C Luhmann, Jr, “Ka-Band E-plane Beam
Steering/Shaping Phased Array System Using Antipodal Elliptically-Tapered Slot
Antenna”, Int. J. o f Infrared and Millimeter Waves, March 2007, pp.283-289.
[3] T.-Y. Yun, “One-Dimensional Photonic Bandgap Structures and Piezoelectric
Transducer Controlled Devices for Microwave Applications,” PhD Dissertation, Texas
A&M University, 2001.
[4] T. Yun, and K. Chang, “A Low-Loss Time-Delay Phase Shifter Controlled by
Piezoelectric Transducer to Perturb Microstrip Line”, IEEE Microwave and Guided
Wave Letters, Vol. 10, No. 3, pp.96-98, March 2000.
[5] T. Yun, and K. Chang, “A Low-Cost
8
to 26.5 GHz Phased Array Antenna Using a
Piezoelectric Transducer Controlled Phase Shifter”, IEEE Tran. On Antenna and
Propagation, Vol. 49, No. 9, pp. 1290-98, Step. 2001.
[6 ] K. Chang, M-Y Li and T.-Y. Yun “Novel Low-Cost Beam-Steering Technologies”,
IEEE Trans. On Antennas and Propagation, Vol. 50, No. 5, pp.618-27, May 2002.
[7] T.-Y. Yun, C. Wang P. Zepeda, C. T. Rodenbeck, M. R. Coutant, M-Y Li and K.
Chang, “A 10-to 21-GHz. Low-Cost, Multifrequency, and Full-Duplex Phased-Array
Antenna System”, IEEE Tran. On Antenna and Propagation, vol. 50, no. 5, pp.641-49,
May 2002.
136
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
[8 ] Sang-Gyu Kim and Kai Chang, “Ultra wideband
8
to 40GHz beam scanning phased
array using antipodal exponentially-tapered slot antennas”, IEEE MTT-S Digest., 2004, 3,
pp.1757-1760.
[9] Tae-Yeoul Yun and Kai Chang, “Analysis and Optimization of a phase shifter
controlled by a Piezoelectric Transducer”, IEEE Trans, on MTT, vol.50, no.l, Jan. 2002,
pp. 105-111.
[10] Lu Yang, C.W. Domier and N.C. Luhmann, Jr., “38 GHz to 75 GHz 1-D and 2-D
MACOR elliptical lens antenna arrays”, IEEE Antenna Propagat. Society Int. Symp.,
Honolulu, June 2007.
[11] Lu Yang, C.W. Domier and N.C. Luhmann, Jr., “Q-band to Y-band 1-D and 2-D
Elliptical Ixns Antenna Arrays”, to be published on Microwave and Optical Technology
Letters, 2007.
[12] H. Nieminen, V.Ermolov, et. al, “Microelectromechanical capacitors for RF
Applications”, Journal o f Micromechanical Microengineering, 12 (2002), pp: 177-186.
[13] http://tempest.das.ucdavis.edu/mmwave/MEMs/RFMEMS/
[14] J. Andrew Yeh, C. Alex Chang, Chih-Cheng Cheng, Jing-Yi Huang and Shawn S.H.
Hsu, “Microwave Characteristics of Liquid-Crystal Tunable Capacitors”, IEEE Electron
Device Letters, vol.26, no.7, July 2005, pp.451-453.
[15] Noham Martin, Paul Laurent, Christian Person Philippe Gelin and Fabrice Huret,
“Patch Antenna Adjustable in Frequency Using Liquid Crystal”, 33rd European
Microwave Conference, Munich 2003, pp.699-702.
137
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
[16] Hirokazu Kamoda, Takao Kuki, Hideo Fujikake and Toshihiro Namoto,
“Millimeter-wave Beam Former Using Liquid Crystal”, Electronics and Communication
in Japan, part 2, vol.8 8 , no.8 , 2005, pp.34-41
[17] Hirokazu
Kamoda, Takao Kuki, Hideo Fujikake and Toshihiro Namoto,
“Millimeter-wave beam former using liquid crystal” 34th European Microwave
Conference, Amsterdam, 2004, pp.l 141-1144.
[18] Hirokazu Kamoda, Takao Kuki and Toshihiro Namoto, “Conductor Loss Reduction
for Liquid Crystal Millimeter-wave Beam Former”, IEICE Electronics Express, vol.2,
no. 18, pp.471-476.
[19] Chao-Yuan Chen, Cho-Fan Hsieh, Yea-Feng Lin Ru-Pin Pan and Ci-Ling Pan,
“Magnetically Tunable Room-temperature 271 Liquid Crystal Terahertz Phase Shifter”,
Optics Express, vol. 12, no. 12, June 2004, pp.2630-2635
[20] Tae-Jong Baek, Baek-Seok Ko, Dong-Hoon Shin, Sung-Chan Kim, Byoung-Ok
Lim, Soon-Koo Kim, Hyun-Chang Park, and Jin-Koo Rhee, “Fabrication of Band-reject
Filter Using Dielectric-Supported Air-Gapped Microstrplines”, Microwave and Optical
Technology Letters, vol.44, n o .l, Jan. 2005, pp. 1-4
[21] Bok-Hyung Lee, Dan An, Mun-Kyo Lee, Byeong-Ok Lim, Sam-Dong Kim, and
Jin-Koo Rhee, “Two-stage Broadband High-gain W-band Amplifier Using 0.1-pm
Metamorphic HEMT Technology”, IEEE Electron Device Letters, vol.25, no. 12, Dec.
2004, pp.766-768
[22] Kang Wook Kim, Chae-Ho Na, and Dong-Sik Woo, “New Dielectric-Covered
Waveguide-to-Microstrip Transitions for Ka-band Transceivers”, IEEE MTT-S Digest,
2003, pp. 1115-1118
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[23] Kang Wook Kim, “Millimeter-wave Module Technology”, Presented at Int.
Workshop at KASTEC, Dec. 15th, 2005
[24] D. F. Filipovic, S. S. Gearhart and G. M. Rebeiz, “Double-slot Antennas on
Extended Hemispherical and Elliptical Silicon Dielectric Lenses,” IEEE Trans, on
Microwave Theory and Tech, 41 (1993), no. 10, pp.1738-1749.
[25] Chung-en Zah, Dayalan Kasilingam, John Steven Smith and Davis Rutledge,
“Millimeter Wave Monolithic Schottky Diode Imaging Arrays”, Int. J. Infrared and
Millimeter Waves, vol.6 , no. 10, 1985.
[26] S.V. Shitov, A.V. Markov, B.D. Jackson, A.M. Baryshev, N.N. Iosad, J.R. Gao and
T.M. Klapwijk, “ 1-THz low-noise SIS Mixer with a Double-Dipole Antenna”, Technical
Physics, vol.47, no.9, 2002, pp. 1152-1157.
[27] D. F. Filipovic, S. S. Gearhart and G. M. Rebeiz, “Double-slot Antennas on
Extended Hemispherical and Elliptical Silicon Dielectric Lenses”, IEEE Transaction on
M TT 41 (1993), no. 10, 1738-1749.
139
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Appendix A
VILLENEUVE
n
Array Distribution Calculation
For an array consisting of N elements, the amplitude excitation coefficients are
slightly different for even and odd N.
For an even number of element N - 2M , the following relations hold:
q = \Qsrft/20
m0 = cosh
'Fp =
2
<7 -
^ l n ^ +V ^ l )
2M
71
arccos —cos( 2 p - l )
,
2(2M -1 )
un
p = 1,......, 2 M - l
rnt
n ln
2M ¥ -
2M arccos
— — COS
fe w -l)
Uq
71------- r
-
2{2M - l )
where SLR is the sidelobe ratio
The coefficient are now given by,
aP = ^ 7
2M
1
2M
2
/^ le x p { -;[(p -l/2 )m 2 ^ /(2 M )]} ,
m=_(„_D V 2M
E(0) + 2X E
m=l
f m 2n^
COS
V
2M
( p - 1/ 2 )
J
-{ M -\)< p < M
mK
M
and
n-1
mn
2 M ( - l ) mf [ s i n
2M
^ m27T^
\2 M j
sin(
mn
\
sin
m7T
,2 M
v
- a
1-----2
/
. ( 2 m n '\j-y . f( m - q ) n ^ \ . f(m + q)n
sin
)sin --------11 sin
2M
I 2M ) l 1
2M
^ 2M
q^m
n
140
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
n-1
9
sin
2A^]~J si
v
9=1
E( 0) = -
r i s'n
9=1
2
/
v2 M y
For an odd number of elements N = 2M + 1 , the relations are:
H7C
rilK
<7 =
in
¥-
(2 M + 1) arccos — cosf (2 n - l ) ^ un
V
AM
Uq = cosh
-cos
'i'p = 2 arccos
AM
v
,
P = 1,......,2M
The coefficient are now given by,
rt-1
m27t
exp{- y[(/? - 1 / 2)m27U!{2M + 1)]},
a n ~ --------
p
2M + i1 m =£- ( n - l) * V 2M +1
1
2M +1
£ (0 ) + 2
yl J
h
m27t
\2 M + \
pm27t
cos
n- 1
^ m 2 ;r N
2 M+1
9=1
■M < p < M
(2M +1)
m 7t
( 2 M + 1 )(—1 ) mJ~[ sin
v
2M + 1
- M < p <M
2
'P.
sin
y
v
2M+1
2
( m - q ) ^ . f{m + q)7T
2m n \ n- 1
.
.
ra/r . .
sin
sin(--------- ) sin
7
j
n
sin
2M+1
2M +1
2M + A/tf==l
V 2M +1
q&m
The aperture efficiency can be computed by summing virtual mutual resistance, using
the formula,
f
G=
N
V2
v«=i
N
N
sin c[(n-m )kd]
n=1 m=l
141
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
MATLAB code is written based on the above formula to calculate the amplitude
distribution.
For N = 8, SLR = 35 dB and n = 4 , the amplitude distribution is plotted in Figure A. 1
1 .0 - 1 ---- 1---- 1---- 1---- 1---- 1---- 1---- 1---- 1
i---- 1---- 1---- 1---- r
0 .8 -
E lem en t N um ber
Fig. A .l YILLENEUVE n amplitude distribution for N = 8 , SLR = 35 dB and n = 4
For N - 16, SLR = 35 dB and n = 4 , the amplitude distribution is plotted in Figure
A.2
142
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
1-0
1 i ■ i 1 i 1 i ■ i ■ i ■ i 1 i 1 i ■ i 1 r~r i ■ i 1 i ■
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16
E lem en t N um ber
Fig. A.2 VILLENEUYE n amplitude distribution for N = 16, SLR = 35 dB and n = 4
143
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Appendix B
Calculation of Far-Field Radiation Patterns of DualDipole Antenna Array on Elliptical Lens in MATLAB
This MATLAB code is written to calculate the far-field radiation patterns of dual­
dipole antenna array on elliptical lens. Scan angles and angular-field-of-view can also be
calculated using this code. This calculation is based on [1-3].
fc= 6 0 e9 ;
% Center frequency
c= 3e8;
lem d a = c/f* 1 0 0 0 ;
%WaveIength in free space [unit: mm]
lem d a c= c/fc* 1 0 0 0 ; %Center w avelength in free space [unit: mm]
er=5.62;
% D ielectric constant o f the lens material
nlens=crA0.5;
% Refractive index o f lens
lem dadie=lem da/(er)A0.5; % WaveIength in the dielectric side
e m = (er + l)/2 ;
% E ffective dielectric constant
lem d am =lem d a/(em )A0.5; %EITective w avelength
k=2*pi/lem da;
km =2*pi/lem dam ;
ke=2 * p i/lem d ad ie;
l= 0 .6 * lem d a c/2 /1 .6 ;
% Dual d ip o le antenna length
d = 0 .3 4 * le m d a c /l .6;
% D ual d ip o le antenna width
a=35;
% M inor radius o f the lens [mm]
b=a/( 1- l/n le n sA2 )A0.5 ; % M ajor radius o f the lens [mm]
c= (b A2 -a A2 )A0.5;
% Focal length
R =aA2/b;
% R adius at the cutting plane
% A ntenna location (dx,dy,dz). A ntenna is in x -z plane
dx=0;
dy=-c;
dz=-0;
%Change dz w ill change the steering angle in E-plane
em ta=377;
% Intrinsic im pedance
th eta= 50* p i/1 8 0 :p i/3 6 0 :1 3 0 * p i/1 8 0 ;
phy=pi/2;
steps=90;
% Plot is from 3 0 to 150 degree
% E-plane plot
% C alculation resolution
%theta2 and phy2 are source point on the aperture
p hy2=0 * p i/180:pi/steps: (p i-0 * p i/180);
theta2=-0 * p i/180 :pi/steps:(p i+ 0 * p i/l 80);
% D efin e unit vector x, y z in cartesian coordinate
xha=[l 0 0];
yh a=[0 1 0];
zha=[0 0 1];
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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
for i= 1 :length(phy2)
coeff(q ,i)= sin (th eta 2 (q ))A2 * co s(p h y 2 (i))A2 /a A2+ co s(th eta 2 (q ))A2 /a A2+sin (th eta2(q ))A2 * sin (p h y 2 (i))A2 /b A2;
%tempR is the radius o f the point(theta, phy) o f the ellip so id in polar coordinate
tem pR (q,i)=( l/c o e ff(q ,i))A0 .5 ;
% any point on the surface o f the lens (xs, ys, zs)
xs(q ,i)= tem p R (q ,i)*sin (th eta2(q ))*cos(p h y2(i));
ys(q ,i)= tem p R (q ,i)*sin (th eta2(q ))*sin (p h y2(i));
zs(q ,i)=tem p R (q ,i)*cos(th eta2(q ));
n = [2 * x s(q ,i)/a A2 2 * y s(q ,i)/b A2 2 * zs(q ,i)/a A2];
n=n/norm (n); %n is the norm alized normal vector o f the ellip soid surface
v = [x s(q ,i)-d x y s(q ,i)-d y zs(q ,i)-d z];
nv=v/norm (v); %nv is the norm alized vector b etw een feeding point and point on the surface
Pv=cross(n,nv); % B asis vector o f the E -filed that lie s in the plane perpendicular to the incident w ave
cth eta(q)=(zs(q,i)-dz)/norm (v); % Coordinate transform ation, ctheta and stheta are cos(thetad)and
stheta(q)=( 1-cthcta(q)A2 )A0 .5 ; % sin(thetad) where thetad is the theta w here d ip ole center is the origin
if ((x s(q ,i)-d x )= = 0 & y s(q ,i)= = 0 ) % lies in the z axis
stheta(q)=0;
phy tem p(q ,i)= p i/2 ;
e ls e if ((x s(q ,i)-d x )= = 0 & y s(q ,i)~ = 0 ) % lies in y axis
sth e ta (q )= l;
p hytem p(q,i)=pi/2;
e lse
if (y s(q ,i)-d y )/(x s(q ,i)-d x )> = 0
p h ytem p (q ,i)= atan ((ys(q ,i)-d y)/(xs(q ,i)-d x));
else
p h ytem p (q ,i)= atan ((ys(q ,i)-d y)/(xs(q ,i)-d x))+ p i;
end
end
cphy(q ,i)=cos(p h ytem p (q ,i)); % Coordinatc transformation, cphy and sphy arc cos(p h yd ) and sin(phyd)
sphy(q,i)=sin(phytem p(q,i)); %whcrc phyd is the phy where dipole center is the origin
%total incident E field o f the antenna elem ent in sid e the lens
E d x = sth eta(q )*sp h y(q ,i)*(cos(k e*l*cth eta(q ))-cos(k m *l))/(k m A2keA2*ctheta(q)A2 )* cos(k e*d /2*sth eta(q )*cp h y(q ,i));
E d y= -sth eta(q )*cp h y(q ,i)*(cos(k e*l*cth eta(q ))-cos(k m *l))/(k m A2k eA2*ctheta(q)A2 )* cos(k e*d /2*sth eta(q )*cp h y(q ,i));
E d=[E dx E dy 0];
if (n orm (P v)==0) % if v and n have the sam e direction (y in this case), then E on ly has E x com ponent
P v n = -(-sin (p h y2(i))*xh a+ cos(p h y2(i))*yh a);
Ppn=n;
E p h yd = -sin (p h y2(i))*E d x+ cos(p h y2(i))*E d y;
Ethetad=0;
sn=n;
else
P vn =P v/n orm (P v);
P pn=cross(Pvn,nv); % B asis vector o f the E -filed that lies in the plane parallel to the incident w ave
P p n x (q ,i)= P p n (l);
P pny(q,i)=P pn(2);
P pnz(q,i)=P pn(3);
cothetai(q,i)=dot(n,nv); %The c o s o f the insident angle is the angle betw een vector n and vector v
sith eta i(q ,i)= (l-co th eta i(q ,i)A2 )A0.5; %The sin o f the insident angle is Lhe angle b etw een vector n
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and vector v
thetai(q,i)=asin(sithetai(q,i)); %The insident angle is the angle betw een vector n and vector v
sithetatr(q,i)=sithetai(q,i)*nlens; %The refractive angle
%tao and gam m a is the transm ission and reflection co efficien t
if abs(sithetatr(q,i))<= 1
thetatr(q,i)=asin(sithetatr(q,i));
coth etatr(q ,i)=(l-sith etatr(q ,i)A2 )A0.5;
ta o v (q ,i)= 2 * n len s* co th eta i(q ,i)/(n len s* co th eta i(q ,i)+ (l-n len sA2*sith etai(q ,i)A2 )A0.5);
gam m av(q,i)=tao v (q ,i)-1;
taop (q ,i)= 2 * n len s* co th eta i(q ,i)/(co th eta i(q ,i)+ n len s* (l-n len sA2*sith etai(q ,i)A2 )A0.5);
g a m m a p (q ,i)= l-ta o p (q ,i)* (l-n le n sA2 * sith etai(q ,i)A2 )A0.5/cothetai(q,i);
else
thetatr(q,i)=pi/2;
cothetatr(q,i)=0;
taov(q ,i)=0;
taop(q,i)=0;
end
%s is the ray path vector outside the lens
s=nv*cos(thetatr(q,i)-thetai(q,i))+Ppn*sin(thetatr(q,i)-thetai(q,i));
sn=s/norm (s);
sx (q ,i)= sn (l);
sy(q ,i)= sn (2);
sz(q ,i)=sn (3);
E phyd=dot(E d, Pvn); % Perpendicular E field in sid e the sphere
E thetad=dot(Ed, Ppn); % Parrallel E field inside the sphere
end
E =taov(q,i)*E phyd*P vn-taop(q,i)*E thetad*cross(sn,P vn); %The electric field outside the lens
H =cross(sn,E )/em ta;
Js=cross(n,H ); % Surface electric current on the lens
J sx (q ,i)= J s(l);
Jsy(q,i)=Js(2);
Jsz(q,i)=Js(3);
M s=-cross(n,E );
% Surface m agnetic current on the lens
M sx (q ,i)= M s(l);
M sy(q ,i)= M s(2);
M sz(q ,i)= M s(3 );
end
end
% B elow is the calcualtiori o f radiation based on integration m ethod once w e know Js and M s
for q = l:len gth (th eta)
r= [sin(theta(q))*cos(phy) sin(theta(q))*sin(phy) cos(theta(q))];
su m N l= 0 ;
% suniNi and sum Li are initial value for integration later
sum N 2=0;
su m L l= 0 ;
sum L2=0;
for m = l :length(theta2)
sum thetaN 1=0;
sum thetaN 2=0;
sum thetaL l=0;
sum thetaL2=0;
for i= l:len gth (p h y2)
sou rce= [tem p R (m ,i)*sin (th eta2(m ))*cos(p h y2(i)) tem pR (m ,i)*sin (th eta2(m ))*sin (p h y2(i))
tem p R (m ,i)*cos(th eta2(m ))];
tem p=dot(source,r);
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Reproduced with permission o f the copyright owner. Further reproduction prohibited without permission.
tem p 2 = tem p R (m ,i)* (sin (th eta 2 (m ))* co s(p h y 2 (i))* sx (m ,i)+ sin (th eta 2 (m ))* sin (p h y 2 (i))* sy (m ,i)+ co s(th eta2(
m ))*sz(m ,i));
tem p=tem p-tem p2;
N th eta= (Jsx(m ,i)*cos(th eta(q ))*cos(p h y)+ Jsy(m ,i)*cos(th eta(q ))*sin (p h y)Jsz(m ,i)*sin (th eta(q )))*exp (j*k *(tem p ))*tem p R (m ,i)A2;
N p h y = (-Jsx(m ,i)*sin (p h y)+ Jsy(m ,i)*cos(p h y))*exp (j*k *(tem p ))*tem p R (m ,i)A2;
L th eta = (M sx(m ,i)*cos(th eta(q ))*cos(p h y)+ M sy(m ,i)*cos(th eta(q ))*sin (p h y)M sz(m ,i)*sin (th eta(q )))*exp (j*k *(tem p ))*tem p R (m ,i)A2;
L p h y = (-M sx (m ,i)* sin (p h y )+ M sy (m ,i)* co s(p h y ))* ex p (j* k * (tem p ))* tem p R (m ,i)A2;
su m th etaN l= su m th etaN l+ N th eta*p i/step s;
sum thetaN 2=sum thetaN 2+N phy*pi/steps;
sum thetaL 1=sum thetaL 1 +Ltheta*pi/steps;
sum thetaL 2=sum thetaL 2+L phy*pi/steps;
end
sum N 1= su m N 1+ su m th etaN 1 *pi/steps *sin (th eta2(m ));
su m N 2=su m N 2+ su m th etaN 2*p i/step s*sin (th eta2(m ));
sumL 1= sum L 1+sum thetaL 1 * p i/step s*sin (th eta2(m ));
su m L 2=sum L 2+sum thetaL 2*pi/steps*sin(theta2(m ));
end
N thetafinal(q)=sum N 1;
N phyfinal(q)=sum N 2;
L thetafinal(q)=sum L 1;
L phyfinal(q)=sum L 2;
E theta(q)=-j*(L phyfinal(q)+em ta*N thetafinal(q));
H theta(q)=-j*(L thetafinal(q)/em ta-N phyfinal(q));
E phy(q)=j*(L thetafinal(q)-em ta*N phyfinal(q));
H phy(q)=-j*(L phyfinal(q)/em ta+N thetafinal(q));
% B elow is the phase calculation
if (im ag(E p h y(q ))<0 & real(E phy(q))<0)
phase(q)=atan(im ag(E phy(q))/real(E phy(q)))-pi;
e ls e if (im ag(E p h y(q ))> 0 & real(E p h y(q ))>0)
phase(q)=atan(im ag(E phy(q))/real(E phy(q)))-2*pi;
e ls e if (im ag(E p h y(q ))< 0 & real(E phy(q))>0)
phase(q)=atan(im ag(E phy(q))/real(E phy(q)));
e ls e if (im ag(E p h y(q ))> 0 & real(E phy(q))<0)
phase(q)=atan(im ag(E phy(q))/real(E phy(q)))-pi;
e ls e if (im ag(E p h y(q ))— 0 & real(E phy(q))>0)
phase(q)=0;
e ls e if (im ag(E p h y(q ))= = 0 & real(E phy(q))<0)
phase(q)=-pi;
e ls e if (im ag(E p h y(q ))> 0 & real(E phy(q))==0)
p h ase(q)=-3*pi/2;
e ls e if (im ag(E p h y(q ))< 0 & real(E phy(q))== 0)
phase(q)=-pi/2;
end
Etotal(q)=((norm (E theta(q)))A2+ (norm (E phy(q)))A2 )A0.5;
H total(q)=((norm (H theta(q)))A2+(n orm (H p h y(q )))A2 )A0.5;
end
N th etafin ald B = 20*logl0(n orm (N th etafin al));
N p h y fin a ld B = 2 0 * lo g l0 (n o rm (N p h y final));
L th etafin ald B =20*logl0(n orm (L th etafin al));
L p h yfin ald B = 20*log 10(norm (L phyfinal));
147
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
E thetad B = 20*log 10(abs(E theta));
E p h y d B = 2 0 * lo g l0 (a b s(E p h y ));
E d B = 2 0 * lo g 10(E to ta l);
figure (1) % Total E -field at E-plane [dB]
plot(theta* 180/p i, ((E d B )-m ax((E d B ))))
axis ([3 0 150 -3 0 0])
figure (2 ) % C ross-polarization at E-plane
plot(theta*180/pi,(E thetadB -m ax(E thetadB )))
figure(3) % C o-polarization at E-plane
plot(theta* 180/p i,(E p h yd B -m ax(E p h yd B )))
axis ([30 150 -3 0 0 ])
figure (4) % Total E -field at E -plane [arbitrary unit]
plot(theta* 180/pi,E total/m ax(E total))
axis ([3 0 150 0 1])
figure (5 ) % Phase plot
plot(theta* 180/pi,phase* 180/p i)
axis ([3 0 150 -3 6 0 0])
148
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References:
[1] Daniel F. Filipovic, Gildas P. Gauthier, Sanjay Raman and Gabriel M. Rebeiz, “OffAxis Properties of Silicon and Quartz dielectric Lens Antennas”, IEEE Trans, on Antenna
and Propag., vol.45, no.5, May 1997, pp.760-766.
[2] W. B. Dou, G. Zeng, and Z. L. Sun, “Pattern Prediction of Extended Hemisphericallens/objective-lens Antenna System at Millimeter Wavelength”, IEE Proceeding, 1998,
pp.295-298.
[3] C. A. Balanis, Antenna theory analysis and design, John Wiley & Sons, 1997.
149
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A ppendix C
Dynamic Range and Standard Gain Horn Measurement
C.l Dynamic Range Measurement of the 8510B Network Analyzer
An HP 8510B Network Analyzer is used to measure the far field radiation patterns.
The dynamic range available for the transmission measurement can be determined from
the operating and programming manual [1]. Figure C .l (a) shows the transmitted power
b 2 [1] with a thru connected and disconnected from 18 to 40 GHz. The difference
between these two is the dynamic range for transmission [1], which is plotted in Figure
C .l (b). The basic trend is that the dynamic range decreases as the frequency increases.
Considering the PAA system loss, cable loss and loss of the transmitted power due to
wave propagation, 18- to 40 GHz LNAs from MITEQ [2] and Spacek Labs [3] before the
horn and after the PAA are used to boost the signal power and increase the dynamic
range.
-40
-60
Dynamic Range
E*
m -80
2 ,
L.
<i>
I
-100
CL
-120
Noise floor
Signal level
-140
20
25
30
35
40
Freq (GHz)
150
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
80
(b)-
75
CO
13
70
(1)
O) 65
C
CO
OC 60
o
E
CO
c
55
>»
Q 50
45
40
20
25
30
35
40
Freq (GHz)
Fig. C .l (a) Transmitted power under thru connected and unconnected conditions and (b)
dynamic range from 18 to 40 GHz
C.2 Standard Gain Horn Measurements
To check the measurement capability of the current experimental setup using an
8510B Network Analyzer together with the UC Davis anechoic chamber, the E-plane far
field radiation patterns of several standard gain horn antennas from X-band to Ka-band
are measured inside the chamber. Theoretical and measured results are compared in
Figure C.2. We can see that the measured and theoretical results agree very well.
151
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Standard X-band horn antenna E plane pattern at 10GHz
-
2
10-
,
0
% -2 0 D.
0
>
M
—>
0
0 -3 0 -
DC
—• — M easurem ent result using 8 5 1 0
—o— Theoretical calculation
-40
-9 0
-60
-30
0
30
60
90
A n g le [d e g r e e ]
(a)
S ta n d a r d K a -b a n d h orn a n te n n a E p la n e p a ttern a t 2 6 .5 G H z
-
10
-
00
|
o
-2 0 -
Q.
0
0
-3 0 -
0
DC
-4 0 -
-9 0
M easurem ent result using 8510
Theoretical calculation
-6 0
-30
0
30
60
90
A n g le [d e g r e e ]
(b)
152
Reproduced with permission o f the copyright owner. Further reproduction prohibited without permission.
Standard Ka-band horn antenna E plane pattern at 40 GHz
-10
m
■o
“
CD
-20
o
Q_
cu - 3 0
>
0
DC
-4 0
-5 0
-9 0
"• Measurement result using 8510
—o —Theoretical calculation
-60
-30
0
30
60
90
A n g le [d e g r e e ]
(c)
Fig. C.2 Comparison of theoretical and measured standard gain horn E-plane far field
radiation patterns at (a) 10 GHz (b) 26.5 GHz and (c) 40 GHz
153
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References:
[1] Agilent Technologies, “8510 Network Analyzer System Operating and Programming
Manual”, 2001.
[2] Model No.: JF-18004000-30-8P
[3] Model No.: SLKKa-30-6
154
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