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Frequency/phase agile microwave circuits on ferroelectric films

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FREQUENCY/PHASE AGILE MICROWAVE CIRCUITS ON FERROELECTRIC
FILMS
ROBERT R. ROMANOFSKY
Bachelor o f Science in Electrical Engineering
Pennsylvania State University
May, 1983
Master o f Science in Electrical Engineering
University o f Toledo
March, 1989
Submitted in partial fulfillment o f requirements for the degree
Doctor of Engineering
at the
Cleveland State University
December, 1999
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UMI N um ber 9989492
Copyright 1999 by
Romanofsky, Robert Raymond
All rights reserved.
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©Copyright by Robert Raymond Romanofsky 1999
ii
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This dissertation has been approved
For the Department of Electrical and Computer Engineering
And the College of Graduate Studies by
^
I
/
\
Dissertation Committee Chairperson, Dr. A. Haq Qureshi, Date
Department of Electrical and Computer Engineering
Dr. James H.qjurghart. Date
Department of Electrical and Computer Engineering
rfZhtZ* - —
lb,
Dr. Murad Hizlan, Date
Department of Electrical and Computer Engineering
k-
VW
I 3>j
Jr. Vijaya K. Konangi, Date
Department of Electrical and Computer Engineering
Dr. Fuqtn Xidofg, Date
Department of Electrical and Computer Engineering
Dr. Rasul Khan, Date
Department of Mathematics
iii
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| 49 °l
This dissertation is dedicated in memory
of my father, Stanley, and my brother, Edward
iv
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Acknowledgement
I am fortunate to have had the opportunity to work with so many dedicated people
during the past several years who are friends as well as colleagues, especially Bruce
Viergutz, Elizabeth McQuaid, Nick Varaljay, Joseph Warner, Dr. Fred VanKeuls and
Dr.Felix Miranda. And I am most indebted to Dr. A. Haq Qureshi whose prodding and
encouragement were of untold influence. It has been an honor learning from the first
Pukhtoon to earn a PhD in engineering.
I am especially grateful for my family. It is they who make hard work worthwhile.
To my mother, who taught me those things that are most important, and to Laura, Jason
and Melissa , Stan (JR) and Merlene, “Cookie” and Ray, I openly say thank you for the
purpose and joy you continue to bring into my life. Finally, I sincerely thank my loving
wife and confidante Kim, who taught me that there is no such thing as tired.
V
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FREQUENCY/PHASE AGILE MICROWAVE CIRCUITS ON FERROELECTRIC
FILMS
ROBERT R ROMANOFSKY
ABSTRACT
This work describes novel microwave circuits that can be tuned in either frequency
or phase through the use o f nonlinear dielectrics, specifically thin ferroelectric films.
These frequency and phase agile circuits in many cases provide a new capability or offer
the potential for lower cost alternatives in satellite and terrestrial communications and
sensor applications. A brief introduction to nonlinear dielectrics and a summary o f some
of the special challenges confronting the practical insertion o f ferroelectric technology
into commercial systems is provided. A theoretical solution for the propagation
characteristics o f the multi-layer structures, with emphasis on a new type o f phase shifter
based on coupled microstrip lines, is developed. The quasi-TEM analysis is based on a
variational solution for line capacitance and an extension o f coupled transmission line
theory. It is shown that the theoretical model is applicable to a broad class o f multi-layer
transmission lines. The critical role that ferroelectric film thickness plays in loss and
phase-shift is closely examined.
Experimental data for both thin film BaxSri.xTiC>3 phase shifters near room
temperature and SrTiC>3 phase shifters at cryogenic temperatures on MgO and LaAK>3
substrates is included. Some o f these devices demonstrated an insertion loss o f less than
5 dB at Ku-band with continuously variable phase shift in excess o f 360 degrees. The
performance of these devices is superior to the state-of-the-art semiconductor
counterparts.
vi
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Frequency and phase agile antenna prototypes including a microstrip patch that can
operate at multiple microwave frequency bands and a new type o f phased array antenna
concept called the ferroelectric reflectarray are introduced. Modeled data for tunable
microstrip patch antennas is presented for various ferroelectric film thickness. A
prototype linear phased array, with a conventional beam-forming manifold, and an
electronic controller is described. This is the first demonstration o f a scanning phased
array antenna based on thin ferroelectric films at K-band. Preliminary results for a Kuband spiral and integral balun are included as well because o f its potential to realize
another type o f reflectarray.
Finally, tunable microstrip ring resonators and a cryogenic Ku-band frequency agile
oscillator based on SrTiC>3 films are described. The voltage-controlled oscillator
demonstrated a tuning range o f more than 3% around 16 GHz. This is the first
electronically tunable Ku-band oscillator demonstrated with thin ferroelectric films.
vii
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TABLE OF CONTENTS
ABSTRACT...................................................................................................................vi
LIST OF TABLES........................................................................................................ ix
LIST OF FIGURES........................................................................................................x
I.
INTRODUCTION.............................................................................................. 1
Background and Motivation...................................................................... 3
Statement o f Problem................................................................................ 13
Dielectric Properties............................................................................13
Previous W ork.................................................................................. 18
Growth Techniques............................................................................ 21
High Voltage Devices-Low Voltage Instrumentation.....................23
Information Systems........................................................................... 27
II.
THEORETICAL APPROACH.......................................................................29
Variational Formulation o f Line Capacitance....................................... 31
Coupled Ferroelectric Microstrip Lines..................................................38
III.
PHASE SHIFTERS......................................................................................... 63
Experimental D a ta....................................................................................64
IV.
ANTENNAS.....................................................................................................69
Frequency Agile Microstrip Patch Antenna...........................................69
Prototype Linear Phased Array................................................................ 82
Ferroelectric Reflectarray......................................................................... 89
Equiangular Spiral with Marchand Baiun.............................................. 96
V.
OSCILLATORS............................................................................................. 100
Tunable Ring Resonators....................................................................... 106
A Cryogenic GaAs PHEMT/Ferroelectric Tunable O scillator
107
VI.
CONCLUSIONS AND FUTURE W O R K .................................................. 116
REFERENCES............................................................................................................122
APPENDICES
A. Ferroelectric Coupled Line Design Graphs.......................................... 132
B. MathCAD Quasi-TEM Variational Solution........................................ 154
C. MathCAD Oscillator Design Program.................................................. 157
D. Surface Wave Limit on Quasi-TEM Solution.......................................160
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LIST OF TABLES
Table
Page
I.
Internet User Distribution..................................................................................4
II.
Lost Data for YBa 2Cuj0 7 VBaxSri.xTi0 3 CPW with s/w=6/25 p m ...........22
III.
Curie Temperature as a Function of Composition........................................ 22
IV.
Modeled Data for a Two pm Ferroelectric Layer on 0.25 mm LaAI0
V.
Theoretical Propagation Characteristics o f a Single Coupled
Microstrip Section on 0.3 mm MgO Based on the Quasi-TEM
M ethod...........................................................................................................117
VI.
Theoretical Propagation Characteristics o f a Single Coupled
Microstrip Section on 0.25 mm LaAlO? Based on the Quasi-TEM
M ethod...........................................................................................................117
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.. 36
LIST OF FIGURES
Figure
Page
1.
Behavior o f Molecules in an Ionic Solid......................................................... 14
2.
High Voltage Bias Tee in SMA/SMC package (a) and Schematic ( b ) .......... 25
3
Measure S-parameters of High Voltage Bias T ee............................................ 26
4.
Cross-Section o f the Coupled Microstripline Phase Shifter............................30
5.
Photograph o f Four-Section BaxSri.xTi0 3 on 0.3 mm MgO............................31
6.
Measured Insertion Loss o f 8-Element «50Q PLD Coupled
Microstripline phase shifter................................................................................ 38
7.
Even and Odd Mode Currents are Superimposed............................................40
8.
Ouasi-TEM Approximation o f Bandpass Characteristics of an 8-Section
Phase Shifter......................................................................................................... 42
9.
Phase Shifter on 0.3 mm MgO with a 2.0 pm Film with
Dielectric Constant 2500.................................................................................... 43
10. Phase Shifter on 0.3 mm MgO with a 2.0 pm Film with
Dielectric Constant 1000.................................................................................... 44
11. Phase Shifter on 0.3 mm MgO with a 2.0 pm Film with
Dielectric Constant 5 0 0 ...................................................................................... 45
12. Phase Shifter on 0.3 mm MgO with a 1.0 pm Film with
Dielectric Constant 2500.................................................................................... 46
13. Phase Shifter on 0.3 mm MgO with a 1.0 pm Film with
Dielectric Constant 1000.................................................................................... 47
14. Phase Shifter on 0.3 mm MgO with a 1.0 pm Film with
Dielectric Constant 5 0 0 ...................................................................................... 48
15. Phase Shifter on 0.3 mm MgO with a 0.5 pm Film with
Dielectric Constant 2500 .................................................................................... 49
x
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16. Phase Shifter on 0.3 mm MgO with a 0.5 pm Film with
Dielectric Constant 1000......................................................................................50
17. Phase Shifter on 0.3 mm MgO with a 0.5 (j.m Film with
Dielectric Constant 5 0 0 ....................................................................................... 51
18. Phase Shifter on 0.25 mm LaAlOs with a 2.0 pm Film with
Dielectric Constant 2500 .................................................................................... 52
19. Phase Shifter on 0.25 mm LaAK>3 with a 2.0 pm Film with
Dielectric Constant 1000.................................................................................... 53
20. Phase Shifter on 0.25 mm LaAlOa with a 2.0 pm Film with
Dielectric Constant 5 0 0 ........................................................................................ 54
21. Phase Shifter on 0.25 mm LaAlOs with a 1.0 pm Film with
Dielectric Constant 2500.................................................................................... 55
22. Phase Shifter on 0.25 mm LaAl(>3 with a 1.0 pm Film with
Dielectric Constant 1000.................................................................................... 56
23. Phase Shifter on 0.25 mm LaAlC>3 with a 1.0 pm Film with
Dielectric Constant 500 ...................................................................................... 57
24. Phase Shifter on 0.25 mm LaAlC>3 with a 0.5 pm Film with
Dielectric Constant 250 0 .................................................................................... 58
25. Phase Shifter on 0.25 mm LaAlC>3 with a 0.5 pm Film with
Dielectric Constant 1000.................................................................................... 59
26. Phase Shifter on 0.25 mm LaAlC>3 with a 0.5 tun Film with
Dielectric Constant 5 0 0 ........................................................................................60
27. Simulated Frequency Response of the Phase Shifter Corresponding
to Figure 6, e= 300.................................................................................................61
28. Simulated Frequency Response o f the Phase Shifter Corresponding
to Figure 6, e=2500, tan5=0.005......................................................................... 62
29. Simulated Frequency Response o f the Phase Shifter Corresponding
to Figure 6, e=2500, tan5=0.05............................................................................62
30. Measured 50Q 4-section Bao.soSro.joTiCb Phase Shifter Loss on
MgO at 297 K.........................................................................................................65
31. Measured Insertion Phased Corresponding to Figure 30...................................65
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32. Measured 50Q 4-section Bao.6oSro.4oTi0 3 Phase Shifter Loss on
MgO at 210 K .........................................................................................................66
33. Measured Insertion Phase Corresponding to Figure 32..................................... 67
34. Measured 8-section 50Q SrTi0 3 Phase Shifter on LaAlOs...............................68
35. Tunable Microstrip Patch Antenna Schematic and dc
Bias Field Configuration....................................................................................... 71
36. Return Loss o f the TMoi Mode o f a Microstrip Patch on 0.046 cm
Thick Silicon..........................................................................................................73
37. Return Loss o f the Patch of Figure 36 for the TM03 Mode................................74
38. E-Field Pattern Corresponding to Figure 37 at 18.1 G H z.................................74
39. Return Loss o f the Patch of Figure 36 for the TMos Mode................................75
40. E-Field Pattern Corresponding to Figure 39 at 30.1 G H z .................................75
41. Insertion Loss of a 4-Element Phase Shifter on Si at 298 K ..............................77
42. Insertion Phase Corresponding to Figure 41....................................................... 77
43. Return Loss o f Tunable Patch on 0.25 mm LaAlOs,
Film Thickness is 2 pm, er is 1200.................................................................... 79
44. Return Loss o f Tunable Patch on 0.25 mm LaAlC>3, Film
Thickness is 2 pm, er is 300................................................................................ 79
45. Return Loss o f Tunable Patch on 0.25 mm LaAlOs, Film
Thickness is 1 pm, er is 1200................................................................................80
46. Return Loss o f Tunable Patch on 0.25 mm LaAlOs, Film
Thickness is 1 pm, er is 300................................................................................ 80
47. Return Loss o f Tunable Patch on 0.25 mm LaAlC>3, Film
Thickness is .65 pm, er is 1200........................................................................... 81
48. Return Loss o f Tunable Patch on 0.25 mm LaAlC>3, Film
Thickness is .65 pm, er is 300............................................................................. 81
49. 16-Element Linear Phased Array L ayout............................................................83
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50. Measured Resonant Frequency o f Some Patches on 0.25 mm Duroid 6010 .. 84
51 Measured Resonant Frequency o f Some Patches on 0.25 mm Duroid 5880 .. 85
52. Measured Boresight Far-Field E-Plane and H-Plane Pattern of the
16-Element Ferroelectric Phased Array at 23.5 GHz........................................86
53. Predicted E-Plane Pattern o f the 16-Element Array,
Scanned o ff to 45 Degrees...................................................................................87
54. High Voltage Controller Board for the 16-Element Phased Array.................. 88
55. Passive 256 element spiral reflectarray on 0.25 mm AI2 O 3 .............................90
56. Reflectarray Coordinate System..........................................................................92
57. A 2832 Element 19 GHz Ferroelectric Reflectarray......................................... 93
58. Microstrip Marchand Baiun on 0.75 mm Duroid 6010.....................................97
59. Measured S21 o f Two Back-to-Back Microstrip Baiuns.................................. 98
60. Measured Bandwidth of Equiangular Spiral Integrated with B aiun............... 99
61. Microstrip Side Coupled Resonator..................................................................106
62. Effect o f dc Bias on S21 o f a 25 O Microstrip Ring Resonator
Patterned on a 2 pm SrTiC>3 film on LaAlC>3 ....................................................107
63. Schematic o f the Voltage Controlled Oscillator.............................................. 108
64. Photograph o f a Ku-Band Au/SrTi0 3 Ring Resonator Tunable Oscillator... 109
65. (a) Smith Chart Showing SI 1 and S22 and (b) Log Magnitude Plot
Showing S21 of the PHEMT at 77 K ................................................................I l l
66. VCO Signals Measured on an HP 8566B Spectrum Analyzer at 43 K
114
67. Proposed Discriminator Stabilized VCO.......................................................... 115
68. Comparison Between Resistivity of a Thin Evaporated Au Film on
AI2O3 and Bulk Au as a Function of Temperature...........................................118
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CHAPTER L INTRODUCTION
This work involves the use o f thin ferroelectric films to enable a new class o f
tunable microwave circuits and antennas. The defining property of ferroelectricity, a
subset o f piezoelectricity, is exhibition o f a spontaneous electric dipole moment. The
property exploited here is the ability to alter the direction o f the spontaneous moment
upon the application of an external dc electric field. The discovery o f ferroelectricity in
Rochelle salt by Valasek in 1921 is generally cited as the original observation o f the
phenomenon [1], The related phenomenon o f piezoelectricity can be traced to the work o f
Pierre and Jacques Curie in 1880. They discovered that certain crystals developed an
electrical charge when squeezed and soon thereafter observed the reverse effect - electrical
charge distorts a piezoelectric crystal [2]. While concerted research on these materials has
been conducted since the 1940s, it is only recently that film deposition techniques and
circuit designs have been advanced enough to allow serious consideration o f technology
insertion for microwave applications.
The device technology holds promise to
revolutionize frequency and phase agile components and subsystems for advanced civil
and military communications and radar applications.
Two tenets govern this work. First, a widespread misconception held that the loss
tangent o f thin ferroelectric films was too high for practical microwave applications. It
1
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2
will be shown that with the proper circuit design and electrode geometry the film’s
contribution to total loss is manageable and possibly secondary to other loss mechanisms.
Second, despite some skepticism and opinion to the contrary, it will be shown that even in
thin film form tunable ferroelectric microwave devices can be realized that rival or exceed
the performance o f state-of-the-art semiconducting or ferrite counterparts.
It is not a goal o f this work to investigate or advance the materials technology
itself It is conceded that much work remains here before we can fully understand and
optimize film properties and develop more economically attractive deposition techniques.
That task is best left to the material scientists, chemists, and physicists. Rather, this work
suggests that certain ferroelectric films can be exploited at their present level o f maturity
to meet growing information technology needs o f industry and society. And hopefully it
points the way for the materials scientist so that he or she can grapple with those issues
that impede the use of ferroelectrics on a grander scale.
For the sake of clarity it must be mentioned that the materials utilized here are
actually operated above the Curie temperature in the paraelectric phase. It has become
customary for workers in the field to still refer to materials operating in a paraelectric
regime as ferroelectrics. This dissertation sticks to that convention.
A number o f frequency and phase agile device concepts and prototypes will be
introduced including coupled-line phase shifters, resonators and oscillators, and microstrip
antennas. These devices and circuits represent successes, at least to some degree, where
others have failed. A theoretical analysis o f the multi-layer microwave circuits is
presented along with experimental and simulation data to validate the theory. While it is
hoped that these prototypes can serve as the vanguard for a new class o f tunable
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3
microwave circuits, the premier application is a potentially low cost scanning phased array
antenna, called the ferroelectric reflectarray (FRA). The case will be made that the FRA is
the best candidate, from a technical and economical point o f view, to meet the
requirements o f the wideband low Earth orbit (LEO) satellite infrastructure o f the near
future, both for the space and ground segments o f the communications links. Several
proposed satellite systems promising an “internet in the sky” are briefly discussed in
Chapter I.
Without pause to consider the long-term social implications, technology advances
in response to immediately perceived demands. The consequences o f the internet, and the
promise o f wideband satellite communications to shrink the world even further, remain to
be seen. Lee DeForest said:
” The whole scheme o f communications, by electricity, by news print, by post, is aiding
mankind to transact its business, its social affairs, its diplomatic relations. But back o f all
this, broader and deeper in results and wide-spread benefits, although quite involuntary
and unforeseen by most o f the agencies now involved, is the quiet, constantly working
tendency toward education, culture, broader-mindedness, community o f aims, mutual
understanding. It is a far-reaching, slowly extending step toward a common, or at least a
commonly understood, language. And finally to international friendship, international
comity - an End o f War.”
He said this in 1930.
Background and Motivation
Just as the industrial revolution characterized the late 18th and 19th century and
marked a turning point in human history, the information revolution is destined to define
our times and chart our future course. We recognize that we are only on the brink o f that
revolution. But, the explosion in telecommunications is upon us, and the expectations
from technology are clear. There is continuously increasing demand for bandwidth to
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4
support business oriented, data intensive services such as video conferencing, tele­
medicine, and various multimedia traffic. However, the greatest growth in demand will
be fueled by consumer (residential) requirements such as: distance learning, electronic
mail, home shopping, entertainment services such as high definition television,
videophones, and tele-commuting. If this premise holds true, the aggregate data
throughput will greatly exceed the capacity offered by conventional twisted-pair wire
service provided to homes. By the end of 1996, commercial use of the internet was
increasing at a rate of 30 % quarterly [5], More recent analysis indicates that World Wide
Web traffic constitutes 30 % of all internet traffic, and is growing at about 25% per
month. There are now 171 million internet users worldwide demographically distributed
as shown in Table I. That number is expected to increase to 350 million by 2005 [6]. The
demand for personalized information services appears insatiable.
Table II. Internet User Distribution
Africa
1.1 million
Asia
27 million
Europe
40 million
Middle East
0.9 million
U.S./Canada
97 million
Latin America
5.3 million
World Total
171 million
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5
Two separate camps emerged from the Global Information Infrastructure brain
trust to address the demand: terrestrial fiber networks and broadband satellite networks
offering fiber-like quality of service. It now looks as if these strategies may complement
rather than compete with each other in the long run. In addition to the fixed (i.e.
stationary user terminal) satellite services alluded to above, more complex mobile
telephony systems are also under development. Many o f the proposed near term satellite
constellations are expected to compete with or supplement terrestrial cellular networks. In
some cases the satellites are interoperable with existing terrestrial cellular networks or
provide coverage to areas where a cellular infrastructure has not been established.
Pioneering status belongs to Motorola's Iridium system, first announced in 1990. The
constellation o f 66 low Earth orbiting (LEO) satellites represents a $3.4 billion
investment targeting a worldwide voice and paging service.
Compared to geostationary (GEO) satellites, LEO satellites offer at least three
major advantages. First, they orbit at an altitude generally below 1000 km instead o f
about 35,000 km. Since signal loss is proportional to distance squared, this means there is
an automatic power saving of about 30 dB. Second, their proximity provides a nearly
imperceptible propagation delay just like terrestrial systems, instead o f the 0.25 second
delay associated with GEO satellites. While this may be nothing more than a nuisance for
voice services, it causes technical problems with higher data rates (e.g. computer
networking) and handshaking (e.g. ATM switching). Third, there is potential for
significantly reduced launch costs, especially if the satellites can be bundled and
deployed from small expendable launch vehicles or Pegasus style launch systems.
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Critical to the success o f LEO networks are scanning phased array antenna
systems, both onboard the spacecraft and on the ground [7,8], For any given network, the
earth terminal may be required to provide multiple beams that can track the satellite at a
rate of about one degree per second. While the technology is in hand for specialized
applications such as military radar systems where the cost can be justified, insertion into
commercial markets is not yet feasible. For example, NASA is sponsoring the
development
of a
prototype
transmit
phased
array
antenna
for commercial
communications satellite applications. (NASA is interested in leveraging commercial
communications assets in the future, rather than relying on its own communications
infrastructure.) The manufacturing technology chosen, namely multilayer printed wiring
board and ball grid array construction employing monolithic microwave integrated
circuits (MMIC), emphasizes low production costs. Still, multiple orders would probably
cost in excess o f SI M each, less than an order o f magnitude below the cost o f the
original. Optimistic projections by array manufacturers claim costs o f about $50 to $100
per radiating element on production scales with a typical phased array requiring several
hundred to perhaps 1000 elements or more[9]. Such arrays are clearly out of reach o f the
mass consumer market. In fact, in a solicitation released in the Commerce Business Daily
in December, 1997, Motorola stated that MMIC based arrays were not regarded as a
viable solution for Celestri tracking ground terminals because o f cost. Their own internal
market survey indicated that the cost to the subscriber for the ground terminal equipment
had to stay around $1000. Other solutions (alternatives to MMIC arrays) were
desperately being sought.
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7
Other LEO systems that have been proposed or are already under construction
include: Iridium (Motorola), ICO (Inmarsat), Global star (Loral), Ellipso (Mobile
Communications
Holdings,
Inc.),
ECCO
(Constellation
Communications,
Inc.),
Skybridge (Alcatel), Spaceway (GM, Hughes), Cyberstar (Loral), Astrolink (Lockheed),
Orbcomm (Orbital Sciences) and Teledesic (McCaw, Gates, Motorola, etc.). The
Teledesic, Cyberstar, Astrolink, Spaceway, Skybridge and Celestri concepts are
remarkable in that data rates in excess of 2 MBPS per channel will be supported. Their
vision has been likened to an internet in the sky.
Motorola's Celestri system is a good example o f one constellation and they were
quite liberal with the release information about their system. The Celestri LEO system, as
originally proposed, was comprised o f 63 satellites in 7 inclined orbital planes. The
system architecture placed considerable burden on the space segment, allowing the use of
relatively small Earth terminals. These terminals are envisioned to have apertures
between 0.3 and 1.0 meters to support data rates from 2.048 to 155.52 MBPS. Service
and gateway links would operate in the 18.8 to 19.3 and 19.7 to 20.2 GHz bands for
space-to-Earth and 28.6 to 29.1 and 29.5 to 30.0 GHz for Earth-to-space. The
constellation was expected to be fully operational in 2003 and provide coverage to 99%
o f the Earth's population. Motorola's estimated market demand, based on projections
from Bellcore, for communications services in the first decade of the new millennium
approaches $1.5 trillion in worldwide annual revenue. Motorola estimated that 20-30% of
this market would have to be provided by other than cable and fiber services [10]. Fairly
consistent with these projections, a study sponsored by NASA and the NSF estimates that
worldwide revenues for all types o f communications satellites will grow to $75 billion by
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8
the end of 2005 [11], Like Teledesic's original strategy, Celestri endeavored to provide
service to geographically or economically handicapped regions. For example, fewer than
5% of potential customers in Africa and Asia have access to basic telephone service.
Clearly, the customer base addressed by Celestri exceeds 10 million and probably
approaches 100 million [subscribers]. Celestri would support about 395,000 simultaneous
equivalent 64 KBPS channels over the contiguous United States (CONUS) and over
1.800.000 simultaneous equivalent 64 KBPS channels worldwide. Similarly, Teledesic’s
original concept touted a capacity equivalent to a peak load o f 2,000,000 simultaneous
full-duplex 16 KBPS connections or 20,000 simultaneous 1.544 MBPS connections or
any combination thereof. The system would provide 24 hour seamless coverage to 95 %
of the earth's surface and nearly 100% o f the Earth's population [12]. Standard terminals
include fixed and portable configurations that operate at multiples o f the 16 KBPS basic
channel rate. Antenna diameters will fall between 16 cm and 1.8 in depending on data
rate, climatic region, and availability requirements. Recently, Celestri and Teledesic
merged. The constellation that evolves from this merger will no doubt be a hybrid
combining the best features of each. Their success will depend on how fast the industry
can recover from the recent bankruptcy filing (August 13, 1999) o f Iridium. Iridium
failed to draw anywhere near the number of subscribers they anticipated, and expects to
default on $800 million in bank loans. Triggering a domino effect, ICO suddenly failed to
complete financing of its own $4.7 billion project as Wall Street and investors hesitate to
risk additional capital. And although comparing these low speed systems to Teledesic is
analogous to comparing the telegraph to television, in the eyes o f skittish investors the
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9
whole market has gone soft. It is unclear who will succeed and when. But the Teledesic
concept is the most ambitious and promises the widest spectrum of services.
There are two known technologies that could satisfy the Teledesic ground
terminal technical specifications. The first is direct radiating phased arrays. In such an
array, MMIC phase shifters and amplifiers, digital control circuits, the beam-forming
manifold, and radiating antenna elements are integrated into the same structure. But as
mentioned earlier manufacturing costs are a deterrent commercial use. While the silicon
chip infrastructure is so well established that silicon wafers can be purchased for less than
$1 per cm2 in volume, gallium arsenide MMICs have not enjoyed much economy of
scale. Gallium arsenide still costs about S I5 per cm2 and is not available in large wafers.
And, because of the high frequencies associated with the proposed LEO systems, silicon
is inadequate. Even with a substantial market pull, it is unlikely that gallium arsenide will
become affordable for this application. Furthermore, because o f demanding fabrication
tolerances at these frequencies, yields may be poor driving costs up even more. The
integration o f the MMICs with all the other components associated with a direct radiating
phased array is labor intensive, exacerbating the cost problem. Manufacturing tolerances
may preclude any form o f automation.
The second and more likely technology to be used for the Teledesic ground
segment is gimbaled parabolic reflectors. This technology is well developed and the
mainstay for civil and military communications systems. The drawbacks are twofold.
First, it is a motorized system requiring precision gear mechanisms. The beam will be
required to point with a precision o f 0.1 degrees or so. The antenna dish will also have to
bear wind-loading stresses and all mechanisms must be sized accordingly. The cost for a
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10
typical 0.5 meter dish with steering in both axes exceeds $50,000. Even a 1 meter dish
and feed sans pedestal can cost in excess o f $10,000. As with almost any product, given
an adequate market, there will be an economy o f scale. Whether market forces can drive
costs to an acceptable level remains to be seen. It may be possible to replace the parabolic
surface, which is either aluminum or a graphite composite, with a flat plate printed
antenna. This could reduce costs somewhat, but the dominant cost o f the gimbaled
antenna system is attributable to the drive machinery. Second, there is a technical
limitation when trying to use a gimbaled dish for LEO tracking, That is, the dish cannot
instantaneously return to the opposite horizon to capture the next satellite. Teledesic, as
well as any other LEO system, will require a make-before-break handoff. Hence, at least
two antennas would be required. So besides doubling the cost, one must wonder about
consumer acceptance o f ungainly roof-top systems.
The ferroelectric reflectarray is an enticing alternative. It basically consists o f a
two-dimensional reflecting surface comprised o f printed antenna elements and integral
phase shifters. The phase shifters can be adjusted so that the surface will reflect a beam
from a feed horn in a preferred direction. A case was made earlier that MMIC-based
phased arrays would have a tough time meeting low cost objectives. This problem is
trivial in comparison to the fatal disadvantage o f a beam-forming manifold that manifests
itself near millimeter wavelengths (greater than 20 GHz or so). The gain o f a phased
array is proportional to the number o f radiating antenna elements only to a point. In
practice, gain actually decreases after the number o f elements exceeds some large
number, perhaps several hundred at K-band. This is because microwave circuit losses in
the beam forming manifold eventually dominate and dictate an upper limit on gain. The
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11
reflectarray does not experience this limitation, inherent to direct radiating MMIC phased
arrays,
since
the beam
forming
is
accomplished
quasi-optically.
Commercial
communications systems (e.g. Hughes, SkyStation International) at frequencies where
this effect becomes a problem are already on the drawing board. There is also a
tremendous military need for frequency and phase agile communications systems. For
example, a Broad Agency Announcement was released in Commerce Business Daily on
February 5, 1998 wherein the Space and Naval Warfare Systems Center was seeking low
cost Ka-band tracking ultra small aperture terminals for mobile satellite communications
applications. The military is also desirous o f replacing multiple aperture antenna systems
onboard space-limited platforms, including ships and aircraft, with so-called smart
antennas. These smart or reconfigurable antennas could perform multiple tasks such as
radar, communications, and jamming from a single aperture using frequency and phase
agile techniques.
Another burgeoning market that the technology is responsive to is the Intelligent
Vehicle Highway System, especially in the context of intelligent cruise control, collision
avoidance radar, and electronic tolling. For collision warning (not collision avoidance)
applications, the phased array can be small and perhaps one-dimensional. That is, the
beam may only have to steer in one plane so that its field o f view would form a fan
shape. Preliminary technical and regulatory specifications suggest an operating frequency
of 77 GHz with a 1.5° by 6° beam width, a 10 Hz scan rate, and 10 mW output power
[13]. Operational systems are being planned for the early-to-mid 2000 time frame,
although full-scale implementation may be 20 years away. Competing alternatives
include laser, infrared, and acoustic systems. Light detection and ranging (LIDAR) is
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12
susceptible to environmental conditions because the sensor cannot penetrate dirt or ice
effectively And, LIDAR’s energy levels, from the laser, may pose health and safety
concerns. Acoustic sensors do not appear to have the necessary resolution or sensitivity.
Radar on the other hand, given the proper choice o f frequency, tends to be immune to the
environment and satisfies the technical requirements. Presumably, every new vehicle will
eventually be equipped, and existing vehicles in service retrofitted, with instruments to
allow them to coexist in the intelligent transportation system o f the future. It appears that
there is a $200 M research and development budget allocated for this vision [14], Early
estimates by GEC (England) indicate that production cost o f cruise control transceiver
should be in the range o f $150 [15]. This is about the price a consumer willingly pays for
a radar detection system. (The reader may find it interesting to note that there are
currently about 20 million police radar detectors in use in the United States.) In a 1994
study. Strategies Unlimited forecast that the intelligent automobile market will be $4.9
billion by 2004 [16]. This should come as no surprise since there are about 140 million
automobiles in service in the U.S. They further predicted that 14 % of the [15 million]
new vehicles in 2004 will be equipped with intelligent cruise control and collision
avoidance systems. A transportation study released by Mercedes-Benz in 1992 reported
that 30% o f head-on fatalities and 60 % o f rear end collisions could be eliminated if the
driver had an additional 0.5 seconds to react [17], Forward looking collision warning
systems and smart airbag deployment are other applications. About 90 % o f all crashes
have been attributed to human error.
Besides smart antennae, other agile components become feasible with thin film
ferroelectric technology. Most notable are tunable oscillators. As the lower microwave
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13
frequency spectrum saturates with applications such as PCS, cellular, and direct TV, the
trend toward higher frequencies will accelerate. A number o f concepts have already been
disclosed such as Local Multi-point Distribution Systems (LMDS) at 28 GHz and
satellite systems at 48 GHz. A critical component in any o f these systems is the oscillator,
which generates the microwave signal. The state-of-the-art is represented by dielectric
resonator oscillators. These devices are expensive because they require cumbersome
(non-lithographic) processing. They do not readily lend themselves to tuning and are in
fact limited to a few tens of MHz at Ka-band frequencies. They have met with
considerable market success because there has been no real competition - until now. The
market is inestimable but includes airborne radar, telecommunications, missile
transponders, and electronic countermeasures. Since the proposed technology is based on
a lithographic process, it holds promise for equivalent performance at lower cost.
Statement of Problem
Dielectric Properties
In a dielectric, the electric flux density (D) differs from that in free space because o f the
polarization (P) of the material. The electric flux density (Coulombs/cm2) is related to the
polarization as:
D = s0E + P
(1)
In classical theory, the dielectric is presumed to contain infinitesimal dipoles at
each site in the crystal lattice. An applied electric field can orient the dipoles in the
direction of the field. For the materials o f interest here, the dipoles result from the
displacement o f ions against the natural restoring force o f the crystal bonds. The
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14
ferroelectrics used in this work belong to the perovskite crystal family, coined by a
Russian mineralogist following the discovery of CaTi0 3 in 1839 after L A . Perovsky who
reigned as Minister o f Lands [3], The crystal structure is given by the general chemical
formula ABO3 where the A element is a large cation situated at the comers o f the unit cell,
the B element is a smaller cation located at the body center, and O are oxygen atoms at the
face centers. A common contemporary material is BaTiOs, known since World War II.
Here Ba2* is the A cation and Ti4' is the B cation. The unit cell stretches in the direction o f
polarization. Figure 1 is a simple rendition of the effect. The electric flux density is
enhanced because o f the induced immobile surface charge caused by the alignment of
these dipoles. In ferroelectric materials, the relationship between the polarization and the
electric field is non-linear and hysteretic, and the ferroelectric behavior is observed only
Figure 1. Behavior o f molecules in an ionic solid: (a) random orientation in the absence o f
an electric field, (b) alignment and dilation in the presence o f an electric field. In a real
crystal, impurities and mechanical stresses establish small regions o f uniform polarization
called domains.
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15
over a narrow temperature range. Above a certain temperature, the material reverts to a
more or less simple dielectric. At the transition or Curie temperature (Tc) a structural
phase change occurs and the relative dielectric constant can rise to remarkably high
values. Typically the ferroelectric (polar) phase exists below Tc and a paraelectric (non­
polar) phase exists above it. The perovskite structure has cubic symmetry in the
paraelectric phase. It is desirable to operate devices slightly above this transition
temperature, where the dielectric constant is high and hysteresis effects are less
pronounced. Some members of the perovskite family do not exhibit a distinct phase
transition, such as SrTiC>3 . These incipient ferroelectrics exhibit a dielectric constant that
increases as temperature decreases, eventually saturating at some maximum value. There
are many more material recipes to choose from including BaTiC>3 , PbTiC>3, KTaC>3,
(Pb,La)(Zr,Ti)C>3, K NO 3 , CaZrC>3 and LiNbOs, not all o f which possess the perovskite
structure. But the perovskite structure does seem particularly amenable to the
ferroelectric phenomenon. This effort concentrated on Bai-xSrxTiC>3 and SrTi03 for room
temperature and cryogenic applications, respectively, because o f the wealth of
information on, and availability of, these thin films. Indeed synthetic SrTiOs, a man-made
analog of the natural mineral perovskite CaTiC>3. was introduced nearly 50 years ago by
the National Lead Company as a facsimile for diamond in the gem industry [4], Referred
to as “Fabulite” in the vernacular, its hardness o f only about 5.5 on the Mho scale,
compared to 10 for diamond, made it a dead giveaway.
When ferroelectric materials are cooled from the paraelectric phase through the
Curie temperature, local regions of aligned electric dipoles, called domains, form. These
domains, responsible for the spontaneous polarization, can grow under an applied electric
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16
field. Frequency limitations are imposed by the domain boundary motion that contributes
to hysteresis and loss. The net polarization is a combination o f spontaneous polarization
from alignment and the electronic and ionic polarization created by the external field. The
orientational polarization occurs because the permanent molecular electric dipoles are
more or less free to respond to an applied electric field. When the field is removed, the
induced field from the essentially elastic ionic and electronic process vanishes but the
spontaneous polarization remains partially aligned, resulting in a remanent polarization.
Analogous to ferromagnetism the magnitude of the electric field required to reduce the
polarization to zero is called the coercive field. The relative dielectric constant is hence a
very nonlinear function o f the electric field and possesses hysteresis that causes energy
loss per cycle o f the microwave frequency. The dielectric constant has been expressed as
a function o f frequency according to the well-known Cole-Cole relation [18]:
e = ScC+ (es-e«)/(l + ( cot)2
(2)
where s s is the dielectric constant due to orientational polarization, e* is the high
frequency dielectric constant due primarily to ionic polarization and
t
is the relaxation
time for the orientational polarization. The dielectric constant of SrTi03 is frequency
independent up to several hundred GHz [19]. As discussed at the beginning o f this
chapter, the dielectric constant is also a function o f temperature that is described by the
Curie-Weiss law above the transition temperature [20]:
e = C/(T - Tc)
(3)
where C is the Curie constant, equal to 8.25 x 104 K for bulk SrTi03 and 1.5 x 10s for
bulk BaTi03. Thermal agitation and
dielectricconstant
molecular interaction prevent
an unbounded
at Tc Despite the appeal o f the strong nonlinearity for device
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17
applications, the high microwave loss is a chronic problem. And, the nonlinear behavior
and dielectric loss has been the subject of dogged research [21-25]. Microwave loss has
been attributed to the damping o f the polarization mode by impurities and the
anharmonicity o f lattice vibrations, i.e. Phonons excited at the microwave frequency can
be scattered by impurities into an acoustic mode. Anharmonic lattice interactions imply a
coupling between phonons that otherwise would have a mean free path limited only by
collisions with the crystal boundary and lattice imperfections [26], The temperature
dependence o f loss tangent has been shown to roughly follow a Curie-Weiss behavior:
tanS = (T - Tc)'l( a + (3T + yT2)
(4)
where a is determined by lattice imperfections and vanishes for single crystal material.
Parameters P and y are related to third and fourth order anharmonic terms in the interionic
potential and have been shown to be intrinsic properties o f the crystal [21,23]. Attempts
to reduce the loss tangent have included annealing and the use o f dopants [21,27-29].
Heat treatment increases the average grain size, reduces stress and presumably improves
the perfection o f the lattice. The role o f substitutional ions is unclear but the introduction
o f dopants evidently reduces the net charge density. Doping with 1% mole fraction of
tungsten reduced the loss tangent o f BaTiC>3 by a factor o f four [30], Results on BaxSru
xTiC>3 films doped with 1% Mn suggest that loss could be slightly reduced without
compromising tunability [31], In order to reconcile results from various researchers, a
figure of merit was introduced to evaluate material quality in terms o f both tunability and
loss. The so-called K-factor is expressed as [32]:
K = (e(0) - e C E ^ M £(0)(tan5W )
(5)
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18
Where e(0) is the zero filed dielectric constant, e(Enux) is the maximum field dielctric
constant, and tan5 is taken at its maximum value. The tuning range is usually limited by
the breakdown field strength, generally in excess o f 5 x 10s V/cm.
It is well known that the properties of bulk ferroelectrics differ from those o f thin
ferroelectric films. Moreover, it has been observed that the dielectric permittivity and loss
tangent increase with increasing film thickness [33-36], The dielectric constant o f single
crystal SrTi03 can be depressed from about 20,000 to 2000 with a dc field of 104 V/cm at
4.4 K and the loss tangent maintained in the range .001 to .0001. Thin films on the other
hand exhibit tan5 as poor as .01 with a peak relative dielectric constant o f perhaps 5000.
The dielectric constant also tends to exhibit a broad maximum with temperature as
opposed to bulk material. The differences in behavior have been attributed to domain
wall motion, compositional inhomogeneities, interface layers between the film and
electrodes, and lattice mismatch induced stress.
Previous Work
Although there have been several attempts to realize ferroelectric phase shifters,
the designs have mostly been confined to bulk or slab implementations. The conventional
approach consists o f patterning a microstrip line onto a ferroelectric substrate and
applying a bias across the strip and the ground plane [38,50], It requires machining the
ferroelectric material and joining the slab to conventional substrates and transmission
lines. Impedance matching is difficult but it is the high loss tangent o f the ferroelectric
that dominates the insertion loss of the phase shifter. A microstrip phase shifter printed
directly onto a thin Bai-xSrxTi03 substrate produced with a sol-gel technique was reported
in [51], The process involved pressing powdered Bai.xSrxTi03 into pellets at a pressure of
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19
2000 kg/cm2 and then sintering at 1300 C for 1 hour. The material was then sanded down
to 0.1 mm and polished. An insertion loss between 2.6 and 4 dB at 2.4 GHz was
measured. An electrically controlled parallel-plate resonator based on bulk ferroelectric
was presented in [52]. A tunable Bai-xSrxTi0 3 slot capacitor was reported in [53] and a
tunable resonator using a SrTi03 film over a microstrip gap was reported in [54], Simple
tunable coplanar waveguide devices, including a 2 GHz phase shifter and filter, were
developed in [55], But most o f the research in this area has concentrated on materials
optimization and characterization, not device implementations. In [43,44] it was shown
that the dielectric constant o f SrTi03 was as high as 5000 at 77 K. Measurements up to 3
GHz were reported. The most common method for analyzing thin ferroelectric films is
based in multilayer interdigital capacitors. Because o f the complicated electromagnetic
structure,
consisting
of
narrow
meandering
electrodes
on
a
multilayer
ferroelectric/dielectric substrate, extracting loss tangent and dielectric constant data is not
so straightforward. Analytical models based on conformal mapping techniques were
presented in [56,57], This method is now commonly used to assess film quality and
optimize growth and annealing processes. A conformal mapping technique to evaluate
coplanar waveguide multi-layer structures was recently published by Carlson et al. [58],
The reflectarray antenna concept was introduced by Berry et al. in 1963 [59]. The
reflectarray consists of a grid of antenna elements attached to phase shifters. The grid
re-radiates incident energy from a feed horn in a preferred direction determined by the
phase shifter settings. Early reflectarrays used waveguide radiating elements and were
expensive and massive [60]. Low profile reflectarrays using printed microstrip patch
antennas are under investigation. In [61], a 0.75 m diameter X-band array demonstrated
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20
an efficiency o f 70 % with a peak gain o f 35 dB. The array was capable o f dual linear and
dual circular polarizations. A small dual polarized array was also demonstrated in [62]. A
novel method of achieving cophasal far-field circularly polarized radiation was
demonstrated in [63]. The technique employed microstrip patches with variable rotation
angles to produce phase shift. (When a circularly polarized antenna element is rotated by
a certain angle, the far field experiences a corresponding phase shift.) However, none of
these antennas were capable of electronic scanning. They were fixed beam only. The
reflectarray to be developed as part o f this dissertation incorporates continuously variable
ferroelecric phase shifters with each patch element and thus is capable o f dynamic
steering.
There has been very little work done on tunable antennas, even though there is
much interest in such structures and especially in active antennas. One advantage o f a
tunable antenna is the ability to compensate for process and material variations. A design
iteration can be eliminated if the antenna frequency can be adjusted electronically after
construction. This may have even more advantages for active antennas used in quasioptical power combining technology. A varactor tuned active antenna was presented in
[64] at X-band. Another method for producing so-called smart antennas was proposed by
Washington [65], That technique used polyvinylidene flouride piezoelectric films
attached to metallized mylar substrates to reshape reflector surfaces. Hence the beam
pattern or direction could be controlled to some extent. Frequency tuning and pattern
control o f antennas fabricated on bulk ferrite substrates has been reported in [66-68],
Other components based on variable magnetization ferrites, including phase shifters and
circulators, were developed in [69,70], A figure o f merit exceeding 1000 degrees o f phase
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21
shift per dB at 77 K and 10 GHz was reported. High dc magnetic fields are required.
Rain vile and Harackiewicz [71] demonstrated magnetic tuning of a patch fabricated on a
yttrium iron garnet film deposited on a gadolinium gallium garnet wafer. The in-plane
magnetic field tuned the resonant frequency o f the cross-polarized field, but not the co­
polarized field.
A different phased array concept using a ferroelectric lens is discussed in [72].
The approach uses ferroelectric slabs sandwiched between conducting plates. Bias
voltages in excess o f 10 kV are required to obtain the necessary phase shift.
Growth Techniques
Various techniques have been used to grow high quality films. Screen-printed
materials have shown reasonably low loss and good tuning up to 20 GHz [37], In sol-gel
processing, the hydrolysis o f titanium isopropoxide, Ba, and Sr in a two-methoxylethanol
solution is used to synthesize powders of BaTiC>3 and SrTiC>3. Ultimately the dried
solution is calcined at 700°C for 10 hours. Powders are then pressed into pellets at 75,000
psi and sintered at 1400°C [38], Most o f the results to be presented later in this work are
based on pulsed laser ablated films. In this process, ceramic targets with the proper
stoichiometric composition are ablated by laser irradiation with energy densities o f * 1.3
J/cm2 to as high as 6 J/cm2 at 10 Hz repetition rates [36,39], Typically, a 248 nm KrF
excimer laser has been used and growth temperature ranges between 750 and 850 °C. In
order to grow epitaxial quality films, single crystal oxide substrates with a good lattice
match to the film must be used. Substrates like MgO and LaAlC>3 are chosen because o f
their excellent loss tangent (CIO-4). Epitaxial films can mimic the behavior o f single
crystal material to a high degree. Chakalov et al. [36] studied the correlation between film
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22
thickness (t) and loss tangent for BaxSn-xTiC>3 with x=0.05. Results are summarized in
Table II. The data is for coplanar waveguide (CPW) phase shifters at 75 K and 20 GHz.
Table II. Loss Data for YBa2Cu307-5/ BaxSri.xTi03/LaA103 CPW with s/w=6/25 pm
240
480
960
TanS, E=0
0.014
0.037
0.093
tan5, E=13.5 kV/cm
0.001
0.032
0.040
tB axS rl-xT i03,
nm
The Curie temperature can be tailored for specific operating temperatures by adjusting
the x value between 0 and 1. Some data for polycrystalline material from [21] is
summarized in Table III.
Table III. Curie Temperature as a Function o f Composition
Composition
Curie Temperature (K)
SrTi03
37
Ba 0.2 Sr o.g TiCh
105
Ba o.j Sr 0.5 Ti0 3
218
Ba
Sr 0.3 TiC>3
280
Ba 0.8 Sr 0.2 TiC>3
324
0.7
The dielectric constant of the mixed crystal increases as the BaTi(>3 mole fraction
increases and the crystal structure of BaxSn.xTi0 3 is cubic for x<0.7. For pure BaTiC>3
Tc=380 K.
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23
Though laser ablated films have exhibited the highest K-factor, the method may
be too expensive for anything except military and high-end business applications. For
example, it has been estimated that to mass produce the ferroelectric reflectarray the
manufacturing cost per element would be $44 using laser ablation and single crystal
ceramic substrates [40], While this is an order of magnitude less expensive than MMIC
phased arrays, it is an order o f magnitude more expensive than the consumer market
would bear. A promising alternative is combustion chemical vapor deposition (CCVD)
[41]. In this process precursors are dissolved in a solvent that also serves as combustible
fuel. The solution is atomized to form submicron droplets that are combusted in an
oxygen rich flame. The vapor is deposited on the substrate by drawing it over the plasma.
A performance o f 53 °/dB was demonstrated at K-band. The advantage o f the CCVD
process is the use o f inexpensive chemical reagents in an open air environment
suggesting that large scale batch processing is possible. Furthermore, unlike laser
ablation, CCVD is inherently scalable to large (> 5 cm) wafers.
High Voltage Devices —Low Voltage Instrumentation
Thin film ferroelectric microwave devices require electric fields of order 10
kV/cm for full tunability.
For microstrip coupled line structures on high permittivity
substrates at frequencies above 10 GHz, this translates into a bias o f up to 500 V.
Standard (commercially available) bias tees, used to isolate sensitive and expensive
automatic network analysis (ANA) instrumentation from the device under test (DUT), are
only rated to 40 V dc or so.
The customized bias tee presented here operates over
approximately 10-22 GHz and offers fail-safe protection to >500 V dc. (The theoretical
maximum voltage is 760 V dc, and the devices have been tested to 550 V dc.) The
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24
microstrip coupled lines are separated by only 0.075 mm to reduce insertion loss.
A
conformal coating o f paraffin increases the breakdown strength o f the structure to >100
k V/cm. The paraffin also protects the coupled lines from the possibility o f being bridged
by metallic particles. It has a negligible effect on the pass band characteristic because o f
its low relative dielectric constant. If an unlikely breakdown event occurs, a wire bond
fuse is designed to melt in about 27 mS and a zener diode shunts the brief voltage surge.
The fuse time “tf” for adiabatic heating can be estimated by [42]:
tr = A2/I2
Jt Cp(T)/p(T) dT
(6)
where the integration is from the initial temperature to the melting temperature (1336 K),
Cp(T) is the heat capacity (2.5 J/cm3K), p(T) is the resistivity taken as 2.4 x 1CT6 Qcm, A
is the cross sectional area o f the bond wire, and I is the fuse current limited by a 2 W
biasing resistor. For a 500 mA fuse current the melt time is about 27 mS. The actual fuse
time will be somewhat greater than this.
The copper cladding o f the «100 Q bias line is 35 microns thick providing a cross
sectional area about 10X greater than the 17.5 micron bond wire. The bias tee is housed
in a metal enclosure made as small as possible and lined with echosorb™. It has standard
SMA type microwave connectors, and is equipped with shielded SMC dc connectors. The
packaged circuit is shown in figure 2a and the schematic is shown in figure 2b.
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25
♦•"S**
::vr:weeSJCf'd
C.07G
Figure 2. High voltage 8-22 GHz bias tee in SMA/SMC package (a-top) and circuit
schematic (b-bottom)
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26
►«Si k5.K c£J
,t
12,45 c£}.'
V
>CQ MPG
m^SHZyi i
2E.72 CS-te
-3.24S <J~
-rS .2 * '-S d S
MfWCR a
.13.7*25 Oiarc
i
3 2 . 7S GHz
"ebTrrs S3?
r.:v)Kr
" i,2 i« 3 c e
a.ssaaaceiaas »•**
,as.sggsaeiag>a3 awa
. o^aSsSB s
Figure 3. Measures S-parameters o f high voltage bias tee
The
ubiquitous
tunable
microwave
circuit
has
been
monopolized
by:
mechanically adjusted structures such as screw-tuned cavity filters or dielectric
resonators, ferrite components such as waveguide phase shifters, and semiconductor
devices such as PIN diode phase shifters and varactor-based voltage controlled
oscillators. None o f these can optimize cost, mass, and performance simultaneously.
Research on bulk ferroelectric materials during the past several decades has shown
promise. But, the microwave community has generally recoiled from the use o f these
materials because o f the high electric fields required for tuning as well as their
comparatively high loss tangent (> 0.01). For example, to tune the material over its entire
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27
dielectric constant range, fields as intense as 20 kV/cm are required. Within the past two
years, thin film deposition techniques have been developed to allow the growth o f high
quality ferroelectric material (e.g., SrTi03 and Bai.xSrxTi0 3 ) on low loss dielectric
substrates such as LaA 103 and MgO. Dielectric constants as large as 5000 have been
measured in SrTi03 films at 77 K from 10 KHz to 3 GHz using capacitors and microstrip
resonators [ 43,44].
Information Systems
Evolving high data rate communications systems demand greater attention to
subtle aspects of information theory and electromagnetic engineering. As the ratio of
signaling bandwidth to carrier frequency decreases, less familiar phenomenon enter into
system performance. And, new coding techniques are pushing channel capacity ever
closer to the Shannon limit [45], Some o f these effects are expected to become quite
pronounced if the trend toward wide-band scanning phased array antennas and efficient
high-speed modulators continues [46], For example, in a phased array antenna inter­
element spacing, the physical size o f the array, and the steering vector can conspire to
introduce pulse distortion from group delay, inter-symbol interference, and beam
squinting [47,48]. And the operating point o f the amplifiers can affect the bit error rate
depending on the modulation type and the number o f carriers. Naturally one wants the
phased array to operate as efficiently as possible given power limitations and thermal
management problems. This desire necessitates that the power amplifiers operate in a
nonlinear region near saturation. Nonlinear effects cause amplitude-to-amplitude
modulation (AM/AM) and amplitude-to-phase modulation (AM/PM) distortion. The net
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28
effect o f AM/AM distortion is to alternately compress and expand the signal
constellation. The net effect o f AM/PM conversion is a rotation o f the signal constellation
[47], In a receive array, the third order intercept o f the low noise amplifiers largely
determines inter-modulation distortion and heat dissipation [49], Phase shifters typically
follow low noise amplifiers in a receive array and precede power amplifiers in a transmit
array. Since the phase shifter's insertion loss depends on its phase setting and since its
switching action represents some finite time domain response, its potential contribution to
bit error rate degradation cannot generally be ignored. There will always be some effects
in any phase shift keyed (PSK) modulation system, to what degree depends on the
steering vector update rate and data rate.
The work presented in the Chapters II and III represents a new design strategy for
compact, low loss phase shifters, based on thin dielectric films, at high microwave
frequencies. Because the best results obtained to date have been with SrTiC>3 , which has
a dielectric constant peak below 100K, and because of the close lattice match and
chemical compatibility with some high temperature superconductors, there will
necessarily be a cryogenic facet to the work. This is especially true in the case of
oscillators, covered in Chapter V, for which the high Q o f the superconductor is
important. For other applications such as phased array antennas, ferroelectrics with a
Curie temperature near 290 K are obviously more desirable. Cooling an entire array is too
daunting a task given the state-of-the-art in cryogenic coolers. Chapter IV provides
insight into the possibility o f agile antennas.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
CHAPTER II. THEORETICAL APPROACH
The phase shifters analyzed here hold promise for reflectarray applications
because they are compact, low-loss, and can be lithographed on the same surface as the
radiating element. The designs used are based on a series o f coupled microstriplines
interconnected with short sections o f nominally 50 Q microstrip. The maximum coupled
voltage occurs when the coupled sections are a quarter wavelength long (i.e. 6=90°). Bias
up to 400 V is applied to the sections via printed bias-tees consisting o f a quarter-wave
radial stub in series with a very high impedance quarter-wave microstrip. A sketch of the
coupled microstrip cross-section is show in figure 4. By concentrating the fields in the
odd mode, the phase shift per unit length is maximized and by using the film in thin film
form the effects o f high loss tangent are minimized. Selecting the strip spacing “s”
involves a compromise among: minimizing insertion loss, simplifying lithography, and
minimizing the tuning voltage.
29
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
30
y I - ----------------- W
Odd m ode
ho»{hi+h2)f fv j« h 2
W » ( 2 w>s)
Figure 4. Cross-section of the coupled microstripline phase shifter showing the
odd-mode electric field configuration. Yi and Y 2 represent the admittance looking in the
positive and negative y direction, respectively, from the charge plane. The thickness o f
the ferroelectric layer is hjwhile the host substrate has thickness I12.
A key advantage o f this technology is the relatively large feature size. Active
devices at the frequencies o f interest here would necessitate submicron gate length GaAs
FETs. The finest feature size associated with the coupled line phase shifters is the
electrode separation s, typically *10 pm. Whereas the GaAs FET performance is largely
dictated by transconductance and hence carrier transit time across the gate region, the
coupled line phase shifters are static devices. The electrode gap separation determines the
degree of electromagnetic coupling and the dc potential required to tune the film. As a
rule-of-thumb the cutoff frequency fc of a MESFET scales roughly with gate size as f =
9.4/1 where the frequency is in GHz and 1 is in microns. Hence the ferroelectric phase
shifters have much larger feature sizes at a given frequency o f operation and
consequently much less demanding process requirements. The total phase shift can be
increased by cascading coupled line sections. Each section is linked by a 50 Ohm or so
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
31
microstrip jumper. A photograph o f a 4-section phase shifter patterned on O.S mm MgO
is shown in figure 5. The fabrication process is described in Chapter HI.
Figure 5. A 4-element BaxSri.xTiC>3 phase shifter on 0.5 mm MgO. The circuit
measures 1 cm x 1 cm.
Variational Formulation of Line Capacitance
The multi-layer structure is analyzed here using a computationally efficient
variational method to calculate the complex propagation constant and characteristic
impedance. If a quasi-TEM type o f propagation is assumed these parameters can be
completely determined from line capacitance. The method is quite general and can be
used for multiple layers o f various dielectrics or other types o f transmission lines. For
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
32
example, a multi-layer microstrip can be analyzed by allowing the strip spacing (s) to
become much greater than the substrate thickness (h) or strip width (w). It was mentioned
that adding sections is used to increase insertion phase. But this occurs at the expense of
bandwidth since the structure resembles a multi-pole filter. Changing the dielectric
constant o f the ferroelectric film to change insertion phase also modifies the pass band
characteristic, resulting in a net bandwidth of perhaps 5 %. The impedance matrix o f the
cascade network can be derived by well-known coupled line theory using the
superposition o f even and odd mode excitation. Then an equivalent S-parameter model
can be extracted and used to predict the pass-band characteristics o f the phase shifter.
Line capacitance (C) can be calculated by adapting the quasi-TEM variational
expression from Koul and Bhat [73] and using the transverse transmission line method of
Crampagne, Ahmadpanah and Guiraud [74],
l/C = (l/q 2)Lp(x,y)4.(x,y>//
where q =
Is
(7)
p(x,y)c/Z and <i>(x,y) is the potential distribution which satisfies Poisson’s
equation and can be expressed in terms of the admittances (Y 1.2) at the charge plane
looking in the positive and negative y directions. According to Crampagne, et al., the
admittance can be expressed in terms o f the dielectric constant o f each layer. The charge
distribution p(x,y) for the even and odd mode excitations was assumed to have the form:
p(x-y)co = l/w{ 1+A*.0 I(2Av) (x - (W-s-w)/2) 13}, (W-s)/2 - w < x < (W-s)/2
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
(8)
33
where A«.0 are constants derived by maximizing the even (e) and odd (o) mode
capacitance. That is, a trial function that maximizes capacitance yields the most accurate
result. It is an attribute o f the variational method that the trial function for the charge
distribution does not have to be known precisely a priori in order to evaluate capacitance.
The variational approach is only valid for electrically thin stratified substrates. But since
the coupling to surface waves represents an operational limit, it is appropriate for
practical microwave applications. Appendix D provides a transcendental solution for the
surface wave cutoff frequency based on a transverse transmission line method.
n
C4 M ( n ) - L O L L O P -ga)
(4 M ( a ) - ^ ) ) MCn) sCn)
3
•where
10
and
11
an d
M (n ) :=
t
■stn
( a - s - w) - 3
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
12
34
Here, n is summed over all odd integers. A summation from 1 to 1999 was adequate for
convergence. Ac is derived similarly, by summing over all even integers.
The coupled line structure can be optimized to minimize loss and maximize phase
shift. In the even mode currents in the strips are equal in amplitude and flowing in the
same direction. In the odd mode currents in the strips are equal in amplitude but flow in
opposite directions. So, Zoe is the characteristic impedance of one strip to ground with
equal currents in the same direction and ZQO is the characteristic impedance of one strip to
ground with equal currents in opposite directions. The microstrip mode exists when
s » h ,w and Z0e=Z00. The thin FE film is most effective when the phase velocity is
dominated by the odd mode fields. The propagation constant is given by:
P = o /V p = ( 7 z / Xo) (8eVEN'!/2 + SODD* 2)
(13)
where
Seven
Ce^CEair
and SoDD
C o/COair
(14)
and Cgair and Coair are obtained by replacing all dielectrics with air (i.e. er=l).
The admittance at the charge plane, corresponding to figure 4, is easily shown to be
[75,76]:
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
35
ian-h£9-coth
Y(n) :=£ O'
'n - n h
h
-coth
coth
1'
n-n-h
£ j -cothl
fn-nhe
15
1 + £9 coth
A more general formulation for the admittance consisting o f an additional dielectric
layer, say air, with thickness lb between the host substrate and the ground plane can be
expressed as:
cothn-n-—
+ So tanh n ?r-—
+ £n-£ j t a n h l n f f —
£ 9 + coth n- n -—
Y(n) = £ 0 c o t h n ^
tanh a n -----
+ £ 0 £ 1'
coth n n
+ £ 9 -tanh n-ff---•tanh n-ff-—
£ 9 + coth n- n
tanh n- n----
Finally, the odd mode capacitance becomes:
U+ C o :=
2 0 C n )(K n )+ A o M(n))2
17
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
36
And the even mode capacitance is similarly obtained, by summing over even integers
with Ac replacing Ao. For a TEM transmission line, the characteristic impedance is
obtained as Zo=[(CCair)I/2c]'* where c is the speed o f light in vacuum.
In general minimum attenuation is obtained when the effect o f the ground plane
loss is minimized, i.e. In the odd or balanced mode current flows into one strip and
returns through the other. Maximum attenuation occurs in the even or unbalanced mode
when equal currents flow into both strips and return through ground.
A comparison between the
quasi-TEM
approximation and a full-wave
electromagnetic simulation is given in table IV for microstrip. The spacing s was allowed
to increase just until the even and odd mode capacitance was equivalent. Choosing
arbitrarily large values for s yields anomalous results.
Table IV. Modeled data for a 2 pm ferroelectric layer on .25 mm thick LaA103,
Zo=50 Ohms, s » w ,h (microstrip mode)
Er Ferroelectric Layer
E eff (Sonnet ™)
Eeff (V'ariational)
300
18.76
18.43
600
21.34
21.00
900
23.49
23.09
1200
25.41
24.93
1500
27.18
26.59
1800
28.84
28.12
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
37
The quasi-TEM solution runs on a Pentium II machine in about 10 seconds
regardless o f the value entered for the ferroelectric film dielectric constant. The same
calculation on a commercial electromagnetic simulator using finite element techniques
can take several hours because the geometry must be fractured into thousands o f cells for
these very high dielectric constants. The MatchCAD program file is reproduced in
Appendix B.
A set o f graphs for propagation parameters o f coupled lines on various substrates
derived with this technique is presented in appendix A for design purposes [77], The even
mode impedance always higher than the odd mode since the odd mode effective
dielectric constant is greater. The dielectric loss is obtained phenomenologically by using
the complex dielectric constant for the ferroelectric and its host substrate (i.e. e=Eo£r(l - j
tan5)). The loss tangent of the ferroelectric was assumed to be 0.05 at zero field, 0.028 at
moderate field, and 0.005 at maximum field tuning. The dielectric loss a is given in
Np/m.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
38
Coupled Ferroelectric Microstrip Lines
The CMPS circuit resembles a series of one-pole bandpass filters. As the dc bias
increases, the dielectric constant o f the BST film decreases, causing the passband to rise
in frequency and the tan 8 of the BST to decrease. The bandwidth compression from
tuning is evident in figure 6 which is data from an 8-section phase shifter on 0.3 mm
MgO using a 400 nm Bao.6oSro.4oTi0 3 laser ablated film. Because o f the inherent circuit
effect that is apart from the intrinsic film properties the figure o f merit introduced in
equation 5 is invalid. A suitable figure o f merit that takes into account both film and
circuit characteristics is simply phase shift per insertion loss in degrees per decibel.
l o g MAG
REF 0 . 0
5
/
dB
2 .0 dB/
—S . 4 0 5 6 c B
_ n .....
p B K E D T e - CMF*S~9STFr£ I 2 r ■] '
1
0.0
•
.
i
.
’
I
j
■ ■ ■f
MARKER 2
1 8 . 0 GHz
- 5 .3 7 5 dB
MARKER 3
8 0 . 0 GHz ;
- 5 .9 9 6 8 dB
-4.0
8.0
MARKER 4
1 8 8 . 0 GHz
- 6 . 8 6 9 5 cB
12.0
►MARKER 5
8 4 . 0 GHz
,- 6 .4 0 5 6 dB
-
-
TlARKER 1 ~!
1 6 . 0 GHz !
—5 .7 * 5 4 9 d B
I__
__I
-16.0 ;
START
1 5 .0 0 0 0 0 0 0 0 0 GHz
STOP
.0 0 0 0 0 0 0 0 0 GHz
I- i S AUG 9 * |
I 1 5 :8 8 :2 3 I
Figure 6. Measured Insertion Loss (dB) o f 8-element «50 Q PLD coupled
microstripline phase shifter. Substrate is 0.3 mm MgO with 400 nm Bao.6oSro.4oTi0 3
film Bias voltages are 0, 25, 50, 100, and 150 V. The coupled lines are 350 pm long
and 30 pm wide separated by 7.5 pm. Bandwidth compression from the filtering
effect is evident. T=295 K.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
39
The roll-off at the upper end o f the frequency range may be attributable to bias-tee
effects. The open circuit impedance matrix has been derived by Jones and Bolljahn [78]
for coupled strip line filters using the superposition o f the even and odd modes as shown
in figure 7. From symmetry:
Zu=Z22=-}/2 (Z oc + Zoo) cot0(V)
(18)
And
Z 13=Z 3 ,=-j/2 (Zoc - Zoo) csce(V )
(19)
Where 0(V) is the voltage dependent electrical length of the coupled lines obtained from
(13) and the physical length of the coupled region (i.e. 0(V) = P(V)1) . The characteristic
impedance can be expressed as the geometric mean of the even and odd mode impedance
such that:
Zo = (Zoe Zoo)17
(20)
Equation (20) is strictly valid only for pure TEM propagation and ignores frequency
dependence. However, for a practical geometry with moderate coupling, like that
considered here, the expression is appropriate.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
40
Zoo
Zo
-V
V
P(V)
Z oe
Zo
/C
nW "
Zo
V
r r n W
V
2
•
20
y T
POO
Zo
Figure 7. Even (bottom) and odd (top) mode currents are superimposed to derive
the impedance matrix of a coupled microstrip line phase shifter section
To facilitate the calculation, the Z-parameters are converted into ABCD or chain
parameters for the cascaded sections. The conversion is:
(21 )
Z21,
Z llf Z22f -Z 12f Z21f
Z2L
221,
222,
221
,
(22)
(23)
(24)
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
41
where the indices are used to show frequency dependence. If the short intervening
sections o f microstrip line (between each coupled line section) are assumed to be o f zero
length the overall two-port chain matrix becomes:
a. b .\
1 1|
ic .
\i
d.l
i/
I/a i.
b .\
/ a 1.
1W
\C
X iij D.\
b .\
/a
1W 1
b .\
l W/a i.
b .\
/a .
1W 1
b .\
i ' Ai Bi /Ai Bi /Ai Bi
i \C. i/ D.\ i \C D./
i/ \C.
\ i D.if \C.
i i D.t,
c i DJ
(25)
c i Di / \ c i Di
Where the indices i and f are intended to be interchangeable. Finally, the two-port
S-parameters of, in this case an 8-section phase shifter, can be converted back according
to:
( ci 2 o) b.
(26)
J L + c i Z o + di
(27)
ai + ^ 1 + c i Z o + di
Figure 8 shows the passband shift and change in insertion phase as the dielectric
constant o f a 500 nm ferroelectric film on 0.3 mm MgO is tuned from 3500 to 500.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
42
-to
100
* H )“
deg
“100
«o
30
10
t GHz
30
30
40
X GHz
ebsto=350C. !an<3=0 G5.t=0 5 microns.er=9 7.h=3CU m icrons.s-10 microns. w=30 microns
100
-3 0
dog
cE
-too
40
10
so
40
x GHz
ebsto=500. tand=0 005.t=0 5 microns.er=9 7.h=3CM microns ,s=*0 microns. >*^30 microns
Figure 8. Quasi-TEM approximation o f bandpass characteristics of an 8-section
phase shifter. Insertion loss in dB is on the left, insertion phase in degrees is on the right.
A set of graphs corresponding to the theoretical amplitude frequency response of
phase shifters on typical substrates is presented in the following pages. This data
elucidates the important effect o f film thickness and illustrates the impact of substrate
choice on bandpass characteristics. In each case the top graph corresponds to a single
phase shifter and the bottom graph to an 8-section device. In all cases the host substrate
loss tangent was assumed to be 0.001.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
43
-2 0
10
20
30
40
GHz
t
/ >•
-10
-2 0
2 0 -:
dB
-3 0
10
20
30
40
i GHz
Figure 9. Phase shifter on 0.3 mm MgO with a 2 nm film with dielectric constant
2500. s= 10 (im, w=30 nm, 1=350 nm. The calculated insertion phase per section was
65.9°, sctT=59.4, Od=66.3 Np/m, Zoe=93.5, Zoo=9.5 (Zo=29.7).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
44
-20
10
30
40
f GHz
-10
dB
-3 0
10
20
30
40
i GHz
Figure 10. Phase shifter on 0.3 mm MgO with a 2 n m film with dielectric constant
1000. s= 10 nm, w=30 nm, 1=350 nm The calculated insertion phase per section was
46.6°. scfr=29.6, o<,=22.5 Np/m, Zoe=l 17.4, Zoo=14.1 (Zo=40.7).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
45
-2 0
10
20
* GHz
30
40
-1 0
-20
dB
-3 0 -
-40
10
20
40
i GHz
Figure 11. Phase shifter on 0.3 mm MgO with a 2 pm film with dielectric constant
500. s= 10 pirn, w=30 pm, 1=350 nm. The calculated insertion phase per section was
37.3°, eCfr=19.0, otd=3.0 Np/m, Zoe=133.0, Zoo=18.6 (Zo=49.7).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
46
-2 0
10
30
*
GHz
s
-10
-2 0
dB
40
-
-30
10
20
i GHz
30
40
Figure 12. Phase shifter on 0.3 mm MgO with a 1 pm film with dielectric constant
2500. s= 10 jam, w=30 pm, 1=350 pm. The calculated insertion phase per section was
50.5°, £ctf=34.9, 0^=45.3 Np/m, Zoe=l 11.9, Zoo=12.8 (Zo=37.9).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
47
-20
10
20
f GHz
30
40
-1 0
20-:
-30
-40
10
20
i GHz
30
40
Figure 13. Phase shifter on 0.3 mm MgO with a 1 tun film with dielectric constant
1000. s= 10 jim, w=30 p.m, 1=350 (im. The calculated insertion phase per section was
37.4°, se(T=19.1, a<j=15.3 Np/m, Zoe=132.9, Zoo=18.5 (Zo=49.6).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
48
S. w
10
20
*
30
40
GHz
-1 0
20-:
dB
-20
-3 0
-40
10
20
i GHz
30
40
Figure 14. Phase shifter on 0.3 mm MgO with a 1 jim film with dielectric constant
500. s= 10 nm, w=30 nm, 1=350 nm. The calculated insertion phase per section was
3 1.2°, sefl=13.3, 0 4 = 2 . 2 Np/m, Zoe=145.6, Zoo=23.4 (Zo=58.4).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
49
“ 20
10
20
f GHz
30
40
-1 0
/ "*•
-30
10
20
i GHz
30
40
Figure 15. Phase shifter on 0.3 mm MgO with a 0.5 pm film with dielectric
constant 2500. s= 10 (im, w=30 jim, 1=350 nm. The calculated insertion phase per section
was 40.0°, eeff=21.9, cx<i=30.7 Np/m, Zoe=l28.2, Zoo=17.0 (Zo=46.7).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
50
-2 0
10
20
f GHz
40
30
-1 0
/■\
-2 0
dB
-30
10
20
i GHz
30
40
Figure 16. Phase shifter on 0.3 mm MgO with a 0.5 |im film with dielectric
constant 1000. s= 10 (am, w=30 (am, 1=350 nm. The calculated insertion phase per section
was 31.2°, eeff=13.3, 0^=103 Np/m, Zoe=145.5, Zoo=23.4 (Zo=58.4).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
51
-2 0
10
20
f GHz
30
40
-10
-2 0
dB
-30
10
20
i GHz
30
40
Figure 17. Phase shifter on 0.3 mm MgO with a 0.5 nm film with dielectric
constant 500. s= 10 nm, w=30 nm, 1=350 nm. The calculated insertion phase per section
was 27.1°, 8efi=10.0, OLd=16 Np/m, Zoe=155.2, Zoo=28.4 (Zo=66.4).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
52
-2 0
10
20
f GHz
30
40
-1 0
-2 0
dB
-30 -
10
20
i GHz
30
40
Figure 18. Phase shifter on 0.25 mm LaAlQj with a 2.0 nm film with dielectric
constant 2500. s= 8 nm, w=25 nm, 1=457 nm. The calculated insertion phase per section
was 100.1°, ecfr=83.1, <^=70.4 Np/m, Zoe=72.5, Zoo=8.2 (Zo=24.4).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
53
-20
10
20
f GHz
30
40
-1 0
20-:
dB
-2 0
-30
10
20
i GHz
30
40
Figure 19. Phase shifter on 0.25 mm LaAIOj with a 2.0 jim film with dielectric
constant 1000. s= 8 jam. w=25 tun, 1=457 nm. The calculated insertion phase per section
was 73.9°, 8cir=45.3, Od=23.9 Np/m, Zoe=86.3, Zoo=l 1.9 (Zo=32.1).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
54
10
20
30
40
i
-1 0
20-:
-2 0
-30
-40
10
20
i GHz
30
40
Figure 20. Phase shifter on 0.25 mm LaAlOa with a 2.0 nm film with dielectric
constant 500. s= 8 pm, w=25 pm, 1=457 pm. The calculated insertion phase per section
was 61.4°, eeflf=31.3, 0^=3 4 Np/m, Zoe=94.7, Zoo=15.2 (Zo=37.9).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
55
-20
10
20
f
30
40
GHz
-1 0
-2 0
dB
-30
10
20
i GHz
30
40
Figure 21. Phase shifter on 0.25 mm LaAl(>3 with a 1.0 nm film with dielectric
constant 2500 s= 8 nm, w=25 nm, 1=457 nm. The calculated insertion phase per section
was 79.4°. setr=52.3, Od=47.9 Np/m, Zoe=83.2, Zoo=l0.9 (Zo=30.1).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
56
-2 0
10
20
t
40
30
GHz
-1 0
-\
-2 0
dB
-3 0
-4 0
10
20
i GHz
30
40
Figure 22. Phase shifter on 0.25 mm LaAIC>3 with a 1.0 (im film with dielectric
constant 1000. s= 8 pirn, w=25 pirn, 1=457 pm. The calculated insertion phase per section
was 61.7°, seflf=31.6, a<i=16.2 Np/m, Zoe=94.7, Zoo=15.1 (Zo=37.8).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
57
-2 0
10
20
t
30
40
GHz
-1 0
-2 0
dB
-30
10
20
i GHz
40
Figure 23. Phase shifter on 0.25 mm LaAlC>3 with a 1.0 pm film with dielectric
constant 500. s= 8 nm, w=25 nm, 1=457 nm. The calculated insertion phase per section
was 53.5°, eeff=23.7, ctd=2.5 Np/m, Zoe=101.1, Zoo=18.3 (Zo=43.1).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
58
-2 0
10
20
t
30
40
GHz
-10
20-:
-2 0
-30
-40
10
20
i GHz
30
40
Figure 24. Phase shifter on 0.25 mm LaAlC>3 with a 0.5 (am film with dielectric
constant 2500. s= 8 (am, w=25 (am, 1=457 (am. The calculated insertion phase per section
was 65.3°, seff=35.4, a<i=32.3 Np/m, Zoe=92.2, Zoo=14.0 (Zo=35.9).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
59
-20
-40
10
20
i GHz
30
40
-1 0
20-:
dB
-2 0
-30
-40
10
20
1
30
40
GHz
Figure 25. Phase shifter on 0.25 mm LaAJCh with a 0.5 |xm film with dielectric
constant 1000. s= 8 nm, w=25 nm, 1=457 nm. The calculated insertion phase per section
was 53.6°, eeff=23.8, ot<j=10.8 Np/m, Zoe=101.1, Zoo=18.3 (Zo=43.0).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
60
-2 0
-4 0
10
30
t
40
GHz
-1 0
-2 0
dB
i—
-30
10
20
i GHz
30
40
Figure 26. Phase shifter on 0.25 mm LaAlC>3 with a 0.5 fim film with dielectric
constant 500. s= 8 urn, w=25 urn, 1=457 pirn. The calculated insertion phase per section
was 4 8 .2 ° , Een = I 9 . 3 , <Xd=l.8 Np/m, Zoe=105.7, Zoo=21.3 (Zo=47.4).
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
61
For the sake of comparison, several full-wave models were constructed on
Zeeland Software’s “IE3D” full-wave electromagnetic simulator. IE3D uses a method of
moments based solution and has proven to be very accurate when compared to
experiment for these multi-layer structures. Figures 27 through 29 correspond to the same
phase shifter as in figure 6. The film apparently contributes about 1.25 dB to the total
loss.
90
60
-5
30
-10
-15
-30
-20
-60
-25
-90
-30
-120
-35
-150
-40
20
21
22
23
24
25
26
27
26
29
-160
30
Frequency (GHz)
Figure 27. Simulated frequency response of the phase shifter corresponing to
figure 6. Substrate is 0.3 mm MgO with 400 nm Bao.6oSro.4oTiC>3 film. The 8 sections of
coupled lines are each 350 pm long and 30 pm wide separated by 7.5 pm. ebsto=300,
tanS=0.05, cr=4.9 x 107 S/m.
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62
180
-5
135
-10
- 80
-15
45
Ang
-45
-30
-90
-35
-135
-40
12
14
16
20
18
22
28
-180
30
Frequency (GHz)
Figure 28. Simulated frequency response o f the phase shifter corresponing to
figure 6. Substrate is 0.3 mm MgO with 400 nm Bao.6oSro.4oTiC>3 film. The 8 sections o f
coupled lines are each 350 pm long and 30 pm wide separated by 7.5 pm. 8bsto=2500,
tan5=0.005, o=4.9 x 107 S/m.
dBfSO.-l)]
AnolS<2.1>]
180
-5
135
-10
80
-15
45
dB -20 r
Ang
-25 ’
-45
-30 r
-90
-35 i-
-135
-40
12
16
18
20
22
24
26
28
-180
30
Frequency (GHz)
Figure 29. Simulated frequency response o f the phase shifter corresponing to
figure 6. Substrate is 0.3 mm MgO with 400 nm Bao.6oSro.4oTi0 3 film. The 8 sections o f
coupled lines are each 350 pm long and 30 pm wide separated by 7.5 pm. ebsto=2500,
tan5=0.05. 0=4.9 x 107 S/m.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
CHAPTER m . PHASE SHIFTERS
Phase shifters like the one in figure 4 are fabricated using standard lithography
techniques. The “lift-off’ processing recipe is straightforward. Starting with a clean
substrate, AX4210 photoresist is spun on at 4000 rpm. This is followed by a soft bake at
75° C for 30 minutes. The photoresist is exposed through a visually translucent iron oxide
mask for 30 seconds using a Carl Zeuss mask aligner with 300 nm optics. To facilitate
the lift-off process, the wafer is soaked in chlorobenzene for 10 minutes at 25° C and
blown dry with N 2 . This is followed by a second bake at 90° C for 10 minutes. The wafer
is developed for about 2 minutes in 4:1 deionized H20:AZ400K developer, rinsed in
deionized H 2O for 5 minutes, and blown dry with N 2 . Metalization consists of
evaporating a 150 Angstrom adhesion layer followed by 1.8 jim o f Ag followed by a 500
Angstrom Au cap. The wafer is then soaked in acetone until the metal lifts off.
It is
advantageous to etch the ferroelectric from all regions except the coupled lines so that the
bias tees are insensitive to tuning. A dilute 5% HF solution has been used to etch a
BaxSri.xTiC>3 rectangular mesa beneath the coupled sections. The tradeoff is that
positioning the pattern over a good region o f material is tougher.
63
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
64
Experimental Data
The performance of these devices is measured using an HP 85IOC automatic
network analyzer. The device is paced in a simple test fixture with SMA connectors and
usually the launchers are attached to the microstrip input and output with silver pint.
Measurements are usually done in a vacuum o f about 10 mT to prevent dielectric
breakdown of the air between the coupled lines. Alternatively, paraffin can be used to
coat the lines but occasionally air bubbles trapped inside may contribute to arcing. In the
future, a spray coated teflon coating will be used to permit safe operation under ambient
conditions. Coupled microstripline
FE phase shifters capitalize on the odd mode
propagation constant and so have much more phase shift per unit length than simple
microstripline while avoiding the need for a coplanar ground. Microwave measurements
of coupled microstripline phase shifters of epitaxial Bao.sSro.sTiOs films grown by CCVD
on 0.5 mm MgO showed very low loss (estimated tan 8 was between 0.03-0.002 at 20
GHz at 23°C). As shown in Figure 30, the magnitude o f transmission coefficient, S2 1 , at
all frequencies exhibits symmetrical curve as a function o f bias voltage at 297 K, as
expected. The best figure of merit was 53°/dB [79], It is evident that the hysteresis is
negligible.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
65
iiii| ii
CQ
•O
»
[
.
Tl| 11
S ~2
CO
° -3
■o
sj
X -4
A
+
*
0
*
a
130
SJ
a -5 /
-6 n_i i.
-3 0 0
-lL
-2 0 0
-1 0 0
11
1*
15
16
20
0
GHz
GHz
GHz
GHz
GHz
\
100
200
300
B ia s V oltage (V)
Figure 30. Measured 50 Ohm 4-section phase shifter on MgO at 297 K. The
Bao.5oSr0.5oTi0 3 film was grown by MicroCoating Technologies using CCVD.
1r-r
*t tana
i"i i*oottam
i i iad.
i »ino
i iannaai
ii i
A
+
x
0
5® 60
■ tt
11 G H z
14
IS
16
20
GHz
GHz
GHz
GHz
-c 20
-3 0 0
-2 0 0
-1 0 0
0
-*■* * 1 * ■*■ 1 * ■■■1 i I*
100
200
300
B ias V o lta g e (V)
Figure 31. Measured insertion phase corresponding to figure 30.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
66
The best films have been deposited by laser ablation at temperatures between 650
and 750 C and a dynamic oxygen pressure near 100 mTorr [80,81], Thicker BaxSri_xTi0 3
films (>350 nm) generally exhibited poorer microwave performance despite having a
clear theoretical advantage in terms o f maximizing tuning. Crystalline quality
unfortunately degrades as film thickness increases. The degradation is faster in BaxSri_
xTi0 3 than in SrTi0 3 . Chapter V reports additional results on SrTiC>3 films that were up to
2 pm thick. The use o f MgO (£,=9.7) allows wider lines for a given impedance compared
to LaA1 0 3 (sr=24). Consequently, the conductor loss is lower on MgO. Figures 32 and 33
show measured insertion loss and phase for 0.5 pm Bao.6oSr0.4oTi0 3 film grown on 0.5
mm MgO. Choosing a operating temperature that approaches the Curie temperature from
the paraelectric phase usually results in larger phase shifts but correspondingly higher
loss.
0.0
t|°°.c ? hr q"?*ol[
+
«
1 6 GHz
1 8 .5 GHz
-0 .5
-1 .5
£
-
2.0
S - 2 .5
- 3 .0
100
200
3 00
40C
B ias V oltage (V)
Figure 32. Measured 50 Ohm 4-element coupled line phase shifter at 210 K with
Au/Cr electrodes patterned on a 0.5 pm Bao.6oSro.4oTi0 3 film grown on 0.5 mm MgO.
The film was grown by the Naval Research Laboratory. These film were 1% Mn doped
and annealed at 1100 C for 6 hours.
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67
100
A
+
x
1 5 GHz
1 6 GHz
1 7 GHz
*
1 8 .5
GHz
QL 20
100
200
300
40C
B ias V oltage (V)
Figure 33. Measured insertion phase corresponding to figure 32.
The best performance to date has been obtained from YBa2Cu3<>7-s and laser
ablated SrTiC>3 films on (100) single crystal LaAlC>3 substrates [82]. Data for an 8-section
nominally 50 Q coupled microstrip device at 16 GHz is shown in figure 34. The
superconducting film was 350 nm thick and the ferroelectric film was 2.0 tun thick. A
figure of merit approaching the goal o f 120 °/dB was obtained. It is unclear what role
surface effects may have played in the superior performance o f this particular phase
shifter that used YBa 2Cu 3 0 ?^ electrodes instead of metal electrodes. Note that while bulk
SrT i03 is an incipient ferroelectric, thin films exhibit a relative dielectric constant
maximum between 40 and 80 K.
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68
P h a se (degrees)
-G— M agnitude (dB)
500
in
w
flf
w
D
>
TO
J
400
300
CO
*—
o
o
200
■V
■C
CO
100
a.
0
-4 0 0
-10
-300
-2 0 0
-1 0 0
0
100
200
300
400
d c V o ltag e (V)
Figure 34. 8-section 50 Ohm coupled microstrip phase shifter at 40 K using
YBa2Cu307-s electrodes and laser ablated SrTiOs films on (100) single crystal 0.25
mm LaAI0 3 . Hysteresis is unremarkable.
Some recent results suggest that after extended voltage cycling an anomalous
discontinuity in loss and phase occurs under certain bias and film growth conditions.
The origin o f this polarization change is not understood at this time. Fatiguing effects
have been observed in ferroelectric films for DRAM applications, where occasionally
micro-cracks occur to absorb the stress. Such effects are irreversible. The study of
this phenomenon is ongoing. Also, it is not known with certainty what effect the film
orientation relative to the applied electric field has on circuit performance. In the
coupled line structure, as opposed to a microstrip or parallel plate structure, the field
is essentially parallel to the surface of the film. In bulk material, depending on the
temperature, the dielectric constant can depend on whether the field is applied parallel
to the c- or a-axis. In the paraelectric state, X-ray analysis indicates that the thin films
are essentially isotropic [83].
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CHAPTER IV. ANTENNAS
Microstrip patch antennas are highly desirable for aerospace applications because
they are lightweight, conformal, and inexpensive since they can be produced using
lithographic methods. They are becoming increasingly important because o f the
proliferation o f low Earth orbiting communications and remote sensing satellites that
generally demand phased array antenna systems. The major drawback o f microstrip
antennas is their inherently narrow instantaneous bandwidth, typically 1% or so.
Intuitively obvious approaches to enhance bandwidth such as the use o f extremely low
permittivity substrates or thick substrates are met with an undesirable increase in antenna
size or the generation o f surface waves that degrade efficiency.
Frequency Agile Microstrip Patch Antenna
A multi-mode broadband patch antenna is introduced here that maintains about the
same instantaneous bandwidth as a conventional microstrip patch but can be tuned over
an extremely broad frequency range [84], For example, the technique permits the same
aperture to be used for reception at 19 GHz and transmission at 29 GHz. Commercial and
military applications include low cost tracking terminals to complement the forthcoming
wide-band low Earth orbiting satellite constellations and stealthy communications and
radar systems.
69
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70
Several approaches are currently used to increase patch antenna bandwidth. Stacked
patches have been used to generate dual resonant frequencies. In this approach, a bottom
patch is covered with a dielectric layer that serves as the substrate for the top patch. The
bottom patch serves as a ground plane for the top one. Bancroft [85] demonstrated such a
structure operating at 9 and 11 GHz, a difference o f about 20%. Another approach is to
use varactor diodes to modify the resonant frequency. Haskins et al. [86] integrated a
diode with a multilayer patch and obtained a 4% tuning range. Navarro and Chang [64]
integrated a varactor with a notch antenna and achieved tuning from 8.9 to 10.2 GHz, a
range of about 14%. Washington and Yoon [65] arranged a patch above a parasitic
element and varied the separation using piezoelectric actuators to shift the frequency.
Rainville and Harackiewicz [71] described a patch fabricated on a ferrite film. The
application o f an in-plane magnetic field tuned the resonant frequency o f the cro sspolarized field but not the co-polarized field. The tuning range was 5.86 to 6.03 GHz,
about 3%.
None o f these technologies demonstrated the ability to operate over the frequency
ranges required by practical communications systems. For example, the Teledesic system
requires the ground terminal to receive at 19 GHz, with a 500 MHz bandwidth, and
transmit a narrow-band signal at around 29 GHz. Either a gimbaled parabolic dish with a
dual frequency feed or two scanning phased array antennas are required. While the dish
could operate at both frequencies, it cannot mechanically respond fast enough to return to
the opposite horizon to track the next satellite. Therefore, two gimbaled dish antennas
would be necessary anyway.
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71
The prior art has other disadvantages as well. The stacked patch arrangement
requires assembly o f a sandwiched structure and does not provide dynamic tuning. The
parasitic patch with the piezoelectric actuator provides some tuning but is bulky and
expensive. The varactor-tuned antenna requires the integration of a solid state device with
the radiator, which is costly. The ferrite film antenna requires an intricate circuit to
generate high magnetic fields and has a very limited tuning range.
The multi-mode broadband patch capitalizes on the ability to modify the
dielectric constant o f a thin ferroelectric film with a dc electric filed. A theoretical
analysis has indicated that the resonant frequency of a patch antenna patterned over a thin
ferroelectric film can be tuned between 5 and 10 %, depending on the substrate and film
thickness.
A schematic o f the multi-mode broadband patch is shown in figure 35. It is of length L
in the x direction and width W in the y direction.
L
Figure 35. Tunable microstrip patch antenna schematic and dc bias field configuration
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72
In order to operate the antenna at multiple high frequencies, it is designed for a
fundamental TMoi mode that is resonant at an odd common denominator o f the desired
radiation frequencies. Using the antenna in an odd mode produces radiation normal to the
antenna, while an even mode would place a null in the normal position. The antenna can
be visualized as a resonant cavity formed by the ground plane and patch. A standing half­
wave is formed at the fundamental frequency with fringing fields at the patch edges. The
edges are interpreted as radiating slots. Since the electric field lines are parallel to the feed
linear polarization results. Using a simple cavity model analysis, the resonant frequency
of the patch is:
fmn * c/(2:Wec(V))[(m/W)2 + (n/L)2] I/2
(28)
where ee(V) is the effective dielectric constant o f the stratified substrate. The actual
frequencies tend to be somewhat lower than predicted by this simple formula because o f
fringing fields.
The lowest order mode (TMoi) requires the length to be about Vi wavelength long
at the fundamental frequency But the cavity defined by magnetic walls at the patch edge
can support an infinite number of modes. The width is chosen to optimize performance.
Narrow widths reduce efficiency but widths greater than about 2L can generate
undesirable higher order modes. For circular polarization, W and L are generally equal
and a feed is constructed to excite orthogonal edges o f the patch 90 degrees out of phase.
The microstrip feed line is inset a distance 5 for matching. Edge impedance (R«dge) can be
calculated using closed-form expressions [87], A reasonable estimate for inset distance
can be calculated using Rjn=RcdgeCOS2(7t5/L) where Ri„ is the desired input resistance. The
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
73
patch antennas discussed below were optimized using 1E3D. In all cases the gap between
the feed inset and the body of the patch was set equal to the width o f the feed line.
The dielectric constant o f SrTi03 can be varied from about 3500 to 500 at electric
field strengths o f 0 and 15 kV/cm, respectively, hence at low potentials the substrate
begins to look electrically thick. As the dielectric constant is tuned past 1000 toward
1500, the input impedance of the antenna becomes entirely inductive and it ceases to
radiate. The generation o f surface waves eventually limits the tuning range o f the
structure. Figure 36 is an IE3D simulation of the TMoi mode o f a microstrip patch on
silicon.
-0.5
dB
-3.5
-4.5
5
5.25
5.S
5.75
6
F req u e n c y
6.25
6.5
6.75
7
(G H z )
Figure 36. Return loss of the TMOI mode of a microstrip patch on 0.046 cm thick silicon. The
length and width of the patch is 0.72 cm. The thickness of the ferroelectric layer is 0.5 pm and its
dielectric constant is 300.
By designing the patch to operate in its fundamental mode near 6.2 GFIz, the
antenna can be tuned to operate in higher order odd modes near *18 GHz and *30 GHz.
The return loss and modeled E-field radiation pattern are shown in figures 37 through 40.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
74
d B [ S ( 1 .1 »
i
-2
dB
-6
-10
-
X
-1 2
17
17.25
17.5
17.75
J.
18
F re q u e n c y
18.25
10.5
18.75
19
(G H z)
Figure 37. Return loss o f the patch o f figure 36 for the TM 03 mode.
o.
-
10
.
-
15
.
—•—TE03 E-total, phl=0. (dag)
dB -20.
-25.
-30.
-35.
-90.
-60. -30.
O.
30.
60.
90.
Elevation Angle (deg)
Figure 38. E-field pattern corresponding to figure 37 at 18.1 GHz
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
75
d B tS ( l.l) ]
-1
dB
-4
-e
29
2 9 .25
2 9 .5
2 9 .7 5
30
F re q u e n c y
3 0 .2 5
30.5
3 0 .7 5
31
(GHz)
Figure 39. Return loss o f the patch o f figure 36 for the TMos mode
teOS E-total, phi«=0. (d«o>
O.
-5.
-15.
-25.
-30.
-35.
-90.
-60.
-30.
O.
30.
60.
90.
Elevation Angle (deg)
Figure 40. E-field pattern corresponding to figure 39 at 30.1 GHz
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76
A -10 GHz microstrip patch patterned on LaAlCh with a Bao.6oSro.4oTiC>3 film showed no
tuning. The disappointing result is attributed to a thinner than expected film (<400 nm)
and a restricted tuning voltage o f <500. Simulated results to follow will show the
importance of film thickness for patch antenna applications. Furthermore, referring to
figure 35, by enforcing the boundary condition that the electric flux density must be
continuous across the dielectric interface (assuming zero surface charge at the interface)
Ei=£2/siE 2 . Therefore the voltage dropped across the ferroelectric layer is only
Vl=S 2/siE 2di. It stands to reason that with a dc field o f only about 0.1 V/ftm, tuning
would be nil. Judiciously choosing the resistivity o f a silicon substrate can yield a good
tunable antenna. For example, given a resistivity o f 1000 Qcm the loss tangent is better
than 10'3, which is a reasonably good substrate from an antenna point o f view.
And,
since the substrate is semi-conductive the counter electrode, which is the ground plane,
translates to a region near the bottom o f the ferroelectric layer. High resistivity silicon in
large wafer sizes is grown by the float zone process and is commercially available.
Phase
shifters
have
been
patterned
on
silicon
using
a
Bai.
xSrxTi0 3 /Bi4Ti3Oi2/(Zr02)o.9i(Y2 0 3 )oo9 heterostructure to reduce chemical interactions
and film strain [88], Figures 41 and 42 illustrate the results obtained so far. The films
were grown at the University of Maryland.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
77
CM
CO
-2
0)
■ g -3
-*->
-M
C
00
<0 - 4
S
>
-5
i
i
20
■ ■
i
40
i
i
1
1
1
1
60
80
Bias Voltage (V)
Figure 41. Insertion loss o f a 4-element phase shifter on Si at 298 K. A mask for 0.5 mm
MgO was used but the dielectric constants differ by only bout 15%.
50
00
40
A 14 GHz
+ 15 GHz
x 16 GHz
0 17 GHz
☆ 19.6 GHz
30
20
20
40
60
B ias V o lta g e (V)
Figure 42. Insertion phase corresponding to Figure 41.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
80
78
While the films are very tunable, leakage currents through the high-resistivity silicon
limit performance. Beyond about 40 V, a current of 5 mA was drawn which was the limit
of the power supply. It is not yet known if the leakage current is due to porous films and
pin holes or Schottky effects, etc.
The potential tuning range and the effect o f ferroelectric film thickness was
studied by analyzing an X-band patch on LaAlC>3 . Despite the fact that the best films
have been grown on this substrate, it is somewhat unattractive for antenna applications
because of its high dielectric constant (23.6) that reduces efficiency and bandwidth.
Nevertheless it provides a good indication o f what is possible in terms o f tuning range.
The patch was designed for 0.25 mm LaAlC>3 . The length L was 0.312 cm and the width
W was 0.533 cm, with a matching inset 8 of 0.114 cm. The microstrip feed line and inset
spacing from the patch were both 75 pm. Figures 43 through 48 illustrate the tuning
based on observing a well defined resonance in SI 1. The data was modeled using LE3D.
The inset depth was held constant.
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79
d B I S I I.I lI
!
-i
-2
-3
dB
-4
-5
-7
7
S
7.5
8.5
9
F req u en cy
9.5
10
10.5
11
(G H z )
Figure 43. Return loss o f tunable patch on 0.25 mm LaA103. Ferroelectric film thickness
is 2 nm and er is 1200. TanS o f the film was assumed to be 0.02.
-i
-2
dB
-7
9
7
7.5
8
8.5
9
9.5
F req u en cy
10
10.5
11
11.5
12
(G H z )
Figure 44. Return loss o f tunable patch on 0.25 mm LaAI03. Ferroelectric film thickness
is 2 |a.m and er is 300. TanS of the film was assumed to be 0.02.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
80
-2
-4
dB
-10
-12
-14
8
8.2
8.4
8. 6
8.8
F re q u e n c y
9
9.2
9.4
9.6
(GHz)
Figure 45. Return loss o f tunable patch on 0.25 mm LaA103. Ferroelectric film thickness
is 1 p.m and sr is 1200. TanS o f the film was assumed to be 0.02
o
i
4
5
6
7
8
8.25
8.5
8.75
9
F re q u e n c y
9.25
9.5
9.75
10
(GHz)
Figure 46. Return loss o f tunable patch on 0.25 mm LaA103. Ferroelectric film thickness
is 1 |dm and er is 300. TanS o f the film was assumed to be 0.02
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
81
2
0
-2
-4
-6
-8
-10
-12
—
9
8.5
10.5
10
9.5
F req u en cy
11
11.5
(G H z)
Figure 47. Return loss o f tunable patch on 0.25 mm LaA103. Ferroelectric film thickness
is 0.65 jam and er is 1200. TanS o f the film was assumed to be 0.02
d B IS ll.D I
-1
-2
dB
-4
-5
-6
- 7 I—
8.5
9
9.5
10
F req u en cy
10.5
11
11.S
12
(G H z )
Figure 48. Return loss o f tunable patch on 0.25 mm LaAJ03. Ferroelectric film thickness
is 0.65 jam and er is 300. TanS o f the film was assumed to be 0.02
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
82
It appears that, at least on this particular substrate, there is somewhat o f a
threshold effect insofar as tunability and film thickness is concerned. Below a film
thickness o f 750 nm or so the resonant frequency is essentially impervious to the changes
in the dielectric constant o f the thin ferroelectric layer. Also, recently developed artificial
dielectrics or so-called photonic bandgap crystals, may offer some relief from the moding
problems associated with these electrically thick substrates. The photonic bandgap
structure involves a periodic array of perturbations embedded in the substrate to suppress
surface modes.
Prototype Linear Phased Array
A prototype scanning 16-element linear phased array using Bao.6oSro.4oTi0 3 films
on 0.3mm thick MgO has been developed [120]. The array is intended to be a
steppingstone to collision avoidance radar suitable for automotive applications. Because
of its potential to provide a much lower cost solution for certain Intelligent Vehicle
Highway Systems, the array will be exhibited at the General Motors “Innovation Zone”.
The exhibit showcases technology that is expected to be introduced into the automotive
marketplace in about a five-year time frame.
The 23 GHz array consists o f a monolithic 1:16 microstrip beam forming
manifold constructed on 0.25 mm thick Duroid 6010, 16 phase shifters patterned on «1
cm x 0.75 cm MgO substrates, and a monolithic set o f microstrip patch radiators
patterned on 0.25 mm thick Duroid 5880. A layout is shown in figure 49. Inter-element
spacing is 7.49 mm, which corresponds to bout 0.57 free-space wavelengths.
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83
The original manifold, which had each successive branch o f the divider networks
separated by only 1.3 mm experienced severe coupling problems resulting in
considerable loss and asymmetry between ports. The distance was increased to 4 mm
c-
y-
U
a
=§
Cr-
fcs y­
fr­
er
cc-
t-
LJ
Figure 49. 16-element linear phased array layout
and resulted in a uniform insertion loss of about 13.0 plus or minus 0.25 dB. The patch
array was originally fabricated on high dielectric constant material (er=10.2). However,
when the resonant frequency of each patch was measured using a HP 8510C automatic
network analyzer a large discrepancy was seen between each one. Figure 50 is the
measured data for a random sampling o f the patches on the high epsilon material. Since
the frequencies do not overlap, it was impossible to utilize this particular array.
Concerned that the problem might be due to mutual coupling, each patch was diced away
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
84
and re-tested individually. But the resonant frequency remained the same. The variation
was attributed to dielectric constant tolerances.
>
Figure 50. Measured resonant frequency o f some patches on 0.25 mm thick high
dielectric constant (er=10.2), 1 oz. Cu clad material. A variation in frequency o f nearly
10% is evident.
Indeed substrate tolerances are known to cause serious errors in phased array
performance [89],
To circumvent the problem a low dielectric constant homogenous
material was selected. When the array was re-designed on 0.25 mm thick Duroid 5880,
the variation in resonant frequency was much smaller, about 5%, and the bandwidth was
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85
suitable for the prototype. Figure 51 depicts the measured frequency response. The patch
dimensions are: L=4.27 mm, W=6.40 mm, and 5=1.04 mm. The gap between the feed
inset and patch was 0.38 mm.
*-
Figure 51. Measured resonant frequency o f some patches on 0.25 mm Duroid 5880
(er=2.2), 1 oz. Cu clad material.
The phase shifters used in this array are the same as those associated with figure 6. The 8
coupled line sections are 350 urn long each with a 7.5 pm gap. The bias tees have a 25pm
wide, 1.83 mm long high impedance line connected to a radial stub with flare angle o f
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86
75° and radius 1.17 mm. No particular attention was given to reducing sidelobe levels or
reducing spurious radiation from the manifold or feed.
The measured boresight principal-plane pattern is shown in figure 52 and a
modeled pattern at a 45° scan is show in figure 53, obtained from PCAAD software. The
3-dB beamwidth of the azimuth pattern is about 6°, while the elevation plane beamwidth
is about 80°. The array was designed to scan out to 45 degrees.
■w
a
■so
1
§o
•100
-to
-to
-70
-00
.5 0
-40
-SO
-20
-10
0
tO
20
30
40
SO
00
70
00
00
100
A
n«i>to* BorttfpUt [Otfrvet]
Figure 52. Measured boresight far-field E-Plane (elevation) and H-PIane (azimuth)
pattern o f the 16-element ferroelectric phased array at 23.5 GHz. The cross-polarization
amplitude was <-27 dB.
An electronic module was designed and built to control with the array. It consists
o f 16 independently addressable dc-to-dc converter channels. A model AOB 16/16
analog to digital converter interfaces the controller with a PC. Since the A/D could only
source 5 mA per channel, an operational amplifier buffer (OPA547) was inserted
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87
between the A/D outputs and Pico Electronics model 12AV500 encapsulated dc-dc
converters. A 1 W, 1 MfJ resistor is strapped across the transformers output to prevent a
no-load condition. Since the dc input resistance of the phase shifters is » 1 Mf2, the
Figure 53. Predicted E-plane pattern o f the 16-element phased array, scanned off to 45
degrees. The grating lobe is just beginning to appear.
applied voltage is essentially the programmed voltage. A 0.1 |iF capacitor rated at 1 KV
provides some filtering. Finally, an LED status indictor on each channel senses whether a
thermal overload condition is present. The controller board is shown in figure 54. It
consumes about 25 mA per channel under normal conditions.
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88
Figure 54. High voltage controller board for the 16-element phased array. The board
measures 19 cm x 14.5 cm. The board accepts a 0-10 V signal from a 16 channel A/D
converter and outputs a linear 0—400 V control signal.
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89
Ferroelectric Reflectarray
In 1963 Berry introduced a new class o f antennas that utilized an array o f
elementary antennas as a reflecting surface [59]]. The “reflectarray” has the potential to
combine the best attributes o f a gimbaled parabolic reflector, low cost and high
efficiency, and a direct radiating phased array, vibration-free beam steering. A key
advantage is the elimination o f a complex corporate feed network. The reflectarray
consists of a two-dimensional aperture characterized by a surface impedance and a
primary radiator to illuminate that surface.
In 1975 Fheian patented a scanning reflectarray based on interleaved Archimedian
spiral antennas [90], Spiral arms are interconnected with diode switches. The spirals are
inherently circularly polarized over a broad bandwidth. Far-field phase shift from a
circularly polarized radiator is proportional to the apparent physical rotation o f the
radiator. The number o f arms that can be intertwined is limited and hence the scanning
resolution may be limited. Diode loss and overall cost may have curtailed wider use o f
the technology.
A photograph o f a passive 30 GHz reflectarray is shown in figure 55. The
elements, barely discemable, consist o f three sets o f spiral arms. One set was wire
bonded together on all 256 elements in a attempt to form a cophasal beam at bore-sight.
The rotation of each element was adjusted a priori to roughly compensate for the
variation in spatial delay from the center to the perimeter of the array, assuming a
spherical phase front. But the E-field pattern was poor since the phase o f each element
could not be adjusted properly.
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90
In 1978 Malagisi proposed a microstrip reflectarray [91]. In a microstrip
reflectarray, stubs aligned with the desired polarization direction and o f varying length
are attached to the elements to effect phase shift. Incident energy from the primary feed
propagates down the stub, where it reflects from the open end, and re-radiates with a
delay corresponding to twice the electrical length o f the stub. A passive 16-element
microstrip reflectarray was reported in [62].
-
■■
Figure 55. A passive 256 spiral element reflectarray on 0.25 mm A I 2 O 3 . A corrugated
feed hom illuminates the reflectarray surface. The diameter is about 25 cm.
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91
A circularly polarized microstrip reflectarray with a 55% efficiency was reported
by Huang and Pogorzelski [92], The antenna used square patches with identical stubs but
varying rotation angles. The coordinate system for the reflectarray analysis is shown in
figure 56. For a planar array o f M x N uniformly illuminated elements with a feed at rf,
the re-radiated field, with free-space wave number ko, in direction u is:
E ( u ) = X X H^mn
rf) A ( I W
Uo) A (U
exp{-jko[ | •"mn * r f| ■+" Tmn
Uo)
U]
+ jtpmn
(29)
where the position vectors r and unit vectors u are as given in figure 56. The feed pattern
function and element pattern function are given by F and A, respectively. The
summations are from m=l to M and n=l to N, respectively. The required phase delay to
form a cophasal beam in the u0 direction is given by (fw
The phase delay required o f
each element is:
cpmn = 2ntt + ko[|rmn - rtj + !•„» ' u0], n= 0,l,2...
(30)
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92
Reflectarray Surface
Observation
Direction
m,nth element
Fmn
iT o
Beam
Direction
Feed
Origin
Figure 56. Reflectarray coordinate system [92].
Inefficiencies results primarily from spillover loss, specular reflections, and crosspolarization. A square patch array with improved cross-polarization and high efficiency
was reported in [93]. The cross-polarization problem was traced to leakage radiation from
the delay lines. To reduce the effect, the delay lines were arranged in mirrored symmetry
instead o f all being collinear. Overall efficiency as high as 70% was reported.
None of these microstrip reflectarrays were active scanning phased arrays. A new
type o f reflectarry is presented here. The phase shifters described in Chapters II and in
can be integrated with microstrip patch radiators to form a phase agile antenna. Because
the antenna elements and phase shifters can be defined using a two-step lithography
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93
process, the ferroelectric reflectarray1 holds promise to dramatically reduce
manufacturing costs of phased array antennas. This compares favorably to a
semiconductor manufacturing process that may require 10 steps or so. And the
reflectarray immediately solves the thermal management problem discussed in Chapter I
since the feed can be a single MMIC power amplifier or perhaps a miniature TWT. A
receive reflectarry has been designed at 19 GHz and is pictured in figure 57. A circular
aperture was approximated arranging 177 subarrays as shown to improve the aperture
efficiency.
Figure 57. A 2832 element 19 GHz ferroelectric reflectarray. The callout shows a 16
element subarray patterned on a 3.1 x 3.1 cm2, 0.25 mm thick MgO substrate. The array
diameter is 48.5 cm. The unit cell area is 0.604 cm2 and the estimated boresight gain is 39
dB.
1 R.R. Romanofskv and F.A. Miranda. “A High Resolution Scanning Reflectarray Antenna”, Pat Pend.
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94
The array was designed to scan past a 45 degree angle with an inter-element spacing o f
0.52 wavelengths. The callout shows 16 4-section phase shifters coupled to a square
patch antenna with a 90 degree hybrid coupler. The phase shifter is terminated abruptly in
an open circuit and is used in a reflection mode. One output o f the coupler has an
additional 45° microstrip extension to feed the orthogonal edges o f the patch 90° out o f
phase. For right hand circular polarization the phase shifter is attached to the left port o f
the coupler so the vertical edge o f the patch receives the reflected energy with a 90°
delay. While a triangular grid pattern permits the fewest elements per unit area, it was
simpler to fit the phase shifters in a square unit cell. The governing assumption in the
design is that a 3 dB insertion loss phase shifter can be consistently reproduced. Indeed
the phase shifter performance drives the performance and cost o f the entire array. Even
with a 3 dB loss device, assuming a receiver noise figure of 2 dB, the system noise
temperature exceeds 800 K. Because the phase shifter is inserted between the antenna
terminals and the low noise amplifier, it has the same effect as a feed line with equivalent
loss in the determination of noise. The array noise does not increase with the number o f
elements since the noise is non-coherent but the signal at each element is correlated [9496]. Assuming an aperture efficiency o f 70% and a scan loss that falls o ff as cosG12, the
gain-to-noise temperature ratio (G/T) o f the array is estimated at « 3 .1 dB/K. This was
the advertised requirement for Motorola’s Celestri system. If the phase shifter loss could
be reduced to 2 dB, the number o f elements would be cut in half.
A cost analysis was performed by surveying vendors for film growth and
substrates, estimating integration and assembly costs including labor, and adding in the
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95
miscellaneous parts like the amplifier and supporting struts. Assuming pulsed laser
ablation was used to deposit the films on a somewhat exotic substrate like MgO, in
quantities of 10,000 annually, the projected manufacturing cost o f the ferroelectric
reflectaray is $44 per element. This is a Herculean advantage compared to state-of-theart phased array costs but still unacceptably high for any conceivable consumer
application. In the future, improved screen printing or CCVD processes may reduce the
manufacturing costs to the «$1 per element needed for wideband residential satellite
communications applications.
In a receive reflectarray, the low noise amplifier represents a small fraction o f the
total cost. In the case o f a transmit reflectarray an interesting tradeoff between power
amplifier cost and cost-per-element may occur. Solid state power amplifiers will probably
represent a substantial part of the overall cost. A simple optimization problem can be set
up to determine the best combination o f amplifier power and aperture gain to minimize
cost. For want o f a better model, it is assumed that there is a linear relationship between
amplifier power (p) and cost, i.e. the cost is equal to Kp where K is a positive constant.
Assuming perfect efficiency, the effective isotropic radiated power (P) * the number o f
antenna elements (n) times p. Here, we are ignoring spillover loss, aperture inefficiency,
and element gain which will tend to offset each other to an extent. If we let the cost per
wafer (c) include all material and processing costs and assume that the total cost is
dominated by the wafer and amplifier cost, then the total cost (C) o f an array requiring N
wafers is:
C = cN + Kp
(31)
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96
And if we let each wafer contain 16 elements equation 31 can be solved for p by taking
the derivative o f the cost function:
d/dp(cP/16p + Kp) = 0
(32)
A constraint on n is that the aperture gain should be much greater than the feed gain.
From (32) it is easy to show that p=[cP/(16K)]l/2.
Equiangular Spiral with Integral Marchand Baiun
Another possible way to realize the ferroelectric reflectrray is to pattern spiral
elements over thin ferroelectric films in order to effect phase shift. The effect o f tuning
the stratified substrate beneath a spiral is still being investigated but it may be possible to
induce a far-field phase shift by causing the apparent electrical length o f the spiral arms
to expand or contract, or by modifying the coupling between adjacent arms. The fact that
the impedance and polarization of the spiral remain constant over a wide bandwidth
would be advantageous.
As a prelude to the tunable spiral, a planar equiangular spiral was fabricated on
Duroid and integrated with a microstrip Marchand balun2. The balun both transforms the
unbalanced microstrip to balanced coplanar coupled lines and provides an impedance
transformation from 50 to about 150 Cl. Hence the spiral, which has a nominal impedance
of rio/2, is fed with equal amplitude but opposing phase currents. A schematic o f the
microstrip realization of a Marchand balun is shown in figure 58.
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97
<------
..
..j
t
h Zo=67Q
J
Zo= 108ft
Zo=70ft
Zo=l12Q
+
+
Figure 58. Microstrip Marchand balun on 0.75 mm Duroid 6010. The length o f the 50 f l
microstrip, the long rectangular bar on the right, is 8.9 cm and its width is 0.75 mm.
The microstrip is on the obverse. The textured region represents slots in the ground plane
on the reverse. The junction between the quarter-wave slot-line section on the reverse and
the quarter wave microstrip section is electromagnetically coupled. The distance from
the end of the slot-line on the backside to the impedance step, corresponding to a quarterwavelength, is 0.306 cm and its characteristic imedance is 112 Q. When two back-toback baluns were tested the insertion loss was better than 4.5 dB from about 4 to 16 GHz
a shown in figure 59. That loss included 17.8 cm o f 50 Q microstrip. The balun is
attached to the spiral from underneath. Two pins are soldered to the coplanar strips and
inserted through the substrate to the spiral terminals. The terminal radii (r0) o f the spiral
are 0.264 cm and 0.376 cm and it can be described by the curve r=r0exp(a<f>) where a was
chosen as 0.221. The spiral, constructed, on 0.318 cm thick Duroid, had 1.5 turns and an
outer diameter of about 6 cm. The antenna was tested by measuring the insertion loss
: J.H. Cloete. “Graphs o f Circuit elements for the Marchand Balun”, Microwave Journal, May. 1981.
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98
from the spiral radiating into a section o f Ku-band waveguide. The bandwidth, which my
have been limited more by the cutoff o f the waveguide rather than the spiral and balun is
illustrated in figure 60. When the waveguide was rotated by 90°, the insertion loss
worsened by about 3 dB, indicating a poorer than anticipated axial ratio.
FBBLDKT
MORKER 1
3 . 8 9 GHz
p o irrfc - 2 2
Figure 59. Measured insertion loss and return loss o f the microstrip Marchand balun. The
scale on the ordinate is 5 dB/division and the scale on the abscissa is 2 to 22GHz. The
loss includes two SMA launchers and 17.8 cm o f 50 f2 microstrip. Marker 1 (S21) is at
3.89 GHz, -4.9 dB and marker 2 (S 11) is at 16.22 GHz, -14.7 dB.
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99
0.0
-50.0
2.0
Frequency (GHz)
20.0
Figure 60. Insertion Loss (S21) of Spiral illuminating a section o f waveguide with its Eplane parallel to the spiral terminals. Marker 1 is at 8.93 GHz, -19.2 dB and marker 2 is at
16.22 GHz.
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CHAPTER V. OSCILLATORS
Oscillators generate the microwave energy for communications, radar, and
navigation systems. For example, modulators, superheterodyne receivers, and phased
locked loops depend on a high quality microwave source to function properly. A typical
specification for a frequency-modulated carrier wave (FMCW) automotive collision
avoidance radar is a phase noise o f «80 dBC/Hz at a 100 kHz offset in order to discern
adjacent targets with adequate resolution [15], For oscillation to occur, the magnitude of
the reflection coefficient of the embedded active device must be >1. In principle, any
amplifier could be made into an oscillator by providing positive feedback to the input
terminals. But, the choice of load and terminating impedances must be made carefully in
order to guarantee the proper operating frequency and maximize efficiency. The
oscillator basically consists of a low noise amplifier with a feedback loop (delay) such
that the overall loop gain is greater than unity. For oscillation, the total delay around the
loop must be an integer multiple o f 2rt. This Chapter focuses on transistor-based
oscillators, and emphasize low phase noise, compactness, thermal stability, and
reliability.
The phase noise (i.e. short-term instability) o f an oscillator is critically important in
Doppler radar for absolute detection o f moving targets. But, the importance o f a good
100
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101
oscillator might best be explained in the context o f the impact o f phase noise on bit error
rate (BER) performance in digital communications systems. Low phase noise, high
efficiency oscillators are critical for evolving transceiver front-ends. This is a growing
concern because for emerging systems the ratio o f signaling bandwidth to carrier
frequency is decreasing. The oscillators used are o f increasingly higher frequencies and
they exhibit an increasingly degraded phase noise profile. In order to better understand
the mathematical significance, consider a general signal described by:
V(t) = [V„ + e(t)]sin[cDot + cp(t)]
(33)
where e(t) is the amplitude noise term and <p(t) is the phase noise term. For | e(t) I«
and I q>(t) | «
V0
1 rad,
V(t) *V0 sin (to0t) + V0 cp(t)cos((0 ot) + e(t) sin(o>0t)
(34)
where the first term is the carrier o f peak amplitude V0 and radian frequency ©o, the
second term represents the phase noise, and the third term represents the amplitude noise.
Since the last two terms produce deviations from the ideal sinusoidal oscillation, they can
be regarded as modulating the carrier. In practice, the phase noise manifests itself as
continuous energy sidebands around the carrier in the frequency domain. For the usual
case when the phase noise dominates (i.e. the amplitude noise is insignificant), the
spectrum around the carrier is symmetrical. The spectral density o f phase fluctuations can
be attributed to the following factors. There is a thermal noise floor associated with the
kinetic energy o f electrons. Thermal noise is broadband and essentially flat with
frequency (w). It is often called "white" noise because o f this behavior, since white light
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102
is broadband. Active devices also exhibit a noise characteristic which scales as o '1. This
noise is called "flicker" noise, evidently because o f historical observations o f plate
current in vacuum tubes. It can be attributed to the generation and recombination of
carriers at semiconductor surfaces, or traps (electrically active defects in the crystal)
within the semiconductor. The phenomenon is the subject o f widespread research and
entire conferences on held on only this subject. Furthermore, in a feedback oscillator, a
phase change anywhere in the loop translates into a frequency change. That is, the phase
modulation is converted directly into frequency modulation (since frequency is the time
derivative o f phase.) The power spectral density (rad2/Hz) o f phase fluctuations is
proportional to the rms phase deviation squared. The net result is that spectral slope o f the
white and flicker noise become twice as steep. A common way to express phase noise is
the ratio o f single-sideband noise power per Hertz to the carrier power at a specific offset
frequency. Following Leeson [97], a model can be summarized as follows. The power
spectral density, as a function o f offset frequency, -^(co) decreases with w: at 9 dB/octave
where flicker noise dominates, at 6 dB/octave up to the feedback loop half-bandwidth,
and at 0 dB/octave up to the system filter bandwidth. The phase noise spectrum is given
by:
^(co) = 10 log[N2 (1 + co02 /(2Qo2)(GFkT/P + ot/co)]
(35)
where N is the multiplication factor, Q is the loaded resonator quality factor, G is the loop
gain, F is the amplifier noise figure, T is the absolute temperature, k is Boltzmann's
constant, P is the oscillator power, and a is an empirically derived flicker noise constant.
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103
Obviously the noise cannot become unbounded at zero offset. A natural limit is set by the
finite operating time o f the amplifier.
Phase deviation cp(t) is generally treated as a zero mean, stationary random
process to facilitate modeling the noise spectrum o f a feedback oscillator. If a Gaussian
process with variance a 2 is assumed, it is possible to estimate the impact o f oscillator
phase noise on BER performance [98.99], For example, for a BPSK modulation format, it
can be shown that the probability o f error (Pb) is:
PB = fcpjca2]'* W c[(E b/N 0),/2 cos0]exp(-02/(2a2)d0
(36)
where the integration limits are the decision boundaries -tc/2 to
energy-per-bit to noise power/Hz ratio. The variance
ct2 can
te/2,
and Eb/N0 is the
be obtained by integrating
the phase noise profile over a specified frequency range, usually from the carrier tracking
loop bandwidth to the system filter bandwidth. The effect becomes quite pronounced for
narrow tracking bandwidths and wide signal bandwidths, and is more severe for higher
order modulation formats [100].
In order to minimize BER degradation, high Q resonators and low co'1 noise
transistors are required. At frequencies below a few hundred MHZ, quartz crystal
oscillators provide extremely stable sources. At low microwave frequencies, sources are
often implemented by multiplying up from a crystal source. But the phase noise degrades
according to (35). The efficiency is also poor and cost is an issue. Metal cavities are often
used as the stabilizing element but are bulky and costly. Planar superconducting
microstrip resonator oscillators have also been developed with excellent characteristics,
but require refrigeration [101], The dielectric resonator oscillator (DRO) has become a
practical compromise at high microwave frequencies in terms o f cost, size, and
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104
performance. Their popularity has grown with the development o f very low loss tangent,
thermally stable ceramics. Still, there is a tremendous interest in lower cost, miniature,
tunable oscillators. Despite the lower Q of MMIC chips, several types o f integrated
oscillators have been successfully developed. Transistor oscillators have been realized
using both MESFET and bipolar devices. GaAs MESFETs can be used at very high
frequencies but exhibit relatively poor baseband noise performance. Bipolar Si transistors
have superior noise behavior but are limited to a frequency range o f about 20 GHz.
Recently, InAlAs/InGaAs, AlGaAs/GaAs, and InGaAs/InP MMIC HBT based oscillators
have been demonstrated with excellent performance from Ku- through Ka-band [102104], At 26 GHz, a phase noise o f -80 dBC/Hz at 100 kHz offset, with a conversion
efficiency of about 10% has been reported.
The design considerations and fabrication processes for several MMIC HBT
oscillators are discussed in [102-104], The designs include integrated varactors fortuning
and coplanar waveguide implementations to eliminate via hole processing. A thorough
discussion of dielectric resonator technology is available from [105]. But the point to be
stressed here is that, for a certain class of applications, planar resonators may be
acceptable. That is, MMIC oscillators may find a niche where low cost and small size, in
addition to reasonably good phase noise characteristics, are a consideration. The lower
close-in (i.e. a ' 1) phase noise o f HBTs makes them an attractive choice for this
application. There is also evidence that GaAs HBT technology is virtually equivalent to
MESFET/HEMT technology insofar as reliability is concerned.
Thermal stability (i.e. long-term drift) problems have been addressed for various
types o f sources. At lower microwave frequencies, ovenized crystal oscillators can be
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105
multiplied up and phase locked. Special packaging approaches can be used to thermally
isolate the active device and resonator from the external environment. Free running
transistor oscillators generally have a negative temperature coefficient. Hence, a
resonator with a positive temperature coefficient is required to compensate for frequency
drift. Procedures to stabilize a DRO have been reported in [106]. A frequency stability o f
+/-
0 .1
ppm/K at 11.5 GHz was obtained. It may be possible to employ digital
temperature compensation techniques by integrating sensors and associated control
circuits with the basic oscillator. Such an approach has been used for monolithic phase
shifter circuits in the past.
As mentioned, the state-of-the-art in phase noise performance is represented by
crystal sources which are multiplied up to the desired signal frequency. Since phase noise
scales as
crystal stabilized LOs are generally restricted to frequencies below several
GHz. Dielectric resonator oscillators (DROs) are commercially available up to at least
20 GHz. However, DROs do not lend themselves to electronic tuning or frequency
locking. Further, the DRO resonator fabrication must be done independently o f the
oscillator circuit and its three-dimensional geometry impedes the fast, high volume
production of the optimized circuit. Similarly, cavity stabilized oscillators offer excellent
performance characteristics but are bulky and expensive. There is also rapidly growing
interest in voltage controlled oscillators (VCOs) at Ku-band and higher frequencies [107109], The purpose o f this work is to explore an entirely new VCO concept involving
several different technologies. It has been shown experimentally that the use o f a
superconducting resonator, instead o f gold, can improve phase noise by as much as 20 dB
at X-band because o f lower surface resistance [110], Nevertheless, knowledge o f the
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106
behavior of solid state devices for microwave applications at cryogenic temperatures,
especially down-converters, is incomplete. The implications o f phenomenon such as I/V
collapse, carrier freeze-out, 1/ f noise, etc. are still being studied [ 1 1 1 , 1 1 2 ].
Tunable Ring Resonator
Microstrip ring resonators patterned on SrTi03 films have demonstrated excellent
tunability. A characteristic impedance o f 25 Ohms offers lower conductor loss without
exiting higher order modes. The ring circumference is an integer multiple o f guide
wavelengths. Figure 61 shows the arrangement tested and figure 62 is typical measured
insertion loss data.
GO STO
Au arKTS
I 1 LAO
n
1 am
1
Top%
Micfoctrtpinp •
\ / H iorHTS
03-2pin
J
2A).m
STO
T
264 urn
LAO
77
7T
2i|m
(a)
(b)
Figure 61. Microstrip side coupled resonator. W=406 p.m for the 25 Q ring and 89 pm for
the 50 Q ring. w= 89 pirn, g=25 fim, and r=1694 pirn.
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107
0
-7
-14
-21
50
100
200
-35 — 300
350
-28
_
84.0
1484
268.0
380.0
433.0
-42
-49
15.2
16.4
17.6
18.8
Frequency (GHz)
Figure 62. Effect o f dc bias on S21 o f a 25 O microstrip ring resonator patterned on a 2
pm SrTiC>3 film on LaAlCh. V r corresponds to the dc bias on the ring and Vf corresponds
to the voltage on the microstrip line. Adjusting both voltages maintains coupling and
maximizes the loaded Q.
The acuteness of the resonance can be controlled by carefully adjusting the bias voltage
on both the line and ring.
A Cryogenic GaAs PHEMT/Ferroelectric Tunable Oscillator
A ring resonator fabricated from a multilayer structure comprised o f an evaporated
Au film with nominal thickness o f 2 pm, an evaporated 15 nm thick titanium adhesion
layer, and a 2 pm SrTiOj film deposited by laser ablation onto a (100) LaA1 0 3 substrate
(254 pm thick), is used as the stabilizing element in a novel VCO [113]. A standard lift­
off etching process was used to pattern the circuit. The ring resonator, which is three
guide wavelengths in circumference at the primary operating frequency, is shown in the
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108
left half o f Fig. 62. The characteristic impedance o f the microstrip ring was 25Q. This
impedance was carefully chosen and nearly optimal in the sense o f providing minimum
conductor loss (to improve Q) while avoiding higher order mode problems. The ratio of
microstrip width to mean radius o f the ring was 0.24, and the dominant (quasi-TEM)
mode was TM 3 1 0 (no azimuthal magnetic field component) [114]. A photograph o f the
oscillator is shown in figure 64.
Figure 63. Schematic o f the voltage controlled oscillator.
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109
Figure 64. Photograph of the Ku-band voltage controlled oscillator.
The estimated maximum unloaded Q was about 500 compared to less than 200 for a 50 Q
ring. These values compare favorably to conventional varactor-loaded rings [115]. For
comparison, the resonator used in [111], which was kept at room temperature but coupled
to a cryogenic PHEMT, had a loaded Q o f 160. The outer circle represents the location o f
the SrTiC>3 after selective etching with 7% hydrofluoric acid. The ring is tuned by
applying a dc electric field to the SrTi0 3
®‘as >s applied via a 25 pm diameter Au
wire bonded by thermal-compression near the 12:00 position on the ring (i.e. a virtual
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110
short circuit position). Tuning to lower (higher) resonant frequencies is achieved by
decreasing (increasing) the magnitude o f the dc bias applied to the ring. Frequency shifts
of
12%
at 16 GHz have been measured at 77 K with a bias o f 450 V [116]. Figure 62
shows the magnitude of the insertion loss as a function o f bias. The resonator was
characterized using the test fixture and techniques described in the next section. The
measurements are referred to the edge (input) o f the 1 cm long circuit. Note that the sharp
resonance is maintained by controlling the potential o f the microstrip line as well as the
ring, relative to the back plane at dc ground. That is, the coupling coefficient o f the side
coupled resonator can be controlled as well as the resonant frequency in order to operate
at an optimal point or “sweet spot.” Resonance splitting, which often plagues sidecoupled resonators, was not a problem [117],
An Avantek/HP 0.25 pm gate length ATF-35076 PHEMT, housed in a ceramic
microstrip package, was chosen as the active device because o f its premium noise figure
and associated gain and low cost. For the purpose o f obtaining the scattering (S-)
parameters o f the PHEMT, the device was attached to a 0.5 mm thick alumina (AI2 O3 )
coplanar waveguide carrier, which was inserted into a modified Design Techniques"
fixture. The fixture was connected to a HP 8510C vector network analyzer with semi­
rigid coaxial cables. A room temperature calibration using “short, open, and through”
standards first established reference planes a few mm from the carrier center. Reference
planes were then shifted to the device ports using an offset short and dialing in an
appropriate port extension with the 8510C. The fixture, carrier, and PHEMT were cooled
to 77 K using liquid nitrogen. The magnitude o f S2 1 , Sj \ and S2 2 ate shown in figure 65
for a drain (V j) and gate (Vg) voltage of 2.1 and -0.2 V, respectively. The corresponding
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I ll
drain current (1^) was about 13 mA A design frequency o f 16.7 GHz was chosen so as to
fall within the performance range of the ring resonator (see Fig. 2). The S-parameter
magnitudes and phase angles were: S jj = 0.462, 141.0°, S j 2 = 0.067, -105.0°, S2 i=
2.28, -81.4°, S2 2 = 0.22, 107.5°. Several devices were measured in this way on different
occasions with consistent results.
S n and 8 a
3004
M
18
17
10
10
IQHri
Figure 65. (a) Smith chart showing Su (bold) and S22 and (b) log-magnitude plot showing
the magnitude o f S21 for the PHEMT at 77 K. Vd=2.1 V, Vg=-0.2 V, and Id=13 mA.
The PHEMT portion o f the VCO was constructed on 0.25 mm thick AI2 O 3 and is
shown in the right half o f Fig. 64. The circuit pattern was defined using a standard
additive, as opposed to etch-back, Au electroplating process. The PHEMT leads were
carefully trimmed so that it fit snugly into the region indicated. Since the PHEMT was
unconditionally stable as tested, an inductance was inserted between the source and
ground. An iterative computer routine was used to vary the source impedance (Z§) to
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112
maximize the negative resistance o f the PHEMT while preserving enough loop gain.
Specifically, with a Z§ o f j35 Q, the new S-parameters became: S j j = 1.59, 94.3°, S j2 —
0.626, 3.7°, S22 = 1 223, 92.4°, S2 i = 2.197, -135.8°. The resulting stability factor (K)
was -0.499 and the magnitude of (S j i S22-S j 2S2 j ) = 1.284. The source inductance was
realized by inserting a section of 50 Q microstrip 1.08 mm long at each source
connection. The normalized impedance (Z&) o f the ring circuit at the design frequency
was 0.639-j0.228 fi, which includes the effects o f the 5 mm section o f microstrip
intervening between the gate terminal and the bisector o f the ring. This impedance
corresponds to the second resonance from the left in Fig. 62. The bias on the ring was 23
V and the bias on the microstrip was 0 V. With this biasing scheme there was no need to
be concerned with floating the PHEMT voltages with respect to ground since the gate and
ring circuit could be directly dc coupled. With the ring resonator circuit connected to the
gate o f the PHEMT as shown in Fig. 64, the impedance looking into the drain was -24.9
+ j47.7 or T = 1.6. The drain matching circuit shown in Fig. 63 provided a Z l = 8.3 j47.7 to ensure oscillation [118], The VCO operates below 77 K, near the dielectric
constant maximum of the SrTiC>3 , where the noise figure o f the PHEMT and the surface
resistance o f the Au resonator are minimized. A particular operating temperature of 43 K
was chosen to provide the maximum field induced tunability o f the SrTiOj. For testing
purposes, both circuits were attached to a brass fixture with conductive epoxy. The
fixture was inserted into the vacuum can o f a closed-cycle He gas refrigerator equipped
with semi-rigid coaxial cables.
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113
Changing the bias on the ring from 0 to 38 V varied the oscillator frequency by about
100 MHz around the center frequency. Figure 66(a) shows the spectrum o f the oscillator
over a very broad bandwidth. No spurs or sub-harmonics were observed. Figure 66(b)
shows a typical signal for the LO at a ring voltage o f 38 V. By increasing the ring voltage
to 250 V, the tuning range was extended over 500 MHz.
In summary, a novel tunable microwave ring resonator at 16.7 GHz has been
developed.
It offers potential advantages over traditional varactor-loaded rings and DROs. This is the
first time that a tunable oscillator based on a thin film ferroelectric structure has been
demonstrated at such a high frequency. A successful design approach for such a
cryogenic oscillator has been developed. In the near future, the Au ring will be replaced
with a YBa 2 Cu3 C>7 _ 5
ring and phase noise measurements will be made to compare
performance. The merits o f this VCO reside in its high performance potential, small size,
simplicity o f implementation, MMIC compatibility and its potential for low cost, high
volume production.
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114
Figure 66. VCO signals measured on a HP 8566B spectrum analyzer at 43 K with
Vd=2.1 V, Vg=-0.2 V, Id=13.9 mA, and VR=38 V. The scale on (a) is 2 to 22 GHz and
(b) shows 500 MHz span with the oscillation frequency at 16.696 MHz.
The MathCAD program written and used for the oscillator design is reproduced in
Appendix C.
A discriminator-stabilized version o f the oscillator is under development that
promises additional improvement in phase noise [119], The concept is depicted in figure
67. If the actual frequency o f oscillation is greater (less) than the crossover frequency,
then the diplexer generates a high-pass (low-pass) output, causing the differential
amplifier to decrease (increase) the dc bias.
This causes the permittivity o f the
ferroelectric material to increase (decrease) thereby causing the frequency o f oscillation
to decrease (increase).
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115
Figure 67. Proposed discriminator stabilized VCO.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
CHAPTER VL CONCLUSIONS AND FUTURE WORK
The crucial role o f ferroelectric film thickness in overall frequency and phase agile
device performance has been demonstrated experimentally and theoretically. Thick (2
pirn) SrTi03 films with superconducting electrodes performed close to the phase shifter
goal of 120°/dB at cryogenic temperatures. But attempts to transfer the performance to
room temperature have been hindered by degradation in film crystal quality when BaxSru
xT i0 3 thin films exceeded «500 nm. Complicated interactions at electrode interfaces, the
roles of surface charge and contamination, and the effects o f tension and compression on
tuning and loss remain subjects for further investigation. Strain and interface effects are
the most likely cause for the high loss observed in thin films as compared to single
crystals. Still, 8-section ferroelectric coupled-microstrip phase shifters have proven
worthy in comparison to their semiconductor counterparts at 295 K. Table V summarizes
several important parameters for a single coupled microstrip section on h2=0.3 mm MgO
(e=9.7) derived using the quasi-TEM analysis where ei and hi correspond to figure 4. The
insertion phase is designated as (fo, the composite dielectric loss as a d , and the
characteristic impedance is taken as Z 0=[ZoeZoo]1/2. In all cases the loss tangent o f the
host substrate was 0.001 and the loss tangent o f the ferroelectric film o f thickness hi was
taken as 0.05, 0.028, and 0.005 forei equal to 2500, 1000, and 500, respectively.
116
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117
>/■>
o
ll
xf
Table V. Theoretical propagation characteristics o f a single coupled microstrip section on
0.3 mm MgO based on the quasi-TEM method described in [7] and [13]. 1=350 pm,
s=10pm, and w=30pm.______________________________________ __________________
hi = 1 pm
hi = 2 pm
El
z o (n>
Zo (Q)
ad
ad
ad
z o (n )
4>1°
<t>.°
*i°
(Np/m)
(Np/m)
(Np/m)
29.7
2500
65.9
66.3
50.5
45.3
37.9
40.0
30.7
46.7
40.7
37.4
1000
46.6
22.5
15.3
49.6
10.3
31.2
58.4
3.0
49.7
500
37.3
31.2
27.1
2.2
58.4
1.6
66.4
The net phase shift is 2.2 times greater for the 2 pm film compared to the 500 nm film.
Table VI summarizes propagation characteristics for a single coupled microstrip section
on h2=0.25 mm LaAlC>3 (e=24) derived using the quasi-TEM analysis. The insertion
phase is greater because the effective permittivity of the composite structure is
substantially greater than that o f Table V. But the correlation between phase shift and
film thickness is about the same.
Table VI. Theoretical propagation characteristics o f a single coupled microstrip section
on 0.25 mm LaAlC>3 based on the quasi-TEM method described in [7] and [13]. /=457
pm, s=8pm, and w=25pm.__________ _________________________ __________________
hi = 2 pm
hi = 1 pm
hi = 0.5 pm
El
Zo (Q)
Zo (Q)
ad
ad
ad
Z o(Q )
4>i °
*i°
♦i°
(Np/m)
(Np/m)
(Np/m)
24.4
2500
100.1
70.4
79.4
47.9
30.1
65.3
32.3
35.9
1000
23.9
61.7
73.9
32.1
16.2
37.8
53.6
10.8
43.0
500
61.4
3.4
37.9
53.5
2.5
43.1
48.2
1.8
47.4
Better process control o f film uniformity and composition is needed. Thickness
uniformity and peak dielectric constant need to be held to tolerances of perhaps 5%. But
it is clear from the experimental and modeled data that the inherent dielectric loss of
epitaxial ferroelectric films isn’t necessarily devastating insofar as microwave device
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118
performance is concerned. Indeed the loss tangent o f a thin dielectric film (hi <2pm) on a
good substrate (tan5<0.001) can deteriorate substantially (tan5<0.05) before the insertion
loss o f the structures presented here is seriously compromised. For other applications like
tunable filters tan5 is more critical. Films that are O 2 annealed generally show higher
structural quality and higher peak dielectric constants near the Curie temperature.
Choosing an operating temperature approaching the Curie temperature from the
paraelectric phase usually results in larger phase shifts but correspondingly higher loss.
Dielectric constant values exceeding 3S00 have been obtained from Bao.6oSro.4oTi0 3 films
near room temperature. A figure o f merit around 70°/dB has been measured using pulsed
laser ablated films at room temperature, though combustion chemical vapor deposited
films have also shown a figure o f merit exceeding 58°/dB.
It is fundamentally important to ensure that a good conductor with the proper
thickness is used for the electrodes and ground plane. Figure 68 illustrates the difference
between the measured resistivity o f a thin gold film and bulk gold. Since the conductor
loss is proportional to surface resistance, there can be a dramatic impact on loss if the
conductor isn’t at least several skin depths thick. And the proper value for resistivity must
be used. For example, for a single section coupled line on 0.3 mm MgO and using the
thin film resistivity values from figure 68, the insertion loss at 19 GHz and 290 K for 1.0
jam and 2.5 pm thick gold electrodes is 0.63 dB and 0.48 dB, respectively. Hence an
excess loss of 1 dB per 8-section phase shifter can easily occur from improper
lithography. Some o f the experimental phase shifter data provided earlier may have
suffered from this effect.
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119
10-*
10
"*
A
p(T),
Qcm
10-*
+ 1 pm Au
A Bulk Au
10~*
0
50
100 150 200 250 300
T, K
Figure 68. Comparison between resistivity o f a thin evaporated Au film on A1203 and
bulk Au as a function o f temperature.
A linear K-band phase array has been demonstrated using these novel coupled
microstrip ferroelectric phase shifters. The phase array realized with these phase shifters
holds promise to significantly reduce manufacturing costs o f phase arrays because the
phase shifters are lithographed using a simple two-step process. And the finest feature
size is the strip spacing, about 10 pm, compared to perhaps a 0.5 pm gate for a MESFET
phase shifter at the same frequency. This was the first demonstration of a K-band phased
array based on ferroelectric films.
Coupled microstripline ferroelectric phase shifters have already demonstrated
performance superior to their semiconductor counterparts at microwave frequencies.
Typical de-embedded insertion loss for these novel *360° phase shifters is about 5 dB.
But in order to realize the full technical and economic benefits o f a new type o f phased
array antenna, called the ferroelectric reflectarray, a 3 dB insertion loss ferroelectric
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120
phase shifter must be produced on a consistent basis. Incorporating a microstrip matching
network between the coupled sections and the terminations can potentially produce a 0.5
to 1 dB improvement. Lower characteristic impedance devices could reduce conductor
loss even further. And the deposition o f dense, high conductivity electrodes that are at
least =3 skin depths thick can result is further improvement. If the tan5 of the
ferroelectric film could be maintained at 0.005 or less, the films contribution to total loss
would be essentially negligible except for the mismatch it introduces as it is tuned. But
even a tanS o f <0.05 is manageable. It is most desirable to maintain the crystalline
properties of the ferroelectric films to a thickness of at least 1 tim. Relatively thick films
increase the phase shift per coupled section while the conductor loss stays more or less
constant. Consequently the number o f sections required to produce a full 360° phase shift
can be reduced. It may be more profitable to redesign the phase shifter to operate
exclusively in the odd mode to further confine the RF electric field. This can be
accomplished by incorporating a microstrip balun before and after the coupled line
structure to excite equal but opposite currents. Then the ground plane, and its
contribution to loss, could be eliminated. The average characteristic impedance o f the
phase shifters can also be changed to reduce loss but this requires a tradeoff with antenna
performance since low impedance would require a deeper inset into the patch element.
Other tunable microwave devices were also introduced including multi-mode
microstrip patch antennas and electronically controlled oscillators. The tunable antennas
offer the possibility o f using the same aperture for both transmit and receive functions.
Future work insofar as antennas are concerned will be directed at the use o f spiral
antenna elements patterned on the ferroelectric multi-layer structures to effect far field
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121
phase shift. The oscillator demonstrated a tuning range in excess o f 3% at Ku-band when
cooled to 43 K. This was the first demonstration o f a tunable Ku-band oscillator based on
thin ferroelectric films. It promises significant cost and performance advantages
compared to alternative tunable oscillators at microwave frequencies. The use o f a
superconducting tunable ring resonator and a discriminator stabilized circuit can reduce
phase noise to levels suitable for the most stringent communications and radar
requirements.
Most certainly there is much work remaining before we can thoroughly
understand the various loss, tuning, aging and fatiguing behavior o f the ferroelectric thin
films. There is a definite correlation between crystalline quality and microwave
performance. Evidence continues to mount indicating that strain plays a critical role in
behavior, and that there are differences in orientational polarization depending on
whether the electric field is perpendicular or parallel to the film. The quasi-TEM solution
based on a variational formulation of line capacitance can be modified to include a
permittivity tensor to account for this possibility. A key achievement on the path to
eventual widespread commercialization o f this frequency and phase agile ferroelectric
technology will be the growth o f high quality films on inexpensive substrates like silicon.
A better understanding o f Schottky effects and the origin o f leakage currents must
precede this achievement. Basic steps also need to be taken to preserve the quality o f the
pristine films prior to metalization, and new protective coatings may need to be
developed to simplify operating conditions and improve reliability.
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122
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Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
132
Appendix A
Design Curves for Microstrip Lines and Coupled Microstrip Lines with thin Ferroelctric
Films on Various Substrates ( a in Np/m)
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coupled m icrostrip on 2 54/im " MgO su b s tra te , er= 2 4 , w = 25 /zm s= 8/z
60
i
1
r
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a a -2 2 .2 5 ,-9 .7 4 ,-1 .1 8 ^
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\
x
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154
Appendix B
MathCAD Quasi-TEM Variational Program
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Variational M ethod for Calculating the C apacitance of Multilayer Microstrip Coupled Lines
C a n t use for slot ine since non TEM (TEM and static fields are the sam e) RRR 12/96
The admittance a t th e charge plane is
Y=Y1 +Y2 where Y1 a n d Y2 are the
adm ittances at th e p lan e y=h1+h2 looking
in the positive an d negative y direction
respectively.
y
I—
w = 3 0-10 ' 6
=
J
s.iaiO -6
c 0 =8.854-10-12
h 2 =30510-6
=1
h
C2 = 9 - 7 - ( 1 - j-tanS)
5 10"6
t
h2,e2
!
<----------------- a------------------>
= 5 0 0 (1 -jta n S )
n = 2 ,4 .. 2000
Shielding walls a re placed sufficiently far away from the coupled microstrips
so
have no effect 00 *be
configuration
h Q = 10 -(h , + h 2)
= 15 ( 2 w - s)
a
h1,e1
j n-a-h 2 '
'n -n h j
: E->-COth
- I c o th ;-----------; - E i I
v' l (, n ). =E0 ji £ , . !; 2
\ a I
a
/
1
------------ i---------- !--------- !---------------
I
j
g(n) =
ho.eo
limiiiiiiiiMiiiitiiimimmiiimiiiiiiiix
= 10
- .0 0 s tanS
lllllllllllllin illllllllllllllllllllllllllllllll
f
s w
/
t _______
/
j
j
t
,
J * * b 0\
- c o th j----;
j n-s-h | \
/n-a-h-j! I
iE |-c o th (
) * E 2 -cothi
j
\
4
/ 2-a ,
|" j
n-j-Y(n) n-a-w/
v
■
2
. i n-j .
. j • /n-a-w\
L<n ) = sin — ■( a - s - w ) sin
' 2-a
J
■ 2-a /
y„ .
/ 2 -a \ J . n-a .
I ’ ; ; n-a-w\* „ I
/ n-a-w,
/ n-a-w\ I n a -w '
. i . ''n-a-w-''
- 0 --------- 1 - 6 i-smi-------- ;
M ( n ) =1------- | - s u v ------ ( a - s - w ) |-! 3-i ; --------i - 2 -c o s |-------- -----\ n-a-w/
. 2 -a
j !_ | > 2 -a «
1
\ 2 -a
\ 2 -a I [ 2 -a
’ 2 -a
y i (4 M ( n ) - U n l ) - L ( n ) g(n)
^ J (4-M (n)-L (n))-M (nV g(n)
n
°
A 0 = 966 802 + 1.079-10 16i
C Q = -1.258-10 I2i
^ g ( n ) - ( L ( n ) <- A 0 -M (n ) : 2
C
2 1 4 iyj
10n
^ oair = J3—
n
n = 1 . 3 .. 2000
.
C cair " 7 993 10
1' =20.0-10,9
V-1 ( 4 M ( n ) - L (n))-L (n)-g(n)
g(n)
n
Ac r2 _(4. ~M------:----- (n )
( n ) - L (n )) -M
/
i
c
Ae
1
A e = 1098 335 + 1.481-10 ‘” i
2
9/
i
2
^ g ( n ) <L(n) - A e M (n )l
C e = 5 768-10 11 - 8 . 9 0 8 - 1 0 I4i
I =356-tO’6
n
Cc
reven '
’
0 (0
2.997 10s
Co
c rodd - ~
M tr
-
c
^ om r
g' V Greven M ^ r o d d ) **
2.997 10
=P(0-M 80*a
1
Q7 I X7 r
cfT
= 7.214 - 0.011 iE
2 1
i
M i
[ M
I
'
n
11 '
M
IUUU
= 13.33 - 0.039i
= | 5 .[ !c
^ c
) |
[ 0 \- ;Erevcn ■ rodd; j
— ---- - -r — • ! ------- -------- 1 = 6 .6 0 6
2
0 ( 0 = 27.099 - 0.032i
E
IL.\CIl
]
z
oc
c r 3 -io 8
c
J lKJ
=____!____
,---------------
e clT= 10.039 - 0 024i
^z 00
P(f) = 1328 539 - 1.558i
-
1
-jC oair'C o ' c
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
60
h-,
,
9.7 + 1
9 .7 -1
ee = ------------f------------
•Ini 8 — + ------ =83.299 +0.098i
\ w
4h I
-'Ecir
1
1- 12
20 ~ y Z o e Z oo
ee = 5.742
2-n
ad
9.7 (e e - l)-tanS
ad = 0.463
Z 0 Q = 28.406 + 0 .0
>.Q 2 , / e e - ( 9 . 7 - 1)
Im (P (0 ) =-1 .5 58
R e ( g ( 0 ) = 1328.539
ORIGIN : 1
f = 1 .2 .. 100
Z 1 I f : t ' Z o c - Z o v c o t(0 (flO 9).deg)
Z22f = - i - (Z ^ + Z ^
Z I2 f
^ ‘r
1 -Z o e ~ Z oo c s c ,9\*' 109 -deg)
Af ^ Z l l f - Zo;
S— f
c o t i e i f 109) dcgj
= - ^ ( Z Oe - Z oo)-c^ e ^ 1 0 9)-<ie g)
Z22f - Z o ; - Z I 2 f Z21f
Z1 l f
\ /Z22f
Zo
■ Zo
_
Z ^ = 155.227 +0.
\
-
Z I 2 f Z 2 If
Zo
:
Zo
,2 ZI1f Z12f):
Z22,
f
•i
Z I I f - Zo
SI 1,
Z22f - Zo- - Z I 2 f Z21f
Z21f Zo
S21
Zo = 66.403 +0.074i
..
2 -a
/
\ c reven *
'rodd*
, j Z oo-Z ^ =66.403 +0.074i
Z o e s*n -9 o' ~ Z o o s*n (9 oi
Z Q = 60.223 +0.08 li
Z o o Z oe
-,Z o c sm 9 o * Z w sini ° c )
Z1 lf
Z11,-Z22f - Z I2 f Z21
Bf
Z2L
Z21,
Z22f
D„ =
Z21,
Z 21,
O RIGIN = 1
l
-
1 . 2 .. 100
-a. b .\
.'A. B .\ /A. B.\ /A. B. \ K
I t i l
t
!c.
* I d I. //
:C.I D .;
I/ \C.I D.tj \C.I D I./J \C.I D.I/
b.
a.i - —
7 - \(c.-Z
i O; - d.i
s ll
^ r\
* i \ l \
Bs\ /A. B .W A . B .W A . B.
1C.
\ I DI .j \C.I D.
tj \C.I D.11 lC.
\ | D.1
b.
a. + —
’ Z„
4-
c.-Z .
1 ‘
. r d .1
a.1-r7---- +- CI.Z O
^O
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
157
Appendix C
MathCAD Oscillator Design Program
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Oscillator Design Program
Robert R ° m anofsky April 4 .1 9 9 7
Z =50 pi =35
electrical d eg rees
Enter S-param eters of
DUT and Zo
S l i m = .462
SI l a = 141
S I2 m -.0 6 7
SI 2a =- 105
S21a =-81.4
S22m =0.22
S22a =107.5
T11
T21
1
Z21\L
Zo = 50
Yo =Zo
A ssum es section (length beta
I) of high im pedance (Z) line
T i l = 1 T I2 =0
( to ground for feedback
T21
(j Z tan( pi d e g ) )
Convert feedback elem ent in
com m on port to z-param eters
T22 = 1
S21m - 2.28
Zll
J = 7-1
T 1 1 -T 2 2 - TI2-T21
Z I2
_
Z22 i
L
T21
T21
T22
T21
S l l r = SI lm -cos(Sl la-deg)
S l l i = SI Im-sin(Sl la-deg)
511 = S I 1r —j-SI Ii
S12r = Sl2m-cos(S12a-deg)
S12i = S12m s in (S l2 a -d e g )
512 = S l 2 r - j S l 2 i
S21r = S21m-cos(S21a-deg)
S21i = S2Im -sin(S21a-deg)
521 = S 2 1 r - j - S 2 l i
S22r = S22m-cos(S22a-deg)
S22i = S22m- sin( S22a- deg)
52 2 = S 2 2 r - j S 2 2 i
D =( 1 * SI 1)-( 1 + S 2 2 ) - S 1 2 S2I
Y l l = Yo-
(1 - SI I ) ( I
S22) ^ S I 2 S21
Yo 2 S I2
Y I2
D
Y22 = Yo-
Y21 =
Yo-2 S21
D
D
Convert to Y param eters fo rth e purpose of changing
from com m on source to com m on gate S param eters if
required
Y12=-(Y12+Y22)
Y21=-(Y21+Y22)
Y22=Y22
( I +- SI 1) (1 - S22) - S12-S2I
D
Y11=Y1 1+Y12+Y21 -*■Y22
DELETE THE LINE ABOVE IF CONVERSION TO COMMON GATE NOT REQUIRED
AY = ( Y l l - Y o)-(Y 22
Yo) - Y12 Y21
( Y o - Y l l ) ( Y o - Y22) - Y l2 Y21
SI I
S12 =
2Y12Yo
s,,
_ ( Yo + Y11 )•( Yo - Y22) - Y l 2 Y2l
AY
((1 - SI 1) C1 - S22) ^ S12 S21) Zo
Zll
Z
II
= Z11 -t-Z ll L
12
AY
Zo-2 S12
Z12 =
( I - SI 1) ( 1 - S22 ) - S I 2 S21
Zo-2 S21
(1 - S I 1 ) (1 - S22) - S12 S2I
Z22
=Z12 ^ Z 1 2 ,
; 'Z 11 +’Zo) ’(Z 22 + ^°j ~Z 12 Z 21
((1 - S l l ) - ( 1 +- S 22) -i- S12-S21 ) Zo
(1 - SI 1) (1 - S 22) - S12 S21
Z 2 1 = Z 21-Z 21L
Z 22 = Z 2 2 - Z 2 2 i
2 Z 1 2 Zo
S12 =
S2I
AZ
S1I
S22 =
2 Y21 Yo
Convert s-param eters of DUT into
z-param eters for the purpose of
adding series feedback
(1 - S I 1 ) (1 - S22) - S12-S21
Z2l
S2I =
AY
AY
[Z 11 - Za)'iZ 22rZo) - Z21Z 12
2-Z 2 j-Zo
=AZ
180
AZ
| SI 11 = 1.59
arg(SII)*—
it
z 11 i- Zo) • (z 22 - Za) - z 2 1 z 12
| S 12 [ = 0 .6 2 6
arg(S I2)-—
i S22| = 1.223
arg (S 2 2 )-—
IS211 = 2 .1 9 7
arg(S21 )■— - = -1 35 .7 82
AZ
Add z-param eters of original two-port
to feedback elem ent z-param eters and
convert new two-port back to s-param eters
A = SI 1 S 2 2 - S I 2 S21
=94.339
180 =3.73
1Cf)
K . I - ( | S 1 1 | ) 2 - ( I S 2 2 | ) 2 <- ( | a | ) 2
=92.375
IOft
K = -0.499
2 - 1S12 S211
|a| =1.284
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
S12 S21
S12S2I
:(! S22; r - f :a| r
r L = 8.939
r c = 1.565
( i S i i ! )2 - ( U ! ) 2 i
S22 - A SH/'
y.S11 - A-S22;
(iS22i )2 - (Ui )2
( !S1 I j )2 - ( A: )2
C L = 9.298 - 1,836i
j C L j = 9.478
C s = -1 .2 9 9 -0.447i
!C s j =1.373
- 180
^
180
Lang ~arS1^'L,' ^
Lang
1^2
C Sang
Sang
161001
Select G am m a Termination (ZT normalized) from Smith C hart (This is th e gate termination for
com m on sou rce) R em em ber, for G am m a-S, if S22<1 the stable region is outside, an f for
G am m a-L, if S 1 1 <1 the stab le region is outside
G am m a-in is looking into the
Z T - zl
z T~
drain-to-source port for a
i r T | = 0 .2 5 8
com m on source oscillator
Z T~
a r g ( r T) —
S12S21T -
r1 in =s"’0
°—
Z in ^z °
- s ii-rT
r , n ; =1.648
Z m
6
-
.33
Ski 1(G) = k ( k - l )
rad
Yin =0.177
N epers
e \ p ( 2 (j ti - a ) )
= - 3 7 815
Ski 2 =Sk21
arg( Ski 1(G)) —
.
(I
z
=jjLSk.ii(e).Zo
1 - Ski 1(0)
=-3 7.8 15
7
Z ^G) =76.17 -93.554i
•Ski 1 = 20-log( [Ski 1(9) )
Sk2I
=20 log( :sk21;)
Sk21 = - 7 0 4 3 8
50
8.3 - j 47.7
Y T = 1.388 +0.496i
a - 24
- ( I - k) * c x p ( - 2 (j t * - a ) )
arg(S k2I) —
=-24.936 +47.73i
Yin
arg T ._ - - = 8 5 21
k =2057
Sk2I
'- n
i - r.
=-139.75
dB
dB
Ski 1 = -4 .1 7 3
G = 0 ,0 .I..5
100
Imt Z
tf)
0
I
2
3
4
5
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
I 017i
160
Appendix D
Surface Wave Limit on Quasi-TEM Solution
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
161
The analysis presented in Chapter II is valid for electrically thin stratified substrates. At
some point, due either to the thickness or permittivity o f the ferroelectric in combination
with the host substrate, higher order surface waves will be excited. The transverse
resonance method can be used to predict the onset of higher order TE and TM modes.
Referring to figure 4, with Zr and Zd taken as the impedance o f the substrate and
ferroelectric layers, respectively, for TM modes:
kxr^o
Zr :=
£rk 0
And
Z d :=
kxdy o
£dko
Where kxr and kxd are the propagation constants in the substrate and ferroelectric regions,
respectively and ko=cj(poe0) 1/2. Since Zinyi(y) + ZXn^iy) = 0 at y=hi+h2 ,
Z a +j-Z
=0
j Z r l a n ( k 3trh 2) + Z d Zd+ j-Za-t«n(kxd-hi)
Assuming n exponentially decaying field for y>hi+h2 let kx,=-jic where k is real. Then Z,
= -jxrio/ko. Finally
— tan(k s -h 2) • (—
k xd (kxd
+ « tan(kxd h j) 1 + — (— -tan(kxd h i ) -
=0
£1 \ £1
Since P must be the same in all regions due to phase matching the dielectric interfaces,
£2 k q2“ k jj-2 = « r k 0a- k xda = k oa + «2
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162
These last two sets o f equations can be solved simultaneously for the propagation
constants. There will be an infinite number o f solutions because o f the integer (i.e. n)
dependence from the tangent functions corresponding to the TMn modes. The TEn
modes can be solves the same way but letting Zj=k0Tio/(erlcXj).
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