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Active microwave bandpass filters using high-temperature superconductors

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Active Microwave B andpass Filters Using
H igh-Tem perature S uperconductors
by
Derek Scott Mallory
Subm itted in Partial Fulfillment
of the
R equirem ents for th e D egree
Doctor of Philosophy
Supervised by
P rofessor Alan Kadin
D epartm ent of Electrical Engineering
The College
School of Engineering and Applied S cien ces
University of R ochester
R ochester, New York
1995
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Curriculum Vitae
The author was bom in Oak Ridge, Tennessee on July 20,1966. He attended
Michigan State University, where he earned his Bachelor of Science in Electrical
Engineering from 1984 to 1988. He came to the University of Rochester in the
summer of 1988 and began graduate studies in Electrical Engineering. He was
granted a teaching assistantship from 1988 to 1989. He received a Masters of
Science in Electrical Engineering from the University of Rochester in 1990 under
the direction of Professor Alan Kadin. He continued with a research assistantship
from 1990 to 1994, again with Professor Alan Kadin.
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Acknowledgements
I would like to acknowledge Dr. Alan Kadin for his tremendous insight and
helpful discussions that have led to my understanding of superconducting and
microwave theory. I also acknowledge Dr. Mike Wengler for his discussions on
microwave theory. I would like to thank Dr. Paul Ballentine and Dr. Kelly
Truman of CVC Products Inc. for their help with my earlier work on film
deposition and support for the microwave tests on YBCO thin films. I also
acknowledge Dr. Antonio Mogro-Campero at General Electric, for supplying
YBCO films, and his discussions on the microwave properties of resonators.
Many thanks as well to my colleagues Noshir Dubash, Mike Fisher, Makoto
Takahashi, and Dexter Hodge for the many hours spent with them working
together to complete the technical phases of the project. I thank all my coworkers
and professors in the electrical engineering department that led to the exciting and
challenging academic experience that was U of R. I also acknowledge the funding
provided by NASA that led to my thesis project. Last, but not least, I would like
to thank my parents and friends. With their help all things were possible.
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Abstract
Passive microwave devices have been demonstrated to be quite feasible with
thin films of superconductors, particularly Y jB a 2Cu 307 .x (YBCO). Surface
resistance measurements have shown that the YBCO thin films are an order of
magnitude better than copper for making high Q resonators. This lower surface
resistance allows for the construction of narrow bandpass filters with little
insertion loss in the 1-50 GHz range. Passive microwave structures have been
designed and tested to verify the properties of the YBCO films for microwave
applications. These patterned devices show degraded properties compared to what
was expected from the measurements of unpatterned films.
Theoretical
calculations for the microstrip test structures show that the high Q devices have
cuiTents in excess of the critical current for moderate power levels of 0 dBm input
power or less.
Tunable high Q 1% bandpass microstripline filters have also been designed and
tested for use as a shiftable filter. These tunable filters have a center frequency of
13 GHz, and the center pole is coupled to a DC control line. When the critical
current of the control line is exceeded, the filter shifts down in frequency by
50-100 MHz. This shift was found to be due to thermal heating of the substrate
that causes a change in the kinetic inductance of the centeipole near the control line.
The data, theoretical calculations, computer simulations, and other issues that
verify the superconducting microwave switching results are presented.
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V
Table of Contents
Title
Page..........................................................................................................
i
Curriculum Vitae.........................................................................................
ii
A cknow ledgem ents.........................................................................................
iii
A b stract................................................................................................................
iv
Table of Contents............................................................................................
v
List of Tables............................................................................................
L ist of Figures...............................................................................................
viii
ix
Chapter
1. Introduction.....................................................................................................
1
2. Deposition and Properties of YBCO ThinFilms.....................................
5
2.1 In situ Sputtering of YBCO Thin Films..........................................
5
2.2 X-ray Analysis of Deposited Films................................................
10
2.3 DC Electrical Measurements of YBCO Films..................................
12
3. Microwave Resonator Measurements of YBCO Thin Films.....................
18
3.1 Introduction to Resonators............................................................
18
3.2 Stripline/Microstrip Resonator.......................................................
26
3.3 Stripline Resonator Theory............................................................
28
3.4 Stripline Rs Measurements at Rochester.......................................
36
3.5 Parallel Plate Resonator.................................................................
41
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3.6
Confocal Resonator......................................................................
54
3.7
Tabulated Rs Data for YBCO....................................................
56
3.8
R s Measurements of Meanderlines.............................................
60
3.9
Power Dependence of the Meanderlines.....................................
64
3.10 Peak Hrf of a Microstripline Resonator.......................................
68
3.11 Experimental Measurementsof Meanderlines.................................
70
3.12 Summary of
R esults.....................................................................
75
4. Filter Design and Modeling.................................................................
77
4.1
Introduction......................................................................................
4.2 Parallel Coupled Filter Design...................................................
77
78
4.2.1 Stripline Parallel-coupled Filter Theory...............................
78
4.2.2 Transfer to Microstrip Geometry........................................
88
Computer Modeling of Microwave Filters...................................
89
4.3.1 Ideal 3-pole Filter Modeling................................................
92
4.3.2 Optimization for Filter Size Constraints...............................
92
Switchable Filter Design................................................................
93
4.4.1 Current Redistribution in a Pole..........................................
97
4.4.2 Modeled Impedance Change................................................
100
5. Mask Layout and Packaging.................................................................
103
4.3
4.4
5.1
Mask Design with L-Edit..............................................................
103
5.2 Microwave Filter Cavities.............................................................
104
5.3
Ill
System Packaging Considerations................................................
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6 . Tunable F ilters........................................................................................
6.1 In tro d u ctio n.......................................................................................
117
6.2 Passive Filter Measurements........................................................
118
6.3 Active Filter Measurements of 3-pole Filters.................................
121
6.4 Tunable Single Pole Resonators..................................................
123
6.5 Comparison to Theoretical Models..............................................
130
117
6.5.1
Kinetic Inductance..............................................................
130
6.5.2
Current Induced Heating...................................................
143
6.5.3
Coupled Resistance............................................................
148
6.6 Summary of Tunable Filters.......................................................
153
7. C onclusions..............................................................................................
156
8 . B iblio g rap h y ...............................................................................................
160
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List of Tables
Table
Page
2.1
Sputtering parameters for YBCO deposition.........................
8
2.2
Substrate properties for use with YBCO thin films.................
9
3.1
Rs values for patterned and unpattemed films......................
76
4.1
Element values for filters with maximally flat attenuation
83
4.2
Even and odd mode impedance factors...............................
5.1
Photolithography procedure for patterning YBCO films
5.2
Process steps required to fabricate a filter............................
7.1
Optimum measured YBCO properties.................................
86
105
115
157
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List of Figures
Figure
Page
1.1
Example of a beam forming network...............................
2.1
Schematic view of CVC SC4000 magnetron sputtering
4
system .....................................................................................
6
2.2
X-ray diffraction data from a YBCO sample.....................
11
2.3
Output from LabVIEW DC measurement...........................
14
2.4
Configuration for measuring Tc and Jc for YBCO films
15
2.5
DC measurement setup for YBCO samples.......................
16
3.1
2-port set up for S-parameter measurements......................
20
3.2
IS x 11 and IS21 1 for a resonator.........................................
23
3.3
End View of common planar transmission line structures
27
3.4
Experimental setup for microwave measurements...............
29
3.5 Network analyzer output for a YBCO stripline measurement
of ISn l...................................................................................
33
3 .6 Temperature dependence of Rs for a stripline resonator at
different input power levels..............................................
37
3.7 Rs power dependence at fixed temperature for a stripline
3.8
reso n ato r................................................................................
38
Frequency dependence of Rs for stripline resonators
40
3.9 Schematic view of a parallel plate resonator for Rs measurements
of unpatterned film s.........................................................
43
3.10 Inferred RS(T) for two YBCO 1 cm^ samples...................
45
3.11 Background for a parallel plate resonator measurement from
10.5 to 15.5 GHz.............................................................
47
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X
Figure
Page
3.12 Xl (T) calculated from a multiparameter fit to the parallel plate
resonator measurements for Rs.........................................
49
3.13 Raw data from a parallel plate resonator measurement for
two unpattemed YBCO films..........................................
50
3.14 Uncorrected surface resistance at 10 GHz as a function of
YBCO film thickness for the selected temperatures
52
3.15 Surface resistance of figure 3.12 corrected for the finite
thickness effect.................................................................
53
3.16 Schematic view of experimental set up for confocal resonator
m easurem ents......................................................................
3.17 Rs data for a YBCO film using the confocal resonator
55
57
3.18 Tabulated Rs data from several different groups for YBCO
thin
film s...........................................................................
3.19 Final design for microstrip meanderline measurements
58
61
3.20 First six harmonic resonances from a microwave
meanderline measurement................................................
63
3.21 Deformed resonance lineshape of sample GE SI due to
power saturation in a microstrip meanderline....................
65
3.22 The distribution of the electric and magnetic fields for a
microstripline structure....................................................
69
3.23 Scaled resonances of GE S2 versus power at 9 K
72
3.24 Scaled resonances of GE S2 versus power at 79 K
73
3.25 Measured Rs versus the estimated peak current................
74
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Page
Figure
4.1
Parallel coupled multi-pole bandpass filter layout.............
4.2
Low-pass prototype response and corresponding bandpass
79
filter response....................................................................
81
4.3
Attenuation characteristics of maximally flat filters
82
4.4
Electric field distributions of the even and odd modes in a
coupled stripline................................................................
4.5
Schematic of a three-pole filter showing the nodal numbering
needed for simulations with Libra...................................
4 .6
90
Comparison of the simulated bandpass performance for
different values o f Rs.......................................................
4.7
85
91
Optimization schematic to conserve space with high Q YBCO
microstrip filters.................................................................
94
4.8
Comparison of final wraparound filter design...................
95
4.9
Center frequency shift for a simulated impedance change of
the center pole of a three-pole filter..................................
96
4.10 Estimated current density change from a control line in order
to cause an impedance change for the center pole................
99
4.11 Simulated phase change of a signal from a change in the center
5.1
Final mask layout from L-edit...........................................
101
106
5.2
Final cavity design for the tunable filter measurements
107
5.3
Early prototype cavity showing cavity resonances...............
109
5.4
Room temperature measurements of the empty cavity
pole im pedance.....................................................................
resonances.................................................................................
5.5
Schematic of a loaded filter in the test cavity for measurement..
110
112
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Page
Figure
5 .6 Time domain reflectometry measurement of SMA connectors..
116
IS21 1 for a patterned filter at 77 K...................................
119
6.2 IS21 I for a final packaged tunable filter............................
120
6.3 Three pole filter design shorted to make a single pole filter....
122
6.4 Preliminary shiftable 3-pole filter in operation...................
124
6.5
126
6.1
Shiftable single pole filter in operation..............................
6.6 Aliasing of the ANA IS211measurement to determine the
switching speed of the single pole filter.............................
128
6.7 Phase shift measurement of a single pole filter in operation....
129
6.8 Current density for a microstrip from equation 6.9..............
135
6.9 Kinetic inductance versus temperature for a microstripline
136
6.10 Raw frequency shift of different thickness resonators
138
6.11 Theoretical match to the frequency shift data showing the
best multiparameter fit for a microstrip resonator................
140
6.12 Theoretical fit to a centeipole coupled to a control line using
the kinetic inductance model.............................................
142
6.13 DC I-V curve for the control line operation of a tunable filter..
144
6.14 The temperature contours for a control line at 1 msec after
applying input current........................................................
6.15 Steady state solutions from FEHT for the control line
146
147
6.16 The lumped element model for a resonator with a coupled
DC control line....................................................................
6.17 Capacitance schematic for two coupled microstriplines
149
151
6.18 Libra simulation of resonance broadening using the lumped
element model for a resonator with a coupled DC control line..
154
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1
Chapter 1
Introduction
The ability to deposit thin films of the high temperature superconductor
Y iBa 2Cu3(>7_x (YBCO) has led to a wide variety of proposed devices, since its
discovery in 1987.* A large portion of these devices that seem practical are
microwave passive elements, delay lines, and resonators. The advantage over
their normal metal counterparts is the reduced surface resistance in the frequency
range less than 100 GHz. This reduced surface resistance (Rs) means that
microwave elements will have a lower attenuation per unit length, and thus higher
Q resonators can be made. A higher Q resonator leads to the possibility of making
very narrow band filters (bandwidth less than 3% of center frequency) with very
small sizes. Typical dielectric resonators can achieve the same Q performance but
are several hundred times larger in volume and weight. 2 YBCO microstrip filters
are already being fabricated commercially and exhibit good properties and much
reduced insertion losses compared to identical normal metal filters (due to the Rs
difference).^
Active YBCO microwave filters can use a control line to exceed the critical
current or magnetic field of a resonating element in the filter. This change in
impedance causes a frequency shift of the filter, as well as a phase change of a
signal traveling over it by altering the phase velocity. If the frequency change is
large enough, these filters will be able to be employed as microwave switches. A
large phase change is equally important and the filters will be able to be employed
in phased array communication receivers and transmitters.
Devices already exist that perform these functions, but at a price in signal
attenuation or device size that could be important in some special applications. For
example, specially made coaxial microwave switches have an insertion loss of
2 dB and excellent switching speeds.^ The advantage of a high temperature
superconducting (HTS) microwave switch is its lower insertion loss, on the order
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2
of 0.5 dB, and its ability to operate at liquid nitrogen temperatures (77 K).
Present day phase shifters are of two different schools: (1) There is a Faraday
rotator phase shifter which uses a magnetic core to alter the phase of a signal
traveling through the magnetic field. 5 (2) Beam forming networks are also used
to shift phase by altering the electrical path length of the signal. 5 Figure 1.1 shows
an example of a beam forming network and a Faraday rotator. A HTS phase
shifter will be many times smaller than either of the currendy used commercial
phase shifting methods, and roughly equivalent in speed. Size is a crucial factor
in a phased array system which utilizes hundreds of phase shifters, and a single
phase shifter is needed for each radiating element such as shown in figure 1. 1.
One such system that will require large numbers of phase shifters is a phased
array antenna. ® Phased array antennas are fixed 2D flat arrays of single radiating
elements. When these elements are incrementally shifted in phase with each
adjacent nearest neighbor, the sum of the radiation from all the antenna elements is
a plane wave emitted from the array in a given direction. By altering this
incremental phase shift, it is equivalent to "steering" the signal emitted from the
array. This phase steering has a similar effect to the radar antenna one sees around
airports which mechanically spin around, sweeping the sky. The phased array
antenna is only limited by the speed at which the phase between each antenna
element can be changed. Another advantage of phased array antennas is high gain
in the direction they are "pointing". This makes possible highly directional
transmission and reception of the microwave signals, with high gain improving the
signal to noise ratio.
Each antenna element in these arrays requires a corresponding phase shifter for
the array to be steerable. A YBCO microstrip phase shifter could be used as such
an element. The principle of operation would be to design a microstrip bandpass
filter with an adjustable impedance element. This impedance change would be
made by a control line close to one or more of the poles of the filter. When a large
current is passed through the control line it will cause a current redistribution in the
pole, changing the effective inductance. The mechanism of such a change and its
magnitude are key issues that have been determined during the course of this thesis
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3
research.
In chapter 2 we will discuss the deposition of YBCO thin films and testing of
the DC properties of the films. Chapter 3 discusses microwave measurements of
the surface resistance (Rs) of YBCO, theory and experiments. Chapter 3 also
shows the measurements of patterned YBCO microstrip meanderlines, and their
performance versus temperature and input power. Chapter 4 covers the filter
design and simulations for a 3-pole 1% bandpass filter at 13 GHz. Chapter 4 also
covers the design considerations for an active filter and control lines necessary for
operation. Chapter 5 discusses the filter packaging and its importance for
successful filter operation. Chapter 6 contains measurements on the passive and
active filters, and the theoretical calculations required to understand their operation.
Chapter 7 summarizes the important considerations for an active filter, and sets
performance operation goals needed for such a device if it is to be made out of
YBCO.
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4
Coaxial Cable Beam Forming Network
Fixed Length Coaxial Cables
Directional Couplers
Signal In
Microwave Switches that
Switch Between the Fixed
Phase Delay of the Coaxial
Cables. This Produces an
Output Signal at each of the
Antenna Feed
Horn Array
r c a i n u ra /siucnnas uiat nas
Evenly Spaced Phase Steps. ( " 7
—
Figure 1.1.
—
Signal Out
e r ®
Example of a beam forming network. Standard beam forming
networks comprise several different sections of coaxial wire of different lengths to
alter the phase in large array antennas.
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5
Chapter 2
Deposition and Properties of YBCO Thin Films
2 .1
In Situ Sputtering of YBCO Thin Films
Thin films of YBCO were deposited by RF magnetron sputtering from a single
oxide target composed of loose powder spread over a 20 cm diameter water-cooled
copper backing plate.? A schematic of the sputtering geometry is shown in Figure
2.1. These films were deposited as a collaborative effort between CVC Products
Inc. and the University of Rochester. The films were deposited at CVC on a
computer controlled CVC 601 sputter system, using one of the four 8" ta r g e ts . ^ >9
At the University of Rochester, the films were made on a CVC SC4000 sputtering
system with a single 8" powder target. Substrates of MgO and LaA103 were
placed above the center of the target, inside the magnetron erosion track, so as to
avoid direct bombardment by energetic oxygen ions (or neutrals). In addition, it
was found necessary to place a “negative ion shield” approximately 3 mm (within
the cathode dark space) above the center of the target to further reduce energetic
particle bombardment. *0 This approach is analogous to off-axis sputtering* 1, but
can be used for coating larger areas with better uniformity and at a higher rate. The
substrates were heated radiatively to 740 - 760 °C during deposition, with
temperature measured using a type K (Chromel/Alumel) thermocouple near the
substrate. The sputtering was carried out with 450 W RF (13 MHz) in 15 mTorr
atmosphere with a two-to-one Ar-to-02 ratio. These parameters yielded a
deposition rate of 10-60 A/min., depending on the target-substrate distance
(nominally 1.75").
After deposition, the chamber vacuum system was backfilled with 10-100 Ton-
02 and the heater was turned off, which allowed the substrate to cool to 100°C in
two hours. A list of these sputtering parameters is given in table 2.1. The
resulting films, typically about 0.5 pm thick, were highly oriented with the c-axis
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6
substrate
r w v w w v w w w ' v vvcvff
Ion shield
'SSSSSSsss’SSSSSSSj'SSSSSrSSSSSSSSSSSss'SSSSS/Ss
YBCO
S
N
____ t_____
magnet
target
racetrack
cathode assembly
Figure 2.1. A schematic view of the CVC SC4000 magnetron sputtering system.
The system has a 3" diameter negative ion shield in the center of the 8" powder
target
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7
of the crystal structure perpendicular to the substrate.
Composition and
microstructure of the films were examined by scanning electron microscope
(SEM), energy dispersive x-ray analysis, inductively coupled plasma atomic
spectroscopy (ICP), and x-ray diffraction. Critical currents were measured using
5 - 1 0 |i.m wide lines that were patterned by a standard photolithography process
followed by a wet etch using 1% H 3PO4 or HC1 acid.
Some superconducting films from General E l e c t r i c ^ Were also tested. These
films are YBCO thin films, but are deposited onto LaA 103 substrates at room
temperature by coevaporation from multiple sources. These sources are Y, BaF 2 ,
and Cu. The films are then annealed at 720°C in a low partial pressure of O 2 with
H 2O vapor. The water vapor removes the F from the film leaving YBCO in the
superconducting phase. The relatively low temperature of GE's processing
method reduces surface roughness and leaves smooth films, which is desirable for
planar microwave circuits.
For high quality microwave circuits, the substrate chosen for deposition is
important. It was found that MgO and LaA103 are the best quality substrates for
making microwave circuits. They both exhibit low loss tangents and have a good
lattice match for growing the YBCO thin films. Table 2.2 shows values of
dielectric constants and loss tangent for several materials. SrTi03 has the best
lattice match for growing the films, but has a high dielectric constant and loss
tangent that makes it unreasonable for use at microwave frequencies for the
resonators designed in chapter 3. Sapphire (AI2Q3) *s a standard substrate for use
with Cu microstrip lines and has excellent microwave properties. However, it was
found that YBCO reacts with the AI2O3 during deposition, and makes poor quality
films. With an appropriate buffer layer the AI2O3 could be useful. Research has
been done investigating Al203 ’s use with either MgO or Yttria stabilized Zirconia
(YSZ) as a buffer layer. *3 YSZ has fair lattice match and fair microwave
properties. The films deposited on YSZ substrates were not as good as the MgO
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8
Sputtering parameters for YBCO deposition
Radiant Heating:
740-60°C
RF Power:
450 W
Ar Pressure:
10 mTorr
O2 Pressure:
5 mTorr
Target to Substrate Distance:
1.75"
Deposition Rate:
33 A/min
8" Diameter Powder YBCO Target
Y l . l B a 1.75Cu3 °7 -x
6" Diameter Magnetron Racetrack
Cool Down in 100 Torr of Oxygen
3" Negative Ion Shield
~2 Hours to T < 300 C
Table 2.1 The nominal sputtering parameters for the deposition of YBCO thin
films with ideal properties are given above. These parameters were experimentally
determined in order to give the best overall YBCO thin film properties.
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g
Substrate properties for use with YBCO thin films
Lattice Match
Dielectric (Ej.)
Loss Tangent (8 )
MgO
Good
9.8
1x10-5
LaA103
Good
23.0
2x l 0"5
SrTi03
Excellent
2200.0
lxlO ’2
AI2O3
Poor
10.0
lxlO "6
YSZ
Fair
25.0
Teflon
-NA-
2.0
1
00
X
0
Substrate
lxlO ’5
Table 2.2 Microwave substrate properties for use with YBCO thin films. The
values for the dielectric constant and loss tangent are for the materials at 77 K .^
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10
or LaA 103 for DC and microwave resonator tests. Teflon is listed because it is
used as a spacer for resonator measurements of YBCO thin films; more is
mentioned on this in chapter 3.
2 .2
X-ray Analysis of Deposited Films
In order to verify that high quality crystallographically oriented films were
deposited, x-ray diffraction measurements were made. The x-ray diffraction peaks
for a high quality sample are shown in figure 2.2. These peaks correspond to the
(00&) plane and the data gives information on the c-axis dimensions using Bragg's
law:
tX = 2 d sin 0
(2. 1)
Here X is the wavelength of the Cu K a radiation of 1.514 A and d is the distance
between the layers of the c-axis. 0 is the angle of the diffracted x-ray beam.
Solving for d, the c-axis spacing of the films was determined to be ~11.68 A.
Another test of film quality using x-ray diffraction measurements is a rocking
curve. The rocking curve is a measure of how good the c-axis alignment is
throughout the entire film. ^ The rocking curve is done by fixing the detector and
"rocking" the sample. The counts of diffracted x-rays are measured versus
rocking angle. High quality films will have very few defects and diffract over a
very narrow rocking angle. Low quality films will have numerous tilted or
misaligned crystals and diffract x-rays over a large angle. A rocking curve value
of less than 0.5 degrees at half height was measured for the (005) peaks of our
YBCO films. This is an excellent measure of high alignment and orientation.
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11
4430CC 7/19/BO 8PDF ( 1)-1-2004
0.040 T- 6.S00 Y1.2BA2CU30X ON M60- U OF R # 73 (B)
(MgO)
(006)
23924 '
(003)
(005)
17943
(002)
(001)
11962
5961
(007)
(004)
15.00
25.00
35.00
2 THETA
45.00
55.00
XRO at Kodak
Figure 2.2. X-ray diffraction data from a YBCO sample. The peaks are the actual
counts measured for the (00C) lines of a high quality YBCO film, and the narrow
lines are what would be expected from random YBCO powder. The large peak at
20=42° is due to the MgO substrate.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
12
2.3
DC Electrical Measurements on YBCO Films.
In order to determine film quality, it is necessary to measure several key factors
for superconductors. These are critical temperature (Tc), critical current density
(Jc), and critical field (Hc). Tc is the temperature at which the sample goes
superconducting, meaning that it can carry applied current with no voltage drop
(zero resistance). For our samples, 1 p.V has been chosen as the threshold for
when a sample is superconducting. The Jc of a sample is the amount of
supercurrent a sample can carry before exceeding the voltage threshold. Typical
values of our samples are 1 MA/cm 2 at 77 K, and these are measured with
patterned microbridges.
Our measurements are made in a cryoprobe at the University of Rochester that
can be dunked into liquid nitrogen or helium. A schematic of the test probe is
shown in figure 2.5. The test probe is evacuated and helium gas is inserted as an
exchange gas to control heating and cooling rates. A small heater is located near
the sample and control of the sample temperature can be achieved between 295 K
to 4.2 K. The data collection is accomplished by a GPIB interfaceable MacSE
with the program called Lab VIEW. LabVIEW is a virtual instrument program that
uses high level icons for programming elements. The code for the R versus T
program was written by Drew Halberstadt as a summer project. The output of the
LabVIEW program can be seen in Figure 2.3, which shows a typical R versus T
measurement for Tc, and also Jc measurements of a microbridge.
The R versus T measurements for good superconducting films show a very
metallic resistance curve with a sudden narrow AT transition to the
superconducting state. 16 For normal metals, as they are cooled, R decreases in
temperature due to reduction in scattering by thermal phonons.
At low
temperatures the resistance levels out, according to the number of defects in the
metal. The lower the collision rate with phonon vibrations of the lattice or defects,
the lower the resistance. The resistive curve for an optimum YBCO film above Tc
shows R(T) extrapolating to zero as T goes to zero. When the YBCO film goes
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13
superconducting, the normal electrons are replaced by superconducting Cooper
pairs of electrons that move through the lattice with no collisions and thus no
resistance.
This transition was measured with a van der Pauw test setup, shown in figure
2.4. ^ This measures the fringe field due to a current path on one side of the film.
Care must be taken to make sure the current leads are not on opposite comers of
the sample, since the net voltage being measured at the opposite comers may be
zero. This measurement is calibrated by a standard 4 point probe measurement at
room-temperature with an input current of ~10pA. The high contact resistance
(typically 100 £2) can be neglected due to the 4 terminal geometry. The films were
measured to have a resistance of ~4 Q/square for a typical high quality 5000 A
film. This corresponds to a p of ~300 p£2-cm at room-temperature. Typical Tc
values for the YBCO films are in the range of 86-91 K measured by this technique.
A strong correlation between low room-temperature resistance, higher Tc> and
higher Jc values has been seen.
The Jc measurements of the films were carried out on patterned microbridges.
These microbridges were photolithographically patterned to be from 5 to 100 pm
wide and tested in the current ranges from 10 pA to 100 mA. Critical current was
considered to have been exceeded when the voltage reached 1 pV across the
bridge. More care with contacts must be taken with critical current measurments,
due to heating of the sample from contact resistance. Typically Ag contact pads
were deposited onto the films and annealed in O 2 at 450°C to lower the contact
resistance of the current leads. The arrangement of the contact pads was that of a
four-point probe measurement in order to eliminate the need for concern about the
voltage lead contact resistance.
Typical values for contact resistance are
200 £2-1 k£2 for pressed indium contacts, 10-50 £2 for deposited silver contacts
and 1-4 £2 (or less) for post-annealed Ag contacts.
The DC measured values of the films are good for initial determination of the
film properties. A microwave measurement for the film properties, however,
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
14
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Figure 2.3. A screen dump of the output from LabVIEW. The top graph is a plot
of the R vs T for measuring Tc. The film can be seen to go superconducting at
-89 K. The bottom graph is for measuring the Jc. Each curve, on the Jc plot, is at
a different temperature.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
15
1+
YBCO Thin Film
Surface
I
van der Pauw Arrangement
I+
1
I v+
1 VI-
I
4-pt. Microbridge Arrangement
Figure 2.4.
Configuration for measuring Tc and Jc on the films.
A
van der Pauw arrangement is on the top and a microbridge schematic is shown on
the bottom.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
16
University of Rochester DC Measurement Setup
GPIB Data Line
Labview
Keithly 224 PrognmaUe
Current Source
T
Mac SE
Keithly 182 Sensitive
Digatal Voltmeter
Lakeshore Ciyotronics
80S Temperature
Controller
Evacuated Chamber
Teflon Thermal Isolator
Thermal Heatsink to Cryogens
Healer Block
Sample Mount
Thermometer Diode
Liquid Cryogen
Figure 2.5. DC measurement set up for YBCO samples.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
would be much more stringent. With a DC measurement, the properties being
measured are the best path of travel for a superconducting current. In a microwave
measurement the entire film surface is tested. It will also be possible to make
measurements on the top surface as well as the substrate interface, giving a better
benchmark for high quality films.
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18
Chapter 3
Microwave resonator measurements of YBCO thin films
3.1 Introduction to resonators
To make microwave devices out of YBCO thin films, it is important to know
some of their basic properties. One can readily measure the films' critical
temperature T c
and critical current density Jc at DC with a patterned
microbridge^ or coupled inductive loop. 19 However, DC measurements do not
measure the overall film uniformity and quality. A 4-point probe Tc measurement
finds the best superconducting path in a film. Likewise, patterned microbridge
measurements of J c only measure a small area of the film. It is necessary to make
RF measurements of the film properties in order to make predictions on the
performance of microwave devices. RF measurements will also be a more
stringent test of overall film quality.
The two results most desired from a microwave measurement of a
superconducting thin film are the surface resistance (Rs), and the penetration depth
(^l ). Rs is related to the attenuation of the microwave signal as it travels along a
conductor, and
is the 1/e depth that microwave current travels along the surface
(analogous to skin depth of normal metals). Ideally, it is important to measure R s
and
versus temperature, AC magnetic field Hjf, AC current density Jrf , and
frequency to determine the overall properties of thin film YBCO. To make these
measurements, a resonating element of some sort must be used. There are four
main types of resonator structures that have been employed. These types are based
on ( 1) patterned stripline, microstrip, or coplanar resonators, (.2) waveguide
cavities^O, (3) dielectric resonators^, and (4) a quasi-optical confocal resonator.
For the R s measurements studied in this thesis, the simple planar resonators of
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19
type (1) and the confocal resonator of type (4) were chosen.
As an introduction into resonators, a few terms need to be explained.
Resonators are characterized by their quality factor (Q) and resonant frequency
(f0=co0/27c). The Q is proportional to the 1/e power ringdown time of a resonating
structure.
Resonators are frequently small sections of a transmission line
structure, and the Q is how many times a signal will bounce back and forth in the
cavity before dissipating to a power level of 1/e. The formal definition of Q is:
Q = 2 jt (energy stored) / (energy dissipated per cycle)
(3.1)
This Q is comprised of 4 different factors: Q due to the conductor loss of the
resonator (Qc), Q due to the radiation losses (Qr), Q due to the dielectric losses
(Qd), and the Q due to the insertion loss of the cavity (Qj). This can be seen from:
Qtot' 1 = Q c ^ + Q d ^ + Q f '+ Q r ' 1
( 3 .2 )
Qc is the term that is needed to be measured for the comparison of the YBCO thin
films to other reported materials. It was necessary to design tests where the values
for Qd, Qj, and Qr could be measured or neglected in order to get a sensitive
measurement of Qc. Qc is proportional to the inverse of the surface resistance
(Rs), and Rs is evaluated for comparison to other samples.
Typically, these resonators are measured with a 1-port or 2-port arrangement.
The S-parameters are used to define these measurements by the amount of power,
at a fixed frequency, is being reflected and/or transmitted. For the purposes of a
S-parameter measurement the device under test (DUT) is considered to be a "black
box". The ports are labeled as seen in figure 3.1. The following equations
describe S-parameter measurements:
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20
t 1
Output
2-port
Microwave
Device
S-parameters define the properties of the
microwave device "black box" in a circuit.
Figure 3.1 Two port set up for S-parameter measurements.
/
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21
.2 _ Power reflected from the input port
11 ~ Power incident on the input port
(3.3)
|2 _ Power reflected from the output port
Power incident on the output port
IS |2 - Power delivered to matched load
Power incident on the input port
|2 _ Power delivered to matched load at the input port
12 ~
Power incident on the output port
(3.5)
(3.6)
Both the source and load impedance are assumed to be matched to the line
impedance Zg.
For a 1-port device, the ISj^l and the phase angle can be measured versus
frequency. The Q for a IS n l measurement of a resonator is found by determining
the frequency width (Af) at the half power height, referenced to the on resonance
maximum. The measurement of ISj i I is accomplished with a HP8753A, or a
HP8720B network analyzer. The HP8753A is capable of making S-parameter
measurements from 300 MHz to 3 GHz with input power levels of -10 to 30 dBm
(0 dBm = 1 mW, and 30 dBm = 1 W). The HP8720B is capable of S-parameter
measurements from 130 MHz to 20 GHz with input power levels of -60 to
-10 dBm. It is of note that these are vector analysis network analyzers, they
supply the phase information as well as the power levels. For the purposes of
measuring Q the phase information is not needed.
Typically, the measurements of IS i jl were made in the linear magnitude mode
for increased resolution due to the background. The data was measured by the
network analyzer and sent via a GPIB bus to a HP217 computer for analysis. The
raw ISj i I data versus frequency for a resonance was then converted to power
(ISn|2). The background was found by fitting a line to the ISj j 1^ data outside of
the resonance area. The half power height at the resonance center frequency was
then determined by:
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22
half height =
height of the resonance dip - background level
2
(3.7)
The computer program then uses interpolation of the frequency data to locate the
exact frequencies on both sides of the resonance that are at the half height power.
The Af is then found from:
(3.8)
The center frequency of the resonance is found as:
^0 = f(ISnlminimum)
(3*9)
Once Af is known, the Q can be easily determined since:
(3.10)
For a 2-port measurement the evaluation of Q is quite similar to that of the
1-port case. However, a 2-port measurement of a resonator has an input and
output port, and the value of interest is the transmission coefficient IS211. Instead
of a resonance dip, as in the IS \ jl measurement, there is a resonance peak. The
background is determined and the half height of the peak transmitted power is
determined for IS21
A Af is found by the aforementioned interpolation method
for the upper and lower frequency half power points. This Af is then used to
determine Q by equation 3.10. A comparison between the IS j jl and IS21I peaks
for a resonator is shown in figure 3.2.
The insertion loss of a 2-port resonator is another important measurement to
know for a filter. Insertion loss (I I ) is a measure of the amount of power
dissapated in the resonator and external coupling circuits referenced to the input
power. Il is defined as:
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23
i "
V *
EEsof - lib ra - Mon Jan 09 04:57:17 1995 - WRAPiP
n MAGfSii] + ms&]
RESON
RESON
1.000
0.500
0.000
12.30
3.2 A comparison of the ISj jl and IS21I peaks for a resonator. The Af is also
shown for determination of the Q.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
24
Il = lOlogio^Po
(3.11)
Pj is the input power into the 2-port network, and P0 is the output power of the
resonator. For the special case of a resonant circuit the insertion loss can be
defined in terms of the Q's. Qu is the unloaded Q of the resonant cavity (which is
Qc in equation 3.2), and Ql is the loaded Q of the resonator (Qtotal *n equation
3.2). Q l is the measured Q from the network analyzer that includes all coupling
losses, radiation losses and dielectric losses. Insertion loss then i s ^ :
II = 10 log10( l - ^ ) - 2 + 10 logio[l + (QL£f)2]
Qu
(3.12)
and
e, = X . |
(3.13)
Here £f is the frequency dependent term of the resonator and fo is the center
frequency of the resonator. At resonance £f = 0, and off resonance the term adds
more to the insertion loss.
Similarily, the coupling loss for 1-port structures can be determined by
measuring the Q, and the SWR (standing wave ratio). SWR is related to ISn I as
shown here:
SWR = i- t |S n |
1 - Ibnl
(3.14)
and is related to Q by:
<3,5)
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
for the overcoupled case, and by:
q
^
. _
Qu SWR
1 + SWR
1 + ISn l q
2
Qu
(
161
'
for the undercoupled c a s e . 23 To explain further, definitions are needed for under,
over, and critical coupling of resonators.
Critical coupling for a 1-port resonator is when the portion of loss due to the
coupling is equal to all other losses in the cavity, and the resonator acts like a
matched load. Overcoupled (strong coupling), is when the losses due to the
coupling dominate the losses in the cavity and make up the majority of the Q.
Undercoupling (weak coupling) is when the losses in the cavity dominate the Q
and very little loss is due to the coupling. For both the over and undercoupled
cases, it is difficult to tell by observing a single measurement what regime the
resonator is operating in. However, for the resonators tested, the resonance shape
was observed while the sample cools, and it can be interpreted whether it is under
or overcoupled. If the sample is overcoupled there is little change in the resonance
curve during cooling since it is dominated by the temperature independent coupling
losses. The undercoupled case for YBCO resonators shows a strong temperature
dependence as the resonator is cooled and is a much better judge for determining
response of the resonators versus temperature.
Thus, switching to a 2-port measurement for the YBCO resonators was needed
to increase the measurement sensitivity. Symmetrical 2-port Rs measurements of
resonators are preferred since they are less susceptible to errors from line
resonances and connector reflections. For a symmetrical 2-port S-parameter
measurement I I is equivalent to the measured IS21 1in dB after subtracting the
input/output line losses. For a 2-port measurement the unloaded Q is related to the
loaded Q by;24
Q u = Q L /(i-iS 2iO
(3-17)
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26
Typically for the Rs measurements on resonators, weak coupling is used so that
the losses are dominated by the cavity. With the knowledge of I I , Q, and
S-parameters, different resonator measurement techniques can then be compared.
The rest of chapter 3 is devoted to different resonator measurements of YBCO thin
films.
3.2
Stripline/Microstrip Resonator
Patterned stripline and microstrip A./2 resonators have been employed by
several groups for measuring R s of YBCO thin films.25,26,27 Patterning is
accomplished with standard photolithography techniques, and the films are wet
etched or ion etched. A stripline resonator differs from a microstrip by having a
top and bottom ground plane versus the microstrips' bottom ground plane, as is
shown in figure 3.3. The stripline has a center conductor and two ground planes,
which are symmetrically spaced from the center conductor by a uniform
microwave dielectric. For all striplines, R s is proportional to 1/Q after correction
for coupling loss. The Q, from the measurements taken at the University of
Rochester, is measured from the back reflected amplitude ISj jl using a HP
network analyzer with an S parameter test set.
The different contributions from the center strip and ground planes to the Q of
the resonator can be determined. It is made possible by replacing one of the
ground planes of a stripline with the sample to be tested. To have maximum
sensitivity, this was done with Nb striplines at 4.2 K for which Rs is negligibly
small.28 The main advantage is that the sample does not need to be patterned
before testing. The disadvantage is limited temperature range where testing can be
done with high sensitivity.
To simplify the measurement, and not have to calculate the different
contributions, the entire resonator must be made out of the material to be tested.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
27
0
Stripline
Microstrip
Coplanar
Figure 3.3. End view of common planar transmission line structures. The
stripline is the best in terms of electromagnetic performance, but is the most
difficult to construct. The coplanar line requires only one side of a coated substrate
to pattern, but has the highest radiation losses. In the figure the dark areas are the
conductors and the white areas are the substrates.
f
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
28
Questions have arisen on the effect of edge damage in the patterned center strip for
YBCO resonators. For most geometries, the center strip carries considerably more
current per unit area than the ground planes. Another noted effect is current
peaking at the edges of the center strip, where the possible damage from etching
has occurred. 29 These two effects mean that the RSeff of a resonator will depend
more on the Rs(centerstrip) 111311the Rs(ground planes)- This has been used to an
advantage for modest input power, since high RF current density and magnetic
fields are produced in the centerstrip. An indication of the dependence of Rs on rf
magnetic field can be obtained over a very large range. Stripline resonator
measurements are able to make measurements of the Rs as a function of frequency,
rf magnetic field, and temperature.
3 .3
Stripline resonator theory
The measurements of R s have been made with large area in situ sputter
deposited films on cleaved MgO substrates in a simple stripline configuration (See
figure 3.4). The stripline consists of a center conductor and two ground planes.
The lower and upper ground planes are symmetrically spaced from the center
conductor by a uniform dielectric (typically MgO) and grounded by Cu foil to the
Cu "cavity walls" surrounding the stripline. The Cu cavity serves as a clamp to
hold the substrates together, but still leaves slight airgaps (due to the cleavage steps
in the substrate) in between the samples. The configuration typically probes the
substrate/film interface of the ground planes since that side will be facing the center
snip. For the samples tested, the microwave radiation does not penetrate much
farther than the estimated penetration depth of ~2000 A. The films are assumed to
be thick enough to be unaffected by the copper surrounding the stripline. The R s
is determined by examining the Q of the resonator found from the back reflected
amplitude ISyl using a HP network analyzer with an S-parameter test set. The
center frequency of the resonances f0 is related to the length of the center conductor
t and the effective dielectric constant between the ground planes:
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
29
RG 58 Coax (50 Ohm)
HP 8753A Network
Analyzer with S
Parameter Test S et
Evacuated Chamber
Stainless Steel Coax
(50 Ohm)
Teflon Thermal
Isolator
Liquid Cryogen
Heater Block
Stripline Resonator
-0 = 1
SMA Launcher
Top View
YBCO
P53 D ielectric
□
End View
Figure 3.4. Experimental setup for the microwave measurements with a schematic
view of the stripline resonator used for determining Rs.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Here n = 1,2,3,— (harmonic) and c = 3x10^ m/s. The fundamental resonance of
the resonator occurs when the length of the center conductor is equal to half the
wavelength X of the applied RF.
For our resonator pattern, the center conductor is typically 41mm long and
2 mm wide. One of the three deposited MgO substrates was chosen for patterning
into a center strip while the other two were used for ground planes. The patterning
of the YBCO center strip was done using standard photolithography techniques
followed by a 1% H 3PO4 acid wet etch. Ideally, Ej. should be ~9.6 for MgO, but
due to air gaps in the structure the effective Ej. is ~8.6. This leads to a fundamental
resonance of f0=1.25 GHz. Modeling of the center conductor as a transmission
line in the stripline simulation program L in e c a lc ^ O gives a characteristic impedance
Zq=27 Q for h=1.5 mm dielectric spacing. Measurements were made with strong
and weak coupling to determine the Q by adjusting the capacitive coupling gap at
the input to the resonator. Special consideration must be taken to determine the
unloaded Q for the case of strong coupling, as will be discussed below. The
typical gap sizes chosen were 1.0 mm for strong coupling and 1.5-2.0 mm for
weak coupling. If the coupling is any weaker, it becomes difficult to pick out the
resonance of the resonator from features due to the input line.
Tne R s of the material in the resonator is inversely proportional to the quality
factor of the conductor, Qc, assuming all other losses are negligible:
Rs = ^ o = G * A f
Qc
(3.19)
G is a geometry factor, and Af is defined as the frequency width at the half height
of the power absorbed in the stripline. Most of the measurements were of the first
harmonic of the resonators; for comparison only a few measurements at the higher
harmonics were taken and they are discussed later in the chapter. The reflected
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31
power ISj j|2 includes losses in the input line, so that the height must be measured
relative to the background just outside the resonance. In the case of weak coupling
(when the resonance dip is small) this can be found directly from ISj jl. The Af is
estimated with the aid of a computer program. The program calculates a baseline
for the resonance and determines the Af at half height of the resonance dip from the
data supplied by the HP8720B Network analyzer.
For the purposes of the experiment it is assumed that Qr» Q Cj and thus Qr is
ignored since radiation losses are small due to the enclosed fields in a stripline
resonator. It is also assumed that Q d»Q c and thus its contribution to the loss is
ignored. Since tan 8 = Q (fl, and high quality MgO substrates were used for the
s u b s tra te ,th u s tan S clxlO '4 at 77 K and <5x10'^ at 4.2 K in the measured
frequency range from 1 to 20 GHz. Some reports had shown that the dielectric
loss could be a limiting factor in YBCO resonating devices for MgO substrates.32
It is believed that the measurements here are not limited by the dielectric and its
contribution to the calculations are ignored. For the case of weak coupling,
Q i» Q c and can also be neglected.
For strong coupling it is necessary to determine the contribution to Q from the
coupling loss. Qj was experimentally found for the case of strong coupling by
comparing the second harmonic of the 41 mm resonator with the first harmonic of
a resonator half as long, while keeping the coupling gap fixed at the desired
spacing. The comparison frequency is the same, thus Q c and Q j should be
equivalent for the two resonators. Assuming Qr is negligible, the only difference
in contribution to the Qtot is the Qj terms after normalizing for energy stored in the
resonator. The energy stored in the smaller resonator is half of the energy stored
in the full resonator, and the coupling loss should be equivalent, so that
2*Qj(short) = Qi(long). By substituting this into equation 3.2, a good estimate of
the coupling loss is obtained by:
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32
1
1
— 1—
Q tot(short)
Qtot(long)
Qi(long)
(3.22)
This coupling loss is modeled as a capacitor in the calculations. By computer
simulation with a microwave CAD package T o u c h s t o n e ^ it was determined to
have a contribution to the coupling loss of -25 kHz measured at the first
fundamental for the unloaded Q. The Af of the unloaded Q in the example was
found to be -82 kHz and the loaded Af=107 kHz (See figure 3.5). This is close
to the value calculated using equation 3.16.
A special case of these measurements is critical coupling, where the resonator
has no back reflected power (IS n l 2=0). At the point of critical coupling,
Q c '^ Q r 1 and can also be used to estimate the contribution due to the input
coupling loss. For purposes of this research, the coupling was kept weak in order
to simplify the analysis and the Q^0t term is dominated by the cavity losses.
However, if the capacitive coupling is made larger (the gap made smaller), the
resonator will be driven into overcoupling where Q t0t is dominated by Qj. For
communications filters and other passive microwave devices, critical coupling
allows maximum power transfer of the signal into the device at the desired
frequency. The critical coupling will also minimize back reflected signals due to
the impedance match between the resonator and the input line.
The geometry factor for any simple transmision-line configuration can be
determined from the attenuation constant, a c:
Qc = _7L = _^fo_
ca
a °vp
(3.23)
For a transmission line resonator,34 a c is in Np/m, and the phase velocity
Vp=c/er1/2. This is equivalent to saying that the loss per period is 2 a c?i in the
limit o f low loss. The attenuation constant is proportional to Rs of the conducting
surfaces within the stripline (ac oe Rs) since a c=R/2Zo where R is the resistance
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
33
CHI
S n
lin
MAG
2
mU/
REF O U
Jj
0 6 5 .7 4
yU
2 2 3 .1 )1 7
5C 0
MHz
.5 0 0
000
MHz
Avg
16
C EN TER
1 2 2 3 .8 1 7
500
MHz
SPAN
Figure 3.5. Example of the frequency dependence of the reflection coefficient
ISi jl near resonance frequency of 1.2 GHz for an all-YBCO stripline resonator at
T=4.2 K, measured using a HP 8573A network analyzer. The frequency width is
Af=107 kHz, corresponding to Q=11,300.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
34
per unit length. Again, by using the stripline simulation program Linecalc,
a c=0.084 Np/m was determined for a known R s=10.05 mQ (Cu at 1.25 GHz).
Solving using £j.=8.6 we get Q=457. The geometry factor is then determined from
eq. 3.23:
3.67 m£2/MHz
(3.24)
This factor of 3.67 mQ/MHz assumes that all the conducting surfaces consist of
the same material with similar properties. For example, this would not hold if the
resonator had copper ground planes and a YBCO center strip.
An average
R seff=GAf for the entire composite resonator could be determined, but it is
desirable to find the contributions from the different conducting surfaces to the
total observed Q of the resonator. In general, a factor C can be determined that
will give the weighted average of the Rs of the resonator from the Rsc of the center
strip and the RSg of the ground planes.
R s e fH l-C R c + C R ,,
(3.25)
Determining the contribution to the total Rs from the ground planes, as
compared to the center strip, requires careful consideration of the fringe fields and
current distributions. A good first order approximation is that the current in the
ground planes is distributed along the width of the center strip plus twice the
thickness of the dielectric separation h.35 For this approximation
In the limit where w » h , the structure approximates a parallel plate resonator and
the center strip surfaces and each ground plane surface will contribute equally to
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
35
Rs (C=0.5). For a stripline geometry where the fringe fields are taken into account
and Rsc and RSg are equal, the ground planes contribution are found to be:
(2w+2h)
Plugging in w=2.0mm and h=1.5 mm gives C=0.29. For the configuration
used, the center strip Rs dominates the contribution of Q to the resonator. If the
surfaces of the center strip were to become degraded, it would have a larger effect
on Q than if the ground planes were lossier. A more accurate analytical solution
for the contribution due to the ground planes has been used by Dilorio et al. 34
Using their method, a determination of a c for a single ground plane is found to be:
(3.28)
2ZoVfio
Here 9Z</9h is the change in the impedance with respect to a change in the distance
between the stripline and the ground plane. It is determined from Linecalc by
finding Z q at h+Ah and at h-Ah (where Ah<0.1h). The contribution of both
ground planes for a stripline R s measurement is calculated to be -36%. This
agrees fairly well with the simple approximation for the ground plane contribution
in equation 3.27. Experimental confirmation of the good agreement of these
approximations was found by calibrating an all Cu resonator and one with Cu
ground planes that had a superconducting Nb center strip. The measurements with
the Nb were done at 4.2 K, where the Nb loss is negligible.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
36
3.4
Stripline Rs measurements at Rochester
Using the calculated contributions to Q from above, two all-YBCO resonators
and several ground planes were tested to characterize the Rs of the films. 36 For
example, the resonance curve shown in figure 3.4 has a Af=107 kHz, where Q =
f()/Af =11,300. Since the capacitive loading has been determined to contribute
~25 kHz to the Af, the unloaded Q is found to be Q=15,000. With the assumption
that this is due entirely to the conductor loss, and using the proportionality constant
of 3.67 m£2/MHz, this corresponds to Rs=0.29 m fi at T=4.2 K and 1.2 GHz.
In figure 3.6, the temperature dependence of R s at 1.2 GHz inferred by the
geometry factor for the all-YBCO resonators is plotted. The data presented was
taken at several different power levels. In all cases, Rs drops sharply at Tc and
then saturates at the lower temperatures. The drop in R s was not as large as was
expected for high quality unpattemed YBCO films. Rs also increases significantly
for small increases in input power levels.
To better understand this power dependence, an identical all-Nb foil resonator
was tested. The measured loaded Q was ~22,000, most of which is coupling loss,
and it exhibited no power dependence at 4.2 K. Next a resonator with YBCO
ground planes and a Nb center strip was tested at 4.2 K. The losses in Nb are
assumed to be small, and the losses in the YBCO ground planes should dominate
the Q of the resonator. The measured Rs of this configuration was <0.2 mO for
the YBCO ground planes and was virtually power independent, as is shown in
figure 3.7.
However, the same ground planes with a YBCO center strip
demonstrated a strong power dependence as did the center strip with Nb ground
planes. Therefore, the excess losses and power dependence of the all-YBCO
resonator stem from the patterned YBCO center strip and not from the ground
planes.
Using the two fluid model for superconductors, the theoretical data predicts that
RS(T) should be equal to the real part of the surface impedance Zs. Zs is found
from37;
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37
100
0 dBm
-15 dBm
-30 dBm
YBCO w/Nb ci
m
a
E
m
EC
20
30
40
SO
60
70
80
90
100
Temperature [K]
Figure 3.6.
Temperature dependence of the surface resistance Rs for the
all-YBCO stripline resonator at f=1.2 GHz, for three levels of input power. The
value of R s=0.1 mQ was obtained for the YBCO ground planes with a Nb center
strip at 4.2 K, over an 80 dBm range of input powers. The corresponding power
independent curve for Cu (dashed line) is shown for reference.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
38
10
1
78.0K
4.4K
4.4KGP
.1
20
30
Power [dBm]
Figure 3.7. Power dependence for fixed temperatures of tfre all-YBCO resonator
at f=1.2 GHz. A resonator with a Nb center strip and YBCO ground planes is
also presented, and is power independent over this range.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
39
Zs = (CD2(io?t3nna n/2n) + jcopoX
(3.20)
which is equivalent to:
Zs = Rs +jcoLs
(3.21)
here X is the penetration depth of the sample, nn is the density of normal electrons,
o n is the conductivity of the normal electrons in the material, and n is the total
density of superconducting and normal electrons. The R s of the samples should
also increase proportionally to the frequency squared for superconductors as seen
in equation 3.20. Usually, the Rs of a normal metal would only increase as the
square root of the frequency.
A comparison of the measured R s from the striplines versus frequency is
shown in figure 3.8. This compares an all YBCO resonator at three different input
powers, and YBCO ground planes with a Nb center strip (power independent)
versus frequency. The losses follow a f2 dependence as would be expected. Also
shown, is an unpattemed YBCO film on LaA 103 on a f2 line at 36 GHz. Clearly,
there is an unknown loss factor contributing to the measurements of the patterned
YBCO on cleaved MgO, especially when compared to the measurements of
unpattemed films.
Several properties of the center strip may contribute to the excess loss
observed. The process of patterning the film may leave damaged material at the
edges of the patterned features. The RF currents and fields are also expected to be
peaked at the edges of the patterned centerstrips. They are estimated to be about 10
to 100 times greater than the currents and fields away from the edges of the film .3 8
We have estimated average rf magnetic fields in the resonator to be about 1 Oe for
input powers of 0
d B m . 36
This leads us to believe that peak fields at the edges
could be as high as 10 to 100 Oe. These large fields from the peak currents will
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40
100
«
a
E
m
a
G P -1 0 < fB m
•
L 0 A IO 3 7 7 K
Unpaterned
100
Frequency [GHz]
Figure 3.8 Frequency dependence of Rs for a stripline measurement. The power
level lines are for different input powers on a YBCO stripline, the GP is a power
independent ground plane measurement, and the single point is for an unpattemed
film. The dashed line shows a f2 dependence for the unpattemed film.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
41
enhance the magnetic field peipendicular to the film (parallel to the c-axis), which
has been shown to reduce Jc in bulk s a m p le s .3 9 A reduced Jc could aid in driving
the edges normal, due to Jc being exceeded in high Q, high power devices. The
patterning damage may also create some normal regions, allowing for vortex flux
penetration at the edges, which will also increase the RF loss. The effect on the
ground planes would be minimal since the RF fields are virtually parallel to the
film surface, and no edge enhancement is possible. One other possible effect could
be the presence of the cleavage steps in the substrates that are available for these
stripline measurements. These cleavage steps could possibly introduce numerous
grain boundaries and weak link Josephson junctions that would contribute to an
excess loss in the measured Rs of the films.40
Microstrip resonators have also been used to measure Rs of thin films. 41
However, microstrips have a center strip and only one ground plane, which makes
radiation losses higher than striplines. Since the radiation losses are not negligible,
when measuring the Q, it has been necessary to calibrate the microstrip resonators
with Nb, or Au. This is compared to the Q of the YBCO resonator and R s can be
inferred. If one makes the dielectric thickness very small compared to the width in
a microstrip resonator (d « w ), then the microstrip fringe fields can be ignored and
it behaves like a parallel plate resonator.
Another structure that has been used for R s measurements from patterned films
is a coplanar waveguide
r e s o n a t o r .42
it requires only one side of a substrate
patterned and no ground planes. The coplanar waveguide uses a conducting
centerline with the surrounding material being ground planes. To make sure that
both sides are at equipotential to ground, several crossover wirebonds between the
two surrounding ground planes are required. This makes the deposition of the
films easier but has several other difficulties associated with the packaging.
3.5
Parallel plate resonator
In order to make more accurate measurements on the surface resistance of high
quality films, a 2-port parallel plate resonator was tested.43 The test setup is able
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42
to characterize film Rs over a broad range of temperatures, and surface resistance
between 20 |if2 to 3 mQ at 10-15 GHz (Cu being ~30 m£2 at room temperature
for the same frequency). The parallel plate resonator consists of a thin dielectric
(usually 0.5 mil Teflon) sandwiched between two flat 1 cm^ YBCO thin films.
These films are placed in a cavity as shown in figure 3.9. For the cavity, the
position of the films and microwave feedthroughs are fixed and cannot be
adjusted. Other cavities for similar measurements have adjustable microwave
input/output coupling for ease of coupling to the sample. Calibration of the cavity
with Nb films was done to insure that proper coupling distance is achieved before
testing of samples. The samples are held in place by a piece of sponge and a
Cu/Be spring.
A HP8720B Network analyzer was used to measure the transmitted IS21I of
the sample resonance. The sample quality factor Q is defined as the center
frequency of the resonance divided by the -3 dB bandwidth Af. For the parallel
plate resonator geometry this relates to Rs b y ; 4 3
Q ' 1 = Q d 4 + O r '1
+ Q c '1 = tan 8 + as + (^Bl)
(3.29)
Here s is the dielectric thickness between the conductors and a and B are
coefficients that depend on geometry and frequency. The coupling losses are
included in the Qr term.
With a parallel plate geometry, neglecting edge effects, B=l/( 7t|i{)fn). For
small s, the R s term will dominate and R s is proportional to 1/Q. It is possible to
make measurements knowing the tan 8 and a terms and correct for them, but in
practice it is easier to avoid them by using a thin dielectric. Equation 3.29 can be
further simplified by assuming a thin dielectric to be:
Rs = 7CM^nS= ^ os(Af)
(3.30)
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43
Microwave Cavity for Rs Measurement
of 1.0 cm x 1.0 cm YBCO Samples
Top View
1.8 cm
YBCO Samples
□
MgO Dielectric
Bs&fil
Brass
4.0 cm
Copper
Microstrip Coupler
(50 0 Impedance)
Input and Output StIA
Connectors
Interior Side View
YBCO Film \
12.5 p m
T
J
■
Teflon . *•*
YBCO Film
-
S ubilnt*
yv
iM nw fiw
-
1 .1 c m
&
1
Figure 3.9. Schematic view of a parallel plate resonator. The experimental test
setup is similar to the one shown in figure 3.4, with the addition of a second
microwave coax for transmission measurement.
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44
For the measurements made at the University of Rochester, the center frequency
was typically 13 GHz. With a 0.5 mil (12 pm) Teflon spacer, the factor for Rs
was found to be Af * 47.4 pQ/MHz. For example, a measured Q of 1000 at
13 GHz would give a Af=13 MHz, which would correspond to R s=0.612 m£2.
Microwave surface resistance R s of YBCO, on polished 1 cm2 MgO
substrates,
has been measured as a function of temperature using the 2-port
parallel plate resonator configuration.^ Typical Rs values for high quality films,
deposited on MgO, were measured at 12.4 GHz and found to be -0.45 m£2 at
77 K and less than 0.2 mO at 40 K as shown in figure 3.10. Since the R s o f
superconductors scales as f2, this can be scaled to 10 GHz, giving a Rs -0.3 mQ
at 77 K. The measured R s values with the parallel plate technique are much lower
than the values previously measured with the stripline. This is possibly because of
the weak link behavior across the cleavage steps of the films used for the stripline
measurements, and the enhanced critical current peaking at the edges of the center
The parallel plate resonator is very sensitive to changes in the films' penetration
depth ^ l . Their high sensitivity has been used to measure small changes in the
penetration depth versus te m p e r a tu r e , 45 and have found good agreement with the
two-fluid model theory. The London penetration depth can be approximated from
the 2-fluid model by:
* l(T) = Xl(0>
(3.31)
This affects the frequency of resonance because it contributes to the inductance per
unit length:
L = Ho [d+2* Xl (T)]/w
(3.32)
Here these equations model the effect on inductance while the dielectric thickness
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45
10-
CVC # 9 3
YBCO o n MgO
T ab er M ethod
N
X
a
ei
©
0?
a
B
B
E
CO
X
1111
10
20
1 1 1 1 1 > 11
-r
30
50
40
T e m p er a tu r e
rn
60
70
80
90
100
[K]
Figure 3.10. Inferred R S(T) for two YBCO 1 cm^ samples measured from the
parallel plate resonator technique.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
46
d « w , and assumes that both planes are superconductors with a film thickness
t» X . As the superconductor is cooled down, the penetration depth gets smaller.
This corresponds to a change in the inductance of the parallel plate resonator and
can be measured by the shift in the center frequency of the resonance peak. In
order to be sensitive to the change in the penetration depth it is necessary to make
the dielectric of the parallel plate resonator thin, on the scale where the penetration
depth is not insignificant compared to the dielectric thickness. For the parallel
resonators measured in this section the dielectric space is 12.5 pm thick. The
A,l (0) penetration depth is estimated to be ~2000 A, but can vary for different
samples. Close to Tc, this value changes rapidly and can be as large as several
microns. This change in penetration depth is similar to a change in the size of the
cavity. Effectively, the volume that carries the current has increased, and this
causes a change in the kinetic inductance, that is seen as the aforementioned
frequency shift of the resonance peak versus temperature.
This frequency shift near Tc can also be of a practical nature. The original
cavity for the Taber measurements had many cavity peaks that got narrower as the
samples went superconducting, due to reduced losses in the cavity. Only the
peaks that correspond to the parallel plate resonator shift in frequency, making
them easier to pick out from the cavity peaks. The latest cavity design reduced the
number of cavity peaks, making this aspect less important but still a noticeable
effect.
Figure 3.11 shows a parallel plate resonator measurement background for two
different temperatures (83 K and 79 K). The marker is on the peak at 79 K, from
the dielectric space between the two films, showing how it shifts in frequency due
to being cooled from 83 K. Meanwhile the cavity resonances, not attributed to the
parallel plate resonator, get slightly narrower but do not shift in frequency. Thus
to insure that the peak being observed is due to the dielectric spacer between the
two resonators and not the cavity, the peak must be observed during cooling.
To find ^ l (T) from the frequency shift data requires a multiparameter fit. For
a parallel plate resonator, the penetration depth versus temperature is found by
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
47
C H I S g jS M
H r.
is
HAG
.4 7 6
IB .015
mU
I iOO 2 ! 7 GH:
MARKER
9 6 0 321"
CENTER
1 3 .0 0 0
000
000
GH
G Hz
SPAN
5 .0 0 0
000
000
GHz
Figure 3.11 Background for a parallel plate measurement from 10.5 to 15.5 GHz.
The parallel plate resonance is seen shifting from 83 K to the marker at 79 K,
while the background cavity resonances do not shift versus temperature.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
48
using the inductance, and the expected center frequency of a transmission-line
resonator formed by the cavity. The following is derived:
(3.33)
^kocr^eVoiJ-1
Here d is the dielectric spacer thickness, I is the resonator length of 1 cm, Ej. for
teflon is ~2.0, and fo(T) is the measured center frequency versus temperature.
From the shift in frequency of the observed resonance as a function of
temperature, the magnetic penetration depth at low temperatures, ^ ( 0 ), was
estimated to be -2000 A. A fit for ^ l (T) of a measured film can be seen in figure
3.12, compared to the raw frequency shift data seen in figure 3.13. This fit was
accomplished with the help of the spreadsheet program Microsoft Excel. The
program needs the frequency shift versus temperature data to determine ^ ( T ) .
The parameters that can be varied during the fitting are the length of the
transmission line resonator ( - 1.0 cm), the dielectric constant of the teflon spacer
(-1.9), and the thickness of the dielectric spacer (-12.5 pm). We then find the
temperature dependent penetration depth by plugging these values into equation
3.33. An excellent fit was obtained by observing a plot of 1A-l (T)2 versus
(T/Tc)4 while adjusting the parameters d, I , and er This plot is quite sensitive to
small changes in the parameters, when an excellent fit is obtained, the plot will be a
straight line. For these simulations, the 0.3% thermal expansion of the PFTE
(Teflon) from 4 to 77 K is ignored since the relevant range for the fit is the 5-10 K
near Tc.46
The penetration depth of the sample at low temperatures was measured to be
-2000 A from the parallel plate measurements, previously assuming that d»A ..
For the 5000 A films it was initially considered that they were thick enough to
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
49
Penetration Depth for CVC#93 vs. Temperature.
Theoretical and Measured.
1.0
E
=t
a
a>
a
e
o
0.8
0.7
Theory
0.6
Measured
0.5
0.4
0.3
a>
e
0.2
0.1
0.0
10
20
30
40
50
60
Temperature
70
80
90
100
[K]
Figure 3.12. Theoretical and experimental X^(T) calculated from a multiparameter
fit.
i
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50
Ttbar Technique Measurement of Samples
GE#3$4W1&W2. 11/21/91
0 .0 5 '
4 .2 K
2SK
40K
SOK
0 .0 4
ook
67K
CM
if)
78K
0.03
OIK
o
€>
•O
3
•*
ft
63K
85K
0.02
E
<
0.01
Frequency [Hz]
Figure 3.13 Raw data for a parallel plate resonator measurement for two
unpattemed YBCO thin films.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
51
ignore a correction. However, near T c the penetration depth will be even larger
and approaches the thickness of the YBCO thin film. The effect this large
penetration depth would have on the accuracy of the Rs measurements of thin films
using the parallel plate resonator technique was considered. For thin films, where
the thickness is comparable to the penetration depth, a portion of the
electro-magnetic fields inside the cavity will penetrate through the YBCO and be
lost as radiation into the substrate and cavity walls. This concentrates the currents
in the resonator and appears as a loss of power from the cavity.
In the
measurements it is seen as a reduced Qc (higher Rs). An estimate for the effective
Rs is given by;47
Reff = Rs f(d/X) + Rtrans
(3.34)
f(dA) = coth(dA) + — ^ —
sinh2(dA)
(3.35)
where:
Here d is the sample thickness and Rtrans 1S the power transmission into the
substrate. Rtrans *s smah due to the large impedance mismatch between the teflon
dielectric cavity and the MgO or LaAK>3 substrate cavity formed with the brass
walls and is ignored for these calculations. To a first order approximation the
Rseff can be divided by coth(dA) to arrive at the R s that would be expected if the
film was thicker.
A study was done on 4 different thicknesses of YBCO thin films to verify the
Rs can be corrected by the factor l/coth(dA,).47 The films were 0.2,0.4,0.6, and
0.8 pm thick. Figure 3.14 shows the measured surface resistance (RSeff) for the
four samples. From the frequency shift data for the samples, it was determined
that the penetration depth was ~0.39 pm. Using this value in equation 3.34 the
corrected Rs was obtained versus temperature as shown in figure 3.15. This
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52
77 K
E
UJ
O
z
£
w
M
UJ
70 K
DC
UJ
o
2
c
3
W
60 K
0.5
10 K
0.4
0.8
YBCO FILM THICKNESS (Mm)
Figure 3.14 Uncorrected surface resistance at 10 GHz as a function of YBCO film
thickness for the selected temperatures shown.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
53
0.8
E.
UJ
77 K
o
z
70 K
% 04
LU
(X
60 K
UJ
O
£
tr
D
10 K
CO
0
0.4
0.8
YBCO FILM THICKNESS (pm)
Figure 3.15 Surface resistance corrected for the finite thickness effect as described
in the text. A value of A.(0) = 0.39 |im was found from the frequency shift data
and was used for the correction.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
54
indicates that the thinner films are inherently lossier, but this excess loss is related
only to the thickness and not the quality of the films. However, for films over
0.5 pm thick, the quality of the films decline. For thick films, microcracks can
occur due to the thermal processing stresses, and defects can occur due to being
farther away from the substrate's lattice match. The optimum YBCO film
thickness for low loss microwave performance was determined to be ~0.5 pm
from these measurements.
3 .6
Confocal R esonator
A quasi-optical confocal resonator has been used and is now commercially
available for measuring the Rs of large area
s a m p le s .4 8
it has the advantage of
being able to scan a sample for the measurement of R s without patterning. A
confocal resonator works by focusing a standing millimeter wave onto a YBCO
sample. Since the mirror focuses the fields onto the sample, the normal metal of
the mirror is a small contributor to the Q of the resonance. The mirror has a radius
of curvature b and the sample is placed at a distance b/2 from the mirror (figure
3.16). The TEM mode is measured to determine the Q in this configuration. The
spot size focused on the sample from Gaussian beam theory is:
(3.37)
The mirror must be larger than the free space wavelength X, and the sample must
be larger than the spot size for the analysis to be valid.
For the mirror
configuration used, the spot size was ~0.5 cm in diameter.
The Q due to the conductor loss is found from perturbation techniques^ and
the following equation is obtained:
Qc =
co3Po2b3£o
(3.38)
32[RSS(0.5 b2k 2+bk) + Rsm(0.375 b2k2)]
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
55
Waveguide to ANA
Spherical Mirror Surface
w / radius of curvature b
b /2
Thin Dielectric
Base Plate
Sample
Sample Holder
(LN2 feed not shown)
Figure 3.16. Schematic view of the experimental setup for the confocal resonator
measurements .48
Reproduced with permission o f the copyright owner. Further reproduction prohibited without permission.
56
Rss is the sample surface resistance and Rsm is the mirror surface resistance. The
wave number k=m/c, and for all b, k pairs with b k » l , Qc will be more sensitive
to the sample than to the mirror. Scanning the sample gives contour plots of the
sample R s on large wafers and thus determines overall uniformity.
The
measurement is only presently usable at 77 K, but with care it is possible that a
large vacuum chamber could be built to cool down to 4.2 K. However, this would
reduce the speed of measurement, which is one of the main advantages of this
method.
The confocal resonator R s measurements, of samples from the University of
Rochester and CVC Products Inc., were carried out at Sandia National Lab. The
sample was a YBCO thin film, 5000 A thick, deposited on a 2-inch LaA 103
substrate. The measurement was made at 36 GHz. The Rs uniformity is seen in
figure 3.17, in which the data was scaled to 10 GHz, assuming the f2 dependence
of Rs. The average Rs was less than 0.62 mO and the uniformity was better than
± 5% at 77 K. The few peaks in the data are from surface contaminants on the
substrate.
3 .7
Tabulated Rs data for YBCO
Rs measurements have been ongoing for several years now on YBCO. It is
possible to compile the measurements from many different Rs techniques and get
an overall performance estimate of R s versus frequency and temperature as shown
in figure 3.18.49,50 Measurements have also been done on many different
deposition techniques and substrates for YBCO thin films. In general YBCO
conforms to an f2 dependence of R s as predicted by the two-fluid model.
However, the Rs is still larger than what is theoretically predicted, especially at
low temperatures. Also, the film quality is heavily process dependent. The best
YBCO films measured were made by CVC Products Inc. The films made at the
University of Rochester tended to be two to five times worse in microwave
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
57
1 0.60-0.61 mil
j 0.61-0.62 ml)
1 0.62-0.63 mil
\ 0.63-0.64 mil
| 0.64-0.65 mil
| 0.65-0.66 mQ
Figure 3.17. The measured R s for a YBCO film at 77 K and 36 GHz using the
confocal resonator technique. The film was deposited at the University of
Rochester on a 2-inch diameter LaAK>3 substrate. This measurement was made
courtesy of Sandia National Labs.
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58
C«i (4.2 K)
C
• MIT UNCOIN
(4.2 Kl
111
O 10.|
Nb (4.2 K) I
A
(4.2 K]
(fl
M
IU
« 10-«
III
u
ss
BTANFORD/UCIA
■ CORNELL
+ WUmRTAL
■ (4.2
♦ UR/CVC 90
|1 . i Kl!
YB*]C<ijOa (BO K. Th*oretie»l)
* Rochester 94
3U
u. 10-4
K
10-*
10»
10”
10 ”
FREQUENCY (Hi|
Figure 3.18. The graph shows tabulated R s data from several different groups for
YBCO thin films. The measurements are Rs versus frequency and temperature.
The University of Rochester R s measurement was taken at 77 K and scaled to 10
GHz. The Rs of Cu at 4.2 K has been included as a
c o m p a r is o n . 50
(Note: The
zigzag arrow points to UR/CVC 90).
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59
performance, but equivalent in DC performance. This excess Rs is currently under
debate, but is believed to be caused by either structural impurities in the films, or
flux creep (other possible loss mechanisms have been proposed as well, but are
too numerous to quote). Still, the data shows that ~300 GHz is where YBCO's
f2 dependence on R S) for the best films, will cross the f ^ dependence of normal
metals like Cu, Au, or Ag. In the standard microwave range from 1-40 GHz, the
superconductor YBCO Rs is at least an order of magnitude better than Cu at 77 K.
This is a promising result, since long delay lines and microwave circuits at these
frequencies will have much less attenuation and dispersion per unit length. This
means that YBCO microwave resonators and filters operating from 1-40 GHz
have much higher Q, making it possible to design narrow band microstrip or
stripline filters that will have lower insertion loss.
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60
3.8 Rs Measurements of Meanderlines
In this section, issues concerning microstrip meanderlines are discussed. The
effective R s of these meanderlines, and the considerations involved in making
these measurements is reviewed. Power dependence is another consideration
discussed for the meanderlines. In addition, frequency dependence for the
meanderlines is determined and shown.
Several factors made microstrip meanderlines the ideal next step in this research
project. Having completed R s measurements on unpattemed YBCO thin films
using the Taber technique, it was desired to make some microwave devices out of
the films. This involved patterning the devices, thus it became necessary to
measure the properties of patterned resonators on these films to determine the Rs
properties of them. The earlier stripline work was also on patterned films, but was
preliminary to the Taber measurements of unpattemed films. The stripline
measurements had shown strong power dependence with poor quality R s films.
With the higher quality films made from the unpattemed samples, information on
the power handling ability of the patterned microstrip devices versus temperature
and frequency was also desired for comparison.
The meanderline design gives the advantage of a low frequency first harmonic
resonator, thus one could observe the higher harmonics and gain knowledge over a
large frequency spread. Also, the narrow patterned lines from a meanderline
resonator would increase the power density and give a good indication of the
power handling ability that would be important for many applications. The main
importance, though, was to make a simple test structure that would help in the
design and understanding of the proposed tunable bandpass filters.
Figure 3.19 shows the final design for the meanderlines which were tested.
The meanderlines are 26.0 mm long x 50 pm wide, and were deposited onto
0.5 mm thick MgO or LaAlC>3 substrates. This final design for the meanderlines
gives a first harmonic resonance of 1.7 GHz for a LaA103 substrate and 2.5 GHz
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61
YBCO Meanderline for U o f R Measurements
2 6 .0 mm long x 1 0 0 pm wide
MgO substrate
1.0 cm
Input
Output
Top View
Figure 3.19 Final design for the microstrip meanderlines that we tested for RS(T)
and power.
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62
for MgO. The films made at the University of Rochester were deposited by the in
situ process described in chapter 2. The films were then patterned by the same
standard photolithographic process as the DC critical current microbridges. Ag
films were evaporated on the backside of the substrate, or Cu tape was adhered to
serve as the groundplane. The meanderlines were then fit into the current Taber
technique cavity for R s measurements shown in figure 3.8, with the only difficult
issue being the coupling to the resonator. Typically a 0.5 mm or less capacitive
gap was used for coupling, thus giving a strong signal compared to the
background noise. A fairly sensitive Rs measurement is then obtained from the
resonances.
It is expected that the Rs of the patterned YBCO films would behave with a
similar dependence on temperature as the unpatterned samples.
Linecalc
calculations obtain the attenuation constant oc=0.86 Np/m for the meanderline
structure, assuming it is entirely made of copper at room temperature. Then using
the method shown in section 3.2, and this attenuation constant, the geometry factor
is found for the fundamental to be 1.37 mQ/MHz for MgO and 0.89 mQ/MHz
forLaA 103 substrates. As an added check, the YBCO thin films were measured
with the parallel plate resonator technique from section 3.5 before they were
patterned into meanderlines. Data was taken for the samples, versus temperature
and frequency.
Figure 3.20 shows the first six harmonics of a microstrip meanderline on
LaA103 at 79K. Above Tc the YBCO is too lossy for detection of any resonances.
To make sure that the Rs calculations were reasonable, a Ag meanderline was
made and tested from room temperature to liquid helium temperatures. This gave a
good feel for where the resonance would be and what sort of coupling gap to use.
For most of the past high Q resonator measurements, it had been possible to use
very large coupling gaps on the order of several millimeters. For the meanderlines
being researched, it was found necessary to have the gaps less than 0.5 mm in
order to detect the resonances from the background noise.
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63
B2 1 G M l i n MAS '
£ o m u/
REF 0 U
aa
CENTER
H
4 B .2 3 4 mU
.B a a D43 s ; e GHZ
B.OOO 0 0 0 0 0 0 GHZ
SPAN
9 .7 4 0 0 0 0 0 0 0 GHZ
Figure 3.20 IS21I measurement of the first six harmonics of a YBCO meanderline
resonator at 77 K.
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64
In most of the previous measurements the coupling loss was mostly ignored,
since it is quite weak. However, for these measurements the coupling was
required to be strong to resolve the data. At low temperatures and low input
powers using a Pb test structure, an accurate evaluation of the coupling loss was
determined. It was found that the contribution due to the coupling is ~5.0 MHz
from measuring an evaporated Pb film meanderline at 4.2 K and was also
consistent with the expected result from equation 3.17. The surface resistance
(Rs) contribution to the Af from the Pb film was estimated to be less than
0.1 MHz, so the measured Af represents the coupling and radiation losses. Once
the coupling loss was known, several YBCO resonators were measured. After
subtracting out the contributions due to the strong coupling for the YBCO
resonators, the Rs values measured are ~ 10 times larger than what are expected
from the Taber measurements.
Part of the intent of the measurements was to
determine the cause of this increased surface resistance. Some proposed reasons
for this loss are edge damage in the resonator elements,51 or excessive radiation
losses for the microstrip
g e o m e tr y .
52 The R s of the YBCO films at a fixed
temperature also requires consideration of the input power. The tested samples
showed a large increase in R s for increased input power and a large distortion of
the ideal resonance curve.
3.9 Power Dependence of the Meanderlines
Figure 3.21 shows that the resonance can be quite distorted from standard
resonance lineshape, depending on input power. The power scale shown is that of
the actual input powers at the port of the network analyzer. Above -40 dBm input
power, the resonance shape is deformed and appears to be clipped. At higher
power levels above -10 dBm, the resonance essentially disappears into the
background as it becomes too lossy to measure. Interestingly, if this was a normal
metal resonator, one would not expect any change in Rs for different applied
power, unless large enough power was input to heat the sample up significantly.
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65
0.004 •
0.003'
/
\
0.002
<N
52
0.001
1XO0E+O9
U2JE+09
M50E+09
147JE«09
Frequency
Figure 3.21 IS21I measurement at 9 K, showing the distorted resonance of sample
GE SI due to the power saturation of the sample.
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66
To understand this power dependence effect on superconductors, one must
determine what the rf power level is on the meanderline.
To determine this meanderline power level, a few assumptions must be made.
The output port power from the network analyzer is found by reading the output
setting, which is calibrated with a HP438A rf power meter. Using the S-parameter
network analyzer, the microwave coax leading down to the cavity at the bottom of
the probe was measured to have an attenuation of ~8 dB at room temperature and
10 GHz. At lower temperatures (~77 K), when parts of the copper coax has a
reduced R s, the attenuation to the test cavity drops to ~6 dB for the same
frequency.
It is of some note that the two different Network Analyzers used for this
experiment did not handle changes in power the same way. The lower frequency
HP8752A (0.2-3.0 GHz) ANA normalizes the output with reference to the power
level specified (from -10 dBm to 30 dBm). The higher frequency HP8720B
(0.13-20.0 GHz) ANA does not normalize the output, but can be used at lower
power levels (from -60 dBm to -10 dBm).
When measuring a large power range
(from -60 dBm to 30 dBm) switching between the two ANAs was required, and it
was necessary to normalize the data from the HP8720B for comparison.
From figure 3.21, the Q of the resonator can be defined up to the point where
clipping occurs (-35 dBm). This clipping is caused by saturation of the power in
the resonator, and is defined as a noticeable distortion from an expected ideal
resonance curve of the IS211measurement for the meanderline. The saturation
along the IS21I resonance curve is apparent by a "plateau" in the transmitted power.
This plateau is at the same level for different applied input power levels. Above
the clipping at -35 dBm, standard definitions for the Q of the resonator are not
valid, and thus approximations for determining the R s are complicated since
portions of the resonator will have differing values of Rs.
With the YBCO meanderline, there is a certain peak power level that it is able to
maintain, and that will define the Q. The reason for the power saturation is that it
is possibly exceeding the critical current or the critical field of the YBCO
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67
meanderlines. This exceeding of the critical current causes a portion of the
meanderline to "go normal" and thus no longer be superconduting. Since a portion
of the YBCO will no longer be superconducting, the R s will be greatly increased.
It is well known that YBCO above the transition temperature is many times more
lossy than copper.
Oates, et al., have done some calculations for determining the peak currents in
superconducting resonators. They have derived a formula for determining the
peak Ijf current in the line as:^3
(3.39)
Z q is the impedance of the microstripline, r v = IS21I (corrected for losses on the
input and output lines) and is the insertion loss as described in section 3.1, Qc is
the Q of the resonator due to the conductor, P is the power input into the resonator,
and n is the harmonic being measured. A measured value of r v=0.16, Qc=200,
P=0.01W, n= l, and characteristic impedance Zq=165 Q were found for a
meanderline measurement. Putting these values into equation 3.39, a peak
Irf=64 mA at 9 K is obtained. After dividing by the width of the resonator and
taking into account the thickness of the sample, this corresponds to an approximate
rf Jc of 2x 1()5 A/cm^. This is compared to the DC critical current density of
-l.OxlO^ A/cm^ at 9 K that is measured with a patterned microbridge. This rf
value for Jc is about 50 times smaller than that for the DC measurements.
For comparison, a similar evaluation of peak currents and power in the
resonator was done for the parallel plate resonator measurements from section 3.5.
For the two 1.0 cm2 films in the parallel plate resonator, the following values were
determined: r v=0.02, Q=1200, Z q= 0.33Cl, and P=lxl0"^ W. Using equation
3.39, Ijf = 43 mA was evaluated at 9 K. This peak current for the parallel plate
resonator is similar to the level measured for the meanderline determined above.
However, the peak current density is much lower since the current is spread out
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68
along the 1.0 cm wide YBCO film. This would correspond to a peak current
density of ~8.6xl0^ A/cm^. Changing the power level delivered to the parallel
plate resonator produced no saturation effects.
Since the coupling to the
meanderlines can be made stronger than a parallel plate resonator, the meanderline
resonator contains ~1000 times more power density.
Thus, meanderline
resonators are much better suited structures for determining power dependence
than the parallel plate resonators, since higher peak current densities and fields can
be obtained.
However, the rf value for Jc from the meaderline measurement is still many
times smaller than that for the DC measurements on microbridges. Edge damage
or radiation losses could also account for such a decreased value, but it is not clear
that rf current is completely comparable to DC current. In order to compare the
results with other measurements done on YBCO samples by other methods, the
relevant amount of the peak fields in the resonator must be considered.
3.10
Peak Hrf of a Microstripline Resonator.
Hjf is also an important factor for determining the power handling capability of
microwave thin films.
The reason for this is that most early microwave
measurements were done with waveguides and cavities. In these waveguides and
cavities, the samples were typically mounted such that they were part of an
endwall. In these cavities the fields are parallel to the surface of the sample and are
easily calculated by determining the surface currents and dividing by the width to
get A/cm (units of Hrf). As a result, a large number of the historically older
microwave measurements for materials are compared by Hrf. Thus it is important
for us to know what the fields are on our samples for comparison.
In cavity measurements it is relatively easy to convert from the surface currents
to the magnetic fields since they are parallel to the surface. For the microstrip
arrangement this is not the case, and is quite complicated. At the edges of a
microstripline the fields have components that are both parallel and perpendicular
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69
Figure 3.22 An end view of a microstrip meanderline showing the electric
(arrows) and magnetic fields ( c o n t o u r s ) .5 4
(
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70
so relating the peak currents to fields is complicated. Shown in figure 3.22 is a
distribution of the electric fields, and magnetic fields of a microstrip. The field
lines are concentrated at the edges and are much higher than the fields parallel to
the top or bottom of the microstrip away from the edge. Some estimates use a
factor of 10-40 higher for the field peaking than what would be found from an
average field. 38 The average factor is found by the dividing the peak currents by
the width of the microstripline. For example, results from equation 3.39 have
found that the peak currents are 64 mA. If this value is divided by the width of
50 |lm the average H rf = 1280 A/m is found. The estimate for the peak value is
at least 10 times higher than the average, so Hrfpgak = ~ 12,000 A/m. A more
accurate way of finding the peak Hrf will be discussed in chapter 6, where
determining the current distribution in the sample is calculated and the kinetic
inductance is found.
3.11 Experim ental M easurem ents of H r f and Rs from M eanderlines.
The main reason for measuring the patterned microstrip meanderlines was to
gain insight for a patterned YBCO film and then compare them to the measurments
of the unpattemed films. Two sets of films from General E lectric^ and several
sets of films made at the University of Rochester, were measured to determine
patterning effects on Rs. For both the U of R and GE films the meanderlines were
measured versus temperature and power for the 1st harmonic resonances. All of
the U of R films were patterned by wet etching, and the GE film SI was patterned
by wet etching. The GE S2 YBCO film sample was patterned by ion milling, thus
checking that method for superior R s assuming less edge damage from the etching
process. For comparison, a few measurements at other frequencies were taken to
verify the f2 dependence of Rs.
For practical uses of YBCO microstrip in microwave devices, the power issue
depends on the application's required performance level. Due to the power
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71
sensitivity, a microwave detector or a communication filter could be operated at
low power levels (~1 (iW) and temperatures (4.2 K). Part of the experiment is to
determine at what power levels nonlinear effects occur, and thus set a
corresponding power rating to the device. At higher temperatures (77 K), there is
not a sharp onset of nonlinearity, but rather a gradual increase in the Q of the
resonator. This increase in Q is shown as an increased Rs versus input power.
Shown in figure 3.21 are the resonances of sample GE SI versus power at a
fixed temperature of 9 K. Figures 3.23 and 3.24 show the resonances of sample
GE S2 versus power at 9 K and 79 K, respectively. Sample S2 was able to carry
considerably more power than sample SI. At a temperature of 9 K, sample S2 did
not show any distortion of the resonance curve until 0 dBm, compared to -35 dBm
for SI. Interestingly, sample S2 did not exhibit distortion of the resonance at the
higher temperature measurement of 79 K, but the Q did decrease significantly with
increased input power.
From the DC critical current measurements on the microbridges setup, the I-V
characteristics are quite sharp at the lower temperatures, and more gradual at higher
temperatures. When the Iff is exceeded at the lower temperature meanderline
measurement of S2, the film edges rapidly heat up and cause a large distortion in
the resonance curve. For the higher temperature measurement of S2, the sample is
not carrying as much current and when the critical Ijf value is exceeded there is a
gradual change in the resonance. The larger response at the low tempertures is due
to the larger critical current, sharper transition, and faster "runaway" similar to Ic
measurements of microbridges. However, this does depend on the samples'
sensitivity to the applied field. Sample SI was too lossy to measure Rs at the
higher temperatures, thus a comparison at 77 K could not be made between the
two samples.
Figure 3.25 shows the measured Rs versus the estimated peak current found
at the edges of the microstrip meanderlines using equation 3.39. Figure 3.26 is
the same data for the peak magnetic field in Oersteds, where a factor of 10 increase
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72
0.2
Input Pow er
•3 dBm
2 dBm
0.15-
4 dBm
6 dBm
8 dBm
10 dBm
12 dBm
1.688e+9
1.713e+9
Frequency [Hz]
1.738e+9
Figure 3.23 Scaled IS211 data for sample GE S2 versus power at 9 K for the first
harmonic resonance.
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73
input Power
-23 dBm
•IS dBm
-13 dBm
c
D
E
-8 dBm
(N
V.
2 dBm
|
7 dBm
Z
17
1.725
1.75
1.775
1.8
Frequency [GHz]
Figure 3.24 Scaled IS211 data for sample GE S2 versus power at 79 K for the first
harmonic resonance.
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74
N
£
®
«■>
o.oi1
®
;
G
V)
0£
^CQ
0.001 t
E
*3
<2
0.0001
0.0001
0.001
0.01
0.1
"H—
"1
Peak <I> [A]
0.0001 •
10
100
1000
HrffOe]
Figure 3.25 The measured R s versus the estimated peak current <I> calculated
from the IS21 1 data for the sample using equation 3.39. Also shown is the
corresponding H jf calculated for the meanderlines using an enhancement factor of
10. The dashed line is what would be expected for weak coupling of the S2
measurement at 8 K.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
75
from the average Hrf values is assumed, as was recommended by Oates et al.^3
These figures show that sample SI is much more sensitive to applied input power
than sample S2. Comparing the measurement of S2 to the low temperature
measurement of SI, indicates that SI is an order of magnitude more sensitive to
the applied field. The difference in processing between the two samples is SI was
wet etched and S2 was ion milled. Both samples were originally from the same
run, so the etching method of using ion milling appears to give an advantage when
comparing the samples with magnetic field (or peak current) and Rs.
3.12 Summary of Results
The measured values of R s for the YBCO patterned microstrip meanderlines
appeared to be ~10 times higher than what was expected from the Taber
measurements on unpattemed thin films. It is believed that either edge damage or
radiation losses are to blame for degradation in R s.^2 Table 3.1 illustrates the
difference in patterned and unpattemed GE and University of Rochester films as
measured by the different R s techniques. The higher critical currents at the low
temperatures (<10 K) are shown from the higher peak Hrf values before distortion
for the patterned films. This is equivalent to only carrying a few (i.W's of power
without distortion. The low power handling of these patterned YBCO thin films
will limit the potential uses as microwave devices.
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76
Rs values for patterned and unpatterned films
Temp. Unpattemed
Wet etched
Ion milled
Stripline
@1.7 GHz
@1.7 GHz
@1.2 GHz
(K)
@13 GHz
4
0.1 mQ
2.0 mQ
0.5 mQ
0.3 mQ
50
0.15 mQ
5.0 mQ
1.0 mQ
0.5 mQ
77
0.5 mQ
3.0 mQ
1.2 mQ
NA
Table 3.1 The measured R s values from the parallel plate measuring apparatus for
unpattemed films as compared to those for a meanderline, and stripline (section
3.4). Scaling for a f2 dependence, it would be expected that the lower frequency
etched/milled and stripline Rs values should be ~25 times lower than the
unpattemed films. However, the Rs values for the etched/milled films are many
times higher. Apparently some edge damage, radiation losses, or other loss
mechanism is causing degradation in the measured Rs values.
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77
Chapter 4
Filter Design and Modeling
4 .1
Introduction
The passive microwave devices that can be made out of YBCO thin films are
delay lines, resonators, filters, and a n t e n n a s . ^5 The motivation for making planar
structures out of YBCO is the reduction in size of the package and the reduction of
dispersion, loss, and attenuation. Modeling and testing have shown that low R s
YBCO devices have much lower propagation loss as compared to similar normal
metal devices. This lower propagation loss translates into less insertion loss
(attenuation of a through signal) with several types of microwave devices.
Dielectric waveguide resonator filters presently in use have similar insertion loss
values, but are ~100 times larger in volume and
w e ig h t.
2 For applications that
require many high quality filters, the savings in size and weight may make YBCO
devices a competitive alternative, even considering the need to cool to liquid
nitrogen temperatures.
For the work at the University of Rochester, it was decided to concentrate on
designing and fabricating microwave filters in the 1-20 GHz range. The stripline
resonator used for R s measurements in section 3.2 was essentially a 1-pole
bandpass filter. The center resonance frequency of the "filter" was made by
designing the pole to be equal to %J2. The -3 dB bandwidth was determined by
the overall film quality. In order to have control over the width and rolloff of the
passive filters, we have used standard filter design techniques. These methods are
straightforward for normal metal filters, but adjustments are necessary so the filter
design is compatible with the YBCO film values found from the R s measurements
(chapter 3).
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78
4 .2
Parallel Coupled Filter Design
Parallel coupled microstrip bandpass filters were used for the filter design
layout shown in figure 4.1. A maximally flat 3-pole filter was designed that has a
center frequency of 13 GHz for the MgO substrates (er = 9.8), and a 1%
bandpass filter response (130 MHz). A frequency of 13 GHz was chosen based
on the size limitation of the available substrates, which were 1.0 cm^ MgO. In
order to minimize coupling to surrounding cavity walls, this left an overall design
area of (~0.8 cm)2. The parallel coupled filter uses half-wavelength stripline
resonators, positioned so that the adjacent resonators parallel each other along half
of their length. This parallel arrangement gives relatively large coupling and is
thus excellent for printed-circuit filters with less than 15 percent b a n d w id th .55
4.2 .1 Stripline parallel-coupled filter theory
The design equations for parallel-coupled stripline filters provides a mapping
of the low-pass prototype response to the bandpass filter r e s p o n s e . 56 This low
pass prototype response co' is derived using the bandwidth w and center frequency
©
q
to determine the rate of attenuation outside of the bandpass. The prototype
response ©' is derived from a conformal mapping of a lowpass filter onto the
response of a bandpass filter and relative to the filter design parameters. The
relations are:
(4.1)
W ©0
where
W = “ 2^ L
©0
(4.2)
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79
M +l
Figure 4.1 Parallel coupled multi-pole bandpass filter layout. ^6 The filter has a
characteristic admittance of Yq and each coupled element is Z=k!4 in length.
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80
coo = ^
(4.3)
Here co^ and 0)2 are the lower and upper bandpass frequencies as defined in figure
4.2. Both w and 00' are dimensionless parameters that represent the relative
bandwidth and relative shift from the center.
These equations are useful in determining the filter performance and prototype
parameters. For example, with the filter design specifying an attenuation of
25 dB at 12.8 GHz, and solving G)q=13 GH z (center frequency), w = 0.01
(percent bandpass), then G)' = 2/0.01 * (12.8 GHz - 13 GHz)/13 GHz = -3.07.
From figure 4.3, a plot of the attenuation characteristics of maximally flat filters
with toj as the 3-dB band-edge point, Ito’l -1 = 2.07 is found. This is
cross-indexed with the required attenuation of 25 dB. The data intersects the
curves for n (where n is the required number of poles for the filter) and are
~10 dB for n=l, ~20 dB for n=2, and ~30 dB for n=3. Thus in order to meet
the attenuation requirement of 25 dB, at least a 3-pole filter is needed. Once the
number of poles has been determined, the element values are determined from:^^
go = 1
gK
- ^ r 1*
2n
I K=l,2
„
(4.4)
Sn+I
The values for n=l to 10 are shown in table 4.1. For the 3-pole filter designed,
the values are gQ=l, g i= l, g2=2, g3= l, g4= l.
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81
w
(o)
(b)
Figure 4.2. Low-pass prototype response and corresponding bandpass filter
response.56
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82
Figure 4.3. Attenuation characteristics of maximally flat filters.^6 The frequency
© l’ is the 3-dB band-edge point.
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83
Element values for filters with maximally flat attenuation
VALUE
or «
1
3
3
4
5
6
7
8
s
10
«1
3.000
1.414
1.000
0.7654
o.eieo
0.5176
0.44S0
0.3902
0.3(73
0.3129
*1
1.000
1.414
3.000
1.140
1.018
1.414
1.247
1.111
1.000
0.9080
•i
•«
1.000
1.000 1.000
1.848 0.76S4
2 .0 0 0 1.618
1.932 1.932
1.802 3.000
1.663 1.962
1.S32 1.879
1.414 1.782
*1
•t
h
1.000
0.6180
1.414
1.802
1.962
2.000
1.975
1.000
0.S176
1.347
1.663
1.879
1.975
1.000
0.4450
1.111
1.532
1.782
*4
»♦
*1*
• ll
1.000
0.3902 1.000
1.000 0.3473 1.000
1.414 0.9080 0.3129 1.000
Table 4.1. Element values for filters with maximally flat attenuation having g 0= l,
£0j'= l and n=l to 10 are shown above. The element values for chosen n will
match the lines given in figure 4.3.56
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84
These element values are then used to determine the even- and odd-mode
impedances of each coupled pole, Zqq and Zqq respectively. 57 Z qq is defined as
the characteristic impedance of the strip-line with respect to ground when equal
currents are flowing in the two coupled lines. Z qq is defined as the impedance to
ground when opposite currents of equal magnitude are flowing in the two lines.
Figure 4.4 shows the electric field configurations for the cross section of the two
configured lines.
These impedances are found by:
r
Joi_
Yo
7 tW
(4.5)
v :2g0gi
V
(46)
Jn,n+1
JIffl__
Y0 '
V 2gngn+l
(4.7)
Here go, g i , ..., gn+i are the element values found earlier, w is the percentage
bandwidth, and coj' is the 3 dB rolloff frequency. The Jj j +1 terms are known as
admittance inverter parameters, and Yo is the characteristic admittance of the
terminating lines into the filter (1/(50 £2) in our case). The even- and odd-mode
impedances are thus:
Z oejj+i -~- yi -0l
-'OOjj+l •
i +£ y ± i + W
Yo
y 02
Yo
W
Y02 .
1
Y0
(4.8)
(4.9)
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I
85
101
CVER-MOOE ELECTRIC FIELD DISTRIBUTION
’M IS OF ODD SYMMETRY
W IDROUNO FOTENTIAL*
ID)
00 0 -MODE ELECTRIC FIELO OISIRlBUWON
- J l—«T-l»0
SOOBCEi Xlaal2U»ttl.Xunnct~BA l«r051'SC-K212, SRI; ntn iau l
U IRE Tma*.. fCHTT <••• Rat 4 . V S. B. Caka).
Figure 4.4. Electric field distributions of the even and odd inodes in coupled strip
lines.
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86
Even and odd mode impedance factors
Zoe(Q)
(£2)
0.125
57.03
44.53
0.671
0.375
0.110
50.55
49.45
0.663
2.725
0.110
0.125
50.55
49.45
0.663
2.725
57.03
44.53
0.671
0.375
Element j,j+l
Jj>j+l/Yo
01
12
23
34
Width (mm)
Spacing (mm)
Table 4.2. Even and odd mode impedances for the three pole filter designed with a
bandpass of 1% at 13 GHz, and an attenuation of 25 dB at 100 MHz away from
the center frequency.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
Here j=0 to n. For our 3-pole filters we can solve the even- and odd-mode
impedances for each pole and we get the results shown in table 4.2.
Once the even and odd mode impedances are found, the geometry of the
strip-lines can be determined.56 For thin striplines ( t« d):
<410>
where
ke=tanh^^j*tanh|n^ +S^j
ke' =V(l-ke2)
(4.11)
(4.12)
and
Z00= ^ * | ^ f i
(4.13)
Ve^ K(ko)
where
k0 = tanh|^^-|*coth|7I^
k0 =V(l-k02J
j
+S^
(4.14)
(4.15)
Here W is the stripline width, b is the dielectric thickness between the two ground
planes, and s is the spacing between the coupled lines. K is the complete elliptical
integral that conformally maps the modulus ke for the even mode and k0 for the
odd mode onto the field configurations shown in figure 4.4. These equations can
be iteratively solved using a computer program with convergence criteria. The
poles are always designed with a length of X/2. Knowing the frequency and
dielectric Ep and using eq. 3.1, X is found.
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88
4 . 2 . 2 Transfer to M icrostrip Geometry
It was decided that a microstrip geometry for the filter design would be more
appropriate, due to packaging considerations. To transfer from stripline to
microstrip, the same Z 00 and Zoe values are used to determine the width w and
spacing s. The even and odd mode impedances can be found from a method called
approximate
s y n t h e s i s . 58
First one finds the static w/h for a given impedance
from:
SL = J ( d E-l)-ln(2de-l)>+^-Jln(de-l)+ 0.293-0 .5 1 7 1
h
(4.16)
Er
where
59.95JI2
d£ —•
(4.17)
zovir
The s/h is then determined from:
cosh{(7t/ 2Xw/h)Se)+cosh((tt/2Xw/h)so}-2
f = ^cosh ' 1
cosh{(7t/2Xw/h)so}-cosh{(7t/2Xw/h)se}
h Jt
(4.18)
Here s is the spacing between the coupled lines and w is the width of the lines.
The value (w/h)se is found by inserting Zoe/2 into equation 4.17 for Z0 and
similarily (w/h)so is found by inserting Z00/2. This method yields geometry
parameter solutions that are 3 percent accurate. The w and s values obtained were
further optimized by simulation in Libra, which yields the best circuit performance.
For the stripline and the microstrip, the length t of the 7J2 coupled elements
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89
scales with EjP-5. Since a microstrip only has dielectric on one side and air on the
other, the effective
the dielectric
is not Ej.. For the microstrip case, an approximation for
is found by;58
(4.19)
Thus for the case of our filters, where MgO has er=10.0, h=0.5 mm and
w q
= 0 .6 5
mm, £r (eff)= 7.02 is obtained. The length of the k/2 poles for our
microstrip is t m = 4.36 mm. This is compared to £s= 3.64 mm for the stripline
case.
4.3 Com puter modeling of microwave filters
Once the geometry of the filter is established, it is desirable to simulate the
performance, which then allows one to optimize the design. For this purpose, the
EESof program L ib ra^ was used for the microwave modeling. Libra is similar to
the low frequency simulation program Spice, in the handling of microwave
elements by nodes. Libra is an upgrade of Touchstone (which was used for some
of the early microwave modeling). In Libra, the microwave circuit is broken down
into its basic elements. These elements are microstrip-lines and parallel-coupled
microstrip-lines. The Libra program, nodal diagram and output are shown in
figures 4.5 and 4.6.
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90
Nodal Numbering for 3-pole Filter Modeling
13
14
15
10
11
12
I Microwave Filter 3-pole 10 GHz 0.01 Bw
I simulation by Derek Mallory 8A38/92
DIM
FREQ GHZ
RES OH
INDNH
CAPUF
LNGMM
TIME PS
COND/OH
ANGDEG
CKT
MSUB ER-10.0 H-0.5T-0.001 RHO-0.01 RGH-0
MCLIN1 3 4 2 W-0.6710 S-0.370 L-2.80
MCLIN 4 6 7 5 W-0.663 S -2.700 L-2.80
MLIN 7 B W-0.663 L-2.8
MCLIN 6 1 0 1 1 7 W-0.663 S-2.700 L-2.80
MCLIN 0 1 2 1 3 1 0 W-0.6710 S-0.370 L-2.60
D E F 2P 112 FILTER
OUT
FILTER DBIS11]GR1
FILTER DB{S21]GR1
FREQ
SWEEP 9.8010.20 0.0050
GRID
RANGE 6.80 1020 0.0025
GR1 -30 0 10
Figure 4.5. Sample schematic of three-pole filter with Libra simulation program.
The circuit is broken down into different elements, which are handled by nodes
(the labeled numbers).
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91
EEsof - Libra - Sun May 16 IS 28; SB 1993 - NRAP3P
q
® S 2 i]
NEHFILT
-5.000
1125
Figure 4.6. Comparison of the simulated bandpass performance of the 3-pole
microstrip filter with room temperature Cu, 77 K Cu and 77 K YBCO at 13 GHz.
The parameter that is altered in the simulation is the R s of the metal. For RT Cu
R s= 25.8 mSI, 77K Cu R s= 10.6 m ft, and for 77 K YBCO Rs= 1 mO at
13 GHz. The larger the Rs, the more the insertion loss.
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92
4.3.1 Ideal 3-pole filter modeling
Shown in figure 4.6 is the layout model for an ideal 3-pole parallel-coupled
microstrip bandpass filter. For this modeled YBCO filter, Rs=0.4 mQ at 77 K.
Figure 4.6 compares the 77 K YBCO filter response to the same filter made with
Cu at 295 K and 77 K. The difference in the insertion loss is the most noticeable
effect For the particular bandpass Cu filter one would need to reamplify the signal
after it had passed through, due to the attenuation losses. The simulations verified
that the YBCO filter design had a center frequency of ~13 GHz and that the
bandpass is on the order of w=l% of the center frequency. The simulated
insertion loss is also on the order of -0.1 dB as compared to the insertion loss of
-4.0 dB for the room temperature Cu filter and -1.2 dB for the 77 K Cu. These
values are for assumed film thicknesses of 0.5 pm. For even thinner films, the
effective Rs is larger and the insertion loss becomes higher.
4.3.2 Optimization for filter size constraints
In designing the ideal passive bandpass filter, one must consider the size
constraints. For narrowband filters, with a bandpass of w<3% and high Q poles,
the coupling spacing becomes large, on the order of the distances to the package
walls. The need for this large spacing is to avoid having the elements load each
other down and broaden the bandpass. Spacings over 2 mm are not uncommon
for high Q poles, compared to spacings on the order of 500 pm or less for typical
room temperature, normal metal, parallel-coupled bandpass filters. Reducing
coupling loss to the package walls was done by optimization with Libra. Libra is
able to iteratively adjust parameters to match S jj and S21 ideal values. The
parameters that were varied are the spacing s, and the width of the coupled
elements W. Replacing the X/4 coupled elements with aX/16 coupled elements
and 3A./16 microstrip lines, allowed the element spacing to be reduced from
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93
2.7 mm to 0.8 mm.
The reduction in spacing s results in less coupling loss to the adjacent package
walls. The tradeoff is that the length of the filter increases by the distance which
the coupled lines are slid as shown in figure 4.7. This increase in length was
accomplished by "wrapping" the center filter pole around in a horseshoe shape
which then fit the filter onto a 1 cm^ substrate. The wrapping was implemented
with 90° mitres on the microstrip part of the center pole. Further optimization with
Libra was used to match the filter S-parameter performance with that of the ideal
case. The layout geometry of this final design is shown in figure 4.8. The
comparison of the final filter design with the ideal case, as modeled on Libra,
showed that slight errors in the optimization broadened the filter peak. An
advantage of this final wrapped filter design is easy access to the center pole where
control lines can make an active microwave device.
4.4 Switchable filter design
A switchable or tunable bandpass filter is possible if a control line is available.
A DC control line was added to the passive bandpass filter design to facilitate this
control. The response of the filter to an applied magnetic field, and the current
redistribution from this control line, close to the center pole, was modeled. In this
modeling it is assumed that an inductive change in the center pole element will
cause a frequency shift of the bandpass, similar to what is shown in figure 4.9.
The simulated shift is for a ~10% inductive change, which is equivalent to a 50 |im
change in the 650 p.m width of the resonating element. This change in inductance
may be caused by exceeding the critical field at the edges of the center pole. As
noted with the earlier stripline m e a s u r e m e n t s , 36 the Q of a single pole resonator
was highly power dependent because of current peaking at the filter edges.
Coupling a DC or RF magnetic field, was expected to assist in driving these edge
regions of the superconductor normal. It was later found that control line heating
is a more important effect This is discussed further in Chapter 6.
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94
Optimization for Spacing Reduction
X/4-----1=
F
c
,___________
I
JL
I
I
W
—
X/4'
Figure 4.7. The filter was optimized to conserve space by sliding the center pole
to a X/16 coupled element and then wrapping with 90° mitres.
(
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95
S tan d ard 3-pole Filter
W rap Around 3-pole Filter
Figure 4.8 Comparison of final wraparound filter design to standard layout of a
coupled pole filter.
(
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
96
EEsof - Libra - Thu J w 14 1 2 Oft 88 1993 - MAP?
n
MSI]
mein
■—
a —
Figure 4.9. Center frequency shift for a 3-pole bandpass filter simulated for an
impedance change of the center pole being driven normal at the edge. The
assumed change was ~10% of the inductance, which corresponded to a decrease of
50 Jim in the 650 pm center pole.
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97
4.4.1 Current redistribution in a pole
To achieve a frequency shift with themicrowave center pole, a current
redistribution is required to change the impedance or the kinetic inductance. The
amount of current redistribution that takes place in a superconducting pole was
modeled for a change in the resistance of an edge. The kinetic inductance effects
are discussed in chapter 6.
To determine the current redistribution due to a resistance change, the case was
considered where a 50 p.m edge of the pole is driven normal. At 77 K and
13 GHz, the R s of a YBCO thin film has been measured to be ~1.0 m£2. The
same YBCO film has a resistivity p=100 |i£2-cm when driven normal at 77 K,
and that corresponds to a Rs=2 £2 at 13 GHz. For a parallel plate transmission line
(neglecting edge effects) the impedances are found with the following equations:
R -if- < ° 4 >
C=Sp
<4-20>
(FJ,,)
(4.21)
L ( H / m )
(4.22)
£ <°>
<4'23>
R, C, and L are the resistance, capacitance and inductance per unit length and Z0 is
the characteristic impedance. Using these equations for the center pole at 13 GHz
with w=0.668 mm, d=0.5 mm,
166.7
R s=1.00 m£2 and £=4.34 mm, gives Z0=
£2. This calculation neglects the fringe fields. Using accepted microstrip
equations that take into account fringe fields, Z0 is found to be 110 £2. These
fringe fields tend to widen the strip, hence lowering its impedance. The parallel
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98
plate equations are a first order approximation.
As an approximate model, the microwave pole is broken up into two regions,
the edge and the center, as shown in figure 4.10. Impedances are determined, and
the corresponding current densities are found, for both of these regions. For the
case where the control line is off, both sections are superconducting and the
current was determined to be uniformly distributed. For the case where the edge is
normal YBCO, with R s=2 £2 (assuming p=100 p£2-cm) at 13 GHz, the
impedance of the edge portion of the strip has a large resistive term. Modeling the
current shift caused by the edge going normal is done by considering the inductive
and resistive impedances of the edge region. The inductive impedance is found to
be -1x10^ £2 for both cases. For the superconducting case, the resistive
impedance is negligible when compared to the inductive component For the case
where the edge is normal the resistive impedance is found to be ~lxl()5 £2. Once
the impedances were found, the current density ratio between the normal and
superconducting edge were determined.
Some, but not all, o f the current
redistribution was due to the resistive increase in the normal edge. This was found
to theoretically account only for a frequency change of 0.2% or about 20 MHz.
However, much larger frequency shifts have been observed from the
measurements on meanderlines, and striplines. These larger shifts are assumed to
be due to a change in the inductive term in the impedance of the edge, which would
require full diversion of the current from the edge regions in the uniformly
distributed current model mentioned above. The resistive shift model is not
sufficient to explain these large shifts. This change in inductance is then roughly
modeled as an equivalent to reducing the width of the line by ~50 pm. This
reduction in width would cause the desired frequency shift and is conceptually
seen as a redistribution of the cuirent to the center portion of the pole as is shown
in figure 4.10.
Additionally, it is known that superconducting thin films have peaked currents
at the edges for both DC and RF resulting from field exclusion. This increases the
current density in the edge acting as if the width of the strip had been reduced.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
C ontrol Line
C e n te r P o le
A
10um
20um
20um
Figure 4.10. Microwave pole and the corresponding current density as determined
from the parallel plate transmission line calculations for (top) the superconducting
case, and (’bottom’! the edge driven normal case. The shaded region o f the
microstrips is the film driven into a partially nonsuperconducting, resistive state.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
100
This current redistribution can then be modeled as an equivalent change in effective
impedance. From the microwave S-parameter simulation program Libra, the best
way to get impedance changes in the elements is to alter the widths of the lines.
The preliminary estimates for switching performance were modeled using the
equivalent line width shifts to gauge the effect on the S-parameters. These current
redistributions are followed up in chapter 6, where a more accurate impedance shift
using the kinetic inductance change due to the temperature dependent penetration
depth of the YBCO is modeled.
4.4.2 Modeled impedance change
A value of 50 (im was chosen as the depth of the edge that is driven normal
for the modeling. The actual distance that becomes normal remains to be
experimentally verified. The change in impedance from the edge effect can be
modeled as a decrease in the width of the pole. This decrease in the center pole
width affects the S parameter results for the bandpass filter and causes a shift in the
center frequency of the bandpass. The effect is easily modeled by Libra, but
several other factors that have not been accounted for may also contribute to the
frequency shift.
Superconducting resonators have demonstrated that the
microwave current peaks at the edges of the poles, and even with high quality
films the power handling becomes an important is s u e d Wet etching tends to
cause edge damage to the YBCO and may contribute to the ease of driving the film
normal. The filter has been patterned with a control line coupled to the center pole.
Applying a large DC current close to I c (or possibly greater than I c) on the control
line causes a mirror current in the center pole. Driving either the center pole or the
control line normal alters the impedance of the coupled area, and this may cause the
desired frequency shift.
Not only will frequency shift be important, but so will the phase of the signal
through the filter. Estimates of the coresponding phase shift of the signal through
the filter were done using Libra. Phase shifts as large as 120° near the edge of the
passband are possible for a 50 pm edge driven normal, as is shown in figure
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101
P h ase
i—i
0)
e>
ak>
D
a>
Q
a>
o
c
0)
0>
D iffe re n c e v s .
F r e q u e n c y for F ilter S h ift
150
100
k .
Q
0)
(0
n
■c
Q.
12.75
13.00
13.25
13.50
F req u en cy [GHz]
Figure 4.11. Phase shift change of a signal through a switchable YBCO filter
versus frequency. A 50 pm change in the width of the center pole is assumed,
following figure 4.10.
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102
4.11. This phase shift works like a variable length delay line, in changing the
electrical length that a signal will travel when it passes through the filter.
The overall center frequency shift expected is from 50-100 MHz and this is
shown in figure 4.9. Another possible "switch" that can be made with a shiftable
filter could be to attenuate a fixed frequency signal at the edge of the passband.
When the control current is turned on the filter passband will shift down in
frequency and the signal is no longer in the passband of the filter. Thus, it should
be possible to attenuate the signal by up to -20 dB with such a switch.
Measurements are needed to determine that it is a linear and controllable effect (see
chapter 6).
Achieving these shifts with the control line meant that the design criteria are
critical. The control line length was optimized to have minimal effect on the
bandpass performance. In order to minimize the control line effects, the ends were
assumed to be wire bonded to a 10 pF chip capacitor. This effectively makes the
ends of the control lines behave like short circuits at high frequencies, thus making
the control line act like a resonating element. Libra's optimization program
determined the length of control line that would cause the least distortion of the
bandpass response and the fewest unwanted resonances. The simulations found
that a length window of ± 0.5 mm for the control line exists for good operation.
Later measurements of the control line showed that the short circuit impedance was
driven by the size of the capacitive contact pad and the inductive wire bond
connections to the DC control line. This meant that chip capacitors were not
needed to achieve the desired performance, and the control line was a resonating
element without them. These packaging issues are an important step in making
effective use of control lines. More packaging effects are discussed in chapter 5.
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103
Chapter 5
Mask layout and packaging
5.1
Mask design with L-edit
The filters from our design calculations were laid out using the CAD program
L-edit for the M acintosh.^ The mask was designed with "Boston" architecture,
which consists of square blocks and 45° lines. The different modeled filter
elements discussed in chapter 4 were laid out, and an overview of the final mask is
shown in figure 5.1. The process of laying out the mask involved several
iterations between the design step and the modeling stage, in order to satisfy all
constraints. The size constraint was to keep the filters under (0.8 cm)2, which
allowed use of the available 1.0 cm^ substrates. Larger substrates could have been
purchased, but the cryogenic measurement probe was also better suited to the 1.0
cm^ sampies that were used for the Taber Rs measurements.
The layout of the filters was symmetrical and the geometrical sizes
corresponded to the values used for modeling in Libra. The control lines were
made at specific lengths which minimized their effects on the bandpass filter
performance, and were laid out with a "freestyle" approach. This is possible since
only the areas of the control line that are nearest the microwave elements are critical
to the bandpass behavior.
Also, for simplicity, they were laid out to be
symmetrical. The control line is 50 (im wide from the contact pads, and narrows
to a 20 (im width in the center pole regions where strongest coupling occurs.
Figure 5.1 shows several layouts on the final mask. From left to right they are:
Top: a meanderline structure for testing a lower frequency resonator, the 3-pole
filter before wraparound, and a U of R logo. Middle: A wrapped filter with a
large coupled line to the center pole (unable to be driven normal with DC current),
a wrapped filter with a centerpole coupled control line, and a wrapped filter with a
control line that is near the edge region of the center pole. Bottom: a DC test
structure to measure field effects of a narrow control line, an overlay for the DC
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
104
test structure which aided in patterning, and a 3-pole filter wrapped with no
control line. The two designs on the mask in figure 5.1 that utilize DC control
lines are the center most (with shown inset) and center right. The design of this
microwave coupled DC control line was also kept simple, with a straight line
running from the contact pads (center left figure 5.1) close to the wrapped center
pole.
The mask was then stored in GDSII format and sent to Applied Image Inc., of
Rochester, where they produced a photolithography mask. Visual inspection of
the mask after fabrication showed no defects in the features. The mask was then
used to pattern YBCO samples for measurement as microwave bandpass filters.
The photolithography process that was used is similar to one from the
semiconductor industry.61 The exact process steps which were developed for
YBCO thin films are shown in table 5.1. The films were deposited in the CVC
SC4000 sputtering system with the same process as described in chapter 2. After
these YBCO films were patterned into filters, Ag groundplanes were evaporated
onto the back side. The films were then ready to be loaded into the microwave
cavity (section 5.3).
In other research, there is also some debate as to the processing steps of YBCO
films for microwave devices. For instance Conductus has published papers saying
that wet etching with citric acid gives the best r e s u lt s .6 2 TRW published a paper
that stated that ion milling was better, and that passivation of the films before a wet
etch avoided additional damage and higher Rs to the patterned
d e v ic e s . 6 3
Our
results presented in chapter 3 , for the meanderline measurements, showed that ion
milled films are less power sensitive than wet etched films.
5 .2
M icrowave filter cavities
Good measurements of the microwave properties of the filters require a
properly designed and fabricated cavity.3 Several problems with cavities needed
to be addressed to minimize effects upon the measurement. These problems are:
cavity resonances, direct signal feedthrough, connector reflections, and physical
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
105
Photolithography procedure for patterning the YBCO films
1. Clean the films with acetone and isopropyl.
2. Spin on 1400-27 photoresist at 4500 ipm for 60 sec.
3. Soft bake for 25 min at 95° C.
4. Cool films for 5 min.
5. Expose film with contact mask aligner for 13 sec of 195W UV light.
6. Cover all but edge of films and expose to UV for 1 min to remove edge bead.
7. Develop with Microposit 452 developer.
8. Rinse in deionized water (DI) for 30 sec to stop developing process.
9. Hard bake for 25 min at 105° C.
10. Cool films for 5 min.
11. Wet etch films in 0.5% HC1 solution for 20 sec.
12. Rinse in DI for 30 sec to stop etch process.
13. Ultrasonically clean the films in acetone to remove the photoresist
14. Rinse with isopropyl to remove the acetone film.
Table 5.1 The photolithography steps required to pattern YBCO thin films into the
test structures. This differs from that of a semiconductor process by reducing the
steps where the YBCO films would be contacted by H20, in order to reduce film
damage.
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106
A
UR-*1E
10 m
H
S
3
20 pm
Control Line Near
Center Pole
Cell: MalnLevel
Hie: HulCombo (Old)
Due: Fri, Dec 4. 1992
Cell bouodi: 15346 x 14746 Lambdt - 38365 x 36665 M lcrou
n i l view: 24904 x 37645 Ltm bdi - 62260 x 94112 Microns
Tanna Tooli L-Edltn*/M»ciiito»h
Figure 5.1. A schematic view of the final mask layout from L-edit. The devices
on the mask are (from left to right): Top: meanderline resonator, 3-pole filter
without wraparound, University of Rochester Logo. Middle: bandpass filter with
microwave control line, 3-pole bandpass filter with center element coupling (and
shown inset), 3-pole bandpass filter with end pole coupling. Bottom: DC test
structure, DC test structure overlay, 3-poie bandpass wrap-around filter.
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107
1.5 cm
1.8 cm
| 0.2 on
SK ttSSSSSatSSSS:;!!;!;;;;;;;;;
1.1cm
I
JU
555«5«t«S«5rt««««««55y 0.8 cm
i:5«5555t?5555«555S55555SS555SU5
m?55'*55\555J5}55555*5555555*5*5,>,‘
Sid* Viow
Front Vitw
Cutaway Sid* Vi*w
0.2 cm
Top Vi*w
1.1 cm
0.3 cm
UUll.UU^UUU.TlUlvU
tab 0.05 cm from ground
1.5 cm
.wwuumBW
Figure 5.2. Final cavity design. The circle around the cavity in the upper left is
0.875" in diameter, which is the required clearance of the cryoprobe.
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108
size constraints.
Cavity resonances are mainly determined by the overall size of a cavity. Cavity
resonances can "drown" out the sample features that one wants to see in the
microwave device under test (DUT). These resonances are reduced by keeping the
overall interior dimensions of the cavity as small as possible. Experimental
verification that the resonances will not overlap the desired frequency range is also
needed. The S21 of our cavity, with no filter inserted, is shown in figure 5.4,
and a cavity resonance is detected at -14.8 GHz. This resonance is outside of the
11-13 GHz window that is needed for the bandpass filter measurement. The IS21I
of an early prototype cavity is shown in figure 5.3, demonstrating the need to
reduce the cavity peaks in the desired measurement range for ease of measurement.
The final cavity design is shown in figure 5.2. The direct couple-throughput
power becomes a problem only above 16 GHz, and thus has no effect on our
measurements. This direct couple-throughput can be seen in the room temperature
empty cavity measurements as the rounded hump starting at 16 GHz (figure 5.4).
A further step, to reduce the width of a cavity resonance, includes coating the
interior of the cavity with Au. This was not needed in the above case. Cavity
resonances were a considerable problem in the earlier Taber R s measurements,
where the cavity was significantly larger than the samples under test
Because of the limited space in the cryoprobes, it was necessary to have the
microwave input and output power coupled in the same side of the cavity. This
design criterion was the motivation behind designing the filter as a wraparound.
Standard microwave filter cavities have the input and output port at the opposite
cavity ends, and this minimizes the direct couple-throughput of the power.
Another problem with the design of the filter is connector reflections to both the
input and output ports. The microwave industry uses ultrasonically bonded gold
ribbon to insure good connections.^ These gold ribbons are flexible and reliable
over a large frequency range. For the test of our samples, initially Ag paint was
used for the connections. The preliminary measurements show that the sample
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109
C H I S21
lin
MAE
10 m u /
BZ
CENTER 1 0 .0 5 5 000 0 0 0 GHZ
REF O U
ii
4 5 .1 1 7 mil
11 .7 6 5 S>64 SC 4 GHz
SPAN 1 9 .8 7 0 0 0 0 0 0 0 GHz
Figure 5.3 IS21I of an early prototype cavity showing the cavity resonances.
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110
lln
HAG
10 tnU /
82
TES"
Avg
16
-10
REF O U
it
3 S . 4 8 7 mU
1 4 .5 6 S ‘ '8 9 IE 4 OHz
PORT
POW E
dEim
CENTER 1 0 .0 0 0 0 0 0 0 0 0 GHz
SPAN 1 9 .7 4 0 0 0 0 0 0 0 GHz
Figure 5.4. Room temperature measurement of the empty cavity resonances.
Only one cavity resonance was present at 14.8 GHz.
The direct
couple-throughput microwave power can be seen as the hump above 16 GHz.
The bandpass filter should operate in the 11-13 GHz range.
(
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111
connections did not cause large reflections. However, the Ag paint contacts are
not ideal for mechanical stability. Also, it is necessary to chisel the samples free
from the cavity after each test. Initial application of the Ag paint contacts is
complicated since it must be applied with high precision. The measurements of
these connections showed that they could not survive several thermal cycles,
introducing uncontrollable microwave reflections.
The contacts to the DC control lines are also critical for device performance. A
low resistance connection is required to minimize sample heating during operation.
Ag paint contacts were used for the initial measurements. For later measurements,
a technique of depositing Ag onto the contact pads and annealing the films at
450°C in flowing C>2 was developed. This lowered the Ag/YBCO contact
resistance to less than 1 £2, making possible high current flow with little sample
heating.
Later, a method using 1-mil-thick A1 ultrasonic wire bonds to the contact pads
was used. These connections allowed optimal filter performance, and higher
mechanical reliability. The YBCO filter chip was bonded to a 10 pF pad chip
which facilitated the wire bonding. After the DC connections were wirebonded,
the chip was mechanically held in place in the cavity by conducting epoxy. Later
measurements showed that this 10 pF chip was not critical, and that the wirebonds
to the contact pads were sufficient for operation of the resonating center pole with
no loading.
The input and output rf connections were also wirebonded to the SMA
connectors of the cavity. The SMA connectors were coated with Indium in order
to make an easier bond. These wirebond connections were more reliable and less
prone to breaking than the Ag paint connections, hence successful measurements
increased.
5 .3
System Packaging Considerations
The filter cavity is shown in figure 5.2. To fit inside the vacuum can, this
cavity needed to be less than a 0.875" circle, which includes the thermometer,
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112
T op View of Filter C avity
DC Current
Feedthrough
Capacitor to Control
Line Wirebonds
g
/
i
E3
\
YBOO
Chip Capacitor
m Copper Tab
1.8 cm
3 Pole Wrap
Around Filter (1.0 cmA2)
DC Control
Line
Input and Output
SMA Connectors
Figure 5.5. Schematic view of a loaded filter in the cavity.
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113
control lines, and microwave coax.36 The cavity connections must be durable
enough to survive the thermal stress and vibrational shock of the experimental
measurement process. The ground connections inside the cavity were initially
made with Ag paint, i.e., the cavity walls were connected to the evaporated Ag
groundplane. The majority of the microwave filter measurements were made with
A1 ultrasonic wirebonds to the input and output connections. A final view of the
loaded filter is shown in figure 5.5. The wirebond pads, minus the 10 pF
capacitors to ground, were used for the majority of the experiments. Another
reason it is important to keep the bonds compact, is that the overall length of the
control lines affects the center frequency of the bandpass. Improper conections at
the ends of the control lines leads to secondary peaks and distortion of the
bandpass. This is due to coupling to the cavity walls.
After devising a new connector design, the control line effects on the filter
response were then tested. First, several passive measurements of the YBCO
filters were made, with different stages for the connections to the DC control line.
At first, the filter response appeared quite distorted. Shaking the input probe
determined that loose or inconsistent contacts were the problem. This problem
with the filter packaging took considerable time to resolve. Finally by improving
the evaporated contacts and wirebonds, the method for making the entire filter
assembly reliable was devised.
Another concern for reliable measurements is the SMA connectors on the input
and output lines of the test probe and Network Analyzer. Over time, they tend to
fail due to the frequent connecting and/or thermal cycling. The Network Analyzer
is used to determine if the SMA connections are still in working order by switching
into the time domain reflectometry mode, which measures the amplitude reflected
from each SMA connecter on the measured lines. The standard time domain
reflectrometry measurement is made by sending a pulse down the transmission
line, and measuring the power reflected at each connector from the return pulse.
The Network Analyzer reconstructs the time domain reflectometry by using the
frequency IS21! data that it measures, and fast fourier transformations to the time
domain.
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114
In order to get a reasonable measurement, the SMA connectors need to have
less than 5% amplitude reflection. If the connectors in the probe had a higher than
5% reflection they needed to be replaced or resoldered. Figure 5.6 shows a time
domain reflectometry measurement for the the first SMA connector at the top of the
probe. The measured reflection is at 11.6 ns, which corresponds to -1.3 m (the
length of the coaxial line to the SMA connector). The time domain mode can also
be used to inspect the copper coax lines for breaks in the interior dielectric, or other
problems that could arise from overbending.
Table 5.2 shows the process steps that were developed to give a succesful
measurement. One important aspect of the assembly process is an evaporation step
which reduced contact resistance to the films. The exact reasons for some of the
processing steps used are hard to justify, but this procedure provided reliable filter
data.
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115
Process steps required to fabricate a filter
1) Deposit YBCO thin films with the SC4000 sputter system.
2) Pattern the films with the photolithography process of table 5.1.
3) Evaporate Ag contacts onto the input/output connections.
4) Evaporate the Ag groundplane onto the backside of the filter.
5) Anneal in O2 @ 450° C for 30 minutes.
6) Bond the DC wirebond pad chip to the 1.0 cm^ YBCO filter.
7) Wirebond the DC control line connections.
8) Fix the chip into the microwave cavity with conducting epoxy.
9) Wirebond the rf input/output to the SMA connectors.
10) Seal the lid and mount the cavity on the rf probe for measuring.
Table 5.2 The processing steps required to manufacture a YBCO filter for testing
are listed. The typical time needed to fully prepare and test a filter is ~3 days.
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116
CHI S al
lln MAG
10 mu/
REF 0 U
AS
21.022 mU
1 1 . £ 8 4 ns
MARKER
1 . 5 EI 4 n
3 . 4 7 38 m
CHI CENTER 10.05 ns
SPAN 2 0 n s
Figure 5.6 Time domain reflectometry measurement of an SMA connector on the
probe input line.
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117
Chapter 6
Tunable Filters
6.1 Introduction
The "switching" of the tunable filters is accomplished by driving the DC control
line near the resonating pole normal. The resonating pole is then heated at the edge
by this now resistive control line. The temperature shift of the resonating pole
changes the penetration depth of the YBCO along the edge, and this causes a
current redistribution. This current redistribution is direcdy related to the kinetic
inductance of the resonating pole, and causes a proportional change in the resonant
frequency. A full understanding of the effects from the control line is determined
so that optimum switching filters can be designed and fabricated.
In this chapter the measurements of the patterned microstrip YBCO filters
will be discussed. The basic principles of operation for the filters are used to fully
explain and model the data. Also, in this chapter data is presented on the passive
and active properties of the filters. Tunable single pole and three pole filters are
demonstrated. A comparison of the single pole filters to the theoretical models is
presented. The theoretical models presented are: kinetic inductance changes caused
by shifts in the penetration depth, thermal diffusion in the substrate, and coupled
resistance of the control line.
To accomplish the experiments, the IS21I of the filters were measured with the
HP8720B Automatic Network Analyzer (ANA) from 0.3 to 20 GHz, and -10 dBm
to -60 dBm. Several YBCO thin films deposited at the University of Rochester,
by the process mentioned in chapter 2.0, where used. They were first patterned
into filters without a control line which makes the filters shiftable. The samples
were measured with the same probe set up that was used for the parallel plate R s
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118
measurements from 300 K to 4.2 K (see figure 3.4). The inductance shift from
the temperature change of the penetration depth was determined by observing the
shift of the center frequency of the filter IS21I for the different applied currents in
the control line.
The practicality of using YBCO microstrip filters requires that several important
factors be demonstrated. The insertion loss and bandpass filter performance were
thus tested. The response of the filter with an active control line was characterized,
both for a single pole and three pole filter. The switching speed for the tunable
filter was measured. Rs estimates from the single pole Q were made to determine
the loading of the centerpole by the coupled control line. First though, a
correlation of the shiftable filters with passive filter measurements versus
temperature was done to verify that the main effect was thermal heating of the
center pole.
6.2 Passive Filter Measurements
After the packaging problems had been solved for the tunable filters, the
passive data gave promising results. The initial passive 3-pole filter measurements
verified that the design for a maximally flat 13 GHz, 1% bandpass filter were
within reasonable specification limits. Figure 6.1 shows a IS211response for a
patterned filter at 77 K. This filter has a center resonance of 12.0 GHz and a
bandwidth of ~ 130 MHz, which was a reasonable match to the design of 1%
bandwidth at 13 GHz. However, there was some ripple in the passband (and a
small secondary resonance at higher frequency), and the insertion losses were
higher than expected (~1 dB at 4.2 K).
Figure 6.2 shows a IS21I measurement for a final packaged filter with all
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119
Passive Filter
CHI SaiSM lln MAG
All YBCO Filter w/Ag G roundplane (UR4300)
SO mU/
REF O U
l; 77.329 mU
11. BBS 1193 Ac 0 GHz
B3
S C A 1 .E
D mllnits/da
CENTER 11.98B 693 4S0 GHz
SPAN
S . 0 0 0 0 0 0 0 0 0 GHz
Figure 6.1 IS211response for a patterned filter at 77 K. The filter response shown
is for a filter with no control line.
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120
CHI 8gi6M lln MAG
SO mU /
REF O U
«a
MARKER
2.5C 940317E
is
100.GB m U
13 .B O B <100 1? B GHZ
GH
CENTER 13.405 000 176 GHz
SPAN
3.000 000 000 GHz
Figure 6.2 A IS21I measurement for a final packaged YBCO tunable filter with a
DC control line and Cu groundplane.
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121
connections made before a switching was attempted. A small resonance peak in
the IS21I at 13.1 GHz was seen near the ideal resonance curve. This is thought to
be a slight mismatch or reflection caused by the control line being in closer
proximity to the center pole than could be accurately simulated by Libra in the intial
design. It was found that the overall length of the control line would drastically
affect the IS21I values, since it is a separately coupled resonating element. Thus,
the actual data provided a check to the Libra simulations of the filter's design
performance. This secondary resonance was far enough away from the main filter
response to be easily distinguishable and had minimal affect on the measurements.
6.3 Active Filter Measurements of 3-Pole Filters
The switching effects of a control line near the center resonating element of a
3-pole filter was tested for comparison to single high Q resonators. Originally, the
tunable filter was to be a three pole filter. The reason for choosing to test a
multi-pole filter, is the sharper rolloff characteristics for the IS21 I. Three pole
filters were also arrived at due to the size contraints of the substrates. After the
first initial measurements of three pole filters, the experimental data was found to
be difficult to interpret. It was apparent that a simpler single pole design was
needed for easier understanding of the data. The intent was to switch back to the
three pole filters, once the single pole filters were fully characterized. However,
due to time constraints, only the preliminary measurements of the tunable three
pole filters were carried out.
This preliminary tunable 3-pole filter data is shown in figure 6.4. The figure
shows the IS211for a tunable 3-pole filter at 4.2 K with no applied current to the
control line, and the same filter shifted by a control current of 70 mA. The overall
shape of the filter response is quite noisy due to reflections off the input and output
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122
Filter Conversion to a Single Pole Resonator
Ag Patches
Figure 6.3 Single pole filter made by shorting the designed three pole filter with
evaporated Ag.
('
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123
connections. The frequency shift of the filter is ~50 MHz, and the insertion loss is
~8 dB (quite poor) prior to packaging optimization. The filter did exhibit
repeatable shiftability, and withstood thermal cycling. The YBCO used to make
the preliminary filter was not of optimum quality. This was indicated by the IS21I
filter response only being measurable below 40 K due to the high losses of the
films.
The preliminary measurements also showed that runaway heating with the
control line was a problem to consider. By driving the control line (above Jc) at
~70 mA and ~3 V the sample would first rapidly shift and then slowly drift as the
temperature rose. The temperature sensor on the outside of the microwave cavity
was used to detect the slow temperature rise from the control line heating. By
using evaporated Ag contacts, the contact resistance to the control line was
minimized, and the heating observed was directly related to the power dissipated
in the control line.
6.4 Tunable Single Pole Resonators
A three pole filter was altered into a strongly coupled single pole resonator by
evaporating a Ag coating which shorted out the input and output poles (see figure
6.3). The packaging and measuring of this filter was the same as the passive three
pole filter. Approximately 20 single pole resonators with coupled control lines
were measured. This characterized the response of the tunable resonance. Single
pole stripline resonators were studied (chapter 3), and the evaluation procedure is
similar to the meanderline resonators. The Q and the center frequency were
measured for these single pole resonators from 4.2K to Tc. One of the reasons
for shifting to a single pole resonator was to simplify the modeling of the
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124
YBCO Filter with Control Line
CHI S S18M lln MAG
S mU/
REF O U
ii
38.645 mU
1 3 .6 9 3 (180 5c 3 GHZ
Smo
1-60 mA
CENTER 1 3 .6 9 4 6 80 5 2 1 GHz
SPAN
1 .0 0 0 0 0 0 0 0 0 GHZ
Figure 6.4 IS211measurement of a preliminary tunable 3-pole filter, at T=4 K.
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125
control lines. A measurement of single poles, and single poles with control lines,
allowed a better understanding of the shiftable filter reacting to an input control
current.
It was apparent that to model the tunable resonators, three main factors must be
considered for a clear understanding. These three factors are: frequency shift,
peak broadening, and switching time.
For the single pole resonator
measurements, the center frequency data (fy) was measured versus temperature
and control line DC current. The Q was measured for the resonance versus
temperature and the control line DC current in order to obtain the necessary
information on broadening. The single poles were modeled with Libra, and a
current density
model. Lastly, the switching speed was measured by applying
an AC signal to the control line and observing the aliasing of the IS21I response of
the filter (this will be fully explained below).
An IS21I measurement of a tunable single pole resonator can be seen in figure
6.5. The center frequency is defined by the maximum peak height of the IS21I
curve and related to the inductance of the microstrip stucture. The Q is measured
by determining the Af at the half height, as was used in chapter 3.0. Of note is a
much narrower passband Af than the 3-pole filter which was designed to be -1%
of center frequency. The Q of the single pole resonator is limited by the
input/output coupling, and R s of the YBCO, not by the designed passband. The
resonator shown in figure 6.5 was measured at 50 K with no applied current. It
was then shifted ~7 MHz by applying an input current of ~80 mA to the control
line.
Switching measurements on the tunable filters were accomplished with the use
of a sine wave function generator connected to the DC control line with a 100 Q
resistor in series. The maximum output of the function generator was 10 V, so
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126
UR #374 Single Pole w/Control Line @ 50 K
H
CHI S alSM lln MAG
1 7 .8 7 9
mU
IS .447 !140 3ZS GHZ
^
U riA
1-80 mA
START 12.404 920 325 GHz
STOP IS.504 920 325 GHz
Figure 6.5 IS211measurement of a single pole tunable filter at 50 K. The two
curves show the filter with no applied current (unswitched), and with ~80 mA
applied current on the control line (switched).
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127
this gave us a peak current of ~100 mA on the control line. At low frequencies
(<10 Hz) the filter switched back and forth between the "off" state and "on" state.
The advantage of using the function generator was that the amount of sample
heating was reduced due to limiting the time that the control line was normal. For
most of the measurements, the control line ^ was exceeded at ~80 mA. As the
function generator frequency was increased the filter switching continued at a
faster pace than could be sampled by the Network Analyzer (200 msec sweep time
for 101 different frequency points). The aliasing that resulted from this is shown
in figure 6.6, which is essentially an average of the two switched curves (seen if
figure 6.5) with aliasing spikes. The switching was measured by the aliasing up to
a little more than 1 kHz, which corresponds to a switching time of ~1 msec.
Along with the switching speed, a phase shift measurement was done on the
switchable single pole filter. The Network Analyzer does a vector analysis of the
microwave signal which preserves all the phase information. Since this is of some
interest when comparing to tunable delay lines or filter arrays some preliminary
measurements of the phase shift caused by switching the filter were done. The
phase was measured to shift 140° for the center frequency of a single pole filter, at
12.3 GHz, by applying 80 mA to the control line (see figure 6.7). This compares
nicely to the simulated phase shift of figure 4.11. This phase shift is large enough
to have several applications, if the high losses that arise from driving the control
line normal can be neglected.
Armed with the measured data for the single pole tunable filters, it was time to
accurately model this device so it could be incorporated in future filter designs. To
start with, the center frequency and kinetic inductance models were deemed to be
most important for describing the observed behavior. To further explain the
results, thermal models, and a model for coupling losses introduced by the control
line, will also be included.
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128
CHI 8 2 i ^ l l n M A ®
S BU/
i:
REF 0 U
M
CENTER 1 C . 4 9 4 0 8 0 & S 0 B H l
C H I B g j- H
1 8 .1 4 1
mU
1 & L 4 B 4 $ 8 0 B dO OHS
lln
MAO
e
m u /
u
CENTER 1 2 . 4 5 4 9 B 0 C 8 0 GHz
S PA N
re f
o
.COO 0 0 0 0 0 0
GHZ
1; t t . y e s »u
u
' 1 C . 4 8 4 I ISO C l 0 OHS
SPA N
.COO 0 0 0 0 0 0
SHz
Figure 6,6 Aliasing of the ANA IS211measurement caused by rapidly switching
the single pole filter. The top shows aliasing at a slow switching of 100 Hz, and
the bottom shows the aliasing when a 1.2 kHz signal is applied.
(
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129
Measured Phase Shift versus Frequency
for a Tunable 3-pole filter
200
Phase Shift
150-
100 JS
O
M
a
j=
a.
50-
12.55
12.575
12.6
12.625
12.65
12.675
Frequency [GHz]
Figure 6.7 Phase shift measurement of a tunable single pole filter. The phase shift
is measured to be ~140° for the center frequency of the unswitched filter by
applying a 80 mA control current.
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130
6.5 Comparison to Theoretical Models
This section is a compilation of the three models used to describe the behavior
of high Q resonators with a coupled DC control line. These are: 1) A current
density model for penetration depth and its effect on kinetic inductance; 2) a finite
element thermal gradient model to describe heating effects; and 3) a lumped
element coupled resistance model for the loading of the resonator to explain peak
broadening. The models are appropriate with single pole resonators, but the results
may be extrapolated to more complicated devices.
The data taken on the single pole resonators required the use of several
multiparameter fits to the models. This task was completed with the computer
packages of MATLAB, and Excel together with Libra. Both programs allowed the
manipulation of large data arrays and real time feedback to achieve parameter fits
with built-in graphing functions.
6.5.1 Kinetic Inductance
A theoretical model for the frequency shift with applied control current to the
center pole was modeled as a variable inductance. It includes the kinetic
inductance of the superconducting microstrip meanderline. The total inductance of
the microstrip resonator is given by the following equation:
Ltotal = Le + Lj + Lk
(6.1)
Le is the external inductance that arises from the fields outside of the film, Lj is the
internal inductance from fields that are present inside the film, and
is the kinetic
inductance which is related to the fields within a penetration depth of the sample
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131
surface.
It is the exclusion of the magnetic flux, that concentrates the currents at the
surface of the superconductor. The surface currents fall off as 1/e into a
superconductor, where this distance is defined as the penetration depth Xl « These
currents satisfy the following set of general equations:
V 2B = ^ L _ B
X L2
V 2J = - L j
( 6 .2 )
Xl 2
Here Xl is the temperature dependent penetration depth for the superconductor.
This assumes that vortices do not penetrate into the film. From the equation for
stored inductive energy, the microstripline contribution from kinetic inductance can
be found. The general form for the total energy stored in the inductance is:
LI2
2 -
i ,f [B2
r n 2+j .ll„
2 i.2T
po2X
l Jf] dV
2H°Jv
(6.3)
The first part of the integral that is related to B 2 is the external and internal
inductance (Le+Lj), the second part is the kinetic inductance (Lj^). From this an
approximation for microstrip geometry yields the total inductance:
Lk = ^ < l + ^ ^ )
(6.4)
Here w is the width of the microstrip, d is the distance to the groundplane, and K is
a geometry factor, that depends upon the w/d ratio, and is assumed to be one for
the samples (The factor of 2 assumes both the ground plane and center strip are
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132
superconducting).
Equation 6.4 is valid only when the groundplane and
centerstrip sections of the superconductor are much thicker than the penetration
depth (t»A,), and (w » d ), and if edge effects are neglected (here t is the film
thickness). The values of kinetic inductance obtained from equation 6.4 did not
match the measured frequency shift data of the single pole resonators versus
temperature. The predicted shift from equation 6.4 would only account for a ~1
MHz shift in the center resonance since X>L«d.
The shifts observed
experimentally are in the range of 50-100 MHz. A better match to the larger
frequency shift seen with the data can be obtained by considering the current
distribution inside the resonator.
No simple analytical expressions exist for the current distribution in a
superconducting strip above a ground plane with rectangular shape and sharp
comers. An approximation for the current in the center of an isolated thin
superconducting strip when t« w , and t<A, is given to b e :^
J s (x ) = J s ( 0 ) [ l - ( 2 x / w ) 2]- 1' 2
(6 .5 )
and near the edge it is found to be:
Js(x) = Js(lw)exp -[(^w - lxl)t/aX2]
(6.6)
Here a is a factor near unity and t is the thickness of the thin strip. Equations 6.5
and 6.6 meet at the point where:
x = ± (lw - aX2/2t)
(6.7)
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133
Equating equations 6.5,6.6, and 6.7 a value for Js(w/2) (the edge current) is
obtained to be:
J(iw ) = (1.165A)(wt/a)1/2Js(0)
(6.8)
A more accurate current evaluation in a thin conducting strip can be found by using
a numerical solution generated by the modified Week's
m e t h o d .6 5
A highly
accurate closed-form expression was determined with this method by Lee et al. to
be:
^cosh(x/li) | 1-cosh(x/l2)/cosh(W/I2) + h w & m
V l (x/ w)^"
cosh(wA)
cosh(tA) cosh(w/lj)
(69)
where
h -
Ji
1.008
w / k ___
cosh(tA) V 4X jA -0.0830aA ±
l0.75
C = ,0'506V 2X±)
^
ii = W iifk i
h = 0.774X2A i + 0.5152X.J.
Xj. = X2/2t
Here A^is the transverse penetration depth. This equation is valid only when the
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134
strip thickness is on the same order as the penetration depth, making it quite useful
for evaluating thin deposited superconducting films.
Figure 6.8 is the current density from equation 6.9 were averaged over
thickness (y) for a sample that has similar parameters as the constructed
superconducting filters. The parameters chosen for this calculation are Xl (0) =
1500 A, Tc = 87 K, the width is 100 (im, and the thickness is 4000 A. This
current density is peaked at the edges compared to the center of the strip. In
comparison, equation 6.5 produces a current distribution that is nearly equivalent
to equation 6.9. Thus for simplicity, equation 6.5 (with a=l) was used for the
current distribution of the resonators.
Once this current distribution has been obtained, the kinetic inductance
is
found to be:
(6. 10)
A computer program was written to determine the kinetic inductance using
equation 6.10 versus temperature. The kinetic inductance versus penetration depth
and different thicknesses, for a microstripline having the dimensions similar to the
centerpole used in the filter is shown in figure 6.9. For a microstripline, Le is
found by considering the geometry with air as the dielectric since MgO and
LaA103 will have no effect on the inductance of the line. The equation for Le is;66
222 iog(8h/w)-t-^-
(6. 11)
Here h is the thickness of the dielectric, w is the width of the microstrip, c is the
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135
Current Density [Arb. Units]
0
Width [urn]
•50
-0.2
Thickness (ftm]
”v k I S
CUITent density found for equation 6.9 where V (0) - jsqq s ~ o / K, the width is inn iir« n * ■ ,
n.u> —jooo A TV.
tun is 100 fim, and the thickness is 4000 A
Reproduced with permission o f the coovrinh,
epynght owner. Further reproduction prohibited without permission.
136
(
Lk versus Penetration Depth for different thicknesses
t » 0.25 (im
t= 1.00 pm
2.5
0.5
Penetration Depth (fn)
Figure 6.9 Kinetic inductance versus penetration depth and different thicknesses
for a microstripline similar to the single pole resonator.
(
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137
speed of light, and Zoa is the characteristic impedance of the structure surrounded
by air. Ltotal is obtained from equation 6.1, using Le+Lk, and assuming the
contribution from Lj is negligible. L^'s effect is largest on the center frequency
near the T c of the superconductor, and makes a percentage change in the total
inductance of ~ 2%. The following equation relates the frequency to the
inductance:
fo = —= — -— = - |L where K = —^—
x 2 M r vu
2ev e
Here v is the velocity, t = X/2, and L and C are the inductance and capacitance per
unit length. By taking the log of both sides we get:
log fo = log K -
log L
then taking the derivative we get:
8f/f = 1/2 (8L/L)
(6.12)
Thus the percentage change in frequency is equal to the half the percentage change
in the total inductance, hence a frequency change of ~1% or 130 MHz is expected.
One thing to consider though is that the kinetic inductance shift effect is larger
for thinner films as can be seen in figure 6.9. Measurements were done on 3 sets
of single pole filters with thicknesses of 0.1, 0.25, and 0.5 pm thick films. The
raw frequency shift data of these three resonators is shown in figure 6.10. As
expected the thinner film resonators had larger shifts, but they also had larger
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138
Single Pole Resonator Center Frequency versus
Temperature For Different Thickness Films
13.5*
e
131
0 0
°
o
"
°
o o
D 0
*eoooooa
8
.
•
V
n a
#,
*
S'
2 - 1Z5-
6
a
12 -
|
0
o
1000 A
«■
2500 A
•
5000 A
11.5-
H i— ------------------!---------------------- 1---------------------- r
25
50
75
100
Temperature [K]
Figure 6.10 Raw frequency shift versus temperature data for 3 single pole
resonators of thicknesses 0.1,0.25, and 0.5 |im. Near Tc, the thinner films have
a larger shift due to the greater change in kinetic inductance.
i
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139
resistive losses.
The 0.5 urn thick films were determined to be the best for
optimum R s losses, and still gave reasonable frequency shifts o f -50 MHz when
switched. Further analysis was carried out on the 0.5 pm thick resonators to verify
that the kinetic inductance model was accurate.
For the 0.5 pm thick microstrip measurements without an adjacent control line,
the frequency change data was compared to the simulated kinetic inductance
change versus temperature. Figure 6.11 shows the data and the theoretical match
achieved with an adjusting of the input parameter A.l (0). The best match was
obtained for a Tc = 86 K, A,l (0) = 4500 A, Ej. = 9.6, h = 0.5 mm, and w = 100
pm. An excellent match was also obtained for the frequency shift of a resonator
without a control line using reasonable parameters. Thus most of the shift seen in
the resonance data versus temperature can probably be related to the kinetic
inductance.
In the case of a control line near a resonating pole, the observed contribution
from the coupled kinetic inductance of the control line must be included. The
frequency shift versus temperature for the passive single pole with a control line
did not match the expected frequency shift for just the single pole determined
above. A simple linear model for the coupling factor of the inductance of the
control line was needed. Thus, the entire inductance to be considered for the
center pole is:
L n ^ + CLj
(6.13)
Ljjj is the modeled inductance, L j is the inductance of the centerpole, L 2 is the
inductance of the control line, and C represents the coupling factor for the
inductance between the two lines. L 2 can be calculated from equations 6.10 and
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140
(
2.4
Theoretical Fit of Fc to URO408 (Kinetic Inductance] 4/21AM
2.35
2.3
2.25
N
X
o
»>
2
2.15
Theoretical
2.05
”*■
Raw Data
1.95
Temperature [K]
Figure 6.11 Theoretical match to the frequency shift data showing the best fit for a
single pole resonator with no control line.
('
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141
6.11. By adjusting C, a reasonable fit to the data was found with C=0.015.
Figure 6.12 shows the frequency shift data for a centerpole with a control line and
the theoretical fit with Tc = 85.8 K, Xl (0) = 1900 A, Er = 9.6, h = 0.5 mm,
w = 660 |im, and C = 0.015.
The shift of frequency also shows good agreement with the change in the
kinetic inductance observed for the tunable resonators. The main effect which
causes this shift is a change in the temperature that shifts the penetration depth,
which changes the kinetic inductance associated with the edge currents. This does
not fully explain the entire resonance shift, since experiments show that the
resonance also broadens. The resonator broadening occurs because the resonator
becomes lossier (decreasing the Q). In order to further understand this active shift,
it was decided to consider the thermal heating of the control line and the effects
caused by it on the Rs of the overall structure.
A comparison of the heating caused by the control line was done by considering
L(T), R<(T), and ^ l (T). From the measured data for single pole resonators
without a control line the expected frequency shift matched the temperature of the
sample. However, when a sample with a control line was switched, it could not
be accurately expressed by just increasing the temperature of the resonator. For
comparison, a tunable single pole resonator was "switched on" and the switched
center frequency determined. Then the resonator control line was turned off and
heated until the center frequency matched. The Af of the sample was broader in the
switched sample than in the resonator that was moved to the higher temperature to
match the center frequency. Thus the Q can not be determined solely by the kinetic
inductance model. Also, the kinetic inductance model gives no indication of the
switching speed that is possible for a sample other than the time to completely heat
up or cool down the entire film to obtain the shift. The nonuniform heating of the
resonator by the control line needed to be correlated with the kinetic inductance
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142
Fe vs. T for UR*405 Single Pole end Coupled Control Line
Mr
l — I W
N
S
o
w
m
— W
..
13
12.S
12
11.5
0
+ Raw Data
* Calculated Without Control Line
• With Control Line and 0.015 Coupling Factor
10
20
30
40
50
60
70
80
VO
Temperature IK)
Figure 6.12 Theoretical fit to a centerpole coupled to a control line using the
kinetic inductance model.
(
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143
model presented in this section.
6.5.2 Current Induced Heating
The current induced heating in the microstripline resonator was determined
using a finite element analysis program called FEHT (finite element heat transfer).
FEHT is a 2-dimensional nodal modeling program. The user selects the scale
(distance between) the grid points and creates a representation of the device to be
modeled similar to using a CAD (computer aided design) program for drafting.
Then the user specifies the material types being used in the layout with the
corresponding specific heats and conductivity. The layout is then further broken
down into nodes, which are assigned initial boundary conditions. These typically
are temperatures or heat flow values. The layout is then further broken down into
smaller triangular nodes so that the program can solve for the temperatures
quasistatically, or in a time domain analysis, and give a good 2-dimensional
display of the temperature results.
For the control line coupled resonator, the geometry of the control line near a
centerpole was laid out to scale and analyzed for temperature gradients (used later
in figure 6.14).
For our layout we used MgO, and YBCO which had a
corresponding specific heat of 88.9, 156.2 (J kg'* K 'l), and a conductivity of
485.7, and 2.2 (W m '* K*l).67
The grid scale used was 1 cm to 100 pm in
order to accurately see what the temperatures were inside the microstrip and
dielectric. The boundary conditions for the analysis were set from the amount of
power heating for the sample from the control line.
Figure 6.13 shows the 2-probe voltage versus input current for the control line.
The current supply is limited by a maximum input voltage of 3 volts. When the
sample is driven normal by exceeding the ~80 mA critical current of the control
line, the source rapidly decreases the current to satisfy the voltage compliance
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144
I ;
Control Line 1v i V for filler UR#374 3/14/94
1)00
1250
r«vj
1000
I
>
750
500
250
0*
100
Control Line Current fmA]
F re q u e n c y
t *5ok
i
an 4/94
12.456
12454
hi
12452
1245
I 'M
10
•«>
loo
Control line Current (mA]
Figure 6.13 DC I-V curve for the control line operation of a tunable filter.
(
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145
limit. We estimate the normal resistance to be ~30 £2 from the I-V curves for the
input DC control current at the point where Jc is exceeded. The length of the
coupled 20 Jim wide section of control line is 2.42 mm, thus the total power being
delivered to the substrate is 6.2x10^ W/m^. This was determined from the
current, resistance, and area of the control line. The other boundary conditions for
the control line were the temperature settings. It was assumed that the entire device
was 77 K before the control line went normal. The groundplane, considered the
heat sink for the entire filter, was always 77 K since it is in contact with the brass
cavity.
A time domain analysis was done, and the temperature versus time was
calculated for the microstrip with a control line driven at 80 mA. At ~1 msec, the
temperature along the first 10 Jim of the centerpole raised to 83 K, and the control
line was above Tc at 93 K. Figure 6.14 shows the temperature contours from the
control line at 1 msec. For comparison figure 6.15 shows the same configuration
in the steady state condition after allowing the temperatures to reach steady state.
The steady state shows that after a long enough time the control line would rise to
~115 K while the edge of the centerpole would be at ~92 K. After the quick intial
shift of the tunable filters (~1 msec), the center frequency of the filter would
slowly drift to the steady state solution temperature values. Unfortunately, the
superconducting and normal YBCO is lossier at higher temperatures, and the peak
would broaden considerably as the temperature of the device increases.
From the time domain analysis, the nonuniform heating of the control line
raises the temperature of the centerpole edge by 5 K within 1 msec. This change in
tempertature is large enough to account for the shifts seen in the center frequency
of the single pole resonator using the kinetic inductance model. Using the Matlab
program for current distributions and Xl (T), the expected inductance shift from the
thermal heating determined in these simulations is approximately equal to the
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146
m m miMa&es
/’
B
76.0 B
8 2 .0 1 3 88.0 1 3 94.0 □
100.0 □
111.9 TC
Figure 6.14 The temperature contours for control line at 1 msec after applying
input current.
(
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
B l 78.0B B 86.OH394.O E31 0 2 .0 Q llO .O D 115.3 «K
Figure 6.15 Steady state solutions for the control line near the center pole
resonator. The control line attains a temperature of -115 K while the edge of the
pole is raised to 93.0 K. This is evident in the measurements by a slow upwards
drift in center frequency after the initial rapid switch of the tunable filter.
(
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148
observed frequency shifts. However, the measured single pole resonators with
control lines showed a considerable peak broadening after being "switched" by the
control line. To gather a complete picture for a model that describes the operation
of the control line, we need to also consider the amount of loading caused by the
normal control line on the main resonating element.
6.5.3 Coupled Resistance
Once a good model has been made from the nonuniform heating, it is possible
to model the equivalent R s of the resonator and control line structure. Since the
control line behaves as a coupled microwave resonator, it was decided to model the
loading to the coupled center pole. The lumped element model that we used is
shown in figure 6.16. It was possible to model this lumped element system using
the microwave simulation program Libra, and to integrate it into the results from
the earlier modeling of tunable filters.
Libra allows the user to input sections of microstripline by only specifying the
geometry of the lines and substrates being used. These are ultimately broken
down into lumped inductances and capacitances as well, but the handling of them
by their geometry makes it much easier for the user to keep track of the layout
being simulated. Like Spice, Libra is able to then do a frequency analysis of the
overall system specified by the user. The information that the program determines
is the IS111and IS22I parameters that would be equivalent to an ANA measurement.
For the coupled control line simulations, it was necessary to model the control
line by its lumped values for inductance, capacitance, and resistance. It was not
possible to model a Libra circuit where different sections of the microstrip were at
different temperatures due to the constraints of the program. In order to accurately
model the heating seen in the control line when it was normal, it was necessary to
add a series resistance R1 that could be changed corresponding to the increase in
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149
LI
R1
V sA V
cicoupling r
'input
JL ci
_ _ coupling
output
Figure 6.16 The lumped element model for a resonator with a coupled DC control
line.
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150
Rs due to the thermal heating.
From the previous section, it was shown that the control line temperature
exceeds Tc and goes normal when switched on for longer than 1 mec. The control
line resistance R was then found by assuming an equivalent p = 100 pQ-cm for
being driven normal (T=l 10 K). The coupling capacitance Cl is determined from
the following equations for the odd mode capacitance of two coupled
microstriplines:66
C ga
1 + VP
= — In
Jt
fo r0 < k2 <0.5
(6.14)
for 0.5 < k2 < 1
(6.15)
1 + V P.
Cga - 7t£o / In
2i±jE1 + VP
where
k = - ■ Sf t- —- and k'2 = 1 - k2
S/h + 2W/h
and
Cga = M . l „ c o ^ ) + 0.65 C ^ V e T + (l - £ }
Clot = Cga + Cgd
(6.16)
(6.17)
Cga is the capacitance in air and Cgd is the capacitance in the dielectric. The
parameters S, h, and W are the spacing, height and width respectively (See figure
6.17). For this structure a coupling capacitance of 0.077 pF between the control
line and the center pole of the resonator was found. The loss due to the increased
resistivity p was modeled as a series resistance. When the control line is driven
normal the capacitance will have little change since there are no geometry changes
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151
End View
Odd m ode capacitance b etw een microstrips
fla
Microstrip
Dielectric
Groundplane
Figure 6.17 Capacitance schematic for two coupled microstrip lines.
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152
taking place. The resonance broadening from the increased p for the assumed
lumped element model is shown in figure 6.18. The values of resistance due to the
resistivity and capacitance for the modeled broadening closely matches the
experimental measurements seen in figure 6.5 for the case when R = 20 Q. The
modeling can accurately predict what loading the normal YBCO control line will
have on the performance of the shiftable filters.
As a check against the inductive coupling factor C = 0.015 in equation 6.13, the
resistive loading for the same factor is considered. The equation is:
Rtotal = R + C R ’
(6.18)
Here Rtotal *s the final resistance factor that determines the measured Af of the
single pole filter with control line, R is the resistive contribution from the
superconducting resonator pole, and R1 is the resistive contribution from the
control line. The values for R are determined from the R s for YBCO at 77 K and
for when it is driven normal. These are ~ 2 mQ/O @10 GHz and 77 K and
1 Q/D at 100 K. The resonating center pole is ~5 squares, (0.5 mm x 2.42 mm)
and the coupled control line section is ~120 squares (20 |im x 2.42 mm). Once
determined, Rtotal *s compared to the effective Rs of the resonator that is
experimentally measured from the Af of the resonance (Rseff= Rtotal / 5CT).
When the control line is superconducting R = 10 mQ, R* = 240 mQ and the
Rtotal = 12.5 mfl, which corresponds to R seff = 2.5 mQ. From Linecalc, the
estimated resonance Af is ~1 MHz/mQ for this geometry, and would be 2.5 MHz
wide. The coupling loss Af of ~7 MHz, that was found with a Pb test structure,
must be added on, producing a resonance width of 9.5 MHz. This closely
matches the measured 10 MHz peak width for the single pole resonator with a
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153
superconducting control line at 77 K.
When the control line is driven normal by exceeding Ic, the heating slightly
raises the center pole to a value of R = ~20 m£2, but it is still superconducting.
The resistive value for control line is estimated to be R1= 120 £2, if the entire
length of the control line was normal (1 £2/0). This would produce a Rtotal=
£2. However, one must consider the measured DC resistance of the control line is
only ~3Q £2 when driven normal by slightly exceeding the I c . This would
correspond to only a small section (or sections) of the line being driven normal,
and producing a localized hotspot. More importandy, if the measured R' = 30 £2 is
used, the calculated Rtotal = 0-49 £2, and Rseff = ~98 m£2. By adding in the
coupling loss of 7 MHz, the Af is in the range of the measured 100-150 MHz for a
shifted single pole resonator with a control line driven normal. These calculations
are consistent, and verify that both the lumped resistance model, and the coupled
inductive model, can be used to determine the peak broadening and frequency shift
expected for the coupled microstrip control line.
6.6
Summary of Tunable Filters
In summary it was possible to make models that quite accurately display the
behavior that is seen experimentally for tunable fitlers using the close proximity
DC control lines. The frequency shift for the resonator is adequately explained by
the temperature dependent penetration depth. The thermal gradients also accurately
modeled the switching speeds observed in the operation of the tunable resonators.
Lastly, the resonance broadening is accurately modeled from the coupling between
the high Q centerpole and the lossy control line.
Now that these models exist for determining the performance of a resonator
with a DC control line in close proximity, more complicated structures and
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154
EEsof - Libra - Fri Jun 17 14:30:38 1994 - WRAP1P
□ DB[S21]
RESON
0.000
R-on
R>sn
-30.00
-60.00
FREQ-GHZ
Figure 6.18 Libra simulations of resonance broadening using the lumped element
model for resonator with a coupled DC control line.
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
multi-pole filters could be designed. However, the losses introduced by the
coupling to the "normal" control line in the "on" state are highly undesirable, and
will largely limit the usefulness of structures designed on the same principles.
Ideally, the YBCO meanderlines could replace bulkier dielectric resonators that are
the current filter standard for communication satellites. The YBCO filters would
be ~200 times smaller in volume and in weight than the dielectric resonators.
However, the 0.1 mW maximum power levels that was determined that the YBCO
filters would support, was found to be less than what is desired for use in
communication applications (typically several mWatts). Discussion of the overall
impact for future uses of YBCO filters will be concluded in chapter 7.
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156
C hapter 7
Conclusions
RF microwave measurements have been made on several superconducting
YBCO structures. The main focus of the project was to prove feasibility for the
shiftable YBCO bandpass filters, and developing the knowledge that led to a firm
understanding of the principles involved. R s, power handling, penetration depth,
kinetic inductance, J c, Tc , Hrf, Irf, and other film quality measurements were
made on many samples for comparison. The films showed a wide variation for
these parameters, which primarily depended on deposition. Table 7.1 is a
compilation of the film qualities for the measured YBCO films.
Shiftable rf YBCO bandpass filters were made. These filters were shiftable by
50-100 MHz, where the critical current of a control line was exceeded.
Calculations confirmed that the shifting was caused by the thermal heating of the
edge of the centerpole, thus changing the kinetic inductance of the pole. A
switching time of ~ 1 msec was measured for this shifting operation. For some
commercial applications, like detectors, these filters could have a use. However,
for communication filters, the power handling ability of the filters would be usable
for small power levels of a few |iW or less. Other groups have made films with
higher power handling
a b ilitie s .2 4
These same considerations would apply to
phase shifters based on these filter designs.
The power dependence of the films was found to be quite sensitive, depending
on processing conditions. Ion milled films exhibited a factor of 10-100 higher
power handling ability than wet etched samples. This improved power handling is
still an order of magnitude below the results determined in the measurements of
unpattemed films. Edge damage from the patterning, as well as nonideal
processing conditions, are thought to be the main culprits for this discrepancy.
The future directions of the superconducting rf microstrip filters is uncertain.
Filters made from YBCO are not considered a large enough leap in performance to
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Optimum measured YBCO properties
Tc
91 K on LaA103,89 K on MgO
Jc
2xl06 A/cm2 @ 77K
Rs
0.3 mQ @ 77 K scaled to 10 GHz
Q
14,200 for a stripiine resonator, 1200 for a meanderline resonator
Peak H jf
~12,800 A/m @ 4.2 K for a meanderline resonator
XjJO)
1500 A measured from a parallel plate resonator measurement
Peak Power ~1 pW at 4.2 K and 2.5 GHz for a 50 pm wide microstrip
meanderline (determined from peak currents)
Table 7.1 A compilation of the optimal measured parameters for YBCO films from
several different measurement techniques. The Q is highly dependent on geometric
dimensions and does not necessarily signify high quality films.
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158
justify the cost of refrigeration and fabrication. An argument is still made for the
films to be used aboard satellites, due to the reduced size and weight for equivalent
performance of the present dielectric filters. The filters that were tested may have a
special niche position as sensitive receivers.
They will not be replacing
commercially available communications filters in the near future. When YBCO
filters can be made that can carry power levels of ~1 W, for the same size as the
currently tested filters, then many more applications of the films will become
available. This will require higher critical currents and better overall film quality.
Matthaei et al.^2 have shown that specially designed cavities and layout can be
made to reduce the peak fields. The power handling of microstrip/stripline filters
using these cavities can be increased, since the H jf fields at the edges are reduced.
This may be a way to improve filter performance.
One should not overlook that there are several other methods currently under
research to make shiftable High-Tc filters. TRW has made single pole filters with
Josephson Junctions along the edge, and they change the center frequency by
applied magnetic field coupling into the j u n c t i o n s . 68 Jackson et al. have made
YBCO filters with ferroelectric coatings that change dielectric constant with applied
electric f i e l d . 69 This altered dielectric constant changes the center frequency of
their filters. Other tunable filter work is being done by switching YBCO filters
with thermal heating from an applied IR laser. This possibly would be faster then
an edge heater, as the control line for our filters turned out to be, since the
resonator can be uniformly heated. Heaters under the substrate or near the films
can also give switching effects similar to those measured in this research, and have
been demonstrated by several g r o u p s JO,71
On a final note, even without coupled control lines, microwave devices made
out of YBCO will have to take into account the frequency shifts due to the change
in kinetic inductance if operated near peak power handling levels. The work
concluded here at the University of Rochester on tunable filters also addresses
many problems with microwave packaging of YBCO filters and the necessary
integration for rf and DC connections on chip. YBCO microwave devices are still
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159
being investigated and built by several groups. With time, many of the current
difficulties may be solved. If so, superconducting microstrip devices offer another
step in the miniaturization of current communications equipment
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160
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1.
C. Chu, P. Hor, R. Meng, L.Gao, Z. Huang, Y. Wang, Phys. Rev. Letters
Vol. 58, p. 405,1987.
2.
D. Kajfez, P. Guillon, Dielectric Resonators. Artech House Inc., Dedham,
MA, pp 1-2,1986.
3.
R. Hammond, G. Hey-Shipton, G. M atthaei, "Designing with
Superconductors", IEEE Spectrum, pp 34-39, April 1993.
4.
Hewlett Packard Test and Measurement Catalog.
HP Marketing
Communications Test and Measurement Sector, p. 357,1991.
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W. Goj, Svnthetic-Aperture Radar and Electronic Warfare. Artech House,
Boston, 1993.
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N. Amitay, V. Galindo, P. Wu, Theory and Analysis of Phased Array
Antennas. Bell Telephone Lab Inc., pp. 1-3,1972.
7.
P.H. Ballentine, A.M. Kadin, D.S. Mallory, "Large Area Sputtering of
in-situ Superconducting YBCO films," J. Vacuum Sci. and Technology, A9, pp.
1118-22,1991.
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