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Retrospective Theses and Dissertations Iowa State University Capstones, Theses andDissertations
1979
The microwave dielectric properties ofchalcogenide glassesJohn S. Davies Jr.Iowa State University
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DA VIES, JOHN S., JR.
THE MICROWAVE DIELECTRIC PROPERTIES OF CHALCOGENIDE GLASSES
Iowa State University PH.D. 1979
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Unlversitv MiciSllms
Intemariona! 300 N Z = S= RD.. ANN AR30B ML UST06'3131 761-4700
The microwave dielectric properties
of chalcogenide glasses
A Dissertation Submitted to the
Graduate Faculty in Partial Fulfillment of
The Requirements for the Degree of
DOCTOR OF PHILOSOPHY
Major: Electrical Engineering
by
John S. Davies, Jr
Approved:
In Charge of Major Work
Dep rtment
For the Graduate College
Iowa State University Ames, Iowa
1979
Signature was redacted for privacy.
Signature was redacted for privacy.
Signature was redacted for privacy.
il
TABLE OF CONTENTS
Page
ABSTRACT vi
INTRODUCTION 1
HISTORICAL BACKGROUND 6
Chalcogenide Glasses 6
Relative Permittivity Measurements 7
TRANSMISSION METHOD THEORY 10
TRANSMISSION METHOD - EXPERIMENTAL APPROACH 16
ERROR ANALYSIS 29
SAMPLE PREPARATION 33
EXPERIMENTAL RESULTS 39
CONCLUSIONS 65
APPENDIX A: COMPUTER PROGRAM AND TABLE 67
APPENDIX B: EPSILAM-10 DATA 83
APPENDIX C: TABLE FOR 1.30 MM SAMPLE 92
APPENDIX D: VON HIPPEL SHORT-CIRCUIT METHOD 103
APPENDIX E: TABLES FOR AS-TE-GE SAMPLES 106
BIBLIOGRAPHY 127
ACKNOWLEDGMENTS 130
ill
LIST OF TABLES
Page
Table 1. Phase shift and amplitude change for Epsilam-10 utilizing least squares 27
Table 2. Epsilam-10 relative permittivity and loss tangent 28
Table 3. Effect of uneveness of sample on relative permittivity 30
Table 4. Effect of minimum resolution on relative permittivity 31
Table 5. Comparison of published and transmission method results 47
Table 6. Comparison of results from the short-circuit and transmission methods 48
Table 7. Phase and amplitude data for the empty case 54
Table 8. Sample 2 phase and amplitude 55
Table 9. Sample 3 phase and amplitude 56
Table 10. Mean and standard deviation of data points shown in Table 2 (t= .4484 cm) 57
Table 11. Mean and standard deviation of data points shown in Table 3 for As-Te-Ge Sample 3 (t= .5003 cm) 58
Table 12. Relative permittivity for (As-Te-Ge) Sample 2 (t=.4484 cm) with least squares fit 59
Table 13. Relative permittivity for (As-Te-Ge) Sample 3 (t = .5003 cm) with least squares fit 60
Table 14. Comparison of the relative permittivity of two samples of As-Te-Ge (transmission method) 61
Table 15. Comparison of the loss tangent of two samples of As-Te-Ge (transmission method) 62
Table 16. Relative permittivity of As-Te-Ge utilizing the short-circuit method 63
iv
Figure 1.
Figure 2.
Figure 3.
Figure 4.
Figure 5.
Figure 6.
Figure 7.
Figure 8.
Figure 9.
Figure 10.
Figure 11.
Figure 12.
Figure 13.
Figure 14.
Figure 15.
Figure 16.
Figure 17.
Figure 18.
Figure 19.
LIST OF FIGURES
The As-Te-Ge phase diagram in atomic percentage (after Hilton)
Von Hippel's transmission method model
Sample placement and fields in an X-Band waveguide
Block diagram of experimental arrangment
Transmission method test set-up
Epsilam-10 sample
Phase versus frequency plot for Epsilam-10, thickness= 0.127 cm
Amplitude versus frequency plot for Epsilam-10, thickness= 0.127 cm
Phase difference versus frequency plot for Epsilam-10
Amplitude difference versus frequency plot for Epsilam-10
A prepared quartz sample
A sealed evacuated ampule filled with arsenic
Dry box used for sample preparation
Ampule ready for furnace
Test samples in their molds
Von Hippel short-circuit method block diagram
Photograph of typical Von Hippel short-circuit method test set-up
Sensitivity of Von Hippel short-circuit measurements to the number of fractional wavelengths in the sample
Short circuit voltage standing-wave pattern relationships in an empty waveguide and in a waveguide with dielectric sample in place
V
Page
Figure 20. Phase shift versus frequency for As-Te-Ge Sample 2 50
Figure 21, Amplitude change versus frequency for As-Te-Ge Sample 2 51
Figure 22. Phase shift versus frequency for As-Te-Ge Sample 3 52
Figure 23. Amplitude change versus frequency for As-Te-Ge Sample 3 53
vl
ABSTRACT
The microwave dielectric properties of the chalcogenide glass
ASggTeggGe^g (by atomic percent) were determined, utilizing the trans
mission method. The relative permittivity was found to be 15.9 + 0.9 for
the 8.0 to 12.4 GHz frequency band. The loss tangent was found to be less
than or equal to 0.3 throughout the same frequency band. The error in the
relative permittivity measurements was determined to be less than 5%.
Samples were prepared from 99.99%.pure arsenic, tellurium, and germa
nium. Quartz ampules containing the As^gTe^^Ge^Q were heated to 1000
degrees centigrade for 24 hours and then quenched in liquid nitrogen-
soaked sand. Test samples were produced by placing the quenched
ASg^Teg^Ge^Q in chrome-plated molds, reheating to 600 degrees centigrade,
and requenching, using dry ice.
The transmission method yielded excellent results for low, medium,
or high relative permittivity samples, regardless of sample thickness.
The method is based on the comparison of the dominant Transverse Electric
fields in a rectangular waveguide with and without a sample being present.
The resulting transcendental equation with two unknowns was solved by
generating tables based on the substitution of various values of complex
relative permittivity, and comparing the corresponding phase shift and
amplitude change with the measured values. A unique solution was found
by comparing results of samples of different thicknesses.
1
INTRODUCTION
In the mid 1960's, much attention was given to the bistable resistivity
characteristics of As-Te-Ge (Ovshinsky, 1963), one of the chalcogenide (or
sulfur-like) glasses. This bistable resistivity characteristic showed
promise as a computer memory material (Kao, 1972; Ovshinsky, 1963; and
Sie, 1968) because only two distinct stable states are required for such
an application.
The As-Te-Ge system is sulfur-like in that it will form a super-cooled
liquid (or glass) if cooled quickly. This state corresponds to the high
resistance state. If As-Te-Ge is cooled slowly, it becomes crystalline,
which corresponds to the low resistance state. The resistivity is roughly
10^ ohm-cm in the high resistance state and 10^ ohm-cm in the low resis
tance state (Sie, 1969),
While in the high resistance state, the As-Te-Ge system does not form
a lattice structure (displays no particular order). For that reason, this
state is also called the amorphous state.
This mixture of the various elements in the As-Te-Ge system is very
important. Figure 1 is a ternary diagram which shows the glass forming
regions for the As-Te-Ge system as published by Hilton, et al, 1966. The
composition chosen was As^gTe^^Ge^Q (by atomic percent) because it is in
the center of the larger of the two glass-forming regions. Also, it was
this composition that others had examined extensively.
Uttecht (1969) demonstrated that a low resistance filament could be
grown on the surface of a sample of As^^Te^gGe^Q which was in the high
resistance or amorphous state. This was accomplished by applying a high-
2
Ge IV A
Ge Te
CRYSTAL REGION
GLASS REGION
Te As
As
Figure 1. The As-Te-Ge phase diagram in atomic percentage (Hilton, et al. 1966)
3
intensity electrical field across the surface. By reversing the polarity
of the field, the filament can be made to disappear. This phenomenon
showed promise for utilization at microwave frequencies. A sample of
As-Te-Ge placed in a waveguide would act as phase shifter because of its
dielectric qualities. As the sample is moved across the waveguide out of
the maximum electric or E field, the phase shift associated with the
sample is reduced. A variable phase shifter could be fabricated, utilizing
this principle.
The maximum E field exists in the center of the guide for the TE^^
or dominant mode in a rectangular waveguide. Since a low resistance fila
ment can be grown on the surface, the E field can essentially be shorted
out. Hence, the growing and reversing of the low resistance filament will
act as microwave switch. With the existence of the low resistance fila
ment, the E field will be shorted out and energy will not pass beyond
that section of the rectangular waveguide. The author reported the
successful development of a microwave switch utilizing As-Te-Ge (Davies,
1970). Most microwave switches utilize moving parts which have to be
activated manually or with the aid of a solenoid. The advantage of the
As-Te-Ge switch is that it does not have moving parts .
In order to mathematically evaluate the effect of an As-Te-Ge sample
inserted in a waveguide, it is necessary to determine its relative permit
tivity and permeability. Once these two characteristics are known, con-
vential analytical techniques can be applied to give an accurate descrip
tion of the fields present in and around the sample. In the phase shifter
4
application, the thickness of the sample necessary to give the desired
maximum phase shift can be determined easily.
Since Uttecht (1969) reported that ASg^Te^^Ge^Q was diamagnetic,.the
relative permeability was approximately equal to unity or the free space
value. The remaining characteristic, relative permittivity, could be
found by reversing the process mentioned in the previous paragraph. By
measuring the effect of a sample of a particular shape and size placed in
a waveguide, the relative permittivity could be determined.
In this dissertation, the historical background of chalcogenide glass
and relative permittivity measurement is presented first (See HISTORICAL
BACKGROUND). The third section (THEORY OF THE TRANSMISSION METHOD) follows
with the mathematical development of the transmission theory used in
determining the relative permittivity of As-Te-Ge.
The fourth section (EXPERIMENTAL APPROACH UTILIZING THE TRANSMISSION
METHOD) presents the mechanics of implementing the theory of measurement.
In this section, a sample of known high relative permittivity is tested
and compared to published results. In addition, the role of the computer
program in determining relative permittivity is discussed.
The fifth section (ERROR ANALYSIS) discusses the accuracy of the
transmission method measurements. The data from the prior section are
changed by the limit of the error and effect on the relative permittivity
results are discussed.
The sixth section (SAMPLE PREPARATION) was developed because the
complexity of sample preparation warranted such a discussion. The prepa
ration of the As-Te-Ge glass is discussed, along with the process of
forming this glass into a usable sample.
5
The transmission method results for low, medium, and high relative
permittivity dielectrics are compared to published and other experimental
results in the seventh section (EXPERIMENTAL RESULTS). Also, the results
for the ASggTe^gGe^Q samples are given and the accuracy of the findings
discussed.
Conclusions are presented in the eighth and final section. Discussed
are relative merits of the transmission method, the suitability of
ASggTe^gGe^Q for use as a dielectric, and recommendations for improving
the test methodology.
6
HISTORICAL BACKGROUND
Chalcogenide Glasses
The interest in the chalcogenide glasses was first generated by
Ovshinsky (1963) and Pearson (1962). These glasses attracted interest
because they displayed bulk bistable resistivity similar to that exhibited
by some metal oxides (Cline, 1962).
Hilton, et al. (1966) studied many of the chalcogenide glasses and
determined that certain percentages of each of the elements were necessary
before the composition formed a glass. One of the glass systems studied
by Hilton was As-Te-Ge. The composition studied extensively at Iowa State
University was As^^Te^^Ge^^Q (by atomic percent) because it switched more
consistently (Sie, 1969).
Uttecht (1969) found that a low resistance filament could be formed
on the surface of the As-Te-Ge glass through the application of a high-
intensity electric field. Kao (1972) examined in detail the filament
growth and its application as a computer memory element. He concluded
that it could be used as a memory device and that there are really two
filaments formed at once -- one on the surface, and one inside the
material.
Several authors have examined the switching mechanism in amorphous
glasses (Fritzsche and Ovshinsky, 1970; Uttecht, et al. 1970, and Saji,
et al. 1977). It is fairly well-accepted that the switching is energy-
controlled. The switching mechanism is thought to be thermally controlled
for samples thicker than 10 micrometers, and electronically controlled
for samples thinner than 10 micrometers.
7
Others have studied the suitability of the amorphous glasses for use
as a read-only memory (Sie, 1969) and electron beam-accessed memory
(Doctor, 1973). Both authors were optimistic about these possibilities.
Amorphous material is gaining acceptance for use in solar cells
(Wronski, 1977 and Carlson, 1977), as well as in transistors (Peterson,
et al. 1976).
Relative Permittivity Measurements
Relative permittivity can be determined simply by inserting a dielec
tric between parallel conducting plates and measuring the change in
capacitance. This procedure provides good results at DC and low frequencies.
At microwave frequencies, the task is much more complex because
energy is transferred, preferably by waveguides. Roberts and Von Hippel
(1946) developed the short circuit method for determining relative permit
tivity at microwave frequencies. The short-circuit approach involved the
measurement of standing waves in a shorted waveguide with and without a
sample present. Dakin and Works (1947) simplified the Von Hippel expres
sions for low and medium loss cases, Marcuvitz (1951) improved the
accuracy of measurement by developing a correction factor for the slot in
the waveguide. A computer program was written for the short-circuit
method by Nelson, Schlaphoff, and Stetson (1972).
A transmission model was developed by Westphal (1954) and is shown
in Figure 2. The change in attenuation and phase is mathematically re
lated to the relative permittivity of the sample. As more sophisticated
equipment became available, relative permittivity could be found directly
8
(Weir, 1974). The resonant method involves inserting a dielectric in a
cavity and relating the change in resonant frequency to the dielectric
constant. One of the more recent approaches was given by Das Gupta (1974).
The relative permittivity of an amorphous semiconductor system
AsTe/AsSe at microwave frequencies was measured via the short-circuit
method by Wilson, O'Reilly and Kinser (1974). The thermal conductivity
and specific heat of As^^Teg^Ge^Q was determined by Thomas and Savage
(1977). Bishop, et al. (1971) measured the far infrared and microwave con
ductivity of TlgSe-ASgTCg and semiconducting glass by the use of the short-
11 circuit method (1 to 6 GHz) and interferometric spectroscopy (3 x10 to
12 2.4x10 Hz) methods. The conductivity was found to be very low (approx
imately 10 ohm-cm). Optical and electrical energy gaps in ASgSe^ were
studied by Fritzsche (1971).
9
SAMPLE
NULL DETECTOR INPUT
PHASE
SHIFT 0
ATT.
SAMPLE
NULL DETECTOR NPUT
PHASE
SHIFT +A0
Figure 2. Von Hippel's transmission method model
10
TRANSMISSION METHOD THEORY
Various methods of relative permittivity measurement were examined.
The Perturbation Method (Harrington, 1961 and Westphal, 1954) was found
to be too dependent upon sample position and shape for the determination
of the relative permittivity in the range of that of As^^Teg^Ge^Q
(approximately 10). The Von Hippel approach of measuring dielectrics by
standing waves (Von Hippel, 1954) showed the greatest promise. Indeed,
Wilson, O'Reilly and Kinser (1974) had reported results on As-Te/As-Se
system utilizing this method. In addition, Nelson, Schlaphoff, and
Stetson (1972) had developed a computer program for this method. However,
even with the Marcuvitz Correction (1951) for the effect of the slot in
the standing wave measuring section, errors greater than 10% were en
countered .
The percent error experienced with the standing wave technique is
dependent upon the sample thickness. As^^^^eg^Ge^Q samples of sufficient
thickness are too difficult to manufacture for this approach to be fruit
ful. Since thin samples with high relative permittivity cause large phase
shifts and amplitude changes when inserted in a waveguide, the trans
mission method was selected as the best approach.
In the past, the transmission method required taking measurements
that were involved and time-consuming, but with the development of sweep
generators, phase comparators, network analyzers, and phase and amplitude
displays, measurements throughout the frequency range of interest can
easily be accomplished in a matter of seconds. With the aid of a computer
program, the relative permittivity can be found.
11
The relative permittivity and loss tangent of a given sample can be
determined by measuring the phase and amplitude of the electromagnetic
wave at a particular point along the transmission medium. The differences
observed between the phases and amplitudes of the empty and sample-present
cases can be related to the relative permittivity and loss tangent of the
sample.
To illustrate this relationship, let us use an X Band (8-12.4 GHz)
waveguide as the transmission medium. The preferred waveguide mode is the
dominant TE^^ (transverse electric) mode. The waveguide is terminated in
its characteristic impedance to prevent reflections. A rectangular-shaped
sample is placed squarely in the guide in order that evanescent modes
will have an appreciable magnitude only in the vicinity of the sample
(Harrington, 1961). The waveguide, sample, arid fields are depicted in
Figure 3. Because the field is the easiest field to measure in the
waveguide, this development will concentrate on comparing this field at
z = c in region III for the case with the sample inserted and the case with
it removed.
. For the TE^^ mode, the x and y components of the wave incident on
the sample in region I are (Stratton, 1941):
Figure 3.
The E , H and H fields exist in all three regions, as shown in
-YiZ sin (ny/b) (1)
where is the propagation constant of the region.
(2)
12
TRANSMITTED WAVE
INCIDENT WAVE
Ex
/Hz
REFLECTED WAVE
REGION r REGION n
Y
Figure 3. Sample placement and fields in an X-Band waveguide
13
where is characteristic impedence of the region. The resulting re
flected components are (Stratton, 1941):
, Yi^ E^= (E^/A) e"^ ^ sin(TTy/b) (3)
,Y,z Hy =-(Ei/(AZi))e sin(TTy/b) (4)
Combining the incident and reflected components in region I yields:
-YiZ 4.Y1Z E^ = E^e sin (rry/b) + (Ej^/A) e sin(Try/b) (5)
-YiZ . YiZ Hy=(Ej^/Zi)e sin (ny/b) - (E^/(AZp)e"^ sin (rry/b) (6)
The fields present in the sample (region II) are (Stratton, 1941):
+ -Y2= - +Y2^ +^2® ) sin (rry/b) (7)
, YoZ , Y^s Hy= (l/Z2)(Eje" -E^e"^ ^ ) sin (rry/b) (8)
The X and y components of the transmitted wave in region III are:
_\3(z-d) E^ = E2e sin (rry/b) . (9)
_Y3(z-d) H = (Eg/Zg) e sin(TTy/b) (10)
The boundary conditions dictate that the E^ fields must be equal at
the surface of the sample. Hence, for z=0 (the boundary between regions
I and II), equations (5) and (7) are equated:
(E^ + E^/A) sin (rry/b) = (E^ + Ep sin (rry/b) (11)
Equating the E^ fields at the boundary between regions II and m
(z = d) yields from equations (7) and (9):
14
. _ , Ypd Eg sin (rry/b) = (E2 e" fE^e )sin(Try/b) (12)
The boundary conditions also dictate that the fields must be equal
at the surface of the sample. Combining equations (6) and (8) at 2= 0
yields:
((Ej/Zj^ -E^/(AZp) sin (rry/b) = (I/Z2) (E^ - E^) sin (rry/b) (13)
Combining equations (8) and (10) yields for z = d;
y.d yd (Eg/Zg) sin (Try/b) = (l/Zg) (E^ e" ^ - E^ e" ^)sin(TTy/b) (14)
Solving for E^ from equations (11) and (13) yields;
E^ = 0.5CE2C1+ (Z^/Z2)] + E2[1 - (Z^/Z^)']'] (15)
Solving for Eg and Eg from equations (12) and (14) yields:
, . Ymd Eg = 0.5 EgClf (Z2/Z3)]e ^ (16)
Y«d Eg = 0.5 Eg[l- (Z2/Zg)]e'" ^ . (17)
When equations (16) and (17) are substituted into equation (15) , the
ratio of the electric field in region III for the case without the sample
(E^) to the case with the sample (E^) is :
^1 1 ^2 +^2^ ^1 ^2 -^2^ ^ = T C(l + )(l + )e +(1-—)(1-—)e ] (18) 3 2 3 2 3
For our case, regions I and III are filled with air and region II con
tains dielectric. The resulting propagation constants are (Harrington, 1961);
15
where U)= IrrS
Y2 = Arr/b)^ - U?|j,^e^(e'- je") (20)
where e'-je" is the complex relative permittivity.
For our case, the characteristic impedances are (Post, et al. 1973);
Zl = Z3 = JWHQ/YI (21)
h " (22)
because Uttecht (1969) found As^^Te^^Gej^^ to be diamagnetic.
The substitution of equations (21) and (22) into equation (18) yields;
= | [ ( ^ + i ) ( i +
YI YO _(Y2 -YJD + (1 - -i)(l - -^)e ] (23)
2 1
With the aid of a computer program, the complex ratio of to was
determined for various values of e' and e". This program and a repre
sentative table are given in Appendix A.
16
TRANSMISSION METHOD - EXPERIMENTAL APPROACH
As shown In Figure 2, the classical approach to the transmission
method required only a frequency generator, line splitters, a variable
attenuator, a variable phase shifter, and a null detector. With the
present-day advances in test equipment, the phase and amplitude can be
read directly, thus eliminating the need for the null detector, variable
phase shifters and attenuators.
A block diagram of the experimental test arrangement is given in
Figure 4. A photograph of this arrangement is given in Figure 5. The
sweep oscillator generates frequencies from 8.0 to 12.4 Gigahertz (GHz).
The RF from this unit is transmitted to the transmission test unit where
it is split equally between the reference leg and the test leg. The
reference leg is composed of an air line and a 10 dB attenuator. The
attenuator protects the reference channel from excess power absorption.
The test leg is composed of a coaxial line to waveguide adapter, a variable
attenuator, the sample holder, a second variable attenuator, and a wave
guide to coaxial line adapter. The variable attenuators are used to re
duce the effect unwanted modes have on the transmission (See ERROR ANALYSIS
section).
The converter section measures the phase and amplitude of reference
and test channels. It also has mechanical and electrical line length
adjustments for the reference channel. These adjustments compensate for
the differences in line lengths between the test and the reference legs.
The network analyzer takes the ratio of the signal in the test channel
to the signal in the reference channel. This power ratio is converted
17
HP 8690A HP X-Y PLOTTER HP 8410 A
NETWORK ANALYZER
SWEEP OSCILLATOR
RF SWEEP
OUTPUT
PHASE
AMPL.
_L
SWEEP HP 8412 A PHASE -MAGNITUDE DISPLAY
AIR LINE ATTENUATOR
K\YN1
HP 8740 A TRANSMISSION TEST UNIT
VARIBLE ATTENUATOR
VARIABLE ATTENUATOR
UNKNOWN SAMPLE
REFERENCE CHANNEL
TEST CHANNEL
HP 8411 A CONVERTER
Figure 4. Block diagram of experimental arrangement
I
Figure 5. Transmission method test set-up
Figure 6. Epsilam-10 sample
qsT
19
into a DC voltage, which is directly proportional to the magnitude of the
ratio. This value can be read off of the magnitude portion (calibrated in
decibels) of the phase-magnitude display. Likewise, the phase difference
is converted into a DC voltage proportional to the magnitude of the dif
ference. This value (calibrated in degrees) can be read off the phase
portion of the phase-magnitude display. The frequency is depicted as the
horizontal axis on the phase-magnitude display. The phase and magnitude
changes are displayed on the vertical axis. Variable, calibrated, offset
controls are built into this display, enabling increments as small as one
degree of phase change per division (cm) and 0.25 dB of magnitude per
division (cm) to be depicted. The X-Y plotter can be used to give a
graphic representation of these values across the spectrum of interest.
In order to determine the relative permittivity of a sample utilizing
the transmission method, only two sets of measurements are required. First,
the phase shift and amplitude change caused by the empty test leg (as
compared to the air line or reference leg) is measured. Then the empty
sample holder is removed from the test leg and replaced with an identical
sample holder containing the dielectric to be measured. The phase shift
and amplitude change attributed to the test leg with the sample present is
measured (again compared to the air line or reference leg). The differences
in the phase shift and amplitude change between the empty and sample present
cases are caused by the sample. This phase shift and amplitude change is
correlated to the complex relative permittivity of the sample in the com
puter generated table.
20
Because the transcendental equation used has an endless number of
solutions, two samples of different thicknesses must be measured to yield
a unique solution.
In order to demonstrate the feasibility of the transmission method, a
standard sample was chosen. Epsilam-10 was selected because it is known
to be well-behaved through the X Band frequency range and is easy to shape
into a regular sample. This sample is shown in Figure 6. The relative
permittivity is given by the manufacturer to be 10.3 + 0.5 with a loss
tangent of 0.001. A specification sheet can be found in Appendix B.
Ten measurements of the phase and amplitude at each frequency (0.5 GHz
intervals) were taken for the sample present cases and also for the empty
waveguide cases (Appendix B, Tables B-1, 2, 3, and 4). The mean and
standard deviation of the ten measurements were calculated (Appendix B,
Tables B-5 and 6). The resulting means are shown in Figures 7 and 8. As
can be seen, the phase and magnitude for the empty case are well-behaved
throughout the frequency range. However, there are a few undesirable
undulations of the phase and magnitude plots àt the higher frequencies,
pointing to possible unwanted resonances in the line. Otherwise, the
data look quite good. The differences in the means between the empty and
sample present (Epsilam-10) cases are shown in Figures 9 and 10.
Normally for high relative permittivity samples, the amplitude change
will be somewhat cyclical throughout the frequency band. This is caused
by the reduction of the reflected wave (hence the loss) as the effective
sample thickness approaches a half-wavelength, or multiples of half-wave
length. This phenomenon can occur many times throughout the frequency •
21-22
PHASE
160
135
90
45 /EMPTY CASE
SAMPLE PRESENT
o -45
-90
-135
-180 8 9 10 II 12
FREQUENCY (GHZ)
Figure 7. Phase versus frequency plot for Epsilam-lO, thickness =
0.127 cm
23
AMPLITUDE
EMPTY CASE
u m -3| o w o —4
-5 WITH SAMPLE
8 9 10 I I 12
FREQUENCY (GHZ)
Figure 8. Amplitude versus frequency plot for Epsilam-10, thickness = 0.127 cm
24
band. However, there should be a tendency toward increased amplitude
change as the frequency increases because the number of fractional wave
lengths present in sample increases. This assumes that the sample is not
lossless and the relative permittivity and loss tangent remain unchanged
throughout the frequency band.
Since Epsilam-10 has a relative permittivity that varies somewhat
through the frequency band, the curves shown in Figures 9 and 10 are
acceptable.
Nonetheless, the Method of Least Squares was utilized to effectively
smooth out the curves without destroying the tendencies of the data. The
results of the Least Squares Fit are given in Table 1. The relative per
mittivity and loss tangent can be determined by finding the phase and
magnitude on the computer-generated table in Appendix A. The results are
shown in Table 2. As can be .seen, the relative permittivity is in the
range of 9.6 to 10.9 and the loss tangent is less than 0.03.for this sample.
The results agree quite well with the manufacturer's published values of
9.8 to 10.8 and 0.001 relative permittivity and loss tangent, respectively.
25
PHASE SHIFT
60
70
60
50 Q % 40
S û 30
LEAST SQUARES FIT
20
8 9 10 I I 12
FREQUENCY (GHZ)
Figure 9. Phase difference versus frequency plot for Epsilam-10
26
AMPLITUDE CHANGE
LEAST SQUARES
8 10 9 I I 12
FREQUENCY (GHZ )
Figure 10. Amplitude difference versus frequency plot for Epsilam-10
27
Table 1. Phase shift and amplitude change for E.psilam-10 utilizing least squares
Frequency Phase Shift Amplitude Change (GHz) (Degrees) (Decibels)
8.0 57.45 5.73
8.5 57.35 5.60
9.0 57.22 5.47
9.5 57.10 5.34
10.0 56.98 5.21
10.5 56.86 5.08
11.0 56.74 4.95
11.5 56.62 4.82
12.0 56.50 4.69
12.4 56.40 4.58
28
Table 2. Epsilam-10 relative permittivity and loss tangent
Frequency Relative Loss Factor Loss Tangent Permittivity
8.0 10.4 0.30 0.03
8.5 10.8 0.25 0.02
9.0 10.9 0.20 0.02
9.5 10.7 0.15 0.01
10.0 10.7 0.15 0.01
10.5 10.5 0.05 less than 0.01
11.0 10.3 less than 0.05 less than 0.01
11.5 10.0 less than 0.05 less than 0.01
12.0 9.6 less than 0.05 less than 0.01
12.4 9.6 less than 0.05 less than 0.01
29
ERROR ANALYSIS
As can be seen from the previous section, large changes in the phase
and amplitude of the ratio of signals in the two paths were experienced
while measuring the complex dielectric constant by the transmission
method. Since the thickness of the sample is relatively small, it is
appropriate to examine possible errors caused by unevenness of the sample.
Although the Epsilam-10 sample was not uneven, other samples tested
had thickness variations up to 3%. The sample thickness of the Epsilam-10
sample was arbitrarily increased by 3% in the computer program. The
resulting table for a sample thickness of 1.30 mm is found in Appendix C.
The results from the 1.30 mm table were compared with the results from
the 1.27 mm table (Appendix A).
A summary of the resulting relative permittivity for sample thickness
of 1.27 and 1.3 mm is given in Table 3. An error of 1% to 2% was found
for an unevenness of 2.36%.
Another area of concern is the accuracy with which the system can
measure the raw data, that is, phase shift and attenuation. According to
the manufacturer, and based on the experience gained in taking many
measurements, the minimum resolution is one degree and 0.1 decibels. In
order to test the system, the relatively thin sample of 1.27 mm was chosen
and the results were changed by subtracting one degree and 0.1 dB from
the phase shift and attenuation given in the third section of this work,
respectively. Table 4 contains the results of the original and altered
case.
30
Table 3. Effect of uneveness of sample on relative permittivity
Frequency Thickness Relative % (GHz) (mm) Permittivity Error
8.0 1.27 10.4
8.0 1.30 10.2 2
8.5 1.27 10.8
8.5 1.30 10.6 2
9.0 1.27 10.9
9.0 1.30 10.7 2
9.5 1.27 10.7
9.5 1.30 10.7 0
10.0 1.27 10.7
10.0 1.30 10.6 1
10.5 1.27 10.5
10.5 1.30 10.4 1
11.0 1.27 10.3
11.0 1.30 10.2 1
11.5 1.27 10.0
11.5 1.30 9.9 1
12.0 1.27 9.6
12.0 1.30 9.6 0
12.4 1.27 9.6
12.4 1.30 9.6 0
31
Table 4. Effect of minimum resolution on relative permittivity
Frequency , (GHz)
Phase Shift (Degrees)
Amplitude change (Decibels)
Relative Permittivity
% Error
8.0 57.45 5.73 10.4
8.0 56.45* 5.63^ 10.2 2
• 8.5 57.34 5.60 10.8
8.5 56.34* 5.50^ 10.6 2
9.0 57.22 5.47 10.9
9.0 56.22* 5.37^ 10.7 2
9.5 57.10 5.34 10.7
9.5 56.10* 5.24^ 10.6 1
10.0 56.98 5.21 10.7
10.0 55.98* 5.11^ 10.5 2
10.5 56.86 5.08 10.5
10.5 55.86* 4.98^ 10.3 2
11.0 56.74 4.95
4.85^
10.3
11.0 55.74*
4.95
4.85^ 10.0 3
11.5 56.62 4.82 10.0
11.5 55.62* 4.72^ 9.8 2
12.0 56.50 4.69 9.6
12.0 55.50* 4.59^ 9.6 -
12.4 56.40 4.58 9.6
12.4 55.40* 4.48^ 9.5 1
^Altered Case (subtracted one degree)
^Altered Case (subtracted 0.1 decibel)
32
The conclusion is that an error of 1% to 3% is attributable to the
minimum resolution of the system.
Another area of concern is the case of unwanted modes present in the
waveguide. Because there are many transitions in the system (e.g., from
coaxial line to waveguide), mismatches can occur, causing standing waves
to exist. This phenomenon is frequency-dependent. The effect of these
modes was minimized by the insertion of variable attenuator sections on
both sides of the sample. These attenuators reduced the Q or quality
factor of the cavity formed by the discontinuities so that no dips in the
frequency response were recognizable.
Unwanted modes can be generated by discontinuities caused by putting
a dielectric slab in the guide. If the discontinuity is regular and the
sample is placed squarely in the waveguide, the modes will be evanescent
in nature and no energy is lost (Harrington, 1961). That is why care was
taken to make sure that the sample was placed in a mold and a tight-fitting
plunger was used to form the sample into a regular parallelepiped.
In summation, the worst error is estimated to be 5%. This would be
the case of a relatively thin uneven sample of relative permittivity
greater than 10. As the thickness of the sample increases and the permit
tivity decreases, the accuracy of the relative permittivity measurement
Improves,
33
SAMPLE PREPARATION
The preparation of As-Te-Ge samples is fairly involved and for this
reason, a whole section is devoted to it.
In order for measurements to be made in an X-band waveguide, the
sample must be at least 0.4" by 0.9" by 0.1" thick. It is important that
the sample be homogeneous and have a uniform thickness (See ERROR
ANALYSIS section).
The first step is the fabrication of ampules that will hold the
As-Te-Ge in powder form. The ampules must be quartz because of the high
temperature used in the preparation. The recommended size of the bulb end
is 4" long and an inside diameter of 18 mm. The next step is to attach a
stem to the bulb. The recommended length of the stem is 5" with an inside
diameter of 11 mm. The stem is necessary in order to evacuate the ampule.
Figure 11 shows a prepared quartz ampule.
The purity of the As-Te-Ge is important for the following reasons:
(1) Oxygen can readily be trapped in various amounts by the arsenic,
resulting in different measurement data.
(2) Impurities can cause the As-Te-Ge glass to lose its bistable
resistivity characteristics.
The purity determined for our application was .9999 for each element.
In addition, the arsenic used must be oxygen-free. Arsenic can be received
and kept in a sealed, evaculated ampule as shown in Figure 12. Because of
the affinity of arsenic for oxygen, it is recommended that a dry box be
used when measuring and filling the ampules. The dry box used for our
work is shown in Figure 13.
Figure 11. A prepared quartz sample
Figure 12. A sealed evacuated ampule filled with arsenic
qi/E
35
First, the sealed arsenic ampule, along with the balance and other
necessary equipment, is placed into the dry box, Desiccant is also placed
in the box to absorb any moisture that might get in. A slight vacuum is
created in the dry box, after which it is backfilled with argon for an
hour before starting. Next, the following steps were accomplished:
(1) The tellurium and germanium are ground up in their respective
crocks ;
(2) The arsenic ampule is broken up and the needed arsenic is ground
up in its own crock;
(3) The remaining arsenic is placed in a separate ampule;
(4) The elements are weighted out and put in the other ampules;
(5) A partial vacuum is again created in the dry box;
(6) The ampules are sealed with a rubber cork and vacuum grease; the
vacuum released in the dry box; and the ampules removed;
(7) The ampules are then evacuated further for an hour by a vacuum
pump and sealed. Figure 14 shows the ampule after sealing and
removal of the stem..
The sealed ampules are placed in a rocking furnace or a furnace where
turning of the ampules can be accomplished without lowering the temperature.
The furnace should be kept under a hood at all times during the heating
cycle of 24 hours at 1000° C, because the ampules may fracture and leak
poisonous gases.
Care must be exercised when removing the ampules from the furnace.
Face protection and asbestos gloves must be used. When the ampule is re
moved from the furnace, it is placed in a bed of sand that has been im-
Figure 13. Dry box used for sample preparation
36b
Figure 14. Ampule ready for furnace
Figure 15. Test samples in their molds
37b
#$##
38
prégnated with liquid nitrogen. This procedure is followed to ensure that
the As-Te-Ge glass samples will cool quickly and remain homogeneous.
Cooling of the sample quickly also guarantees that the sample will be in
the necessary high resistance state. If the sample is allowed to cool
slowly, it will end up in the low resistance state or be inhomogeneous.
The samples can be prepared for measurement by using a diamond saw
for cutting and standard glass polishing techniques for shaping. Because
the sample in the high resistance state is fragile, the yield from this
process is very low - typically, 1 in 20. In order to achieve a higher
yield and a uniform sample, the following technique was used. The ampule
was broken and pieces of the sample were placed in an X-band mold. The
mold is fabricated from chrome-plated brass. The plating is necessary to
prevent contamination of the As-Te-Ge when reheating is accomplished.
Since it was difficult to cool the mold fast enough to prevent the As-Te-Ge
from switching into the low resistance state, holes were drilled in the
mold to reduce the amount of metal that had to be cooled.
When the As-Te-Ge is heated to 600° C for 15 minutes, it flows into
the comers of the mold. The mold is removed and a chrome-plated plunger
is inserted to eliminate a meniscus in the sample. The mold is quickly
cooled by bringing it in contact with dry ice. The test samples are
shown in Figure 15.
39-40
EXPERIMENTAL RESULTS
The objective of this experimental effort is to determine the complex
relative permittivity of the chalcogenide glass compound As-Te-Ge at micro
wave frequencies. The amorphous glass system As-Te-Ge was chosen because
certain compounds exhibited bistable resistivity (Sie, 1969). The
particular compound As^^Te^gGe^g (by atomic percent) was also diamagnetic
(Uttecht, 1969).
These two properties made As^^Te^^Ge^^^ particularly attractive for use
in a waveguide at microwave frequencies. It could be used as a dielectric
in its high resistance state and allow the passage of electromagnetic waves
through the sample. These waves will be greatly attenuated by the As-Te-Ge
sample when it is in the low resistance state.
The frequency range chosen was 8.0 to 12.4 GHz. The waveguide used
at this frequency range was readily available and had a sufficiently small
cross-sectional area to make sample preparation feasible.
The Von Hippel Short-Circuit Method of measuring complex relative
permittivity was initially accepted as the most promising and accurate
technique. A block diagram of this test set-up is shown in Figure 16.
A photograph of a typical Von Hippel short-circuit test set-up is
shown in Figure 17, and a detailed description of the Von Hippel Short-
Circuit Method is given in Appendix D. This method works quite well for
thick samples of medium permittivity, the accuracy of the method is re
duced unless the sample has a thickness that is very nearly an odd number
of quarter wavelengths (See Figure 18).
41
HP 5342 A HP 415 MICROWAVE FREQUENCY STANDING WAVE COUNTER INDICATOR
1000 Hz
DETECTOR
ISOLATOR
10 dB DIRECTIONAL SHORT
SLOTTED LINE
WITH CARRIAGE AND MOVEABLE PROBE ASSEMBLY
HP 8690 A RF OSCILLATOR
WITH 1000 Hz SQ WAVE
MODULATOR
Figure 16. Von Hippel short-circuit -method block diagram
Figure 17. Photograph of typical Von Hippel short-circuit method test set-up
42b
43
0.5 1000
JOOO 100
2,6 0,4
0.3
3. A
0.2
0.6 0.4 WAVELENGTHS IN SAMPLE
0.7 0.3 0.9 02
0.1
0,01
0.001
0.0001
O.OOOOl 0.7 0 8 0.6 0.4 0.5
WAVELENGTHS IN SAMPLE 0 9 0.2
Zo/A AND INVERSE STANDING-WAVE RATIO V8 LENGTH OF SAMPLE, TAN 0 = 0.0001. SAMPLE AT END OF LINE.
Figure 18. Sensitivity of Von Hippel short-circuit measurements to the number of fractional wavelengths in the sample
44
The reasons are two-fold: (1) The error associated with determination
of the distance from the sample to the first node, z^. Figure 19, causes
increased uncertainty in the relative permittivity as the sample becomes
thinner; (2) The sensitivity of the measurement increases as the rela
tive permittivity increases (See-Figure 18). Because the relative permit
tivity of ASg^Te^gGe^Q is high (greater than 10), many samples of various
thickness might have to be manufactured before one would be suitable for
the frequency range of interest (have a thickness corresponding to an odd
number of quarter wavelengths).
Little success had been achieved in making relatively thick As-Te-Ge
samples (See sample preparation section for details). Many refinements
were made in the sample preparation process before acceptable samples were
manufactured. Some of these refinements were: (1) Use of a section of
waveguide as the sample mold; (2) Drilling additional holes in the sample
mold flanges to facilitate quicker cooling (quick cooling or quenching is
necessary for switching the As-Te-Ge sample to the high resistance state);
and (3) The use of dry ice (a more efficient cooling agent than liquid
nitrogen-soaked sand). Even with those refinements, the sample designated
as Sample 1 did not switch completely to the high resistance state. The
mold temperature (prior to quenching) was raised to 600° C from 400° C,
and samples 2 and 3 were prepared. Both of these samples were found to
be acceptable.
As the sample preparation procedure was being refined, so was the
transmission method. The transition from coaxial to rectangular waveguide
creates undesirable resonances in the transmission medium. The resonances
45
5 iSf
I I I I I
Figure 19. Short-circuit voltage standing-wave pattern relationships in an empty waveguide and in a waveguide with dielectric sample in place
46
are exhibited as undulations in the phase and amplitude versus frequency
plots (for details see the ERROR ANALYSIS section). As the relative
permittivity of a sample increases, these undulations became more pro
nounced. These resonances were systematically removed or their effect
minimized by altering the test leg of the test set-up (Figure 4) and
applying the Method of Least Squares to the data.
Care was taken to- prove that the transmission method yielded correct
results for low, medium, and high relative permittivities.
First, a sample of paraffin (low relative permittivity) was tested
by the transmission method and compared to published results. The Epsilam-
10 sample (high relative permittivity) has already been compared with
published results (See TRANSMISSION METHOD - EXPERIMENTAL APPROACH section).
Table 5 shows that the transmission method agrees with published results
for both low and high relative-permittivity samples.
Medium relative-permittivity pyrite samples, along with Epsilam-lO,
were measured, using both the short circuit and transmission methods.
These results are compared in Table 6. Both methods agree fairly well for
medium relative-permittivity (pyrite). However, for the high relative-
permittivity sample (Epsilam-lO), the short-circuit method yields results
that differ somewhat from those published, while the transmission method
does not.
Accordingly, both methods were applied to Samples 2 and 3 of the
ASggTeggGe^Q. First, the transmission method was used. Five sets of
phase and amplitude versus frequency plots were generated for each sample,
using the transmission method. Next, one set of phase and amplitude
47
Table 5. Comparison of published and transmission method results
Sample Relative Permittivity Material Thickness Frequency Published Transmission
Paraffin Wax 0.63cm 10 GHz 2.22* 2.21
Epsilam-10 0.127 cm 8-12.4 GHz 10.3 + 0.5^ 10.25+.65
^on Hippel, 1954
^Manufacturer
48
Table 6. Comparison of results from the short-circuit and transmission methods
Relative Permittivity
Sample Frequency Short Circuit Transmission Material Thickness (GHz) e ' c" e ' e"
(cm)
Pyrite 3.57 9.789 5.85 1.097
Pyrite 3.57 9.789 5.62 1.093
Pyrite 2.54 9.789 5.14 0.952
Pyrite 2.45 9.789 5.10 1.018
Pyrite 1.42 9.789 5.05 0.949
Pyrite .625 9.5 5.05 1.0
Pyrite 2.34 9.5 5.15 0.9
Epsilam-10 .127 8.0 11.5 1.7 10.4 .3
Epsilam-10 .127 8.5 16.7 .9 10.8 .2
Epsilam-10 .127 9.0 15.5 3.8 10.9 .2
Epsilam-10 .127 9.5 14.5 1.4 10.7 .1
Epsilam-10 .127 10.0 13.2 .1 10.7 .1
Epsilam-10 .127 10.5 13.3 .2 10.5 .1
Epsilam-10 .127 11.0 11.8 1.1 10.3 .1
Epsilam-10 .127 11.5 12.3 .4 10.1 .1
Epsilam-10 .127 12.0 13.2 .2 9.9 .1
Epsilam-10 .127 12.4 13.5 .1 9.8 .1
49
versus frequency plots was generated for the empty case. Data were taken
from the plots for the empty case and Samples 2 and 3 at selected frequen
cies and put in tabular form in Tables 7, 8, and 9, respectively. The
mean and standard deviation of each of the five data point sets were cal
culated and put into tabular form (Tables 10 and 11). The mean phase
shifts and amplitude changes attributed to Samples 2 and 3 are plotted in
Figures 20-23. A least-squares fit of the data was then accomplished to
minimize the effect of unwanted resonances. The results of the least-
squares fit are shown in Tables 12 and 13. The complex relative-permit-
tivity for both samples is given in Table 14. The two samples have rela
tive permittivity which agree within 2% throughout the frequency range
in question. The relative permittivity of Sample 2 was found to be
15.9 + 0.7. Sample 3 exhibited a measured relative permittivity of
15.9 + 0.9. The loss tangents (e"/e') for As-Te-Ge Samples 2 and 3 are
shown in Table 15.
The short-circuit method was applied to the samples and results are
shown in Table 16. As can be seen, the transmission method yields the
more consistent results.
It should be noted that values of imaginary and real relative-permit
tivity for Sample 2 could not be read directly from the computer-generated
program for the 12.0 and 12.4 GHz point. The values for 12.4 GHz were
read from the table utilizing the mean phase shift and amplitude change
values versus the least-square calculated values. The values for the
12.0 GHz reading were the result of interpolating the 11.5 and 12.4 GHz
values.
50
PHASE SHIFT
240
220
LEAST SQUARES FIT 200
180
o 140
120
100
V\ \K
20
FREQUENCY (GHZ)
20. Phase shift versus frequency for As-Te-Ge Sample 2.
51
AMPLITUDE CHANGE
12
11
t o
M _1 111 m o ui o
.
—e
k
( ) y / ( ) ^ )
( ) y
/ c ) r
, X X
r ( )
\
V
LEAST SQUARES FIT
8 9 10 II 12
FREQUENCY (GHZ)
Figure 21. Amplitude change versus frequency for As-Te-Ge Sample 2
52
PHASE SHIFT
240
220
•LEAST SQUARES FIT 200
160
« Ul Ul
a 140 Ul Û
120
100
ON
20
FREQUENCY(GHZ)
Figure 22. Phase shift versus frequency for As-Te-Ge Sample 3
53
AMPLITUDE CHANGE
LEAST SQUARES FIT
.00
FREQUENCY(GHZ)
Figure 23. Amplitude change versus frequency for As-Te-Ge Sample 3
54
Table 7. Phase and amplitude data for the empty case
Frequency Phase Amplitude (GHz) (Degrees) (Decibels)
8.0 -6.0 +2.5
8.5 -80.0 +2.00
9.0 -120.5 +1.90
9.5 -137.5 +1.60
10.0 -139.0 +1.10
10.5 -123.0 +0.10
11.0 -100.0 -0.50
11.5 -60.0 -1.30
12.0 -21.0 -0.80
12.4 0.0 -0.40
Table 8. Sample 2 phase and amplitude
Frequency Data Set 1 Data Set 2 Data Set 3 Data Set 4 Data Set 5 0 Â 0 Â 0 À 0 A 0 - Â
8 -140 -2.9 -143 -3.0 -147 -2.7 -142 -2.5 -145 -2.2
8.5 -232 -5.2 -234 -5.3 -235.5 -4.9 -234.5 -4.7 -234 -4.3
9 -271.5 ^4.8 -272.5 -5.0 -273.5 -4.65 -273 -4.4 -272 -4.2
9.5 -300 -4.3 -300 -4.45 -301.5 -4.0 -302.5 -3.7 -300.5 -3.6
10 -317.5 -3.75 -317.5 -3.85 -318.5 -3.65 -320 -3.4 -311 -3.2
10.5 -318 -5.75 -319.5 -5.75 -320.5 -5.55 -321.5 -5.25 -318 -5.15
11 -301 -7.25 -303 -7.4 -303 -7.25 -306 -6.95 -300 -6.8
11.5 -262 -8.3 -264 -8.4 -266 -8.1 -269.5 -7.7 -263 -7.55
12 -237.5 -8.85 -239 -9.1 -240 -9.2 -244.5 -9.0 -236 -8.5
12.4 -207.5" -10.3 -208.5 -10.3 -212 -10.25 -216 -10.2 -209.5 -9.5
Table 9. Sançle 3 phase and amplitude
Frequency Data Set 1 Data Set 2 Data Set 3 Data Set 4 Data Set 5 0 A 0 A ( ^ A 0 - A
8 -138 -9.7 -136.5 -9.35 -135 -9.35 -138.5 -9.05 -137 -9.0
8.5 -257.5 -5.5 -264.5 -4.4 -262 -4.35 -260 -4.0 -260 -3.95
9 ^ -327.5 -7.65 -326 -6.85 -323 -6.85 -321 -6.4 -323 -6.2
9.5 -345 -11.45 -347 -10.2 -344.5 -10.2 -343 -9.6 -345 -9.5
10 -327.5 -12.1 -333 -10.55 -329 -10.55 -328 rlO.25 -331.5 -10.2
10.5 -307 -10.75 -316 -11.3 -312 -11.4 -314 -11.0 -314.5 -11.2
11 -302 -7.8 -297.5 -10 -293 -10.15 -293 -9.95 -292.5 -9.7
11.5 -281.5 -9.1 -260.5 -9.15 -255.5 -9.3 -259 -9.15 -259 -8.6
12 -257 -9.6 -249 -8.6 -244 -9 -243 -8.2 -243.5 -8.2
12.4 -228 • -9.7 -224 -9.4 -221 -9.55 -221 -8.75 -222 -8.6
Table 10. Mean and standard deviation of data points shown in Table 2 for As-Te-Ge- Sample 2 (t = .4484 cm)
Frequency S.D. àé • 4* S.D. aA
8 -143.4 2.7 136.9 (-223.10)
-2.66 .32 4.91
8.5 -234 1.27 154 (-206)
-4.88 .40 6.88
9 -272.5 .79 152 (-208)
-4.61 .32 6.21
9.5 -300.9 1.08 163.4 (-196.6)
-4.01 .37 5.61
10 -318.5 1.06 179.5 (-180.50)
-3.57 .27 4.67
10.5 -319.5 1.54 196.5 (-163.5)
-5.49 .28 5.59
11 -302.6 2.3 202.6 (-157.4)
-7.13 .25 6.63
11.5 -264.9 2.97 204.9 (-155.1)
-8.01 .37 6.71
12 -239.4 3.23 218.4 (-141.6)
-8.93 .27 8.13
12.4 -210.7 3.4 210.7 (-149.3)
-10.11 .34 9.71
Table 11. Mean and standard deviation of data points shown in Table 3 for As-Te-Ge Sanglë 3 (t=.5003 cm)
Frequency ^ S.D. A0 A S.D. && (GHz) (in degrees) (in decibels)
8 -137 1.37 130.5 9.29 .28 11.54 (-220.5)
8.5 -262.8 3.21 182.8 4.44 .63 6.44 (-177.2)
9 -324.1 2.61 203.6 6.79 .56 8.69 (-156.4)
9.5 -344.9 1.43 207.4 10.19 .78 11.79 (-152.6)
10 -329.8 2.36 190.8 10.73 .78 11.83 (-169.2)
10.5 -312.7 3.49 189.7 11.13 .26 11.23 (-170.3)
11 -295.6 4.11 195.6 9.52 .98 9.02 (-164.4)
11.5 -263.1 10.45 603.1 9.06 .27 7.76 (-156.90)
12 -247.30 5.93 226.3 8.72 .59 7.92 (-133.7)
12.4 -223.2 2.95 223.2 9.20 .49 8.8 (-136.8)
59
Table 12. Relative permittivity for (As-Te-Ge) Sample 2 (t = .4484 cm) with least squares fit
Frequency *ADJ. \DJ. €' e" (GHz) (degrees) (decibels)
8.0 139.69 4.9 16.8 2.10
8.5 149.11 5.26 16.0 2.45
9.0 158.53 or (-201.47) 5.62 15.4 2.50
9.5 167.95 or (-192.05) 5.98 15.1 2.40
10.0 177.37 or (-182.63) 6.34 15.0 2.15
10.5 186.79 or (-173.21) 6.70 15.0 1.75
11.0 196.21 or (-163.79) 7.06 15.3 1.15
11.5 205.63 or (-154.37) 7.42 15.7 0.4
12.0 215.05 or (-144.95) 7.78 16.3® 1.5*
12.4 222.54 or (-137.41) 8.07 16.7^ 2.6^
^Interpolated
^Based on mean value of phase and amplitude shift
60
Table 13. Relative permittivity for (As-Te-Ge) Sample 3 (t= .5003 cm) with least squares fit
Frequency (GHz)
^ADJ. (degrees)
*ADJ. (decibels)
c ' e"
8 164.72 or -195.28) 10.28 16.3 5.10
8.5 171.55 or -188.45) 10.11 15.8 4.75
9 178.38 or -181.62) 9.93 15.5 4.25
9.5 185.21 or -174.79) 9.76 15.2 3.75
10 192.04 or -167.95) 9.58 15.1 3.15
10.5 198.87 or -161.13) 9.41 15.1 2.55
11 205.70 or -154.3) 9.24 15.4 2.00
11.5 212.53 or -147.47) 9.06 15.9 1.65
12 219.36 or -140.64) 8.89 16.4 1.85
12.4 226.19 or -133.81) 8.71 16.7 2.20
61
Table 14. Comparison of the relative permittivity of two samples of As!-Te-Ge (transmission method)
Frequency (GHz)
Sample 2 e ' e"
Sample 3
e' e" I>
A
8.0 16.8 2.1 16.4 5.0 2
8.5 16.0 2.4 15.8 4.5 1
9.0 15.4 2.5 15.5 4.0 1
9.5 15.2 2.4 15.2 3.5 -
10.0 15.0 2.2 15.2 3.0 1
10.5 15.1 1.8 15.2 2.5 1
11.0 15.4 1.2 15.4 2.0 -
11.5 15.7 0.4 15.8 2.0 1
12.0 16.3* 1.5* 16.4 2.0 1
12.4 16.7^ 2.6^ 16.6 2.25 1
^Interpolated
Based on mean value of phase and amplitude shift
62
Table 15. Comparison of the loss tangent of two samples of As-Te-Ge (transmission method)
Frequency Loss Tangent (GHz) Sample 2 Sample 3
8.0 0.13 0.30
8.5 0.15 0.28
9.0 0.16 0.26
9.5 0.16 0.23
10.0 0.15 0.20
10.5 0.12 0.16
11.0 0.08 0.13
11.5 0.03 0.13
12.0 0.09* 0.12
12.4 0.16^ 0.14
^Interpolated from data at 11.5 and 12.4
^Utilizing mean phase and amplitude from Table 5
63
Table 16. Relative permittivity of AsrTe-Ge utilizing the short-circuit method
Frequency Sample 2. Sample 3
8.0 29.7 - 28.2 -
8.5 31.4 - 25.6 -
9.0 27.7 - 23.3 -
9.5 25.7 - 21.2 -
10.0 23.6 - 16.3 -
10.5 21,6 - 17.5 .2
11.0 19.-9 .05 16.3 .7
11.5 18.3 - 14.4 .9
12.0 17.2 .03 12.5 .3
12.4 16.4 .2 12.1 .3
64
In order for the table to have been used directly, the amplitude
change needed to be greater. If the least-squares fit had yielded a
greater amplitude change, the loss tangent would also differ less between
Samples 2 and 3.
There is a possible explanation for the least-squares fit yielding
too low an amplitude change for Sample 2, There were two very low ampli
tude change readings - one at 8.0 GHz and another at 10.0 GHz (See Table
10). The 8.0 GHz value was approximately 2 dB less than the 8.5 GHz value.
The 10.0 GHz value was approximately 1 dB less than adjacent values. Low
values can result when an undesired mode is generated in the transmission
line.
The error in determining the real portion relative-permittivity for
As^gTe^gGe^Q was estimated at 5%. However, the error in determining the
imaginary portion of the relative-permittivity could be greater than 50%
because of the inherently low loss of the samples. The loss was so low
that many of the points were not determinable by the short-circuit test
set-up used. However, the short-circuit method showed Sample 2 to have a
lower loss than Sample 3,,as was the case for the transmission method
(See Tables 15 and 16).
The high estimated error in determining the loss factor results from
the sample attributing less loss to the system than does the transmission
line.
As the loss of a sample increases, so does the accuracy of the trans
mission method in determining the loss factor (the imaginary relative-
permittivity) . This accuracy could approach that of the real relative-
permittivity measurements.
65
CONCLUSIONS
ASggTe^gGe^Q is a low-loss, high relative-permittivity dielectric
material. Measurements based on the transmission method yielded real
relative-permittivity values of 15.9 + 0.7 and 15.9 + 0.9 for Samples 2 and
3, respectively, for the frequency range of 8.0 to 12.4 GHz. The corre
sponding loss tangents were 0.095+.065 and 0.21 + 0.09 for Samples 2 arid
3, respectively.
Although the real relative-permittivity values agreed within 2% at
each sampled point throughout the frequency range, the accuracy of the
transmission method is estimated at 5% (See ERROR ANALYSIS section).
ASggTCggGe^Q would make an excellent dielectric for use at microwave
frequencies if the samples were easier to make and the elements were not
poisonous.
The possible application of the bistable resistivity characteristic
of ASggTe^gGe^Q as a microwave switch is regarded as feasible, but not
too practical. An electric field strength in the order of 1000 volts/cm
would be necessary to grow the desired low-resistance filament on the
surface of the As^^Te^gGe^Q sample.
Because the As-Te-Ge glass does have a high relative-permittivity,
and relatively low loss, it would be useful as a microwave substrate
material. However, other materials exist with high relative-permittivities
which do not have the disadvantages of the As-Te-Ge glass.
Two methods were considered for use in measuring the relative-permit
tivity of ASggTCggGe^Q. The first method attempted was the Von Hippel
short-circuit method.
66
The Von Hippel short-circuit method was found to have a serious de
ficiency when measuring high relative-permittivity. The accuracy of the
method is reduced considerably unless the sample thickness is very nearly
equal to an odd multiple of quarter-wavelengths. Because As^^Te^gGe^Q
sample preparation is difficult and the relative-permittivity of the sample
was unknown, samples of the desired thickness were not obtained.
The next method attempted was the transmission method. This method
was developed in a fundamental form at least two decades ago (Westphal,
1954). The measurement techniques were revised and refined over the last
six years by the author. The main disadvantage of the transmission method
was found to be the existence of unwanted modes in the transmission line.
Although their effect was minimized, the accuracy of the method was
judged to be limited to 5%.
In practice, the transmission method was judged to be more accurate
overall in determining high real relative-permittivities than the Von
Hippel short-circuit method and was judged to be as accurate as the short-
circuit method in determining loss factors.
It is recommended that future transmission method computer-generated
tables utilize increments of real relative-permittivity equal to 0.05
instead of 0.1. This will improve the correlation between the measured
parameters (phase shift and amplitude change) and the relative-permittivity
(real and imaginary). It is also recommended that a microwave frequency
counter be utilized to improve the accuracy and repeatability of the data.
67
APPENDIX A:
COMPUTER PROGRAM AND TABLE
1 2
3
4 5 6
7 8 9
1 0 11 1 2 13 14 15 16
17 1 8 19 20 21 22 23 24 25
26 27 28 29 30 3! 32 33 34 35 36
37 38 39 40
68
WR1TE(6«1005) 1005 FORMAT** FREQ AMPL-DB PHASE-DG ER PRIME
C THIS PROGRAM IS GOOU FOR X BAND GUIDE ONLY. €=29.97925
C F IS IN GIGAHERTZ C D IS IN CM
0=0.4484
A=1.88863 I 78 1 DO 10 1=1,10
READ(5.1001)F 1001 FORMAKF 10.5)
8=0.0439 25651«(F)**2 GI=B-A GI=SORT{GI) GID=GI*D DO 11 J=1.15 ERP=15.5 E1=J ERP=ERP+El*0.1 AR=B*ERP-A DO 12 K= 1 .50
ERPP=0.3
F1=K-1 ERPP=ERPP+F1*0.05 AI=-(B*ERPP)
T1=0.5»ATAN2(AI,AR)+1.570 79632 7 AR1=(AI*AI+AR*AR)**.25 GMR= AR1*C0S( T1 ) GMRO=GMR*D
GMI = ARI*SIN( T1 ) GMID=GMI*D Z0MR=GMI/GI Z0MI=-GMR/GI AR1=GMR*GMR + GMI *GMI ZM0I=GI*GMR/AR1 ZM0R=GI*GMI/AR1 ZR=ZOMR+ZMOR ZI=ZOMI+ZMOI E4=EXP{GMRD) E5=-GMRD E1N=EXPCE5) E6=C0S(GM10) EGMRP=E4*E6
41 42 43 44 45
46 47 48 49 50 51 52 53 54
55 56
57 58 59 60 61
69
E7=SIN(GMIDÎ EGMIP=E4*E7 EGMRK=E1N*E6 EGMIN=-E1N*E7 ET1R=.5*<EGMRP+EGMRN)
ETH =«5«(EGM IP+EGMIN> ET2R=(EGMRP-EGMRN)/4. ET2I=(EGMIP-EGMIN>/4«
AMAGR=ET1H+ET2R*ZK-ET2I*ZI AMAGI=ET:I+ET2R«ZI+ET2I*ZR AM=ANAGR*AMAGR+AMAGr*AMAGI AMAG = SQR T( AM ) AMAGCB=20.*AL0G10(AMAG) THETA=57.2957795*(ATAN2(AMAGI#AMAGR)-GID)
WRITE(6.1004)F,AMAGOB.THETAtERP.ERPP.D 1004 F0RMAT(1X,6F9«4)
12 CONTINUE 11 CONTINUE 10 CONTINUE
STOP END
70
$ENTRY
FREQ AMPL-D0 PH AS E-DG ER PRIME ER PP THICKNESS
8.0000 5.0893 56. 4156 9. 6000 0 .0000 0.1270
8.0000 5.1113 56. 2017 9. 6000 0 .0500 0.1270
8.0000 5.1334 55. 9889 9. 6000 0 .1000 0.127 0
8.0000 5. 1557 55. 7773 9. 6000 0 • 1500 0 .1270
8.0000 5.1780 55. 5669 9. 6000 0 .2000 0.1270
8.0000 5.2004 55. 3578 9. 6000 0 .2500 0.1270
8.0000 5.2229 55. 1498 9. 6000 0 .3000 0.1270
8.0000 5.2455 54. 9429 9. 6000 0 .3500 0 .1270
8.0000 5.2681 54. 7 373 9. 6000 0 .4000 0.1270
8.0000 5.2909 54. 5328 9. 6000 0 .4500 0.1270
8.0000 5. 1541 56. 7036 9. 7000 0 .0000 0.1270
8.0000 5.1758 56. 4909 9. 7000 0 .0500 0.127 0
8.0000 5.1976 56. 2 793 9. 7000 0 .1000 0.1270
8.0000 5.2195 56. 0689 9. 7000 0 .1500 0.1270
8.0000 5.2414 55. 8596 9. 7000 0 .2000 0.1270
8.0000 5.2635 55. 6516 9. 7000 0 .2500 0. 1270
8.0000 5.2856 55. 4447 9. 7000 0 .3000 0. 1270
8.0000 5.3079 55. 2309 9. 7000 0 .3500 0.1270
8.0000 5.3301 55. 0344 9. 7000 0 .4000 0.1270
8.0000 5.3525 54. 8309 9. 7000 0 .4500 0.1270
8.0000 5.2186 56. 9869 9. 8000 0 .0000 0.1270
8.0000 5.2399 56 . 7754 9. 3000 0 .0500 0.1270
6.0000 5.2614 56. 5650 9. 8000 0 .1000 0 . 1270
8.0000 5.2029 56. 3559 9. 8000 0 .1500 0.127 0
8.0000 5.3045 56. 1477 9. 3000 0 .2000 0 .1270
8.0000 5.3262 55. 94 08 9. 8000 0 .2500 0.1270
8.0000 5.3480 55. 7350 9. 8000 0 .3000 0.1270
8.0000 5.3699 55. 5303 9. 8000 0 .3500 0. 1270
8.0000 5.3919 55. 3268 9. 8000 0 .4000 0.1270
8.0000 5.4139 55. 1244 9. 8000 0 .4500 0.1270
8.0000 5.2827 57. 2657 9. 9000 0 .0000 0.1270
6.0000 5.3037 57. 0554 9. 9000 0 .0500 0.1270
8.0000 5.3248 56. 8463 9. 9000 0 .1000 0.1270
8.0000 5.3460 56. 6382 9. 9000 0 . 1500 0.1270
8.0000 5.3673 56. 4313 9. 9000 0 .2000 0. 1270
8.0000 5.3886 56. 2254 9. 9000 0 .2500 0.1270
8.0000 5.4101 56. 0 20 8 9. 9000 0 .3000 0.1270
8.0000 5.4316 55. 81 72 9. 9000 0 .3500 0.1270
8.0000 5.4532 55. 6147 9. 9000 0 .4000 0. 1270
8.0000 5.4749 55. 4133 9. 9000 0 .4500 0.1270
71
6 . 0 0 0 0 5.3465 57. 5399
8 . 0000 5.3671 57. 3309
8 . 0000 5-3879 57. 1230
8 . 0000 5.4087 56. 9161
8 . 0000 5.4297 56. 71 03
8 . 0000 5.4507 56. 5 056
8 . 0000 5.471 8 56. 3020
8 . 0000 5.4930 56. 0995
8 . 0000 5.5143 55. 8982
8 . 0000 5.5357 55. 6978
8 . 0000 5.4098 57. 8 098
8 . 0000 5.4302 57. 6019
8 . 0000 5.4506 57. 3952
8 . 0000 5.471i 57. 1896
8 . 0000 5. 4917 56. 9850
8 . 0000 5.5124 56. 7815
8 . 0000 5.5332 56. 5790
8 * 0000 5.554 1 56. 3776
8 . 0000 5.5750 56. 1773
8 . 0000 5.596 1 55. 9780
8 . 0000 5.4728 58. 0754
8 . 0000 5.4928 57. 8689
8 . 0000 5.5129 57. 6633
8 . 0000 5.533 1 57. 4588
8 . 0000 5.5534 57. 2554
8 . 0 0 00 5.5738 57. 0530
8 . 0 0 00 5.5943 56. 8517
8 , 0000 5.6148 56. 65 14
8 . 0000 5.6354 56. 4521
8 . 0000 5.6562 56. 2539
8 . 0000 5.5354 58. 3368
8 . 0000 5.5551 58. 1314
8 . 0000 5.5749 57. 9272
8 . 0000 5.5948 57. 7238
8 . 0000 5.6148 57. 5215
8 . 0000 5.6348 5 7. 3204
8 . 0000 5. 6550 57. 1201
8 . 0000 5.6752 56. 92 10
8 . 0000 5.6955 56. 7228
8 . 0 0 0 0 5.7159 56. 5257
0. 0000 0 .0000 0 .1270
0. 0000 0 .0500 0.1270 0. 0000 0 .1000 0.127 0
0. 0000 0 .1500 0 . 1270
0. 0000 0 .2000 0.1270
0. 0000 0 .2500 0.1270
0. 0000 0 .3000 0.1270
0. 0000 0 .3500 0.1270
0. 0000 0 .4000 0.1270
0. 0000 0 .4500 0.1270
0. 1000 0 • 0000 0.1270
0. 1000 0 .0500 0.1270 0. 1000 0 . 1 000 0.1270
0. 1000 0 .1500 0.1270
0. 1000 0 . 2000 0.1270
0. 1000 0 .2500 0.1270
0. 10 00 0 .3000 0. 1270
0. 1 000 0 .3500 0 .1270
0. 1000 0 .4000 0.1270
0. I 000 0 .4500 0.1270
0. 2000 0 .0000 0 . 1270
0. 2000 0 .0500 0.1270
0. 2000 0 .1000 0. 1270
0. 2000 0 .1500 0.1270
0. 2000 0 .2000 0.1270
0. 2000 0 .2500 0.1270
0. 2000 0 . 3000 0.1270
0. 2000 0 .3500 0.1270
0. 2000 0 .4000 0.1270
0. 2000 0 .4500 0.1270
0. 3000 0 .0000 0.1270
0. 3000 0 . 0500 0.1270
0. 3000 0 .1000 0.1270
0. 3000 0 . 1500 0.1270
0. 3000 0 .2000 0.1270
0. 3000 0 .2500 0.1270
0. 3000 0 .3000 0.1270
0. 3000 0 .3500 0.1270
0. 3000 0 .4000 0.1270
0. 3000 0 .4500 0.1270
1 1 1 1 1 1 I 1 1 1 1 1
1 1 1 1
1 1 1 1 1
1 1 1 1
1 1 1 1 1 1 1
1 1 1
1 I 1 1 1
72
8.0000 5. 5976 58. 5941
8*0000 5. 61 70 58* 3899
8.0000 5. 636 5 58. 1 869
8.0000 5. 6561 57. 9 847
8.0000 5. 6757 57. 7837
8.0000 5. 6955 57. 5835
8.0000 5. 71 54 57. 3 845
8.0000 5. 7353 57. 1864
8.0000 5. 7553 56. 9893
8.0000 5. 7754 56. 7933
8.0000 5. 6595 58. 8474
8.0000 5. 6786 58. 6445
8.0000 5. 6978 58. 4426
8.0000 5. 71 70 58. 2417
8.0000 5. 7364 58. 0417
8.0000 5. 7559 57. 8428
8.0000 5. 7754 57. 6448
8.0000 5. 7950 57. 4479
8.0000 5. 6147 57. 2519
8.0000 5. 8345 57. 0569
8.0000 5. 7209 59. 0967
8.0000 5. 7397 58. 8950
8.0000 5. 7586 58. 6943
8.0000 5. 7776 58. 4946
8.0000 5. 796 7 58. 2959
8.0000 5. 81 59 58. 0981
8.0000 5. 8351 57. 9013
8.0000 5. 8544 57. 7054
8.0000 5. 8738 57. 5105
8.0000 5. 8933 57. 3165
8.0000 5. 7820 59. 3422
8.0000 5. 8006 59. 1418
0* 4000 0 .0000 0.1270
0. 4000 0 .0500 0.1270
0. 4000 0 .1000 0.1270
0. 4000 0 .1500 0.1270
0. 4000 0 .2000 0.1270
0. 4000 0 .2500 0.1270 0. 4000 0 .3000 0.1270
0. 4000 0 .3500 0.1270
0. 4000 0 .4000 0.1270
0. 4000 0 .4500 0.1270
0. 5000 0 .0000 0.1270
0. 5000 0 .0500 0.1270
0. 5000 0 .1000 0 .1270
0. 5000 0 .1500 0.1270
0. 5000 0 .2000 0.1270
0. 5000 0 .2500 0. 1270
0. 5000 0 .3000 0.1270
0. 5000 0 .3500 0.1270
0. 5000 0 .4000 0.1270
0. 5000 0 .4500 0 .1270
0. 6000 0 .0000 0.1270
0. 6000 0 .0500 0.1270
0. 6000 0 .1000 0.1270
0. 6000 0 .1500 0 .1270
0. 6000 0 .2000 0. 1270
0. 6000 0 .2500 0.1270
0. 6000 0 .3000 0.1270
0. 6000 0 .3500 0.1270
0. 6000 0 .4000 0.1270
0. 6000 0 .4500 0.1270
0. 7000 0 .0000 0.1270
0. 7000 0 .0500 0. 1270
1 1 1 1
1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 I 1 1 1 1 1
1 1 1
1 1 1 1
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o o o o o o o o o o o o o o o o o o o o o o o o o o o "o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o 3 o o o o o o o CO CO CO CO CO CO CO CO CO CO o 0* o 0\ 0» o o o o 0» o o o o o o o o o o m# «H t • • • • • • • • • • • # • • t • t t • • • • # • • * • # t • •
0> c> » 0* o o o » 0* 0» » 0> o> 3 0> a> c* o o o o o o o o o o o o o o O o o o o o »»é W #4 •4 '* —1 W4
m m <*- N tn o » o <t N CM in w vO CM v O o m o m P J CO m #4 •st o N • CM » v û n o o vO n w o o N CM n o CO to o CM -0 o o m -4 m m 0* n 0* \0 CO CO O o n N •* CM CO o w n in N 0> n vO in N CO o CM m N 0> CM •4" CM •* vO oo o CM -* N CM 00 o CM m N 0\ CM <t N O vO <" m c N m CM O 0» N in CM o CO o in m CM o 00 o m ro (T s O 4 n 0» N m CM o 0* • • • • • « • • • • • « • * • * • * s « • • • • • • • • • in in tn in 4- •it •d- in in m m in in •» •e <t <0 o m m in m m •d" <t <0 o v O m m il) m m m -t (fl in m in in m in in in in m in in m in in in m m in m in m m m m m m m m m m m m m m m tn tn m
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o CO o N N ro o rM vO 00 o CM <t *0 CO in N o m m K 0» <t o CM •«t vO c n m N o N N s CO CO CO CO CO o » N CO 00 00 00 0» » 0\ CO 03 00 0\ <> o> 0» Ct o o o c (T- 0» o O o o O o * • • • « • • • • ( t • • • * * • • • • • • • • # • • • • • < <• •e •St -c 4- 4- •?J- •it <- •d" St •5t •» •d- •ct •<t • 4t <t <t m m <t st •» st m m m m m
O o o o o O o o o o O o o o o o O o o o o O o o O o o o o o o o O O O o o o Q o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o O o O o o o O o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o o O o in in in in in m in in in in in tn tn m in m m in m in in m m m m tn m m m m m m m m m m m m m m • • • • • • • • • • • • • • • • • « * • • • • • « • * • • • • • • • • • # • «
#4 #4 •*4 —4 *>4 m* «•1 mI «w M
81
1 2 . 0 0 0 0 4 . 6 8 2 5 5 5 . 5 4 1 6 9 . 6 0 0 0 0 . 0 0 0 0 0 . 1 2 7 0
1 2 . 0 0 0 0 4 . 7 0 3 9 5 5 . 3 5 6 8 9 . 6 0 0 0 0 . 0 5 0 0 0 . 1 2 7 0
1 2 . 0 0 0 0 4 . 7 2 5 4 5 5 . 1 7 3 0 9 . 6 0 0 0 0 • 1 0 0 0 0 . 1 2 7 0
1 2 . 0 0 0 0 4 . 7 4 7 0 5 4 . 9 9 0 5 9 . 6 0 0 0 0 . 1 5 0 0 0 . 1 2 7 0
1 2 . 0 0 0 0 4 . 7 6 8 7 5 4 . 8 0 9 0 9 . 6 0 0 0 0 . 2 0 0 0 0 . 1 2 7 0
1 2 . 0 0 0 0 4 . 7 9 0 5 5 4 . 6 2 8 6 9 . 6 0 0 0 0 . 2 5 0 0 0 . 1 2 7 0
1 2 . 0 0 0 0 4 . 8 1 2 4 5 4 . 4 4 9 4 9 . 6 0 0 0 0 . 3 0 0 0 0 . 1 2 7 0
1 2 . 0 0 0 0 4 . 8 3 4 4 5 4 . 2 7 1 3 9 . 6 0 0 0 0 . 3 5 0 0 0 . 1 2 7 0
1 2 . 0 0 0 0 4 . 8 5 6 5 5 4 , 0 9 4 4 9 . 6 0 0 0 0 . 4 0 0 0 0 . 1 2 7 0
1 2 . 0 0 0 0 4 . 8 7 8 6 5 3 . 9 1 8 5 9 . 6 0 0 0 0 . 4 5 0 0 0 . 1 2 7 0
1 2 . 0 0 0 0 4 . 7 3 8 5 5 5 . 8 2 1 2 9 . 7 0 0 0 0 . 0 0 0 0 0 . 1 2 7 0
1 2 . 0 0 0 0 4 . 7 5 9 5 5 5 . 6 3 7 7 9 . 7 0 0 0 0 . 0 5 0 0 " 0 . 1 2 7 0
1 2 . 0 0 0 0 4 . 7 8 0 7 5 5 . 4 5 5 3 9 . 7 0 0 0 0 . 1 0 0 0 0 . 1 2 7 0
1 2 . 0 0 0 0 4 . 8 0 2 0 5 5 . 2 7 4 0 9 . 7 0 0 0 0 . 1 5 0 0 0 . 1 2 7 0
1 2 . 0 0 0 0 4 . 8 2 3 4 5 5 . 0 9 3 8 9 . 7 0 0 0 0 . 2 0 0 0 0 . 1 2 7 0
1 2 . 0 0 0 0 4 . 8 4 4 8 5 4 . 9 1 4 6 9 . 7 0 0 0 0 . 2 5 0 0 0 . 1 2 7 0
1 2 . 0 0 0 0 4 . 8 6 6 4 5 4 . 7 3 6 6 9 . 7 0 0 0 0 . 3 0 0 0 0 . 1 2 7 0
1 2 . 0 0 0 0 4 . 8 8 8 0 5 4 . 5 5 9 8 9 . 7 0 0 0 0 . 3 5 0 0 0 . 1 2 7 0
1 2 . 0 0 0 0 4 . 9 0 9 8 5 4 . 3 8 4 0 9 . 7 0 0 0 0 . 4 0 0 0 0 . 1 2 7 0
1 2 . 0 0 0 0 4 . 9 3 1 6 5 4 . 2 0 9 3 9 . 7 0 0 0 0 . 4 5 0 0 0 . 1 2 7 0
1 2 . 0 0 0 0 4 . 7 9 4 1 5 6 . 0 9 6 4 9 . 8 0 0 0 0 . 0 0 0 0 0 . 1 2 7 0
1 2 . 0 0 0 0 4 « 8 1 4 8 5 5 . 9 1 4 3 9 . 8 0 0 0 0 . 0 5 0 0 0 . 1 2 7 0
1 2 . 0 0 0 0 4 . 8 3 5 7 5 5 . 7 3 3 1 9 . 8 0 0 0 0 . 1 0 0 0 0 . 1 2 7 0
1 2 . 0 0 0 0 4 . 8 5 6 6 5 5 . 5 5 3 2 9 . 8 0 0 0 0 . 1 5 0 0 0 . 1 2 7 0
1 2 . 0 0 0 0 4 . 8 7 7 7 5 5 . 3 7 4 1 9 . 8 0 0 0 0 . 2 0 0 0 0 . 1 2 7 0
1 2 . 0 0 0 0 4 . 8 9 8 8 5 5 . 1 9 6 3 9 . 8 0 0 0 0 . 2 5 0 0 0 . 1 2 7 0
1 2 . 0 0 0 0 4 . 9 2 0 0 5 5 . 0 1 9 5 9 . 8 0 0 0 0 . 3 0 0 0 0 . 1 2 7 0
1 2 . 0 0 0 0 4 . 9 4 1 3 5 4 . 8 4 3 8 9 . 8 0 0 0 0 . 3 5 0 0 0 . 1 2 7 0
1 2 . 0 0 0 0 4 . 9 6 2 7 5 4 . 6 6 9 2 9 . a o o o 0 . 4 0 0 0 0 . 1 2 7 0
1 2 . 0 0 0 0 4 . 9 8 4 2 5 4 . 4 9 5 6 9 . 8 0 0 0 0 . 4 5 0 0 0 . 1 2 7 0
1 2 . 0 0 0 0 4 . 8 4 9 3 5 6 . 3 6 7 3 9 . 9 0 0 0 0 . 0 0 0 0 0 . 1 2 7 0
1 2 . 0 0 0 0 4 . 8 6 9 7 5 6 . 1 8 6 5 9 . 9 0 0 0 0 . 0 5 0 0 0 . 1 2 7 0
1 2 . 0 0 0 0 4 . 8 9 0 2 5 6 . 0 0 6 7 9 . 9 0 0 0 0 . 1 0 0 0 0 . 1 2 7 0
1 2 . 0 0 0 0 4 . 9 1 0 8 5 5 . 8 2 8 0 9 . 9 0 0 0 0 . 1 5 0 0 0 . 1 2 7 0
1 2 . 0 0 0 0 4 . 9 3 1 5 5 5 . 6 5 0 2 9 . 9 0 0 0 0 . 2 0 0 0 0 . 1 2 7 0
1 2 . 0 0 0 0 4 . 9 5 2 4 5 5 . 4 7 3 7 9 . 9 0 0 0 0 . 2 5 0 0 0 . 1 2 7 0
1 2 . 0 0 0 0 4 . 9 7 3 3 5 5 . 2 9 8 1 9 . 9 0 0 0 0 . 3 0 0 0 0 . 1 2 7 0
1 2 . 0 0 0 0 4 . 9 9 4 3 5 5 . 1 2 3 5 9 . 9 0 0 0 0 . 3 5 0 0 0 . 1 2 7 0
1 2 . 0 0 0 0 5 * 0 1 5 4 5 4 . 9 5 0 1 9 . 9 0 0 0 0 . 4 0 0 0 0 . 1 2 7 0
1 2 . 0 0 0 0 5 . 0 3 6 5 5 4 . 7 7 7 7 9 . 9 0 0 0 0 . 4 5 0 0 0 . 1 2 7 0
82
1 2 . 4 0 0 0 1 2 . 4 0 0 0 1 2 . 4 0 0 0 1 2 . 4 0 0 0 1 2 . 4 0 0 0 1 2 . 4 0 0 0
1 2 . 4 0 0 0
1 2 . 4 0 0 0 1 2 . 4 0 0 0 1 2 . 4 0 0 0
1 2 . 4 0 0 0 1 2 . 4 0 0 0 1 2 . 4 0 0 0 1 2 . 4 0 0 0 1 2 . 4 0 0 0
1 2 . 4 0 0 0
1 2 . 4 0 0 0 1 2 . 4 0 0 0 1 2 . 4 0 0 0
1 2 . 4 0 0 0
1 2 . 4 0 0 0 1 2 . 4 0 0 0
4 . 7 2 6 1 4 . 7 4 7 3 4 . 7 6 8 7 4 . 7 9 0 2 4 . 6 1 1 7 4 . 6 3 3 4 4 . 8 5 5 1 4 . 8 7 7 0 4 . 8 9 8 9 4 . 9 2 0 9
4 . 7 8 1 6 4 . 8 0 2 5 4 . 8 2 3 6 4 . 8 4 4 7 4 . 8 6 5 9
4 . 8 8 7 2
4 . 9 0 8 6
4 . 9 3 0 1 4 . 9 5 1 8 4 . 9 7 3 4 4 . 8 3 6 7 4 . 8 5 7 3
5 5 . 9 0 0 4 5 5 . 7 1 7 1
5 5 . 5 3 5 0 5 5 . 3 5 4 0 5 5 . 1 7 4 0 5 4 . 9 9 5 3
5 4 . 8 1 7 6 5 4 . 6 4 1 1 5 4 . 4 6 5 7 5 4 . 2 9 1 3 5 6 . 1 7 7 9 5 5 . 9 9 6 0
5 5 . 8 1 5 2 5 5 . 6 3 5 4 5 5 . 4 5 6 9 5 5 . 2 7 9 4 5 5 . 1 0 3 0 5 4 . 9 2 7 7 5 4 . 7 5 3 5 5 4 . 5 8 0 4
5 6 . 4 5 0 9 5 6 . 2 7 0 4
9.6000 9 . 6 0 0 0 9 . 6 0 0 0 9 . 6 0 0 0 9 . 6 0 0 0 9 . 6 0 . 0 0 9 . 6 0 0 0 9 . 6 0 0 0 9 . 6 0 0 0 9.6000 9 . 7 0 0 0 9 . 7 0 0 0 9 . 7 0 0 0 9 . 7 0 0 0 9 . 7 0 0 0 9 . 7 0 0 0 9 . 7 0 0 0 9 . 7 0 0 0 9 . 7 0 0 0 9 . 7 0 0 0 9 . 8 0 0 0 9 . 8 0 0 0
0.0000 0 . 0 5 0 0 0 . 1 0 0 0 0 . 1 5 0 0 0.2000 0 . 2 5 0 0 0 . 3 0 0 0 0 . 3 5 0 0 0 .4000 0 . 4 5 0 0 0 . 0 0 0 0 0 . 0 5 0 0 0 . 1 0 0 0 0 . 1 5 0 0 0.2000 0 . 2 5 0 0 0 . 3 0 0 0 0 . 3 5 0 0 0 . 4 0 0 0 0 . 4 5 0 0 0 . 0 0 0 0 0 . 0 5 0 0
0 . 1 2 7 0 0 . 1 2 7 0 0 . 1 2 7 0 0 . 1 2 7 0 0 . 1 2 7 0 0 . 1 2 7 0
0 . 1 2 7 0
0 . 1 2 7 0
0 . 1 2 7 0
0 . 1 2 7 0
0 . 1 2 7 0 0 . 1 2 7 0 0 • 1 2 7 0 0 . 1 2 7 0 0 . 1 2 7 0 0 . 1 2 7 0 0 . 1 2 7 0 0 . 1 2 7 0 0 . 1 2 7 0 0 . 1 2 7 0
0 . 1 2 7 0
0 . 1 2 7 0
83
APPENDIX B:
EPSILAM-10 DATA
84
March, 1975
j NU.V'C »' $
Copper Clad Laminate and
Confrotlcd Dielectric
303 GpsHoRi-IO HIGH DIELECTRIC CONSTANT MICROWAVE SUBSTRATE
A now Microwave Substrate Is now available from 3M Company wtiich offers the designer new freedom in microwave stripline and microstrip circuit design and fabrication.
CPSILAM-10 is a ceramic filled TeflotPcompound that has the flexible, mechanical properties of a plastic, and electrical properties similar to alumina.
6PSILAM-10 is supplied with 1 oz. copper two sides. It can be processed like a conventional printed circuit board. The 9" x 9" sheet size allows for multiple circuit layout and processing using typical resists and etchonts. The substrate is easily machined, drilled, punched or routed. Supplied .025 and .050 mil thicknesses, it can bo cut with a shear or razor.
CPSILAM-10 is an excellent substrate for stripline designs at L, S, C, and X-band frequencies. The dielectric constant of 10.3 allows for reductions in package size and weight and Increased circuit density.
&PSILAM-10 has a coefficient of expansion close to that of aluminum and a low modulus of elasticity, making it an excellent choice for microstrip designs that are soldered or clamped into place.
For applications where ceramic is required, GPSILAM-10 serves as an excellent prototype substrate. It has electrical properties similar to alumina, and will not break or crack when stressed.
This new microwave substrate material has shown itself to combine many of the desirable mechanical properties of polymeric substrates with the high dielectric constant of alumina.
85
TYPICAL PROPERTIES Dielcctric Constant (L and X Bands)
Z — direction XY — directions
103+0.5 Approximately 15
Dissipation Factor .001
Temperature Coefficient of Er (ppm/°C) <500
Coefficient of Ttiermai Expansion (ppm/^C) 20 - 25 (est.)
Tensile Strengtli (psi) 1400
Elongation at Break >6%
Tensile tvloduius (psi) 35,000
Shore Hardness D-65
Cladding t oz, copper both sides (other cladding possible)
Copper Adiiesion (Ibs./in.) 8 (ED Copper)
Bonding Process Direct — no interlayer
Processing Standard printed circuit methods
Solderabiiitv At least 520°F — stands red hot hand soldering
Thermal Stability Probably SOCC for short intervals such as TO bonding if gold plated. Dielectric constant appears stable at 150°C after conditioning.
Fabrication Can be machined, drilled, sheared, and punched - the limitation on bonding and forming is the elongation of the copper.
Substrate Color Grey
Substrate Thickness .025" and .050"
Sheet Size
at X
cn
•
IMPORTANT NOTICE TO PURCHASER
An tutements. technical information and recommendations contained herein are based on tests we believe to be rflliabte, but the accuracy or completeness thereof is not guaranteed, and the following is made in hcu of all warranties, expressed or implied.
Seller's and manufacturer's only obligation shall be to replace such quantity of the product Droved to be ^defective. Neither seller nor /nonufacturer shall be liable for any mtury. loss or damage, direct or cnnsenucntial. arising out of the use of or the injbihty (o use ihe orwjucts. Before using, user shall determine the suitability of the product for his intended me. and user assumes all risk and liability whatsoever in connection therewith. No Statement or recommeniiJtion not contained herein shall have any force or effect unless in an agreement signed by officers of seller and manufacturer.
Electronic Products Division 3 M C E N T E R • S A I N T P A U L . M I N N E S O T A b b l O l
Table B-1. Phase, in degrees, for sample of Epsilam-lO
Frequency (GHz)
8.0 8.5 9.0 9.5 10.0 10.5 11.0 11.5 12.0 12.4
110 47 7 -27 -48 -68 -89 -87 -97 -112
114 50 12 -20 -42 -79 -100 -95 ' -100 -116
115 50 10 -24 -45 -66 -83 -79 -86 -108
110 47 8 -26 -48 -67 -91 -93 -99 -115
113 48 7 -28 -50 -71 -92.5 -91 -98 -112
114 50 10 -24 -45.5 -66.5 -84.5 -80 -87 -96
113 49 9 -25 • -47 -69 -91 -91 -98 -113
115 51 10 -22 -44 -64 -81 -78.5 -91 -119
113 49 8.5 -25 -47 -68 -88 -90 -100 -115
115 47 1.0 -30 -52 -73 -92 -90 -98 -112
Table B-2. Amplitude, in decibels, for sample of Epsilam-10
8.0 8.5 9.0 9.5 10.0
Frequency (GHz)
10.5 11.0 11.5 12.0 12.4
-6.6 -7.0 -5.2 -5.9 -5.0 -4.1 -6.2 -5.2 -3.9 -4.8
-6.6 -6.9 -4.9 -5.2 -2.6 -2.6 -6.0 -5.8 -4.2 -5.1
-6.6 -7.0 -5.0 -5.7 -4.8 -4.1 -6.2 -4.6 -2.4 -1.3
-6.6 -6.7 -5.1 -5.8 -4.8 -3.9 -5.6 -5.1 -3.9 -4.8
-6.55 -6.9 -4.8 -5.6 -4.7 -4.0 -6.3 -5.6 -4.3 -5.2
-6.5 -6.9 -5.0 -5.7 -4.7 -4.0 -6.2 -4.95 -3.6 -3.4
-6.55 -6.9 -5.0 -5.6 -4.6 -3.6 -5.9 -5.1 -3.9 -5.0
-6.5 -6.9 -4.9 -5.6 -4.6 -3.8 -5.5 -4.0 -1.4 -1.3
-6.5 -7.0 -5.1 -5.8 -4.7 -3.9 -5.8 -4.4 -3.7 -5.0
-5.9 -5.9 -4.5 -5.7 -4.7 -4.0 -6.5 -5.5 -4.2 -5.3
00
Table B-3. Phase, in degrees, for empty case
8.0 8.5 9.0 9.5
Frequency (GHz)
10.0 10.5 11.0 11.5 12.0 12.4
170 109 62 26.5 2 -15.5 -25 -34 -41 -50
173- 112 67 35 12 -18 -35 -40 -43 -50
174 112 66 32 9 -7 -15 -49 -48 -54
170 109 63 28.5 3 -15.5 -25 -33 -39 -48
169 108 62 27 3 -16 -25 -33.5 -40.5 -50
171 109 63 29 4 -15 -25 -33.5 -40 -48
173 110 63.5 29 4 -14 -24.5 -33.5 -39.5 -48
173.5 110 63 29 3.5 -14 -24 -33 -40 -49
173 110 63 28.5 4 -14 -23 -32 -39.5 -48
173 112 66 32.5 10 -5 -25.5 -48 -47 -53
Table B-4. Amplitude, in decibels, for empty case
Frequency (GHz)
8.0 8.5 9.0 9.5 10.0 10.5 11.0 11.5 12.0 12.4
-1.0 • -0.6 0.0 +0.2 +0.2 -0.3 -0.3 +0.25 +0.4 +0.35
-1.0 -0.6 -0.1 +0.6 +1.4 +2,3 +0.4 -0.1 +0.1 40.1
-1.0 -0.6 -0.2 +0.2 +0.3 +0.2 +2.0 +2.3 +0.5 +0.5
-1.0 -0.7 -0.3 0.0 +0.1 -0.4 -0.6 -0.1 +0.1 +0.1
-1.0 -0.7 -0.4 0.0 +0.1 -0.4 -0.45 +0.15 +0.4 +0.35
-0.9 -0.55 -0.2 -H).2 +0.35 -0.1, -0.2 +0.25 +0.4 +0.4
-1.0 -0.55 -0.2 +0.2 +0.3 -0.1 -0.2 +0.3 +0.5 +0.45
-1.0 -0.6 -0.2 +0.2 +0.3 -0.3 -0.2 +0.3 +0.5 +0.4
—0.9 -0.5 -0.2 +0.1 +0.2 -0.3 -0.2 +0.4 +0.6 +0.5
-0.8 -0.5 -0.05 +0.4 +0.7 +0.9 +2.7 +1.1 +0.6 +0.5
90
Table B-5. .Mean and standard deviation of the phase and amplitude for a sample of Epsilam-10
Phase (Degrees) Amplitude (Decibels) Frequency Mean Standard Mean Standard (GHz) Phase Deviation Phase Deviation
8.0 113.20 1.87 -6.49 0.21
8.5 48.80 1.48 -6.79 0.39
9.0 8.25 2.97 • -4.95 0.20
9.5 -25.10 2.89 -5.66 0.19
10.0 -46.85 2.91 -4.52 0.68
10.5 -69.15 4.30 -3.80 0.45
11.0 -89.20 5.49 -6.02 0.32
11.5 -87.45 6.09 -5.03 0.56
12.0 -95.40 5.34 -3.55 0.93
12.4 -111.80 6.29 -4.12 1.58
91
Table B-6. Mean and standard deviation of the phase and amplitude for the. empty case
Phase (Degrees) Amplitude (Decibels) Frequency Mean Standard Mean Standard (GHz) Deviation Deviation
8.0 171.95 1.77 -0.96 0.07
8.5 110.10 1.45 -0.59 0.07
9.0 63.85 1.80 -0.19 0.12
9.5 29.70 2.65 +0.21 0.18
10.0 5.45 3.50 +0.40 0.39
10.5 -13.40 4.11 +0.15 0.85
11.0 -24.70 4.77 +0.30 1.13
11.5 -36.90 6.50 +0.49 0.72
12.0 -41.75 3.23 +0.41 0.18
12.4 -49.80 2.15 +0.35 0.15
92
APPENDIX C:
TABLE FOR 1.30 MM SAMPLE
93
F R E O A M P L - O B P H A S E - O G
8 * 0 0 0 0 5 . 5 7 3 6 5 7 * 9 2 3 2
8 * 0 0 0 0 5 . 5 9 3 9 5 7 . 7 1 6 0
8 . 0 0 0 0 5 . 6 1 4 3 5 7 . 5 0 9 9
8 * 0 0 0 0 5 . 6 3 4 8 5 7 * 3 0 4 7
8 . 0 0 0 0 5 . 6 5 5 3 5 7 * 1 0 0 7
8 * 0 0 0 0 5 . 6 7 6 0 5 6 . 8 9 7 8
8 * 0 0 0 0 5 . 6 9 6 7 5 6 . 6 9 5 9
8 . 0 0 0 0 5 . 7 1 7 6 5 6 * 4 9 5 1
8 . 0 0 0 0 5 . 5 9 6 7 5 8 . 6 0 3 5
8 * 0 0 0 0 5 . 6 1 6 5 5 8 . 3 9 5 4
8 . 0 0 0 0 5 . 6 3 6 4 5 8 * 1 8 8 4
8 . 0 0 0 0 5 . 6 5 6 3 5 7 * 9 8 2 3
8 . 0 0 0 0 5 . 6 7 6 4 5 7 * 7 7 7 4
8 . 0 0 0 0 5 . 6 9 6 6 5 7 * 5 7 3 5
8 . 0 0 0 0 5 . 7 1 6 8 5 7 . 3 7 0 7
8 . 0 0 0 0 5 . 7 3 7 2 5 7 . 1 6 8 9
8 . 0 0 0 0 5 . 7 5 7 6 5 6 . 9 6 8 1
8 . 0 0 0 0 5 . 7 7 8 2 5 6 » 7 6 8 4
8 . 0 0 0 0 5 . 6 5 9 7 5 8 . 8 6 1 8
8 . 0 0 0 0 5 . 6 7 9 2 5 8 . 6 5 5 0
8 . 0 0 0 0 5 . 6 9 8 8 5 8 . 4 4 9 3
8 . 0 0 0 0 5 . 7 1 8 5 5 8 * 2 4 4 5
8 * 0 0 0 0 5 . 7 3 8 2 5 8 * 0 4 0 8
8 . 0 0 0 0 5 . 7 5 3 1 5 7 * 8 3 8 2
8 * 0 0 0 0 5 . 7 7 8 0 5 7 . 6 3 6 4
8 . 0 0 0 0 5 . 7 9 8 0 5 7 . 4 3 5 8
8 . 0 0 0 0 5 . 8 1 8 2 5 7 . 2 3 6 2
8 . 0 0 0 0 5 . 8 3 8 4 5 7 . 0 3 7 6
8 . 0 0 0 0 5 . 7 2 2 4 5 9 . 1 1 6 1
8 . 0 0 0 0 5 . 7 4 1 6 5 8 . 9 1 0 6
8 . 0 0 0 0 5 . 7 6 0 8 5 8 . 7 0 6 1
8 . 0 0 0 0 5 . 7 8 0 2 5 8 . 5 0 2 6
8 . 0 0 0 0 5 . 7 9 9 6 5 8 . 3 0 0 1
8 . 0 0 0 0 5 . 8 1 9 2 5 8 . 0 9 8 6
8 . 0 0 0 0 5 . 8 3 8 8 5 7 . 8 9 8 1
8 * 0 0 0 0 5 . 8 5 8 6 5 7 . 6 9 8 6
8 . 0 0 0 0 5 . 8 7 8 4 5 7 . 5 0 0 1
8 * 0 0 0 0 5 . 8 9 8 3 5 7 . 3 0 2 7
P R I M E E R P P T H I C K N E S S
0 . 1 0 0 0 0 1 0 0 0 0 * 1 3 0 0
0 . 1 0 0 0 0 1 5 0 0 0 . 1 3 0 0
0 . 1 0 0 0 0 2 0 0 0 0 . 1 3 0 0
0 . 1 0 0 0 0 2 5 0 0 0 , 1 3 0 0
0 . 1 0 0 0 0 3 0 0 0 0 . 1 3 0 0
0 * 1 0 0 0 0 3 5 0 0 0 . 1 3 0 0
0 * 1 0 0 0 0 4 0 0 0 0 . 1 3 0 0
0 . 1 0 0 0 0 4 5 0 0 0 . 1 3 0 0
0 . 2 0 0 0 0 0 0 0 0 0 . 1 3 0 0
0 . 2 0 0 0 0 0 5 0 0 . 0 . 1 3 0 0
0 . 2 0 0 0 0 1 0 0 0 0 . 1 3 0 0
0 . 2 0 0 0 0 1 5 0 0 0 . 1 3 0 0
0 . 2 0 0 0 0 2 0 0 0 0 . I 3 0 0
0 . 2 0 0 0 0 2 5 0 0 0 . 1 3 0 0
0 . 2 0 0 0 0 3 0 0 0 0 . 1 3 0 0
0 . 2 0 0 0 0 3 5 0 0 0 . 1 3 0 0
0 * 2 0 0 0 0 4 0 0 0 0 . 1 3 0 0
0 . 2 0 0 0 0 4 5 0 0 0 . 1 3 0 0
0 * 3 0 0 0 0 0 0 0 0 0 . 1 3 0 0
0 * 3 0 0 0 0 0 5 0 0 0 . 1 3 0 0
0 . 3 0 0 0 0 1 0 0 0 0 . 1 3 0 0
0 . 3 0 0 0 0 1 5 0 0 0 . 1 3 0 0
0 * 3 0 0 0 0 2 0 0 0 0 . 1 3 0 0
0 . 3 0 0 0 0 2 5 0 0 0 , 1 3 0 0
0 . 3 0 0 0 0 3 0 0 0 0 . 1 3 0 0
0 . 3 0 0 0 . 0 3 5 0 0 0 . 1 3 0 0
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0 . 4 0 0 0 0 0 0 0 0 0 . 1 3 0 0
0 . 4 0 0 0 0 0 5 0 0 0 . 1 3 0 0
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0 . 6 0 0 0 0 . 0 0 0 0 0 . 1 3 0 0
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o o o o o o
o o o o o o o o
99
1 • 0 0 0 0 5 . 0 0 2 8 5 6 ^ 2 6 9 1
1 • 0 0 0 0 5 . 0 2 3 0 5 6 - 0 8 8 3
1 • 0 0 0 0 5 . 0 4 3 3 5 5 ^ 9 0 8 5
1 • 0 0 0 0 5 . 0 6 3 6 5 5 . 7 2 9 8
1 • 0 0 0 0 s . 0 8 4 1 5 5 . 5 5 2 1
1 • 0 0 0 0 5 . 1 0 4 6 5 5 . 3 7 5 4
1 • 0 0 0 0 5 . 1 2 5 2 5 5 ^ 1 9 9 7
1 • 0 0 0 0 5 . 1 4 5 9 5 5 . 0 2 5 1
1 • 0 0 0 0 5 . 0 1 0 1 5 6 . 8 9 4 8
1 • 0 0 0 0 5 . 0 3 7 8 5 6 . 7 1 3 2
1 • 0 0 0 0 5 » 0 5 7 6 5 6 . 5 3 2 7
1 • 0 0 0 0 5 . 0 7 7 5 5 6 . 3 5 3 1
1 • 0 0 0 0 5 . 0 9 7 4 5 6 . 1 7 4 5
1 • 0 0 0 0 5 . 1 1 7 5 5 5 . 9 9 7 1
1 • 0 0 0 0 5 . 1 3 7 6 5 5 . 8 2 0 4
1 • 0 0 0 0 5 . 1 5 7 9 5 5 . 6 4 4 9
1 • 0 0 0 0 5 . 1 7 8 2 5 5 . 4 7 0 4
1 • 0 0 0 0 5 . I 9 8 6 5 5 . 2 9 6 8
1 . 0 0 0 0 5 . 0 7 3 1 5 7 . 1 5 1 9
1 • 0 0 0 0 5 . 0 9 2 5 5 6 . 9 7 1 6
1 • 0 0 0 0 5 . 1 1 2 0 5 6 . 7 9 2 3
1 • 0 0 0 0 5 . 1 3 1 6 5 6 . 6 1 3 9
1 • 0 0 0 0 5 . 1 5 1 2 5 6 . 4 3 6 6
1 • 0 0 0 0 5 . 1 7 1 0 5 6 . 2 6 0 2
1 • 0 0 0 0 5 « 1 9 0 8 5 6 . 0 8 4 8
1 • 0 0 0 0 5 . 2 1 0 8 5 5 . 9 1 0 4
1 • 0 0 0 0 5 . 2 3 0 8 5 5 . 7 3 7 0
1 • 0 0 0 0 5 . 2 5 0 9 5 5 . 5 6 4 5
1 • 0 0 0 0 5 . 1 2 7 8 5 7 . 4 0 5 1
1 • 0 0 0 0 5 . 1 4 6 6 5 7 . 2 2 6 0
1 • 0 0 0 0 5 . 1 6 6 0 5 7 . 0 4 8 0
1 • 0 0 0 0 5 . 1 8 5 3 5 6 . 8 7 0 9
1 • 0 0 0 0 5 . 2 0 4 7 5 6 . 6 9 4 7
1 • 0 0 0 0 5 . 2 2 4 1 5 6 . 5 1 9 5
1 • 0 0 0 0 5 . 2 4 3 7 5 6 . 3 4 5 3
1 • 0 0 0 0 5 . 2 6 3 3 5 6 . 1 7 2 0
1 • 0 0 0 0 5 . 2 0 3 1 5 5 . 9 9 9 7
1 • 0 0 0 0 5 . 3 0 2 9 5 5 . 8 2 8 3
0 . 1 0 0 0 0 . 1 0 0 0 0 . 1 3 0 0
0 . 1 0 0 0 0 . 1 5 0 0 0 . 1 3 0 0
0 . 1 0 0 0 0 . 2 0 0 0 0 . 1 3 0 0
0 . 1 0 0 0 0 . 2 5 0 0 0 . 1 3 0 0
0 . 1 0 0 0 0 . 3 0 0 0 0 . 1 3 0 0
0 . 1 0 0 0 0 . 3 5 0 0 0 . 1 3 0 0
0 . 1 0 0 0 0 . 4 0 0 0 0 . 1 3 0 0
0 . 1 0 0 0 0 . 4 5 0 0 0 . 1 3 0 0
0 . 2 0 0 0 0 . 0 0 0 0 0 . 1 3 0 0
0 . 2 0 0 0 0 . 0 5 0 0 0 . 1 3 0 0
0 . 2 0 0 0 0 . 1 0 0 0 0 . 1 3 0 0
0 . 2 0 0 0 0 . 1 5 0 0 0 . 1 3 0 0
0 . 2 0 0 0 0 . 2 0 0 0 0 . 1 3 0 0
0 . 2 0 0 0 0 . 2 5 0 0 0 . 1 3 0 0
0 . 2 0 0 0 0 . 3 0 0 0 0 . 1 3 0 0
0 . 2 0 0 0 0 . 3 5 0 0 0 . 1 3 0 0
0 . 2 0 0 0 0 . 4 0 0 0 0 . 1 3 0 0
0 . 2 0 0 0 0 . 4 5 0 0 0 . 1 3 0 0
0 . 3 0 0 0 0 . 0 0 0 0 0 . 1 3 0 0
0 . 3 0 0 0 0 . 0 5 0 0 0 . 1 3 0 0
0 . 3 0 0 0 0 . 1 0 0 0 0 . 1 3 0 0
V ) . 3 0 0 0 0 . 1 5 0 0 0 . 1 3 0 0
0 . 3 0 0 0 0 . 2 0 0 0 0 . 1 3 0 0
0 . 3 0 0 0 0 . 2 5 0 0 0 . 1 3 0 0
0 . 3 0 0 0 0 . 3 0 0 0 0 . 1 3 0 0
0 . 3 0 0 0 0 . 3 5 0 0 0 . 1 3 0 0
0 . 3 0 0 0 0 . 4 0 0 0 0 . 1 3 0 0
0 . 3 0 0 0 0 . 4 5 0 0 0 . 1 3 0 0
0 . 4 0 0 0 0 . 0 0 0 0 0 . 1 3 0 0
0 . 4 0 0 0 0 . 0 5 0 0 0 . 1 3 0 0
0 . 4 0 0 0 0 . 1 0 0 0 0 . 1 3 0 0
0 . 4 0 0 0 0 . 1 5 0 0 0 . 1 3 0 0
0 . 4 0 0 0 0 . 2 0 0 0 0 . 1 3 0 0
0 . 4 0 0 0 0 . 2 5 0 0 0 . 1 3 0 0
0 . 4 0 0 0 0 . 3 0 0 0 0 . 1 3 0 0
0 . 4 0 0 0 0 . 3 5 0 0 0 . 1 3 0 0
0 . 4 0 0 0 0 . 4 0 0 0 0 . 1 3 0 0
0 . 4 0 0 0 0 . 4 5 0 0 0 . 1 3 0 0
1 1 1 1 1 1
1 1
1 1 1 1
1 1 1
i 1 1 I 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 I
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o o c o o • • • • •
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o o o o o o o o o O O o o o o o O O C O O
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o o o
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o o o o o o o o o • • * • • • • • * o^-p-ojuruw"-'^ ooiooicoioyio o o o o o o o o o o o o o o o o o o
o o o o o o o o o o • • • • • • • • • •
o i o o i o o i o o i o y i o o o o o o o o o o o o o o o o o o o o o
o o o o o o o o o o o • * • • • • • • • « •
O O O O O O O O O O O O O O O O O O O O O O # # # # # # # # # # # # # # # # # # # # # #
o o o o o
W U U W U W U U W U U U U U U W U U W U W W W W U W W W W U W W W W W W W W O O O O O O O O C O O O O C O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O C O O C C O O O O C O O O O O O O O O O O O O O O O O O
101
12.0000 12.0000 12.0000 12.0000 12.0000 12.0000 12.0000 12.0000 12.0000 1 2 . 0 0 0 0 12.0000 12.0000 12 .0000 12 .0000 12 .0000 12.0000 1 2 . 0 0 0 0 12.0000 12 .0000 12 .0000 12 .0000 12 .0000 12 .0000 12 .0000 12 .0000 12 .0000 12 .0000 12 .0000 12 .0000 12 .0000 12 .0000 12 .0000 12 .0000 12 .0000 12 .0000 12 .0000 12 .0000 12 .0000 12 .0000 12 .0000
4 .7703
4 .7915
4 .8128
4 .8343
4 .8558
4 .8774
4 .8991
4 .9210
4 .9429
4 .9649
4 .8263
4 .8472
4 .8682
4 .8893
4 .9105
4 .9318
4 .9532
4 .9747
4 .9962
5 .0179
4 .8819
4 .9025
4 .9232
4 .9439
4 .9648
4 .9857
5 .0068 5 . 0280 5 .0492 5 .0706
4 .9371
4 .9574 4 .9777 4 .9981
5 .0187
5 .0393 5 .0601 5 . 0809
5 .1018
5 .1228
56 .0490
55 .8640
55 .6801
55 . 4975
55 .3158
55 .1354
54 .9560
54 .7778
54 .6 007 54 . 4248
56 .3260
56 .1424 55 .9599 55 .7786
55 . 5983
55 .4191
55 .2410
55 .0641
54 .3882
54 . 7135
56 . 5987
56 .4165
56 .2354
56 .0553
55 . 8763 55 . 6985
55 .5217
55 . 3460 55 .1714 54 .9978 56 .8670
56 .6863
56 . 5065 56 .3278 56 .1501
55 . 9736
55 . 7981
55 .6236
55 .4501
55 .2778
9 .6000 9 .6000 9 .6000 9 .6000
9 .6000
9 .6000
9 .6000
9 .6000
9 .6000 9 .6000
9 .7000
9 .7000
9 .7000 9 .7000
9 .7000
9 .7000
9 .7000
9 .7000
9 .7000
9 .7000
9 .8000
9 .8000 9 .3000 9 . 8 0 0 0 9 .8000
9 .8000 9 .8000
9 .8000
9 .8000
9 .8000 9 .9000
9 .9000
9 .9000
9 .9000
9 .9000
9 .9000
9 .9000
9 .9000 9 .9000 9 .9000
0.0000 0 .0500
0 . 1 0 0 0 0 .1500
0 . 2 0 0 0 0 .2500 0 .3000
0 .3500
0 .4000
0 .4500
0 . 0 0 0 0 0 .0500
0 . 1 0 0 0 0 .1500
0 . 2 0 0 0 0 .2500
0 .3000
0 .35 0 0 0 . 4000
0 .4500
0 . 0 0 0 0 0 .0500 0 . 1 0 0 0 0 . 1500
0.2000 0 .2500
0 .3000
0 .3500
0 .4000
0 .4500
0.0000 0 .0500
0 . 1 0 0 0 0 .1500
0 .2000 0 .2500
0 .3000
0 .3500
0 .4000
0 .4500
0 .1300 0 .1300 0 .1300 0 .1300
0 .1300
b . 1300 0 .1300 0 .1300 0 .1300 0 .1300
0 . 1300
0 .1300
0 .1300
0 . 1300
0 .1300
0 . 1300
0 .1300
0 .1300
0 . 1300
0 .1300
0 .1300
0 .1300
0 .1300
0 . 1300
0 . 1300 0 .1300 0 . 130 0
0 .1300
O . 1300
0 . 1300
0 .130 0
0 .1300
0 .1300
0 . 1300
0 . 1300
0 . 1300
0 . 1300
0 . 1300 0 .1300 0 .1300
102
12 .4000
12 .4000
12 .4000
12 .4000
12 .4000
12 .4000
12 .4000
12 .4000
12 .4000
12 .4000
12 .4000
12 .4000
12 .4000
12 .4000
12 .4000
12 .4000
12 .4000
12 .4000
12 .4000
12 .4000
12 .4000
12 .4000
4 .8106
4 .8319
4 .8U30
4 .8743
4 .8957
4 .9172
4 .9388
4 .9605
4 .9823
5 .0041
4 .8663
4 .8870
4 .9079
4 .9288
4 .9498
4 .9710
4 .9922
5 .0136
5 . 0350
5 . 0566
4 .9213
4 .9417
56 .4026
56 .2194
56 .0374
55 . 8565 55 . 6767
55 .4980 55 . 3205
55 .1441
54 .9688
54 .7946
56 .6775
56 .4957
56 .3152
56 . 1356
55 . 95 73 55 .7799 55 . 6038
55 . 42 87
55 .2547
55 .0817
56 . 94 80
56 . 7677
9 .6000
9 .6000
9 .6000
9 .6000
9 .6000
9 .6000
9 .6000
9 .6000
9 .6000
9 .6000
9 .7000
9 .7000
9 .7000
9 .7000
9 .7000
9 .7000
9 .7000
9 .7000
9 .7000
9 .7000
9 .8000
9 .8000
0.0000 0 .050 0
0 .1000 0 .1500 0.2000 0 .2500 0 .3000
0 .350 0
0 .4000
0 .4500
0 . 0 0 0 0 0 .0500
0 .1000 0 .1500
0.2000 0 .2500
0 .3000
0 .3500
0 .4000
0 .4500 0.0000 0 .0500
0 .1300
0 .1300
0 .1300
0 .1300
0 .1300
0 .1300
0 .1300 0 .1300 0 .1300
0 .1300
0 .1300
0 .1300
0 . 1300
0 .1300
0 .1300
0 .1300
0 . 1300
0 . 1300
0 .1300
0 .1300
0 .1300
0 .1300
103-104
APPENDIX D;
VON HIPPEL SHORT-CIRCUIT METHOD
The technique of deriving relative permittivity from Voltage Standing
Wave Ratio (VSWR) measurements was first reported by Von Hippel (1954).
Standing waves are established in a waveguide whenever a mismatch occurs.
For our purposes, a short was placed at the end of the waveguide. Figure
19 shows the standing wave pattern for the shorted waveguide. By inserting
a regular shaped dielectric sample in front of the short, the standing wave
pattern is altered as shown in Figure 19.
Once the null location and width is determined for the empty and sample
present cases, the relative permittivity can be determined from equations
(D-1) and (D-2).
(D-1) c
tanh Y/ -IX 1= - J £_ = —a (D-2)
1 - J ISS
where = free space wavelength
= cutoff wavelength of waveguide
= guide wavelength
d = thickness of sample
105
^2 = +
» complex propagation constant of the sample
Emin Emax '
= inverse standing wave ratio
2^ = distance from sample to first null
Note that equation (d-2) is a transcendental equation and has an
infinite number of solutions. Prior knowledge of the approximate dielectric
constant and the use of two samples of different thicknesses but like
material will yield a unique solution.
If the dielectric to be measured has an anticipated loss tangent less
than 0.1, the real portion of the propagation constant can be disregarded
and the equations simplified to;
(P-3) c
tan p„d "^g X )
-o
2 2TT2
2 l + tanTfy--
loss tangent = •^ [l - —][ ^ ] (D-5) X e' „ tan P d
l + t a r f p g d .
These equations can be solved by a computer program. Such a program
was developed by Nelson, et al. (1972).
106
APPENDIX E:
TABLES FOR AS-TE-GE SAMPLES
107
F R E O A M P L - 0 8 P H A S E - O G E R P R I M E E R P P T H I C K N E S
8 * 0 0 0 0 Z s 8 0 0 0 1 3 6 , 2 8 6 8 1 6 * 8 0 0 0 1 . 0 0 0 0 C . 4 4 8 4
a „ 0 0 0 0 9 7 9 4 1 3 6 . 4 5 7 9 1 6 . S O O O 1 . 0 5 0 0 G . 4 * 3 4
8 . 0 0 0 0 0 7 8 0 1 , 3 6 r 6 2 4 4 Î . 5 - 8 0 0 0 1 - 1 0 0 0 0 . 4 4 8 4
8 - 0 0 0 0 3 . I 7 5 9 1 3 6 , 7 8 6 4 1 6 . 8 0 0 0 1 , 1 5 0 0 0 f 4 4 8 A -
8 » 0 0 0 0 3 r 2 7 3 0 1 3 6 - 9 4 4 1 1 6 » 8 0 0 0 1 - 2 0 0 0 0 , & 4 8 &
8 . 0 0 0 0 3 . 3 6 9 3 1 3 7 , 0 9 7 4 1 6 r 3 0 0 0 1 . 2 5 0 0 0 * 4 4 8 4
8 . 0 0 0 0 3 - 4 6 4 8 1 3 7 . 2 4 6 7 J . e . 8 0 0 0 1 r 3 0 0 0 0
8 . 0 0 0 0 3 . 5 5 0 6 1 3 7 . 3 9 2 2 1 6 . 8 0 0 0 1 . 3 5 0 0 0 . A A R A
8 . 0 0 0 0 3 . 6 5 3 7 1 3 7 . 5 3 3 7 1 6 . 8 0 0 0 1 . 4 0 0 0 0 . 4 4 8 4
8 . 0 0 0 0 3 . 7 4 7 1 1 3 7 . 6 7 1 5 1 6 . 8 0 0 0 1 . 4 5 0 0 0 . 4 4 8 4
8 . 0 0 0 0 3 . 8 3 9 8 1 3 7 . 8 0 5 7 1 6 . 8 0 0 0 1 . 5 0 0 0 0 . 4 4 8 4
8 . 0 0 0 0 3 . 9 3 1 7 1 3 7 . 9 3 6 4 1 6 . 8 0 0 0 1 . 5 5 0 0 0 . 4 4 8 4
8 . 0 0 0 0 4 . 0 2 3 1 1 3 8 . 0 6 3 9 1 6 . 8 0 0 0 1 . 6 0 0 0 0 . 4 4 8 4
8 . 0 0 0 0 4 . I 1 3 7 1 3 8 . 1 8 8 0 1 6 . 8 0 0 0 1 . 6 5 0 0 0 . 4 4 8 4
8 . 0 0 0 0 4 . 2 0 3 7 1 3 8 . 3 0 8 9 1 6 . 8 0 0 0 1 . 7 0 0 0 0 . 4 4 8 4
8 . 0 0 0 0 4 . 2 9 3 1 1 3 8 . 4 2 6 6 1 6 . 8 0 0 0 1 . 7 5 0 0 0 . 4 4 8 4
8 . 0 0 0 0 4 . 3 8 1 8 1 3 8 . 5 4 1 5 1 6 . 8 0 0 0 1 . 8 0 0 0 0 . 4 4 8 4
8 . 0 0 0 0 4 . 4 6 9 9 1 3 8 . 6 5 3 5 1 6 . 8 0 0 0 I . 8 5 0 0 0 . 4 4 8 4
8 . 0 0 0 0 4 . 5 5 7 3 1 3 8 . 7 6 2 6 1 6 . 8 0 0 0 1 . 9 0 0 0 0 . 4 4 8 4
8 . 0 0 0 0 4 . 6 4 4 2 1 3 8 . 8 6 9 0 1 6 . 8 0 0 0 1 . 9 5 0 0 0 . 4 4 8 4
8 . 0 0 0 0 4 . 7 3 0 5 1 3 8 . 9 7 2 8 1 6 . 8 0 0 0 2 . 0 0 0 0 0 . 4 4 8 4
8 . 0 0 0 0 4 . 8 1 6 2 1 3 9 . 0 7 4 0 1 6 . 8 0 0 0 2 . 0 5 0 0 0 . 4 4 8 4
8 . 0 0 0 0 4 . 9 0 1 4 1 3 9 . 1 7 2 6 1 6 . 8 0 0 0 2 . 1 0 0 0 0 . 4 4 3 4
8 . 0 0 0 0 4 . 9 8 5 9 1 3 9 . 2 6 9 0 1 6 . 8 0 0 0 2 . 1 5 0 0 0 . 4 4 8 4
8 . 0 0 0 0 5 . 0 6 9 9 1 3 9 . 3 6 2 8 1 6 . 8 0 0 0 2 . 2 0 0 0 0 . 4 4 8 4
8 . 0 0 0 0 5 . 1 5 3 4 1 3 9 . 4 5 4 5 1 6 . 8 0 0 0 2 . 2 5 0 0 0 . 4 4 8 4
8 . 0 0 0 0 5 . 2 3 6 4 1 3 9 . 5 4 4 0 1 6 . 8 0 0 0 2 . 3 0 0 0 0 . 4 4 8 4
8 . 0 0 0 0 5 . 3 1 8 8 1 3 9 . 6 3 1 2 1 6 . 8 0 0 0 2 . 3 5 0 0 0 . 4 4 8 4
8 . 0 0 0 0 5 . 4 0 0 7 1 3 9 . 7 1 6 4 1 6 . 8 0 0 0 2 . 4 0 0 0 0 . 4 4 8 4
8 . 0 0 0 0 5 . 4 8 2 0 1 3 9 . 7 9 9 5 1 6 . 8 0 0 0 2 . 4 5 0 0 0 . 4 4 8 4
8 . 0 0 0 0 5 . 5 6 2 9 1 3 9 . 8 8 0 7 1 6 . 8 0 0 0 2 . 5 0 0 0 0 . 4 4 8 4
8 . 0 0 0 0 5 . 6 4 3 3 1 3 9 . 9 6 0 0 1 6 . 8 0 0 0 2 . 5 5 0 0 0 . 4 4 8 4
8 . 0 0 0 0 5 . 7 2 3 2 1 4 0 . 0 3 7 3 1 6 . 3 0 0 0 2 . 6 0 0 0 0 . 4 4 8 4
8 . 0 0 0 0 5 . 8 0 2 6 1 4 0 . 1 1 3 0 1 6 . 8 0 0 0 2 . 6 5 0 0 0 . 4 4 8 4
8 . 0 0 0 0 5 . 8 8 1 6 1 4 0 . 1 8 6 8 1 6 . 8 0 0 0 2 . 7 0 0 0 0 . 4 4 8 4
108
8 . 5 0 0 0 5 . 0 7 4 8 1 4 9 . 4 2 4 0 1 6 . 0 0 0 0 2 . 3 5 0 0 0 . 4 4 8 4
8 . 5 0 0 0 5 . 1 6 1 1 1 4 9 . 4 0 7 0 1 6 . 0 0 0 0 2 . 4 0 0 0 0 . 4 4 8 4
8 . 5 0 0 0 5 . 2 4 6 8 1 4 9 . 3 8 9 8 1 6 . G O O D 2 . 4 5 0 0 0 . 4 4 8 4
8 . 5 0 0 0 5 . 3 3 1 0 1 4 9 . 3 7 2 7 1 6 . 0 0 0 0 2 . 5 0 0 0 0 . 4 4 8 4
8 . 5 0 0 0 5 . 4 1 6 4 1 4 9 . 3 5 5 4 1 6 . 0 0 0 0 2 . 5 5 0 0 Q . 4 4 8 4
8 . 5 0 0 0 5 . 5 0 0 3 1 4 9 . 3 3 8 0 1 6 . 0 0 0 0 2 . 6 0 0 0 0 . 4 4 8 4
8 . 5 0 0 0 5 . 5 8 3 7 1 6 9 . 3 2 0 7 1 6 . 0 0 0 0 2 - 6 5 0 0 0 . 4 4 8 4
8 . 5 0 0 0 5 . 6 6 6 6 1 4 9 . 3 0 3 2 1 6 . 0 0 0 0 2 . 7 0 0 0 0 , 4 4 8 4
8 . 5 0 0 0 0 . 6 7 6 4 - 2 0 8 . 4 9 0 2 1 6 . 1 0 0 0 0 . 2 5 0 0 0 . 4 4 3 4
8 . 5 0 0 0 0 . 3 0 6 2 - 2 0 8 . 5 0 5 1 1 6 . 1 0 0 0 0 . 3 0 0 0 0 , 4 A S A
8 . 5 0 0 0 0 . 9 3 4 2 - 2 0 8 - 5 2 0 6 1 6 - 1 0 0 0 0 . 3 5 0 0 0 . 6 6 8 4
8 . 5 0 0 0 1 . 0 6 0 7 - 2 0 8 . 5 3 6 9 1 6 . 1 0 0 0 0 . 4 0 0 0 0 . 4 4 8 4
8 . 5 0 0 0 1 . 1 8 5 5 -2 0 8 . 5 5 3 8 1 6 . 1 0 0 0 0 . 4 5 0 0 0 . 4 4 8 4
8 . 5 0 0 0 1 . 3 0 0 8 -2 0 8 . 5 7 1 4 1 6 . 1 0 0 0 0 . 5 0 0 0 0 .4. A 34
8 . 5 0 0 0 1 . 4 3 0 5 - 2 0 8 . 5 0 9 5 1 6 . 1 0 0 0 0 . 5 5 0 0 0 . 4 4 8 4
8 . 5 0 0 0 1 . 5 5 0 9 -2 0 8 . 6 0 8 1 1 6 . 1 0 0 0 0 . 6 0 0 0 o . 4 4 8 4
8 . 5 0 0 0 1 . 6 6 9 8 - 2 0 6 . 6 2 7 3 1 6 . 1 0 0 0 0 . 6 5 0 0 0 , 4 < 1 8 4
8 . 5 0 0 0 1 . 7 8 7 3 - 2 0 8 . 6 4 6 9 1 6 . 1 0 0 0 0 . 7 0 0 0 0 . 6 4 8 4
8 . 5 0 0 0 1 . 9 0 3 5 - 2 0 3 . 6 6 7 0 1 6 . 1 0 0 0 0 . 7 5 0 0 0 . 4686
8 . 5 0 0 0 2 . 0 1 8 4 - 2 0 8 . 6 8 7 7 1 6 . 1 0 0 0 0 . 8 0 0 0 0 o 4 ' 4 8
8 . 5 0 0 0 2 . 1 3 2 1 - 2 0 8 . 7 0 8 5 1 6 . 1 0 0 0 0 . 8 5 0 0 0 . 4 4 8 4
8 . 5 0 0 0 2 . 2 4 4 4 - 2 0 8 . 7 2 9 8 1 6 . 1 0 0 0 0 . 9 0 0 0 0 . 4 4 8 4
8 . 5 0 0 0 2 . 3 5 5 6 - 2 0 8 . 7 5 1 6 1 6 . 1 0 0 0 0 . 9 5 0 0 0 . 4 4 8 4
8 . 5 0 0 0 2 # 4 6 5 6 — 2 0 8 . 7 7 3 7 1 6 . 1 0 0 0 1 . 0 0 0 0 0 . 4 4 8 4
8 . 5 0 0 0 2 . 5 7 4 5 - 2 0 8 . 7 9 5 9 1 6 . 1 0 0 0 1 . 0 5 0 0 0 . 4 4 8 4
8 . 5 0 0 0 2 . 6 8 2 3 - 2 0 8 . 8 1 8 5 1 6 . 1 0 0 0 1 . 1 0 0 0 0 . 4 4 8 4
8 . 5 0 0 0 2 . 7 8 8 9 -2 0 8 . 8 4 1 5 1 6 . loop 1 . 1 5 0 0 0 . 4 4 8 4
8 . 5 0 0 0 2 . 8 9 4 5 - 2 0 8 . 8 6 4 6 1 6 . 1 0 0 0 1 . 2 0 0 0 0 . 4 4 8 4
8 . 5 0 0 0 2 . 9 9 9 1 - 2 0 8 . 8 8 8 0 1 6 . 1 0 0 0 1 . 2 5 0 0 0 . 4 4 8 4
8 . 5 0 0 0 3. 1 0 2 7 - 2 0 8 . 9 1 1 6 1 6 . 1 0 0 0 1 . 3 0 0 0 0 . 4 4 8 4
8 . 5 0 0 0 3. 2 0 5 2 - 2 0 8 . 9 3 5 5 1 6 . 1 0 0 0 1 . 3 5 0 0 0 . 4 4 8 4
8 . 5 0 0 0 3. 3 0 6 9 -2 0 8 . 9 5 9 6 1 6 . 1 0 0 0 1 . 4 0 0 0 0 . 4 4 8 4
8 . 5 0 0 0 3. 4 0 7 6 - 2 0 8 . 9 8 3 8 1 6 . 1 0 0 0 1 . 4 5 0 0 0 . 4 4 8 4
8 . 5 0 0 0 3. 5 0 7 3 - 2 0 9 . 0 0 8 0 1 6 . 1 0 0 0 1 . 5 0 0 0 0 . 4 4 8 4
8 . 5 0 0 0 3. 6 0 6 2 — 2 0 9 . 0 3 2 5 1 6 . 1 0 0 0 1 . 5 5 0 0 0 . 4 4 8 4
8 . 5 0 0 0 3. 7 0 4 2 - 2 0 9 . 0 5 7 2 1 6 . 1 0 0 0 1 . 6 0 0 0 0 . 4 4 8 4
8 . 5 0 0 0 3. 8 0 1 3 -2 0 9 . 0 8 1 9 1 6 . 1 0 0 0 1 . 6 5 0 0 0 . 4 4 8 4
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9.0000 2.7594- 198. 0851 15. 4000 1 .0000 0 .4484
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9.5000 5. 6636-192. 3527 15. 1000 2 .35 00 0 «4484
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116
12.4000 9. 5463- 149. 2135 16. 7 0 0 0 2 .4000 0 .4484
12.4000 9.5875- 149. 2505 16. 7000 2 .4500 0 .4484
12.4000 9.6290-149. 2867 16. 7000 2 .5000 0 .4484
12.4000 9.670 7- 149. 3220 16. 7000 2 .5500 0 .4484
12.4000 9.7127-149. 3565 16. 7000 2 .6000 0 .4484
12.4000 9. 754 9-149. 3901 16. 7000 2 .6500 0 .4484
12.4000 9.7974- 149. 4228 16. 7000 2 . 7000 0 .4484
12.4000 9.8402- 149. 4546 16. 7000 2 .7500 0 .4484
12.4000 8. 1087-146. 5314 16. 8000 0 .3000 0 .4484
12.4000 8.1361- 146. 5981 1 6. 8000 0 .3500 . 0 . 4484
12.4000 8. 1639-146. 6641 16. 8000 0 .4000 0 .4484
12.4000 8.1921-146. 7294 16. 8000 0 .4500 0 .4484
12.4000 8.2206- 146. 7940 1 6. 8000 0 .5000 0 .4484
12.4000 8.2496-146. 8579 16. 8000 0 .5500 0 .4484
12.4000 8.2789- 146. 9210 1 6. 8000 0 .6000 0 .4484
12.4000 8.3 08 6— 1 46. 9834 16. 8000 0 .6500 0 .4484
12.4000 8.338 6-147. 0451 16. 8000 . 0 .7000 0 .4484
12.4000 8.3690- 147. 1060 16. 8000 0 .7500 0 .4484
12.4000 8.3998-147. 1661 16. 8000 0 .8000 0 .4484
12.4000 8.4309- 147. 2255 16. 8000 0 .8500 0 .4484
12.4000 8.462 4-147. 2842 16. 8000 0 .9000 0 .4484
12.4000 8.4942- 147. 3421 16. 8000 0 .9500 0 .4484
12.4000 8.5264- 147. 3991 16. 8000 1 • 0000 0 .4484
12.4000 8.5590-147. 4555 16. 8000 1 .0500 0 .4484
12.4000 8.5918-147. 51 10 16. 8000 1 .1000 0 .4484
12.4000 8.6251-14 7. 5658 16. 8000 1 .1500 0 .4484
12.4000 8.6586-147. 6198 16. 8000 1 .2000 0 .4484
12.4000 8.6925- 147. 6730 16. 8000 1 .2500 0 .4484
12.4000 8. 726 7-147. 7254 16. 8000 1 .3000 0 .4484
12.4000 8.7613-147. 7770 16. 8000 1 .3500 0 .4484
12.4000 8.7962-147. 82 78 16. 8000 1 .4000 0 .4484
12.4000 8.8314-147. 8779 16. 8000 1 .4500 0 .4484
12.4000 8.8669- 147. 9270 16. 8000 1 .5000 0 .4484
12.4000 8.9027- I 47. 9754 1 6. 8000 1 .5500 0 .4484
12.4000 8. 9389-148. 0230 16. 8000 1 .6000 0 .4484
12.4000 8.9753- 148. 0697 16. 8000 1 .6500 0 .4484
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118
8.5000 9. I 200-186. 7844 15. 8000 4 • 0000 0 .5003
8.5000 9.1873-186. 9140 15. 8000 4 .0500 0 .5003
8.5000 9.2544- 18 7. 04 19 IS. 8000 4 .1000 0 .5003
8.5000 9.3213-187. 1677 15. 3000 4 . 1500 0 .5003
8.5000 9.3879-187. 2913 15. 8000 4 .2000 0 .5003
8.5000 9.4544— 187. 4131 15. 8000 4 .2500 0.5003
8.5000 9.5206- 187. 5328 15. 8000 4 .3000 0 .5003
8.5000 9.5866— 187. 6507 15. 8000 4 .3500 0 .5003
8.5000 9.652 5-187. 7668 15. 8000 4 .4000 0 .5003
8.5000 9.7181-187. 8809 15. 8000 4 .4500 0 .5003
8.5000 9.7835-187. 9932 15. 8000 4 .5000 0 .5003
8.5000 9.8487-188. 1037 15. 8000 4 .5500 0 .5003
8.5000 9.9 138-188. 2124 15. 8000 4 .6000 0.5003
8.5000 9.9786- 188m 3194 1 5. 8000 4 .6500 0 .5003
8.5000 10.0433-188. 4246 15. 80 0 0 4 .7000 0 .5003
8.5000 10.1077- 18 8. 5280 15. 8000 4 .7500 0 .500 3
8.5000 10.172 0-188. 6298 15. 8000 4 .8000 0 .5003
8.5000 10.2361-188. 7300 15. 8000 4 .8500 0 .5003
8.5000 10.3000- 168. 8284 15. 8000 4 .9000 0 .500 3
8.5000 10.3637- 188. 9253 15. 8000 4 .9500 0 .5003
8.5000 10.4273- 189. 02 06 15. 8000 5 .0000 0 .5003
8.5000 10.4906- 189. 1 142 15. 8000 5 .0500 0 .5003
8.5000 10.553 8- 189. 2063 15. 8000 5 .1000 0 .5003
8.5000 10.6168- 189. 2968 15. 8000 5 .1500 0 .5003
8.5000 10.6797- 189. 3858 1 5. 3000 5 .2000 0 .5003
8.5000 10.7423-189. 4733 15. 8000 5 .2500 0 .5003
8.5000 10.8049- 189. 5593 15. 80 00 5 .3000 0 .5003
8.5000 10.8672-189. 6439 15. 8000 5 .3500 0 .5003
8.5000 10.9294-189. 72 70 15. 8000 5 .4000 0 .5003
8.5000 10.9914- 189. 8086 15. 8000 5 .4500 0 .5003
8.5000 11.0532-189. 8888 15. 8000 5 .5000 0 .5003
8.5000 11.114 8-1 89. 96 75 15. 8000 5 .5500 0 .5003
8.5000 11.1764- 190. 0450 1 5. 8000 5 .6000 0 .5003
8.5000 11.2377- 190. 1210 15. 8000 5 .65 00 0 .5003
8.5000 11.2989- 1 90. 1957 15. 8000 5 . 7000 0 .5003
8.5000 11.3599- 190. 2691 15. 8000 5 .7500 0 .5003
8.5000 11.42 oe 19 0. 3409 1 5. 8000 5 .8000 0 .5003
8.5000 il .4815-190. 41 17 15. 8000 5 .8500 0 .5003
8.5000 11.5421- 19 0. 4811 1 5. 8000 5 .9000 0 .5003
8.5000 11.6025- 190. 5492 15. 8000 5 .9500 0 .5003
119
9.0000 7. 8269-175. 6400 15. 5000 2 .6000 0 .5003
9.0000 7. 891 8-175. 8559 15. 50 00 2 .6500 0 .5003
9.0000 7. 9567- 176. 0687 1 5. 5000 2 .7000 0 .5003
9.0000 6. 021 6-176. 2783 15. 5000 2 .7500 0 .5003
9.0000 8. 0863- 176. 4847 15. 5000 2 .8000 0 .5003
9.0000 8. 1509-176. 6881 15. 5000 2 .8500 0 .5003
9.0000 8. 2155- 176. 8883 15. 5000 2 .9000 0 .5003
9.0000 8. 2799- 177. 0 857 15. 5000 2 .9500 0 .5003
9.0000 8. 3443-177. 2801 15. 5000 3 .0000 0 .5003
9.0000 8. 4086- 177. 4714 15. 5000 3 .0500 0 .5003
9.0000 8. 472 8-17 7. 6600 15. 5000 3 .1000 0 .5003
9.0000 8. 5369-177. 8457 15. 5000 3 • 1500 0 .5003
9.0000 8. 6009- 178. 0285 15. 5000 3 .2000 0 .5003
9.0000 8. 664 7— 178. 2085 15. 5000 3 .25 00 0 .5003
9.0000 8. 7285-178. 3858 15. 5000 3 .3000 0 .500 3
9.0000 8. 7922- 178. 5604 15. 5000 3 .350 0 0 .5003
9.0000 8. 8559-178. 7325 15. 5000 3 .4000 0 .5003
9.0000 8c 9194-1 78. 9013 15. 50 00 3 .4500 0 .5003
9.0000 8. 982 8-179. 0686 1 5. 5000 3 .5000 0 .5003
9.0000 9. 046 l-179. 2327 15. 5000 3 .5500 0 .5003
9.0000 9. 109 2- 179. 3944 15. 5000 3 .6000 0 .5003
9.0000 9. 1724-1 79. 5536 15. 5000 3 .6500 0 .5003
9.0000 9. 2353-179. 7103 1 5. 5000 3 . 7000 0 .5003
9.0000 9. 2982- 179. 8645 15. 5000 3 .7500 0 .5003
9.0000 9. 361 0-180. 0165 15. 5000 3 .8000 0 .5003
9.0000 9. 423 7- 180. 1660 1 5. 5000 3 .8500 0 .5003
9.0000 9. 4863-180. 3132 15. 5000 3 .9000 0 .5003
9.0000 9. 5488- 180. 4581 15. 5000 3 .9500 0 .5003
9.0000 9. 6112-180. 60 07 15. 5000 4 .0000 0 .5003
9.0000 9. 6734-180. 741 1 15. 5000 4 .0500 0 .5003
9.0000 9. 735 6-180. 8792 15. 5000 4 .1 000 0 .5003
9.0000 9. 7976-181 . 0152 15. 5000 4 .1500 0 .5003
9.0000 9. 8596-181. 1490 15. 5000 4 .2000 0 .5003
9.0000 9. 92 15- 181. 2806 15. 5000 4 .2500 0 .5003
9.0000 6. 8619- 170. 8438 1 5. 6000 1 .8000 0 .5003
9.0000 6* 9266-171. 1 185 15. 6000 1 .8500 0 .5003
120
9.5000 9. 3659- 1 74. 0585 15. 2000 3 .4000 0 .5003
9.5000 9. 4248- 174. 2204 15. 2000 3 .4500 0 ,5003
9.5000 9. 4 83 8- 174. 3799 15. 2000 3 .5000 0 .5003
9.5000 9. 542 7- 174. 5363 15. 2000 3 .5500 0 .5003
9.5000 9. 6017-174. 6914 1 5. 2000 3 .6000 0 .5003
9.5000 9. 6606-174. 8435 15. 2000 3 .6500 0 .5003
9*5000 9. 7195- 174. 9934 15. 2000 3 .7000 0 .5003
9.5000 9. 7784-175. 14 08 15. 2000 3 .7500 0 .5003
9.5000 9. 837 3- 175. 2858 15. 2000 3 .8000 0 .5003
9.5000 9. 8961- 175. 4286 15. 2000 3 .8500 0 .5003
9.5000 9. 9550- 175. 5691 1 5. 2000 3 .9000 0 .5003
9.5000 10. 0 138-175. 7 075 15. 2000 3 .9500 0 .5003
9.5000 10. 0726- 175. 8435 1 5. 2000 4 .0000 0 .5003
9.5000 10. 1314- 175. 9774 15. 2000 4 .0500 0 .5003
9.5000 10. 1902- 176. 1 090 15. 2000 4 .1000 0 .5003
9.5000 10. 2489- 176. 2385 15. 2000 4 . 1500 0 .5003
9.5000 10. 3076- 176. 3659 1 5. 2000 4 .2000 0 .5003
9.5000 10. 3663- 176. 4911 15. 2000 4 .2500 0 .5003
9.5000 7. 5704- 166. 6360 1 5. 3000 1 .8000 0 .5003
9.5000 7. 6269-166. 8919 15. 3000 1 .8500 0 .5003
9.5000 7. 6836- 167. 1445 15. 3000 1 .9000 0 .5003
9.5000 7. 7404- 167. 3936 15. 3000 1 .9500 0 ,5003
9.5000 7. 7973- 167. 6393 15. 3000 2 .0000 0 .5003
9.5000 7, 854 3-167. 8817 15. 3000 2 .0500 0 .5003
9.5000 7. 9113-168. 12 07 15. 3000 2 .1000 0 .5003
9.5000 7. 9685- 168. 3566 15. 3000 2 .1500 0 .5003
9.5000 8. 0258- 168. 5892 15. 3000 2 .2000 0 .5003
9.5000 a. 0831- 168. 8186 15. 3000 2 .2500 0 .5003
9.5000 8. 1 405- 169. 0449 15. 3000 2 .3000 0 .5003
9.5000 6. 1980- 169. 2681 1 5 . 3000 2 .350 0 0 .5003
9.5000 8. 2555- 1 6 9 . 4881 15. .3000 2 .4000 . 0 . 5003
9.5000 8. 3132- 169. 7052 15. 3000 2 .4500 0 .5003
9.5000 8. 3708- 169. 9190 15. 3000 2 .5000 0 .5003
121
1 0 . 0 0 0 0 8 . 1 6 8 8 - 1 6 3 . 0 5 5 4 1 5 . 1 0 0 0 1 • 8 0 0 0 . 0 . 5 0 0 3
1 O m 0 0 0 0 a . 2 1 9 5 - 1 6 3 . 2 7 9 5 1 5 . 1 0 0 0 1 • 8 5 0 0 0 . 5 0 0 3
1 0 . 0 0 0 0 a . 2 7 0 3 - 1 6 3 . 5 0 0 7 1 5 . 1 0 0 0 1 • 9 0 0 0 0 . 5 0 0 3
1 0 . 0 0 0 0 8 . 3 2 1 4 - 1 6 3 . 7 1 9 0 1 5 . 1 0 0 0 1 . 9 5 0 0 0 . 5 0 0 3
1 0 . 0 0 0 0 a . 3 7 2 7 - 1 6 3 . 9 3 4 6 1 5 . 1 0 0 0 2 . 0 0 0 0 0 . 5 0 0 3
1 0 . 0 0 0 0 8 . 4 2 4 1 - 1 6 4 . 1 4 7 2 1 5 . 1 0 0 0 2 . 0 5 0 0 0 . 5 0 0 3
1 0 . 0 0 0 0 8 . 4 7 5 8 - 1 6 4 . 3 5 7 2 1 5 . 1 0 0 0 2 . 1 0 0 0 0 . 5 0 0 3
1 0 . 0 0 0 0 a . 5 2 7 5 - 1 6 4 . 5 6 4 3 1 5 . 1 0 0 0 2 . 1 5 0 0 0 . 5 0 0 3
1 0 . 0 0 0 0 8 . 5 7 9 5 - 1 6 4 . 7 6 8 7 1 5 . 1 0 0 0 2 . 2 0 0 0 0 . 5 0 0 3
1 0 . 0 0 0 0 a . 6 3 1 6 - 1 6 4 . 9 7 0 4 1 5 . 1 0 0 0 2 • 2 5 0 0 0 . 5 0 0 3
1 0 . 0 0 0 0 8 . 6 8 3 9 - 1 6 5 . 1 6 9 3 1 5 . 1 0 0 0 2 . 3 0 0 0 0 . 5 0 0 3
1 0 . 0 0 0 0 8 . 7 3 6 4 - 1 6 5 . 3 6 5 7 1 5 . 1 0 0 0 2 . 3 5 0 0 0 . 5 0 0 3
1 0 . 0 0 0 0 8 . 7 8 9 0 - 1 6 5 . 5 5 9 2 1 5 . 1 0 0 0 2 . 4 0 0 0 0 . 5 0 0 3
1 0 . 0 0 0 0 8 . 8 4 1 7 - 1 6 5 . 7 5 0 0 1 5 . 1 0 0 0 2 . 4 5 0 0 0 . 5 0 0 3
1 0 . 0 0 0 0 8 . 8 9 4 6 - 1 6 5 . 9 3 8 5 1 5 . 1 0 0 0 2 . 5 0 0 0 0 . 5 0 0 3
1 0 . 0 0 0 0 8 . 9 4 7 6 - 1 6 6 . 1 2 4 0 1 5 . 1 0 0 0 2 . 5 5 0 0 0 . 5 0 0 3
1 0 . 0 0 0 0 9 . 0 0 0 7 - 1 6 6 . 3 0 7 2 1 5 . 1 0 0 0 2 . 6 0 0 0 0 . 5 0 0 3
1 0 . 0 0 0 0 9 . 0 5 4 0 - 1 6 6 . 4 8 7 7 1 5 . 1 0 0 0 2 . 6 5 0 0 0 . 5 0 0 3
1 0 . 0 0 0 0 9 . 1 0 7 4 - 1 6 6 . 6 6 5 6 1 5 . 1 0 0 0 2 . 7 0 0 0 0 . 5 0 0 3
1 0 . 0 0 0 0 9 . 1 6 0 9 - 1 6 6 . 8 4 1 0 1 5 . 1 0 0 0 2 . 7 5 0 0 0 . 5 0 0 3
1 0 . 0 0 0 0 9 . 2 1 4 6 - 1 6 7 . 0 1 3 8 1 5 . 1 0 0 0 2 . 8 0 0 0 0 . 5 0 0 3
1 0 . 0 0 0 0 9 . 2 6 8 3 - 1 6 7 . 1 8 4 2 1 5 . 1 0 0 0 2 . 8 5 0 0 0 . 5 0 0 3
1 0 . 0 0 0 0 9 . 3 2 2 2 - 1 6 7 . 3 5 2 2 1 5 . 1 0 0 0 2 . 9 0 0 0 0 . 5 0 0 3
1 0 . 0 0 0 0 9 . 3 7 6 2 - 1 6 7 . 5177 1 5 . 1 0 0 0 2 . 9 5 0 0 0 . 5 0 0 3
1 0 . 0 0 0 0 9 . 4 3 0 2 - 1 6 7 . 6 8 0 7 1 5 . 1 0 0 0 3 • 0 0 0 0 0 . 5 0 0 3
1 0 . 0 0 0 0 9 . 4 8 4 4 - 1 6 7 . 8413 15. 1 0 0 0 3 .0500 0 .5003
1 0 . 0 0 0 0 9. 5 3 8 7 - 167. 9996 15. 1 0 0 0 3 • 1 0 0 0 0 .5003
1 0 . 0 0 0 0 9. 5930- 1 6 8 . 1 5 5 4 15. 1 0 0 0 3 .1500 0 .5003
1 0 . 0 0 0 0 9 . 6 4 7 5 - 1 6 6 . 3089 15. lOOO 3 . 2 0 0 0 0 .5003
1 0 . 0 0 0 0 9. 7020- 1 6 8 . 4 6 0 1 15. looa 3 .2500 0 .5003
1 0 . 0 0 0 0 9. 7 5 6 6 - 1 6 8 . 6 0 8 9 15. 1 0 0 0 3 .3000 0 .5003
1 0 . 0 0 0 0 9 . 8113- 1 6 8 . 7 5 5 4 1 5 . 1 0 0 0 3 . 3500 0 .5003
122
10.5000 8. 6896-159. 0441 15. 1000 1 .8000 0 .5003
10.5000 8. 7355- 159. 2232 15. 1000 1 .8500 0 .5003
10.5000 8. 781 6-159. 4000 15. 1000 1 .9000 0 .5003
10.5000 8. 8280- 159. 5746 15. 1 000 1 -9500 0 .5003
10.5000 8. 8747-159. 7470 15. 1000 2 .0000 0 .5003
10.5000 8. 9216-159. 9170 15. lOÔO 2 .0500 0 .5003
10.5000 8. 9687-160. 0848 15. 1000 2 .1000 0 .5003
10.5000 9. 0161-160. 2504 15. 1000 2 .1500 0 .5003
10.5000 9. 0637- 160. 4138 15. 1000 2 .2000 0 .5003
10.5000 9. 1115-160. 5749 15. 1000 2 .2500 0 .5003
10.5000 9. 159 5-160. 7339 1 5. 1000 2 .3000 0 .5003
10.5000 9. 2078- 160. 8906 15. 1000 2 .3500 0 .5003
10.5000 9. 2562-161. 0452 15. 1000 2 .4000 0 .5003
10.5000 9. 3 04 9- 161. 1976 15. 1000 2 .4500 0 .5003
10.5000 9. 3538- 161. 34 78 15. 1000 2 .5000 0 .5003
10.5000 9. 4029- 161. 4959 1 5. 1000 2 .5500 0 .5003
10.5000 9. 4521- 161. 6418 15. 1000 2 .6000 0 .5003
10.5000 9. 50 16- 161. 7856 1 5. 1000 2 . 6500 0 .5003
10.5000 9. 551 2-161. 9273 15. 1000 2 .7000 0 .5003
10.5000 9. 6010- 162. 0668 15. 1000 2 .7500 0 .5003
10.5000 9. 651 0- 162. 2044 15. 1000 2 .8000 0 .5003
10.5000 9. 701 2- 162. 3398 15. 1000 2 .8500 0 .5003
10.5000 9. 7516- 162. 4731 15. 1000 2 .9000 0 .5003
10.5000 9. 8021-162. 6043 15. 1000 2 .9500 0 .5003
10.5000 9. 8528- 162. 7335 15. 1 000 3 .0000 0 .5003
10.5000 9. 9036-162. 8608 15. 1000 3 .0500 0 .5003
10.5000 9. 9546- 162. 9860 15. 1000 3 .1000 0 .5003
10.5000 10. 0058-163. 1092 15. 1000 3 .1500 0 .5003
10.5000 10. 057 1-163. 2303 1 5. 1000 3 .2000 0 .5003
10.5000 10. 1085- 163. 3495 15. 1000 3 • 2500 0 .5003
10.5000 10. 1601- 163. 4668 15. 1000 3 .3000 0 .5003
123
11 • 0000 10. 8487- 157* 8206
11 .0000 10.8 9 9 8 - 157. 8812
11 .0000 10. 951 1-15 7. 9404
11 • 0000 11.0026- 157. 9981
11 • 0000 11.05 42- 158. 0545
11 .0000 11.1059- 158. 1 094
11 • 0000 11.1579- 158. 1629
11 • 0000 11 .2099- 158. 2150
11 • 0000 11.2621- 158. 2657
11 • 0000 11.3145-158. 3150
11 • 0000 11.3670- 158. 3629
11 • 0000 11.4196- 158. 4096
11 • 0000 9^0933-153. 8233
11 .0000 9.1353- 153. 9397
11 .0000 9.1776-154. 0546
11 . 0000 9.2202-154. 1677
11 • 0000 9.2631- 154. 2793
11 .0000 9. 30 6 3- 154. 3894
11 • 0000 9.3498- 154. 4978
11 .0000 9.3935- 154. 6046
11 .0000 9.43 76- 154. 7099
11 • 0000 9.4819- 154. 8134
11 • 0000 9^5264- 154. 9156
11 .0000 9.5712- 155. 0160
11 .0000 9.616 3— 155. 1 148
11 .0000 9.6616— 155. 2122
11 .0000 9.7072- 155. 3 080
11 .0000 9.7531-155. 4022
11 .0000 9.7991-155. 4948
11 .0000 9. 84 54- 155. 5859
11 .0000 9.8920- 155. 6754
11 .0000 9.9387- 155. 7634
11 .0000 9.9857- 155. 8498
11 .0000 10.0330- 155. 9347
5. 3000 3 • 7000 0 • 5003
5. 3000 3 • 7500 0 • 5003
5. 3000 3 • 8000 0 • 5003
S. 3000 3 • 8500 0 • 5003
5# 3000 3 • 9000 0 • 5003
5. 3000 3 • 9500 0 .5003
5. 3000 4 • 0000 0 .5003
5. 30 00 4 • 0500 0 .5003
5. 3000 4 • 1000 0 .5003
5. 3000 4 • 1500 0 .5003
5. 3000 4 • 2000 , 0 .5003
5* 3000 4 • 2500 0 .5003
5. 4000 1 .8000 0 .5003
5. 4000 1 .8500 0 .5003
5. 40 00 1 .9000 0 .5003
5. 4000 1 .9500 0 .5003
5. 4000 2 .0000 0 .5003
5. 4000, 2 .0500 0 . 5003
5^ 4000 2 • 1000 0 .5003
5. 4000 2 • 1500 0 • 5003
5. 4000 2 • 2000 0 .5003
5. 4000 2 .2500 0 .5003
5. 4000 2 • 3000 0 .5003
5. 4000 2 .3500 0 .5003
5. 4000 2 .4000 0 .5003
5. 4000 2 .4500 0 .5003
5. 4000 2 .5000 0 .5003
5. 4000 2 .5500 0 .5003
5. 4000 2 .6000 0 .5003
5. 4000 2 .6500 0.5003
5. 4000 2 • 7000 0 .5003
5. 4000 2 .7500 0 .5003
5. 4000 2 .8000 0 .5003
5. 4000 2 .8500 0 .5003
1 1 1
1 1 1 1
1 1 1 1 1 1
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124
11 • 5000 8.8763- 147. 2812
11 • 5000 8.9143- 147. 3261
11 • 5000 8.952 6- 147. 3701
11 .5000 8.99 14- 147. 4133
11 • 5000 9.0304-147. 4555
11 • 5000 9. 0699- 147. 4970
11 • 5000 9. 1096- 147. 5375
11 • 5000 9.1497-147. 5772
11 • 5000 9.190 1- 147. 6161
11 • 5000 9.2309-147. 6540
11 • 5000 9.2719- 14 7. 6911
11 • 5000 9.3134- 147. 7273
11 • 5000 9.3551-147. 7627
11 • 5000 9.3971- 147. 7971
11 • 5000 9.4394-147. 8307
11 • 5000 9. 482 I- 147. 8635
11 • 5000 9.5251- 147. 8953
11 • 5000 9.5683- 147. 9263
11 • 5000 9.6119- 147. 9564
11 • 5000 9.6557-147. 9855
11 • 5000 9.6999- 148. 0140
11 • 5000 9.7443- 14 8. 04 14
11 • 5000 9.7890- 148. 0 680
11 • 5000 9.8340- 148. 0937
11 • 5000 9.8793- 148. 1 187
11 • 5000 9.9246-140. 1426
11 • 5000 9. 9706- 14 8. 1657
11 • 5000 10.0166- 148. 1879
5. 9000 1 .4000 0 .5003
5. 9000 1 .4500 0 .5003
5. 9 0 0 0 1 .5000 0 .5003
5 • 9 0 0 0 1 .5500 0 .5003
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5. 9 0 0 0 1 .6500 0 «5003
5. 9 0 0 0 1 . 7000 0 .5003
5. 9000 1 .7500 0 .5003
5. 9000 1 .8000 0 .5003
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5. 9000 1 .9000 0 .5003
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5. 9000 2 .0000 0 .5003
5. 9000 2 .0500 0 .5003
5. 9000 2 .1000 0 .5003
5. 9000 2 . 1500 0 .5003
5. 9000 2 .2000 0 .5003
5. 9000 2 .2500 0 .5003
5. 9000 2 .3000 0 .5003
5. 9000 2 .350 0 0 .5003
5. 9000 2 .4000 0 .5003
5. 9000 2 .4500 0 .5003
5. 9000 2 .5000 0 .5003
5. 9000 2 .5500 0 .5003
5. 9000 2 .6000 0 .5003
5. 9000 2 .6500 0 .5003
5. 9000 2 . 7000 0 .5003
S. 9 0 0 0 2 .7500 0 .5003
1 1 1 1
1
1 1
1 I
1
1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1
125
12.0000 8.2020- 141. 4364 16. 4000 1 .0000 0 .5003
12.0000 8.2398- 141. 3883 16. 4000 1 .0500 0 .5003
12.0000 8.27-79- 141. 3403 16. 4000 1 . 1000 0 .5003
12.0000 8.3165-141. 2922 16. 4000 1 . 1500 0 .5003
12.0000 8.3554- 141. 2442 16. 4000 1 .2000 0 .5003
12.0000 8.3948- 141. 1963 16. 4000 1 .2500 0 .5003
12.0000 8.4345-141. 1484 16. 4000 1 .3000 0 .5003
12.0000 8.4747- 141. 1006 16. 4000 1 .3500 • 0 .5003
12.0000 8.5152- 141. 0526 16. 4000 1 .4000 0 .5003
12.0000 8.5561- 141. 0048 16. 4000 1 .4500 0 .5003
12.0000 8.5974-140. 9570 16. 4000 1 .5000 0 .5003
12.0000 8# 63 91 — 140. 9091 16. 4000 1 .5500 0 .5003
12o0000 8.6812- 140. 8614 16. 4000 1 .6000 0 • 5003
12.0000 8.7236-140. 8135 16. 4000 1 .6500 0 .5003
12.0000 8, 766 4- 140. 7658 16. 400 0 1 .7000 0 ,5003
12.0000 8.8095- 140. 7 180 16. 4000 1 .7500 0 .5003
12.0000 8.8531- 140. 6701 16. 4000 1 .8000 0 .5003
12.0000 8.8969- 140. 6224 1 6. 40 0 0 1 .3500 0 .5003
12.0000 8.941 1-140. 5745 16. 4000 1 • 9000 0 .5003
12.0000 8. 985 7-140. 5267 16. 4000 1 .9500 0 .5003
12.0000 9. 030 6— 140. 4788 16. 4000 2 .0000 0 .5003
12.0000 9.0758- 140. 4310 16. 4000 2 .0500 0 .5003
12.0000 9.1213-140. 3831 16. 4000 2 .1000 0 .5003
12.0000 9. 1672- 140. 3352 16. 4000 2 .1500 0 .5003
12.0000 9.2134- 140. 2872 16. 4000 2 .2000 0 .5003
12.0000 9.2599- 140. 2392 16. 4000 2 .2500 0 .5003
12.0000 9.3067- 140. 1912 16. 4000 2 .300 0 0 .5003
12.0000 9.3539-140. 1432 16. 4000 2 .350 0 0 .5003
126
12.4000 7.5515-136. 4125 16. 7000 1 • 0000 P .5003
12.4000 7.5955- 136. 2 830 16. 7000 1 .0500 0 .5003
12.4000 7.6399- 136. 1545 16. 7000 1 . 1000 0 .5003
12.4000 7.684 8— 136. 0269 16. 7000 1 .1500 0 .5003
12.4000 7.7301- 135. 9004 16. 7000 1 .2000 0 .5003
12.4000 7.7758-135. 7749 16. 7000 1 .2500 0 .5003
12.4000 7.8219- 135. 6503 16. 7000 1 .3000 0 .5003
12.4000 7.8684- 135. 5268 16. 7000 1 .3500 0 .5003
12.4000 7.9154-135. 4041 16. 7000 1 .4000 0 .5003
12.4000 7.9627- 135. 2 824 16. 7 0 0 0 1 .4500 0 .5003
12.4000 8.0104- 135. 1617 16. 7000 1 .5000 0 .5003
12.4000 8.0585- 135. 0420 16. 7000 1 .5500 0 .5003
12.4000 8. 1070- 134. 9231 16. 7000 1 . 6000 0 .5003
12.4000 8.1559-134. 8052 16. 7000 1 .6500 0 .5003
12.4000 8. 205 1- 134. 6882 1 6. 7 0 0 0 1 .7000 0 .5003
12.4000 8.2547-134. 5721 16. 7000 1 .7500 0 .5003
12.4000 8. 3047- 134. 4569 16. 7000 I .8000 0 .5003
12.4000 8.3550- 134. 3427 16. 7000 1 .8500 0 .5003
12.4000 8.4056- 134. 2293 16. 7000 1 .9000 0 .5003
12.4000 8. 4566— 134. 1 168 16. 7000 1 .9500 0 .5003
12.4000 8.5079- 134. 0051 16. 7000 2 .0000 0 .5003
12.4000 8. 5596- 133. 8942 16. 7000 2 .0500 0 .5003
12.4000 8.61 16- 133. 7843 16. 7000 2 • 1 000 0 .5003
12.4000 8.6639-133. 67 52 1 6. 7000 2 .1500 0 .5003
12.4000 8.7165-133. 5668 16. 7000 2 .2000 0 .5003
12.4000 8.7695- 133. 4594 1 6. 7000 2 «2500 0 .5003
12.4000 8.8227-133. 3527 16. 7000 2 .3000 0 .5003
12.4000 8.8762- 133. 2468 16. 7000 2 .3500 0 .5003
127
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130
ACKNOWLEDGMENTS
This author is deeply grateful to Dr. Robert E. Post for his guidance
and instruction throughout my graduate career.
I wish to thank,Dr. Gordon Danielson for his encouragement. I am
indebted to Mr. Duke Sevde, Mr. Howard Shanks, Mr. Paul Sidles, and
especially Dr. Chip Comstock and Mr. Curtiss Buck for their assistance in
the preparation of the samples. A special thanks goes to Dr. Glenn Fanslow
who furnished data, on pyrite.
I would like to express my appreciation to Dr. A. V. Pohm, Dr. Warren
B. Boast, Dr. J. 0. Kopplin, and the Engineering Research Institute for
their support throughout the years.
Last, but not least, I thank my wife, Vonda Sines Davies, for her
material and spiritual assistance.
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