286
IEEE
TRANSACTIONS
ON
MICROWAVE
THEORY
AND
TECHNIQUES,
VOL.
MTT-30,
NO.
3,
MARCH
1982
Measurement
of
the
Dielectric
Constant
and
Loss
Tangent
of
Thallium
Mixed
Halide
Crystals
KRS-5
and
KRS-6
at
95
GHz
WILLIAM
B.
BRIDGES,
FELLOW,
IEEE,
MARVIN
B.
KLEIN,
AND
EDGARD
SCHWEIG
Abstract
—The
dielectric
constants
and
loss
tangents
of
KRS-5
and
KRS-6
thallium
halide
mixed
crystals
have
been
measured
at
95
GHz
using
both
the
shorted
wavegnide
(SWG)
reflection
method
and
the
Fabry-Perot
(F-P)
transmission
method
on
samples
filfing
standard
WR-10
waveguide.
The
results—KRS-S
C:
=
31,
tan8
=
1.8x
10-2;
KRS-6
c;=
29,
tans
=
2
X
10–
z
—agree
reasonably
well
with
a
simple
theoretical
fit
to
the
far-in-
frared
Iatilce
absorption
of
TfBr
and
TICI
centered
at
about
1400
GHz.
The
dielectric
samples
were
hot-pressed
into
copper
wafers
with
dimen-
sions
matching
WR-
10
wavegoide,
and
then
machined
and
polished
to
obtain
flat,
parallel
air-dielectric
interfaces.
I.
INTRODUCTION
T
HE
MIXED
CRYSTAL
thallium
bromide-iodide
(KRS-5)
has
long
been
known
as
an
infrared
transmit-
ting
window
material
for
the
wavelength
range
0.6–40
pm.
However,
little
was
known
about
its
microwave
transmis-
sion
properties,
and
nothing
of
its
properties
in
the
milli-
meter
wave
range.
Recently,
long
fibers
of
KRS-5
have
been
fabricated,
and
their
infrared
transmission
has
been
reported
[1].
Soon
afterward,
propagation
in
a
KRS-5
fiber
at
95
GHz
was
demonstrated
[2],
thus
raising
the
possibil-
ity
of
waveguide
applications
in
the
millimeter-wave
range.
The
low-frequency
dielectric
constant
of
KRS-5
is
given
by
von
Hippel
[3]
as
32,
which
would
imply
a
very
small
fiber
diameter
for
such
a
millimeter-wave
guide
(less
than
1
mm
diameter)
and
allow
a
wide
range
of
dielectrics
for
cladding
material,
for
example,
Teflon
or
polyethylene.
Von
Hippel
also
reports
a
loss
tangent
of
2
X
10–3
in
KRS-5
at
10
GHz
[3],
while
Popa
and
Johnson
[2]
measured
a
value
of
2.3
X
10-3
at
37
GHz.
The
losses
are
expected
to
be
larger
at
higher
frequencies
due
to
lattice
absorption,
but
no
literature
values
are
available.
The
reported
low-frequency
losses
in
KRS-6
(thallium
bromide-chloride)
are
also
quite
low
[3].
Accordingly,
we
undertook
a
study
of
the
dielectric
properties
of
KRS-5
and
KRS-6
at
94
GHz
to
assess
the
potential
of
these
materials
in
a
practical
flexible
wave-
guide.
Our
measurement
techniques
utilize
samples
mounted
in
Manuscript
received
July
24,
198
1;
revised
October
16,
1981.
This
work
was
supported
by
the
Office
of
Naval
Research
under
Contract
NOOO
14-
79-C-0839,
and
by
the
Hughes
Aircraft
Company,
Independent
Research
and
Development
Funds.
W.
B.
Bridges
and
E.
Schweig
are
with
the
California
Institute
of
Technology,
Department
of
Electrical
Engineering,
Pasadena,
CA
91125.
M.
B.
Klein
is
with
the
Hughes
Research
Laboratories,
Malibu,
CA
90265.
standard
metal
waveguide,
in
contrast
to
past
work
at
95
GHz,
which
was
based
primarily
on
quasi-optical
tech-
niques.
Our
preference
arises
from
the
simplicity
and
accu-
racy
of
waveguide
techniques
and
a
novel
sample
mounting
configuration
which
eliminates
gaps
between
sample
and
wall.
Two
different
waveguide
measurement
techniques
were
used
with
the
same
samples:
1)
measurement
of
the
transmission
through
or
reflection
from
a
planar
slab
of
dielectric,
taking
into
account
the
multiple
reflections
be-
tween
the
two
faces—a
Fabry–Perot
(F–P)
resonator
(our
method
is
a
modification
of
that
described
by
Redheffer
[5]);
2)
measurement
of
the
reflection
from
a
sample
backed
by
a
short
(a
well-known
technique;
see
Roberts
and
von
Hippel
[4]).
In
addition,
samples
of
Teflon
and
Rexolite
were
mea-
sured
by
these
same
two
techniques
as
a
check
on
the
validity
and
accuracy
of
the
methods.
II.
SAMPLE
PREPARATION
In
preparing
samples
for
any
waveguide
measurement,
it
is
very
important
that
a
tight
fit
be
obtained
to
the
waveguide
walls.
The
errors
introduced
by
any
gap
be-
tween
the
wall
and
the
sample
increase
as
the
dimensions
of
the
waveguide
and
sample
decrease
and
as
the
dielectric
constant
increases.
In
order
to
obtain
the
best
fit
for
the
95-GHz
measurements,
the
samples
of
KRS-5
were
hot-
pressed
into
a
waveguide-shaped
opening
in
a
copper
wafer.
The
cross
section
of
the
opening
was
2.54X
1.27
mm,
corresponding
to
standard
WR-
10
waveguide.
This
open-
ing
was
formed
by
electroplating
a
thick
layer
of
copper
onto
a
precision
machined
aluminum
mandrel,
and
then
etching
away
the
mandrel.
Before
the
copper
electroplat-
ing,
a
thin
(5-pm)
layer
of
gold
was
evaporated
on
the
mandrel;
after
electroplating
and
etching,
this
gold
layer
remains
on
the
interior
surfaces
of
the
waveguide
and
prevents
oxidation
during
the
hot-pressing
procedure.
Samples
of
KRS-5
and
KRS-6
were
machined
from
commercial
stockl
into
billets
which
were
slightly
undersize
in
both
thickness
and
transverse
dimensions.
A
sample
was
then
inserted
into
a
wafer
opening
and
pressed
with
an
1
The
sources
of
the
materials
were:
KRS-5,
Harshaw
Chemical
Co.,
Solon,
OH;
KRS-6,
British
Drug
House,
Poole,
England.
0018-9480/82/0300-286$00
.75
01982
IEEE
BRIDGES
et
a[.:
DIELECTRIC
CONSTANT
AND
LOSS
TANGENT
OF
THALLIUM
MIXED
HALIDE
CRYSTALS
287
Fig.
1.
Photograph
of
the
copper-wafer-mounted
samples
of
KRS-5.
undersized
mandrel
at
an
elevated
temperature
until
it
expanded
laterally
to
fill
the
opening.
The
best
results
were
obtained
by
applying
-
2X
106
kg/m2
for
periods
of
6
h
at
a
temperature
of
250°
C.
The
wafers
with
the
sample
in
place
were
then
machined
to
~
the
desired
thickness
and
lapped
to
obtain
a
flat
polished
surface.
The
KRS-5
samples
prepared
in
this
manner
were
free
from
cracks
or
voids
under
inspection
by
microscope.
Typical
samples
are
shown
in
Fig.
1.
KRS-6
is
substan-
tially
less
ductile
than
KRS-5,
and
the
pressed
samples
of
this
material
were
not
as
free
from
defects.
Waveguide
wafers
containing
samples
of
Teflon
and
Rexolite
were
also
prepared
by
hot
pressing.
Because
of
the
high
ductility
of
Teflon,
lower
values
of
pressure
and
temperature
were
used
when
pressing
the
material.
111.
WAVEGUIDE
F–P
MEASUREMENTS
The
first
measurement
technique
used
the
wafers
as
F-P
resonators
in
a
waveguide;
different
combinations
of
sam-
ples
are
inserted
to
vary
the
length
of
the
resonator.
The
arraiigement
shown
in
Fig.
2(a)
was
employed
to
measure
the
transmission
and
reflection
from
the
dielectric
wafers.
A
waveguide
isolator
was
used
to
prevent
frequency
pull-
ing
of
the
klystron
source
by
reflections
from
the
samples;
a
second
isolator
was
used
in
front
of
the
transmission
detector
to
eliminate
reflections
from
any
detector
mis-
match.
A
reference
transmission
level
was
first
established
with
no
wafers
in
the
system.
Transmission
and
reflection
coefficients
with
the
wafers
in
place
were
then
determined
by
changing
the
precision
attenuator
until
the
detector
signals
were
equal
to
the
reference
level,
thus
eliminating
detector
nonlinearity
as
a
source
of
error.
The
power
transmission
coefficient
at
normal
incidence
through
a
plane-parallel
dielectric
sample
filling
the
wave-
guide
cross
section
is
easily
derived
by
the
standard
tech-
niques
for
handling
multiple
beam
interference
in
optics
(see,
for
example,
the
text
by
Hecht
and
Zajac
[12]).
The
transmission
is
given
by
P
transmitted
_
—
DETECTOR
n
~t-
l-l
WAFER(S)
DETECTOR
%4
f
A
i
ISOLATOR
I
/
II
KLYSTRON
WAVE-
PRECISION
(94
GHzI
ISOLATOR
ETE
R
ATTENUATOR
SLOTTEO
LINE
WAFER
Fig.
2.
Experimental
arrangements
used
for
the
waveguide
measurement
of
complex
dielectric
constant.
(a)
F–P
resonances
in
reflection
and
transmission.
(b)
SWG
method.
where
R
is
the
power
reflection
coefficient
of
a
single
air–dielectric
interface
and
a
+
jj3
is
the
complex
propaga-
tion
constant
for
TE,0
waves
in
the
dielectric-filled
region
!
.=;d&
=&n’/*
‘2)
B=++
-(+J2
(3)
where
X
is
the
free
space
wavelength,
a
is
the
width
of
the
waveguide,
c;
–
je~
is
the
complex
relative
dielectric
con-
stant,
and
tan
8
is
the
loss
tangent.
These
expressions
are
valid
for
low-loss
materials
(tan
8<
1).
The
reflection
coefficient
R
in
(1)
is
simply
the
Fresnel
reflection
from
an
air-dielectric
interface,
modified
by
the
change
in
phase
velocity
resulting
from
the
presence
of
the
metallic
waveguide
walls
For
t;=
32
and
k
=
3.0
mm,
R
%
0.76
in
a
WR-10
wave-
guide.
Equations
(l)–(4)
assume,
of
course,
that
all
the
power
remains
in
the
TE,0
mode
as
the
wave
passes
through
the
dielectric-filled
section,
despite
the
fact
that
many
higher
order
modes
are
above
cutoff
in
that
section.
We
argue
for
this
simplification
by
noting
that
the
planar,
normal
air–
dielectric
interfaces
and
the
constant
physical
cross
section
of
the
metallic
boundaries
do
not
encourage
mode
conver-
sion.
Nevertheless,
this
could
be
a
source
of
error
in
long
sample
sections.
Waveguide
wall
losses
in
the
sample
length
L
are
indis-
‘1
(1)
Pincident
[1-
Rexp(-2aL)]2
+
4R
sin2PL
LAJ
(1-
R)2exp(-2aL)
(1-R)2
288
IEEE
TRANSACTIONS
ON
MICROWAVE
THEORY
AND
TECHNIQUES,
VOL.
MTT-30,
NO.
3,
MARCH
1982
er
=
31,2
I
I
I
I
I
I
I
I
I
o
0.025
0.050
0.075
0.100
0.125
0.150
0.175
0.2W
0225
0250
THICKNESS,
cm
Fig.
3.
Measured
transmission
coefficients
and
fitted
F–P
curve
for
KRS-5
wafer
samples.
TABLE
I
EXPERIMENTAL
VALUES
OF
e;
AND
TAN
8
BY
THE
WAVEGUIDE
F-P
METHOD
AT
94.75
GHz
1
IUn
13merial
=;
Tan
6
Methoda
Fitb
Wafer
ThIcknemm
(m)
Combent
1
Km-s
31.2
1,8
X
10-2
T
0.01
0.335,
0.526,
0.686,
0.940
2
KfC1-5
30.5
2
x
10-2
T
0.075
0.315,
0.516,
0.678,
0.932
waferm
of
run
#l
machined
l
nd
3
ins-5
30.
h
-2
1.9
x
10
T
0.019
S.wr.m
am
run
2,
plue
0.414,
0.947
only
combimt
ions
up
to
3
mf
em
at
a
tim
taken
6
KSS-6
2S.5
2.3
X
10
-2
T
0.11
0.310,
0.35s,
0.4s3,
0.777,
0.973
5
KSS-6
2S.9
2.3
X
10-2
T
0.11
0.307,
0.357,
0.483,
0.775,
0.96S
wafers
of
r“n
#4
repolished
6
KM-6
25.5
1.4
x
10-2
T
0.0014
0.307,
0.357,
0.4s3
only
thinnest
3
wafera
of
run
#5
used
7
Teflon
2.04
9
x
10-3
R
0.0029
0.s1s,
1.2ss.
1.s49
s
Sexolite
2.56
2.6
X
10
-3
R
0.0061
0.812,
1.2S5,
1.88
Notes:
(a)
T
_
trmmmiaaion,
R
-
reflection
measured
to
fit
to
theory
(b)
Root
=an
nquare
deviation
of
data
point
n
f
mm
theory.
tinguishable
from
bulk
dielectric
losses
and
could
con-
stitute
a
source
of
error.
However,
standard
WR-
10
wave-
guide
loss
is
usually
quoted
as
4
dB/m,
which
would
yield
an
apparent
loss
tangent
of
4.4X
10’4
if
the
dielectric
filling
were
completely
lossless.
This
turns
out
to
be
at
least
an
order
of
magnitude
smaller
loss
than
the
samples
mea-
sured,
and
we
have
not
corrected
for
it.
The
transmission
and
reflection
for
all
possible
combina-
tions
of
wafer
thicknesses
were
measured
at
a
fixed
frequency
of
94.75
GHz.
These
data
were
then
used
as
input
to
a
computer
program
that
systematically
varied
the
complex
dielectric
constant
to
yield
a
least-squared-error
fit
of
the
theoretical
transmission
or
reflection
coefficient
to
the
data.
To
reduce
the
data
with
this
program
the
user
specifies
a
range
of
complex
dielectric
constant
to
be
explored
for
a
possible
fit
by
specifying
maximum
and
minimum
values
of
a
and
~
and
the
step
size
for
each.
Starting
at
one
corner
of
the
(a,
~)
space,
the
program
computes
the
sum
of
the
squared
differences
between
the
theoretical
expression
(1)
and
the
measured
transmissions
for
all
samples
lengths.
The
program
repeats
this
calcula-
tion,
stepping
a
through
its
complete
range,
and
stores
the
minimum
rms
error
found
and
the
value
of
a
that
gives
the
minimum.
The
program
then
steps
~
and
repeats
this
procedure.
If
the
new
minimum
is
less
than
the
previous
minimum,
it
continues
to
step
~;
if
not,
it
prints
out
the
previous
minimum
and
the
corresponding
values
of
a
and
~.
These
are
converted
to
c:
and
tantl
by
(2)
and
(3).
Some
idea
of
the
sensitivity
of
this
method
can
be
gained
by
tracking
the
minimum
rms
error
as
the
program
runs;
an
BRIDGES
et
ai.:
DIELECTRIC
CONSTANT
AND
LOSS
TANGENT
OF
THALLIUM
MIXED
HALIDE
CRYSTALS
289
increment
of
5–
10
percent
in
either
c;
or
tan,ti
away
from
the
final
value
typically
doubled
the
rms
error
for
KRS-5
or
KRS-6.
Several
sets
of
measurements
were
made
with
the
KRS-5
and
KRS-6
wafers
under
different
conditions
as
specified
in
Table
I.
Fig.
3
shows
the
data
points
corresponding
to
a
specific
run
for
KRS-5
and
illustrates
the
quality
of
the
fit
to
the
theoretical
transmission
(solid
curve).
The
reduced
accuracy
for
the
KRS-6
measurement
is
presumed
to
be
due
to
sample
imperfections,
which
had
an
especially
strong
effect
when
several
samples
were
stacked
together
to
give
large
thicknesses.
In
order
to
check
on
the
accuracy
of
this
technique
and
its
ability
to
measure
still
lower
values
of
loss
tangent,
we
also
measured
the
dielectric
constant
and
loss
tangent
of
Rexolite
and
Teflon.
The
resulting
values
were
c;
=
2.56
tan8=3X10-3,
for
Rexolite
c;
=
2.04
tan8=
9X10-3,
for
Teflon.
(5)
The
measured
values
of
dielectric
constant
are
in
good
agreement
with
literature
values
[6]–[8]
for
Rexolite
(2.47–
2.58)
and
Teflon
(2.0–2.
1),
while
the
measured
values
for
loss
tangent
are
larger
than
the
literature
values
[6]-[8]
for
Rexolite
(1.2X
10-3)
and
Teflon
(2X
10-4-3X
10-3).
We
should
note,
however,
that
the
literature
values
cited
cover
the
frequency
range
70–400
GHz,
and
that
the
tan
8
values
do
not
exhibit
a
simple
increase
with
frequency
over
this
range;
thus
it
is
somewhat
difficult
to
cite
an
“accepted”
value
for
tan
8
at
95
GHz.
The
sensitivity
of
the
curve-fit-
ting
program
was
also
somewhat
reduced
for
the
low-di-
electric
constant
materials;
a
10-
to
20-percent
change
in
c:
or
tan
8
away
from
the
final
value
doubled
the
rms
error.
In
any
case,
our
measured
tan
8
values
are
high,
and
we
do
not
known
if
this
discrepancy
is
due
to
metallic
waveguide
wall
loss
or
sample
imperfection.
However,
since
our
mea-
sured
values
of
tan
8
for
KRS-5
and
KRS-6
are
larger
still,
we
feel
the
method
should
be
reasonably
accurate
for
those
materials.
From
our
experience,
it
appears
that
in
the
case
of
high-dielectric
constant
material,
the
best
data
are
obtained
from
the
measurement
of
the
transmission
coefficient,
whereas
for
low-dielectric
constant
material
the
reflection
coefficient
should
be
used,
and
a
fit
made
to
the
reflection
equation
analogous
to
(1)
R[l–exp(–2aL)]2
+
4R
sinzpL
P
reflected
_
(1-
R)2exp(-2aL)
(1-R)2
—
_
P,ncident
[1-
Rexp(-2aL)]2
+
4R
sin2~L
“
(1-
R)2exp(-2aL)
(1-R)2
(6)
IV.
WAVEGUIDE
REFLECTION
MEASUREMENTS
In
a
second
experiment
we
measured
the
complex
reflec-
tion
coefficient
from
a
single
wafer
inserted
at
the
shorted
end
of
a
waveguide.
An
experimental
arrangement
similar
to
the
one
described
by
Roberts
and
von
Hippel
[4]
was
used
for
the
reflection
measurements,
as
shown
in
Fig.
2(b).
A
short
was
placed
at
the
end
of
the
empty
waveguide,
creating
a
reference
standing
wave
pattern.
The
position
of
a
node
was
determined
with
a
slotted
line
(TRG
Model
W740).
A
wafer
was
then
inserted
between
the
end
of
the
waveguide
and
the
short,
and
the
position
and
magnitude
of
the
standing
wave
were
again
determined
with
the
slotted
line.
As
before,
the
precision
attenuator
was
used
to
return
the
detector
output
to
the
reference
level,
so
that
the
VSWR
accuracy
depended
solely
on
the
attenuator
calibra-
tion,
and
not
on
the
detector
linearity,
The
measurements
were
made
at
a
frequency
of
94.75
GHz.
The
theoretical
equation
relating
the
shift
of
the
VSWR
minimum
from
the
reference
position
and
VSWR
magni-
tude
to
the
complex
dielectric
constant
of
the
sample
is
transcendental
and
implicit
in
dielectric
constant
()
2mS
VSWR-l
–
jtan
~
j~g
tanh[(a+
jP)L]
=
__
g
[(a+
jB)L]
2
TL
()
21rs
1
–
jVSWR-
1
tan
—
Ag
(7)
where
Ag
is
the
wavelength
in
the
air-filled
guide
and
S
is
the
distance
from
the
dielectric
interface
to
the
first
node
of
the
standing
wave
in
the
air-filled
sections;
S
is
also
equal
to
the
shift
in
position
of
the
standing
wave
mode
when
the
sample
is
inserted.
As
before,
the
assumption
is
that
the
power
remains
in
the
TE,0
mode
throughout,
even
though
higher
order
modes
can
exist
in
the
dielectric-filled
section.
The
right-hand
side
of
(7)
contains
the
measured
quanti-
ties
and
is
evaluated,
resulting
in
a
single
complex
number.
The
propagation
constant
a
+
jfl
is
then
determined
numerically
from
this
complex
number
and
c;
—
jc~
from
a
+
j~
by
(2)
and
(3).
A
computer
program
to
solve
these
equations
was
written
along
the
lines
of
the
program
used
by
Nelson
et
al.
[9].
The
values
of
complex
dielectric
constant
obtained
for
the
samples
of
KRS-5
and
KRS-6
are
given
in
Table
II.
The
agreement
between
the
various
samples
is
quite
good
and
provides
an
increased
level
of
confidence
in
the
results.
In
order
to
provide
a
further
check
on
our
experiments,
we
measured
the
dielectric
properties
of
Rexolite
and
Teflon
at
95
GHz
and
obtained
values
similar
to
those
obtained
with
the
F–P
technique.
Unfortunately,
the
wafer-mounted
samples
of
Teflon
and
Rexolite
were
not
thick
enough
to
yield
good
results.
In
the
case
of
very
low-loss
low
dielec-
tric
constant
materials,
it
is
desirable
to
use
samples
that
are
significantly
larger
physically
because
the
additional
losses
when
the
dielectric
is
introduced
in
the
waveguide
must
be
larger
than
the
losses.
due
to
the
metallic
walls.
Accordingly,
we
cut
longer
samples
of
Teflon
and
Rexolite
(
-13
mm)
for
a
slip
fit
in
WR-10
waveguide
from
the
same
lots
of
Teflon
and
Rexolite
used
for
the
wafers.
Our
290
IEEE
TRANSACTIONS
ON
MICROWAVE
THEORY
AND
TECHNIQUES,
VOL.
MTT-30,
NO.
3,
MARCH
1982
TABLE
II
EXPERIMENTAL
VALUES
OF
c;
AND
TAN
6
AT
94.75
GHz
BY
THE
Sample
Thickness
(m)
0.942
o.9&o
0.686
o.41fl
0.973
0.77’7
0.483
0.358
12.532
12.517
14.030
13.872
results
with
these
samples
were
SWG
MSTHOD
Mat
erial
SRS-5
KRS-5
SRS-5
SRS-5
KRS-6
SRS-6
KM-6
KRS-6
Rexolite
Rexolite
Teflon
Teflon
c~=
2.4
tan8=3.3X10–3,
for
Rexolite
C;=l.9
tanfS
=4X10-3,
for
Teflon.
As
a
check
on
the
1O-GHZ
values
of
c;
and
tan
8
quoted
without
reference
by
von
Hippel
[3]
for
KRS-5,
we
also
made
a
waveguide
reflection
measurement
at
10
GHz,
using
a
setup
similar
to
the
one
depicted
on
Fig.
2(b).
In
this
case,
the
samples
were
machined
to
size
and
slipped
into
the
end
of
a
standard
X-band
waveguide.
The
average
values
for
the
complex
dielectric
constant
of
KRS-5
at
10
GHz
were
e’=
30.6
tan8=4X10–3.
V.
COMPARISON
OF
THE
Two
METHODS
Two
different
methods
of
measurement
were
used
prim-
arily
to
gain
added
confidence
in
the
results.
However,
it
may
be
useful
to
make
some
comparison
between
the
two
techniques.
The
shorted
waveguide
(SWG)
method
requires
a
slotted
line
or
other
means
of
determining
the
shift
in
standing
wave
position
while
the
F–P
method
does
not:
since
slotted
lines
are
increasingly
expensive
and
difficult
to
make
at
shorter
wavelengths,
this
is
a
definite
advantage
for
the
F–P
method.
On
the
other
hand,
the
SWG
method
requires
only
a
single
sample
and
no
curve
fitting,
while
the
F–P
method
requires
several
samples
to
vary
~L
in
order
to
remove
ambiguity
and
obtain
reasonable
accuracy
by
curve
fitting.
(The
F–P
method
could
perhaps
be
used
with
a
single
sample
if
a
wide
range
swept
frequency
source
were
available
to
vary
/3
rather
than
L,
but
this
is
another
expensive
item
at
millimeter
wavelengths.)
The
SWG
method
has
“preferred”
lengths
of
samples
(see
[5])
that
31.7
31.9
31.1
31.5
30.
s
31.0
30.8
30.
s
2.41
2.41
1.94
1.98
Tan
6
1.7
x
10
-2
1.7
x
10
-2
1.9
x
10
-2
1.6
X
10-2
1.1
x
10-2
3.3
x
10-2
3.6
X
10
-2
1.0
x
10-2
3.4
x
10-3
3.2
X
10
-3
4.1
x
10-3
4.7
x
10-3
give
more
accurate
results;
the
F-P
method
also
should
yield
more
accurate
results
with
fewer
sample
points
if
the
lengths
happen
to
be
resonant.
The
two
methods
should
be
comparable
in
their
sensitivity
to
wall
losses,
sample
finish,
flatness,
fit
in
the
waveguide,
etc.
However,
the
SWG
method
has
the
added
problem
of
a
possible
gap
in
the
fit
between
the
sample
and
the
end
short.
VI.
FREQUENCY
DEPENDENCE
OF
DIELECTRIC
PROPERTIES
As
stated
earlier,
no
measurements
of
the
dielectric
properties
of
KRS-5
or
KRS-6
above
10
GHz
have
been
reported
previously.
However,
measured
values
are
availa-
ble
at
lower
frequencies,
especially
for
KRS-5.
Our
mea-
sured
values
of
c;
at
10
and
94
GHz
for
KRS-5
are
essentially
the
same
as
the
values
reported
by
von
FIippel
[3]
at
102-107
Hz
and
1010
Hz.
In
order
to
compare
our
measured
values
of
loss
tangent
for
KRS-5
with
the
other
values,
we
have
plotted
all
measurements
as
a
function
of
frequency
in
Fig.
4.
It
is
clear
that
the
frequency
variation
can
be
divided
into
two
separate
regimes.
Below
-108
Hz,
ionic
conductivity
dominates
and
the
loss
tangent
varies
as
1
tan
8
=
277fpf;Eo
(8)
where
f
is
the
frequency
and
p
is
the
resistivity.
As
ex-
pected,
the
data
points
closely
follow
a
l/~
variation,
corresponding
to
p
=
2
X
108
Q.
cm
and
c;=
31.
The
ab-
sorption
at
microwave
and
millimeter
wavelengths
appears
to
be
dominated
by
the
low-frequency
tail
of
the
strong
lattice
absorption
centered
at
-1400
GHz.
If
we
model
the
lattice
vibration
as
a
single
harmonic
oscillator,
the
loss