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FROMDistribution authorized to U.S. Gov't.agencies and their contractors;Administrative/Operational Use; JAN 1966.Other requests shall be referred to AirForce Materials Laboratory, Attn: MAYT,Wright-Patterson AFB, OH 45433.
AUTHORITY
AFML ltr, 7 Dec 1972
THIS PAGE IS UNCLASSIFIED
Jr•
AFML-TR.66-28
Measurement of
OA Dielectric Parametersof High-Loss Materialsin Distributed Circuits
W. B. WestphalLaboratory for Insulation Research
LL" Massachusetts Institute of Technology
Cambridge, Massachusetts-- _
Technical Report AFMI-TR.66o28
Janaary, 19b6
This docmnent i Abject to special export controls and eachtransmittal to foreign governments "- fore;gr natimal's m~aybs made only- with prior approval of AF Materials Laboratory
(MAYT), WPAFB, Ohdo 45433
AIR FORCE MATERIALS L.ABORATOR Y I~~Y SRESEARCH AND'TEChNOLOGY DIVISION L'U.•z
'WRIGHT-PATTERSON AIR FORCE BASE, GHiO U.,A,0
't-
VAL
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• : :.,•. •,
SFo r m•Z
MESUREMENT OF' DIELECTRIC PARAMETERS OF FUGHoLOSS
~MATERIALS IN DISTRIBUTED CIRCUITS
Q W.B. Westphal -
Laboratory for Insulation ResearchMassachusetts Institute of Technology
Cambridge, Massachusetts
Ja P066I
4) 3 5 p,
AF - 7 3 71
( 7,371701
This document is subject to special export controls and eachtransmittal to foreign governments or foreign nationals maybe made only with prior approval of AF Materials Laboratory
(MAYT). WPAFB, Ohio 45433
FOREWORD
This report was prepared by the Massachusetts Institute of
Technology, Laboratory for Insulation Research, Cambridge,
Massachusetts, under USAF Contract AF 33(615)-2199. This
contract was initiated under Project No. 7371, "Exploratory
Development in Electrical, Electronic, and Magnetic Materials,"
Task No. 737101, "Dielectric Materials. " The work was
administered under the direction of the AF Materials Laboratory,
Research and Technology Division, with W., G. D. Frederick
acting as project engineer.
This technical report has been reviewed and approved.
State BranchMaterials Physics DivisionAF Materials Laboratory
SLj
V
Illustrations
Page
Fig. 1. Inverse standing-wave ratio and xo/k for 3"infinite -length" nonmagnetic materials(TEM mode).
Fig. 2. Sample thickness d (in cm) for electrical .4thickness of 0.3 radians for various mag-nitudes of (E*/E 0)(*Io) vs. frequency.
Fig. 3. Method of clamping silvered sample in 5coaxial line.
Fig. 4. Soldered sample in a thin-walled (0.005 5to 0. 010") tubing.
Fig. 5. Magnetic ring sample in coaxial line. 6
Fig. 6. Sample clamped in a thin-walled (<0. 10") 7wave guide.
Fig. 7. Equipment for measurement of input 7impedance and transmission.
Fig. 8. Coaxial phase shifter for fixed frequency. 8
Fig. 9. Suggested cavity measurements for 9determining IA of conductors.
Fig. 10. Lumped-capacitor sample at end of co- 10axial line.
Fig. 11. A, nonmagnetic three-layer dielectric. 11
rr
MEASUREMENT OF DIELECTRIC PARAMETERS OF HIGH-LOSS
MATERIALS IN DISTRIBUTED CIRCUITS
by
W.B. Westphal
Taboratory for Insulation ResearchMassachusetts Institute of Technology
Cambridge, Massachusetts
Abstract: Measurement techniques for determination of the complexdielectric constant and complex permeability are given a short
review with emphasis on the problems encountered in practical
high-loss materials. Typical calculations and descriptions of
special sample holders are included.
Introduction
For purposes of discussing measurement techniques, we can divide
electromagnetic energy-absorbing materials for perpendicular impedance
into several categories.
1. In uniform materials the macroscopic parameters t* and gP are
invariant along the axis of wave propagation, They may be (a) isotropic
or (b) anisotropic, depending on whether or not these parameters are the
same in other directions also. When reflected as well as traveling waves
are considered, the question of reciprocity arises, and additional classifi-
cations are: (c) for reciprocal materials, (d) for nonreciprocal.
2. Uniform-layered materials are composites of layers, each layer
being uniform, and the thickness of the junction is very small compared
to wavelength in adjacent layers.
3. Nonuniform materials have i* and/or 10, varying gradually along
the axis of propagation. The nonuniformity may arise from external
shaping (tapers) or gradual change in chemical composition or loading.
Combinations of uniform and nonuniform layers constitute a nonuniform
material.
*G-I--.-
-2-
Obviously all layered materials may be symmetric or unsymmetric
in reference to their center plane.
Composite materials of mixed ingredients are uniform if particle
szcs arc s,,allA compared t&o wavelengthl ad iH the materials are homo-
geneous. Clumping of particles causes electrical inhomogeneities; the
measured values of i* and • will then be dependent on sample thickness
and how the measurement techniques are affected by scattering.
Measurement Techniques
The general methods for determining both Er and ;[ are (a) the in-
put impedance measurements with sample in two positions using resonant
cavities or standing-wave detectors; (b) perturbation measurements with a
small sample in two positions of resoaant cavity; (c) combination of input
impedance and transmission measurement.
In (a) the use of resonant cavities is limited by the need for at least
moderately high loaded Q's (50 or more) to obtain accurately measurable
amplitude resonance characteristics. When approximate sample properties
are not known before measurement, this is a severe restriction. The
standing-wave method limitations arise at much higher values of loss
(lower values of impedance) when the sample in both positions has the
same impedance, that of an infinite-length sample. Then only the
ratio */AA * will be measured with poor accuracy. because the separation
of node and sample face will be very small. Figure 1, for nonmagnetic
materials, illustrates the difficulties. The x0 values are generally small
fractions of a wavelength, and inverse standing-wave ratios are high
except for materials having very high K' values and/or very high tan 6
values. Also the fractional errors in dielectric constant and loss are
always nearly twice the error in experimental quantities because of the
suare-law dependence. For example, for K' and tan 6 = 10, Emin /Emax
M 75 and x0A =. 012 or approximately • (Ax/4.. If the node position is
located to within l/ZO of Ax, a reasonable error, and EminEmax is
accurate to 5%, the resultant error in K" is 14%.
In the two-position measurement system. good results dipend mainly
on having a thin enough sample to avoid "indinite-lenSth" conditions and
3I
., - ±-0.1,
S" .*: :"1 "___ __ __ __. :
0.00 0.I I I0 100ton
Fig. I. Inverse standing-wave ratio and Xo/k for "infinite-length" nonrnagnetic materials (TEM mode).
making good contact with the metallic conductor(s). If the approximate
magnitude of the product .*/ o"p*/po is known, the physical thickness
of ssmplh for an electrical thickness of 0. 3 radian can be readilyS~determined (Fig. 2). This thickness assures good measurements in the
sense that the experimentally measured quantities vazy almost linearly
S~with sample parameters, and nearly separate measurements of electric! and magnetic paramneters are achieved. Alecu higher order modes can
hardly exist. Limitationw of the method arise when sample thickness
must be so small to achieve electrical thinness that the sample no longeris representative of bulk material; e. g., evaporated 1fires often have k
dif~ferent electrical parameter s.H-igh-constant and/or high-loss samples require good contact with
the conductor(s) in the measurement system. For example, in a l-incb
~!
-4-
E T1
S;---4- -4-- - r- f- +-+ -4 -. 4- --
, - ._: • • __ .t -¢ f .....
' j@-f-
j 4 uý 4
Freqiecy an cycle per send
Fig. 2. Sample thickness d (in cm) for electrical thick-hess of 0. 3 radians for various magnitudes of(EVE 0/L 4/s0 versus frequency.
60-ohm coaxial line a clearance of 0. 0005 inch on the center conductor
causes a 13%• error in measuring a material with K' 1 00. Correction
equations and charts are given in the Appendixes IU and IXIC. Usuallythe clearance cannot be defined with suficic'ent accuracy for good measure-
ments and intimately bonded electrodes should be added. To avoid leakage
and insure contact the sample holder of Fig. 3 is used. A peripheral
coat of silver paint is allowed to overflow onto the faces which are clamped
" ~between silver conductors, one of which is thin-walled and collapses to
' ~accommodate variatilo. "_• sample thickness. The samples must bestrong enough to withstand the compressive strain: repeated use dulls
S~the tubing edge which can be reformed by lathe turning. The silver on
oIo
Frwerc in cyle seon
5
ISilver inlay\
"____._____ ICopper Sample Thin wall silver tubing
Fig. 3. Method of clamping silvered sample in coaxial line.
the faces introduces additional fringing field and limits the accuracy of
measurements to about 5%. A better arrangement uses coated samples
soldered to thin-walled tubing as shown in Fig. 4.
'Thin wall silvertubing
Fig. 4. Soldered sample in a thin-walled (0. 005 to 0. 010") tubing.
In measuring the magnetic properties of materials, ring-shaped
samples are sometimes used in a coaxial line or cavity. 1) This procedureleads to a different and more subtle source of error. If the electricalthickness along either the axa' or radiai direction exceeds 0. 3 radian.
r'.
-6-
. Ring E- FIELDSsomple
line
(c)(a) (b) H-FIELDS
Fig. 5. Magnetic ring sample in coaxial line: (a) physicalarrangement, (b) electric and magnetic fields inradially thin sample, (c) electric and magneticfields in longitudinally thin sample.
other i,,odes exist which are readily coupled by the magnetic field as
sh- -n in Figs. 5a and 5b. Good contact at coaxial conductors by a full-
sized sample reduces chance for this type of error. Highly conducting
samples car give false diamagnetic readings caused by eddy current
shielding of the sample interior.
SIn hollow waveguide the same ideas apply, but in addition one can
possibly deform the center of the broad faces of rectangular guide to
make contact with a sarr le coated on the longer edges only (Fig. 6).
The two-position, thin-sample technique gives best separation of
electric and magnetic parameters. When thick samples only can bc used,
the input-1mpedance measurement givres the ratio K'n/I' and the difference
in loss angles. Since .his is essentially a measurement of the ratio of
magnetic to electric field strengths, nam-nely, ratio of two different kinds of
uuits, this deterrrm.nation will be done with less precision than achieved
in measurement of the propagation function. rhe latter can be measured
7
1- Fig. 6.
7 &c. Sample Sample clamped in a
thin-walled ( < 0. 10)wWa-eguide.
T''hin wall waveguide
It
Isolato wave Sample holder -indicator J
ii
Oscillator ,-audio null indicator
"Islao Phase L•VariableSquatre! shif ter Jattenuator
Squlatre
modulator
Fig. 7. Equipment for measurement of input impedanceand transmission.
with either electric or magnetic indicators. Figure 7 is a schematic
diagram of equipment for combination measurement of input impedance
t •and transmission. A suitable phase shifter for coaxial line is shown in
Fig. 8. The calculation procedure follows the two-position method
1 • I
-8-
h.
z2I-s
* S
'N'S
.' *�1.a�1...o UEA
*YL.o4-o $4
'44C �0
4-4-
* '44
$40
0) '44
$4
-� 4.''44__ .44
*14-4
IU
00
I '.4
I if
-9 -
cavity
KlystronI
Sow-tooth , ments for determining JA*generator Differential of conductors. Laser head
O e aplifier would be mounted on cavity.Sample surface is bottom
swI c of measuring cavity.
except that 702/Z01 and y 2 (e. g., 12 and 15, Appendix ID) are given di-rectly by the input impedance measurement and the change in amplitude
and phase per unit length of sample increase.
Metallic materials, even as thin foils, have attenuations greater
than can be readily measured in transmission. The sample can serve as
a conducting wall in a waveguide, a resonant cavity, or surface-guided
wave system. A proposed measurement system is shown in Fig. 9. A gas
laser interferometer is suggested to measure the position of the cavity
wall, so the small changes in resonant frequency due to the ji' term can
be detected. Measurements of the complex permeability of iron were
made some years ago by Dr. Rado at NRL. He superimposed a
saturating magnetic field to reduce g* to A to establish a nonmagnetic
reference condition in a coaxial cavity with the sample serving as center
conductor.
The small-sample technique is similar to common ferromagnetic reso-
-10-
Signal
,, , 1 Zc generatorYI ZC1
L50modulator plunger
IZ{ }Tuned audio Measuringfrequency amplifier line
- with outputindicator ••
detector
Fig. 10. Lumped-capacitor sample at end of coaxial line: (a) sample inline, (b) equivalent circuit, (c) equipment arrangement.
nance experiments3) with external d-c field. A spherical sample placed in
two positions in a cavity, or in two different cavities, allows both E* and
A to be determined. Since the dipole field corrections4) used are
derived from magneto- and electrostatics, the diameter of the sphere
should be 0. 1 radian or less. At high frequencies very small spheres
(0.005-inch) are required, and surface finish becomes important. To
cover a wide range of frequencies, a series of spheres are required.
For nonmagnetic materials, rodlike samples can be used as lumped
capacitors at the end of a coaxial line (Fig. 10).
Measurements on uniform-layered materials with parallel electric
iitilds to determine t* and g.* have progressively less meaning when
the electrical thickness along layer rises above 0. 3 radian.
With uniform-layered materials, the two-position method for mag-
netic dielectrics or the single-position measurement of nonmagnetic
dielectrics have progressively less meaning as frequencies rise, so that
the total electrical thickness exceeds 0. 3 radian. In an extreme case
the measurements are meaningless as an example will show. Figure 11
shows a symmetrical-layered sample having nonmagnetic pararmters
S- 11 -
i
K' = 3 K' 100 K' = 3
6 =0 tan6=0.1 6 =0
Thickness (in radians) 0. 512 0. 300 0. 512
Relative physical thickness 10 1 10
Fig. 11. A nonmagnetic thr%ýe-layer dielectric.
for simplicity. Measurements against the short circuit place the high-
constant portion in a region of high field strength and and give an effective
K' value of 9.22 and an equivalent length of 1. 88 radians. In the open-
circuit measurement, the high-K center receives lower field strength,
the effective constant is 7. 78 and the length is 1. 73 radians. The com-
bined two-position calculation gives K' = 7.4 and K 0. 44. The average
K value in a uniform field is 2d~lc + d2 Kj = 7. 68. If many of these three-
layer laminates are stacked, the phase change and attenuation rer unit
length will vary as each laminate is added, but if enough layers are used,
an average value can be defined (if only one mode exists). Because of
internal reflections between successive high-K layers, the K and tan 6values obtained will not be the same as the uniform-field value. With a
thicker high-K section, the difference would be appreciable. The same
reasoning regarding the necessity for overall thinness applies to nonuniform
layers.Thus absorbers are best defined by input impedance (or reflection
factor) as a function of angle of incidence, not by attempts to measure or
define t* and p
- 12 -
APPENDIX I
Calculation Procedures for Standing-Wave Methods
A. General Notation:
x = distance from face of sample (Fig. AL. 1) to first minimum.0
AN = node shift toward short with introduction of sample (N a-N )
Lx = width of minimum with measured at twice minimum power
points (2/I current ratio with square-law, detector) corrected
for line lobs between mi.imum and sample face.
N = node reading, sample in.
Nq = node reading without sample, X/4 spacer in.
U = (X /c)ý- 0 for TEM modes.
w l+U.
X = wavelength in air-filled section of line.
X cutoff wavelength = 3.412586 times radius ol guide for TEll
mode, = twice broad dimension in rectangular waveguide
TE1 0 mode.
E mi/E = inverse standing-wave ratio = w- xmin max -- c15
B. General Relations for Nonmagnetic Sample X/4 From Short
x0 aN q- ,(r T
I- /h\]O~_____ _____Axa
Ax~nk AXAx ax s'lý
~Izz
E Emin Zxo0__d_________-_ns _ 01 1l- J - tan W
L B max1
0' cothy•td 1 ZBd : Zj• (Amt. 2)
Fig. A. -1.
=Yl 01
m l ml u to m imm ~ l lmm u ig A Lm -1. m u • m w mm lmn lm ~ mw mml u m~m m m i l I• )
-13-
y 2 d is determined from charts or tables of cothx/x in literature or
Appendix ILIA if 3ample is less than Xs/4 in thickness:
2
u-- T y2 d) (Al.3)
C. Thin Sample Calculations
Restriction 1:
Y2 d < 0. IV for 0. 5A error,
< 0.15r for 1% error,
< 0. 3V for 5% error.
ZO I
- w"• + u(Al. 4)
Restriction 2:2-o x z01 -) Afx 1 rUf(Emi )az << Iland tan• > 1, then =- + j cot
andt
Ice : tan + u"A .5
goAX (lA. 6)
Restriction 3:
tan 2wA d_!R < 0. 1 for 3% error,
< 0. 15 for 1% error,
< 0. 3 for 3% error.
Ie + A 'N JAI. 7)
WT!
- 14 -
If after calculating K* with Restrictions 2 or 3 satisfied, Restriction I
is not satisfied, the value of. w* already calculated can be corrected if
if y2 d < 0. 5r by noting that
Z 01 'Y2 2[.
T_- =•- tanhy 2 d2•- [Y 2 d - .(v/-d)3]. 1•..8)
Then
K r + AK' - jA*" (A. 1. 9)correctf~d ab~ort ialc. ' J"'ts. c.l
where
2
1 Awd 2 2]AK' -r k-7 (s. c. s ) (l.c. A 1 0
2K" -2 (2wd K" (K w - u) (A. I. 11)
" = •s/ "rc"
D. General Relations for Magnetic Samples, TE or TEM Waves
Z, 01 U 01
10
- 15 -
1/2
tanh yd = r (A. L. 13)
From charts of tanh (a + jb) = r18
y 2 d = a + (A. L 14)
y 2 y 2dYZ -Y d A (A. 1. 15)
tan 6m = -tan (4-*) (A. L 16)
, AB (A. L 17)0 (1 + tan 6 )1/Z
A- = -(A.L 18)0
i. " A Uin1÷4}$ito +-=•- sin (0 - ,)(A. 1. 19)
0
For TEM mode only
A -o (+4 (A. 1. l8a)to 7 r
tan 6 d * tan 1+#) (A. L 19a)
Two sample calculations follow in Appendix m.
E. Thin •gnpetic Saple Calculations
With Restrictions I and 3 satisfied for sample in both positions:
AN, (A. LZ)
I 1
-16-
(A. 1. 1)
AN +d.l0
4o ("" A. I.22 )
E' AN2 4-d u /oi
,~ ~~(o Po w•Z(•, A .2
Gt Ax2 + Ao (A. 1. 23)0 00) IA
For TEM modes:
- N -(A. 1. 22a)
0
A�- •(A. 1. 23a)
0
if Restriction 3 is satisfied only for sample at short,
+u ,, ,(A.1. Z4)
which reduces if Restriction 2 is satisfied to
\0ol ijo/
ta -WI 0 (A. 1.2Z5)
0~
I 1 lAX 2Z (A. 1. 26)
r- 17 -
If after calculating i*/E and lfbo from Eq. 20 through Z6 Restriction I
is not satisfied, the values already calculated can be corrected if
Y2 d < 0. 5 r by making use of the series expansion as in Eq. A. I. 18. Then
=K = Kshort caxc - jAK" (A. I. 9)
0
•" • •mshort calc. ÷A
go + AA - :^K"ý (A. 1. 27)
where, for TEM mode,
AK, = ?- ( ) (K') - (K,)- 2 )- 2KPIWK',11 (A.1.28)
I (.Z aw(x 2 (sc 012) + 2IcMK',K"jI (A. 1. 29)
2&.a- (, [x'(c.a, -. 1,)2- Zic.,.A . (2wd)• [if (( C)Z- (Ki )z )-I. ,KwK;mK"I I (A. 1. 30)
".e)2).)' -n 20 (. 1. 31)
F. Input Impedance of Infinite Length Sample (TE or TEM waves)
For nounmagnetic dielectrics
•'-•"� u u+ (z--l (A.1. 32)0B
For conductors g" >> c'; V and tan are smanll and equal in
mapitude. Then
•" = '"-z-' (A. 1. 33)
tw' w( i T)
-18-
- (A. I. 34)
a will be in zeciprocal ohm-cm when e is given in fd/cm and X in cm.
APPENDIX II
Corrections for Sample Fit in Coaxial Line
Letting D1 = diam. of center conductor,
D2 = diam. of hole in sample,
D = outside diam. of sample,3
D4 = inside diam. of outer conductor,
and defining
L 1 log D2 /DI + lot, D4 /Dy
L2 log D3 /D 2 ,
L 3 leg D4 /DI,
gives:
1I, (l+t2nI- -K ( +ta 26 )
m-;eas. meas.' =K' 3(A. 31. 1)
cor. meas. L 3 L 1 (1)-2• K' r1s+ +tan
m2 2 aas. 1 meas. meav.
tan6 cor =tan 6 eas (A.I. 2)
K 1 (1 + tan6 )Ineas. meas.
2When tan 610< «1, the above equations simplify to
IC' fiK' , (A. I1. 3)o3. me as. 1"3 ineas.
n ot. tan6 r-eau" [1+ e. L] - t(A. U. 4)
(A. 11.4 )
- 19 -
In addition, when clearances are small, they may both be referred to
"the same diameter and added
2[(K)eas) - KneasI clearance
K' -KI diameter (A. 11. 6)cor. KMeas. .30lgoD 42. 30 loglo10
D1
1 1+ c clearance1tan 6 = tanr ;neas. diameter (A. II. ?)L 2.30 log1 0 D4
APPENDIX III
Charts and Sample Calculations
A. Charts of the complex function cothx/x. These have been refined
and extended since previously given and show values of the function
coth T .L
T h
8r .3 0Chart XVI. T, 0 to 0. ; l; 380 to 90 (abscissa is l/C)
XVII. T, 0.8 tol. Sr; 500 to 90°
- 20 -
CHART XVI
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.6
170
WIT
X1. C ha XVI1 94 Oi: 1 -.14 to l t90 t
: I00
f717
MR SAM 0°2 0.N 0.4ý 0.5 0, 0. 0i N~if.8fýh ~
0 ~r 0VI. T, 00. 0.4 • 0',3 Ole 07 0.*I/C
Chart. . . . . .. . .. .. ....... . . ... . ......
- 21 -
CHART XVU
ii
I •[
I7 ; fi l l
II4 -T
17 m l,,° iEA
101
;A ihfr XVII Ml 0.Ao15 r,5 0
13
-22-
B. Charts of the complex function tanhx. These are shown in the form
tanh (a + jb) = r/e . Chart I is a survey chart7) with b in quadrants,
showing the symmetry properties. Chart II shows the first half-
quadrant of Chart I in enlarged form with b in radians. Chart III
shows an enlarged section of Chart II near the origin. Charts IV,
b and c, show parts of the first quadrant for low-loss samples only
(a 0 0. 1).
Acknowledgments
We are grateful to Barbara B. East and John J. Mara for preparation
of all charts shown in this section.
-23-
c.
0
Ii)0u
'4 0
ra
00
k 14
4 54
INI VWVI7TT
!I~ klt
- 24 -
CHART 11
tar*h (o Jb) r LO
1.40 9 8 .5.~ 8 .7 8.M'WI
-25-
CHART M
tanh (a+jb) * r/.
aJ
.52 I
.44
.361
• ~.32 d
S~~.24!
.1,2
0 A4 .0 .12t .4i .-O -194 el e .40
-26-
CHART IVb
.10
.09
.08
.07
.06
.05
.04
.01
.30 ,4 .38 .42 .46 .50 .54
CHART l~c
.1
Ar.
.01
.0
-28-
C. Charts for Sample Fit Corrections in Coaxial Line with DiameterRatio 8/3
Somple-fit Correctiom Chart, 2 O-"c'€- 4 .04.0
ot,
S.8
AC .6ANM." ANAftoo mio inJrt WC W*
-29-
Sample-fit Correcton Chart, 3.6ure4 c7.6
-IM
RatoW..f ckeonce w, dkmwters k Drwhc1F w cLcurtf
30
/Samplv-fit Correcdon Chart, t" 8 r be I 2D0 to 7.5
0.11
LII
I.0S
4-
1.03
off
.00 .01 .02 -04 orRatio of clearance on diameters to conductor diameter
-31 -
D. 1. Sample Calculation for an Epoxy-Loaded with Al in Coaxial Line
l~e f *, =30.300 e/so = 7.90coaxial line
tM # Date w I/I 0 90825
Sample: Al~usini-loakded epoxy Tamp ten 8d - 0.01511
Ibicknsu* 1.8665 e tanOn. 0.076.4
I &A-le on triul plate II Saplt X/h fr terminal plate
/-N" /Yt804 -1-04 0/ "," i8"-Ia
zo Im-. "/-)" 7.50° -7-0
40k. + 0 + si 0T
S1.8665LiL 6961 17.7820 d 1.8W65
rn30 - 2.1573 i .06201620
Lo - .•o a • ' .•a .1324
.1321
• ~~r .W -To 1, .01-382 ••oQ )•m5 •.4. o.o0
,Wi
:36OZO 360z:--tan 25.8e-*.1111 4~ tan X..~- 0 teni 12.77 - .2268
1 23)4 1[2c~i 051[0 023 2+00
-960 + 5*51 9d-.060 F- 0 9W9 0 - 3o29.41
07 w- z@ =.03W-io2v07ta-l' x .03F.do30.8
tanz .02]1 1.003.22 0 + 2 Ot ]w
0A6 Z, M 0 0 J4 Qj 10.8' T
a W~7 f0.21 w.22 40
*Pr65. T.R. 182.
- 32 -
i3
z 0
tan -. &Y,,c'2.4 12c .2148 ,45/9052
,.-r--•
from Char't IVe
Y n d n (?-) =01.57682 0• o.8
dA
oo'
'2%d/oo•5
0-01405 -, oos(.0 + 0. l9-o ,
0.07635 xi(J 1.06 *0.05
tan b - t,=(9, -,i o.oe i
@ "-:.=- • - o.825
-A wAB
For coaxial lime omit steps 17. 20p) 21., 24j 25 above
tan d;' tan"•(q +, 0 .0146
0.0.-43 x =1.0'6 0.0154 ,fsame fit
- 33-
D. 2. Sample Calculation for a Ferrite in Hollow Wave Guide
S;2le=# 2 ,31 5.748 e#/t w 18,7
Date - 5/23/50 . 0.51
5m tm.=?wic C rew a 2?C tM 8 d - 0.58
!bS~cknea8m t an8 1.26
I SMAmpl on trMInal plate 11 SMple Xi/ 14 frm termndl plate
1.! @ -Nou *)
(7[x* ' N®' N...
a 0 U ,64GC + sicH.5a a a ao
at. 3611 B..x
3 P
,- 033 W tan - tan 14.030 2
(6Da + 6~~ @ ta 1 0 [- 206 'Q ~ Z
.30 Ie3.5 .. 3D82 106
Ppag 65, T.R. 3&2.
-34-
Surn~ 2.33 @ V I+u U .3
Z2 1/2 Z __z__ = 1 .21o33, =/BLooi7,
[Z1.-z1 ] -2 4p B/ O -03316
1/2
tan y2d2 = = 1. oo 2 58°39,) 2920,
from Chart II
N =2 .675 + . 785' 1.033 /tan" 1•163 = 49°19'
'2d
2 *03 xL 2(7 "7.55) /•°•= =~ 6.28 x .1250
(~ e+)= 29054, (~ sin (rp +w= .4i98 @~ coo (jo+~r .867
(Cr-) -5 1o2 8 ' @~ si (rCe.f - -. 623 @~ coo (Scr - .782
F tan bm tan (rft 1.256
) I, AB . %86 x 7.55 0 510Pro 1 /2 1• .)/2
( (1+ 1.58)
20 - Sf- + -2 (~69.5.~ + 5.337'~ x 18.o6 + .668- 18.73
0 . -.1 +A 3 UldA @ +tan *d A uAq.~ .527
For coaxial line omit steps 17, 20, 21, 24., 25 above.
0
ta 5= . ton +•,
Sm f I I NIII1 =/IT@
- 35 -
References
1. H..J. Lindenhovius and J. C. van der Breggen, Philips Res.
Repts. 3, 37 (1948); C. M. van der Burgt, M. Gevers,
J. P. J. Wijn, Tech. Rev. 14, 245 (1953); P.H. Haas,
R. D. Harrington, and R. C. Powell, J. Research Natl. Bur.
Standards 56, 129 (1956).
2. M. H. Johnson and G. T. Rado, Phys. Rev. 75, 841 (1949); see
also A. Wieberdink, Appl. Sci. Res. BI, 439 (1950); and
G. Eicholz and G. F. Hodsman, Nature 160, 302 (1947).
3. E.G. Spencer, R.C. LeCraw, and F. Reggia, Proc. IRE 44,
790 (1956).
4. E.G. Spencer, L.A. Ault, and R. C. LeCraw, ibid. 44, 1311(1956).
5. Tech. Rep. 182, Lab. Ins. Res., Mass. Inst. Tech., October,
1963.
6. W. B. Westphal, in "Dielectric Materials and Applications,",
A. von Hippel, Ed., M.I.T. Press and John Wiley and Sons,
New York, 1954, pp. 102 and 103.
7. H. E. Hartig, Physics 1, 386 (1931).
I
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'¶*mwmt techniques tow detezulnation of the oemlez dLielectric owistantenoeqlex pez•blt awe gie '- a.---- .... r vith emauise wi the probiemeoo~mtere in :practical haleeslo mtaw-als. 1•pioal calculatimi andGeacriptiwi of secialJ~ sap3a bolAsr are 1noludl.
DD,'"..1473
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Materials, lossy, laminated
Dielectric-measurement techniques
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