162 IRE TRANSACTIONS ON INSTRUMENTATION December oersteds at room temperature and is comparable to (a = FAH12c) be much less than unity. At 5 Gc the other reported results. assumption is satisfied even if the line width is in the The present equipment can be improved to provide range of 100 oersteds. greater precision by decreasing the tolerance on the alignment of the probe, the loop and the crystal mount. CONCLUSION The ac magnetic field in the experiment was derived The method for measuring narrow line width ferro- from the common 60 cycle power line and while the volt- magnets has been shown to have the precision necessary age was well regulated the frequency variations caused to distinguish the anisotropy in a very narrow line some limitation on precision. A limitation on accuracy width. It is expected that the precision could be im- can be seen in Fig. 3. If the sample is too close to the proved if necessary. pickup loop or the walls of the guide, radiation damping ACKNOWLEDGMENT causes a broadening of the resonance. This precludes, at the present, an accurate measurement of this type in The author wishes to acknowledge his gratitude to the millimeter region. The limiting assumption in the W. M4. Hubbard and J. V. Gilfrich for orienting the analysis is that the square of the damping constant samples and to C. G. Reed for preparing the samples Measurement and Standardization of ielectric Samples* H. E. BUSSEYt, SENIOR MEMBER, IRE, AND J. E. GRAYt Summary-The selection of a material suitable for use as a emphasis in this paper is on accurate dielectric measure- standard of dielectric properties at microwave frequencies is dis- ments. Material problems have been reduced by choos cussed, and tests are described which indicate that a glass and a glass ceramic are satisfactory for such standards. The probable ac- ingmterialsbwitho curacy of measurement of the real part of the dielectric constant is long-term stablity. estimated at +0.3 per cent. Loss measurements are discussed. A correction is developed for the error resulting from the small airgap THE MATERIAL FOR DIELECTRIC SAMPLES often present around the sample in transmission-line measurements. The main materials of the present investigation are a The effects of humidity and temperature variations are examined, glass and a glass ceramic, both of which are available and preliminary results of measurements to 8000C are given. in optical quality. This ensures that the homogeneity, isotropy, and aging requirements are satisfied. There INTRODUCTION remains mostly the dependence of the complex dielectric STANDARD SAMPLES, i.e., samples with the constant on temperature, pressure, relative humidity, limits of error well known for the property in ques- and surface conditions. tion, are useful in a laboratory in order to improve The temperature and relative humidity dependence or confirm the accuracy of the measuring procedures of the glass standard samples were investigated over a and equipment being used. reasonable range of values near usual laboratory condi- There are two main requirements for standard sam- tions. In addition, a high temperature measuring system ples of dielectric materials. The material properties has been developed. should be understood sufficiently to avoid such prob- lems as those associated with inhomogeneity, sensitivity THE MEASUREMENT OF DIELECTRIC CONSTANT to the environment, and chemical changes or aging. The accuracy of the measuring procedures is deter- After satisfying this first requirement, the measure- mined mainly by comparing several independent meth- ments then must be investigated sufficiently so that ods. Corrections are made for some small departures of their accuracy can be specified with confidence. The the measuring system from the ideal mathematical model. * Received September 4, 1962. Presented at the 1962 Interna- Dielectric measurements depend upon knowing elec- tional Conferenlce on Precision Electromagnetic Measurements as tromagnetic wave solutions in some space containing t National Bureau of Standards, Boulder, Colo, the material in question. The different methods investi-
Transcript
162 IRE TRANSACTIONS ON INSTRUMENTATION December
oersteds at room temperature and is comparable to (a = FAH12c) be much less than unity. At 5 Gc theother reported results. assumption is satisfied even if the line width is in theThe present equipment can be improved to provide range of 100 oersteds.
greater precision by decreasing the tolerance on thealignment of the probe, the loop and the crystal mount. CONCLUSIONThe ac magnetic field in the experiment was derived The method for measuring narrow line width ferro-from the common 60 cycle power line and while the volt- magnets has been shown to have the precision necessaryage was well regulated the frequency variations caused to distinguish the anisotropy in a very narrow linesome limitation on precision. A limitation on accuracy width. It is expected that the precision could be im-can be seen in Fig. 3. If the sample is too close to the proved if necessary.pickup loop or the walls of the guide, radiation damping ACKNOWLEDGMENTcauses a broadening of the resonance. This precludes,at the present, an accurate measurement of this type in The author wishes to acknowledge his gratitude tothe millimeter region. The limiting assumption in the W. M4. Hubbard and J. V. Gilfrich for orienting theanalysis is that the square of the damping constant samples and to C. G. Reed for preparing the samples
Measurement and Standardization ofielectric Samples*
H. E. BUSSEYt, SENIOR MEMBER, IRE, AND J. E. GRAYt
Summary-The selection of a material suitable for use as a emphasis in this paper is on accurate dielectric measure-standard of dielectric properties at microwave frequencies is dis- ments. Material problems have been reduced by chooscussed, and tests are described which indicate that a glass and aglass ceramic are satisfactory for such standards. The probable ac- ingmterialsbwithocuracy of measurement of the real part of the dielectric constant is long-term stablity.estimated at +0.3 per cent. Loss measurements are discussed. Acorrection is developed for the error resulting from the small airgap THE MATERIAL FOR DIELECTRIC SAMPLESoften present around the sample in transmission-line measurements. The main materials of the present investigation are aThe effects of humidity and temperature variations are examined, glass and a glass ceramic, both of which are availableand preliminary results of measurements to 8000C are given. in optical quality. This ensures that the homogeneity,
isotropy, and aging requirements are satisfied. ThereINTRODUCTION remains mostly the dependence of the complex dielectricSTANDARD SAMPLES, i.e., samples with the constant on temperature, pressure, relative humidity,
limits of error well known for the property in ques- and surface conditions.tion, are useful in a laboratory in order to improve The temperature and relative humidity dependence
or confirm the accuracy of the measuring procedures of the glass standard samples were investigated over aand equipment being used. reasonable range of values near usual laboratory condi-There are two main requirements for standard sam- tions. In addition, a high temperature measuring system
ples of dielectric materials. The material properties has been developed.should be understood sufficiently to avoid such prob-lems as those associated with inhomogeneity, sensitivity THE MEASUREMENT OF DIELECTRIC CONSTANTto the environment, and chemical changes or aging. The accuracy of the measuring procedures is deter-After satisfying this first requirement, the measure- mined mainly by comparing several independent meth-ments then must be investigated sufficiently so that ods. Corrections are made for some small departures oftheir accuracy can be specified with confidence. The the measuring system from the ideal mathematical
model.* Received September 4, 1962. Presented at the 1962 Interna- Dielectric measurements depend upon knowing elec-
tional Conferenlce on Precision Electromagnetic Measurements as tromagnetic wave solutions in some space containing
t National Bureau of Standards, Boulder, Colo, the material in question. The different methods investi-
1962 Bussey and Gray: Measurement and Standardization of Dielectric Samples 163
SAMPLE t
SAMPLE,-U? ~ ~~~~~~TRAVELING
PROBE
(a) (b)Fig. 1-TEol resonator and TE11 line or resonator.
TABLE ICOMPARISON OF TE011 RESONANT CAVITY RESULTS FOR k' (PERMITTIVITY) WITH THOSE FROM THE IMPEDANCE
0.25-inch diameter rod Uncorrected Corrected for airgap Sample diameter
Glass: from one corner of sheet 6.195 6.128 6.204 1.0001From another location 6.196 6.127 6.203 1.0000From another location 6.202 6.139 6.207 1.0004Glass ceramic, from one corner of sheet 5.730 5.647 5.711 1.0001From another location 5.708 5.648 5.708 1.0002From another location 5.731 5.651 5.714 1.0001
A1203 porcelain (All samples from same batch 8.784 8.642 8.794 1.0002but random locations in the ceramic body.) 8.775 8.674 8.822 1.0003
8.775 8.594 8.743 1.0002
Average porcelain 8.778 8.636 8.786
gated are represented by the diagrams in Fig. 1. In Fig. error to the real part of the permittivity. The results in1(a) there is a circular cylindrical dielectric rod centered Table I show that when the TE11 data for the dis' arein a circular cylindrical cavity.1 For the TEo11 mode of corrected for the fit of the sample in the line there isresonance used, the corrections for imperfections due to good agreement with the TEo,, rod data. The glassthe insertion port, the irises, and the gap around the showed the best agreement. The glass and glass ceramicplunger are small and known. These are obtained by used were not of optical quality, but both are availableperturbation theory using as a basis the exact solution in such quality. The results of such measurements onof the ideal resonator with the sample in place. optical quality material are not expected to differ from
In Fig. l(b) there is a circular transmission line op- those given here, except that the scatter of measurederated in the TE11 mode with a disk sample at a shorted values may be less as a result of greater homogeneity ofend. Either by impedance measurement with a traveling the optical quality material. The A1203 ceramic body, asprobe or by resonating the line with another short, or might be expected, shows some variation from sampleboth, the dielectric properties may be determined. The to sample, but the averages show good agreement be-main error here is due to airgaps between the sample tween the two methods.and the walls of the line. Such gaps not only permit the A general treatment of the error due to an airgapinsertion and removal of the sample, but also leave it around a sample is not available, though some specificfree to rest squarely on the short circuit, a condition cases are covered.2'3 Therefore, a general treatmentwhich must be met if an even larger error is to be based on perturbation theory, which seems to be ade-avoided. quate for practical cases, will be given.A comparison of the two methods showed that the air-
gap around the disk sample contributed a significant 2 XV B.Wspa,"ehiuso MauigtePritvtand Permeability of Liquids and Solids in the Frequency Range3 c/s to 50 kMc/s," M.I.T. Laboratory for Insulation, Cambridge,
1 H. E. Bussey, "Cavity resonator dielectric measurements on Mass., Res. Tech. Rept. No. 36; 1950.rod samples," 1959 Annual Rept. of the Conf. on Electrical Insulation, 3E. S. Hotston, "Correction term for dielectric measurementsPocono Manor, Pennsylvania, October 26-28, 1959, publication 756 with cavity resonators," J. of Sci. Instr., vol. 38, pp. 130-131; April.of the Nat'l Research Council of the Nat'l Acad. of Sci. 1961.
164 IRE TRANSACTIONS ON INSTRUMENTATION December
CORRECTION FOR GAP AROUND A DISK SAMPLE
The complex propagation constant y in the section oftransmission line containing the sample is obtained from TABLE IIappropriate measurements and calculations and then COMPARISON OF Loss TANGENT MEASUREMENTS
* * * * 7 , * * * * 1 ~~~~~~~ONRODS AND DISKSthe relative permittivity k = e/ Eo, which may be complex ONRODS AND DISKS
to indicate losses, is obtained from RodMaterial (TE011) DiSk
(c./c)2k = y2 + k,2, Gs5--Glass 53 X1-4 56*X 10-4
where kc is the characteristic or cutoff wave number for Glass ceramic 52.4 53.8the mode and cross section of the line. Glass ceramic 2.7 3.5
Based on perturbation theory4'5 the change in the Glass ceramic 9 ±0.2 9. 70.2tpropagation constant of a TE or TEM line, due to anairgap between the dielectric cylinder and the cylindri- * Slotted line, except last sample.cal wall, is t Disk in TE113 resonator at room temperature.
2 2 TABLE I I I'Ygap -Yno gap
MEASUREMENT OF A PLASTIC SAMPLE BEFORE AND AFTER A REDUC-f TION IN DIAMETER TO ILLUSTRATE THE EFFECT OF AN AIRGAP.j E, E2dS THE TRANSMISSION LINE DIAMETER WAS 1.0029 INCHES
'A =y2 (k- 1(2)c ~~~~~~Diameter kk tan bX104 tan 6X104
0.9808 2.4694 2.5364 5.17 5.26where E1 is the electric field of the dielectric filled line 0.9601 2.4188 2.5412 5.46 5.65with no gap, E2 is the electric field with an airgap pres- 0.9186 2.3588 2.5525 5.68 6.030.8505 2.2085 2.5478 5.27 5.94ent, S is the cross section of the line and dS is an ele-ment of S. When k is complex the change in 'y is com-plex, and a loss correction is obtained concomitantly. TABLE IV
For a first-order theory the normal (n) and tangential Loss TANGENTX 104 MEASURED AT 9200 Mc VS TEMPERATURE(t) components of E2 are obtained from E1 by satisfying AND HUMIDITY VARIATIONSboundary conditions at the dielectric interface. These = _ _ [Uncleanrequire that E2, =k'E., and E2,t=E, t, where k' is the 4 Per 31.5 Per 48 Per 83 Per surfacereal part of k. Using these components in (2) Material Cent Cent Cent Cent 83 Per
The second term becomes appreciable only for large Glass 53 52 53 54 55gaps because Et vanishes at the conducting wall. Verylarge gaps are only practicable when using the TEommodes, in which case the usually predominant term in TABLE VEn vanishes; a case already treated.1 From (1) and (3) COMPLEX PERMITTIVITY OF Al203 CERAMIC VS TEMPERATUREthe error in a measurement of permittivity k due to an Temperature °C Dielectric Constant Loss TangentX10airgaP iS
23 8.81 9.9308 9.32 11
F1k,IE, 12±+ E,F1,, 505 9.71 14813 10.58 34
A For comparison see M.I.T. Tables.
1 2dS6"Tables of Dielectric Materials," M.I.T. Laboratory for Insula-
4H. A. Bethe and J. Schwinger, "Perturbation theory for cavities"2 tion Research, Cambridge, MIass., Tech. Rept. No. 119, vol. V? p. 40;NDRC, Washington, D. C., Rept. No. DI-117; 1943. 1957.
5The general method is described by E. L. Ginzton in "Micro-wave Measurements," McGraw-Hill Book Co., Inc., New York,sN. Y., ch. 10; 1957.
1962 Bussey and Gray: Measurement and Standardization of Dielectric Samples 165
Eq. (4) was applied to a TEM coaxial transmission cavity whose Q and resonant frequency yield the com-line and a TEo1 rectangular line and it agreed with the plex permittivity of the sample. The first measurementsusual correction2 for these modes when the gap was made with this system are reported in Table V.small. Eq. (4) may be applied to the important case of acircular TE11 transmission line for which no correction DISCUSSIONfor fit was previously available. For a sample with The 1723 glass appears to be quite homogeneous andradius b -Ab in a waveguide of radius b, isotropic, based on the results in Table I. It seems prob-
able that the various systems are capable of measure-Ak' = - k'(k' - 1)(0.8368)Ab b. (5) ments on k' to an accuracy of 0.3 per cent.
This equation was used to correct the results in Table I The results shown in Table II confirm the accuracyas shown. of the present loss tangent measurements to + 10 per
cent + 0.0001. It is expected that future work will im-EXPERIMENTAL prove this accuracy.
The samples compared in Tables I and II were ob- Based on Table III we estimate that with large gaps,tained as follows. Pairs of samples, a rod and a disk were corrections of more than 4 or 5 per cent will leave inac-cut side-by-side from the various corners of a glass and curacies of 1 per cent or more in the final results for k'.a glass-ceramic sheet about 12 inches square. Samples The results make it doubtful whether the imaginaryfrom the same batch of A1203 porcelain were available part of (4) should be used. When there is a gap therein each shape, but were not pairs from side-by-side loca- may be extra mode-conversion losses that makes up fortions. the missing sample material. The dielectric constant at
In order to estimate the size of the airgap that may 9200 AMc of these materials, for two decimal accuracy, isbe treated by (4) without too much error, measurements independent of temperature and relative humidity overwere made with larger airgaps. The results appear in the normal range of laboratory conditions. Relative hu-Table III. The same sample was used throughout this midity and surface contamination do alter the apparentexperiment, its diameter being cut down in steps as indi- loss, as shown in Table IV, presumably by lowering thecated. It was carefully centered in the line to minimize surface resistivity of the sample. The magnitude of thismode conversion. effect should vary for different measuring systemsTo determine the effects of temperature and humid- which may concentrate the applied electric field at the
ity variations on the measured properties, the TEoll surface of the sample to varying degrees. It does appear,resonant cavity and samples were enclosed in a glove however, that when measurements can be made at lowbox where the temperature and humidity could be con- relative humidity, say below 30 per cent humidity, cor-trolled. The results of these measurements appear in rections are unnecessary.Table IV (loss variation); the real part to two decimalplaces did not vary. ACKNOWLEDGMENTThe high temperature equipment uses the method of The authors wish to thank Dr. W. H. Barney of the
Fig. 1(b). A section of silver circular TE11 transmission Corning Glass Works, Corning, N. Y., and L. E. Ferrieraline is closed with a second short circuit which contains of the Coors Porcelain Company, Golden, Colo., fora coupling iris, forming a TE113 cylindrical resonant furnishing various samples.
