1960 Powell and Rasmussen: A Radio-Frequency Permittimeter 179 ooF l 10 t l l l l lll ll |sistivity of 0.8 ohm cm, the same thickness line of 0.012 inch is intersected by the vertical construction lines. APENETRATDOIPH OF I - The resistivity is then 0.8 ohm cm and the thickness A _ \; METHOD A 0.012 inch. IC 0.018"~~~~~~~~O[ SLICE- BACKED WITH PREXCISION BRASS E METHOD B Fig. 10 shows plots of measurements on two different °I.0 _ BAC8KEDWITH LICE-/ - _ - _ test samples, made on sixteen successive working days. OOAcm< MATERIAL - X_ - - -It shows that the degree of reproduceability of the test _ process which can be depended upon is + 1 per cent. F _ _ METHOD B, ~~~~~~~~METHOD A _) .007" THICK SLICE- THICK l I'BACKED WITH 100Icm SLICE BACKED MATERIAL ITH BRASS - CONCLUSION z=zi Z< 1 \ | These results show that dependable resistivity meas- OlL < urements can be made at 9000 Mc. After the equip- .17 16 S 5 14 13 12 iI 10 9 8 7 6 5 4 3 2 0 ment is calibrated, by means of direct current tech- CHANGES IN CAVITY TRANSMISSION IN DECIBELS niques samplesc Fig. 8 Showing the effects of two methods of backing the sample. ably at microwave frequencies. 100-~~~~~~~~~~~~~~~~~~~~~~~.0 8 E 10 SN- - ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ .0 0 * 1716 I 14 3 lo 8 76 5 3 21 o12 1314 15IB 19 20 21 22 2526 27 2829 2 34 5 Q E~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~FB CHANGES IN TRANSMISSION IN DECIBELS JAN. Fig. 9-Showing how Methods A and B can be used to determline Fig. 10-Measurements made on two samples, both resistivity and thickness. on sixteen successive days. A Radio-Frequency Permittimeter* R. C. POWELLt, MEMBER, IRE, AND A. L. RASMUSSENt INTRODUCTION diffcult since errors due to electrode impedance, con- T' MHE measurem1ent of low-impedance materials, tact poten1tials, inlteraction of electrodes with the ma- such as conductors, semiconductors, electrolytes, terials, series inductance and connection impedance and high-permittivity materials has always been can cause errors mnaly timaes the actual quantity being measured. M\/ethods that have been used at low fre- *Received by the PGI, June 23, 1960. Presented at the 1960 quenlcies involve four-terminal bridges [i], and double Conference on Standards and Electronic Measurements as paper 3-5. transformers using an electrodeless ring of the material Tbhe work reported here was partially supported by the Dept. of the as a coupling loop [2] Such measurements at micro- t National Bureau of Standards, Boulder, Col, wave frequencies have been made in a circular electric
Transcript
1960 Powell and Rasmussen: A Radio-Frequency Permittimeter 179
ooFl10 t l llllll l l |sistivity of 0.8 ohm cm, the same thickness line of 0.012inch is intersected by the vertical construction lines.
APENETRATDOIPHOF I- The resistivity is then 0.8 ohm cm and the thicknessA _ \; METHOD A 0.012 inch.
IC 0.018"~~~~~~~~O[ SLICE-BACKED WITH PREXCISIONBRASS
E METHOD B Fig. 10 shows plots of measurements on two different°I.0 _ BAC8KEDWITH LICE-/ - _ -_ test samples, made on sixteen successive working days.
OOAcm<MATERIAL - X_ - - -It shows that the degree of reproduceability of the test_ process which can be depended upon is + 1 per cent.F _ _ METHOD B , ~~~~~~~~METHOD A
_) .007" THICK SLICE- THICKl I'BACKED WITH 100Icm SLICE BACKED
MATERIAL ITH BRASS - CONCLUSION
z=ziZ< 1 \ | These results show that dependable resistivity meas-OlL < urements can be made at 9000 Mc. After the equip-
.17 16 S 5 14 13 12 iI 10 9 8 7 6 5 4 3 2 0 ment is calibrated, by means of direct current tech-CHANGES IN CAVITY TRANSMISSION IN DECIBELS niques samplesc
Fig. 8 Showing the effects of two methods of backing the sample. ably at microwave frequencies.
Fig. 9-Showing how Methods A and B can be used to determline Fig. 10-Measurements made on two samples,both resistivity and thickness. on sixteen successive days.
A Radio-Frequency Permittimeter*R. C. POWELLt, MEMBER, IRE, AND A. L. RASMUSSENt
INTRODUCTION diffcult since errors due to electrode impedance, con-
T'MHE measurem1ent of low-impedance materials, tact poten1tials, inlteraction of electrodes with the ma-such as conductors, semiconductors, electrolytes, terials, series inductance and connection impedanceand high-permittivity materials has always been can cause errors mnaly timaes the actual quantity being
measured. M\/ethods that have been used at low fre-*Received by the PGI, June 23, 1960. Presented at the 1960 quenlcies involve four-terminal bridges [i], and double
Conference on Standards and Electronic Measurements as paper 3-5. transformers using an electrodeless ring of the materialTbhe work reported here was partially supported by the Dept. of the as a coupling loop [2] Such measurements at micro-
t National Bureau of Standards, Boulder, Col, wave frequencies have been made in a circular electric
180 IRE TRANSACTIONS ON INSTRUMENTATION September
field [3] or by using samples large compared to a wave- then ground and lapped. The optimum polish on thelength. None of these methods are useful at radio fre- surfaces is somewhat rougher than a mirror finish. Itquencies where many materials exhibit interesting and was found that too fine a surface caused poor repro-useful properties. ducibility, probably because of microscopic magneticThe RF permittimeter (so-called because of its anal- coupling across the boundary.
ogy to the RF permeameter [4]) also utilizes a circu- The following analysis produces the equations neces-lar electric field in a ring-shaped sample to eliminate sary to determine the impedance around the ring of ma-electrode and series inductance problems. The circular terial and also the complex permittivity or dielectricelectrical field is created in a transformer yoke of ap- constant. The complex conductivity o'* can be obtainedpropriate symmetry. This instrumenit is a two-termi- from the complex permittivity K*Ko bynal coaxial system designed for making measurements * wK*KO.on conventional HIF impedance measuring equipment.
Since the yoke of the transformer is made of mag- It should be realized that, while conductivity and per-netic materials, the principal limit of the ranige of the mittivity are two different phenomena, it is difficult toinstrumenit is the maximumii initial permeability of separate themii experimentally. The measured valueyoke materials available. This falls from about 5000 at genierally is the sum of the two effects; hence, such a10 kc to about 50 at 100 Mc and determinies the effec- conversioni is acceptable.tive impedance of the single turn sample and hence thesensitivity of the instrument. Using bridges with 0.1 percent precision and 1 per cent error, the maximum resis-tivity which can be mieasured to 1 per cent error rangesfrom about 10-2 ohm meters at 10 kc to about 1 ohmimeter at 100 Mc while the minyimum relative permittiv-ity which can be measured to the samge accuracy rangesfrom about 1081 at 10 kc down to about 102 at 100 Mc.These accuracy figures wereobtaiened empirically bymiieasuring keownd impeandace rings. By chancging thernuber of turns on the primisarywinding, the permtit-
timieter cain be imiatched to masimpedanice measurin|ginstruiets, but the rainge of materials that cain ber >measured cainbe changed only by smicall aimountts.The ilnstruement is aalyzed as a 7'enetworkaind cali- Fig. I-An RF pernmittieter with standard ring, shortiNg
brated using the cases of ro secondary, a low-resistance ring atd various rings of materials to be mneasured.copper ring seconidary, anid a known resistanucesecond-ary consisting of a ring of fine resistance wire such that 02"00'skin effect is eliminated. The specien to be measured FERRITE, j z2400,consists of a solid ring of material or a liquid in a ring- Ian0RF.. peritep,shaped constainer. Sintce the magndetic path msustberbroken anid reformied for insertioni of solid rinigs, preci- SECONDARY REGION
sion of greater thani 1 per cent is difficult to obtain. or 9Y1/2 YARN PRIMARYMeasurementsmiade to date have shown values of
perinittivity of iay ferrites to be mruch higher thani 0g200tthose obtainied by electrode methods, explaining res-loonance effects at frequencies lower than those previ-ously calculated. Measurciements of stronig electrolytic Fig. 2-Section drawing of ani RF pernmittiniieter.solutionis have showni that the conductivity has a strongout-of-phase comiponient which can be either leadinig or ANALYSIS OF THF PERMITTIMETERlagging, dependinig oni the niature of the solutioni, anidthus conitributes either a positive or niegative comi- At a single frequency, the perimittinmeter withi a sec-
ponient to the permiittivity. Good agreemient with ex- onidary impedanice cani be represented by an equivalenittrapolated values for the in-phase component of the loaded T network [5] as shown in Fig. 3.conductivity of these solutions as well as several metals Using the symbol definitions given in Table I, thewas obtained. impedance ZL can be written in terms of this circuit asThe permittimeter shown in Figs. 1 and 2 was made - - + Z
from a solid piece of high-permeability ferrite using an Z 23 \lfl)(Z2 + (2)ultrasonic cutter; the plate and mating surfaces were Zi -Z-Z2
1960 Powell and Rasmussen: A Radio-Frequency Permittimeter 181
If no material is inserted into the secondary region, ZLcan be considered to have infinite impedance and
Z2 = Zin -Z1. (3)
Zin *Z2 ZLIf the shorting ring is inserted into the secondary re-
gion, ZL has exactly zero impedance and
0~~~~~~~~~~~~~~~~~~~~~~~(ZinsZ) (Zin o Zi)(4Fig. 3-Equivalent Tee network. Z )Z -Zi ) (Zin 0 - ZnS
TABLE I Therefore, (2) can be rewritten asDEFINITION OF SYMBOLS
Capacitance Z (Zin - Z1)2 (Zi. s - Zi) ()C* The complex self capacitance of the secondary region (Zi o -Zin S) (Zin - Zin O)
in farads.
Dimension and soa Inside diameter of a ring in meters.b Outside diameter of a ring in meters. Zx- Zs /Zin - Zin A /Zin X-Zin Sc (b-a)/2 in meters ) (6)D Diameter of a ring equal to (a+b)/2 in meters. ZA - ZS Zin A -Zin S Zin o-Zin Xd Diameter of the section of a ring of circular section in
meters.h Hleight of a ring of rectangular section in meters. which is the equation used to determine Zx and hence
Greek Symbol K* of the material measured in terms of ZA a knownI Effective depth of penetration of the field into the mate- impedance, Zs an effective short circuit, and the in-
rial; equal to the skin depth in meters = (Xo//ur0Zo)1j2 dicated measurements.K* The complex relative permittivitv of the material.Ko The permittivity of free space, 8.85 10-12 farads per The impedance ZL is described by
meter.NO Free-space wavelengthAu* The complex relative permeability of the material.,uo 'The permeability of free space, 4r 10-7 henries per ZL =j coL*- )
meter. WC* /a* The complex conductivity equal to jcoKoK* in mhos secondary
per meter.co The angular frequency 27rf in radians per second. /
)
Impedance c'0C* shcrting ring
Zl, Z2 Z3 The impedances of the equivalent T network repre-senting the permittimeter in ohms.
ZL The difference between the impelance of the secondary so the complex self inductance and capacitance of theand the impedance of the shorting ring, Zs, in ohms. shorting ring, the known impedance ring and the ring
Zin The impedance looking into the terminals of the per- of materl to emesue must beclculatd toer-mittimeter in ohms. of material to be measured must be calculated to inter-
ZA The impedance of a ring of knowni i-npedance used as pret the results.a calibration standard in ohms.
Z in A Zin when the ring of known impedance is inserted into For the case where the secondary is a circular ring ofthe secondary region.
Zo The characteristic impedance of free space = (o/Ko)12 circular section (Fig. 4) with diameters D and d, respec-= 376.7 ohms. tively
Z in o Zi,, when no material is inserted into the secondary re-gion in ohms. K*
Zs The impedance of the shorting ring in ohms. C* K D_D2 _Kd212] (8)Z in S Zi. when the shorting ring is inserted into the second- 2 [ - D -
arv region in ohms.Zx The impedance of the ring of material to be measured
in ohms. andZ in x Zin when the ring of material to be measured is inserted
into the secondary region. 8D\Inductance L*~ D(j. .-- Ln d) (9)LA Inductive part of ZA determinled from dim1ensionls and2 4dJ
expressed in henries.L* The complex self inductance of the secondary region in if th curn eertsteeniescnay si
henries. ftecretpntae th nrescnay as1assumed in the case of the known impedance ring and
Resistance ~~~~~~~~~~thering of material to be measured. If the current pene-RA Resistive part of ZA measured directly in ohms. trtsaelivysm ldph6asntecseote
182 IRE TRANSACTIONS ON INSTRUMENTATION September
shorting ring The above expressions for capacity are exact and canbe computed directly or obtained by dividing the in-
KK= ° { [D2 _ (d-2^)2]l/2 _ (D2-d2)ll2} (10) ductance of a ring of the same geometry in which the2 magnetic field occupies the position and direction of
the electric field by Zo2. The expressions for inductanceare approximations of sufficient accuracy for this use.
PuO + 8DL More nearly exact expressions and formulas for otherL*---D8-2+LnD) (11) configurations are available in the literature [6]-[9].2 d A sample calculation is given below, and Tables II and
III give examples of results. The accuracies for graphite,-dt the films, lead, and molybdenum are lower due either
to uncertainties of the dimensions (the metals), or im-
perfect field penetration (graphite).
t-t4 --} I D tt d b EXAMPLE OF A MEASUREMENT OF THE COMPLEXDIELECTRIC CONSTANT OF A FERRITE
RING CORE
Using the permittimeter shown in Fig. 2, a ring ofFig. 4-Dimensions of a ring of circular section. ferrite of rectangular section as the material to be meas-
ured, Zx, a copper ring of rectangular section for Zs anda ring of resistance wire of circular section for ZA, the
1 1 following data were obtained. All impedance measure-' < , r < ments were made on a Maxwell-type bridge circuit.
Ferrite Ring Zx
9<JJ 1_LiJ ; ,ax 1.53t10-2 meters
j i bx = 2.48.102 meters
Fig. 5-Dimensions of a ring of rectangular section. hx = 3.82 10-3 meters
1x* = 1950 - j146.For the case where the secondary is a circular ring of
rectangular section (Fig. 5) with an inside diameter a, Copper Shorting Ring Zan outside diameter b, and a height h as = 1.43. 10-2 meters
K*KoA b b$ = 2.34 10-2 metersC* = -Ln (12)
2 7r a hs = 4.15 10-3 meters
and Js* = 5.65 107 + jO mhos per meter (hard drawn
if the current penetrates the entire secondary as in the DA = 2.22* 10-2 meterscase of the known impedance ring and the ring of ma- dA = 6.99- 10- meters.terial to be measured. If the current penetrates only asmall depth a as in the case of the shorting ring Measured Impedances at a Frequency of 3. 1O1 cps
K KFb(a + 2)L (b_-23) ] Zin O = (122.7 + j1582) ohms= 2wLna(b- 23) + a-+ 23/ Zin S = (16.49 + j127.6) ohms
anld Zin~A = (722.8 + j1043) ohms
F17r 1.9D] Zin~X = (178.6 +j1636) ohmsL*D L-2+Ln j. (15) R 32 hs
196O Powell and Rasmussen: A Radio-Frequency Permittimeter 183
TABLE IIRES'ULTS FOR VARIOUS MATERIALS USING SMALL RF FIELDS AT 240C
Material Frequency in Mc a' in mhos per meter a" in mhos per meter
Ferrite ring I ,=615 -j63 0.3 43.7 1.9,*582 -j61 0.6 44.7 4.0,*=576 -jl38 1.0 45.6 6.0
Ferrite ring I I A* = 1000-j28 0.3 1.36 3.10,u* = 1050 -j73 0.6 2.39 4.42,u* = 1050-jl93 1.0 3.91 6.63
Ferrite ring III ,* = 3800-j36 0.1 17.9 9.6,u* =3510 -jl530 0.3 22.6 24.3,u*= 1850-j2310 0.6 31.2 50.0
L*= 1.96 10-8 henry calculated from (15) where Z3 = (137 94.0°) ohms from (4).
184 IRE TRANSACTIONS ON INSTRUMENTATION September
ACKNOWLEDGMENT [3] Collie, Hasted, and Ritson, "The cavity method of measuringthe dielectric constants of polar liquids in the centimeter band,"L. A. Steinert calculated the inductance of a ring of Proc. Phys. Soc. (London), vol. 60, pp. 71-82; January, 1948.[4] A. L. Rasmussen and A. E. Hess, "R-F permeameter techniques
rectangular section of which (13) is an approximation. for testing ferrite cores, " Elec. Manufacturing, vol. 6 1, pp. 86-9 1,XV. A. Pittman made most of the measurements. C. A. 308; May, 1958.V5]W. L. Everitt, "Communication Engineering," McGraw-HillHoer programmed and processed the data on an elec- Book Co., Inc., New York, N. Y.; 1937.tronic computer. Dr. P. MVI. Gruzensky, H. C. Leistner, [6] C. Snow, "Formulas for Computing Capacitance and Induct-
P. L. Lodo A .anoe,W.KSepesoaance," Natl. Bur. of Standards Circular 544, U. S. Govt. Print-P. L. London, A. J. Pannone, W. K. Stephenson and ing Office, Washington, D. C.; 1954.H. C. Stump prepared the specimens and ferrite parts. [7] E. B. Rosa and F. W. Grover, "Formulas and Tables for the Cal-culation of Mutual and Self-Inductance," (Revised), Sci. Papers
of the Bur. of Stalndards No. 169, U. S. Govt. Printing Office,REFERENCES Washington, D. C.; 1948.
[8] F. W. Grover, "Inductance Calculations," D. Van Nostrand Co.,[1] P. A. Miles, XV. B. WVestphal, and A. von Hippel, "Dielectric Inc., New York, N. Y.; 1946.
spectroscopy of ferromagnetic semiconductors," Rev. Mlod. Phys., [9] F. E. Terman, "Radio Engineering Handbook," McGraw-Hillvol. 29, pp. 279-307; JulY, 1957. Book Co., Inc., New York, N. Y.; 1943.
[2] S. R. Gupto and G. J. Hills, "A precision electrode-less conduct- [10] D. E. Bromley and P. T. Good, "Capacitance-coupled cell forance cell for use at audio-frequencies," J. Sci. Instr., vol. 33, electrolytic conductivity measurements," J. Sci. Instr., vol.pp. 313-314; August, 1956. 36, pp. 326-327; July, 1959.
The Measurement of Microwave Resistivity by EddyCurrent Loss in Small Spheres
T. KOHANEt
INTRODUCTION that method, that the electric field applied to theT HE commonly used microwave ferrite materials sample is uniform throughout the sample, is no longer
have resistivities which are much greater than valid because of the skin effect. This limits measure-100 ohm cm. For such materials there exists a ments for convenient diameters at X band to resis-
widely used cavity perturbation technique1'2 for meas- tivities much greater than one ohm cm. Considerationsuring the resistivity at microwave frequencies. (Actu- of sensitivity with usual cavities and irises may be evenally, the real and imaginary parts of the dielectric con- more restrictive.stant may be measured.) In this method, the sample is Described below is another cavity perturbationin the form of a rod of small diameter and is inserted in method3 for measuring resistivity which is applicablea resonant cavity at a region of maximum microwave to small samples of relatively high conductivity ma-electric field and zero microwave magnetic field. In es- terials.sence, the sample resistivity is obtained from thechange in the Q of the cavity resulting from the inser- PR N IPLE OF METHODtion of the -sample. This method uses a sample in the form of a smallAt the Raytheon Research Division, we have become sphere. In contrast to the usual method, the sample is
interested in ferrites of relatively high conductivity, placed in the cavity at a point of maximum magnetic:specifically, ferrites containing some divalent iron. field and zero electric field. The sample is small com-An extreme but nonetheless pertinent example is mag- pared to the wavelength of the microwave radiation innetite, which has a resistivity of less than 10-2 ohm cm. the cavity, so that we may regard the sample as being,For such high conductivities, the method nmentioned exposed to an alternating but uniform magnetic field.,above is no lonlger applicable. The assumption made in We thus have a spherical conductor in an alternating:
magnetic field, with the result that eddy currents are
* Received hy the PGI, June 23, 1960. Presented at the 1960 Con- inue4 ntecnutr hsi o oul rbference on Standards and Electronic Measurements as paper 3-6. -lem;4 the important result for the present purpose iS,
t Raytheon Mfg. Co., XValtham, Mfass.1 H. A. Bethe and J. Schwinger, "Perturhation Theory for Cavi-
ties," Natl. Defense Res. Committee Contractor's Rept., Cornell 3T. Kohane and M. H. Sirvetz, "Measurement of resistivity hy-University, Ithaca, N. Y., Rept. No. NDRC-14-117; March, 1943. eddy current loss in spheres," Rev. Sci. Instr., vol. 30, pp. 1059-1060;:
2 E. G. Spencer, L. C. LeCraw, and F. Reggia, "Measurement of Novemher, 1959.microwave dielectric constants and tensor permeahilities of ferrite 4XV. R. Smythe, "Static and Dynamic Electricity," McGraw--spheres," PROC. IRE, vol. 44, pp. 790-800; June, 1956. Hill Book Co., Inc., New York, N. Y., 2nd ed.; 1950.
