1、Designation: D 5568 01An American National StandardStandard Test Method forMeasuring Relative Complex Permittivity and RelativeMagnetic Permeability of Solid Materials at MicrowaveFrequencies1This standard is issued under the fixed designation D 5568; the number immediately following the designation
2、 indicates the year oforiginal adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon (e) indicates an editorial change since the last revision or reapproval.1. Scope1.1 This test method covers a procedure
3、for determiningrelative complex permittivity (relative dielectric constant andloss index) and relative magnetic permeability of isotropic,reciprocal (nongyromagnetic) solid materials. If the material isnonmagnetic, this procedure may be used to measure permit-tivity only.1.2 This measurement method
4、is valid over a frequencyrange of approximately 1 MHz to 50 GHz. These limits are notexact and depend on the size of the specimen, the size and typeof transmission line used as a specimen holder, and on theapplicable frequency range of the network analyzer used tomake measurements. The lower frequen
5、cy is limited by thesmallest measurable phase shift through a specimen, and theupper frequency limit is determined by the excitation ofhigher-order modes that invalidates the dominant-mode trans-mission line model. Any number of discrete measurementfrequencies may be selected in this frequency range
6、. Toachieve maximum measurement accuracy, use of differenttransmission line sizes and types may be required. For ex-ample, use of a 7-mm diameter coaxial geometry can providefor measurements from 1 MHz to 18 GHz. However, air gapsthat exist between the specimen and the transmission linesconductors i
7、ntroduce errors2that may necessitate the use of alarger diameter coaxial transmission line and a series ofrectangular wave guides of different size to cover this fre-quency range.1.3 The values stated in SI units are to be regarded as thestandard. The values given in parentheses are for informationo
8、nly.1.4 This standard does not purport to address all of thesafety concerns, if any, associated with its use. It is theresponsibility of the user of this standard to establish appro-priate safety and health practices and determine the applica-bility of regulatory limitations prior to use.2. Referenc
9、ed Documents2.1 ASTM Standards:D 1711 Terminology Relating to Electrical Insulation33. Terminology3.1 For other definitions used in this test method, refer toTerminology D 1711.3.2 Definitions:3.2.1 relative complex permittivity (relative complex dielec-tric constant) (relative complex capacitivity)
10、, eR, nthe ratioof the admittance of a given configuration of the material to theadmittance of the same configuration with vacuum as dielec-tric:e*R5YYy5YjvCy5e8R2 je9R, (1)where Y is the admittance with the material and jvC8y is theadmittance with vacuum.3.2.1.1 DiscussionIn common usage the word “
11、relative”is frequently dropped. The real part of complex relativepermittivity (e8R) is often referred to as simply relative permit-tivity, permittivity or dielectric constant. The imaginary part ofcomplex relative permittivity (e9R) is often referred to as theloss index. In anisotropic media, permit
12、tivity is described by athree dimensional tensor.3.2.2 For the purposes of this test method, the media isconsidered to be isotropic, and therefore permittivity is a singlecomplex number.3.3 Definitions of Terms Specific to This Standard:3.3.1 A list of symbols specific to this test method is givenin
13、 Annex A1.3.3.2 calibration, na procedure for connecting character-ized standard devices to the test ports of a network analyzer tocharacterize the measurement systems systematic errors. Theeffects of the systematic errors are then mathematically re-moved from the indicated measurements. The calibra
14、tion alsoestablishes the mathematical reference plane for the measure-ment test ports.3.3.2.1 DiscussionModern network analyzers have thiscapability built in. There are a variety of calibration kits that1This test method is under the jurisdiction of ASTM Committee D09 onElectrical and Electronic Ins
15、ulating Materials and is the direct responsibility ofSubcommittee D09.12 on Electrical Tests.Current edition approved Mar. 10, 2001. Published May 2001. Originallypublished as D 5568 94. Last previous edition D 5568 95.2ASTM STP 926 “Engineering Dielectrics, Volume 11B, Electrical Properties ofSolid
16、 Insulating Materials: Measurement Techniques,” 1987.3Annual Book of ASTM Standards, Vol 10.01.1Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.can be used depending on the type of test port. The modelsused to predict the measurement
17、response of the calibrationdevices depends on the type of calibration kit. Most calibrationkits come with a tape or disc that can be used to load thedefinitions of the calibration devices into the network analyzer.Calibration kit definitions loaded into the network analyzermust match the devices use
18、d to calibrate. Since both transmis-sion and reflection measurements are used in this standard, atwo-port calibration is required.3.3.3 network analyzer, na system that measures thetwo-port transmission and one-port reflection characteristics ofa multiport system in its linear range and at a common
19、inputand output frequency.3.3.3.1 DiscussionFor the purposes of this standard, thisdescription includes only those systems that have a synthesizedsignal generator, and that measure both magnitude and phase inthe forward and reverse directions of a two-port network (S11,S21,S12,S22).3.3.4 relative co
20、mplex permeability, *R, na term used toexpress the relationship between magnetic induction and mag-netizing force defined by the ratio of the absolute permeabilityto the magnetic constant, given by*R5 8R2 j9R5| B|0| H|(2)where 0is the permeability of free space.3.3.5 DiscussionIn common usage the wo
21、rd “relative” isfrequently dropped. The real part of complex relative perme-ability (8R) is often referred to as relative permeability orpermeability. The imaginary part of complex relative perme-ability (9R) is often referred to as the magnetic loss index. Inanisotropic media, permeability is descr
22、ibed by a three dimen-sional tensor.3.3.5.1 For the purposes of this test method, the media isconsidered to be isotropic, and therefore permeability is asingle complex number.3.3.6 scattering parameter (S-parameter), Sij, na complexnumber consisting of either the reflection or transmissioncoefficien
23、t of a component at a specified set of input and outputreference planes with all other planes terminated by a non-reflecting termination.3.3.7 DiscussionAs most commonly used, these coeffi-cients represent the quotient of the complex electric fieldstrength (or voltage) of a reflected or transmitted
24、wave dividedby that of an incident wave. The subscripts i and j of a typicalcoefficient Sijrefer to the output and input ports, respectively.For example, the forward transmission coefficient S21is theratio of the transmitted wave voltage at Reference Plane 2 (Port2) divided by the incident wave volt
25、age measured at ReferencePlane 1 (Port 1). Similarly, the Port 1 reflection coefficient S11is the ratio of the Port 1 reflected wave voltage divided by thePort 1 incident wave voltage.3.3.8 transverse electric (TEmn) wave, nan electromag-netic wave in which the electric field is everywhere perpen-di
26、cular to the direction of propagation.3.3.8.1 DiscussionThe index m is the number of half-period variations of the field along the wave guides largertransverse dimension, and n is the number of half-periodvariations of the field along the wave guides smaller trans-verse dimension. The dominant wave
27、in a rectangular waveguide is TE10. The electric field lines of the TE10mode areparallel to the shorter side.3.3.9 transverse electromagnetic (TEM) wave, nan elec-tromagnetic wave in which both the electric and magneticfields are perpendicular to the direction of propagation.3.3.9.1 DiscussionIn coa
28、xial transmission lines the domi-nant wave is TEM.4. Summary of Test Method4.1 A carefully machined test specimen is placed in anelectromagnetic transmission line and connected to a calibratednetwork analyzer that is used to measure the S-parameters ofthe transmission line-with-specimen. A specified
29、 data-reduction algorithm is then used to calculate permittivity andpermeability. If the material is nonmagnetic a different algo-rithm is used to calculate permittivity only. Error correctionsare then applied to compensate for the existence of air gapsbetween the specimen and the transmission lines
30、 conductors.5. Significance and Use5.1 Design calculations for Radio Frequency (RF), micro-wave and millimeter-wave components require the knowledgeof values of complex permittivity and permeability at operatingfrequencies. This test method is useful for evaluating batchtype or continuous production
31、 of material for use in electro-magnetic applications. It may be used to determine complexpermittivity only or both complex permittivity and permeabil-ity simultaneously.6. Interferences6.1 The upper limits of permittivity and permeability thatcan be measured using this test method are restricted by
32、 thetransmission line and specimen geometries. No specific limitsare given in this standard, but this test method is practicallylimited to low-to-medium values of permittivity and perme-ability. In 7-mm coaxial lines, specimen permittivities 200.9.4.5 Perform a two-port network analyzer calibration
33、inaccordance with the manufacturers procedures.10. Procedure10.1 The following procedure specifically applies to a 7-mmcoaxial setup. Minor differences concerning the connector existif other transmission line configurations are used. All otheraspects of this procedure remain the same.10.2 Calibratio
34、n Verification:10.2.1 Connect the empty specimen holder between Ports 1and 2.10.2.2 Measure the scattering parameters of the emptyspecimen holder.10.2.3 Calculate the permittivity of air from the measuredscattering parameters, as described in the section on calcula-tion. Use a specimen length equal
35、to the physical length of thespecimen holder. If a method described in Appendix X2 is usedto remove specimen holder conductor losses, use the appropri-ate specimen length, as described. To verify the calibration, thereal part of permittivity for air should be 1.001 6 0.001.10.3 Specimen Measurement:
36、10.3.1 Slide specimen about halfway onto the Port 1 side ofthe center conductor. Be careful not to chip the edges of thespecimens bore hole when inserting the center conductor.10.3.2 Note how the specimen fits on the center conductor(loose, snug, tight, loose at first, then tight, etc). This subject
37、iveobservation helps the operator to determine the dimensionalqualities of the specimen, and can aid in repeating themeasurement.10.3.3 Retract the connector threads at both ends of thespecimen holder, if applicable.10.3.4 Slide the specimen and center conductor into theouter conductor. Note how the
38、 specimen fits into the outerconductor. Leave the specimen sticking out of the Port 1 sideabout halfway.10.3.5 Connect one end of the specimen holder to Port 2.10.3.6 Bring the Port 1 connector and the Port 1 end of thespecimen holder together in left hand, holding them slightlyapart.10.3.7 Use the
39、end of a wood or plastic small-diameterdowel to push the specimen flush with the Port 1 referenceplane. If the data-reduction algorithm to be used is notdependent on the specimen location, special care in making thespecimen flush with the Port 1 reference plane is not necessary.Note the approximate
40、location of the specimen relative to thePort 1 end of the specimen holder.10.3.8 Slowly connect the Port 1 connectors. Look to makesure that the specimen does not protrude into the Port 1test-cable connector. Tighten both Port 1 and Port 2 connectorswith the proper torque wrench.FIG. 2 Typical Dimen
41、sional Specifications for 7-mm Coaxial Test SpecimensFIG. 3 Typical Dimensional Specifications for X-band RectangularWave-guide Test SpecimensD 5568410.3.9 Measure the scattering parameters of the specimenholder containing a specimen. If one wishes to archive thescattering parameter data or to calcu
42、late permittivity andpermeability at a later time, save the S-parameter data on disk.10.3.10 Disconnect the Port 1 cable from the specimenholder. Disconnect the Port 2 cable from the specimen holder.10.3.11 Remove the specimen from the Port 1 side of thespecimen holder by pushing out the center cond
43、uctor from thePort 2 side. Push the center conductor straight out, withoutapplying lateral forces that may bend the center conductor anddamage the specimen. Be careful that the specimen does notbind or twist.10.4 Reverify CalibrationMeasure the permittivity of airin the empty specimen holder at the
44、beginning and end ofspecimen measurements and prior to any measurement whenmore than 2 h has lapsed since the previous air measurement.11. Calculation11.1 The selection of data reduction algorithm for calcula-tion of material characteristics depends on whether the materialis magnetic or nonmagnetic.
45、 In both of the following algo-rithms, specimen location is not critical. That is, the location ofthe specimen does not enter the solution.11.2 The general procedure for both algorithms is to firstgenerate initial estimates at all frequencies for permittivity (andpermeability) using an explicit solu
46、tion, and then to refine theinitial estimates with an iterative technique. There are manypossible solutions to the equations being used, and an initialestimate is necessary so as to select the proper root. Initialestimate calculation is not necessary if good permittivity andpermeability estimates ar
47、e available. One can determine if theinitial estimates are reasonable by the stability of permittivityand permeability results. If the initial estimates start theiterative calculation on the wrong root, the calculated resultstend to vary up and down and sometimes jump suddenly toanother root. A set
48、of equations relating scattering parametersand specimen length, permittivity and permeability is given asfollows:5F 5 S11S222 S21S125 exp $ 22g0Lair2 L!%G22 Z21 2G2Z2(6)G 5 S211 S12!/2 5 exp$2g0Lair2 L!%Z1 2G2!1 2G2Z2(7)11.2.1 Initial Estimate for Magnetic MaterialsIf a goodinitial estimate for perm
49、ittivity and permeability for eachfrequency is available, the calculations detailed in this sectionare not necessary. At each measured frequency, a solutionsimilar to that described by Nicholson and Ross6and by Weir7for permittivity and permeability can be derived from (Eq 6)and (Eq 7) as follows:*NRW51 1G21 1G21g0Lln Z 1 j2pn!. (8)e*NRW5c02pf*NRWFS2pgcD221L2ln Z 1 j2pn!2G(9)The ambiguity in the plus-or-minus sign in G2can beresolved by choosing | G2| |G3| # 1. Note that an estimate ofthe distance between the specimen and the Port 1 reference
