1、Designation: D 7449/D 7449M 08Standard Test Method forMeasuring Relative Complex Permittivity and RelativeMagnetic Permeability of Solid Materials at MicrowaveFrequencies Using Coaxial Air Line1This standard is issued under the fixed designation D 7449/D 7449M; the number immediately following the d
2、esignation indicates theyear of original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of lastreapproval. A superscript epsilon () indicates an editorial change since the last revision or reapproval.1. Scope1.1 This test method covers a p
3、rocedure for determiningrelative complex permittivity (relative dielectric constant andloss) and relative magnetic permeability of isotropic, reciprocal(non-gyromagnetic) solid materials. If the material is nonmag-netic, it is acceptable to use this procedure to measurepermittivity only.1.2 This mea
4、surement method is valid over a frequencyrange of approximately 1 MHz to over 20 GHz. These limitsare not exact and depend on the size of the specimen, the sizeof coaxial air line used as a specimen holder, and on theapplicable frequency range of the network analyzer used tomake measurements. The pr
5、actical lower and upper frequen-cies are limited by specimen dimension requirements (large,thick specimens at low frequencies and small specimens athigh frequencies). For a given air line size, the upper frequencyis also limited by the onset of higher order modes thatinvalidate the dominant-mode tra
6、nsmission line model and thelower frequency is limited by the smallest measurable phaseshift through a specimen. Being a non-resonant method, theselection of any number of discrete measurement frequenciesin a measurement band would be suitable. The coaxial fixtureis preferred over rectangular wavegu
7、ide fixtures when broad-band data are desired with a single sample or when only smallsample volumes are available, particularly for lower frequencymeasurements1.3 The values stated in either SI units or inch-pound unitsare to be regarded separately as standard. The values stated ineach system may no
8、t be exact equivalents; therefore, eachsystem shall be used independently of the other. Combiningvalues from the two systems may result in non-conformancewith the standard. The equations shown here assume an e+jvtharmonic time convention.1.4 This standard does not purport to address all of thesafety
9、 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. Referenced Documents2.1 ASTM Standards:2D 1711 Terminology Relating to Ele
10、ctrical Insulation3. Terminology3.1 For definitions of terms used in this test method, refer toTerminology D 1711.3.2 Definitions:3.2.1 relative complex permittivity (relative complex dielec-tric constant), r*, nthe proportionality factor that relates theelectric field to the electric flux density,
11、and which depends onintrinsic material properties such as molecular polarizability,charge mobility, etc.:r*5r jr”5D0E(1)where:0= permittivity of free spaceD= electric flux density vector, andE= electric field vector.3.2.1.1 DiscussionIn common usage the word “relative”is frequently dropped. The real
12、 part of complex relativepermittivity ( r) is often referred to as simply relativepermittivity, permittivity or dielectric constant. The imaginarypart of complex relative permittivity ( r”) is often referred toas the loss factor. In anisotropic media, permittivity is de-scribed by a three dimensiona
13、l tensor. For the purposes of thistest method, the media is considered to be isotropic, andtherefore permittivity is a single complex number at eachfrequency.1This test method is under the jurisdiction of ASTM Committee D09 onElectrical and Electronic Insulating Materials and is the direct responsib
14、ility ofSubcommittee D09.12 on Electrical Tests.Current edition approved Nov. 15, 2008. Published December 2008.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at serviceastm.org. For Annual Book of ASTMStandards volume information, refer to the
15、standards Document Summary page onthe ASTM website.1Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.3.2.2 relative complex permeability, r*, nthe proportion-ality factor that relates the magnetic flux density to themagnetic field, and
16、 which depends on intrinsic material prop-erties such as magnetic moment, domain magnetization, etc.:r*5 r jr”5B0H(2)where:0= permeability of free spaceB= magnetic flux density vector, andH= magnetic field vector.3.2.2.1 DiscussionIn common usage the word “relative”is frequently dropped. The real pa
17、rt of complex relativepermeability ( r) is often referred to as relative permeabilityor simply permeability. The imaginary part of complex relativepermeability ( r”) is often referred to as the magnetic lossfactor. In anisotropic media, permeability is described by athree dimensional tensor. For the
18、 purposes of this test method,the media is considered to be isotropic, and therefore perme-ability is a single complex number at each frequency.3.3 Definitions of Terms Specific to This Standard:3.3.1 A list of symbols specific to this test method is givenin Annex A1.3.3.2 calibration, na procedure
19、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 calibration alsoestablishes the mathematical refe
20、rence 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 thatcan be used depending on the type of test port. The modelsused to predict the measurement response of the calibrationdevices depends on the
21、 type of calibration kit. Most calibrationkits come with media that can be used to load the definitions ofthe calibration devices into the network analyzer. Calibrationkit definitions loaded into the network analyzer must match thedevices used to calibrate. Since both transmission and reflec-tion me
22、asurements are used in this standard, a two-portcalibration is required.3.3.3 cutoff frequency, nthe lowest frequency at whichnon-evanescent, higher-order mode propagation can occurwithin a coaxial transmission line3.3.4 network analyzer, na system that measures thetwo-port transmission and one-port
23、 reflection characteristics ofa multiport system in its linear range and at a common inputand output frequency.3.3.4.1 DiscussionFor the purposes of this standard, thisdescription includes only those systems that have a synthesizedsignal generator, and that measure the complex scatteringparameters (
24、both magnitude and phase) in the forward andreverse directions of a two-port network (S11, S21, S12, S22).3.3.5 scattering parameter (S-parameter), Sij, na complexnumber consisting of either the reflection or transmissioncoefficient of a component at a specified set of input and outputreference plan
25、es with an incident signal on only a single port.3.3.5.1 DiscussionAs most commonly used, these coeffi-cients represent the quotient of the complex electric fieldstrength (or voltage) of a reflected or transmitted wave dividedby that of an incident wave. The subscripts i and j of a typicalcoefficien
26、t 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 voltage measured at ReferencePlane 1 (Port 1). Similarly, the Port 1 reflection coefficien
27、t S11is the ratio of the Port 1 reflected wave voltage divided by thePort 1 incident wave voltage at reference plane 1 (Port 1).3.3.6 transverse electromagneticc (TEM) wave, nan elec-tromagnetic wave in which both the electric and magneticfields are everywhere perpendicular to the direction of propa
28、-gation.3.3.6.1 DiscussionIn coaxial transmission lines the domi-nant wave is TEM.4. Summary of Test Method4.1 A carefully machined test specimen is placed in acoaxial air line and connected to a calibrated network analyzerthat is used to measure the S-parameters of the transmissionline-with-specime
29、n. A specified data-reduction algorithm isthen used to calculate permittivity and permeability. If thematerial is nonmagnetic, a different algorithm is used tocalculate permittivity only. Error corrections are then appliedto compensate for air gaps between the specimen and thetransmission line condu
30、ctor surfaces.5. Significance and Use5.1 Design calculations for radio frequency (RF), micro-wave and millimetre-wave components require the knowledgeof values of complex permittivity and permeability at operatingfrequencies. This test method is useful for evaluating smallexperimental batch or conti
31、nuous production materials used inelectromagnetic applications. Use this method to determinecomplex permittivity only (in non-magnetic materials) or bothcomplex permittivity and permeability simultaneously.6. Interferences6.1 The upper limits of permittivity and permeability thatcan be measured usin
32、g this test method are restricted by thetransmission line and specimen geometries, which can lead tounwanted higher order waveguide modes. In addition, exces-sive electromagnetic attenuation due to a high loss factorwithin the test specimen can prevent determination of permit-tivity and permeability
33、. No specific limits are given in thisstandard, but this test method is practically limited to low-to-medium values of permittivity and permeability.6.2 The existence of air gaps between the test specimen andthe transmission line introduces a negative bias into measure-ments of permittivity and perm
34、eability. In this test method,compensation for this bias is required, and to do so requiresknowledge of the air gap sizes. Air gap sizes are estimatedfrom dimensional measurements of the specimen and thespecimen holder. Several different error correction modelsD 7449/D 7449M 082have been developed,
35、and a frequency independent seriescapacitor model is described in Annex A2. Air gap correctionsare only approximate and therefore this test method is practi-cally limited to low-to-medium values of permittivity andpermeability.7. Apparatus7.1 Experimental Test FixtureThe test fixture includes aspeci
36、men holder connected to a network analyzer, as shown inFig. 1.7.2 Network AnalyzerThe network analyzer needs a full2-port test set that can measure transmission and reflectionscattering parameters. Use a network analyzer that has asynthesized signal generator in order to ensure good frequencystabili
37、ty and signal purity.7.3 Coaxial Air Line Calibration KitTo define Port 1 andPort 2 measurement reference planes, calibration of the coaxialtest fixture is required. A calibration kit consists of well-characterized standard devices and mathematical models ofthose devices. Use a through-reflect-line
38、(TRL), an open-short-load-through (OSLT), or any other calibration kit that yieldssimilar calibration quality to calibrate the coaxial test fixture.7.4 Specimen Holder:7.4.1 Because parameters such as specimen holder lengthand cross-sectional dimensions are of critical importance to thecalculation o
39、f permittivity and permeability, carefully measureand characterize the physical dimensions of the specimenholder.7.4.2 If a separate length of transmission line is used to holdthe specimen, ensure that the empty length of line is also inplace during calibration of the specimen holder.7.4.3 The theor
40、etical model used for this test methodassumes that only the dominant mode of propagation exists(TEM). This fundamental mode has no lower cutoff frequency,so low frequency measurements are possible. The existence ofhigher-order modes restricts the upper measurement frequencyfor a given coaxial air li
41、ne test fixture.7.4.4 Be sure that the specimen holder dimensions arewithin proper tolerances for the transmission line size in use.For a rectangular coaxial transmission line, the diameter of thecenter conductor, D1, and the inside diameter of the outerconductor, D2, are the critical dimensions. Pr
42、oper tolerancesfor a “7-mm” coax are then:7-mm coax center conductor diameter:D15 3.04 6 0.01 mm 0.1197 6 0.0004 in. (3)7-mm coax outer conductor diameter:D25 7.00 6 0.01 mm 0.2756 6 0.0004 in. (4)Dimensions and tolerances of other standard coaxial trans-mission lines are in the appropriate manufact
43、urers specifica-tions.8. Test Specimen8.1 Make the test specimen long enough to ensure goodalignment inside the holder. Also, make the test specimen longenough to ensure that the phase shift through the specimen ismuch greater than the phase measurement uncertainty of thenetwork analyzer at the lowe
44、st measurement frequency. If aspecimen is expected to have low loss, sufficient length is alsorequired to insure accurate determination of the loss factor.Finally, for high loss specimens, the specimen length cannot beso long that high insertion loss prevents material propertyinversion.8.2 A test sp
45、ecimen that fits into a coaxial transmission lineis a toroidal cylinder. Accurately machine the specimen so thatits dimensions minimize the air gap that exists between theconductor surfaces and the specimen. In this respect, measurethe specimen holders dimensions in order to specify thetightest tole
46、rances possible for specimen preparation. Keepphysical variations of specimen dimensions as small as ispracticable and include specimen dimensions and uncertaintiesin the report.FIG. 1 Diagram of Experimental FixtureD 7449/D 7449M 0839. Preparation of Apparatus9.1 Inspect Network Analyzer Test Ports
47、Insure that therecession of both test ports center conductor shoulder behindthe outer conductor mating plane meets the minimum specifi-cations. Refer to network analyzer manufacturers documenta-tion to provide connector specifications.9.2 Flexing and Tightening Cables and ConnectorsCableflexing and
48、improperly tightened connectors introduce phaseand magnitude errors into S-parameter data. For this reason,bend the test cables as little as possible, and under nocircumstances bend the test cables smaller than the manufac-turers minimum recommended radius. Use of phase-stablecables is highly recomm
49、ended. Insofar as possible, return thenetwork analyzer cables to the same position during measure-ment of calibration standards and specimen. Use a torquewrench with the manufacturers recommended torque totighten connectors.9.3 Inspect and Clean Specimen, Specimen Holder, andConnectorsIf contamination is a concern, handle specimenswith laboratory gloves. Clean specimens, connectors, andtransmission lines using lint-free swabs and isopropyl alcohol(not less than 99 % pure). Blow out specimens, connectors, andtransmission lin
