1、Designation: D7449/D7449M 081An American National StandardStandard 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 D7449/D7449M; the number i
2、mmediately following the designation 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.1NOTEEquation
3、 5 was editorially updated in March 2012.1. Scope1.1 This test method covers a procedure 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,
4、 it is acceptable to use this procedure to measurepermittivity only.1.2 This measurement 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 theapp
5、licable frequency range of the network analyzer used tomake measurements. The practical 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
6、 limited by the onset of higher order modes thatinvalidate the dominant-mode transmission 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
7、 band would be suitable. The coaxial fixtureis preferred over rectangular waveguide 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 unitsa
8、re to be regarded separately as standard. The values stated ineach system may not 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+jvtharmoni
9、c time convention.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 u
10、se.2. Referenced Documents2.1 ASTM Standards:2D1711 Terminology Relating to Electrical Insulation3. Terminology3.1 For definitions of terms used in this test method, refer toTerminology D1711.3.2 Definitions:3.2.1 relative complex permittivity (relative complex dielec-tric constant), r*, nthe propor
11、tionality factor that relates theelectric field to the electric flux density, 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.
12、1 DiscussionIn common usage the word “relative”is frequently dropped. The real part of complex relativepermittivity r! is often referred to as simply relative permit-tivity, permittivity or dielectric constant. The imaginary part of1This test method is under the jurisdiction of ASTM Committee D09 on
13、Electrical and Electronic Insulating Materials and is the direct responsibility ofSubcommittee D09.12 on Electrical Tests.Current edition approved Nov. 15, 2008. Published December 2008. DOI:10.1520/D7449_D7449M-08E01.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact AS
14、TM Customer Service at serviceastm.org. For Annual Book of ASTMStandards volume information, refer to the standards Document Summary page onthe ASTM website.1Copyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United Splex relative permittivity r”! is
15、often referred to as the lossfactor. In anisotropic media, permittivity is described by a threedimensional tensor. For the purposes of this test method, themedia is considered to be isotropic, and therefore permittivityis a single complex number at each frequency.3.2.2 relative complex permeability,
16、 r*, nthe proportion-ality factor that relates the magnetic flux density to themagnetic field, and 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 fi
17、eld vector.3.2.2.1 DiscussionIn common usage the word “relative”is frequently dropped. The real part of complex relativepermeability r! is often referred to as relative permeability orsimply permeability. The imaginary part of complex relativepermeability r”! is often referred to as the magnetic los
18、s factor.In anisotropic media, permeability is described by a threedimensional tensor. For the purposes of this test method, themedia is considered to be isotropic, and therefore permeabilityis a single complex number at each frequency.3.3 Definitions of Terms Specific to This Standard:3.3.1 A list
19、of symbols specific to this test method is givenin 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-
20、moved from the indicated measurements. The calibration 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 thatcan be used depending on the type of test port.
21、 The modelsused to predict the measurement response of the calibrationdevices depends on the 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
22、analyzer must match thedevices used to calibrate. Since both transmission and reflec-tion measurements 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 transmissi
23、on line3.3.4 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 inputand output frequency.3.3.4.1 DiscussionFor the purposes of this standard, thisdescription includes only those systems
24、that have a synthesizedsignal generator, and that measure the complex scatteringparameters (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
25、 transmissioncoefficient of a component at a specified set of input and outputreference planes 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 transm
26、itted 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 wav
27、e voltage 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 at reference plane 1 (Port 1).3.3.6 transverse electromagneticc (TEM) wave, nan elec-tromagnetic wave in which
28、 both the electric and magneticfields are everywhere perpendicular to the direction of propa-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 n
29、etwork analyzerthat is used to measure the S-parameters of the transmissionline-with-specimen. 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 ar
30、e then appliedto compensate for air gaps between the specimen and thetransmission line conductor 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 oper
31、atingfrequencies. This test method is useful for evaluating smallexperimental batch or continuous production materials used inelectromagnetic applications. Use this method to determinecomplex permittivity only (in non-magnetic materials) or bothcomplex permittivity and permeability simultaneously.6.
32、 Interferences6.1 The upper limits of permittivity and permeability thatcan be measured using 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 los
33、s factorwithin the test specimen can prevent determination of permit-tivity and permeability. 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 and
34、the transmission line introduces a negative bias into measure-ments of permittivity and permeability. In this test method,D7449/D7449M 0812compensation for this bias is required, and to do so requiresknowledge of the air gap sizes. Air gap sizes are estimatedfrom dimensional measurements of the spec
35、imen and thespecimen holder. Several different error correction modelshave been developed, 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 permittivit
36、y andpermeability.7. Apparatus7.1 Experimental Test FixtureThe test fixture includes aspecimen 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 netwo
37、rk analyzer that has asynthesized signal generator in order to ensure good frequencystability 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-characte
38、rized standard devices and mathematical models ofthose devices. Use a through-reflect-line (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
39、 holder lengthand cross-sectional dimensions are of critical importance to thecalculation of 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 emp
40、ty length of line is also inplace during calibration of the specimen holder.7.4.3 The theoretical 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 existen
41、ce ofhigher-order modes restricts the upper measurement frequencyfor a given coaxial air line 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 conduc
42、tor, D1, and the inside diameter of the outerconductor, D2, are the critical dimensions. Proper 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 a
43、nd tolerances of other standard coaxial trans-mission lines are in the appropriate manufacturers 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 specim
44、en ismuch greater than the phase measurement uncertainty of thenetwork analyzer at the lowest 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
45、cannot beso long that high insertion loss prevents material propertyinversion.8.2 A test specimen 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. I
46、n this respect, measurethe specimen holders dimensions in order to specify thetightest tolerances possible for specimen preparation. KeepFIG. 1 Diagram of Experimental FixtureD7449/D7449M 0813physical variations of specimen dimensions as small as ispracticable and include specimen dimensions and unc
47、ertaintiesin the report.9. Preparation of Apparatus9.1 Inspect Network Analyzer Test PortsInsure 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
48、connector specifications.9.2 Flexing and Tightening Cables and ConnectorsCableflexing and 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
49、 the manufac-turers minimum recommended radius. Use of phase-stablecables is highly recommended. 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-fr
