1、Designation: D7449/D7449M 081D7449/D7449M 14Standard 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 immediately fol
2、lowing 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.1 NOTEEquation 5 was editor
3、ially updated in March 2012.1. Scope Scope*1.1 This test method covers a procedure for determining relative complex permittivity (relative dielectric constant and loss) andrelative magnetic permeability of isotropic, reciprocal (non-gyromagnetic) solid materials. If the material is nonmagnetic, it i
4、sacceptable to use this procedure to measure permittivity only.1.2 This measurement method is valid over a frequency range of approximately 1 MHz to over 20 GHz. 20 GHz. These limitsare not exact and depend on the size of the specimen, the size of coaxial air line used as a specimen holder, and on t
5、he applicablefrequency range of the network analyzer used to make measurements. The practical lower and upper frequencies are limited byspecimen dimension requirements (large, thick specimens at low frequencies and small specimens at high frequencies). size ofspecimen dimension is limited by test fr
6、equency, intrinsic specimen electromagnetism properties, and the request of algorithm. Fora given air line size, the upper frequency is also limited by the onset of higher order modes that invalidate the dominant-modetransmission line model and the lower frequency is limited by the smallest measurab
7、le phase shift through a specimen. Being anon-resonant method, the selection of any number of discrete measurement frequencies in a measurement band would be suitable.The coaxial fixture is preferred over rectangular waveguide fixtures when broadband data are desired with a single sample or whenonly
8、 small sample volumes are available, particularly for lower frequency measurements1.3 The values stated in either SI units or of in inch-pound units are to be regarded separately as standard. The values statedin each system mayare not benecessarily exact equivalents; therefore,therefore each system
9、shall be used independently of theother. Combining values from the two systems may is likely to result in non-conformance non conformance with the standard. Theequations shown here assume an e+jt harmonic time convention.1.4 This standard does not purport to address all of the safety concerns, if an
10、y, associated with its use. It is the responsibilityof the user of this standard to establish appropriate safety and health practices and determine the applicability of regulatorylimitations prior to use.2. Referenced Documents2.1 ASTM Standards:2D1711 Terminology Relating to Electrical Insulation3.
11、 Terminology3.1 For definitions of terms used in this test method, refer to Terminology D1711.3.2 Definitions:3.2.1 relative complex permittivity (relative complex dielectric constant), r*, nthe proportionality factor that relates the electricfield to the electric flux density, and which depends on
12、intrinsic material properties such as molecular polarizability, chargemobility, etc.:and so forth:1 This test method is under the jurisdiction of ASTM Committee D09 on Electrical and Electronic Insulating Materials and is the direct responsibility of SubcommitteeD09.12 on Electrical Tests.Current ed
13、ition approved Nov. 15, 2008Nov. 1, 2014. Published December 2008December 2014. DOI: 10.1520/D7449_D7449M-08E01. Originally approved in 2008. Lastprevious edition approved in 2008 as D7449/D7449M 081. DOI: 10.1520/D7449_D7449M-14.2 For referencedASTM standards, visit theASTM website, www.astm.org, o
14、r contactASTM Customer Service at serviceastm.org. For Annual Book of ASTM Standardsvolume information, refer to the standards Document Summary page on the ASTM website.This document is not an ASTM standard and is intended only to provide the user of an ASTM standard an indication of what changes ha
15、ve been made to the previous version. Becauseit may not be technically possible to adequately depict all changes accurately, ASTM recommends that users consult prior editions as appropriate. In all cases only the current versionof the standard as published by ASTM is to be considered the official do
16、cument.*A Summary of Changes section appears at the end of this standardCopyright ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States1r*5r 2jr”5 DW0EW(1)where:0 = permittivity of free spaceDW = electric flux density vector, andEW = electric field v
17、ector.3.2.1.1 DiscussionIn common usage the word “relative” is frequently dropped. The real part of complex relative permittivity (r) is often referred toas simply relative permittivity, permittivity, or dielectric constant. The imaginary part of complex relative permittivity (r”) is oftenreferred t
18、o as the loss factor. In anisotropic media, permittivity is described by a three dimensional tensor. For the purposes of thistest method, the media is considered to be isotropic, and therefore permittivity is a single complex number at each frequency.3.2.2 relative complex permeability, r*, nthe pro
19、portionality factor that relates the magnetic flux density to the magnetic field,and which depends on intrinsic material properties such as magnetic moment, domain magnetization, etc.:and so forth:r*5r 2jr”5 BW0HW(2)where:0 = permeability of free spaceBW = magnetic flux density vector, andHW = magne
20、tic field vector.3.2.2.1 DiscussionIn common usage the word “relative” is frequently dropped. The real part of complex relative permeability (r) is often referredto as relative permeability or simply permeability. The imaginary part of complex relative permeability (r”) is often referred to asthe ma
21、gnetic loss factor. In anisotropic media, permeability is described by a three dimensional tensor. For the purposes of thistest method, the media is considered to be isotropic, and therefore permeability is a single complex number at each frequency.3.3 Definitions of Terms Specific to This Standard:
22、3.3.1 A list of symbols specific to this test method is given in Annex A1.3.3.2 calibration, na procedure for connecting characterized standard devices to the test ports of a network analyzer tocharacterize the measurement systems systematic errors. The effects of the systematic errors are then math
23、ematically removedfrom the indicated measurements. The calibration also establishes the mathematical reference plane for the measurement test ports.3.3.2.1 DiscussionModern network analyzers have this capability built in. There are a variety of calibration kits that can be used depending on thetype
24、of test port. The models used to predict the measurement response of the calibration devices depends on the type of calibrationkit. Most calibration kits come with media that can be used to load the definitions of the calibration devices into the networkanalyzer. Calibration kit definitions loaded i
25、nto the network analyzer must match the devices used to calibrate. Since bothtransmission and reflection measurements are used in this standard, a two-port calibration is required.3.3.3 cutoff frequency, nthe lowest frequency at which non-evanescent, higher-order mode propagation can occur within ac
26、oaxial transmission lineline.3.3.4 network analyzer, na system that measures the two-port transmission and one-port reflection characteristics of amultiport system in its linear range and at a common input and output frequency.D7449/D7449M 1423.3.4.1 DiscussionFor the purposes of this standard, this
27、 description includes only those systems that have a synthesized signal generator, and thatmeasure the complex scattering parameters (both magnitude and phase) in the forward and reverse directions of a two-port network(S11, S21, S12, S22).3.3.5 scattering parameter (S-parameter), Sij, na complex nu
28、mber consisting of either the reflection or transmissioncoefficient of a component at a specified set of input and output reference planes with an incident signal on only a single port.3.3.5.1 DiscussionAs most commonly used, these coefficients represent the quotient of the complex electric field st
29、rength (or voltage) of a reflectedor transmitted wave divided by that of an incident wave. The subscripts i and j of a typical coefficient Sij refer to the output andinput ports, respectively. For example, the forward transmission coefficient S21 is the ratio of the transmitted wave voltage atRefere
30、nce Plane 2 (Port 2) divided by the incident wave voltage measured at Reference Plane 1 (Port 1). Similarly, the Port 1reflection coefficient S11 is the ratio of the Port 1 reflected wave voltage divided by the Port 1 incident wave voltage at referenceplane 1 (Port 1).3.3.6 transverse electromagneti
31、cc (TEM) wave, nan electromagnetic wave in which both the electric and magnetic fields areeverywhere perpendicular to the direction of propagation.3.3.6.1 DiscussionIn coaxial transmission lines the dominant wave is TEM.4. Summary of Test Method4.1 Acarefully machined test specimen is placed in a co
32、axial air line and connected to a calibrated network analyzer that is usedto measure the S-parameters of the transmission line-with-specimen.Aspecified data-reduction algorithm is then used to calculatepermittivity and permeability. If the material is nonmagnetic, a different algorithm is used to ca
33、lculate permittivity only. Errorcorrections are then applied to compensate for air gaps between the specimen and the transmission line conductor surfaces.5. Significance and Use5.1 Design calculations for radio frequency (RF), microwave, and millimetre-wave components require the knowledge of values
34、of complex permittivity and permeability at operating frequencies. This test method is useful for evaluating small experimentalbatch or continuous production materials used in electromagnetic applications. Use this method to determine complex permittivityonly (in non-magnetic materials)materials), o
35、r both complex permittivity and permeability simultaneously.6. Interferences6.1 The upper limits of permittivity and permeability that can be measured using this test method are restricted by thetransmission line and specimen geometries, which can lead to unwanted higher order waveguide modes. In ad
36、dition, excessiveelectromagnetic attenuation due to a high loss factor within the test specimen can prevent determination of permittivity andpermeability. No specific limits are given in this standard, but this test method is practically limited to low-to-medium values ofpermittivity and permeabilit
37、y.6.2 The existence of air gaps between the test specimen and the transmission line introduces a negative bias into measurementsof permittivity and permeability. In this test method, compensation for this bias is required, and to do so requires knowledge ofthe air gap sizes. Air gap sizes are estima
38、ted from dimensional measurements of the specimen and the specimen holder. Severaldifferent error correction models have been developed, and a frequency independent series capacitor model is described in AnnexA2. Air gap corrections are only approximate and therefore this test method is practically
39、limited to low-to-medium values ofpermittivity and permeability.7. Apparatus7.1 Experimental Test FixtureThe test fixture includes a specimen holder connected to a network analyzer, as shown in Fig.1.7.2 Network AnalyzerThe network analyzer needs a full 2-port test set that can measure transmission
40、and reflection scatteringreflection-scattering parameters. Use a network analyzer that has a synthesized signal generator in order to ensure good frequencystability and signal purity.D7449/D7449M 1437.3 Coaxial Air Line Calibration KitTo define Port 1 and Port 2 measurement reference planes, calibra
41、tion of the coaxial testfixture is required.Acalibration kit consists of well-characterized standard devices and mathematical models of those devices. Usea through-reflect-line (TRL), an open-short-load-through (OSLT), or any other calibration kit that yields similar calibration qualityto calibrate
42、the coaxial test fixture.7.4 Specimen Holder:7.4.1 Because parameters such as specimen holder length and cross-sectional dimensions are of critical importance to thecalculation of permittivity and permeability, carefully measure and characterize the physical dimensions of the specimen holder.7.4.2 I
43、f a separate length of transmission line is used to hold the specimen, ensure that the empty length of line is also in placeduring calibration of the specimen holder.7.4.3 The theoretical model used for this test method assumes that only the dominant mode of propagation exists (TEM). Thisfundamental
44、 mode has no lower cutoff frequency, so low frequency low-frequency measurements are possible. The existence ofhigher-order modes restricts the upper measurement frequency for a given coaxial air line test fixture.7.4.4 Be sure that the specimen holder dimensions are within proper tolerances for the
45、 transmission line size in use. For arectangular coaxial coaxial transmission line, the diameter of the center conductor, D1, and the inside diameter of the outerconductor, D2, are the critical dimensions. Proper tolerances for a “7-mm” coax are then:7mm coax center conductor diameter:D153.0460.01 m
46、m 0.119760.0004 in.# (3)7mm coax outer conductor diameter:D257.0060.01 mm 0.275660.0004 in.# (4)7mm coax center conductor diameter:D153.0460.01 mm 0.119760.0004 in.# (3)7mm coax outer conductor diameter:D257.0060.01 mm 0.275660.0004 in.# (4)Dimensions and tolerances of other standard coaxial transmi
47、ssion lines are in the appropriate manufacturers specifications.8. Test Specimen8.1 Make the test specimen long enough to ensure good alignment inside the holder. Also, make the test specimen long enoughto ensure that the phase shift through the specimen is much greater than the phase measurement un
48、certainty of the network analyzerat the lowest measurement frequency. If a specimen is expected to have low loss, sufficient length is also required to insure accuratedetermination of the loss factor. Finally, for high loss specimens, the specimen length cannot be so long that high insertion losspre
49、vents material property inversion.8.2 A test specimen that fits into a coaxial transmission line is a toroidal cylinder. Accurately machine the specimen so that itsdimensions minimize the air gap that exists between the conductor surfaces and the specimen. In this respect, measure theFIG. 1 Diagram of Experimental FixtureD7449/D7449M 144specimen holders dimensions in order to specify the tightest tolerances possible for specimen preparation. Keep physicalvariations of specimen dimensions as small as is practicable and include
