ASTM D7449/D7449M-22a

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it 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 version
of the standard as published by ASTM is to be considered the official document.
Designation: D7449/D7449M − 22 D7449/D7449M − 22a
Standard Test Method for
Measuring Relative Complex Permittivity and Relative
Magnetic Permeability of Solid Materials at Microwave
Frequencies Using Coaxial Air Line
This standard is issued under the fixed designation D7449/D7449M; the number immediately following the designation indicates the
year of original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last
reapproval. A superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1. Scope*
1.1 This test method covers a procedure for determining relative complex permittivity (relative dielectric constant and loss) and
relative magnetic permeability of isotropic, reciprocal (non-gyromagnetic) solid materials. If the material is nonmagnetic, it is
acceptable to use this procedure to measure permittivity only.
1.2 This measurement method is valid over a frequency range of approximately 1 GHz to over 20 GHz. These limits are not exact
and depend on the size of the specimen, the size of coaxial air line used as a specimen holder, and on the applicable frequency
range of the network analyzer used to make measurements. The size of specimen dimension is limited by test frequency, intrinsic
specimen electromagnetism properties, and the request of algorithm. For a given air line size, the upper frequency is also limited
by the onset of higher order modes that invalidate the dominant-mode transmission line model and the lower frequency is limited
by the smallest measurable phase shift through a specimen. Being a non-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 when only small sample volumes are available, particularly for
lower frequency measurements.
1.3 The values stated in either SI units of in inch-pound units are to be regarded separately as standard. The values stated in each
system are not necessarily exact equivalents; therefore each system shall be used independently of the other. Combining values
+jωt
from the two systems is likely to result in non conformance with the standard. The equations shown here assume an e harmonic
time convention.
1.4 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility
of the user of this standard to establish appropriate safety, health, and environmental practices and determine the applicability of
regulatory limitations prior to use.
1.5 This international standard was developed in accordance with internationally recognized principles on standardization
established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued
by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
2. Referenced Documents
2.1 ASTM Standards:
This test method is under the jurisdiction of ASTM Committee D09 on Electrical and Electronic Insulating Materials and is the direct responsibility of Subcommittee
D09.12 on Electrical Tests.
Current edition approved March 15, 2022Sept. 1, 2022. Published April 2022October 2022. Originally approved in 2008. Last previous edition approved in 20142022 as
D7449/D7449M – 14.D7449/D7449M – 22. DOI: 10.1520/D7449_D7449M-22.10.1520/D7449_D7449M-22A.
For referenced ASTM standards, visit the ASTM website, www.astm.org, or contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM Standards
volume information, refer to the standard’s Document Summary page on the ASTM website.
*A Summary of Changes section appears at the end of this standard
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
D7449/D7449M − 22a
D150 Test Methods for AC Loss Characteristics and Permittivity (Dielectric Constant) of Solid Electrical Insulation
D1711 Terminology Relating to Electrical Insulation
3. Terminology
3.1 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), ε , n—the proportionality factor that relates the electric
r
field to the electric flux density, and which depends on intrinsic material properties such as molecular polarizability, charge
mobility, and so forth:
W
D
* ’ ”
ε 5 ε 2 jε 5 (1)
r r r
W
ε E
where:
ε = permittivity of free space
W
= electric flux density vector, and
D
W
= electric field vector.
E
3.2.1.1 Discussion—
’
In common usage the word “relative” is frequently dropped. The real part of complex relative permittivity (ε ) is often referred to
r
”
as simply relative permittivity, permittivity, or dielectric constant. The imaginary part of complex relative permittivity (ε ) is often
r
referred to as the loss factor. In anisotropic media, permittivity is described by a three dimensional tensor. For the purposes of this
test 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, μ , n—the proportionality factor that relates the magnetic flux density to the magnetic field,
r
and which depends on intrinsic material properties such as magnetic moment, domain magnetization, and so forth:
W
B
* ’ ”
μ 5 μ 2 jμ 5 (2)
r r r
W
μ H
where:
μ = permeability of free space
W
= magnetic flux density vector, and
B
W
= magnetic field vector.
H
3.2.2.1 Discussion—
’
In common usage the word “relative” is frequently dropped. The real part of complex relative permeability (μ ) is often referred
r
”
to as relative permeability or simply permeability. The imaginary part of complex relative permeability (μ ) is often referred to as
r
the magnetic loss factor. In anisotropic media, permeability is described by a three dimensional tensor. For the purposes of this
test method, the media is considered to be isotropic, and therefore permeability is a single complex number at each frequency.
3.2 Definitions of Terms Specific to This Standard:
3.2.1 A list of symbols specific to this test method is given in Annex A1.
D7449/D7449M − 22a
3.2.2 calibration, n—a procedure for connecting characterized standard devices to the test ports of a network analyzer to
characterize the measurement system’s systematic errors. The effects of the systematic errors are then mathematically removed
from the indicated measurements. The calibration also establishes the mathematical reference plane for the measurement test ports.
3.2.2.1 Discussion—
Modern network analyzers have this capability built in. There are a variety of calibration kits that can be used depending on the
type of test port. The models used to predict the measurement response of the calibration devices depends on the type of calibration
kit. Most calibration kits come with media that can be used to load the definitions of the calibration devices into the network
analyzer. Calibration kit definitions loaded into the network analyzer must match the devices used to calibrate. Since both
transmission and reflection measurements are used in this standard, a two-port calibration is required.
3.2.3 cutoff frequency, n—the lowest frequency at which non-evanescent, higher-order mode propagation can occur within a
coaxial transmission line.
3.2.4 network analyzer, n—a system that measures the two-port transmission and one-port reflection characteristics of a multiport
system in its linear range and at a common input and output frequency.
3.2.4.1 Discussion—
For the purposes of this standard, this description includes only those systems that have a synthesized signal generator, and that
measure the complex scattering parameters (both magnitude and phase) in the forward and reverse directions of a two-port network
(S , S , S , S ).
11 21 12 22
3.2.5 scattering parameter (S-parameter), S , n—a complex number consisting of either the reflection or transmission coefficient
ij
of a component at a specified set of input and output reference planes with an incident signal on only a single port.
3.2.5.1 Discussion—
As most commonly used, these coefficients represent the quotient of the complex electric field strength (or voltage) of a reflected
or transmitted wave divided by that of an incident wave. The subscripts i and j of a typical coefficient S refer to the output and
ij
input ports, respectively. For example, the forward transmission coefficient S is the ratio of the transmitted wave voltage at
Reference Plane 2 (Port 2) divided by the incident wave voltage measured at Reference Plane 1 (Port 1). Similarly, the Port 1
reflection coefficient S is the ratio of the Port 1 reflected wave voltage divided by the Port 1 incident wave voltage at reference
plane 1 (Port 1).
3.2.6 transverse electromagneticc (TEM) wave, n—an electromagnetic wave in which both the electric and magnetic fields are
everywhere perpendicular to the direction of propagation.
3.2.6.1 Discussion—
In coaxial transmission lines the dominant wave is TEM.
4. Summary of Test Method
4.1 A carefully machined test specimen is placed in a coaxial air line and connected to a calibrated network analyzer that is used
to measure the S-parameters of the transmission line-with-specimen. A specified data-reduction algorithm is then used to calculate
permittivity and permeability. If the material is nonmagnetic, a different algorithm is used to calculate permittivity only. Error
corrections are then applied to compensate for air gaps between the specimen and the transmission line conductor surfaces.
5. Significance and Use
5.1 Design calculations for radio frequency (RF), microwave, and millimetre-wave components require the knowledge of values
of complex permittivity and permeability at operating frequencies. This test method is useful for evaluating small experimental
batch or continuous production materials used in electromagnetic applications. Use this method to determine complex permittivity
only (in non-magnetic materials), or both complex permittivity and permeability simultaneously.
*
5.2 Relative complex permittivity (relative complex dielectric constant), ε , is the proportionality factor that relates the electric
r
field to the electric flux density, and which depends on intrinsic material properties such as molecular polarizability, charge
mobility, and so forth:
W
D
* ’ ”
ε 5 ε 2 jε 5 (1)
r r r
W
ε E
D7449/D7449M − 22a
where:
ε = permittivity of free space
W
= electric flux density vector, and
D
W
= electric field vector.
E
’
NOTE 1—In common usage the word “relative” is frequently dropped. The real part of complex relative permittivity (ε ) is often referred to as simply
r
”
relative permittivity, permittivity, or dielectric constant. The imaginary part of complex relative permittivity (ε ) is often referred to as the loss factor. In
r
anisotropic media, permittivity is described by a three dimensional tensor.
NOTE 2—For the purposes of this test method, the media is considered to be isotropic and, therefore, permittivity is a single complex number at each
frequency.
*
5.3 Relative complex permeability, μ , is the proportionality factor that relates the magnetic flux density to the magnetic field, and
r
which depends on intrinsic material properties such as magnetic moment, domain magnetization, and so forth:
W
B
* ’ ”
μ 5 μ 2 jμ 5 (2)
r r r
W
μ H
where:
μ = permeability of free space,
W
= magnetic flux density vector, and
B
W
= magnetic field vector.
H
’
NOTE 3—In common usage the word “relative” is frequently dropped. The real part of complex relative permeability (μ ) is often referred to as relative
r
”
permeability or simply permeability. The imaginary part of complex relative permeability (μ ) is often referred to as the magnetic loss factor. In
r
anisotropic media, permeability is described by a three dimensional tensor.
NOTE 4—For the purposes of this test method, the media is considered to be isotropic, and therefore permeability is a single complex number at each
frequency.
5.4 Relative permittivity ((relative dielectric constant) (SIC) κ'(ε )) is the real part of the relative complex permittivity. It is also
r
the ratio of the equivalent parallel capacitance, C , of a given configuration of electrodes with a material as a dielectric to the
p
capacitance, C , of the same configuration of electrodes with vacuum (or air for most practical purposes) as the dielectric:
υ
κ'5 C /C (3)
p v
NOTE 5—In common usage the word “relative” is frequently dropped.
NOTE 6—Experimentally, vacuum must be replaced by the material at all points where it makes a significant change in capacitance. The equivalent circuit
of the dielectric is assumed to consist of C , a capacitance in parallel with conductance. (See Fig. 3 of Test Methods D150.)
p
NOTE 7—C is taken to be C , the equivalent parallel capacitance as shown in Fig. 3 of Test Methods D150.
x p
NOTE 8—The series capacitance is larger than the parallel capacitance by less than 1 % for a dissipation factor of 0.1, and by less than 0.1 % for a
dissipation factor of 0.03. If a measuring circuit yields results in terms of series components, the parallel capacitance must be calculated from Eq 5 of
Test Methods D150 before the corrections and permittivity are calculated.
NOTE 9—The permittivity of dry air at 23 °C and standard pressure at 101.3 kPa is 1.000536. Its divergence from unity, κ' − 1, is inversely proportional
to absolute temperature and directly proportional to atmospheric pressure. The increase in permittivity when the space is saturated with water vapor at
D7449/D7449M − 22a
23 °C is 0.00025, and varies approximately linearly with temperature expressed in degrees Celsius, from 10 °C to 27 °C. For partial saturation the increase
is proportional to the relative humidity.
6. Interferences
6.1 The upper limits of permittivity and permeability that can be measured using this test method are restricted by the transmission
line and specimen geometries, which can lead to unwanted higher order waveguide modes. In addition, excessive electromagnetic
attenuation due to a high loss factor within the test specimen can prevent determination of permittivity and permeability. No
specific limits are given in this standard, 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 the transmission line introduces a negative bias into measurements
of permittivity and permeability. In this test method, compensation for this bias is required, and to do so requires knowledge of
the air gap sizes. Air gap sizes are estimated from dimensional measurements of the specimen and the specimen holder. Several
different error correction models have been developed, and a frequency independent series capacitor model is described in Annex
A2. Air gap corrections are only approximate and therefore this test method is practically limited to low-to-medium values of
permittivity and permeability.
7. Apparatus
7.1 Experimental Test Fixture—The test fixture includes a specimen holder connected to a network analyzer, as shown in Fig. 1.
7.2 Network Analyzer—The network analyzer needs a full 2-port test set that can measure transmission and reflection-scattering
parameters. Use a network analyzer that has a synthesized signal generator in order to ensure good frequency stability and signal
purity.
7.3 Coaxial Air Line Calibration Kit—To define Port 1 and Port 2 measurement reference planes, calibration of the coaxial test
fixture is required. A calibration kit consists of well-characterized standard devices and mathematical models of those devices. Use
a through-reflect-line (TRL), an open-short-load-through (OSLT), or any other calibration kit that yields similar calibration quality
to calibrate 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 the
calculation of permittivity and permeability, carefully measure and characterize the physical dimensions of the specimen holder.
7.4.2 If a separate length of transmission line is used to hold the specimen, ensure that the empty length of line is also in place
during calibration of the specimen holder.
FIG. 1 Diagram of Experimental Fixture
D7449/D7449M − 22a
7.4.3 The theoretical model used for this test method assumes 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 of higher-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 transmission line size in use. For a coaxial
transmission line, the diameter of the center conductor, D , and the inside diameter of the outer conductor, D , are the critical
1 2
dimensions. Proper tolerances for a “7-mm” coax are then:
7–mm coax center conductor diameter:
D 5 3.04 mm60.01 mm @0.1197 in.60.0004 in.# (4)
7–mm coax outer conductor diameter:
D 5 7.00 mm60.01 mm 0.2756 in.60.0004 in. (5)
@ #
Dimensions and tolerances of other standard coaxial transmission lines are in the appropriate manufacturer’s specifications.
8. Test Specimen
8.1 Make the test specimen long enough to ensure good alignment inside the holder. Also, make the test specimen long enough
to ensure that the phase shift through the specimen is much greater than the phase measurement uncertainty of the network analyzer
at the lowest measurement frequency. If a specimen is expected to have low loss, sufficient length is also required to insure accurate
determination of the loss factor. Finally, for high loss specimens, the specimen length cannot be so long that high insertion loss
prevents 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 its
dimensions minimize the air gap that exists between the conductor surfaces and the specimen. In this respect, measure the
specimen holder’s dimensions in order to specify the tightest tolerances possible for specimen preparation. Keep physical
variations of specimen dimensions as small as is practicable and include specimen dimensions and uncertainties in the report.
9. Preparation of Apparatus
9.1 Inspect Network Analyzer Test Ports—Insure that the recession of both test ports’ center conductor shoulder behind the outer
conductor mating plane meets the minimum specifications. Refer to network analyzer manufacturer’s documentation to provide
connector specificat
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