ASTM D5568-22a

Standard Test Method for Measuring Relative Complex Permittivity and Relative Magnetic Permeability of Solid Materials at Microwave Frequencies Using Waveguide

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), εr*, is the proportionality factor that relates the electric field to the electric flux density, and which depends on intrinsic material properties such as molecular polarizability, charge mobility, and so forth:
   where:
  ε0  =  the permittivity of free space,   D→  =  the electric flux density vector, and   E→  =  the electric field vector.  
Note 1: In common usage the word “relative” is frequently dropped. The real part of complex relative permittivity (εr′) is often referred to as simply relative permittivity, permittivity, or dielectric constant. The imaginary part of complex relative permittivity (εr′′) is often referred to as the loss factor. In 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, μr*, is the proportionality factor that relates the magnetic flux density to the magnetic field, and which depends on intrinsic material properties such as magnetic moment, domain magnetization, and so forth:
   where:
  μ0  =  the permeability of free space,   B→  =  the magnetic flux density vector, and   H→  =  the magnetic field vector.  
Note 3: In common usage the word “relative” is frequently dropped. The real part of complex relative permeability (μr′) is often referre...
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 100 MHz to over 40 GHz. These limits are not exact and depend on the size of the specimen, the size of rectangular waveguide transmission 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. Being a non-resonant method, the selection of any number of discrete measurement frequencies in a measurement band would be suitable. Use of multiple rectangular waveguide transmission line sizes are required to cover this entire frequency range (100 MHz to 40 GHz). This test method can also be generally applied to circular waveguide test fixtures. The rectangular waveguide fixture is preferred over coaxial fixtures when samples have in-plane anisotropy or are difficult to manufacture precisely.  
1.3 The values stated in SI units are to be regarded as the standard. The values given in parentheses are in inch-pound units and are included for information only. The equations shown here assume an e+jωt 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 sta...

General Information

• Status: Published
• Publication Date: 31-Aug-2022
• ICS: 17.220.01 - Electricity. Magnetism. General aspects
• Technical Committee: D09 - Electrical and Electronic Insulating Materials
• Drafting Committee: D09.12 - Electrical Tests

Relations

• Refers: ASTM D1711-24 - Standard Terminology Relating to Electrical Insulation
• Effective Date: 01-Mar-2024
• Refers: ASTM D1711-15 - Standard Terminology Relating to Electrical Insulation
• Effective Date: 01-Nov-2015
• Refers: ASTM D1711-14a - Standard Terminology Relating to Electrical Insulation
• Effective Date: 01-Nov-2014
• Refers: ASTM D1711-14 - Standard Terminology Relating to Electrical Insulation
• Effective Date: 01-May-2014
• Refers: ASTM D1711-13 - Standard Terminology Relating to Electrical Insulation
• Effective Date: 01-Nov-2013
• Refers: ASTM D1711-11a - Standard Terminology Relating to Electrical Insulation
• Effective Date: 01-Aug-2011
• Refers: ASTM D1711-08 - Standard Terminology Relating to Electrical Insulation
• Effective Date: 01-May-2008
• Refers: ASTM D150-98(2004) - Standard Test Methods for AC Loss Characteristics and Permittivity (Dielectric Constant) of Solid Electrical Insulation
• Effective Date: 01-Mar-2004
• Refers: ASTM D1711-02 - Standard Terminology Relating to Electrical Insulation
• Effective Date: 10-Mar-2002
• Refers: ASTM D1711-99 - Standard Terminology Relating to Electrical Insulation
• Effective Date: 10-Oct-1999
• Refers: ASTM D150-98 - Standard Test Methods for AC Loss Characteristics and Permittivity (Dielectric Constant) of Solid Electrical Insulation
• Effective Date: 10-Feb-1998

Overview

ASTM D5568-22a is the standard test method published by ASTM International for measuring the relative complex permittivity (dielectric constant and loss) and relative magnetic permeability of isotropic, reciprocal (non-gyromagnetic) solid materials at microwave frequencies using waveguide techniques. This method plays a crucial role in evaluating material properties required for designing radio frequency (RF), microwave, and millimeter-wave components. It is suitable for both small experimental batches and production materials used in electromagnetic applications.

This standard is valid over a frequency range of approximately 100 MHz to over 40 GHz, depending on factors such as specimen size, type of waveguide, and network analyzer operating range. It accommodates both materials with only dielectric properties (non-magnetic) and those where both permittivity and permeability need to be determined.

Key Topics

• Complex Permittivity Measurement: Assesses both the real (dielectric constant) and imaginary (loss factor) components, important for understanding how materials respond to electric fields at high frequencies.
• Complex Permeability Measurement: Determines the real (relative permeability) and imaginary (magnetic loss factor) components, which relate to a material’s response to magnetic fields.
• Waveguide Techniques: Utilizes rectangular or circular waveguide test fixtures connected to a calibrated network analyzer to evaluate material specimens under non-resonant conditions.
• Specimen Preparation: Emphasizes precision in dimensioning specimens and minimizing air gaps to reduce measurement errors.
• Calibration and Error Correction: Describes procedures for instrument calibration and compensation techniques for air gaps using correction models.

Applications

The ASTM D5568-22a standard is essential across a range of industries and research sectors, including:

• RF and Microwave Component Design: Accurate values of permittivity and permeability are required for simulations and practical design of antennas, filters, and substrate materials.
• Material Characterization: Useful for measuring properties of polymers, ceramics, composites, and other insulating materials used in electromagnetic and electronic applications.
• Quality Control & Material Development: Applicable for both experimental sample evaluation and routine quality assurance in continuous production environments.
• Electromagnetic Compatibility (EMC) Testing: Provides key data to ensure materials meet performance criteria in EMI shielding and absorption applications.
• Academic and Industrial Research: Supports the development of new materials tailored for specific electromagnetic properties in communications and sensing technologies.

Related Standards

To ensure comprehensive material evaluation and compatibility, ASTM D5568-22a references several other important ASTM standards, including:

• ASTM D150: Standard Test Methods for AC Loss Characteristics and Permittivity (Dielectric Constant) of Solid Electrical Insulation
• ASTM D1711: Terminology Relating to Electrical Insulation

Other relevant standards and resources include technical notes from NIST and IEEE publications on permittivity and permeability measurement techniques.

---

Keywords: ASTM D5568-22a, complex permittivity, complex permeability, dielectric constant, loss factor, magnetic permeability, microwave measurement, waveguide, network analyzer, RF materials, electromagnetic materials testing, material characterization, scattering parameters, quality control.

Standards Content (Sample)

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.
Designation: D5568 − 22a
Standard Test Method for
Measuring Relative Complex Permittivity and Relative
Magnetic Permeability of Solid Materials at Microwave
Frequencies Using Waveguide
This standard is issued under the fixed designation D5568; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision.Anumber in parentheses indicates the year of last reapproval.A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1. Scope* 1.5 This international standard was developed in accor-
dance with internationally recognized principles on standard-
1.1 This test method covers a procedure for determining
ization established in the Decision on Principles for the
relative complex permittivity (relative dielectric constant and
Development of International Standards, Guides and Recom-
loss)andrelativemagneticpermeabilityofisotropic,reciprocal
mendations issued by the World Trade Organization Technical
(non-gyromagnetic) solid materials. If the material is
Barriers to Trade (TBT) Committee.
nonmagnetic, it is acceptable to use this procedure to measure
permittivity only.
2. Referenced Documents
1.2 This measurement method is valid over a frequency
2.1 ASTM Standards:
rangeofapproximately100MHztoover40GHz.Theselimits
D150Test Methods forAC Loss Characteristics and Permit-
are not exact and depend on the size of the specimen, the size
tivity (Dielectric Constant) of Solid Electrical Insulation
of rectangular waveguide transmission line used as a specimen
D1711Terminology Relating to Electrical Insulation
holder, and on the applicable frequency range of the network
3. Terminology
analyzer used to make measurements. The size of specimen
dimension is limited by test frequency, intrinsic specimen
3.1 For other definitions used in this test method, refer to
electromagnetism properties, and the request of algorithm.
Terminology D1711.
Being a non-resonant method, the selection of any number of
3.2 Definitions of Terms Specific to This Standard:
discrete measurement frequencies in a measurement band
3.2.1 A list of symbols specific to this test method is given
would be suitable. Use of multiple rectangular waveguide
in Annex A1.
transmission line sizes are required to cover this entire fre-
3.2.2 calibration, n—a procedure for connecting character-
quencyrange(100MHzto40GHz).Thistestmethodcanalso
ized standard devices to the test ports of a network analyzer to
be generally applied to circular waveguide test fixtures. The
characterize the measurement system’s systematic errors. The
rectangularwaveguidefixtureispreferredovercoaxialfixtures
effects of the systematic errors are then mathematically re-
when samples have in-plane anisotropy or are difficult to
moved from the indicated measurements. The calibration also
manufacture precisely.
establishes the mathematical reference plane for the measure-
1.3 The values stated in SI units are to be regarded as the
ment test ports.
standard. The values given in parentheses are in inch-pound
3.2.2.1 Discussion—Modern network analyzers have this
units and are included for information only. The equations
capability built in. There are a variety of calibration kits that
+jωt
shown here assume an e harmonic time convention.
can be used depending on the type of test port. The models
used to predict the measurement response of the calibration
1.4 This standard does not purport to address all of the
devicesdependsonthetypeofcalibrationkit.Mostcalibration
safety concerns, if any, associated with its use. It is the
kitscomewithmediathatcanbeusedtoloadthedefinitionsof
responsibility of the user of this standard to establish appro-
the calibration devices into the network analyzer. Calibration
priate safety, health, and environmental practices and deter-
kitdefinitionsloadedintothenetworkanalyzermustmatchthe
mine the applicability of regulatory limitations prior to use.
devices used to calibrate. Since both transmission and reflec-
tion measurements are used in this standard, a two-port
calibration is required.
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. For referenced ASTM standards, visit the ASTM website, www.astm.org, or
Current edition approved Sept. 1, 2022. Published October 2022. Originally contact ASTM Customer Service at [e-mail]. For Annual Book of ASTM
approved in 1994. Last previous edition approved in 2022 as D5568–22. DOI: Standards volume information, refer to the standard’s Document Summary page on
10.1520/D5568-22A. 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
D5568 − 22a
3.2.3 network analyzer, n—a system that measures the determine complex permittivity only (in non-magnetic
two-porttransmissionandone-portreflectioncharacteristicsof materials), or both complex permittivity and permeability
a multiport system in its linear range and at a common input simultaneously.
and output frequency.
5.2 Relative complex permittivity (relative complex dielec-
*
3.2.3.1 Discussion—For the purposes of this standard, this
tric constant), ε , is the proportionality factor that relates the
r
descriptionincludesonlythosesystemsthathaveasynthesized
electric field to the electric flux density, and which depends on
signal generator, and that measure the complex scattering
intrinsic material properties such as molecular polarizability,
parameters (both magnitude and phase) in the forward and
charge mobility, and so forth:
reverse directions of a two-port network (S , S , S , S ).
11 21 12 22
W
D
* ' ''
3.2.4 scattering parameter (S-parameter), S ,n—acomplex ε 5ε 2 jε 5 (1)
ij r r r
W
ε E
number consisting of either the reflection or transmission
coefficientofacomponentataspecifiedsetofinputandoutput
where:
reference planes with an incident signal on only a single port.
ε = the permittivity of free space,
3.2.4.1 Discussion—As most commonly used, these coeffi-
→
D = the electric flux density vector, and
cients represent the quotient of the complex electric field
→
strength (or voltage) of a reflected or transmitted wave divided
E = the electric field vector.
by that of an incident wave. The subscripts i and j of a typical
NOTE 1—In common usage the word “relative” is frequently dropped.
'
The real part of complex relative permittivity (ε ) is often referred to as
coefficient S refer to the output and input ports, respectively.
r
ij
simply relative permittivity, permittivity, or dielectric constant. The
For example, the forward transmission coefficient S is the
''
imaginary part of complex relative permittivity (ε ) is often referred to as
r
ratioofthetransmittedwavevoltageatReferencePlane2(Port
the loss factor. In anisotropic media, permittivity is described by a three
2)dividedbytheincidentwavevoltagemeasuredatReference
dimensional tensor.
Plane 1 (Port 1). Similarly, the Port 1 reflection coefficient S
NOTE 2—For the purposes of this test method, the media is considered
is the ratio of the Port 1 reflected wave voltage divided by the to be isotropic and, therefore, permittivity is a single complex number at
each frequency.
Port 1 incident wave voltage at reference plane 1 (Port 1).
*
5.3 Relative complex permeability, µ , is the proportional-
r
3.2.5 transverse electric (TE ) wave, n—an electromag-
mn
ity factor that relates the magnetic flux density to the magnetic
netic wave in which the electric field is everywhere perpen-
field, and which depends on intrinsic material properties such
dicular to the direction of propagation.
as magnetic moment, domain magnetization, and so forth:
3.2.5.1 Discussion—The index m is the number of half-
W
period variations of the field along the waveguide’s larger
B
* ' ''
µ 5 µ 2jµ 5 (2)
r r r
transverse dimension, and n is the number of half-period
W
µ H
variationsofthefieldalongthewaveguide’ssmallertransverse
where:
dimension. The dominant wave in a rectangular waveguide is
TE . The electric field lines of the TE mode are parallel to µ = the permeability of free space,
10 10 0
the shorter side. →
B = the magnetic flux density vector, and
3.2.6 cutoff frequency, n—the lowest frequency at which
→
H = the magnetic field vector.
non-evanescent, dominant mode propagation can occur within
NOTE 3—In common usage the word “relative” is frequently dropped.
a rectangular waveguide.
'
The real part of complex relative permeability (µ ) is often referred to as
r
relative permeability or simply permeability. The imaginary part of
"
4. Summary of Test Method complexrelativepermeability(µ )isoftenreferredtoasthemagneticloss
r
factor. In anisotropic media, permeability is described by a three dimen-
4.1 A carefully machined test specimen is placed in an
sional tensor.
electromagnetic waveguide transmission line and connected to 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
a calibrated network analyzer that is used to measure the
each frequency.
S-parameters of the transmission line-with-specimen. A speci-
fied data-reduction algorithm is then used to calculate permit-
5.4 Relativepermittivity((relativedielectricconstant)(SIC)
tivity and permeability. If the material is nonmagnetic a
κ'(ε )) is the real part of the relative complex permittivity. It is
r
different algorithm is used to calculate permittivity only. Error
also the ratio of the equivalent parallel capacitance, C,ofa
p
correctionsarethenappliedtocompensateforairgapsbetween
givenconfigurationofelectrodeswithamaterialasadielectric
the specimen and the transmission line conductor surfaces. to the capacitance, C , of the same configuration of electrodes
υ
with vacuum (or air for most practical purposes) as the
5. Significance and Use dielectric:
κ' 5 C /C (3)
5.1 Design calculations for radio frequency (RF), p v
NOTE 5—In common usage the word “relative” is frequently dropped.
microwave, and millimetre-wave components require the
NOTE 6—Experimentally, vacuum must be replaced by the material at
knowledge of values of complex permittivity and permeability
all points where it makes a significant change in capacitance. The
at operating frequencies. This test method is useful for evalu-
equivalent circuit of the dielectric is assumed to consist of C,a
p
ating small experimental batch or continuous production ma-
capacitance in parallel with conductance. (See Fig. 3 of Test Methods
terialsusedinelectromagneticapplications.Usethismethodto D150.)
D5568 − 22a
NOTE 7—C is taken to be C , the equivalent parallel capacitance as
7. Apparatus
x p
shown in Fig. 3 of Test Methods D150.
7.1 Experimental Test Fixture—The test fixture includes a
NOTE 8—The series capacitance is larger than the parallel capacitance
specimen holder connected to a network analyzer, as shown in
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
Fig. 1.
ofseriescomponents,theparallelcapacitancemustbecalculatedfromEq
7.2 Network Analyzer—The network analyzer needs a full
5 of Test Methods D150 before the corrections and permittivity are
2-port test set that can measure transmission and reflection
calculated.
NOTE 9—The permittivity of dry air at 23°C and standard pressure at scattering parameters. Use a network analyzer that has a
101.3 kPa is 1.000536. Its divergence from unity, κ'−1, is inversely
synthesized signal generator in order to ensure good frequency
proportional to absolute temperature and directly proportional to atmo-
stability and signal purity.
spheric pressure. The increase in permittivity when the space is saturated
with water vapor at 23°C is 0.00025, and varies approximately linearly
7.3 Waveguide Calibration Kit—To define Port 1 and Port 2
with temperature expressed in degrees Celsius, from 10°C to 27°C. For
measurement reference planes, calibration of the waveguide
partial saturation the increase is proportional to the relative humidity.
test fixture is required. A calibration kit consists of well-
characterized standard devices and mathematical models of
6. Interferences
thosedevices.Useathrough-reflect-line(TRL),anopen-short-
6.1 The upper limits of permittivity and permeability that load-through (OSLT), or any other calibration kit that yields
can be measured using this test method are restricted by the similar calibration quality to calibrate the waveguide test
transmission line and specimen geometries, which can lead to fixture.
unwanted higher order waveguide modes. In addition, exces-
7.4 Specimen Holder:
sive electromagnetic attenuation due to a high loss factor
7.4.1 Because parameters such as specimen holder length
within the test specimen can prevent determination of permit-
andcross-sectionaldimensionsareofcriticalimportancetothe
tivity and permeability. No specific limits are given in this
calculation of permittivity and permeability, carefully measure
standard, but this test method is practically limited to low-to-
and characterize the physical dimensions of the specimen
medium values of permittivity and permeability.
holder.
7.4.2 Ifaseparatelengthoftransmissionlineisusedtohold
6.2 The existence of air gaps between the test specimen and
the transmission line introduces a negative bias into measure- the specimen, ensure that that empty length of line is also in
place during calibration of the specimen holder.
ments of permittivity and permeability. In this test method
compensation for this bias is required, and to do so requires 7.4.3 The theoretical model used for this test method
knowledge of the air gap sizes. Air gap sizes are estimated assumes that only the dominant mode of propagation exists
from dimensional measurements of the specimen and the (TE for rectangular waveguide or TE for circular wave-
10 11
specimen holder, which can be measured with micrometers, guide). The existence of higher-order modes restricts the
feeler gauges, or other precision instruments. Several different measurable bandwidth for a given waveguide test fixture.
error correction models have been developed, and a frequency 7.4.4 Be sure that the specimen holder dimensions are
independent series capacitor model is described in Annex A2. within proper tolerances for the waveguide transmission line
Airgapcorrectionsareonlyapproximateandthereforethistest size in use. For an X-band rectangular waveguide transmission
method is practically limited to low-to-medium values of line, the dimensions of the inner opening are denoted by “a”
permittivity and permeability. the width and “b” the height. Proper tolerances are then:
FIG. 1 Diagram of Experimental Fixture
D5568 − 22a
X-band waveguide width: 9.4.1 Turn on the network analyzer before beginning cali-
bration and measurements. Refer to manufacturer documenta-
a 5 22.86mm60.10mm ~0.900in.60.004in.! (4)
tion for minimum warm-up period.
X-band waveguide height:
9.4.2 Put network analyzer into step frequency mode. Set
b 5 10.16mm60.10mm ~0.400in.60.004in.! (5) the start frequency and stop frequency as desired. Set the
number of measurement points to the desired value.
7.4.4.1 Dimensions and tolerances of other standard wave-
9.4.3 If available, set the network analyzer’s variable inter-
guides are in the appropriate manufacturer’s specifications and
3 mediate frequency (IF) bandwidth to less than 30 Hz, other-
U.S. military specifications.
wise set the network analyzer data-averaging factor to a value
>200.
8. Test Specimen
9.4.4 Perform a two-port test fixture calibration using a
8.1 Make the test specimen long enough to ensure good
waveguide calibration kit in accordance with the manufactur-
alignment inside the holder.Also, make the test specimen long
er’s procedures and in accordance with 7.3.
enough to ensure that the phase shift through the specimen is
much greater than the phase measurement uncertainty of the
10. Procedure
network analyzer at the lowest measurement frequency. If a
specimen is expected to have low loss, sufficient length is also
10.1 The following procedure applies to rectangular and
required to ensure accurate determination of the loss factor.
circular waveguide.
Finally,forhighlossspecimens,thespecimenlengthcannotbe
10.2 Calibration Verification:
so long that high insertion loss prevents material property
10.2.1 Insert a known verification specimen, such as cross-
inversion.
linked polystyrene or polytetrafluoroethylene, into the wave-
8.2 Accurately machine the specimen so that its dimensions
guidesothatthefrontsurfaceisflushwiththePort1reference
minimizetheairgapthatexistsbetweentheconductorsurfaces
plane.
and the specimen. In this respect, measure the specimen
10.2.2 Connectthewaveguideflangesbacktogethertotheir
holder’s dimensions in order to specify the tightest tolerances
original configuration.
possible for specimen preparation. Keep physical variations of
10.2.3 Make sure that the position of the waveguide feed
specimen dimensions as small as is practicable and include
cables are as close to the same as when the calibration was
specimen dimensions and uncertainties in the repor
...

This document is not an ASTM standard and is intended only to provide the user of an ASTM standard an indication of what changes have been made to the previous version. Because
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: D5568 − 22 D5568 − 22a
Standard Test Method for
Measuring Relative Complex Permittivity and Relative
Magnetic Permeability of Solid Materials at Microwave
Frequencies Using Waveguide
This standard is issued under the fixed designation D5568; 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 100 MHz to over 40 GHz. These limits are not
exact and depend on the size of the specimen, the size of rectangular waveguide transmission 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. Being a non-resonant method, the
selection of any number of discrete measurement frequencies in a measurement band would be suitable. Use of multiple
rectangular waveguide transmission line sizes are required to cover this entire frequency range (100 MHz to 40 GHz). This test
method can also be generally applied to circular waveguide test fixtures. The rectangular waveguide fixture is preferred over
coaxial fixtures when samples have in-plane anisotropy or are difficult to manufacture precisely.
1.3 The values stated in SI units are to be regarded as the standard. The values given in parentheses are in inch-pound units and
+jωt
are included for information only. 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:
D150 Test Methods for AC Loss Characteristics and Permittivity (Dielectric Constant) of Solid Electrical Insulation
D1711 Terminology Relating to Electrical Insulation
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 1994. Last previous edition approved in 20142022 as
D5568 – 14.D5568 – 22. DOI: 10.1520/D5568-22.10.1520/D5568-22A.
For referenced ASTM standards, visit the ASTM website, www.astm.org, or contact ASTM Customer Service at [e-mail]. 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
D5568 − 22a
3. Terminology
3.1 For other definitions 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 = the permittivity of free space,
→
D = the electric flux density vector, and
→
E = the electric field vector.
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
r
''
to as simply relative permittivity, permittivity, or dielectric constant. The imaginary part of complex relative permittivity (ε ) is
r
often referred to as the loss factor. In anisotropic media, permittivity is described by a three dimensional tensor.
3.2.1.2 Discussion—
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 = the permeability of free space,
→
B = the magnetic flux density vector, and
→
H = the magnetic field vector.
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
r
as the magnetic loss factor. In anisotropic media, permeability is described by a three dimensional tensor.
3.2.2.2 Discussion—
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.
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
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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 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.
3.2.3.1 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
3.2.4 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.
3.2.4.1 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).
3.2.5 transverse electric (TE ) wave,n—an electromagnetic wave in which the electric field is everywhere perpendicular to the
mn
direction of propagation.
3.2.5.1 Discussion—
The index m is the number of half-period variations of the field along the waveguide’s larger transverse dimension, and n is the
number of half-period variations of the field along the waveguide’s smaller transverse dimension. The dominant wave in a
rectangular waveguide is TE . The electric field lines of the TE mode are parallel to the shorter side.
10 10
3.2.6 cutoff frequency, n—the lowest frequency at which non-evanescent, dominant mode propagation can occur within a
rectangular waveguide.
4. Summary of Test Method
4.1 A carefully machined test specimen is placed in an electromagnetic waveguide transmission 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
where:
ε = the permittivity of free space,
→
D = the electric flux density vector, and
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→
E = the electric field vector.
'
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.
r
In 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 = the permeability of free space,
→
B = the magnetic flux density vector, and
→
H = the magnetic field vector.
'
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
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, which can be
measured with micrometers, feeler gauges, or other precision instruments. Several different error correction models have been
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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 Waveguide Calibration Kit—To define Port 1 and Port 2 measurement reference planes, calibration of the waveguide 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 waveguide 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 that empty length of line is also in place
during 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 (TE for
rectangular waveguide or TE for circular waveguide). The existence of higher-order modes restricts the measurable bandwidth
for a given waveguide test fixture.
7.4.4 Be sure that the specimen holder dimensions are within proper tolerances for the waveguide transmission line size in use.
For an X-band rectangular waveguide transmission line, the dimensions of the inner opening are denoted by “a” the width and “b”
the height. Proper tolerances are then:
X-band waveguide width:
a 5 22.86 mm60.10 mm ~0.900 in.60.004 in.! (4)
X-band waveguide height:
b 5 10.16 mm60.10 mm ~0.400 in.60.004 in.! (5)
FIG. 1 Diagram of Experimental Fixture
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7.4.4.1 Dimensions and tolerances of other standard waveguides are in the appropriate manufacturer’s specifications and U.S.
military 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 ensure
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 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 tha
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