ASTM D5568-95
(Test Method)Standard Test Method for Measuring Relative Complex Permittivity and Relative Magnetic Permeability of Solid Materials at Microwave Frequencies
Standard Test Method for Measuring Relative Complex Permittivity and Relative Magnetic Permeability of Solid Materials at Microwave Frequencies
SCOPE
1.1 This test method covers a procedure for determining relative complex permittivity (relative dielectric constant and loss index) and relative magnetic permeability of isotropic, reciprocal (nongyromagnetic) solid materials. If the material is nonmagnetic, this procedure may be used to measure permittivity only.
1.2 This measurement method is valid over a frequency range of approximately 1 MHz to 50 GHz. These limits are not exact and depend on the size of the specimen, the size and type of transmission line used as a specimen holder, and on the applicable frequency range of the network analyzer used to make measurements. The lower frequency is limited by the smallest measurable phase shift through a specimen, and the upper frequency limit is determined by the excitation of higher-order modes that invalidates the dominant-mode transmission line model. Any number of discrete measurement frequencies may be selected in this frequency range. To achieve maximum measurement accuracy, use of different transmission line sizes and types may be required. For example, use of a 7-mm diameter coaxial geometry can provide for measurements from 1 MHz to 18 GHz. However, air gaps that exist between the specimen and the transmission line's conductors introduce errors that may necessitate the use of a larger diameter coaxial transmission line and a series of rectangular wave guides of different size to cover this frequency range.
1.3 The values stated in SI units are to be regarded as the standard. The values given in parentheses are for information only.
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 and health practices and determine the applicability of regulatory limitations prior to use.
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Designation: D 5568 – 95 An American National Standard
Standard Test Method for
Measuring Relative Complex Permittivity and Relative
Magnetic Permeability of Solid Materials at Microwave
Frequencies
This standard is issued under the fixed designation D 5568; 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 (e) indicates an editorial change since the last revision or reapproval.
1. Scope 2. Referenced Documents
1.1 This test method covers a procedure for determining 2.1 ASTM Standards:
relative complex permittivity (relative dielectric constant and D 1711 Terminology Relating to Electrical Insulation
loss index) and relative magnetic permeability of isotropic,
3. Terminology
reciprocal (nongyromagnetic) solid materials. If the material is
3.1 For other definitions used in this test method, refer to
nonmagnetic, this procedure may be used to measure permit-
tivity only. Terminology D 1711.
1.2 This measurement method is valid over a frequency 3.2 Definitions:
3.2.1 relative complex permittivity (relative complex dielec-
range of approximately 1 MHz to 50 GHz. These limits are not
exact and depend on the size of the specimen, the size and type tric constant) (relative complex capacitivity), e , n—the ratio
R
of the admittance of a given configuration of the material to the
of transmission line used as a specimen holder, and on the
applicable frequency range of the network analyzer used to admittance of the same configuration with vacuum as dielec-
tric:
make measurements. The lower frequency is limited by the
smallest measurable phase shift through a specimen, and the
Y Y
e* 5 5 5e8 2 je9 , (1)
R R R
upper frequency limit is determined by the excitation of
Y jvCy
y
higher-order modes that invalidates the dominant-mode trans-
where Y is the admittance with the material and jvC8y is the
mission line model. Any number of discrete measurement
admittance with vacuum.
frequencies may be selected in this frequency range. To
3.2.1.1 Discussion—In common usage the word “relative”
achieve maximum measurement accuracy, use of different
is frequently dropped. The real part of complex relative
transmission line sizes and types may be required. For ex-
permittivity (e8 ) is often referred to as simply relative permit-
R
ample, use of a 7-mm diameter coaxial geometry can provide
tivity, permittivity or dielectric constant. The imaginary part of
for measurements from 1 MHz to 18 GHz. However, air gaps
complex relative permittivity (e9 ) is often referred to as the
R
that exist between the specimen and the transmission line’s
loss index. In anisotropic media, permittivity is described by a
conductors introduce errors that may necessitate the use of a
three dimensional tensor.
larger diameter coaxial transmission line and a series of
3.2.2 For the purposes of this test method, the media is
rectangular wave guides of different size to cover this fre-
considered to be isotropic, and therefore permittivity is a single
quency range.
complex number.
1.3 The values stated in SI units are to be regarded as the
3.3 Definitions of Terms Specific to This Standard:
standard. The values given in parentheses are for information
3.3.1 A list of symbols specific to this test method is given
only.
in Annex A1.
1.4 This standard does not purport to address all of the
3.3.2 calibration, n—a procedure for connecting character-
safety concerns, if any, associated with its use. It is the
ized standard devices to the test ports of a network analyzer to
responsibility of the user of this standard to establish appro-
characterize the measurement system’s systematic errors. The
priate safety and health practices and determine the applica-
effects of the systematic errors are then mathematically re-
bility of regulatory limitations prior to use.
moved from the indicated measurements. The calibration also
establishes the mathematical reference plane for the measure-
ment test ports.
This test method is under the jurisdiction of ASTM Committee D-9 on
3.3.2.1 Discussion—Modern network analyzers have this
Electrical and Electronic Insulating Materials and is the direct responsibility of
capability built in. There are a variety of calibration kits that
Subcommittee D09.12 on Electrical Tests.
can be used depending on the type of test port. The models
Current edition approved July 15, 1995. Published October 1995. Originally
published as D 5568 – 94. Last previous edition D 5568 – 94.
ASTM STP 926 “Engineering Dielectrics, Volume 11B, Electrical Properties of
Solid Insulating Materials: Measurement Techniques,” 1987. Annual Book of ASTM Standards, Vol 10.01.
Copyright © ASTM, 100 Barr Harbor Drive, West Conshohocken, PA 19428-2959, United States.
D 5568
used to predict the measurement response of the calibration guide is TE . The electric field lines of the TE mode are
10 10
devices depends on the type of calibration kit. Most calibration parallel to the shorter side.
kits come with a tape or disc that can be used to load the 3.3.9 transverse electromagnetic (TEM) wave, n—an elec-
definitions of the calibration devices into the network analyzer. tromagnetic wave in which both the electric and magnetic
Calibration kit definitions loaded into the network analyzer fields are perpendicular to the direction of propagation.
must match the devices used to calibrate. Since both transmis- 3.3.9.1 Discussion—In coaxial transmission lines the domi-
sion and reflection measurements are used in this standard, a nant wave is TEM.
two-port calibration is required.
4. Summary of Test Method
3.3.3 network analyzer, n—a system that measures the
4.1 A carefully machined test specimen is placed in an
two-port transmission and one-port reflection characteristics of
a multiport system in its linear range and at a common input electromagnetic transmission line and connected to a calibrated
network analyzer that is used to measure the S-parameters of
and output frequency.
3.3.3.1 Discussion—For the purposes of this standard, this the transmission line-with-specimen. A specified data-
reduction algorithm is then used to calculate permittivity and
description includes only those systems that have a synthesized
signal generator, and that measure both magnitude and phase in permeability. If the material is nonmagnetic a different algo-
rithm is used to calculate permittivity only. Error corrections
the forward and reverse directions of a two-port network (S ,
S ,S ,S ). are then applied to compensate for the existence of air gaps
21 12 22
between the specimen and the transmission line’s conductors.
3.3.4 relative complex permeability, μ* , n—a term used to
R
express the relationship between magnetic induction and mag-
5. Significance and Use
netizing force defined by the ratio of the absolute permeability
5.1 Design calculations for Radio Frequency (RF), micro-
to the magnetic constant, given by
wave and millimeter-wave components require the knowledge
¯
| B |
of values of complex permittivity and permeability at operating
μ* 5 μ8 2 jμ9 5 (2)
R R R
¯
μ | H |
frequencies. This test method is useful for evaluating batch
where μ is the permeability of free space.
type or continuous production of material for use in electro-
3.3.5 Discussion—In common usage the word “relative” is
magnetic applications. It may be used to determine complex
frequently dropped. The real part of complex relative perme-
permittivity only or both complex permittivity and permeabil-
ability (μ8 ) is often referred to as relative permeability or
ity simultaneously.
R
permeability. The imaginary part of complex relative perme-
6. Interferences
ability (μ9 ) is often referred to as the magnetic loss index. In
R
anisotropic media, permeability is described by a three dimen-
6.1 The upper limits of permittivity and permeability that
sional tensor.
can be measured using this test method are restricted by the
3.3.5.1 For the purposes of this test method, the media is
transmission line and specimen geometries. No specific limits
considered to be isotropic, and therefore permeability is a
are given in this standard, but this test method is practically
single complex number.
limited to low-to-medium values of permittivity and perme-
3.3.6 scattering parameter (S-parameter), S , n—a complex
ability. In 7-mm coaxial lines, specimen permittivities <30 and
ij
number consisting of either the reflection or transmission
permeabilities <100 can be determined if the air gap between
coefficient of a component at a specified set of input and output
the specimen and the inner and outer conductors is known.
reference planes with all other planes terminated by a non-
Rectangular wave guides yield higher limits, and in general
reflecting termination.
these upper limits increase as transmission line cross-sectional
3.3.7 Discussion—As most commonly used, these coeffi-
area increases.
cients represent the quotient of the complex electric field
6.2 The existence of air gaps between the test specimen and
strength (or voltage) of a reflected or transmitted wave divided
the transmission line introduces a negative bias into measure-
by that of an incident wave. The subscripts i and j of a typical ments of permittivity and permeability. In this test method
coefficient S refer to the output and input ports, respectively.
compensation for this bias is required, and to do so requires
ij
For example, the forward transmission coefficient S is the knowledge of the air gap sizes. Air gap sizes are estimated
ratio of the transmitted wave voltage at Reference Plane 2 (Port
from dimensional measurements of the specimen and the
2) divided by the incident wave voltage measured at Reference specimen holder. Several different error correction models
Plane 1 (Port 1). Similarly, the Port 1 reflection coefficient S
have been developed, and a frequency independent series
is the ratio of the Port 1 reflected wave voltage divided by the capacitor model is described in Annex A2.
Port 1 incident wave voltage.
7. Apparatus
3.3.8 transverse electric (TE ) wave, n—an electromag-
mn
netic wave in which the electric field is everywhere perpen- 7.1 Experimental Setup is given in Fig. 1 as a block
dicular to the direction of propagation. diagram.
3.3.8.1 Discussion—The index m is the number of half- 7.2 Network Analyzer—The network analyzer needs a full
period variations of the field along the wave guide’s larger 2-port test set that can measure scattering parameters in both
transverse dimension, and n is the number of half-period directions. Use a network analyzer that has a synthesized signal
variations of the field along the wave guide’s smaller trans- generator in order to ensure good frequency stability and signal
verse dimension. The dominant wave in a rectangular wave purity. To define the Port 1 and Port 2 Reference Planes with
D 5568
frequencies. The upper frequency limit of a coaxial line is
limited by overmoding, determined by the diameters of the
outer and inner conductors. As these diameters become larger,
the cutoff frequencies of higher-order modes become lower.
The theoretical model used for this test method assumes that
only the dominant mode of propagation exists (TEM for
coaxial lines, TE for rectangular wave guides). The existence
of higher-order modes limits the applicability of the model.
Use of rectangular wave guide has two distinct advantages over
coaxial line: (1) test specimen is easier to machine, and (2) for
a given gap size, air gap corrections are smaller for rectangular
wave guides than for coaxial lines.
FIG. 1 Block Diagram of Experimental Setup
7.5.4 Be sure that the specimen holder dimensions are
within proper tolerances for the transmission line size in use. If
respect to magnitude and phase, perform a two-port calibration
a 7-mm coaxial transmission line is used, let L , D , L , and D
1 1 2 2
of the network analyzer.
be the length and diameter of the inner conductor and the
7.3 Computer—Use a computer for network analyzer data
length and diameter of the outer conductor, respectively. Proper
acquisition and computation of permittivity and permeability
tolerances are then:
from the measured scattering parameters. Any computer ca-
center conductor: (3)
pable of these functions is sufficient for the purposes of this test
D 5 3.040 6 0.005 mm ~0.1197 6 0.0002 in.!,
method.
outer conductor: (4)
7.4 Network Analyzer Calibration Kit—To define Port 1 and
Port 2 Measurement Reference Planes, calibration of the
D 5 7.000 6 0.006 mm ~0.2756 6 0.00025 in.!, and
network analyzer is required. A network analyzer calibration
L2 $ L1 . L2 2 0.00102 mm ~L $ L . L 2 0.0004 in.!.
2 1 2
kit consists of well characterized standard devices and math- (5)
ematical models of those devices. A through-reflect-line (TRL),
Dimensions and tolerances of other coaxial sizes are in the
open-short-load-through (OSLT), or other calibration kit that
appropriate manufacturer’s specifications.
yields similar calibration quality may be used to calibrate the
Dimensions and tolerances of standard rectangular wave
network analyzer. 4
guides are in various references.
7.5 Specimen Holder:
7.5.1 Because parameters such as specimen holder length
8. Test Specimen
and cross-sectional dimensions are of critical importance to the
8.1 Make the test specimen long enough to ensure good
calculation of permittivity and permeability, carefully measure
alignment inside the holder. Also, make the test specimen long
and characterize the physical dimensions of the specimen
enough to ensure that the phase shift through the specimen is
holder.
much greater than the phase measurement uncertainty of the
7.5.2 Although not required, it is helpful if the specimen is
network analyzer at the lowest measurement frequency.
nearly the same length as the specimen holder. This minimizes
8.2 Accurately machine the specimen so that its dimensions
conductor losses that cause a positive bias to e9 results. If
R
minimize the air gap that exists between the conductor(s) and
desired, use measurement techniques to remove conductor
the specimen. In this respect, measure the specimen holder’s
losses. Two possible procedures to remove specimen holder
dimensions in order to specify the tightest tolerances possible
conductor losses are outlined in Appendix X2.
for specimen preparation. A test specimen that fits into coaxial
7.5.3 Either rectangular wave guides or beadless coaxial
transmission lines is a toroidal cylinder. Typical dimensional
lines may be used as the specimen holder. Coaxial lines consist
specifications for a 7-mm coaxial test specimen are given in
of tw
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