ASTM D2520-95
(Test Method)Standard Test Methods for Complex Permittivity (Dielectric Constant) of Solid Electrical Insulating Materials at Microwave Frequencies and Temperatures to 1650oC
Standard Test Methods for Complex Permittivity (Dielectric Constant) of Solid Electrical Insulating Materials at Microwave Frequencies and Temperatures to 1650<sup>o</sup>C
SCOPE
1.1 These test methods cover the determination of relative (Note 0) complex permittivity (dielectric constant and dissipation factor) of nonmagnetic solid dielectric materials. Note 0The word "relative" is often omitted.
1.1.1 Test Method A is for specimens precisely formed to the inside dimension of a waveguide.
1.1.2 Test Method B is for specimens of specified geometry that occupy a very small portion of the space inside a resonant cavity.
1.1.3 Test Method C uses a resonant cavity with fewer restrictions on specimen size, geometry, and placement than Test Methods A and B.
1.2 Although these methods are used over the microwave frequency spectrum from around 0.5 to 50.0 GHz, each octave increase usually requires a different generator and a smaller test waveguide or resonant cavity.
1.3 Tests at elevated temperatures are made using special high-temperature waveguide and resonant cavities.
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 2520 – 95 An American National Standard
Standard Test Methods for
Complex Permittivity (Dielectric Constant) of Solid Electrical
Insulating Materials at Microwave Frequencies and
Temperatures to 1650°C
This standard is issued under the fixed designation D 2520; 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.
This standard has been approved for use by agencies of the Department of Defense.
1. Scope Nonmetallic Magnetic Materials at Microwave Frequen-
cies
1.1 These test methods cover the determination of relative
(Note 1) complex permittivity (dielectric constant and dissipa-
3. Terminology
tion factor) of nonmagnetic solid dielectric materials.
3.1 Definitions:
NOTE 1—The word “relative” is often omitted.
3.1.1 neper, n—a division of the logarithmic scale wherein
the number of nepers is equal to the natural logarithm of the
1.1.1 Test Method A is for specimens precisely formed to
the inside dimension of a waveguide. scalar ratio of either two voltages or two currents.
1.1.2 Test Method B is for specimens of specified geometry
NOTE 2—The neper is a dimensionless unit. 1 neper equals 0.8686 bel.
that occupy a very small portion of the space inside a resonant
With I and I denoting the scalar values of two currents and n being the
x y
cavity.
number of nepers denoted by their scalar ratio, then:
1.1.3 Test Method C uses a resonant cavity with fewer
n 5 ln ~l /l !
e x y
restrictions on specimen size, geometry, and placement than
Test Methods A and B. where:
ln 5 logarithm to base e.
e
1.2 Although these methods are used over the microwave
frequency spectrum from around 0.5 to 50.0 GHz, each octave
3.1.2 For other definitions used in these test methods, refer
increase usually requires a different generator and a smaller test
to Terminology D 1711.
waveguide or resonant cavity.
4. Significance and Use
1.3 Tests at elevated temperatures are made using special
high-temperature waveguide and resonant cavities.
4.1 Design calculations for such components as transmis-
1.4 This standard does not purport to address all of the
sion lines, antennas, radomes, resonators, phase shifters, etc.,
safety concerns, if any, associated with its use. It is the
require knowledge of values of complex permittivity at oper-
responsibility of the user of this standard to establish appro-
ating frequencies. The related microwave measurements sub-
priate safety and health practices and determine the applica-
stitute distributed field techniques for low-frequency lumped-
bility of regulatory limitations prior to use.
circuit impedance techniques.
4.2 Further information on the significance of permittivity
2. Referenced Documents
may be found in Test Methods D 150.
2.1 ASTM Standards:
4.3 These test methods are useful for specification accep-
D 150 Test Methods for AC Loss Characteristics and Per-
tance, service evaluation, manufacturing control, and research
mittivity (Dielectric Constant) of Solid Electrical Insulat-
and development of ceramics, glasses, and organic dielectric
ing Materials
materials.
D 618 Practice for Conditioning Plastics and Electrical
TEST METHOD A—SHORTED TRANSMISSION
Insulating Materials for Testing
LINE METHOD
D 1711 Terminology Relating to Electrical Insulation
F 131 Test Method for Complex Dielectric Constant of
5. Scope
5.1 This test method covers the determination of microwave
1 dielectric properties of nonmagnetic isotropic solid dielectric
These test methods are under the jurisdiction of ASTM Committee D-9 on
Electrical and Electronic Insulating Materials and are the direct responsibility of materials in a shorted transmission line method. This test
Subcommittee D09.12 on Electrical Tests.
Current edition approved July 15, 1995. Published March 1996. Originally
e1
published as D 2520 – 66 T. Last previous edition D 2520 – 86 (1990) .
2 3
Annual Book of ASTM Standards, Vol 10.01. Annual Book of ASTM Standards, Vol 03.04.
Copyright © ASTM, 100 Barr Harbor Drive, West Conshohocken, PA 19428-2959, United States.
D 2520
FIG. 1 Standing Wave Established Within Empty Shorted Waveguide
method is useful over a wide range of values of permittivity
where:
and loss (1). It may be used at any frequency where suitable
l 5 cut-off wavelength for the cross section and
c
transmission lines and measuring equipment are available.
the mode in question,
Transmission lines capable of withstanding temperatures up to
l( 5 c/f ) 5 wavelength of the radiation in free space, and
1650°C in an oxidizing atmosphere can be used to hold the k* 5 relative complex permittivity of the nonmag-
specimen. netic medium.
Since k* is complex, g is complex, that is,
6. Summary of Test Method
g5a1 jb (4)
6.1 In an isotropic dielectric medium, one of Maxwell’s curl
−ax
the field dependence on distance is therefore of the form e
equations may be written
−j bx
e . The wave attenuation is a in nepers per unit length; b is
curl H 5 jvk*e E, (1)
the phase constant, b5 2 p/l where l is the guide
g g
wavelength in the line. The method of observing a and b by
assuming exp (jvt) time dependence,
impedance measurements and of representing the behavior of a
where:
line containing a dielectric by means of the formalism of
k* 5 relative complex permittivity,
transmission line impedance will be outlined briefly (1).
e 5 (absolute) permittivity of free space, and
6.3 Impedance Representation of the Ideal Problem—The
v5 2pf, f being the frequency.
impedance representation of the ideal problem is illustrated by
The notation used will be as follows:
Fig. 1 for a uniform line terminated by a short. In Fig. 2 a
k*5k8 2 jk95k8~1 2 j tan d! (2)
dielectric specimen of length d is supposed to fill completely
s
the cross section of the line and be in intimate contact with the
where:
flat terminating short. The impedance of a dielectric filled line
tand5k9/k8,
terminated by a short (1), observed at a distance d from the
s
k8 5 real part, and
short (at what is defined as the input face of the specimen) is
k9 5 imaginary part.
The value of k* may be obtained from observations that
Z 5 ~jvμ /g tanh ~g d ! (5)
in 0 2 2 s
evaluate the attenuation and wavelength of electromagnetic
where μ is the permeability of free space and of the material
wave propagation in the medium.
and g is given by Eq 2, using the dimensions of the line
6.2 The permittivity of the medium in a transmission line
around the specimen.
affects the wave propagation in that line. Thus, the dielectric
6.4 Impedance Measurement:
properties of a specimen may be obtained by using a suitable
6.4.1 The object of the measurement is to obtain the
line as a dielectric specimen holder. The electromagnetic field
impedance at the input face of the specimen so that the
traveling in one direction in a uniform line varies with time, t,
unknown g in Eq 4 may be evaluated, which in turn allows K*
and with distance along the line, x, as exp (jv t 6gx) where
to be evaluated in Eq 2. The impedance in question may be
g is the propagation constant. Assuming that the metal walls of
measured by a traveling probe in a slotted section of the line.
the line have infinite conductivity the propagation constant g of
As illustrated schematically in Fig. 1 and Fig. 2, the position of
any uniform line in a certain mode is
an electric node, that is, an interference minimum of the
22 22 1/2
g5 2p l 2k*l ! (3)
~
c
standing wave, is observed, and also the “width,” Dx, of this
node is observed. Dx is the distance between two probe
positions on either side of the node position where the power
meter indicates twice the power existing at the node minimum.
The boldface numbers in parentheses refer to the list of references appended to
these test methods. The voltage standing wave ratio denoted by r (r 5 VSWR) is
D 2520
FIG. 2 Standing Wave Established Within Shorted Waveguide After Insertion of Specimen
obtained from Dx by the equation (see l , Section 11) at room and substantially higher temperatures. Dielectric
gs
measurement capabilities over wide ranges of temperature and
r5l/pDx (6)
over wide, continuous ranges of frequency provide significant
NOTE 3—Refer to Appendix X2 and Appendix X3 for additional
usefulness of this method for research and development work.
comments on errors and refinements in the method to improve accuracy.
Also refer to Refs (1-4) for information on air gap corrections and use of
8. Apparatus
standard materials to reduce errors and improve accuracy.
8.1 See Fig. 3 for a block diagram of equipment compo-
When r is small, a correction is necessary (5). The load
nents. Some characteristics of the component in each block are
impedance at a phase distance u away from an observed
as follows:
electric node having VSWR 5 r is
8.1.1 Generator—Stable in power and frequency with low
Z 5 Z ~1 2 jr tan u!/~r 2 j tan u! (7)
meas 01
harmonic output.
where Z 5 jvμ /g 5 fμ l assuming the line is uniform 8.1.2 Square-Wave Modulator—1.0 kHz output or fre-
01 0 1 0 g
quency required for VSWR meter.
and lossless.
6.4.2 It remains to determine r and u correctly, taking into 8.1.3 Frequency Meter—Heterodyne or cavity absorption;
uncertainty 1 part in 10 .
account losses of the line and nonuniformity due to tempera-
8.1.4 Isolator—30-dB isolation, and having an output
ture differences, then to equate Z and Z from Eq 6 and Eq
meas in
4, and finally to lay out a convenient calculation scheme for k*. VSWR of less than 1.15.
8.1.5 Slotted Section—A slotted waveguide section and
The measuring procedure for obtaining r and u is discussed in
Section 10. carriage capable of measuring gross distances to 0.025 mm
−4
(0.001 in.) and small distance to 0.0025 mm (10 in.) (for
7. Significance and Use
node width). A micrometer head is required; it should move
7.1 This test method is useful for quality control and parallel to the axis of the line.
acceptance tests of dielectric materials intended for application 8.1.6 Probe—Adjustable for depth. The detector must be
FIG. 3 Block Diagram of Apparatus Used to Perform the Measurement of Dielectric Properties by the Short Circuit Line Method
D 2520
square law (6) if one uses the voltage-decibel scale of the frequency of the source and the temperature distribution of the
standing wave ratio (SWR) meter. The detector must be line are to be the same for both observations. With no specimen
operated in the square law region. Crystal detectors may be (Fig. 1) read the position x of a voltage minimum (a node), on
square law if they are not overdriven. The law of a crystal may a scale of arbitrary origin; also measure the separation between
be checked by adding a good rotating-vane microwave attenu- positions either side of x where the power is +3.01 dB from
ator. the minimum. This is the width Dx of the node. Likewise
8.1.7 VSWR Meter—Readable in decibels. measure this analogous x and Dx with the specimen against
2 2
8.1.8 Temperature Isolation Section— Includes a bend. the termination (Fig. 2). As an additional check measurement,
8.1.9 Cooling Sink—Sufficient conduction to water or air in one case measure the distance between two adjacent nodes.
stream to maintain suitable temperature and waveguide dimen- This distance is l /2, where l is the guide wavelength in the
gs gs
sions. slotted section.
8.1.10 Waveguide Specimen Holder—Platinum-20 %
rhodium for 1650°C; platinum for temperature 1300°C; copper 12. Calculation
or silver for lower temperatures within their abilities to
12.1 Measurements Transformed to Input Face of
withstand thermal damage and corrosion. Length shall be
Specimen—When measurements are made at elevated tem-
sufficient to have a main transition region of temperature of the
peratures, the guide width and the guide wavelength, l , vary
g
order of l in extent and still keep sample temperature uniform
g
because of the temperature gradient between the heated section
to 5°C.
and the cool (room temperature) slotted section. Fortunately
8.1.11 Tube Furnace—Platinum-wound tube furnace to ac-
the argument of the tangent in Eq 6 may be found, assuming
cept test section, and maintain a 50-mm (2-in.) length at a
the change in l is not abrupt. The correct argument is
g
constant temperature 65°C up to 1650°C.
u 5 2p@N/2 2 d/l 6 ~x 2x /l # (8)
gh 2 1 gs
8.2 The so-called slope of the attenuation characteristic of
where l is calculated for the empty heated dielectric holder
the slotted line should be normal, that is, the VSWR should
gh
section from the dimensions duly adjusted for thermal expan-
change by the expected amount in going from one node to
sion. In Eq 7 the plus sign is used if the scale for x increases
another while looking into a shorted termination. Items 8.1.5,
away from the short, the minus sign if the opposite. N is the
8.1.8, and 8.1.10 shall have initial dimensions plus differential
smallest integer 0, 1, etc., that makes u positive. To calculate
expansions at the temperature of a junction so that the change
l use the general equation
in dimensions is less than 0.25 mm (0.01 in.). The dielectric
gh
22 22 22
holder shall slope downward at 45 to 90° to maintain specimen
l 5l 2l (9)
gh c
against termination. Termination shall be flat to 0.010 mm
where:
(0.0004 in.) and perpendicular to axis of waveguide within
l5 c/f 5 free space wavelength, and
60.05°. The cross section of the holder shall meet EIA
l 5 cutoff wavelength calculated from the dimensions.
specifications; at 9 GHz this requires 60.075-mm (0.003-in.) c
For the TE mode rectangular guide discussed below,
tolerance on transverse dimensions.
l 5 2 a* where a* is the wide dimension. It remains to find
c
9. Sampling
the Dx (width of the node) that would have been measured at
9.1 Determine the sampling by the applicable material the face of the specimen. The node width Dx without the
specification.
specimen is assumed to arise from the attenuation factor of the
empty line, and can be treated as if it increased smoothly with
10. Test Specimen
distance from the short. The width contribution accumulated
10.1 The transverse dimensions of the specimen shall be
due to attenuation in going from the sample face to the place x
0.05 6 0.025 mm (0.002 6 0.001 in.) less than those of the
where it is observed is Dx (L − d )/L where L is the total
1 2 s 1 i
transmission line. The front and back faces shall be parallel
length of path, i 5 1 or 2, to the shorting termination and d is
s
within 0.01 mm (0.0004 in.) and perpendicular to the axis of
the le
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