ASTM D150-22

Standard Test Methods for AC Loss Characteristics and Permittivity (Dielectric Constant) of Solid Electrical Insulation

SIGNIFICANCE AND USE
5.1 Permittivity—Insulating materials are used in general in two distinct ways, (1) to support and insulate components of an electrical network from each other and from ground, and (2) to function as the dielectric of a capacitor. For the first use, it is generally desirable to have the capacitance of the support as small as possible, consistent with acceptable mechanical, chemical, and heat-resisting properties. A low value of permittivity is thus desirable. For the second use, it is desirable to have a high value of permittivity, so that the capacitor is able to be physically as small as possible. Intermediate values of permittivity are sometimes used for grading stresses at the edge or end of a conductor to minimize ac corona. Factors affecting permittivity are discussed in Appendix X3.  
5.2 AC Loss—For both cases (as electrical insulation and as capacitor dielectric) the ac loss generally needs to be small, both in order to reduce the heating of the material and to minimize its effect on the rest of the network. In high frequency applications, a low value of loss index is particularly desirable, since for a given value of loss index, the dielectric loss increases directly with frequency. In certain dielectric configurations such as are used in terminating bushings and cables for test, an increased loss, usually obtained from increased conductivity, is sometimes introduced to control the voltage gradient. In comparisons of materials having approximately the same permittivity or in the use of any material under such conditions that its permittivity remains essentially constant, it is potentially useful to consider also dissipation factor, power factor, phase angle, or loss angle. Factors affecting ac loss are discussed in Appendix X3.  
5.3 Correlation—When adequate correlating data are available, dissipation factor or power factor are useful to indicate the characteristics of a material in other respects such as dielectric breakdown, moisture content, degree o...
SCOPE
1.1 These test methods cover the determination of relative permittivity, dissipation factor, loss index, power factor, phase angle, and loss angle of specimens of solid electrical insulating materials when the standards used are lumped impedances. The frequency range addressed extends from less than 1 Hz to several hundred megahertz.  
Note 1: In common usage, the word relative is frequently dropped.  
1.2 These test methods provide general information on a variety of electrodes, apparatus, and measurement techniques. A reader interested in issues associated with a specific material needs to consult ASTM standards or other documents directly applicable to the material to be tested.2,3  
1.3 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. For specific hazard statements, see 10.2.1.  
1.4 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.

General Information

• Status: Published
• Publication Date: 31-Aug-2022
• ICS: 83.060 - Rubber
• 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 D5032-19 - Standard Practice for Maintaining Constant Relative Humidity by Means of Aqueous Glycerin Solutions
• Effective Date: 01-Mar-2019
• 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 E104-02(2012) - Standard Practice for Maintaining Constant Relative Humidity by Means of Aqueous Solutions
• Effective Date: 01-Apr-2012
• Refers: ASTM D1711-11a - Standard Terminology Relating to Electrical Insulation
• Effective Date: 01-Aug-2011
• Refers: ASTM D5032-11 - Standard Practice for Maintaining Constant Relative Humidity by Means of Aqueous Glycerin Solutions
• Effective Date: 01-Aug-2011
• Refers: ASTM D618-08 - Standard Practice for Conditioning Plastics for Testing
• Effective Date: 01-Nov-2008
• Refers: ASTM D1711-08 - Standard Terminology Relating to Electrical Insulation
• Effective Date: 01-May-2008
• Refers: ASTM E104-02(2007) - Standard Practice for Maintaining Constant Relative Humidity by Means of Aqueous Solutions
• Effective Date: 01-Oct-2007
• Refers: ASTM D1531-06 - Standard Test Methods for Relative Permittivity (Dielectric Constant) and Dissipation Factor by Fluid Displacement Procedures (Withdrawn 2012)
• Effective Date: 01-Oct-2006
• Refers: ASTM D618-05 - Standard Practice for Conditioning Plastics for Testing
• Effective Date: 01-Nov-2005
• Refers: ASTM D5032-97(2003) - Standard Practice for Maintaining Constant Relative Humidity by Means of Aqueous Glycerin Solutions
• Effective Date: 10-Mar-2003

Overview

ASTM D150-22 - Standard Test Methods for AC Loss Characteristics and Permittivity (Dielectric Constant) of Solid Electrical Insulation establishes procedures to determine the fundamental electrical properties of solid insulating materials. Developed by ASTM, this internationally recognized standard is critical for evaluating relative permittivity (dielectric constant), dissipation factor, loss index, power factor, and related parameters that influence the performance of electrical insulation in a wide range of environments and applications. Covering frequencies from less than 1 Hz up to several hundred megahertz, ASTM D150-22 enables manufacturers, engineers, and laboratories to assess insulation quality, reliability, and suitability for end-use applications.

Key Topics

• Permittivity (Dielectric Constant):
  • Measures a material's ability to store electrical energy in an electric field.
  • Relevant for assessing insulation used to support components or as capacitor dielectrics.
  • Low permittivity is preferred for insulation supports; high permittivity is desirable for capacitors.
• AC Loss Characteristics:
  • Analysis of how much energy is lost as heat during AC operation.
  • Important for minimizing power loss and temperature rise in electrical networks, especially at higher frequencies.
• Dissipation Factor and Power Factor:
  • Indicators of insulation quality and efficiency.
  • Provide insight into potential degradation mechanisms such as moisture ingress, aging, and breakdown.
• Measurement Techniques:
  • Guidance on electrode types (contacting and non-contacting), geometry considerations, and methods for accurate results.
  • Addresses handling fringing and stray capacitance, ground corrections, and specimen dimensions.
• Frequency Range:
  • Procedures specified for frequencies from below 1 Hz to several hundred MHz, accommodating diverse testing needs.

Applications

ASTM D150-22 is widely applied in the development, quality control, and research of solid electrical insulation materials. Key practical uses include:

• Capacitor Manufacturing:
  • Determining suitable dielectric materials for compact, high-performance capacitors by evaluating their permittivity and AC loss.
• High Voltage Equipment:
  • Assessing insulation that supports and separates conductors in transformers, circuit breakers, cables, and switchgear.
• Quality Assurance and R&D:
  • Routine screening of insulation batches for consistency and reliability.
  • Investigating the impact of environmental factors (humidity, heat, aging) on insulation properties.
• Failure Analysis:
  • Diagnosing breakdowns or performance issues related to dielectric properties using standardized parameters like dissipation factor and power factor.
• Standards Compliance:
  • Supporting compliance with industrial, regulatory, and international quality assurance programs through recognized test methods.

Related Standards

For comprehensive electrical insulation testing and material characterization, ASTM D150-22 is used alongside these related standards:

• ASTM D374 - Test Methods for Thickness of Solid Electrical Insulation
• ASTM D618 - Practice for Conditioning Plastics for Testing
• ASTM D1711 - Terminology Relating to Electrical Insulation
• ASTM D5032 - Practice for Maintaining Constant Relative Humidity by Means of Aqueous Glycerin Solutions
• ASTM E104 - Practice for Maintaining Constant Relative Humidity by Means of Aqueous Solutions

These documents provide guidance on specimen preparation, environmental conditioning, and terminology essential for obtaining repeatable, accurate measurements in line with ASTM D150-22.

---

ASTM D150-22 is a cornerstone standard for testing dielectric constant and AC loss characteristics in electrical insulation, ensuring that materials perform reliably in critical electrical and electronic applications. Testing in conformance with this standard helps manufacturers and engineers optimize material selection, maintain product safety, and advance innovation in the rapidly evolving field of electrical insulation technology.

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: D150 − 22
Standard Test Methods for
AC Loss Characteristics and Permittivity (Dielectric
Constant) of Solid Electrical Insulation
This standard is issued under the fixed designation D150; 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.
This standard has been approved for use by agencies of the U.S. Department of Defense.
1. Scope* 2. Referenced Documents
2.1 ASTM Standards:
1.1 These test methods cover the determination of relative
D374Test Methods for Thickness of Solid Electrical Insu-
permittivity, dissipation factor, loss index, power factor, phase
lation (Metric) D0374_D0374M
angle,andlossangleofspecimensofsolidelectricalinsulating
D618Practice for Conditioning Plastics for Testing
materialswhenthestandardsusedarelumpedimpedances.The
D1531Test Methods for Relative Permittivity (Dielectric
frequency range addressed extends from less than 1 Hz to
Constant) and Dissipation Factor by Fluid Displacement
several hundred megahertz.
Procedures (Withdrawn 2012)
D1711Terminology Relating to Electrical Insulation
NOTE 1—In common usage, the word relative is frequently dropped.
D5032PracticeforMaintainingConstantRelativeHumidity
1.2 These test methods provide general information on a
by Means of Aqueous Glycerin Solutions
variety of electrodes, apparatus, and measurement techniques.
E104Practice for Maintaining Constant Relative Humidity
Areaderinterestedinissuesassociatedwithaspecificmaterial
by Means of Aqueous Solutions
needs to consultASTM standards or other documents directly
2,3
applicable to the material to be tested.
3. Terminology
1.3 This standard does not purport to address all of the
3.1 Definitions:
safety concerns, if any, associated with its use. It is the
3.1.1 Use Terminology D1711 for definitions of terms used
responsibility of the user of this standard to establish appro-
in these test methods and associated with electrical insulation
priate safety, health, and environmental practices and deter-
materials.
mine the applicability of regulatory limitations prior to use.
3.2 Definitions of Terms Specific to This Standard:
For specific hazard statements, see 10.2.1.
3.2.1 capacitance, C, n—that property of a system of
1.4 This international standard was developed in accor- conductors and dielectrics which permits the storage of elec-
dance with internationally recognized principles on standard- trically separated charges when potential differences exist
between the conductors.
ization established in the Decision on Principles for the
Development of International Standards, Guides and Recom-
4. Summary of Test Method
mendations issued by the World Trade Organization Technical
Barriers to Trade (TBT) Committee.
4.1 Capacitance and ac resistance measurements are made
on a specimen. Relative permittivity is the specimen capaci-
tancedividedbyacalculatedvalueforthevacuumcapacitance
(for the same electrode configuration), and is significantly
These test methods are under the jurisdiction of ASTM Committee D09 on
Electrical and Electronic Insulating Materials and are the direct responsibility of
dependent on resolution of error sources. Dissipation factor,
Subcommittee D09.12 on Electrical Tests.
generally independent of the specimen geometry, is also
Current edition approved Sept. 1, 2022. Published October 2022. Originally
calculated from the measured values.
approved in 1922. Last previous edition approved in 2018 as D150–18. DOI:
10.1520/D0150-22.
R. Bartnikas, Chapter 2, “Alternating-Current Loss and Permittivity
Measurements,” Engineering Dielectrics, Vol. IIB, Electrical Properties of Solid
Insulating Materials, Measurement Techniques, R. Bartnikas, Editor, STP 926, For referenced ASTM standards, visit the ASTM website, www.astm.org, or
ASTM, Philadelphia, 1987. contact ASTM Customer Service at [e-mail]. For Annual Book of ASTM
R. Bartnikas, Chapter 1, “Dielectric Loss in Solids,” Engineering Dielectrics, Standards volume information, refer to the standard’s Document Summary page on
VolIIA,ElectricalPropertiesofSolidInsulatingMaterials:MolecularStructureand the ASTM website.
Electrical Behavior, R. Bartnikas and R. M. Eichorn, Editors, STP 783, ASTM The last approved version of this historical standard is referenced on
Philadelphia, 1983. www.astm.org.
*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
D150 − 22
4.2 This method provides (1) guidance for choices of While the initial value of dissipation factor is important, the
electrodes, apparatus, and measurement approaches; and (2) change in dissipation factor with aging is often much more
directions on how to avoid or correct for capacitance errors. significant.
4.2.1 General Measurement Considerations:
5.4 Capacitance is the ratio of a quantity, q, of electricity to
Fringing and Stray Capacitance Guarded Electrodes
a potential difference, V. A capacitance value is always
Geometry of Specimens Calculation of Vacuum Capacitance
positive. The units are farads when the charge is expressed in
Edge, Ground, and Gap Corrections
coulombs and the potential in volts:
4.2.2 Electrode Systems - Contacting Electrodes
C 5 q/V (1)
Electrode Materials Metal Foil
Conducting Paint Fired-On Silver
5.5 Dissipation factor ((D), (loss tangent), (tan δ)) is the
Sprayed Metal Evaporated Metal
ratioofthelossindex(κ")totherelativepermittivity(κ')which
Liquid Metal Rigid Metal
is equal to the tangent of its loss angle (δ) or the cotangent of
Water
its phase angle (θ) (see Fig. 1 and Fig. 2).
4.2.3 Electrode Systems - Non-Contacting Electrodes
D 5 κ"/κ' (2)
Fixed Electrodes Micrometer Electrodes
Fluid Displacement Methods
5.5.1 It is calculated via Eq 3:
4.2.4 Choice of Apparatus and Methods for Measuring
D 5 tan δ 5 cotθ 5 X /R 5 G/ωC 51/ωC R (3)
p p p p p
Capacitance and AC Loss
Frequency Direct and Substitution Methods
where:
Two-Terminal Measurements Three-Terminal Measurements
G = equivalent ac conductance,
Fluid Displacement Methods Accuracy considerations
X = parallel reactance,
p
R = equivalent ac parallel resistance,
5. Significance and Use
p
C = parallel capacitance, and
p
5.1 Permittivity—Insulating materials are used in general in
ω =2πf (sinusoidal wave shape assumed).
twodistinctways,(1)tosupportandinsulatecomponentsofan
The reciprocal of the dissipation factor is the quality factor,
electricalnetworkfromeachotherandfromground,and(2)to
Q, sometimes called the storage factor. The dissipation factor,
function as the dielectric of a capacitor. For the first use, it is
D, of the capacitor is the same for both the series and parallel
generally desirable to have the capacitance of the support as
representations as follows:
small as possible, consistent with acceptable mechanical,
chemical, and heat-resisting properties.Alow value of permit-
D 5 ωR C 51/ωR C (4)
s s p p
tivity is thus desirable. For the second use, it is desirable to
The relationships between series and parallel components
have a high value of permittivity, so that the capacitor is able
are as follows:
to be physically as small as possible. Intermediate values of
permittivityaresometimesusedforgradingstressesattheedge C 5 C /~11D ! (5)
p s
2 2 2 2
or end of a conductor to minimize ac corona. Factors affecting
R /R 5 ~11D !/D 5 11~1/D ! 5 11Q (6)
p s
permittivity are discussed in Appendix X3.
5.5.2 Series Representation—While the parallel representa-
5.2 AC Loss—For both cases (as electrical insulation and as
tionofaninsulatingmaterialhavingadielectricloss(Fig.3)is
capacitor dielectric) the ac loss generally needs to be small,
usually the proper representation, it is always possible and
both in order to reduce the heating of the material and to
occasionally desirable to represent a capacitor at a single
minimize its effect on the rest of the network. In high
frequency by a capacitance, C , in series with a resistance, R
s s
frequencyapplications,alowvalueoflossindexisparticularly
(Fig. 4 and Fig. 2).
desirable, since for a given value of loss index, the dielectric
5.6 Lossangle((phasedefectangle),(δ))istheanglewhose
loss increases directly with frequency. In certain dielectric
tangent is the dissipation factor or arctan κ"/κ' or whose
configurations such as are used in terminating bushings and
cotangent is the phase angle.
cables for test, an increased loss, usually obtained from
5.6.1 The relation of phase angle and loss angle is shown in
increased conductivity, is sometimes introduced to control the
Fig. 1 and Fig. 2. Loss angle is sometimes called the phase
voltage gradient. In comparisons of materials having approxi-
defect angle.
matelythesamepermittivityorintheuseofanymaterialunder
such conditions that its permittivity remains essentially
constant, it is potentially useful to consider also dissipation
factor, power factor, phase angle, or loss angle. Factors
affecting ac loss are discussed in Appendix X3.
5.3 Correlation—When adequate correlating data are
available, dissipation factor or power factor are useful to
indicate the characteristics of a material in other respects such
as dielectric breakdown, moisture content, degree of cure, and
deterioration from any cause. However, it is possible that
deterioration due to thermal aging will not affect dissipation
factor unless the material is subsequently exposed to moisture. FIG. 1 Vector Diagram for Parallel Circuit
D150 − 22
2 2
PF 5 W/VI 5 G/=G 1 ωC 5 sin δ 5 cos θ (8)
~ !
p
Whenthedissipationfactorislessthan0.1,thepowerfactor
differs from the dissipation factor by less than 0.5%. Their
exact relationship is found from the following:
PF 5 D/=11D (9)
D 5 PF/=1 2 PF
~ !
5.10 Relative permittivity ((relative dielectric constant)
(SIC) κ'(ε ))istherealpartoftherelativecomplexpermittivity.
r
FIG. 2 Vector Diagram for Series Circuit
It is also the ratio of the equivalent parallel capacitance, C,of
p
a given configuration of electrodes with a material as a
dielectric to the capacitance, C , of the same configuration of
υ
electrodes with vacuum (or air for most practical purposes) as
the dielectric:
κ' 5 C /C (10)
p v
NOTE 3—In common usage the word “relative” is frequently dropped.
NOTE 4—Experimentally, vacuum must be replaced by the material at
all points where it makes a significant change in capacitance. The
FIG. 3 Parallel Circuit
equivalent circuit of the dielectric is assumed to consist of C,a
p
capacitance in parallel with conductance. (See Fig. 3.)
NOTE 5—C is taken to be C , the equivalent parallel capacitance as
x p
shown in Fig. 3.
NOTE 6—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
ofseriescomponents,theparallelcapacitancemustbecalculatedfromEq
FIG. 4 Series Circuit
5 before the corrections and permittivity are calculated.
NOTE 7—The permittivity of dry air at 23°C and standard pressure at
101.3 kPa is 1.000536 (1). Its divergence from unity, κ'−1, is inversely
5.7 Loss index (κ" (ε ") is the magnitude of the imaginary
r
proportional to absolute temperature and directly proportional to atmo-
partoftherelativecomplexpermittivity;itistheproductofthe
spheric pressure. The increase in permittivity when the space is saturated
relative permittivity and dissipation factor. with water vapor at 23°C is 0.00025 (2, 3), and varies approximately
linearly with temperature expressed in degrees Celsius, from 10°C to
5.7.1 The loss index is expressed as:
27°C. For partial saturation the increase is proportional to the relative
κ" 5 κ' D (7)
humidity.
5powerloss/~E 3f 3volume 3constant!
6. General Measurement Considerations
.
6.1 Fringing and Stray Capacitance—These test methods
When the power loss is in watts, the applied voltage is in
are based upon measuring the specimen capacitance between
voltspercentimeter,thefrequencyisinhertz,thevolumeisthe
electrodes, and measuring or calculating the vacuum capaci-
cubic centimeters to which the voltage is applied, the constant
−13
tance (or air capacitance for most practical purposes) in the
has the value of 5.556×10 .
same electrode system. For unguarded two-electrode
NOTE 2—Loss index is the term agreed upon internationally. In the
measurements, the determination of these two values required
United States, κ" was formerly called the loss factor.
to compute the permittivity, κ ' is complicated by the presence
x
5.8 Phase angle (θ) is the angle whose cotangent is the
of undesired fringing and stray capacitances which get in-
dissipationfactor,arccot κ"/κ'andisalsotheangulardifference
cludedinthemeasurementreadings.Fringingandstraycapaci-
in the phase between the sinusoidal alternating voltage applied
tances are illustrated by Figs. 5 and 6 for the case of two
to a dielectric and the component of the resulting current
unguarded parallel plate electrodes between which the speci-
having the same frequency as the voltage.
menistobeplacedformeasurement.Inadditiontothedesired
5.8.1 The relation of phase angle and loss angle is shown in
direct interelectrode capacitance, C , the system as seen at
v
Fig. 1 and Fig. 2. Loss angle is sometimes called the phase
terminals a-a' includes the following:
defect angle.
5.9 Power factor (PF) is the ratio of the power in watts, W,
dissipated in a material to the product of the effective sinusoi-
dal voltage, V, and current, I, in volt-amperes.
5.9.1 Power factor is expressed as the cosine of the phase
The boldface numbers in parentheses refer to the list of references appended to
angle θ (or the sine of the loss angle δ). these test methods.
D150 − 22
distribution in the guarded area will be identical with that
existing when vacuum is the dielectric, and the ratio of these
two direct capacitances is the permittivity. Furthermore, the
field between the active electrodes is defined and the vacuum
capacitancecanbecalculatedwiththeaccuracylimitedonlyby
the accuracy with which the dimensions are known. For these
reasons the guarded electrode (three-terminal) method is to be
used as the referee method unless otherwise agreed upon. Fig.
8 shows a schematic representation of a completely guarded
and shielded electrode system. Although the guard is com-
FIG. 5 Stray Capacitance, Unguarded Electrodes
monly grounded, the arrangement shown permits grounding
either measuring electrode or none of the electrodes to accom-
modate the particular three-terminal measuring system being
used.Iftheguardisconnectedtoground,ortoaguardterminal
onthemeasuringcircuit,themeasuredcapacitanceisthedirect
capacitance between the two measuring electrodes. If,
however, one of the measuring electrodes is grounded, the
FIG. 6 Flux Lines Between Unguarded Electrodes
capacitancetogroundoftheungroundedelectrodeandleadsis
inparallelwiththedesireddirectcapacitance.Toeliminatethis
source of error, surround the ungrounded electrode with a
C = fringing or edge capacitance,
e
shield connected to guard as shown in Fig. 8. In addition to
C = capacitance to ground of the outside face of each
g
guardedmethods,whicharenotalwaysconvenientorpractical
electrode,
andwhicharelimitedtofrequencieslessthanafewmegahertz,
C = capacitance between connecting leads,
L
C = capacitance of the leads to ground, and techniques using special cells and procedures have been
Lg
C = capacitance between the leads and the electrodes. devisedthatyield,withtwo-terminalmeasurements,accuracies
Le
comparable to those obtained with guarded measurements.
Only the desired capacitance, C , is independent of the
v
Such methods described here include shielded micrometer
outsideenvironment,alltheothersbeingdependenttoadegree
electrodes (7.3.2) and fluid displacement methods (7.3.3).
on the proximity of other objects. It is necessary to distinguish
between two possible measuring conditions to determine the
6.3 Geometry of Specimens—Fordeterminingthepermittiv-
effects of the undesired capacitances. When one measuring
ity and dissipation factor of a material, sheet specimens are
electrode is grounded, as is often the case, all of the capaci-
preferable. Cylindrical specimens can also be used, but gener-
tances described are in parallel with the desired C - with the
v
allywithlesseraccuracy.Thesourceofthegreatestuncertainty
exception of the ground capacitance of the grounded electrode
in permittivity is in the determination of the dimensions of the
and its lead. If C is placed within a chamber with walls at
v
specimen, and particularly that of its thickness. Therefore, the
guard potential, and the leads to the chamber are guarded, the
thickness shall be large enough to allow its measurement with
capacitance to ground no longer appears, and the capacitance
therequiredaccuracy.Thechosenthicknesswilldependonthe
seen at a-a' includes C and C only. For a given electrode
v e
method of producing the specimen and the likely variation
arrangement, the edge capacitance, C , can be calculated with
e
from point to point. For 1% accuracy a thickness of 1.5 mm
reasonable accuracy when the dielectric is air. When a speci-
(0.06 in.) is usually sufficient, although for greater accuracy it
men is placed between the electrodes, the value of the edge
is desirable to use a thicker specimen.Another source of error,
capacitance can change requiring the use of an edge capaci-
whenfoilorrigidelectrodesareused,isintheunavoidablegap
tance correction using the information from Table 1. Empirical
between the electrodes and the specimen. For thin specimens
correctionshavebeenderivedforvariousconditions,andthese
theerrorinpermittivitycanbeasmuchas25%.Asimilarerror
are given in Table 1 (for the case of thin electrodes such as
occurs in dissipation factor, although when foil electrodes are
foil). In routine work, where best accuracy is not required it is
applied with a grease, the two errors are not likely to have the
convenient to use unshielded, two-electrode systems and make
same magnitude. For the most accurate measurements on thin
the approximate corrections. Since area (and hence C ) in-
v
specimens, use the fluid displacement method (7.3.3). This
creases of the square diameter while perimeter (and hence C )
e
method reduces or completely eliminates the need for elec-
increases linearly with diameter, the percentage error in per-
trodes on the specimen. The thickness must be determined by
mittivity due to neglecting the edge correction decreases with
measurements distributed systematically over the area of the
increasingspecimendiameter.However,forexactingmeasure-
specimen that is used in the electrical measurement and shall
ments it is necessary to use guarded electrodes.
be uniform within 61% of the average thickness. If the whole
6.2 Guarded Electrodes—The fringing and stray capaci- area of the specimen will be covered by the electrodes, and if
tance at the edge of the guarded electrode is practically the density of the material is known, the average thickness can
eliminatedbytheadditionofaguardelectrodeasshowninFig. be determined by weighing. The diameter chosen for the
7 and Fig. 8. If the test specimen and guard electrode extend specimen shall be such as to provide a specimen capacitance
beyond the guarded electrode by at least twice the thickness of that can be measured to the desired accuracy. With well-
the specimen and the guard gap is very small, the field guarded and screened apparatus there need be no difficulty in
D150 − 22
TABLE 1 Calculations of Vacuum Capacitance and Edge Corrections (see 8.5)
NOTE 1—See Table 2 for Identification of Symbols used.
Direct Inter-Electrode Capacitance
Type of Electrode Correction for Stray Field at an Edge, pF
in Vacuum, pF
A
Disk electrodes with guard-ring: C =0
e
C 5ε 5
v 0
t
A
0.0088542
t
π
A 2
A5 sd 1B gd
Disk electrodes without guard-ring:
Diameter of the electrodes = diameter of the specimen: where a << t, C = (0.0087 – 0.00252 ln t) P
e
d
Equal electrodes smaller than the specimen: 1 C = (0.0019 κ ' – 0.00252 ln t + 0.0068)P
e x
C 50.0069541
v
t
where: κ ' = an approximate value of the specimen permit
x
tivity, and a << t.
Unequal electrodes: C = (0.0041 κ '– 0.00334 ln t + 0.0122)P
e x
where: κ ' = an approximate value of the specimen
x
permittivity, and a << t.
A
0.055632 sl 1B gd
Cylindrical electrodes with guard-ring: 1 C =0
e
C 5
v
d
ln
d
0.055632 l t 1
Cylindrical electrodes without guard-ring:
C 5 If ,
v
d t1d 10
2 1
ln
C = (0.0038 κ ' – 0.00504 ln t + 0.0136)P
d
e x
P = π (d + t)
where κ ' = an approximate value of the specimen
x
permittivity.
A
See Appendix X2 for corrections to guard gap.
FIG. 8 Three-Terminal Cell for Solids
FIG. 7 Flux Lines Between Guarded Parallel Plate Electrodes
factor shall be contributed by the series resistance of the
electrodes and that in the measuring network no large capaci-
measuring specimens having capacitances of 10 pF to a tance shall be connected in parallel with that of the specimen.
resolution of 1 part in 1000. If a thick specimen of low The first of these points favors thick specimens; the second
permittivity is to be tested, it is likely that a diameter of 100 suggests thin specimens of large area. Micrometer electrode
mm or more will be needed to obtain the desired capacitance methods (7.3.2) can be used to eliminate the effects of series
accuracy. In the measurement of small values of dissipation resistance.Useaguardedspecimenholder(Fig.8)tominimize
factor, the essential points are that no appreciable dissipation extraneous capacitances.
D150 − 22
6.4 Calculation of Vacuum Capacitance—The practical electrode system is employed. When equal-size electrodes
shapesforwhichcapacitancecanbemostaccuratelycalculated smallerthanthespecimenareused,itisdifficulttocenterthem
are flat parallel plates and coaxial cylinders, the equations for unless the specimen is translucent or an aligning fixture is
which are given in Table 1. These equations are based on a employed. For three-terminal measurements, the width of the
uniform field between the measuring electrodes, with no guard electrode shall be at least twice the thickness of the
fringing at the edges. Capacitance calculated on this basis is specimen (6, 8). The gap width shall be as small as practical
known as the direct interelectrode capacitance. (0.5 mm is possible). For measurement of dissipation factor at
the higher frequencies, electrodes of this type are likely to be
6.5 Edge, Ground, and Gap Corrections—Theequationsfor
unsatisfactory because of their series resistance. Use microm-
calculating edge capacitance, given in Table 1, are empirical,
eter electrodes for the measurements.
based on published work (4) (see 8.5). They are expressed in
terms of picofarads per centimetre of perimeter and are thus
7.2 Electrode Materials:
independentoftheshapeoftheelectrodes.Itisrecognizedthat
7.2.1 Metal Foil—Lead or tin foil from 0.0075mm to
they are dimensionally incorrect, but they are found to give
0.025mm thick applied with a minimum quantity of refined
better approximations to the true edge capacitance than any
petrolatum, silicone grease, silicone oil, or other suitable
other equations that have been proposed. Ground capacitance
low-loss adhesive is generally used as the electrode material.
cannot be calculated by any equations presently known. When
Aluminum foil has also been used, but it is not recommended
measurements must be made that include capacitance to
because of its stiffness and the probability of high contact
ground, it is recommended that the value be determined
resistance due to the oxidized surface. Lead foil is also likely
experimentally for the particular setup used. The difference
to give trouble because of its stiffness. Apply such electrodes
betweenthecapacitancemeasuredinthetwo-terminalarrange-
under a smoothing pressure sufficient to eliminate all wrinkles
ment and the capacitance calculated from the permittivity and
and to work excess adhesive toward the edge of the foil. One
the dimensions of the specimen is the ground capacitance plus
very effective method is to use a narrow roller, and to roll
the edge capacitance. The edge capacitance can be calculated
outward on the surface until no visible imprint can be made on
using one of the equations of Table 1. As long as the same
the foil. With care the adhesive film can be reduced to 0.0025
physicalarrangementofleadsandelectrodesismaintained,the
mm.As this film is in series with the specimen, it will always
ground capacitance will remain constant, and the experimen-
causethemeasuredpermittivitytobetoolowandprobablythe
tally determined value can be used as a correction to subse-
dissipation factor to be too high. These errors usually become
quently measured values of capacitance. The effective area of
excessive for specimens of thickness less than 0.125 mm. The
a guarded electrode is greater than its actual area by approxi-
error in dissipation factor is negligible for such thin specimens
mately half the area of the guard gap (5, 6, 7). Thus, the
only when the dissipation factor of the film is nearly the same
diameter of a circular electrode, each dimension of a rectan-
as that of the specimen. When the electrode is to extend to the
gular electrode, or the length of a cylindrical electrode is
edge, it shall be made larger than the specimen and then cut to
increasedbythewidthofthisgap.Whentheratioofgapwidth,
the edge with a small, finely ground blade. A guarded and
g, to specimen thickness, t, is appreciable, the increase in the
guard electrode can be made from an electrode that covers the
effective dimension of the guarded electrode is somewhat less
entire surface, by cutting out a narrow strip (0.5 mm is
than the gap width. Details of computation for this case are
possible) by means of a compass equipped with a narrow
given in Appendix X2.
cutting edge.
7.2.2 Conducting Paint—Certaintypesofhigh-conductivity
7. Electrode Systems
silver paints, either air-drying or low-temperature-baking
7.1 Contacting Electrodes—It is acceptable for a specimen
varieties, are commercially available for use as electrode
to be provided with its own electrodes, of one of the materials
material. They are sufficiently porous to permit diffusion of
listed below. For two-terminal measurements, the electrodes
moisture through them and thereby allow the test specimen to
shall either extend to the edge of the specimen or be smaller
condition after application of the electrodes. This is particu-
thanthespecimen.Inthelattercase,itisacceptableforthetwo
larly useful in studying humidity effects. The paint has the
electrodes to be equal or unequal in size. If they are equal in
disadvantage of not being ready for use immediately after
size and smaller than the specimen, the edge of the specimen
application. It usually requires an overnight air-drying or
must extend beyond the electrodes by at least twice the
low-temperature baking to remove all traces of solvent, which
specimen thickness. The choice between these three sizes of
otherwise has the potential to increase both permittivity and
electrodes will depend on convenience of application of the
dissipation factor. It is often also not easy to obtain sharply
electrodes, and on the type of measurement adopted. The edge
defined electrode areas when the paint is brushed on, but it is
correction (see Table 1) is smallest for the case of electrodes
possible to overcome by spraying the paint and employing
extending to the edge of the specimen and largest for unequal
either clamp-on or pressure-sensitive masks. The conductivity
electrodes. When the electrodes extend to the edge of the
of silver paint electrodes is often low enough to give trouble at
specimen, these edges must be sharp. Such electrodes must be
the higher frequencies. It is essential that the solvent of the
used, if attached electrodes are used at all, when a micrometer
paint does not affect the specimen permanently.
7.2.3 Fired-On Silver—Fired-on silver electrodes are suit-
able only for glass and other ceramics that are able to
Additional information on electrode systems can be found in Research Report
RR:D09-1037 available from ASTM Headquarters. withstand, without change, a firing temperature of about
D150 − 22
350°C. Its high conductivity makes such an electrode material
satisfactory for use on low-loss materials such as fused silica,
even at the highest frequencies, and its ability to conform to a
rough surface makes it satisfactory for use with high-
permittivity materials, such as the titanates.
7.2.4 Sprayed Metal—A low-melting-point metal applied
with a spray gun provides a spongy film for use as electrode
materialwhich,becauseofitsgrainystructure,hasroughlythe
same electrical conductivity and the same moisture porosity as
conductingpaints.Suitablemasksmustbeusedtoobtainsharp
edges.Itconformsreadilytoaroughsurface,suchascloth,but
does not penetrate very small holes in a thin film and produce
short circuits. Its adhesion to some surfaces is poor, especially
FIG. 9 Micrometer-Electroder System
after exposure to high humidity or water immersion. Advan-
tages over conducting paint are freedom from effects of
solvents, and readiness for use immediately after application.
frequencies. A built-in vernier capacitor is also provided for
7.2.5 Evaporated Metal—Evaporatedmetalusedasanelec-
use in the susceptance variation method. It accomplishes this
trodematerialhasthepotentialtohaveinadequateconductivity
by maintaining these inductances and resistances relatively
because of its extreme thinness, and must be backed with
constant,regardlessofwhetherthetestspecimenisinoroutof
electroplated copper or sheet metal. Its adhesion is adequate,
the circuit. The specimen, which is either the same size as, or
and by itself it is sufficiently porous to moisture.The necessity
smallerthan,theelectrodes,isclampedbetweentheelectrodes.
for using a vacuum system in evaporating the metal is a
Unless the surfaces of the specimen are lapped or ground very
disadvantage.
flat,metalfoiloritsequivalentmustbeappliedtothespecimen
7.2.6 Rigid Metal—For smooth, thick, or slightly compress-
before it is placed in the electrode system. If electrodes are
ible specimens, it is permissible to use rigid electrodes under
applied, they also must be smooth and flat. Upon removal of
highpressure,especiallyforroutinework.Electrodes10mmin
the specimen, the electrode system can be adjusted to have the
diameter,underapressureof18.0MPahavebeenfounduseful
same capacitance by moving the micrometer electrodes closer
for measurements on plastic materials, even those as thin as
together. When the micrometer-electrode system is carefully
0.025mm.Electrodes50mmindiameter,underpressure,have
calibrated for capacitance changes, its use eliminates the
alsobeenusedsuccessfullyforthickermaterials.However,itis
corrections for edge capacitance, ground capacitance, and
difficult to avoid an air film when using solid electrodes, and
connectioncapacitance.Inthisrespectitisadvantageoustouse
the effect of such a film becomes greater as the permittivity of
it over the entire frequency range. A disadvantage is that the
the material being tested increases and its thickness decreases.
capacitance calibration is not as accurate as that of a conven-
Theuncertaintyinthedeterminationofthicknessalsoincreases
tional multiplate variable capacitor, and also it is not a direct
as the thickness decreases. It is possible that the dimensions of
reading. At frequencies below 1 MHz, where the effect of
aspecimenwillcontinuetochangeforaslongas24hafterthe
series inductance and resistance in the leads is negligible, it is
application of pressure.
permissible to replace the capacitance calibration of the mi-
7.2.7 Water—Water can be used as one electrode for testing
crometer electrodes by that of a standard capacitor, either in
insulated wire and cable when the measurements are made at
parallel with the micrometer-electrode system or in the adja-
low frequency (up to 1000 Hz, approximately). Care must be
cent capacitance arm of the bridge. The change in capacitance
taken to ensure that electrical leakage at the ends of the
with the specimen in and out is measured in terms of this
specimen is negligible.
capacitor. A source of minor error in a micrometer-electrode
7.3 Non-Contacting Electrodes:
system is that the edge capacitance of the electrodes, which is
7.3.1 Fixed Electrodes—Itispossibletomeasurespecimens included in their calibration, is slightly changed by the pres-
of sufficiently low surface conductivity, without applied
enceofadielectrichavingthesamediameterastheelectrodes.
electrodes, by inserting them in a prefabricated electrode
Thiserrorcanbepracticallyeliminatedbymakingthediameter
system, in which there is an intentional air gap on one or both
of the specimen less than that of the electrodes by twice its
sides of the specimen. Assemble the electrode system rigidly
thickness (3).Whennoelectrodesareattachedtothespecimen,
and ensure that it includes a guard electrode. For the same
surfaceconductivityhasthepotentialtocauseseriouserrorsin
accuracy, a more accurate determination of the electrode
dissipationfactormeasurementsoflowlossmaterial.Whenthe
spacing and the thickness of the specimen is required than if
bridge used for measurement has a guard circuit, it is advan-
direct contact electrodes are used. However, these limitations
tageous to use guarded micrometer electrodes. The effects of
are likely to be removed if the electrode system is filled with a
fringing,andsoforth,arealmostcompletelyeliminated.When
liquid (see 7.3.3).
the electrodes and holder are well made, no capacitance
7.3.2 Micrometer Electrodes—The micrometer-electrode calibration is necessary, as it is possible to calculate the
system, as shown in Fig. 9, was developed (9) to eliminate the capacitance from the electrode spacing and the diameter. The
errors caused by the series inductance and resistance of the micrometer itself will require calibration, however. It is not
connecting leads and of the measuring capacitor at high practicable to use electrodes on the specimen when using
D150 − 22
guarded micrometer electrodes unless the specimen is smaller 8. Choice of Apparatus and Methods for Measuring
in diameter than the guarded electrode. Capacitance and AC Loss
7.3.3 Fluid Displacement Methods—When the immersion
8.1 Frequency Range—Methods for measuring capacitance
medium is a liquid, and no guard is used, the parallel-plate
and ac loss can be divided into three groups: null methods,
system preferably shall be constructed so that the insulated
resonance methods, and deflection methods. The choice of a
high potential plate is supported between, parallel to, and
method for any particular case will depend primarily on the
equidistant from two parallel low-potential or grounded plates,
operating frequency. It is permissible for the resistive- or
the latter being the opposite inside walls of the test cell
inductive-ratio-arm capacitance bridge in its various forms to
designed to hold the liquid. This construction makes the
be used over the frequency range from less than 1 Hz to a few
electrode system essentially self-shielding, but normally re-
megahertz. For frequencies below 1 Hz, special methods and
quires duplicate test specimens. Provision must be made for
instruments are required. Parallel-T networks are used at the
precise temperature measurement of the liquid (10, 11). Cells higher frequencies from 500 kHz to 30 MHz, since they
shall be constructed of brass and gold plated. The high-
partake of some of the characteristics of resonant circuits.
potential electrode shall be removable for cleaning. The faces Resonance methods are used over a frequency range from 50
must be as nearly optically flat and plane parallel as possible.
kHz to several hundred megahertz. The deflection method,
Asuitable liquid cell for measurements up to 1 MHz is shown using commercial indicating meters, is employed only at
in Fig. 4 ofTest Method D1531. Changes in the dimensions of power-line frequencies from 25Hz to 60 Hz, where the higher
thiscellarenecessarytoprovidefortestingsheetspecimensof voltages required are easily obtained.
various thicknesses or sizes, but such changes shall not reduce
8.2 Direct and Substitution Methods—In any direct method,
thecapacitanceofthecellfilledwiththestandardliquidtoless
the values of capacitance and ac loss are in terms of all the
than 100 pF. For measurements at frequencies from 1MHz to
circuit elements used in the method, and are therefore subject
about 50 MHz, the cell dimensions must be greatly reduced,
to all their errors. It is possible a greater accuracy can be
and the leads must be as short and direct as possible. The
obtained by a substitution method in which readings are taken
capacitance of the cell with liquid shall not exceed 30pF or
with the unknown capacitor, both connected and disconnected.
40pFformeasurementsat50MHz.Experiencehasshownthat
The errors in those circuit elements that are unchanged are in
acapacitanceof10pFcanbeusedupto100MHzwithoutloss
general eliminated; however, a connection error remains (Note
of accuracy. Guarded parallel-plate electrodes have the advan-
10).
tage that single specimens can be measured with full accuracy.
8.3 Two- and Three-Terminal Measurements—The choice
Also a prior knowledge of the permittivity of the liquid is not
between three-terminal and two-terminal measurements is
required as it is possible to measure directly (12). If the cell is
generallyonebetweenaccuracyandconvenience.Theuseofa
constructed with a micrometer electrode, it is possible to
guard electrode on the dielectric specimen nearly eliminates
measure specimens having widely different thicknesses with
the effect of edge and ground capacitance, as explained in 6.2.
high accuracy since the electrodes can be adjusted to a spacing
Theprovisionofaguardterminaleliminatessomeoftheerrors
only slightly greater than the thickness of the specimen. If the
introducedbythecircuitelements.Ontheotherhand,theextra
permittivity of the fluid approximates that of the specimen, the
circuit elements and shielding usually required to provide the
effect of errors in the determination of specimen thicknesses
guard terminal add considerably to the size of the measuring
are minimized. The use of a nearly matching liquid and a
equipment, and it is possible to increase many times the
micrometer cell permits high accuracy in measuring even very
number of adjustments required to obtain the final result.
thin film.
Guard circuits for resistive-ratio-arm capacitance bridges are
7.3.3.1 All necessity for determining specimen thickness
rarely used at frequencies above 1 MHz. Inductive-ratio-arm
andelectrodespacingiseliminatedifsuccessivemeasurements
bridges provide a guard terminal without requiring extra
are made in two fluids of known permittivity (13, 14, 7). This
circuits or adjustments. Parallel-T networks and resonant
method is not restricted to any frequency range; however, it is
circuits are not provided with guard circuits. In the deflection
besttolimituseofliquidimmersionmethodstofrequenciesfor
methodaguardcanbeprovidedmerelybyextrashielding.The
which the dissipation factor of the liquid is less than 0.01
use of a two-terminal micrometer-electrode system provides
(preferably less than 0.0001 for low-loss specimens).
many of the advantages of three-terminal measurements by
7.3.3.2 Whenusingthetwo-fluidmethoditisimportantthat
nearly eliminating the effect of edge and ground capacitances
both measurements be made on the same area of the specimen
but has the potential to increase the number of observations or
as the thickness will not always be the same at all points. To
balancingadjustments.Itsusealsoeliminatestheerrorscaused
ensure that the same area is tested both times and to facilitate by series inductance and resistance in the connecting leads at
the handling of thin films, specimen holders are convenient.
the higher frequencies. It is permissible to use over the entire
TheholdercanbeaU-shapedpiecethatwillslideintogrooves frequency range to several hundred megahertz. When a guard
in the electrode cell. It is also necessary to control the is used, the possibility exists that the measured dissipation
temperature to at least 0.1°C, which is possible by providing factor will be less than the true value. This is caused by
the cell with cooling coils (14). resistanceintheguardcircuitatpointsbetweentheguardpoint
D150 − 22
of the measuring circuit and the guard electrode. This has the 8.5.5 When two-terminal specimens are measured in any
potential to arise from high contact resistance, lead resistance, other manner, the calculation of edge capacitance and deter-
orfromhighresistanceintheguardelectrodeitself.Inextreme minationofgroundcapacitancewillinvolveconsiderableerror,
cases, the dissipation factor will appear to be negative. This since each has the potential to be from 2% to 40% of the
specimen capacitance. With the present knowledge of these
condition is most likely to exist when the dissipation factor
withouttheguardishigherthannormalduetosurfaceleakage. capacitances, there is the potential for an error of 10% in
calculating the edge capacitance and an error of 25% in
Anypointcapacitivelycoupledtothemeasuringelectrodesand
resistively coupled to the guard point can be a source of evaluating the ground capacitance. Hence the total error
involvedcanrangefromseveraltenthsof1%to10%ormore.
difficulty. The common guard resistance produces an equiva-
However, when neither electrode is grounded, the ground
lent negative dissipation factor proportional to C C R , where
h l g
capacitance error is minimized (6.1).
C and C are guard-to-electrode capacitances and R is the
h l g
8.5.6 With micrometer electrodes, it is possible to measure
guard resistance (15).
dissipation factor of the order of 0.03 to within 60.0003 and a
8.4 Fluid Displacement Methods—The fluid displacement
dissipationfactoroftheorderof0.0002towithin 60.00005of
method has the potential to be employed using either three-
the true values. The range of dissipation factor is normally
terminal or self-shielded, two-terminal cells. With the three-
0.0001 to 0.1 but it is possible for it to extend above 0.1.
terminal cell, it is possible to determine directly the permittiv-
Between 10MHz and 20 MHz it is possible to detect a
ity of the fluids used. The self-shielded, two-terminal cell
dissipation factor of 0.00002. Permittivity values from 2 to 5
provides many of the advantages of the three-terminal cell by
are able to be determined to 62%. The accuracy is limited by
nearly eliminating the effects of edge and ground capacitance,
theaccuracyofthemeasurementsrequiredinthecalculationof
and it has the potential to be used with measuring circuits
direct interelectrode vacuum capacitance and by errors in the
having no provision for a guard. If it is equipped with an
micrometer-electrode system.
integral micrometer electrode, the effects on the capacitance of
9. Sampling
seriesinductanceintheconnectiveleadsatthehigherfrequen-
cies will potentially be eliminated.
9.1 See materials specifications for instructions on sam-
pling.
8.5 Accuracy—The methods outlined in 8.1 contemplate an
accuracy in the determination of permittivity of 61% and of
10. Procedure
dissipation factor of 6(5%+0.0005). These accuracies de-
10.1 Preparation of Specimens:
pend upon at least three factors: the accuracy of the observa-
10.1.1 General—Cut or mold the test specimens to a suit-
tionsforcapacitanceanddissipationfactor,theaccuracyofthe
able shape and thickness determined by the material specifi-
corrections to these quantities caused by the electrode arrange-
cation being followed or by the accuracy of measurement
ment used, and the accuracy of the calculation of the direct
required, the test method, and the frequency at which the
interelectrodevacuumcapacitance.Underfavorableconditions
measurements are to be made. Measure the thickness in
and at the lower fr
...

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: D150 − 18 D150 − 22
Standard Test Methods for
AC Loss Characteristics and Permittivity (Dielectric
Constant) of Solid Electrical Insulation
This standard is issued under the fixed designation D150; 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.
This standard has been approved for use by agencies of the U.S. Department of Defense.
1. Scope Scope*
1.1 These test methods cover the determination of relative permittivity, dissipation factor, loss index, power factor, phase angle,
and loss angle of specimens of solid electrical insulating materials when the standards used are lumped impedances. The frequency
range addressed extends from less than 1 Hz to several hundred megahertz.
NOTE 1—In common usage, the word relative is frequently dropped.
1.2 These test methods provide general information on a variety of electrodes, apparatus, and measurement techniques. A reader
interested in issues associated with a specific material needs to consult ASTM standards or other documents directly applicable
2,3
to the material to be tested.
1.3 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. For specific hazard statements, see 10.2.1.
1.4 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:
D374 Test Methods for Thickness of Solid Electrical Insulation (Metric) D0374_D0374M
D618 Practice for Conditioning Plastics for Testing
D1531 Test Methods for Relative Permittivity (Dielectric Constant) and Dissipation Factor by Fluid Displacement Procedures
(Withdrawn 2012)
D1711 Terminology Relating to Electrical Insulation
These test methods are under the jurisdiction of ASTM Committee D09 on Electrical and Electronic Insulating Materials and are the direct responsibility of Subcommittee
D09.12 on Electrical Tests.
Current edition approved May 1, 2018Sept. 1, 2022. Published May 2018October 2022. Originally approved in 1922. Last previous edition approved in 20112018 as
D150 – 11.D150 – 18. DOI: 10.1520/D0150-18.10.1520/D0150-22.
R. Bartnikas, Chapter 2, “Alternating-Current Loss and Permittivity Measurements,” Engineering Dielectrics, Vol. IIB, Electrical Properties of Solid Insulating Materials,
Measurement Techniques, R. Bartnikas, Editor, STP 926, ASTM, Philadelphia, 1987.
R. Bartnikas, Chapter 1, “Dielectric Loss in Solids,” Engineering Dielectrics, Vol IIA, Electrical Properties of Solid Insulating Materials: Molecular Structure and
Electrical Behavior, R. Bartnikas and R. M. Eichorn, Editors, STP 783, ASTM Philadelphia, 1983.
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.
The last approved version of this historical standard is referenced on www.astm.org.
*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
D150 − 22
D5032 Practice for Maintaining Constant Relative Humidity by Means of Aqueous Glycerin Solutions
E104 Practice for Maintaining Constant Relative Humidity by Means of Aqueous Solutions
3. Terminology
3.1 Definitions:
3.1.1 Use Terminology D1711 for definitions of terms used in these test methods and associated with electrical insulation
materials.
3.2 Definitions of Terms Specific to This Standard:
3.2.1 capacitance, C, n—that property of a system of conductors and dielectrics which permits the storage of electrically separated
charges when potential differences exist between the conductors.
3.2.1.1 Discussion—
Capacitance is the ratio of a quantity, q, of electricity to a potential difference, V. A capacitance value is always positive. The units
are farads when the charge is expressed in coulombs and the potential in volts:
C 5q/V (1)
3.2.2 dissipation factor, (D), (loss tangent), (tan δ), n—the ratio of the loss index (κ") to the relative permittivity (κ') which is equal
to the tangent of its loss angle (δ) or the cotangent of its phase angle (θ) (see Fig. 1 and Fig. 2).
D 5κ"/κ' (2)
3.2.2.1 Discussion—
a:
D 5 tan δ5cotθ5X /R 5 G/ωC 5 1/ωC R (3)
p p p p p
where:
G = equivalent ac conductance,
X = parallel reactance,
p
R = equivalent ac parallel resistance,
p
C = parallel capacitance, and
p
ω = 2πf (sinusoidal wave shape assumed).
The reciprocal of the dissipation factor is the quality factor, Q, sometimes called the storage factor. The dissipation factor, D,
of the capacitor is the same for both the series and parallel representations as follows:
D 5ωR C 5 1/ωR C (4)
s s p p
The relationships between series and parallel components are as follows:
C 5 C / 11D (5)
~ !
p s
2 2 2 2
R /R 5 11D /D 5 11 1/D 5 11Q (6)
~ ! ~ !
p s
3.2.2.2 Discussion—
b: Series Representation—While the parallel representation of an insulating material having a dielectric loss (Fig. 3) is usually the
proper representation, it is always possible and occasionally desirable to represent a capacitor at a single frequency by a
capacitance, C , in series with a resistance, R (Fig. 4 and Fig. 2).
s s
3.2.3 loss angle (phase defect angle), (δ), n—the angle whose tangent is the dissipation factor or arctan κ"/κ' or whose cotangent
is the phase angle.
FIG. 1 Vector Diagram for Parallel Circuit
D150 − 22
FIG. 2 Vector Diagram for Series Circuit
FIG. 3 Parallel Circuit
FIG. 4 Series Circuit
3.2.3.1 Discussion—
The relation of phase angle and loss angle is shown in Fig. 1 and Fig. 2. Loss angle is sometimes called the phase defect angle.
3.2.4 loss index, κ" (ε ") , n—the magnitude of the imaginary part of the relative complex permittivity; it is the product of the
r
relative permittivity and dissipation factor.
3.2.4.1 Discussion—
a—It is expressed as:
κ"5κ' D (7)
5power loss/ E 3f 3volume 3constant
~ !
When the power loss is in watts, the applied voltage is in volts per centimeter, the frequency is in hertz, the volume is the
−13
cubic centimeters to which the voltage is applied, the constant has the value of 5.556 × 10 .
3.2.4.2 Discussion—
b—Loss index is the term agreed upon internationally. In the U.S.A. κ" was formerly called the loss factor.
3.2.5 phase angle, θ, n—the angle whose cotangent is the dissipation factor, arccot κ"/κ' and is also the angular difference in the
phase between the sinusoidal alternating voltage applied to a dielectric and the component of the resulting current having the same
frequency as the voltage.
3.2.5.1 Discussion—
The relation of phase angle and loss angle is shown in Fig. 1 and Fig. 2. Loss angle is sometimes called the phase defect angle.
3.2.6 power factor, PF,n—the ratio of the power in watts, W, dissipated in a material to the product of the effective sinusoidal
voltage, V, and current, I, in volt-amperes.
3.2.6.1 Discussion—
Power factor is expressed as the cosine of the phase angle θ (or the sine of the loss angle δ).
2 2
PF 5 W/VI 5 G/=G 1 ωC 5 sin δ5 cos θ (8)
~ !
p
When the dissipation factor is less than 0.1, the power factor differs from the dissipation factor by less than 0.5 %. Their
D150 − 22
exact relationship is found from the following:
PF 5 D/=11D (9)
D 5 PF/=12 PF
~ !
3.2.7 relative permittivity (relative dielectric constant) (SIC) κ'(ε ), n—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 (10)
p v
3.2.7.1 Discussion—
a—In common usage the word “relative” is frequently dropped.
3.2.7.2 Discussion—
b—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.)
p
3.2.7.3 Discussion—
c—C is taken to be C , the equivalent parallel capacitance as shown in Fig. 3.
x p
3.2.7.4 Discussion—
d—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 before the corrections and permittivity are calculated.
3.2.7.5 Discussion—
e—The permittivity of dry air at 23°C and standard pressure at 101.3 kPa is 1.000536 (1). 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 (2, 3), and varies approximately linearly with temperature expressed
in degrees Celsius, from 10 to 27°C. For partial saturation the increase is proportional to the relative humidity
4. Summary of Test Method
4.1 Capacitance and ac resistance measurements are made on a specimen. Relative permittivity is the specimen capacitance
divided by a calculated value for the vacuum capacitance (for the same electrode configuration), and is significantly dependent on
resolution of error sources. Dissipation factor, generally independent of the specimen geometry, is also calculated from the
measured values.
4.2 This method provides (1) guidance for choices of electrodes, apparatus, and measurement approaches; and (2) directions on
how to avoid or correct for capacitance errors.
4.2.1 General Measurement Considerations:
Fringing and Stray Capacitance Guarded Electrodes
Geometry of Specimens Calculation of Vacuum Capacitance
Edge, Ground, and Gap Corrections
4.2.2 Electrode Systems - Contacting Electrodes
Electrode Materials Metal Foil
Conducting Paint Fired-On Silver
Sprayed Metal Evaporated Metal
Liquid Metal Rigid Metal
Water
4.2.3 Electrode Systems - Non-Contacting Electrodes
Fixed Electrodes Micrometer Electrodes
Fluid Displacement Methods
The boldface numbers in parentheses refer to the list of references appended to these test methods.
D150 − 22
4.2.4 Choice of Apparatus and Methods for Measuring Capacitance and AC Loss
Frequency Direct and Substitution Methods
Two-Terminal Measurements Three-Terminal Measurements
Fluid Displacement Methods Accuracy considerations
5. Significance and Use
5.1 Permittivity—Insulating materials are used in general in two distinct ways, (1) to support and insulate components of an
electrical network from each other and from ground, and (2) to function as the dielectric of a capacitor. For the first use, it is
generally desirable to have the capacitance of the support as small as possible, consistent with acceptable mechanical, chemical,
and heat-resisting properties. A low value of permittivity is thus desirable. For the second use, it is desirable to have a high value
of permittivity, so that the capacitor is able to be physically as small as possible. Intermediate values of permittivity are sometimes
used for grading stresses at the edge or end of a conductor to minimize ac corona. Factors affecting permittivity are discussed in
Appendix X3.
5.2 AC Loss—For both cases (as electrical insulation and as capacitor dielectric) the ac loss generally needs to be small, both in
order to reduce the heating of the material and to minimize its effect on the rest of the network. In high frequency applications,
a low value of loss index is particularly desirable, since for a given value of loss index, the dielectric loss increases directly with
frequency. In certain dielectric configurations such as are used in terminating bushings and cables for test, an increased loss, usually
obtained from increased conductivity, is sometimes introduced to control the voltage gradient. In comparisons of materials having
approximately the same permittivity or in the use of any material under such conditions that its permittivity remains essentially
constant, it is potentially useful to consider also dissipation factor, power factor, phase angle, or loss angle. Factors affecting ac
loss are discussed in Appendix X3.
5.3 Correlation—When adequate correlating data are available, dissipation factor or power factor are useful to indicate the
characteristics of a material in other respects such as dielectric breakdown, moisture content, degree of cure, and deterioration from
any cause. However, it is possible that deterioration due to thermal aging will not affect dissipation factor unless the material is
subsequently exposed to moisture. While the initial value of dissipation factor is important, the change in dissipation factor with
aging is often much more significant.
5.4 Capacitance is the ratio of a quantity, q, of electricity to a potential difference, V. A capacitance value is always positive. The
units are farads when the charge is expressed in coulombs and the potential in volts:
C 5 q/V (1)
5.5 Dissipation factor ((D), (loss tangent), (tan δ)) is the ratio of the loss index (κ") to the relative permittivity (κ') which is equal
to the tangent of its loss angle (δ) or the cotangent of its phase angle (θ) (see Fig. 1 and Fig. 2).
D 5κ"/κ' (2)
5.5.1 It is calculated via Eq 3:
D 5 tan δ5cotθ5X /R 5 G/ωC 5 1/ωC R (3)
p p p p p
where:
G = equivalent ac conductance,
X = parallel reactance,
p
R = equivalent ac parallel resistance,
p
C = parallel capacitance, and
p
ω = 2πf (sinusoidal wave shape assumed).
The reciprocal of the dissipation factor is the quality factor, Q, sometimes called the storage factor. The dissipation factor, D,
of the capacitor is the same for both the series and parallel representations as follows:
D 5ωR C 5 1/ωR C (4)
s s p p
The relationships between series and parallel components are as follows:
C 5 C / 11D (5)
~ !
p s
D150 − 22
2 2 2 2
R /R 5 11D /D 5 11 1/D 5 11Q (6)
~ ! ~ !
p s
5.5.2 Series Representation—While the parallel representation of an insulating material having a dielectric loss (Fig. 3) is usually
the proper representation, it is always possible and occasionally desirable to represent a capacitor at a single frequency by a
capacitance, C , in series with a resistance, R (Fig. 4 and Fig. 2).
s s
5.6 Loss angle ((phase defect angle), (δ)) is the angle whose tangent is the dissipation factor or arctan κ"/κ' or whose cotangent
is the phase angle.
5.6.1 The relation of phase angle and loss angle is shown in Fig. 1 and Fig. 2. Loss angle is sometimes called the phase defect
angle.
5.7 Loss index (κ" (ε ") is the magnitude of the imaginary part of the relative complex permittivity; it is the product of the relative
r
permittivity and dissipation factor.
5.7.1 The loss index is expressed as:
κ"5κ' D (7)
5power loss/ E 3f 3volume 3constant
~ !
.
When the power loss is in watts, the applied voltage is in volts per centimeter, the frequency is in hertz, the volume is the cubic
−13
centimeters to which the voltage is applied, the constant has the value of 5.556 × 10 .
NOTE 2—Loss index is the term agreed upon internationally. In the United States, κ" was formerly called the loss factor.
5.8 Phase angle (θ) is the angle whose cotangent is the dissipation factor, arccot κ"/κ' and is also the angular difference in the phase
between the sinusoidal alternating voltage applied to a dielectric and the component of the resulting current having the same
frequency as the voltage.
5.8.1 The relation of phase angle and loss angle is shown in Fig. 1 and Fig. 2. Loss angle is sometimes called the phase defect
angle.
5.9 Power factor (PF) is the ratio of the power in watts, W, dissipated in a material to the product of the effective sinusoidal
voltage, V, and current, I, in volt-amperes.
5.9.1 Power factor is expressed as the cosine of the phase angle θ (or the sine of the loss angle δ).
2 2
PF 5 W/VI 5 G/=G 1~ωC ! 5 sin δ5 cos θ (8)
p
When the dissipation factor is less than 0.1, the power factor differs from the dissipation factor by less than 0.5 %. Their exact
relationship is found from the following:
PF 5 D/=11D (9)
D 5 PF/=12 PF
~ !
5.10 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 (10)
p v
NOTE 3—In common usage the word “relative” is frequently dropped.
NOTE 4—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.)
p
NOTE 5—C is taken to be C , the equivalent parallel capacitance as shown in Fig. 3.
x p
D150 − 22
NOTE 6—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 before
the corrections and permittivity are calculated.
NOTE 7—The permittivity of dry air at 23 °C and standard pressure at 101.3 kPa is 1.000536 (1). 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 (2, 3), 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. General Measurement Considerations
6.1 Fringing and Stray Capacitance—These test methods are based upon measuring the specimen capacitance between electrodes,
and measuring or calculating the vacuum capacitance (or air capacitance for most practical purposes) in the same electrode system.
For unguarded two-electrode measurements, the determination of these two values required to compute the permittivity, κ ' is
x
complicated by the presence of undesired fringing and stray capacitances which get included in the measurement readings.
Fringing and stray capacitances are illustrated by Figs. 5 and 6 for the case of two unguarded parallel plate electrodes between
which the specimen is to be placed for measurement. In addition to the desired direct interelectrode capacitance, C , the system
v
as seen at terminals a-a' includes the following:
C = fringing or edge capacitance,
e
C = capacitance to ground of the outside face of each electrode,
g
C = capacitance between connecting leads,
L
C = capacitance of the leads to ground, and
Lg
C = capacitance between the leads and the electrodes.
Le
Only the desired capacitance, C , is independent of the outside environment, all the others being dependent to a degree on the
v
proximity of other objects. It is necessary to distinguish between two possible measuring conditions to determine the effects of the
undesired capacitances. When one measuring electrode is grounded, as is often the case, all of the capacitances described are in
parallel with the desired C - with the exception of the ground capacitance of the grounded electrode and its lead. If C is placed
v v
within a chamber with walls at guard potential, and the leads to the chamber are guarded, the capacitance to ground no longer
appears, and the capacitance seen at a-a' includes C and C only. For a given electrode arrangement, the edge capacitance, C ,
v e e
can be calculated with reasonable accuracy when the dielectric is air. When a specimen is placed between the electrodes, the value
of the edge capacitance can change requiring the use of an edge capacitance correction using the information from Table 1.
Empirical corrections have been derived for various conditions, and these are given in Table 1 (for the case of thin electrodes such
as foil). In routine work, where best accuracy is not required it is convenient to use unshielded, two-electrode systems and make
the approximate corrections. Since area (and hence C ) increases of the square diameter while perimeter (and hence C ) increases
v e
linearly with diameter, the percentage error in permittivity due to neglecting the edge correction decreases with increasing
specimen diameter. However, for exacting measurements it is necessary to use guarded electrodes.
6.2 Guarded Electrodes—The fringing and stray capacitance at the edge of the guarded electrode is practically eliminated by the
addition of a guard electrode as shown in Fig. 7 and Fig. 8. If the test specimen and guard electrode extend beyond the guarded
electrode by at least twice the thickness of the specimen and the guard gap is very small, the field distribution in the guarded area
will be identical with that existing when vacuum is the dielectric, and the ratio of these two direct capacitances is the permittivity.
Furthermore, the field between the active electrodes is defined and the vacuum capacitance can be calculated with the accuracy
limited only by the accuracy with which the dimensions are known. For these reasons the guarded electrode (three-terminal)
method is to be used as the referee method unless otherwise agreed upon. Fig. 8 shows a schematic representation of a completely
guarded and shielded electrode system. Although the guard is commonly grounded, the arrangement shown permits grounding
FIG. 5 Stray Capacitance, Unguarded Electrodes
D150 − 22
FIG. 6 Flux Lines Between Unguarded Electrodes
either measuring electrode or none of the electrodes to accommodate the particular three-terminal measuring system being used.
If the guard is connected to ground, or to a guard terminal on the measuring circuit, the measured capacitance is the direct
capacitance between the two measuring electrodes. If, however, one of the measuring electrodes is grounded, the capacitance to
ground of the ungrounded electrode and leads is in parallel with the desired direct capacitance. To eliminate this source of error,
surround the ungrounded electrode with a shield connected to guard as shown in Fig. 8. In addition to guarded methods, which
are not always convenient or practical and which are limited to frequencies less than a few megahertz, techniques using special
cells and procedures have been devised that yield, with two-terminal measurements, accuracies comparable to those obtained with
guarded measurements. Such methods described here include shielded micrometer electrodes (7.3.2) and fluid displacement
methods (7.3.3).
6.3 Geometry of Specimens—For determining the permittivity and dissipation factor of a material, sheet specimens are preferable.
Cylindrical specimens can also be used, but generally with lesser accuracy. The source of the greatest uncertainty in permittivity
is in the determination of the dimensions of the specimen, and particularly that of its thickness. Therefore, the thickness shall be
large enough to allow its measurement with the required accuracy. The chosen thickness will depend on the method of producing
the specimen and the likely variation from point to point. For 1 % accuracy a thickness of 1.5 mm (0.06 in.) is usually sufficient,
although for greater accuracy it is desirable to use a thicker specimen. Another source of error, when foil or rigid electrodes are
used, is in the unavoidable gap between the electrodes and the specimen. For thin specimens the error in permittivity can be as
much as 25 %. A similar error occurs in dissipation factor, although when foil electrodes are applied with a grease, the two errors
are not likely to have the same magnitude. For the most accurate measurements on thin specimens, use the fluid displacement
method (6.3.3).(7.3.3). This method reduces or completely eliminates the need for electrodes on the specimen. The thickness must
be determined by measurements distributed systematically over the area of the specimen that is used in the electrical measurement
and shall be uniform within 61 % of the average thickness. If the whole area of the specimen will be covered by the electrodes,
and if the density of the material is known, the average thickness can be determined by weighing. The diameter chosen for the
specimen shall be such as to provide a specimen capacitance that can be measured to the desired accuracy. With well-guarded and
screened apparatus there need be no difficulty in measuring specimens having capacitances of 10 pF to a resolution of 1 part in
1000. If a thick specimen of low permittivity is to be tested, it is likely that a diameter of 100 mm or more will be needed to obtain
the desired capacitance accuracy. In the measurement of small values of dissipation factor, the essential points are that no
appreciable dissipation factor shall be contributed by the series resistance of the electrodes and that in the measuring network no
large capacitance shall be connected in parallel with that of the specimen. The first of these points favors thick specimens; the
second suggests thin specimens of large area. Micrometer electrode methods (6.3.2)(7.3.2) can be used to eliminate the effects of
series resistance. Use a guarded specimen holder (Fig. 8) to minimize extraneous capacitances.
6.4 Calculation of Vacuum Capacitance—The practical shapes for which capacitance can be most accurately calculated are flat
parallel plates and coaxial cylinders, the equations for which are given in Table 1. These equations are based on a uniform field
between the measuring electrodes, with no fringing at the edges. Capacitance calculated on this basis is known as the direct
interelectrode capacitance.
6.5 Edge, Ground, and Gap Corrections—The equations for calculating edge capacitance, given in Table 1, are empirical, based
on published work (4) (see 8.5). They are expressed in terms of picofarads per centimetre of perimeter and are thus independent
of the shape of the electrodes. It is recognized that they are dimensionally incorrect, but they are found to give better
approximations to the true edge capacitance than any other equations that have been proposed. Ground capacitance cannot be
calculated by any equations presently known. When measurements must be made that include capacitance to ground, it is
recommended that the value be determined experimentally for the particular setup used. The difference between the capacitance
measured in the two-terminal arrangement and the capacitance calculated from the permittivity and the dimensions of the specimen
is the ground capacitance plus the edge capacitance. The edge capacitance can be calculated using one of the equations of Table
1. As long as the same physical arrangement of leads and electrodes is maintained, the ground capacitance will remain constant,
and the experimentally determined value can be used as a correction to subsequently measured values of capacitance. The effective
area of a guarded electrode is greater than its actual area by approximately half the area of the guard gap (5, 6, 7). Thus, the
diameter of a circular electrode, each dimension of a rectangular electrode, or the length of a cylindrical electrode is increased by
D150 − 22
TABLE 1 Calculations of Vacuum Capacitance and Edge Corrections (see 8.5)
NOTE 1—See Table 2 for Identification of Symbols used.
Direct Inter-Electrode Capacitance
Type of Electrode Correction for Stray Field at an Edge, pF
in Vacuum, pF
Disk electrodes with guard-ring: A C = 0
e
C 5ε 5
v 0
t
A
0.0088542
t
π
A 2
A5 sd 1B gd
Disk electrodes without guard-ring:
Diameter of the electrodes = diameter of the specimen: where a << t, C = (0.0087 – 0.00252 ln t) P
e
d
Equal electrodes smaller than the specimen: C = (0.0019 κ ' – 0.00252 ln t + 0.0068)P
1 e x
C 50.0069541
v
t
where: κ ' = an approximate value of the specimen permit
x
tivity, and a << t.
Unequal electrodes: C = (0.0041 κ '– 0.00334 ln t + 0.0122)P
e x
where: κ ' = an approximate value of the specimen
x
permittivity, and a << t.
A
0.055632 sl 1B gd
Cylindrical electrodes with guard-ring: C = 0
1 e
C 5
v
d
ln
d
0.055632 l t 1
Cylindrical electrodes without guard-ring:
C 5 If ,
v
d t1d 10
2 1
ln
C = (0.0038 κ ' – 0.00504 ln t + 0.0136)P
d e x
P = π (d + t)
where κ ' = an approximate value of the specimen
x
permittivity.
A
See Appendix X2 for corrections to guard gap.
FIG. 7 Flux Lines Between Guarded Parallel Plate Electrodes
the width of this gap. When the ratio of gap width, g, to specimen thickness, t, is appreciable, the increase in the effective dimension
of the guarded electrode is somewhat less than the gap width. Details of computation for this case are given in Appendix X2.
D150 − 22
FIG. 8 Three-Terminal Cell for Solids
7. Electrode Systems
7.1 Contacting Electrodes—It is acceptable for a specimen to be provided with its own electrodes, of one of the materials listed
below. For two-terminal measurements, the electrodes shall either extend to the edge of the specimen or be smaller than the
specimen. In the latter case, it is acceptable for the two electrodes to be equal or unequal in size. If they are equal in size and smaller
than the specimen, the edge of the specimen must extend beyond the electrodes by at least twice the specimen thickness. The choice
between these three sizes of electrodes will depend on convenience of application of the electrodes, and on the type of
measurement adopted. The edge correction (see Table 1) is smallest for the case of electrodes extending to the edge of the specimen
and largest for unequal electrodes. When the electrodes extend to the edge of the specimen, these edges must be sharp. Such
electrodes must be used, if attached electrodes are used at all, when a micrometer electrode system is employed. When equal-size
electrodes smaller than the specimen are used, it is difficult to center them unless the specimen is translucent or an aligning fixture
is employed. For three-terminal measurements, the width of the guard electrode shall be at least twice the thickness of the specimen
(6, 8). The gap width shall be as small as practical (0.5 mm is possible). For measurement of dissipation factor at the higher
frequencies, electrodes of this type are likely to be unsatisfactory because of their series resistance. Use micrometer electrodes for
the measurements.
7.2 Electrode Materials:
7.2.1 Metal Foil—Lead or tin foil from 0.00750.0075 mm to 0.025 mm 0.025 mm thick applied with a minimum quantity of
refined petrolatum, silicone grease, silicone oil, or other suitable low-loss adhesive is generally used as the electrode material.
Aluminum foil has also been used, but it is not recommended because of its stiffness and the probability of high contact resistance
due to the oxidized surface. Lead foil is also likely to give trouble because of its stiffness. Apply such electrodes under a smoothing
pressure sufficient to eliminate all wrinkles and to work excess adhesive toward the edge of the foil. One very effective method
is to use a narrow roller, and to roll outward on the surface until no visible imprint can be made on the foil. With care the adhesive
film can be reduced to 0.0025 mm. As this film is in series with the specimen, it will always cause the measured permittivity to
be too low and probably the dissipation factor to be too high. These errors usually become excessive for specimens of thickness
less than 0.125 mm. The error in dissipation factor is negligible for such thin specimens only when the dissipation factor of the
film is nearly the same as that of the specimen. When the electrode is to extend to the edge, it shall be made larger than the
specimen and then cut to the edge with a small, finely ground blade. A guarded and guard electrode can be made from an electrode
that covers the entire surface, by cutting out a narrow strip (0.5 mm is possible) by means of a compass equipped with a narrow
cutting edge.
7.2.2 Conducting Paint—Certain types of high-conductivity silver paints, either air-drying or low-temperature-baking varieties,
are commercially available for use as electrode material. They are sufficiently porous to permit diffusion of moisture through them
and thereby allow the test specimen to condition after application of the electrodes. This is particularly useful in studying humidity
effects. The paint has the disadvantage of not being ready for use immediately after application. It usually requires an overnight
air-drying or low-temperature baking to remove all traces of solvent, which otherwise has the potential to increase both permittivity
and dissipation factor. It is often also not easy to obtain sharply defined electrode areas when the paint is brushed on, but it is
possible to overcome by spraying the paint and employing either clamp-on or pressure-sensitive masks. The conductivity of silver
paint electrodes is often low enough to give trouble at the higher frequencies. It is essential that the solvent of the paint does not
affect the specimen permanently.
7.2.3 Fired-On Silver—Fired-on silver electrodes are suitable only for glass and other ceramics that are able to withstand, without
change, a firing temperature of about 350°C.350 °C. Its high conductivity makes such an electrode material satisfactory for use
Additional information on electrode systems can be found in Research Report RR:D09-1037 available from ASTM Headquarters.
D150 − 22
on low-loss materials such as fused silica, even at the highest frequencies, and its ability to conform to a rough surface makes it
satisfactory for use with high-permittivity materials, such as the titanates.
7.2.4 Sprayed Metal—A low-melting-point metal applied with a spray gun provides a spongy film for use as electrode material
which, because of its grainy structure, has roughly the same electrical conductivity and the same moisture porosity as conducting
paints. Suitable masks must be used to obtain sharp edges. It conforms readily to a rough surface, such as cloth, but does not
penetrate very small holes in a thin film and produce short circuits. Its adhesion to some surfaces is poor, especially after exposure
to high humidity or water immersion. Advantages over conducting paint are freedom from effects of solvents, and readiness for
use immediately after application.
7.2.5 Evaporated Metal—Evaporated metal used as an electrode material has the potential to have inadequate conductivity
because of its extreme thinness, and must be backed with electroplated copper or sheet metal. Its adhesion is adequate, and by itself
it is sufficiently porous to moisture. The necessity for using a vacuum system in evaporating the metal is a disadvantage.
7.2.6 Rigid Metal—For smooth, thick, or slightly compressible specimens, it is permissible to use rigid electrodes under high
pressure, especially for routine work. Electrodes 10 mm in diameter, under a pressure of 18.0 MPa have been found useful for
measurements on plastic materials, even those as thin as 0.025 mm. Electrodes 50 mm in diameter, under pressure, have also been
used successfully for thicker materials. However, it is difficult to avoid an air film when using solid electrodes, and the effect of
such a film becomes greater as the permittivity of the material being tested increases and its thickness decreases. The uncertainty
in the determination of thickness also increases as the thickness decreases. It is possible that the dimensions of a specimen will
continue to change for as long as 24 h after the application of pressure.
7.2.7 Water—Water can be used as one electrode for testing insulated wire and cable when the measurements are made at low
frequency (up to 1000 Hz, approximately). Care must be taken to ensure that electrical leakage at the ends of the specimen is
negligible.
7.3 Non-Contacting Electrodes:
7.3.1 Fixed Electrodes—It is possible to measure specimens of sufficiently low surface conductivity, without applied electrodes,
by inserting them in a prefabricated electrode system, in which there is an intentional air gap on one or both sides of the specimen.
Assemble the electrode system rigidly and ensure that it includes a guard electrode. For the same accuracy, a more accurate
determination of the electrode spacing and the thickness of the specimen is required than if direct contact electrodes are used.
However, these limitations are likely to be removed if the electrode system is filled with a liquid (see 7.3.3).
7.3.2 Micrometer Electrodes—The micrometer-electrode system, as shown in Fig. 9, was developed (9) to eliminate the errors
caused by the series inductance and resistance of the connecting leads and of the measuring capacitor at high frequencies. A built-in
vernier capacitor is also provided for use in the susceptance variation method. It accomplishes this by maintaining these
inductances and resistances relatively constant, regardless of whether the test specimen is in or out of the circuit. The specimen,
which is either the same size as, or smaller than, the electrodes, is clamped between the electrodes. Unless the surfaces of the
specimen are lapped or ground very flat, metal foil or its equivalent must be applied to the specimen before it is placed in the
electrode system. If electrodes are applied, they also must be smooth and flat. Upon removal of the specimen, the electrode system
can be adjusted to have the same capacitance by moving the micrometer electrodes closer together. When the micrometer-electrode
system is carefully calibrated for capacitance changes, its use eliminates the corrections for edge capacitance, ground capacitance,
FIG. 9 Micrometer-Electroder System
D150 − 22
and connection capacitance. In this respect it is advantageous to use it over the entire frequency range. A disadvantage is that the
capacitance calibration is not as accurate as that of a conventional multiplate variable capacitor, and also it is not a direct reading.
At frequencies below 1 MHz, where the effect of series inductance and resistance in the leads is negligible, it is permissible to
replace the capacitance calibration of the micrometer electrodes by that of a standard capacitor, either in parallel with the
micrometer-electrode system or in the adjacent capacitance arm of the bridge. The change in capacitance with the specimen in and
out is measured in terms of this capacitor. A source of minor error in a micrometer-electrode system is that the edge capacitance
of the electrodes, which is included in their calibration, is slightly changed by the presence of a dielectric having the same diameter
as the electrodes. This error can be practically eliminated by making the diameter of the specimen less than that of the electrodes
by twice its thickness (3). When no electrodes are attached to the specimen, surface conductivity has the potential to cause serious
errors in dissipation factor measurements of low loss material. When the bridge used for measurement has a guard circuit, it is
advantageous to use guarded micrometer electrodes. The effects of fringing, and so forth, are almost completely eliminated. When
the electrodes and holder are well made, no capacitance calibration is necessary, as it is possible to calculate the capacitance from
the electrode spacing and the diameter. The micrometer itself will require calibration, however. It is not practicable to use
electrodes on the specimen when using guarded micrometer electrodes unless the specimen is smaller in diameter than the guarded
electrode.
7.3.3 Fluid Displacement Methods—When the immersion medium is a liquid, and no guard is used, the parallel-plate system
preferably shall be constructed so that the insulated high potential plate is supported between, parallel to, and equidistant from two
parallel low-potential or grounded plates, the latter being the opposite inside walls of the test cell designed to hold the liquid. This
construction makes the electrode system essentially self-shielding, but normally requires duplicate test specimens. Provision must
be made for precise temperature measurement of the liquid (10, 11). Cells shall be constructed of brass and gold plated. The
high-potential electrode shall be removable for cleaning. The faces must be as nearly optically flat and plane parallel as possible.
A suitable liquid cell for measurements up to 1 MHz is shown in Fig. 4 of Test Method D1531. Changes in the dimensions of this
cell are necessary to provide for testing sheet specimens of various thicknesses or sizes, but such changes shall not reduce the
capacitance of the cell filled with the standard liquid to less than 100 pF. For measurements at frequencies from 11 MHz to about
50 MHz, the cell dimensions must be greatly reduced, and the leads must be as short and direct as possible. The capacitance of
the cell with liquid shall not exceed 3030 pF or 40 pF 40 pF for measurements at 50 MHz. Experience has shown that a capacitance
of 10 pF can be used up to 100 MHz without loss of accuracy. Guarded parallel-plate electrodes have the advantage that single
specimens can be measured with full accuracy. Also a prior knowledge of the permittivity of the liquid is not required as it is
possible to measure directly (12). If the cell is constructed with a micrometer electrode, it is possible to measure specimens having
widely different thicknesses with high accuracy since the electrodes can be adjusted to a spacing only slightly greater than the
thickness of the specimen. If the permittivity of the fluid approximates that of the specimen, the effect of errors in the determination
of specimen thicknesses are minimized. The use of a nearly matching liquid and a micrometer cell permits high accuracy in
measuring even very thin film.
7.3.3.1 All necessity for determining specimen thickness and electrode spacing is eliminated if successive measurements are made
in two fluids of known permittivity (13, 14, 7). This method is not restricted to any frequency range; however, it is best to limit
use of liquid immersion methods to frequencies for which the dissipation factor of the liquid is less than 0.01 (preferably less than
0.0001 for low-loss specimens).
7.3.3.2 When using the two-fluid method it is important that both measurements be made on the same area of the specimen as the
thickness will not always be the same at all points. To ensure that the same area is tested both times and to facilitate the handling
of thin films, specimen holders are convenient. The holder can be a U-shaped piece that will slide into grooves in the electrode
cell. It is also necessary to control the temperature to at least 0.1°C,0.1 °C, which is possible by providing the cell with cooling
coils (14).
8. Choice of Apparatus and Methods for Measuring Capacitance and AC Loss
8.1 Frequency Range—Methods for measuring capacitance and ac loss can be divided into three groups: null methods, resonance
methods, and deflection methods. The choice of a method for any particular case will depend primarily on the operating frequency.
It is permissible for th
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