## ASTM D150 – **Standard Test Methods for AC Loss Characteristics and Permittivity (Dielectric Constant) of Solid Electrical Insulation**

**Description**:

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.

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).

The reciprocal of the dissipation factor is the quality factor, *Q*, sometimes called the storage factor.

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*_{s}, in series with a resistance, *R*_{s} .

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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_{r}“) is the magnitude of the imaginary part of the relative complex permittivity; it is the product of the relative permittivity and dissipation factor.

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 centimeters to which the voltage is applied, the constant has the value of 5.556 × 10^{−13}.

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 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).

When the dissipation factor is less than 0.1, the power factor differs from the dissipation factor by less than 0.5 %.

5.10 Relative permittivity ((relative dielectric constant) (SIC) κ′(ε_{r})) is the real part of the relative complex permittivity. It is also the ratio of the equivalent parallel capacitance, *C*_{p}, of a given configuration of electrodes with a material as a dielectric to the capacitance, *C*_{υ}, of the same configuration of electrodes with vacuum (or air for most practical purposes) as the dielectric:

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*_{p}, a capacitance in parallel with conductance.

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