The relative permittivity (in older texts, dielectric constant) is the permittivity of a material expressed as a ratio with the electric permittivity of a vacuum. A dielectric is an insulating material, and the dielectric constant of an insulator measures the ability of the insulator to store electric energy in an electrical field. Permittivity is a material's property that affects the Coulomb force between two point charges in the material. Relative permittivity is the factor by which the electric field between the charges is decreased relative to vacuum. Likewise, relative permittivity is the ratio of the capacitance of a capacitor using that material as a dielectric, compared with a similar capacitor that has vacuum as its dielectric. Relative permittivity is also commonly known as the dielectric constant, a term still used but deprecated by standards organizations in engineering as well as in chemistry.
Definition Relative permittivity is typically denoted as εr(ω) (sometimes κ, lowercase kappa) and is defined as
ε r ( ω ) = ε ( ω ) ε 0 , {\displaystyle \varepsilon _{\text{r}}(\omega )={\frac {\varepsilon (\omega )}{\varepsilon _{0}}},}
where ε(ω) is the complex frequency-dependent permittivity of the material, and ε0 is the vacuum permittivity. Relative permittivity is a dimensionless number that is in general complex-valued; its real and imaginary parts are denoted as:
ε r ( ω ) = ε r ′ ( ω ) − i ε r ″ ( ω ) . {\displaystyle \varepsilon _{\text{r}}(\omega )=\varepsilon _{\text{r}}'(\omega )-i\varepsilon _{\text{r}}''(\omega ).}
The relative permittivity of a medium is related to its electric susceptibility, χe, as εr(ω) = 1 + χe. In anisotropic media (such as non cubic crystals) the relative permittivity is a second rank tensor. The relative permittivity of a material for a frequency of zero is known as its static relative permittivity.
Terminology The historical term for the relative permittivity is dielectric constant. It is still commonly used, but has been deprecated by standards organizations, because of its ambiguity, as some older reports used it for the absolute permittivity ε. The permittivity may be quoted either as a static property or as a frequency-dependent variant, in which case it is also known as the dielectric function. It has also been used to refer to only the real component ε′r of the complex-valued relative permittivity.
Physics In the causal theory of waves, permittivity is a complex quantity. The imaginary part corresponds to a phase shift of the polarization P relative to E and leads to the attenuation of electromagnetic waves passing through the medium. By definition, the linear relative permittivity of vacuum is equal to 1, that is ε = ε0, although there are theoretical nonlinear quantum effects in vacuum that become non-negligible at high field strengths. The following table gives some typical values.
The relative low frequency permittivity of ice is ~96 at −10.8 °C, falling to 3.15 at high frequency, which is independent of temperature. It remains in the range 3.12–3.19 for frequencies between about 1 MHz and the far infrared region.
Determination The relative static permittivity, εr, can be determined for static electric fields as follows: first the capacitance of a test capacitor, C0, is measured with vacuum between its plates. Then, using the same capacitor and distance between its plates, the capacitance C with a dielectric between the plates is measured. The relative permittivity can be then calculated as
ε r = C C 0 . {\displaystyle \varepsilon _{\text{r}}={\frac {C}{C_{0}}}.}
For time-variant electromagnetic fields, this quantity becomes frequency-dependent. An indirect technique to calculate εr is conversion of radio frequency S-parameter measurement results. A description of frequently used S-parameter conversions for determination of the frequency-dependent εr of dielectrics can be found in this bibliographic source. Alternatively, resonance based effects may be employed at fixed frequencies.
Applications
Energy The relative permittivity is an essential piece of information when designing capacitors, and in other circumstances where a material might be expected to introduce capacitance into a circuit. If a material with a high relative permittivity is placed in an electric field, the magnitude of that field will be measurably reduced within the volume of the dielectric. This fact is commonly used to increase the capacitance of a particular capacitor design. The layers beneath etched conductors in printed circuit boards (PCBs) also act as dielectrics.
Communication Dielectrics are used in radio frequency (RF) transmission lines. In a coaxial cable, polyethylene can be used between the center conductor and outside shield. It can also be placed inside waveguides to form filters. Optical fibers are examples of dielectric waveguides. They consist of dielectric materials that are purposely doped with impurities so as to control the precise value of εr within the cross-section. This controls the refractive index of the material and therefore also the optical modes of transmission. However, in these cases it is technically the relative permittivity that matters, as they are not operated in the electrostatic limit.
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