11.1: Permittivity of Some Common Materials
- Page ID
- 24856
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)The values below are relative permittivity \(\epsilon_r \triangleq \epsilon/\epsilon_0\) for a few materials that are commonly encountered in electrical engineering applications, and for which permittivity emerges as a consideration. Note that “relative permittivity” is sometimes referred to as dielectric constant.
Here we consider only the physical (real-valued) permittivity, which is the real part of the complex permittivity (typically indicated as \(\epsilon'\) or \(\epsilon_r'\)) for materials exhibiting significant loss.
Permittivity varies significantly as a function of frequency. The values below are representative of frequencies from a few kHz to about 1 GHz. The values given are also representative of optical frequencies for materials such as silica that are used in optical applications. Permittivity also varies as a function of temperature. In applications where precision better than about 10% is required, primary references accounting for frequency and temperature should be consulted. The values presented here are gathered from a variety of references, including those indicated in “Additional References.”
Free Space (vacuum): \(\epsilon_r \triangleq 1\)
| Material | \(\epsilon_r\) | Common uses |
|---|---|---|
| Styrofoam\(^1\) | 1.1 | |
| Teflon\(^2\) | 2.1 | |
| Polyethylene | 2.3 | coaxial cable |
| Polypropylene | 2.3 | |
| Silica | 2.4 | optical fiber\(^3\) |
| Polystyrene | 2.6 | |
| Polycarbonate | 2.8 | |
| Rogers RO3003 | 3.0 | PCB substrate |
| FR4 (glass epoxy laminate) | 4.5 | PCB substrate |
\(^1\) Properly known as extruded polystyrene foam (XPS).
\(^2\) Properly known as polytetrafluoroethylene (PTFE).
\(^3\) Typically doped with small amounts of other materials to slightly raise or lower the index of refraction (\(=\sqrt{\epsilon_r}\)).
Non-conducting spacing materials used in discrete capacitors exhibit \(\epsilon_r\) ranging from about 5 to 50.
- Semiconductors commonly appearing in electronics – including carbon, silicon, geranium, indium phosphide, and so on – typically exhibit \(\epsilon_r\) in the range 5–15.
- Glass exhibits \(\epsilon_r\) in the range 4–10, depending on composition.
- Gasses, including air, typically exhibit \(\epsilon_r\cong 1\) to within a tiny fraction of a percent.
- Liquid water typically exhibits \(\epsilon_r\) in the range 72–81. Distilled water exhibits \(\epsilon_r \approx 81\) at room temperature, whereas sea water tends to be at the lower end of the range.
- Other liquids typically exhibit \(\epsilon_r\) in the range 10–90, with considerable variation as a function of temperature and frequency. Animal flesh and blood consists primarily of liquid matter and so also exhibits permittivity in this range.
- Soil typically exhibits \(\epsilon_r\) in the range 2.5–3.5 when dry and higher when wet. The permittivity of soil varies considerably depending on composition.