# Relative Permittivity & Dielectric Constant

### Capacitance tutorial includes

Permittivity and dielectric constant are two terms that are at the very heart of capacitor technology.

The dielectric is the material that provides the insulation between the capacitor plates, and many of the characteristics of the capacitor will be dependent upon the properties of the dielectric used.

Capacitor diagram showing dielectric between the plates

## Capacitor permittivity and dielectric constant

The terms permittivity and dielectric constant are essentially the same for most purposes, although there are instances where the different terms do have very specific meanings.

It is that property of a dielectric material that determines how much electrostatic energy can be stored per unit of volume when unit voltage is applied, and as a result it is of great importance for capacitors and capacitance calculations and the like.

In general permittivity uses the Greek letter epsilon as its symbol: ε.

Definitions of some specific terms related to dielectric constant and permittivity are given below:

• Absolute permittivity:   is the measure of permittivity in a vacuum and it is how much resistance is encountered when forming an electric field in a vacuum. The absolute permittivity is normally symbolised by ε0. The permittivity of free space - a vacuum - is equal to approximately 8.85 x 10-12 Farads / metre (F/m)
• Relative permittivity:   is permittivity of a given material relative to that of the permittivity of a vacuum. It is normally symbolised by: εr.
• Static permittivity:   of a material is its permittivity when exposed to a static electric field. Often a low frequency limit is placed on the material for this measurement. A static permittivity is often required because the response of a material is a complex relationship related to the frequency of the applied voltage.
• Dielectric constant:   This is the relative permittivity for a substance or material.

Although these terms may be seen to be related, it is important to use the correct terms in the required place.

## Relative permittivity (dielectric constant)

Using the fact that the permittivity ε of a medium is governs the charge that can be held by a medium, it can be seen that the formula to determine it is:

Where:
ε = permittivity of the substance in Farads per metre
D = electric flux density
E = electric field strength

It can be seen from the definitions of permittivity that constants are related according to the following equation:

Where:
εr = relative permittivity
εs = permittivity of the substance in Farads per metre
ε0 = permittivity of a vacuum in Farads per metre

## Choice of capacitor dielectric

Capacitors use a variety of different substances as their dielectric material. The material is chosen for the properties it provides. One of the major reasons for the choice of a particular dielectric material is its dielectric constant. Those with a high dielectric constant enable high values of capacitance to be achieved - each one having a different permittivity or dielectric constant. This changes the amount of capacitance that the capacitor will have for a given area and spacing.

The dielectric will also need to be chosen to meet requirements such as insulation strength - it must be able to withstand the voltages placed across it with the thickness levels used. It must also be sufficiently stable with variations in temperature, humidity, and voltage, etc.

## Relative permittivity of common substances

The table below gives the relative permittivity of a number of common substances.

Relative Permittivity of Common Substances
Substance Relative
Permittivity
Calcium titanate 150
Ebonite 2.7 - 2.9
FR4 PCB material 4.8 typically
Glass 5 - 10
Marble 8.3
Mica 5.6 - 8.0
Paper 3.85
Paraffin wax 2 - 2.4
Polyethylene) 2.25
Polyimide 2.25
Polypropylene 2.2 - 2.36
Porcelain (ceramic) 4.5 - 6.7
PTFE (Teflon) 2.1
Rubber 2.0 - 2.3
Silicon 11.68
Silicon dioxide 3.9
Strontium titanate 200

Air 0°C 1.000594
Air 20°C 1.000528
Carbon monoxide 25°C 1.000634
Carbon dioxide 25°C 1.000904
Hydrogen 0°C 1.000265
Helium 25°C 1.000067
Nitrogen 25°C 1.000538
Sulphur dioxide 22°C 1.00818

The values given above are what may be termed the "static" values of permittivity. They are true for steady state or low frequencies. It is found that the permittivity of a material usually decreases with increasing frequency. It also falls with increasing temperature. These factors are normally taken into account when designing a capacitor for electronics applications.

Some materials have a more stable level of permittivity and hence they are used in the higher tolerance capacitors. However this often has to be balanced against other factors. Some materials have very high levels of permittivity, and hence they enable capacitors to be made much smaller. This factor may be particularly useful when the size of the capacitor is particularly important.

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