# Dielectric Constant & Relative Permittivity

### The dielectric constant & relative permittivity are key to the operation of capacitors and the determination of the levels of capacitance achievable.

Permittivity and dielectric constant are two terms that are central to capacitor technology. Often talk will be heard of capacitors with different dielectrics being used. Electrolytic, ceramic, paper, tantalum and all the common names for capacitors refer to the dielectric material that is used.

The dielectric material provides the insulation between the capacitor plates, and in addition this it determines many of the characteristics of the capacitor. It capacitance achievable in a certain volume, the temperature stability whether it is polarised or not. These and many other characteristics are governed by the dielectric material used – many properties being governed by the dielectric constant itself.

## 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.

## Permittivity & dielectric constant definitions

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

• Absolute permittivity:   Absolute permittivity is defined as 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:   Relative permittivity is defined as the permittivity of a given material relative to that of the permittivity of a vacuum. It is normally symbolised by: εr.
• Static permittivity:   The static permittivity of a material is defined as 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:   The dielectric constant is defined as the relative permittivity for a substance or material.

Although these terms may be seen to be related, it is often 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:

$\epsilon =\frac{D}{E}$

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:

${\epsilon }_{r}=\frac{{\epsilon }_{s}}{{\epsilon }_{0}}$

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
FR4 PCB material 4.8 typically
Glass 5 - 10
Mica 5.6 - 8.0
Paper 3.85
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.

When the design of a capacitor is undertaken the characteristics of the dielectric form one of the main decisions about the capacitor. Some materials have a very stable dielectric constant and can be used in high stability capacitors, whereas other dielectric materials enable very high levels of volumetric capacitance to be achieved, i.e. high levels of capacitance in a small volume. Normally there is a balance as no single dielectric has ideal characteristics for everything.

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