Permittivity

Electric permittivity is an extremely important concept in electromagnetics. This is a material parameter also known as “distributed capacitance” as evidenced by its units [Farads/meter]. The absolute permittivity (∈) is used in the calculation of the capacitance of a parallel plate capacitor and is inherent to a material. The relative permittivity (∈_r) is the ratio of the absolute permittivity of a material to the permittivity of a vacuum (8.85E-12 F/m). This is also known as the dielectric constant.

A good way to understand permittivity is to consider two conductive plates separated by a distance with an equal and opposite amount of charge applied. As you can probably guess, a static electric field exists between the plates due to the charge, since the charges are separated by nonconducting medium.

As the figure demonstrates, a dielectric material will polarize itself and create a field opposing the external field applied. This is because even though the molecules of a dielectric are mostly stationary due to their lattice structure, they can rearrange a bit due to an externally applied field. In addition, dielectrics can become conducting if a large enough field is applied (dielectric breakdown). The rearranging of these molecules reduces the overall field and increases the “distributed capacitance”.

It is important to know that for normal materials, the electric permittivity is generally a complex number, because permittivity is dependent on the frequency of the field applied. This is because the polarization of a dielectric cannot happen instantaneously due to “causality” (a system’s response depends on past or present inputs, not on future inputs). Permittivity can also be affected by temperature and humidity. The complex permittivity equation can be written as

It is seen that the imaginary part of the equation depends on frequency and accounts for conductivity. The response of the material to a static (DC) field is found be decreasing the frequency to zero. The high frequency limit is found by increasing the frequency.

It is important to distinguish between dielectric constant and dielectric strength. Dielectric strength is the ability of the material to resist dielectric breakdown (units V/mil). A high dielectric breakdown means that a high voltage can be applied before the dielectric conducts appreciable current.