# `Permittivity`

 Antenna Tutorial (Home)

Permittivity is a property of a medium or a region of space. On this page, I'm going to give its meaning as it relates to antenna theory, with only a small explanation on the physics behind it. The permittivity, as we saw relates the electric flux density to the electric field. The permittivity is given in units of Farads/meter; since Farads relates to capacitance, a material with a higher permittivity can be thought of as storing more electrical energy.

The permittivity of a vaccum (often called free space) is given by:

The above is roughly the permittivity of air on earth. Suppose we have some other dielectric medium (glass, rubber, wax or other non-conducting material). The permittivity describes how an electric field is affected within a medium. The E-field tends to polarize the molecules within the material, which make up a net electric field that opposes the applied E-field. As a result, the total E-field is less than it would be in a vacuum. This effect is quantized in terms of the permittivity - which can be anisotropic (direction dependent) and frequency dependent.

As an antenna engineer, the permittivity affects the speed of propagation of a wave through a medium and also its wavelength. The permittivity of a medium is most often given as a relative permittivity:

The speed of wave propagation in a given medium is given as:

Hence, if a medium has , then the speed of wave propagation in the medium will be half as fast as in free space (1.5*10^8 m/s). As a result of the speed being slowed, the wavelength of a plane wave decreases in size as well (the frequency remains constant):

The above fact is often used in antenna-miniaturization: since resonant antennas are often a half-wavelength in size, if they are placed in a medium with a higher permittivity the required length decreases and hence the antenna will be smaller.

Permittivity alters the direction of travel of a wave incident upon a medium through snell's law. In addition, the reflection and transmission coefficients of a wave travelling from one medium to another is influenced by the permittivity.