Permittivity

Updated August 19, 2008

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Permittivity is a property which is associated with how much electrical charge a material can store in a given volume. The units of permittivity are Farads/meter. The Farad is named after Michael Faraday. Permittivity is what controls the value of a capacitor, beyond its physical dimensions.

Permittivity of free space

The permittivity in vacuum (free space) is denoted as ₀. Its value is 8.85418782E-12 Farads per meter (see our page on physical constants). No material has a permittivity lower than that of a vacuum.

Relative permittivity (the dielectric constant)

Materials other than vacuum have permittivity higher than ₀, often they are referred to by their relative permittivity, denoted _R:

_material=0x_R

In microwaves, we often refer to relative permittivity as the "dielectric constant". These terms are interchangeable, but "relative permittivity" sounds more scholarly if you want to pretend to be a nerd. Saying "relative dielectric constant" is like saying "deja vu again".

Note: an alert professor points out the the relative permittivity is not always a constant for a given material, it can change with frequency, temperature, date of manufacture or supplier, or even direction of propagation. Pay attention to this valuable comment, because some day you will design a microstrip filter and find out the hard way that we usually don't know EXACTLY what the dielectric "constant" (which really isn't a constant) is. If you know the value within +/-1%, you are in better shape than the rest of us!

Most microwave materials have dielectric constant between 2.2 (PTFE) and 9.9 (alumina), because so many materials are engineered by mixing these two materials. If particle size is kept small compared to a wavelength, and the ratio of materials is well maintained from batch to batch, the mixture will be well behaved. See our pages on soft and hard substrate materials for data on a wide variety of materials. Here's a page on miscellaneous materials.

Permittivity can also be a function of direction, which leads us to the definitions of two classes of materials:

Isotropic material
A material in which the permittivity is NOT a function of direction. Most materials are isotropic, thankfully!

Anisotropic material
A material in which the permittivity IS a function of direction. An example is sapphire.

Effective permittivity

In non-TEM transmission lines such as those realized in microstrip media, most of the electric fields are constrained within the substrate, but a fraction of the total energy exists within the air above the board. The effective permittivity (a.k.a. effective dielectric constant) takes this into account. The effective dielectric constant of a fifty-ohm transmission line on ten mil alumina is a number somewhere around 7, which is less than the dielectric constant of the substrate bulk material (9.8), but more than that of air (which is 1).

Another example of an effective dielectric constant is if you were to create a stripline circuit using two sheets of substrates with different dielectric constants. To a first order, the effective dielectric constant would be the average of the two materials' dielectric constants. A third example is coplanar waveguide transmission lines with air above the substrate. Here the effective dielectric constant is very nearly the average of the substrate dielectric constant and one (the relative dielectric constant of air). Thus the effective dielectric constant of CPW circuits on GaAs (E_R=12.9) is approximately 6.5.

Measuring dielectric constant

This topic has been moved to a new page.

Complex permittivity and loss tangent

Permittivity is actually a complex number, so "epsilon" is made up of two parts:

(Thanks to Maarten for correcting another recurrence of us mixing up "permeability" with "permittivity" on this dyslexic web site...) Epsilon single-prime is the number we usually deal with, and causes no loss, and in most day-to-day engineering you don't see the prime notation. The imaginary epsilon double-prime is the culprit. Microwave engineers usually deal with the ratio between the two, which is called tangent delta, or tanD (say "tan-dee"), for short. If tanD is zero, there is no loss due to dielectric. For example, air has no dielectric loss.

Note that relative permittivity is the ratio of epsilon prime to epsilon zero:

The loss tangent creates a loss that is proportional to frequency. See our page on transmission line loss calculations for more information.