Updated December 9,
here to go to our page on isotropy and anisotropy
here to go to our page on Keffective
here to go to a page on measuring dielectric constant
here to go to our companion page on permeability
here to go to our basic concepts of microwaves page
here to go to our main microwave materials page
here to go to our list of dielectric constants of miscellaneous
here to go to our discussion of capacitors
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.
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.
permittivity (the dielectric constant)
Materials other than vacuum have
permittivity higher than 0,
often they are referred to by their relative permittivity, denoted
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 Yogi Berra saying "deja
vu again". Quite often dielectric constant is referred to as "DK" or "Dk". It's not "DC" for obvious reasons, Grasshopper.
But lots of otherwise-smart people flub this microwave IQ test. Here is a screen capture from a well-known EDA software package you might recognize. The user has pulled up the information on his/her microstrip substrate parameters. Er is described as "relative dielectric constant". Come on, guys, fix that! This is a good reason for holding a design review on a software product....
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
Permittivity can also be a function
of direction, which leads us to the definitions of two classes of
A material in which the permittivity is NOT a function of direction.
Most materials are isotropic, thankfully! More information on isotropy
and anisotropy is provided on this
A material in which the permittivity IS a function of direction.
An example is sapphire.
The interesting thing about sapphire is it has the same atomic composition
as pure alumina (Al2O3)
but alumina is amorphous while sapphire is crystalline. Thanks to
Luciano for pointing this out!
Note: Keffective is further discussed
on this page.
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 (ER=12.9) is approximately 6.5.
This topic has been moved to
a new page.
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, dry 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.
Loss tangent is often called "dissipation factor" and abbreviated "DF" or "Df" (as opposed to dielectric constant which is abbreviated "DK".