here to go to our page on Keffective
here to go to our page on TEM
here to go learn about our Dk and Df extraction spreadsheet
New for August 2010! Filling
factor is what connects Keffective to ER. Filling factor is a measure
of the percentage of the electric fields in a transmission line
that cut through the substrate.
In non-TEM transmission lines
such as CPW and microstrip, the electric fields cut through two
(or sometimes more) dielectric materials. For now, we will only
consider the case of two materials, and one of them is air (ER=1).
If FF is the percentage of fields
in the material, then 1-FF is the percentage of fields in air.
Solving for FF,
In most calculations, engineers
are only interested in Z0 and Keff. But they miss what is really
going on by ignoring FF. Let's start by stating a Microwaves101
Rule of Thumb, and then back it up by way of example:
For a given microstrip or stripline geometry, the filling factor
is very nearly a constant versus the value of the dielectric constant
of the substrate. The inductance per length does not change versus
the dielectric constant of the substrate, only the capacitance/length
Microstrip filling factor example
Let's look at an example geometry.
Suppose you were evaluating
an unknown board material, with transmission line of the following
Let's look at the filling factor,
for any dielectric constant ER from 1.01 to 10 (we can't use ER=1,
because it results in divide-by-zero situation!)
We used ADS to calculate the
Keff and Z0 for all of these dielectrics, and came up with the following
A note about calculating Keff...
you could use the Microwaves101
microstrip calculator, and come up with values of filling factor.
But we'll let you in on a secret... our microstrip calculator is
not as accurate as ADS, because we used simplified equations that
don't take into account thickness of the metal strip. In the case
of this geometry, the error is large enough so that we decided to
go with the better calculation, indeed, the Microwaves101 Keff value
is almost 10% too high. In the future, we'll try to post a calculator
with the full microstrip solution, but for now, let's just say beware
of free calculators on the web!
As you can see from the table,
FF pretty much remains constant with regard to ER. Let's look at
a plot, a picture is worth a thousand words:
Now let's calculate the inductance
and capacitance per length (L' and C'), and plot them.
Guess what? Inductance/length
doesn't change much, when you radically change the dielectric ER
in a non-TEM transmission line. The capacitance/length changes linearly,
as you'd expect. This is a direct result of FF remaining constant
For ideal coplanar
waveguide (with very thick substrate and no ground plane on
the back side, thin, perfect conductors), filling factor is 50%.
Therefore the Keff is equal to:
This is the average value of
air (ER=1) and the substrate.