Measuring
dielectric constant
Updated August
16, 2008
Click
here to go to our page on permittivity
New for January 2008!If
anyone wants to contribute info on a dielectric measurement techniques,
contact us!
New for August 2008! We'll
show you how to calculate
dielectric constant from group delay!
There are many ways to measure
dielectric constant of a material or effective dielectric constant
of a media. You can actually make a career out of this measurement,
once you know all the nuances and practice a bit. A "complete"
dielectric constant measurement include loss tangent data, which
can be even harder to measure, because its effect is usually swamped
by other loss mechanisms. For now let's just concentrate on obtaining
accurate measurements of the real part of ER, shall we?
Before we attempt describe any
methods in various amounts of detail, let's first point out that
1. dielectric constant can vary with frequency (but usually not
a lot) and 2. the measurement techniques can be fraught with errors,
which we'll try to explain.
Here's a true story. Someone
once boasted that they had a method of measuring dielectric constant
at microwave frequency that would provide three digits of accuracy.
We employed them to measure a single sample, and the results came
back something like "6.045". The next week we asked them
to perform a second sample measurement but submitted the same sample
(pretty sneaky, huh?) The "new" results came back "6.267".
We averaged the two data points and came up with 6.1 +/0.2! So yes
indeed this measurement technique could provide three digits of
accuracy, but the accuracy of the second and third digit were questionable.
We told this "expert" to lose the charge number after
the second sample. Moral of the story: permittivity measurements
might be easy to do, but it is hard to measure permittivity
with great accuracy.
The IPC (Institute for interconnecting
and Packaging electronic Circuits) has documented many dielectric
constant measurement technique, under IPC TM 650. Some of the techniques
are at low frequencies, but some are suitable for Xband. You'll
learn a lot about dielectric constant measurements by perusing IPC
TM 650 section 2.5.
If you search Agilent's web site
you will find app notes on this type of measurement as well.
Dielectric constant or effective
dielectric constant?
Let's mention the difference
between "dielectric constant" and "effective dielectric
constant". Dielectric constant is a bulk material property,
effective dielectric constant is a parameter that depends on transmission
line geometry. Most often the dielectric constant that engineers
try to measure is the bulk measurement.
If you are considering measuring
permittivity with a microstrip structure, you will be measuring
the effective dielectric constant, no ifs ands or buts. If the technique
involves coax, waveguide or stripline, and you are careful not to
introduce appreciable air gaps or glue layers, you just might be
able to directly measure the "real" dielectric constant!
Sheet measurement technique
This is how most soft
substrate suppliers measure permittivity. They merely take a
very large sheet of known thickness, and measure the capacitance
and back out the dielectric constant. So what's the problem? There's
actually two problems. First this is (usually) low frequency (MHz,
not GHz) measurement (a big sheet won't act like a lumpedelement
capacitor at Xband!). Again we must point out that dielectric constant
may be different at microwave frequencies. The second problem is
that the accuracy of the measurement is affected by the ability
of the manufacturers to maintain the sample thickness; a 10% thickness
tolerance equates to a potential 10% permittivity error.
A transformer technique
If you go to our page on measuring
cable lengths, there's a method that we describe as a rule of
thumb for measuring cable length when you know the dielectric constant.
However, you could use the same technique to measure dielectric
constant of a material if you could use it to construct a long TEM
transmission line, if you know the length, and if you can ensure
that your measurement is done at a fifty ohm interface. We figure
you could achieve 1% accuracy if you made a stripline measurement
this way and included deembedding standards.
We'll add some math and some
"predicted results" to back this up one of these days.
The formula is
ER=[c/(2*deltaF*L)]^2
where c is the speed of light
in vacuum
deltaF is the frequency differences
between two adjacent resonances
L is the known length of the
transformer
(Thanks for the correction, Daniel!)
Note that this doesn't give you the loss tangent, nor does it give
you an ER measurement for every frequency point. It turns out with
some complex math you could get all of that, plus the relative permeability.
It will take us a while to develop the math into an example, if
anyone wants to help us out we can supply the app note that suggests
how to do this, if we can remember where we put it...
Ring resonator techniques
There are two ways to loosely
couple to a ring resonator, one is end coupling, the other is edge
coupling. The end coupled structure (shown below) provides a passband
whenever the ring is a multiple of wavelengths.
The edge coupled technique a
"suckout" is seen in the reflection coefficient (S11)
whenever the ring is an integer number of wavelengths. This is behaving
like a bandreject filter, sometimes called a spur line filter (a
topic we still need to cover!)
This is the preferred method
if you ask us, the dips in S11 are very narrowband and therefore
the resonant frequency is more accurately known.
More to come!
Coupled halfwave resonator
technique
There are papers on this technique
that show you how to measure both the real and imaginary parts of
ER.
Coming soon!
