Destructive interference is common when measuring the reflection from a sample. When the microwave radiation encounters the dielectric sample under test, some is reflected from the surface and some is transmitted into the material, reflects back again

1
Improved free space microwave permittivity
measurements
Andrew Amiet
Supervisor Dr. Greg Cambrell
Associate supervisor Dr Peter Jewsbury (DSTO)
Introduction
The technique involves measuring the reflection
and/or transmission from a sample over the
frequency range 1 to 40 GHz. The sample is placed
between two microwave horn antennas as shown on
the left. A vector network analyzer controls the
frequency generation and data collection, the
information is then sent to a PC for analysis.
The network analyzer measures S-parameters, which
are related to the permittivity (?) and
permeability (?) by the formulas
below. Reflection
Transmission where
and d thickness of
sample, c speed of light, ? angular frequency
Measurement of permittivity and permeability of
materials in the microwave band can be performed
in free space. It is a very effective non
destructive method but the absence of an enclosed
waveguide leads to some serious errors if the
measurement is not carefully performed.
Researchers have been using the technique for
many years but a thorough investigation of the
sources of errors, together with their resolution
has not been performed. It is more difficult to
calibrate a free space system because of the
absence of appropriate standards. Errors can
occur from stray reflections, diffraction if the
sample is not sufficiently large, near-field
effects, sample positioning and flatness, and
destructive interference effects.
Removing errors involved with the technique
Reflection effects
Destructive interference is common when measuring
the reflection from a sample. When the microwave
radiation encounters the dielectric sample under
test, some is reflected from the surface and some
is transmitted into the material, reflects back
again from the rear of the sample and
destructively interferes with the return
reflection. The measured reflection from a 5.4mm
thick sample of Teflon is shown in the upper left
figure. When the permittivity is calculated using
the formulas above using both reflected and
transmitted data, the trace shows spikes at
destructive interference frequencies, seen on the
lower left figure. However since the permeability
is known be equal to that of free space, the
formulas above can be rearranged to remove S11
and use only the transmitted signal to extract
permittivity. The equation used to extract
permittivity is shown below, note that an
iterative technique is used to extract the
solution. The effect of using transmission
data alone can be seen in the graphs on the
right. The real permittivity of Teflon is 2.04
0.02 with the imaginary component being very
close to zero. The transmission only technique is
very effective in removing the sharp spikes.
Time gating
Diffraction removal
The technique assumes the sample is infinite in
size ie. the only signal received by the horns
travels through the sample. However real samples
have a finite size, and if the horns have a wide
enough spread or are a sufficient distance away
from the sample then some of the wave can
diffract around it and be collected by the
receive horn. The diffracted wave can be measured
by placing a metal plate with the same size and
shape as the sample under test between the horns.
The diffracted signal can be removed easily on
the computer, the results of this shown in the
figures to the right. Measurements of imaginary
permittivity of a lossy sample with the receive
horn at three locations are shown, with distance
increasing as the configuration number. The lower
figure shows result with diffraction removed.
Stray reflections will always occur when
measuring in free space, no matter how well the
area is shielded or covered in absorbing foam.
Reflections from inside the horns, the specimen
holder and walls, together with multiple
reflection paths from the sample to horns all add
to the signal received by the horns. However some
of these reflections can be removed using time
gating, which involves performing a Chirp-Z
transform on the frequency data, isolating the
peak of interest in the time domain then
converting back to the frequency domain having
effectively removed all the stray peaks. The time
domain trace can be seen on the upper left figure
showing the effect of gating, the effect on
permittivity is seen on the lower figure.
Unwanted reflections
Time Gate
Real
Imaginary
Electrical and Computer Systems
Engineering Postgraduate Student Research Forum
2001