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 S 11 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. Electrical and Computer Systems Engineering Postgraduate Student Research Forum 2001 Improved free space microwave permittivity measurements Andrew Amiet Supervisor: Dr. Greg Cambrell Associate supervisor: Dr Peter Jewsbury (DSTO) 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 Receive horn Sample Send/receive horn Vector Network Analyzer 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. Reflection effects 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. 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. Time gating Diffraction removal Removing errors involved with the technique Unwanted reflections Real Imaginary Introduction Time Gate