# Measurement of the dielectric constant and loss tangent of materials in microwave frequency band using a rectangular waveguide cavity.

This experiment shows how a piece of sample material affects the center frequency (f) and quality fator (Q) of the cavity. From these parameters, the complex permittivity or permeability of material can be calculated at a single frequency. For calculation of these parameters, we used cavity perturbation method. This method uses a rectangular waveguide with iris coupled end plates, operating in TE10n mode. For a dielectric measurement the sample should be placed in a maximum electric field, while for a magnetic measurement, in a maximum magnetic field.

In this experiment, we will consider n=2k+1 because if the sample is inserted through a hole in the middle of waveguide length then half number of wavelength will bring the maximum electric field to the sample location, so that the dielectric properties of sample can be measured.

First step of the experiment is to design a rectangular waveguide cavity resonator in the designated frequency band. The design should then preferably be validated before fabricating the actual sample holder in order to carry out the required measurements. At present, there are, however, a number of numerical methods, which can simulate the exact geometry of the structure quite accurately, and whose accuracy has been tested against the measured data. It is mainly due to this reason that the scattering coefficient data of the sample in the present situation has been generated using the numeircal simulation. A special care has been taken to refine the mesh size especially in the areas of interest so that the simulated data quite accurately represent the real experiment scenario. The major steps for the design of the cavity resonator in order to perform the actual measurement of the dielectric properties of the material under test are as follows:

• Design a waveguide for TE107 mode (7 half wavelength long at the designated frequency) with a hole drilled exactly at the middle of the waveguide length.

• Design two iris coupled metal plates to close the ends of the waveguide. The dimension of the iris hole is typically b / 2.2, where b is the narrow dimension of the waveguide.

• Drill a small hole at the middle of the waveguide length in order to insert the sample through it. The dimensions and geometry of the hole would be same as that of the sample, which is to be measured. The dimensions of the sample are chosen in such a way that its volume is typically less than 1 percent of the total volume of the cavity.

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