An Open Hemispherical Resonant Cavity for Relative Permittivity Measurements of Fluid and Solid Materials at mm-Wave Frequencies

In this paper, we present a hemispherical Fabry-Pérot open cavity resonator based measurement technique to estimate the relative permittivity of dielectric materials. The open cavity is realized by combining a spherical and a planar mirror, suitable for the characterization of both solid and fluid materials in the frequency range from 25 GHz to 42 GHz. The planar mirror is surrounded by a 0.5 mm high metal wall which allows the reflector to be filled with the liquid material to characterize. The measurement method is based on the Gaussian beam theory, which allows extracting the dielectric properties of the material by analyzing the resonant frequency shift of the fundamental mode from, in this case, the reflection coefficient only. This is made possible thanks to the optimized shape of the coupling aperture.