Modelling the behaviour of an open-ended coaxial probe to assess the permittivity of heterogeneous dielectrics solids

The study presents the development of a new two-dimensional axisymmetric finite element model describing the operation of a large open-ended coaxial probe. This numerical simulation, combined with a capacitive approach describing the behaviour of the system, enabled to prove the suitability of such device to determine the permittivity of homogeneous dielectric solids over the frequency range [1MHz; 4GHz]. Finding back the permittivity of a specified material thanks to the simulation is achieved by calculating the input port reflection coefficients S
₁₁
at the TEM wave emission port. A capacitive model is then applied to calculate a permittivity value. Very good matching between set and calculated dielectric constants is a first noticeable result. Measurements performed onto different homogeneous materials like rocks also show good similarities with the numerical simulations. A comparison between measurements and simulations obtained for samples with different electromagnetic properties can therefore be used as a very simple way to calculate permittivity of dielectrics solids. This study is not restricted to homogeneous solids. Measurements performed onto heterogeneous samples like a dry sand made up by crushing a homogeneous rock are compared to FEM simulations with different dielectric constants set as an entry of the calculus. Permittivity of the heterogeneous material is thereby deduced and compared to different mixing laws estimating the effective permittivity of a media made of heterogeneities dispersed into a matrix with different electromagnetic properties. Good matching between dielectric constants resulting from specific effective medium theories and measurements performed onto a dry sand is obtained.