Effect of materials with different permittivity on the sensing depth of open-ended coaxial probes at different frequencies

At present, there is a lack of accurate analysis of the effect of frequency on probe depth of sensing, and studies of the relationship between probe depth of sensing and frequency have focused mainly on the frequency range below 20 GHz. First, in this paper, the relationship between frequency and probe sensing depth within the 0.5-20 GHz range is experimentally analyzed. Using spatial interpolation techniques, frequency extrapolation is performed based on experimental data to derive the sensing depths of open-ended coaxial probes for materials with permittivity ranging from 2 to 80 across an extended frequency spectrum of 0.1-40 GHz. Second, we developed the first computational model of the probe sensing depth based on the exponential function using the least squares method according to the obtained data. Finally, we selected typical materials to experimentally validate the resulting computational model of sensing depth. The research results in this paper provide a method for the accurate calculation of probe sensing depth in a wide frequency range, and a theoretical reference for sample preparation based on the open-ended coaxial probe method as well as for the accurate measurement of the complex permittivity of materials.