An industrial approach towards traceable moisture measurements in microwave domain

Moisture measurements in solid materials, both in terms of industrial measurements and calibration, represent a great challenge namely for choosing the measurand of interest, then for defining the measurement method, including the sample handling, and at last for ensuring SI traceability with a primary method.

Within the framework of JRP 19ENG09 BiofMET, LNE-CETIAT and Fresnel Institute have developed an instrument that uses radiofrequencies and microwaves, with the aim of developing an infrastructure that measures moisture in line. It is a stainless steel cylindrical resonant cavity with a sizable internal volume 6,7 10³ cm³. The method used in this work is the cavity perturbation method (CPM), which is based on a comparative analysis of some electromagnetic characteristics between an empty and a partially loaded cylindrical resonant cavity.

Thanks to a vector network analyzer connected to the measurement system (cavity + antennas), transmission coefficient, S₁₂ or S₂₁, are measured as a function of the frequency. And from the analysis of the two spectrum obtained, one "empty" and one "loaded", it is possible to go back to the resonance frequency of the cavity. Why resonance frequency? The assumption of the cavity perturbation theory is that the electromagnetic fields inside the cavity, after the introduction of a material into the cavity, change accordingly by a very small amount compared to the fields inside the empty cavity. Then, using Maxwell's equations for the original and perturbed cavities, analytical expressions for the resonant frequency shift and the quality factor change Q can be derived. In this case, we can use perturbation theory to derive the values of the real and imaginary parts of the complex permittivity of the material. Moreover, the dielectric permittivity is influenced by several factors like the humidity present in this material, the temperature...

Numerical simulations have been performed using the HFFS software, in order to define the final design, which consists in two straight antennas, placed on the upper cover of the cavity, mounted on either side of a sample holder consisting of a cylindrical glass tube, with an internal volume about 188;35 cm³, located in the center of the cavity. Moreover, in order to facilitate the experimental work and to obtain better performance by using the perturbation technique, the experimental measures in parallel with numerical modeling of the EM processes in an empty and loaded cavity. It leads to a resonance phenomenon which appears in the 2,1 and 2,3 GHz band. Indeed, the resonance frequency obtained with the empty tube, which is equal to 2,294 GHz, shifts towards 2,222 GHz by filling the tube with COGRA wood pellets.

The reproducibility of the measurement system has been studied by using different materials such as liquids, like distilled water and alcohols, and solids or powders, like wood pellets or Alpha D lactose or PTFE. The results of the transmission coefficient, in the frequency band from 1,6 to 2,4 GHz, show the reproducibility of our system specially in terms of frequency shift. The standard deviation obtained for different repetitions of measurement cycles, with wood pellets, is about 8,4 10^-3 GHz.This deviation is related to the density change in between each reproduced filling: indeed the product compaction differs from one experiment to another.

In the next steps, wood pellets are going to be more investigated namely with different humidity levels, in order to model a correlation between humidity content, measured with primary techniques, and dielectric parameters, to ensure SI traceability.

Figure 1: The resonant cavity, developed at LNE-CETIAT, connected to a vector network analyzer.

Figure 2: 3D representation of the distribution of the electric field of the cavity in the presence of the empty tube.

Figure 3: Study of the reproducibility of measurements of empty tube (right) tube filled with wood pellets(left).

Figure 4: Comparison between several types of wood pellets (different sources).