Permittivity extraction of sandy soils through uncalibrated and thickness-independent meniscus-free measurements using a hollow coaxial line

Measurement techniques for accurate moisture level determination of various soil conditions are becoming popular in recent studies. Microwave-driven techniques, as positioned into indirect methods, could be tailored for precise and real-time detection of soil moisture. However, improper implementation of calibration techniques or usage of imperfect calibration standards required for precise measurements by these techniques presents a challenging limitation for their widespread usage. Besides, meniscus formation on top of soil samples with a sufficient moisture level could adversely influence the performance of these techniques. In this study, we present a microwave extraction method for eliminating the requirement of a formal calibration procedure and additionally removing the effect of meniscus on measurements through relative measurements of sandy soil samples while maintaining accurate permittivity extraction with no information of sample thickness. To achieve our goal, a mathematical framework unifying wave-cascading matrix and state-transition matrix presentations is proposed for permittivity determination from three measurement configurations (empty line, the (sandy) soil sample sandwiched between two identical plugs, and a shifted version of this plug-sample-plug configuration) and their inverses implemented by port switching operation. The proposed method is first validated by permittivity measurements of two liquid samples (distilled water and methanol). Then, permittivity measurements of two sandy soil samples (having more than 90% sand content) were conducted using Type-N-to-EIA 1-5/8” coaxial lines (with no universal calibration standard) over 0.05 GHz–3.0 GHz. From these measurements, it is noted that our meniscus-free method determines permittivity with a maximum absolute difference of 3.4% (evaluated from five independent measurements) while another similar method, suffering from meniscus presence, extracts permittivity with a maximum absolute difference of 4.0%. This indicates a clear advantage of our method for measurements of sandy soil samples having meniscus formation. We then utilized to construct a calibration curve, compared with other calibration curves using by other methods, allowing prediction of moisture volume content () of the tested sandy soil samples from measured permittivity data whose conformity analysis implemented by the three-pole Debye model and the Mironov-Fomin model. It is observed that this calibration curve could be utilized to predict within margin from measured permittivity data.