Permittivity Extraction of Soil Samples Using Coaxial-Line Measurements by a Simple Calibration

Abstract

A new microwave method is proposed for accurate determination of complex permittivity <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\varepsilon _{\textrm {rs}} = \varepsilon _{\textrm {rs}}^{\prime }--j \varepsilon _{\textrm {rs}}^{\prime \prime }$ </tex-math></inline-formula> of soil samples inserted over a holder within the Electronic Industries Association (EIA) 1-5/8” coaxial measurement cell. Such a determination could be indirectly correlated with the volumetric moisture content of soil samples by microwave measurements. The method has three main advantages. First, it utilizes a simple calibration procedure involving uncalibrated measurements of an empty cell, the same cell loaded with a soil holder (a dielectric sample), and the same cell with a soil sample over this holder, thus eliminating the need for any formal calibration procedure. Second, it uses one measurement cell for extracting <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\varepsilon _{\textrm {rs}}$ </tex-math></inline-formula> . Third, it does not require any numerical toolbox for determining <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\varepsilon _{\textrm {rs}}$ </tex-math></inline-formula> . The method is validated by simulations of a synthesized soil sample and by experiments with a low-loss polyethylene sample. Its accuracy is examined in reference to: 1) two measurement cells with different lengths (length independence); 2) the position of the holder in the cell; and 3) an offset in sample length. Calibration curves (the volumetric moisture content <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\theta _{V}$ </tex-math></inline-formula> versus <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\varepsilon _{\textrm {rs}}^{\prime }$ </tex-math></inline-formula> ) obtained from fitting measured <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\varepsilon _{\textrm {rs}}^{\prime }$ </tex-math></inline-formula> by our method to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\theta _{V}$ </tex-math></inline-formula> at 2 and 3 GHz are compared with other calibration curves in the literature for the analysis of the performance of the proposed method (PM). It is shown that calibration curves obtained from our method are similar to those obtained from other methods requiring complex calibration procedures.