Presentation of a complex permittivity-meter with applications for sensing the moisture and salinity of a porous media

Abstract

This paper describes a sensor dedicated to measuring the vertical profile of the complex permittivity and the temperature of any medium in which sensor electrodes are inserted. Potential applications are the estimate of the humidity and salinity in a porous medium, such as a soil. It consists of vertically-stacked capacitors along two conductive parallel cylinders of 5 cm in diameter and at a 10-cm distance to scan a significant volume of the medium (~1 L). It measures their admittances owing to a self-balanced impedance bridge operating at a frequency in the range of 1-20 MHz, possibly 30 MHz. Thanks to accurate design and electronic circuit theory-based modeling, the determination of the admittances takes into account all distortions due to lead and bridge electromagnetic effects inside the sensor when working at high frequencies. Calibration procedures and uncertainties are presented. The article also describes developments to make the present sensor autonomous on digital acquisition, basic data treatment and energy, as well as able to transfer stored data by a radio link. These steps in progress are prerequisites for a wireless network of sensors.

Figure 1.

Photograph of sensor electrodes and their five channels. The dimensions for one channel are shown by a ruler: ϕ is the electrode diameter (ϕ = 50 mm), D the distance between their axes (D = 100 mm) and h their height (h = 50 mm).

Figure 2.

Photograph of the whole sensor with its electrodes and two aerial polyvinyl chloride tubes. Tubes house, respectively, the printed circuit boards and the battery for autonomous operations. (a) With the tubes; (b) Without the tubes.

Figure 3.

Schematic view of an ideal admittance bridge. When in balance, the current i_eq generated by the bridge through the conductance G_eq under the voltage v_osc ΔV_G (using a multiplier) and through the capacitance C_eqω under the voltage v_osc ΔV_C offsets the current i_x from the admittance to be determined, Y_x = G_x + j C_xω. ω is the bridge angular frequency in rad·s⁻¹.

Figure 4.

The total current $i_k^{\prime }$ in the circuit of channel k comprises a contribution i_k due directly to the admittance Y_k under study and another i_km due to the influence of channel m through its magnetic field B_m.

Figure 5.

Bridge phase drifts φ_C/G and φ_G/C. (a) Schematic view of the admittance bridge as in Figure 3 taking into account the phase drifts φ_G/C and φ_C/G due to multipliers at the conductance and capacitance branches, respectively; (b) Voltage interferences ΔV_C/G and ΔV_G/C between the conductance and capacitance branches, due to the phase drifts φ_C/G and φ_G/C.

Figure 6.

The breakdown of the admittance Y_x = G_x + jC_xω actually measured by the bridge. In addition to the admittance Y = G + j Cω under study, Y_x includes a capacitance C_S, an inductance L_S and a resistance r_S in series, as well as parasitic admittances in parallel of Y, Y_p = G_p + j C_pω, all due to the leads.

Figure 7.

Sensor output ΔV_G (a) and ΔV_C (b) as a function of the reference G_ref = 1/R_ref using calibration data and Equation (19). For each voltage, the difference in mV between data and its fit from Equation (19) are also plotted. Channel parameters are deduced from the fits. (a) Plot ΔV_G (G_ref) and difference with fit. Hence, G_eq = −3.57 μS·mV⁻¹. r_S= 2.8 Ω; (b) Plot ΔV_C (G_ref) and difference with fit. Hence, φ_G/C = 0.3110⁻³ rad.

Figure 8.

Four-day trial started at 13:54 GMT, 17 July 2014. Data of temperature for all five channels, permittivity and conductivity at 20 MHz for the three middle channels (see Figure 1). They have been recorded with a five-minute resolution. Data accuracy is specified in the text.