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Laboratory Characterization of a Commercial Capacitance Sensor for Estimating Permittivity and Inferring Soil Water Content

^a Institute of Terrestrial Ecosystems (ITES), Swiss Federal Institute of Technology (ETH), CHN E29, Universitätstr. 16, CH-8092 Zürich, Switzerland
^b USDA-ARS, Great Plains Systems Research Unit, Fort Collins, CO, USA
^c Institute of Applied Physics, University of Bern, Sidlerstrasse 5, CH-3012 Bern, Switzerland
^d Laboratory for Electromagnetic Fields and Microwave Electronics, ETHZ, ETZ K 88, Gloriastrasse 35, CH-8092 Zürich, Switzerland
^e Institute of Terrestrial Ecosystems (ITES), Swiss Federal Institute of Technology (ETH), CHN F 28.1, Universitätstr. 16, CH-8092 Zürich, Switzerland

View larger version (116K): [in a new window]   Fig. 1. (a) Installation of the access tube in the field; (b) EnviroSMART soil water content probe with capacitance sensors; (c) sensor with symbolized field lines; (d) sensor electronic board; and (e) equivalent circuit diagram. The dashed line in (e) represents the sensor electronics board, neglecting capacitors and resistors on the board.

View larger version (54K): [in a new window]   Fig. 2. Sketch of the solvent-resistant container with the tools used. The heater, dielectric probe, the thermometer, and the tools for removing air bubbles from the access tube and the dielectric probe are retracted during the capacitive measurements and the sensor readings. Dimensions are not to scale.

View larger version (112K): [in a new window]   Fig. 3. Picture of the experimental setup used for characterizing the EnviroSMART soil water content sensor.

View larger version (75K): [in a new window]   Fig. 4. Cylindrical metal sheet disturbance used for investigating the sampling volume of the sensor.

View larger version (39K): [in a new window]   Fig. 5. Rotation symmetrical model setup used for simulating the electric field E caused by a potential difference between the ring electrodes of the sensor. Capacitance C is calculated from the field distribution E.

View larger version (20K): [in a new window]   Fig. 6. Sensor responses fr–2 to surface mounted device (SMD) added capacitance CSMD with and without the ring capacitor attached to the instrument.

View larger version (22K): [in a new window]   Fig. 7. Measured relation between permittivity of the dioxane–water mixture outside the access tube and normalized sensor reading N. The light gray data are the laboratory measurements; the data represented by the black circles are corrected for the calculated effect N() of the fluorinated ethylene-propylene (FEP) coating. The solid lines are the approximations using Eq. [29] and is the standard deviation between Nik measured with the sensors k = 1 to 4.

View larger version (13K): [in a new window]   Fig. 8. Measured sensor capacitance C versus permittivity of the dioxane–water mixture outside the access tube.

View larger version (55K): [in a new window]   Fig. 9. Electric field strength |E| resulting from the potential difference U = 2 V between the ring electrodes calculated using permittivities of access tube, electrode holder, and environmental material of acc = hold = 3.35 and = 20, respectively.

View larger version (23K): [in a new window]   Fig. 10. (a) Modeled and measured capacitances Cmodel and Cexp between the ring electrodes as a function of the permittivity of the environmental material. The permittivity of the access tube and sensor holder are acc = hold = 3.35. (b) Modeled normalized sensor readings Nmodel and normalized readings Nexp measured in the laboratory (with the FEP shrink tube on the access tube) together with the interpolation function (Nexp).

View larger version (26K): [in a new window]   Fig. 11. (a) Calculated sensor capacitances Cmodel with FEP() and Cmodel without FEP() for the case where the access tube is coated (hollow circles) and not coated (solid squares) with the 0.5 mm thick the FEP shrink fit with permittivity FEP = 2. (b) Normalized sensor readings Nmodel with FEP() and Nmodel without FEP() derived from Cmodel, with FEP() and Cmodel, without FEP() using Eq. [11] for the case with (hollow circles) and without (solid squares) the shrink fit on the access tube.

View larger version (21K): [in a new window]   Fig. 12. (a) Difference C() between simulated capacitances Cmodel with FEP() with the FEP coating on the access tube and Cmodel without FEP() without the FEP coating taken from Fig. 11a. (b) Difference N() between corresponding sensor readings Nmodel with FEP() and Nmodel without FEP() taken from Fig. 11b.

View larger version (22K): [in a new window]   Fig. 13. (a) Temperature dependency w(T) of the permittivity of pure water (d = 0) measured with the VNA dielectric sensor (solid dots) and derived from the capacitance sensor readings (hollow circles). (b) Temperature dependencies d(T) and dw98(T) of pure dioxane (d = 1, hollow squares) and a solution with d = 0.98 (hollow diamonds) deduced from the capacitance sensor readings.

View larger version (31K): [in a new window]   Fig. 14. Normalized sensor reading N versus distance D between the access tube and the metal sheet: (a) measured at 10 distances up to D = 96.3 mm for = (a = 1, 16.4, 20.3, w = 78.38); and (b) N(D) calculated from the electromagnetic model. The distance D between the access tube and the metallic cylinder is varied between 0 and 162 mm, and the permittivity was between the air and the water value. The solid lines are the best fits with the exponential model (Eq. [23]).

View larger version (56K): [in a new window]   Fig. 15. Electric field strength |E| resulting from the potential difference U = 2 V between the ring electrodes calculated using the model configuration with the metal foil disturbance at distance D = 27 mm from the access tube (acc = hold = 3.35 and = 20).

View larger version (25K): [in a new window]   Fig. 16. Comparison between the default calibration proposed by the vendor (Sentek) and three different dielectric mixing models (Topp et al., 1980; Roth et al., 1990; Wang and Schmugge, 1980) with respect to: (a) the water content [(N)] calculated using relation [29] for (N) and (b) water content–permittivity relationships ().