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Calibration of Capacitance Probe Sensors using Electric Circuit Theory

^a USDA-ARS, George E. Brown, Jr. Salinity Lab., 450 W. Big Springs Rd, Riverside, CA 92507
^b USDA-ARS, Water Management Research Lab., 9611 S. Riverbend Ave., Parlier, CA 93648
^c Alterra-ILRI, P.O. Box 47, 6700 AA Wageningen, The Netherlands
^d Dep. of Plants, Soils, and Biometeorology, Utah State Univ., Logan, UT 84322-4820

View larger version (13K): [in a new window]   Fig. 1. Equivalent circuit for the capacitance probe sensor where L is the inductor, C is the capacitance of the medium, Cp is the capacitance of the plastic access tube, Cs is the stray capacitance and G is the energy loss due to relaxation and ionic conductivity.

View larger version (16K): [in a new window]   Fig. 2. Measured and optimized resonant frequency of Sensor 2.15 as a function of the inserted Capacitor Cc.

View larger version (18K): [in a new window]   Fig. 3. Resonant frequency of Sensor 1.10 as a function of measured and optimized relative permittivity. The six data points representing the brasso and the sugar-water mixtures are not incorporated in the optimization.

View larger version (14K): [in a new window]   Fig. 4. Resonant frequency as a function of relative permittivity for all 29 sensors. Each curve is calculated by inserting the sensor constants of Table 1 into Eq. [4] (assuming no losses due to relaxation or conductivity).

View larger version (32K): [in a new window]   Fig. 5. Measured (dots) and calculated (lines plus symbols) resonant frequency as a function of relative permittivity for different levels of the dielectric losses expressed as G. The numbers in the figure show the range of G values for the propanol-water, the sugar-water, and the water. Results for Sensor 1.10.

View larger version (23K): [in a new window]   Fig. 6. Measured (symbols) and calculated (lines) resonant frequency as a function of the dielectric losses G for propanol-water, sugar-water, and water. Results for Sensor 1.10.

View larger version (23K): [in a new window]   Fig. 7. Measured versus calculated relative permittivity. Both corrected data (dots, Eq. [11] solved for C) and uncorrected data (crosses, Eq. [4]) are shown. Results for Sensors 1.5, 1.10, 2.5, and 2.10.

View larger version (22K): [in a new window]   Fig. 8. Resonant frequency of Sensor 1.10 as a function of measured, optimized, and calculated relative permittivity. The six data points representing the brasso and the sugar-water mixtures are not incorporated in the optimization.