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Frequency Dependence of the Complex Permittivity and Its Impact on Dielectric Sensor Calibration in Soils

^a Dep. of Plants, Soils, and Biometeorology, Utah State Univ., Logan, UT 84322
^b USDA-ARS, George E. Brown, Jr. Salinity Lab., 450 W. Big Springs Road, Riverside, CA 92507
^c USDA-ARS, Water Management Research Lab., 9611 S. Riverbend Ave., Parlier, CA 93648

View larger version (21K): [in a new window]   Fig. 1. (a) Real and (b) imaginary permittivity in bentonite as a function of frequency. Results are from the network analyzer for different volumetric water contents (1 = 0.088; 2 = 0.190; 3 = 0.292; 4 = 0.326; 5 = 0.413; 6 = 0.521; 7 = 0.594). Losses due to ionic conductivity –1–10 (c) were computed from resistance measurements with a LRC bridge. Losses due to relaxation (d) were calculated by subtracting –1–10 from ''r. Frequency values on the x axis are on log scale.

View larger version (23K): [in a new window]   Fig. 2. Real permittivity as a function of water content for bentonite. Results are from the network analyzer for five different frequencies. The a() relationships according to Topp and the refractive index model are also shown.

View larger version (16K): [in a new window]   Fig. 3. Real and apparent permittivity as a function of water content for (a) fine quartz sand and (b) bentonite. Results are for the uncorrected capacitance sensor and TDR. Values for the TDR in bentonite for 0.401 0.877 are missing due to signal attenuation.

View larger version (20K): [in a new window]   Fig. 4. Dielectric losses (G) as a function of water content. Losses due to ionic conductivity were calculated from the resistance measurements in (a) the bucket and (b) the dielectric sample, respectively. The bulk electrical conductivity (EC) of the dielectric sample was corrected for temperature differences between the sample and the bucket using ECb = ECs – 0.02ECs(Ts – Tb), where the subscripts b and s stand for bucket and sample, respectively, and T is the temperature in degrees Celsius.

View larger version (17K): [in a new window]   Fig. 5. Real permittivity as a function of water content for bentonite. Results are from the network analyzer and the capacitance sensor. The comments between parentheses stand for uncorrected data (0), data corrected for the total dielectric losses (G), data corrected for the ionic conductivity as derived from the resistance measured in the sample (Rs), and data corrected for the ionic conductivity as derived from the resistance measured in the bucket (Rb). Plot (b) is a close-up of plot (a).

View larger version (20K): [in a new window]   Fig. 6. Scaled frequency as a function of water content. Results for fine quartz sand, bentonite, and a saline silty clay soil. The curves were calculated by combining the respective a() relationships with the electric circuit model that assumes no dielectric losses (Eq. [8]).