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Accuracy of Bulk Electrical Conductivity Measurements with Time Domain Reflectometry

^a Inst. of Chemistry and Dynamics of the Geosphere, Inst. IV: Agrosphere, Forschungszentrum Jülich, 52425 Jülich, Germany
^b National Chiao Tung Univ., Hsinchu, Taiwan

View larger version (16K): [in this window] [in a new window]   FIG. 1. Time domain reflectometry (TDR) sample conductivity vs. reference electrical conductivity. Open circles represent TDR sample conductivity uncorrected for deviations in open-circuit reflection coefficient. Error bars indicate 5 and 95% confidence intervals of TDR sample conductivity determination. The inverse of the regression line corresponds to the probe constant Kp.

View larger version (22K): [in this window] [in a new window]   FIG. 2. Measured and modeled time domain reflectometry sample conductivity as a function of reference electrical conductivity for different cable lengths (1, 5, 10, and 25 m of RG58C/U cable).

View larger version (52K): [in this window] [in a new window]   FIG. 3. Sum of squared residuals (SSR) plotted as a function of the model parameters probe constant (Kp), cable resistance (Rc), and the extra series resistance caused by the probe head, cable tester, multiplexers, and connectors (R0) for Probe 1.

View larger version (12K): [in this window] [in a new window]   FIG. 4. Load resistance determined from short-circuit measurements on cables of 1, 5, 10, and 25 m. Error bars indicate 5% and 95% confidence intervals. The dashed line is based on the average cable resistance (Rc) and extra series resistance caused by the probe head, cable tester, multiplexers, and connectors (R0) determined in the Monte Carlo analysis.

View larger version (21K): [in this window] [in a new window]   FIG. 5. Total uncertainty in time domain reflectometry bulk conductivity measurements as a function of the reflection coefficient for two cables of 1- and 25-m length for Probe 1.

View larger version (30K): [in this window] [in a new window]   FIG. 6. Uncertainty in time domain reflectometry bulk conductivity measurements due to several error sources as a function of the reflection coefficient for a 25-m-long cable and Probe 1. Error sources considered are: (i) reproducibility of the reflection coefficient (r); (ii) reproducibility of the open reflection coefficient (open); (iii) uncertainty in the calibrated probe constant (Kp); (iv) uncertainty in the calibrated cable resistance (Rc); and (v) uncertainty in the calibrated extra series resistance caused by the probe head, cable tester, multiplexers, and connectors (R0).

View larger version (13K): [in this window] [in a new window]   FIG. A1. Ratio of the thin wire approximation (Z0,app, Eq. [A1]) and the approximation by Castiglione (Eq. [A2]) to the full analytical solution of Ball (Z0, Eq. [5]) as a function of the spacing/diameter ratio.