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A Single-Rod Probe for Time Domain Reflectometry Measurements of the Water Content

^a Inst. of Terrestrial Ecology, Swiss Federal Inst. of Technology Zurich, Grabenstrasse 11, CH-8952 Schlieren, Switzerland (currently, Inst. of Environmental Physics, Univ. of Heidelberg, D-69120 Heidelberg, Germany)
^b Lab. for Electromagnetic Fields and Microwave Electronics, Swiss Federal Inst. of Technology Zurich, Gloriastrasse 35, CH-8092 Zurich, Switzerland
^c Inst. of Terrestrial Ecology, Swiss Federal Inst. of Technology Zurich, Grabenstrasse 11, CH-8952 Schlieren, Switzerland

View larger version (77K): [in a new window]   Fig. 1. Plot showing that a Sommerfeld wire is an uncoated metallic rod, operating as a surface waveguide, with direct contact to the medium being tested.

View larger version (36K): [in a new window]   Fig. 2. Components of the dominant transverse-magnetic mode field components, Ez, Er, H, of the single-rod probe (SRP), normalized with respect to amplitudes at a radius r = 0.005 m (interface between the SRP's copper core and the medium being tested), with r = 1, µr = 1, f = 1 GHz. The axial electric component Ez in the plot is significantly larger than Er and H, but, depending on frequency and dielectric permittivity, its absolute value can also be several orders of magnitude smaller than its radial electric counterpart Er. Because the absolute values of H and Er only differ by a constant factor, their curves are identical when normalized.

View larger version (45K): [in a new window]   Fig. 3. Fraction of electromagnetic power transported by the transverse-magnetic mode along a single-rod probe (SRP) within a cylinder of radius r, coaxial to the SRP. Radius of SRP rSRP = 0.005 m. In all cases SRP = 5.8 x 107 S m–1 and µr = 1.0. Top: SRP in air, r = 1; middle: SRP in dry sand, r = 2.8; bottom: SRP in wet sand, r = 20.

View larger version (102K): [in a new window]   Fig. 4. Conceptual view of the experimental setup used for measuring the TDR traces with a single-rod probe.

View larger version (20K): [in a new window]   Fig. 5. Sample trace with approximate starting and end points, of a single-rod probe (SRP), as measured with SRP300 (300 mm). The travel time is extracted between inflection points, indicating maximum slopes, and then corrected by offsets obtained from measurements in air.

View larger version (21K): [in a new window]   Fig. 6. Time domain reflectometry traces recorded in air, water, and sand–water mixtures of different volumetric water contents, with single rod probes (SRP) of different lengths L. Top: SRP300 (300 mm); middle: SRP200 (200 mm); bottom: SRP150 (150 mm). The start of the probe section embedded in the sand–water mixture is the point after which the traces diverge and have travel times proportional to .

View larger version (18K): [in a new window]   Fig. 7. Plots showing calibration curves () obtained with the model by Roth et al. (1990), (s = 2.8, w = 80.36, a = 1.0, = 0.52), and from traces measured with twin-rod probes (TRP) and single-rod probes (SRP) of different lengths. Top: SRP300 (300 mm); middle, SRP200 (200 mm); bottom, SRP150 (150 mm). Traces were recorded and analyzed when metallic rods with the same lengths were inserted parallel to the SRPs. The distance between the SRP and the metallic rod were 50 mm (circles), 100 mm (diamonds), and 200 mm (squares); the plus (+) symbols identify the TRP traces.