Considerations for Improving the Accuracy of Permittivity Measurement using Time Domain Reflectometry
Air-Water Calibration, Effects of Cable Length
D. A. Robinson*,a,
M. Schaapa,
S. B. Jonesb,
S. P. Friedmanc and
C. M. K. Gardnerd
a George E. Brown Jr Salinity Laboratory USDA-ARS, 450 W. Big Springs Road, Riverside, CA 92507
b Dep. Plants, Soils and Biometeorology, Ag. Sci Building-Old Main Hill 4820, Utah State University, Logan, UT 84322S
c The Institute of Soil, Water and Environmental Science, (ARO) The Volcani Center, Bet Dagan, Israel
d Jesus College, University of Oxford, Oxford OX1 3DW, UK
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Fig. 1. Waveforms in air with a 20-cm probe shorted at (A) the base of the electrodes and (B) at the electrodes tips.
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Fig. 2. (2.1) A waveform in water illustrating how the travel time is usually measured from the waveform. WINTDR measures from the apex of the bump to the end point located by the tangent lines. (2.2) The software of Heimovaara (1993) can either use a fixed start point based on cable length or can find the tangents for the first bump and calculate the travel time according to ts = tp - to.
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Fig. 3. The left-hand figure shows the input function with the point at which the first element of the signal leaves the cable tester. The right-hand diagram shows two waveforms for permittivities of 78.5 and 50. The dashed lines illustrate the calculated points at which the signal first enters the sensor head, leaves the sensor head and is reflected from the end of the probe respectively.
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Fig. 4. The top figure shows modeled waveforms for permittivities of 1 and 50. The equivalent probe is shown below and then three graphs showing start points for sensors with 40, 50, and 60 ohm impedance heads, 3 cm long; the solid lines represent the calculated start and end of the sensor head. The 40-ohm head creates a dip in the waveform, the 50-ohm head is matched and the 60-ohm head creates a bump.
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Fig. 5. Waveforms for water, acetone, penetrating oil, and air measured in a 19.5-cm coaxial cell. The right-hand figure illustrates the bump apex and the fixed start point that was found to correspond with cited permittivity values.
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Fig. 6. Permittivity estimated from calibration of probe adjusting the electrical length of the probe according to measurements in water using the bump apex as a timing reference. The arrow on the left-hand diagram indicates to calibrated permittivity using Heimovaara's calibration method. This point is located 0.035 ns to the right of the bump apex and corresponds to an electrical length of 0.1956 m. The dashed lines on the left-hand diagram correspond to the positions of the lines used to measure travel time on the right-hand diagram.
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Fig. 7. A sequence of waveforms measured using a 20-cm probe sequentially dipped into a water column 1 cm at a time. Note how the bump apex at the start of the probe electrodes moves.
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Fig. 8. Permittivity calculated as a function of immersion length using a fixed start point and one following the bump apex. Note how the moving apex causes underestimation of the permittivity.
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Fig. 9. Sensor-head waveform reflections for a probe and cable immersed in a constant temperature bath between 1 to 50°C. The upper figure is for a 2.6-m cable and the lower figure for a 10.3-m cable. Note how the reflection coefficient of the head reduces as the cable becomes longer and how it moves with temperature. Using a fixed start point in these circumstances would result in erroneous measurements.
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Copyright © 2003 by the Soil Science Society of America.
