Considerations for Improving the Accuracy of Permittivity Measurement using Time Domain Reflectometry: Air-Water Calibration, Effects of Cable Length

to measure permittivity. In this discussion we will demonstrate the need for carefully choosing the correct In a paper presented by Heimovaara (1993) a method of calibrating waveform analysis method to obtain the best measureTDR sensors was presented using air and water. Time has moved on but time domain reflectometry (TDR) sensors are still calibrated in ment of permittivity. This is crucial for the subsequent a number of different ways. In this article we present a rigorous stage, which is the calibration between permittivity and investigation of the method proposed by Heimovaara and demonthe desired physical quantity. Errors in the measurestrate its accuracy. We demonstrate that the placement of a starting ment of permittivity are systematically carried over into point in any place other than the one determined using Heimovaara’s the next calibration stage and can lead to erroneous method results in erroneous permittivity measurement. This will be interpretations of physical quantities. most significant at low values of permittivity. We propose that HeimoThe velocity (v) of an electromagnetic-plane wave vaara’s method be adopted as a standard method for calibrating TDR sensors for measuring permittivity. The discussion centers on the propagating through a dielectric material is a function placement of the first time marker used to measure the signal travel of both the relative permittivity (εr) and the relative time from which permittivity is measured. Our modeling results sugmagnetic permeability ( r) of the material. gest that this point is slightly forward of the apex of the bump on the waveform which corresponds to the impedance increase as the wave v c √ r,εr [1] travels from the cable into the TDR sensor head. We also demonstrate that using the apex of this bump as a starting point reference can lead to erroneous measurements of travel time in layered dielectric The relative permeability in most soils (which are media. Finally we examine the use of long cables to connect sensors nonmagnetic) can be assumed equal to unity, making to the TDR. We demonstrate that the travel time in the cable changes the velocity an inverse function of the square root of as a function of temperature and that fixed travel time markers based the permittivity. Conversely, the permittivity of a mateon cable length cause error in the measurement of travel time. For a 2.6-m cable the error was 1.6% at 50 C, and 4.7% for a 10.3-m rial can be calculated knowing the velocity of a wave cable, relative to calibration at 25 C. Software that tracks the sensor travelling over a known distance in a transmission line. head either through the impedance mismatch caused by the head or The permittivity measured using TDR is termed the using an electrical marker eliminates this source of error. apparent or measured permittivity (Ka), if the complete transmission line system is considered with back and forth wave propagation Eq. [2a] should be used and if O a permittivity measurement with TDR is only the one way travel time is considered as measured relatively straightforward; to obtain good quality from the waveform Eq. [2b] is appropriate: measurements with TDR requires careful TDR probe construction and waveform analysis. The measurement Ka cts2 2L 2 [2A] of porous media permittivity has been used to provide estimates of a number of physical properties including water content (Topp et al., 1980; Gardner et al., 2001; Noborio, 2001), porosity (Sen et al., 1981), surface area Ka cts1 L 2 [2B] (Or and Wraith, 1999), and density (Perdok et al., 1996, Feng et al., 1999). The accuracy of these estimates dewhere ts2 is the travel time in two directions and ts1 is pends on a two-stage calibration. The first element of the travel time in one direction only, usually in the range this is the measurement of permittivity and the second of nanoseconds, c is the velocity of light (3 108 m s 1), is to obtain a calibration between permittivity and the and L is the length (m) of the probe over which the estimated physical quantity. Time domain reflectometry signal travels in a single direction. It is important to has been proven to be a very successful technique for consider that this measured permittivity is a function of measuring the permittivity of materials. However, a number of methods and a variety of software packages not only the energy storage of the dielectric material with varying algorithms are used to analyze waveforms but also any losses that may arise because of ionic conductivity or dielectric relaxation phenomena. In many D.A. Robinson, and M. Schaap, George E. Brown Jr Salinity Laboracases it is assumed that Ka ε where ε is the real part tory USDA-ARS, 450 W. Big Springs Road, Riverside, CA 92507; of the permittivity associated with energy storage and S.B. Jones, Dep. Plants, Soils and Biometeorology, Ag. Sci Buildingdipole orientation. As White et al. (1994) demonstrated Old Main Hill 4820, Utah State University, Logan, UT 84322S; P. Friedman, The Institute of Soil, Water and Environmental Science, this is not always the case such that the measured per(ARO) The Volcani Center, Bet Dagan, Israel; and C.M.K. Gardner, mittivity of a material using a TDR transmission line is: Jesus College, University of Oxford, Oxford OX1 3DW, UK. Received 22 Jan. 2002. *Corresponding author ([email protected]). Abbreviations: TDR, time domain reflectometry. Published in Soil Sci. Soc. Am. J. 67:62–70 (2003).