Considerations for Improving the Accuracy of Permittivity Measurement using Time Domain Reflectometry

In a paper presented by Heimovaara (1993) a method of calibrating TDR sensors was presented using air and water. Time has moved on but time domain reflectometry (TDR) sensors are still calibrated in a number of different ways. In this article we present a rigorous investigation of the method proposed by Heimovaara and demonstrate its accuracy. We demonstrate that the placement of a starting point in any place other than the one determined using Heimovaara's method results in erroneous permittivity measurement. This will be most significant at low values of permittivity. We propose that Heimovaara's method be adopted as a standard method for calibrating TDR sensors for measuring permittivity. The discussion centers on the placement of the first time marker used to measure the signal travel time from which permittivity is measured. Our modeling results suggest that this point is slightly forward of the apex of the bump on the waveform which corresponds to the impedance increase as the wave 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 media. Finally we examine the use of long cables to connect sensors to the TDR. We demonstrate that the travel time in the cable changes as a function of temperature and that fixed travel time markers based on 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 cable, relative to calibration at 25°C. Software that tracks the sensor head either through the impedance mismatch caused by the head or using an electrical marker eliminates this source of error.