Theoretical model of a multisection time domain reflectometry measurement system

Abstract

Abstract. A multisection model is presented to simulate electromagnetic wave propagation in an unmatched time domain reflectometry (TDR) probe and layered soil system. The model uses a linear-time-invariant feedback system to model each section and links each section in a bottom-up fashion. Multiple sections can be incorporated in this model by a simple extension of a single-section system. An unmatched TDR probe system is modeled by dividing it into equivalent sections and matching the simulated waveform with the actual waveform. The excellent match between the simulated and the recorded waveforms verifies the model. This model eliminates the requirement of a matched 50-12 probe handler in probe design for dielectric measurement. It can also be used to assist probe design and TDR data interpretation. The reflected waveforms in layered soil specimens are modeled, and the simulated waveforms are compared to those obtained from experiments. The method of using apparent dielectric constant to obtain average volumetric water content is examined for the layered soil system. The results show that apparent dielectric constant is applicable for the measurement of average volumetric water content for a layered soil, but caution has to be used when interpreting the waveforms. The TDR method consists of two parts: (1) the physical measurement system that includes the TDR apparatus, probe, and other equipment leading to the generation of a consistent TDR waveform and (2) the interpretation of the TDR waveform including its rclationshi• to the desired material propcrty. The success of the interpretation is the key to applying this technology. Tooeoe et al. [1980] The electromagnetic properties of a material are characterized by three parameters: (1) dielectric permittivity e, (2) electrical conductivity tr, and (3) magnetic permeability/x. In general, these parameters are functions of frequency. However, for materials like soils t•e magnetic permeability differs from magnetic permeability of free space/x o by a negligible fraction, and the frequency dependency of conductivity can be neglected. Owing to the dipole polarization mechanism of water, wet soil is a dielectric material that h as a frequency-dependent complex relative permitfivity:2,n-f 6'r(f) 6r ( Analysis of a Typical TDR Measurement SystemA typical TDR measurement system consists of a cable test device, which sends out a step (or other shape) EM wave through a pulse generator and records the incident and reflection signal with an oscilloscope, and a probe that acts as a waveguide to transmit the EM wave into the soil specimen. A step wave or impulse wave is usually used in order to obtain recognizable reflections at the soil surface and the end of the probe.Transmission line theory is used to model the TDR measurement system in which the field structure in the transmission line is assumed to be of transverse electromagnetic mode (TEM). Owing to the special structure of TEM, (5) Scatter Function for Multisection TDR Measurement SystemDuring field measurement i...

Spatial time domain reflectometry and its application for the measurement of water content distributions along flat ribbon cables in a full‐scale levee model

“…Therefore different approaches based on electromagnetic measurement methods have been proposed for determining water content profiles. The simplest way is to use multisectional transmission lines to receive water content profiles in a limited spatial resolution [Hook et al, 1992;Feng et al, 1999]. One of the first approaches for the inverse determination of moisture profiles was introduced by Laurent [2000] which is based on the analysis of the impedance profile of a TDR signal.…”

“…Another possibility is to develop inversion algorithms based on a straightforward calculation of the wave propagation along the transmission line due to an incident voltage step. Here the response of the transmission line can be calculated either in the time domain [Lundstedt and Stroem, 1996;Lundstedt and He, 1996;Feng et al, 1999;Oswald, 2000;Todoroff and Lan Sun Luk, 2001;Lundstedt and Norgren, 2003;Rahman and Marklein, 2005;Greco, 2006] or in the frequency domain [Norgren and He, 1996;Heimovaara et al, 2004;Lambot et al, 2004;Leidenberger et al, 2006;Scheuermann and Huebner, 2009].…”

Time-Domain Reflectometry (TDR) Technique for the Estimation of Soil Permittivity

“…This means that 2τ a √ ǫ ∞ , i.e., the probe electrical length, must be limited in order to obtain low-attenuation operation. As a consequence of (11), two limitations on the instrument resolution and on the length of the probe should be taken (Feng et al, 1999) into account. The instrument resolution must be significantly finer than 10 ǫ ∞ /ω rel (ǫ s − ǫ ∞ ).…”

“…If the assumption is made that the imaginary part of the complex electrical permittivity is small compared to the real part, only the real part of permittivity changes with soil water content, and if the real part is close to the apparent dielectric permittivity K a (effective bulk permittivity), then water content can be evaluated by means of empirical formulas based on known value of K a Topp et al, 1980). Evaluation of the dielectric permittivity of a medium from its reflection response is an inverse problem in which the medium propagation behavior is used to infer its constitutive relations (Feng et al, 1999;Heimovaara, 1994;Lin, 2003;Oswald et al, 2006). Owing to this application, over the past twenty years great efforts have been spent on the calibration of the TDR system, i.e.…”

Spatially resolved water content profiles from inverted time domain reflectometry signals

“…Todoroff et al [1998] also use an approach based on a decomposition of forward and back traveling partial waves in the time domain, similar to Yanuka et al [1988], but implement a genetic algorithm for the reconstruction of the water content profile. Feng et al [1999] investigated a frequency domain approach to discriminate transitions between wet and dry sections. Oswald [2000] formulates an inverse problem to reconstruct dielectric and ohmic profiles in the time domain.…”