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...