FREQUENCY-DOMAIN ANALYSIS OF TIME-DOMAIN REFLECTOMETRY WAVE-FORMS .1.MEASUREMENT OF THE COMPLEX DIELECTRIC PERMITTIVITY OF SOILS

The S-11 scatter function of a coaxial probe in the frequency domain i s shown to be an accurate model for predicting waveforms of a seven-wi re coaxial probe in the time domain. Reproducibility of discrete Fouri er analyses carried out on waveforms measured with the Tektronix 1502b cable tester (Tektronix, Incorporated, Beaverton, Oregon) indicated a frequency band width ranging from 20 kHz to approximately 1.5 GHz. Th e frequency dependent complex dielectric permittivity can be calculate d from measured waveforms by inverting the S-11 scatter function. Resu lts indicate that a seven-wire coaxial probe, connected to a 1-m RG214 coaxial cable, emulates a coaxial tube for frequencies up to 150 MHz. Application of the frequency domain model to time domain reflectometr y waveforms shows that the apparent dielectric permittivity calculated from the travel time in the probe is very dependent on the relaxation frequency of the material in which the probe is embedded. For materia ls with low relaxation frequencies the apparent dielectric permittivit y is much lower than the static permittivity. Inversion of the frequen cy domain model allows for solving the frequency dependent complex die lectric permittivity of soils from measured waveforms.