Multiple Reflection Analysis of TDR Signal for Complex Dielectric Spectroscopy

Most dielectric spectroscopy techniques require careful system calibration, tedious measurement, specially designed probes, precise input source, and some even involved complicated inversion models. This paper proposed a rapid, robust, and model-free multiple reflection analysis (MRA) of time-domain reflectometry (TDR) signals to measure the complex dielectric permittivity (CDP) spectrum. The key to MRA approach is to decompose the first top reflection and the subsequent multiple reflections from TDR signal and to compare their spectral ratio (MRA ratio). This ratio was theoretically derived from the transmission line theory and found to be independent of source function and impedance mismatches in the leading sections. Based on this theoretical formulation, the CDP spectrum can be uniquely inverted from the measured MRA ratio through optimization and an iterated initial guess method. Numerical evaluations and experimental verifications had proven that MRA is a reliable algorithm for measuring CDP spectrum covering 10 MHz-1 GHz. Factors influencing the reliable frequency region were discussed and recommendations on enhancing CDP measurement was proposed for highly dispersive materials. The MRA approach enables dielectric spectroscopy to be conveniently conducted in both laboratory and field, without complicated system setup and calibration.