Smith-chart diagnostics for multi-GHz time-domain-reflectometry dielectric spectroscopy

A time-domain-reflectometry Smith-chart display is demonstrated to be a valuable diagnostic tool in a variety of situations in time-domain-reflectometry dielectric spectroscopy. A relative reflection coefficient is formed by dividing the Laplace transform of the reflected sample transient by the Laplace transform of the empty-sensor transient and displaying in the complex plane, with the approximate sensor admittance read from susceptance and conductance circles. The Smith chart provides, as a diagnostic tool, an initial estimate of the dielectric behavior in the multi-GHz range and a means of identifying artifacts in acquisition and Laplace transform, in a way which does not require multiple steps of calibration and is only one step removed from the direct transient. Results are presented for a simple 3.5-mm flat sensor immersed in various liquid media, showing variations in the Smith chart for typical variations in sample permittivity, loss, and conductivity. Results are matched to vector network analyzer (VNA) measurement over an identical frequency range, as well as to finite-element field simulation. Results are also presented for a 3.5-mm sensor with various terminating pin lengths, typically employed at low frequencies and low permittivity media to increase sensor capacitance. For an unshielded pin, the Smith chart detects reflections from sample boundaries and measures the effectiveness of shielding used to eliminate these reflections. For a shielded pin, it characterizes the effect of pin length on the susceptance variation and the onset of pin resonance at high frequencies and high-permittivity values. The effect of artifacts appearing in the Smith chart on the actual calibration is shown by tracking them through the calibration process to the final result. Results are also presented for a 9-mm flat termination used for concrete hydration monitoring, showing effects of transmission-line discontinuities within a terminating plug and the onset of waveguide-like modes in a surrounding shield, with results compared to VNA measurement.