Spread Spectrum Time Domain Reflectometry With Lumped Elements on Asymmetric Transmission Lines

Spread spectrum time domain reflectometry (SSTDR) has been traditionally used to detect hard faults (open and short circuit faults) in transmission lines. Prior work has focused on loads at the end of the line with little research on impedances from circuit elements located in the middle of the line (i.e., not at the load) or on only one wire of the line. In this work we consider cases of transmission lines with different impedances on each wire. We refer to lines with the same impedance on both wires (positive and negative) as symmetric. Lines with different impedances on each wire are asymmetric. For highly localized impedances (approximately infinitesimal in length, i.e. with a length significantly smaller than the wavelength of the incident signal), the reflections and their effects on the propagating wave become difficult to describe with traditional transmission line theory. We provide analytical expressions for reflection coefficients for symmetric and asymmetric transmission lines and show that these formulae describe experimental measurements of capacitors and resistors to about 99% accuracy for the magnitudes and 75% for the phases.