Incorporating vertical risers in the transmission line equations with external sources

In this work, the effects that transmission line (TL) terminations with non-negligible electrical length play on TL susceptibility to external interference are investigated. To this end, TL terminations are interpreted as the series connection of vertical down-leads (or risers) with lumped impedances attached to ground, and the interfering electric field is described as a plane wave. From the circuit standpoint, the overall structure is modeled as the cascaded chain of a uniform horizontally-shaped TL and two non-uniform vertically-shaped TL with terminal impedances. Closed-form expressions are derived for the current induced by the external field in the terminal loads. By comparing model predictions against the outputs of a full-wave solver it is shown that the proposed circuit model extends the conventional TL theory to wiring structures with vertically shaped terminations and with larger values of the height/length aspect-ratio. A low-frequency model and a statistical analysis of TL susceptibility are also developed.