An Embedded Double Reference Transmission Line Theory Applied to Cable Harnesses

In this paper, an embedded double reference transmission line theory (EDRTLT) is presented. This approach is based upon taking an arbitrary wire among the n wires constituting the harness and considering it as an internal reference conductor. Then, the initial transmission line (TL) of n wires above a ground reference is split into two coupled subsets of wires. The internal subset is composed of n - 1 wires with the internal reference wire as the return wire. The per unit length (p.u.l.) parameters of this internal TL are calculated with respect to this internal reference wire. They do not depend on the ground reference. The external subset is composed of only the internal reference wire with the ground plane as a reference. As a result, any change of relative position of the bundle and the ground reference involves the p.u.l. calculation of a mono-conductor TL. This double reference TL theory is shown to be equivalent to the classical single reference approach and the corresponding p.u.l. parameters are approximately retrieved from those of the single reference TLs to form the EDRTLT. The results obtained by this theory are in good agreement with those obtained from the single reference case where all p.u.l. parameters are directly calculated using the ground plane as a single reference. The main advantage provided by the EDRTLT is to reduce the complexity of analysis of the bundle-to-ground interaction.