CLOSED FORM FORMULAS FOR ELF INDUCTIVE COUPLING BETWEEN FINITE LENGTH WIRES WITH EARTH RETURN

This paper deals with the evaluation of the inductive coupling between an overhead finite length wire circuit and a buried wire circuit, both with earth return, in the range of Extremely Low Frequencies (ELF). In particular, the attention is focused on the key parameter for this kind of problems i.e. the per unit length (p.u.l.) mutual impedance between the two circuits. Starting from the exact formula involving a Sommerfeld’s integral, two new approximated analytical formulas, having different levels of approximation, are derived; the advantage of these formulas is that, in such a way, the p.u.l. mutual impedance is expressed only by means of elementary functions so avoiding numerical calculations of the Sommerfeld’s integral. Finally, a comparison between the two proposed formulas is made