Efficient computation of the impedance of a single vertical current in a periodic line

In this paper a formulation is proposed for an efficient computation of the impedance of the nonperiodic vertical impressed current sheet. In fact, the calculation of these impedances requires the evaluation of field values exactly at source points, thus leading to highly singular expressions in the spatial domain, or, alternatively, to extremely slowly-converging expressions in the spectral domain. The latter, used in our formulation, requires ad-hoc acceleration techniques, described with some details in this work. Although the formulation is dependent on the actual structure and the excitation, the general approach can also be useful for a more general study, where the spectral-domain quantities could be replaced with their spatial-domain counterparts.