Charge correction formulation on the staircase edges and effective length of inclined wires in FDTD mesh

Abstract

This work presents improvements for inclined thin wire simulation in finite-difference time-domain (FDTD). Modelling of the corners of staircase geometries is proposed by adding the accumulated charges at an edge region. This correction is important due to the delay of the electromagnetic fields propagation on the stairs. To test the validity of the proposition, the v-dipole fed by a resistive voltage source is designed and implemented. A significant improvement can be noted in the calculation of the impedance when the stairs of the geometry are more discretised and the charge correction is applied. Also, a surprising outcome is issued when the stair formed by an inclined thin wire has only one cell per stair: a perfect emulation of an inclined wire happens when the charge correction is applied, showing that a correction of the propagation time of the electromagnetic fields is automatically performed. Based on the propagation time adjustments, an effective length model has also been proposed to emulate the real size of the inclined wire by the size correction of the staircase geometry. Although the effective length depends on the FDTD parameters initial setup, it has a fast response and a low complexity implementation with good accuracy.