Transient analysis of multiconductor lines above a lossy ground

In this paper, we first extend the Sunde logarithmic approximation for the single-wire line ground impedance to the case of a multiconductor line. The new approximate forms are compared to the general expressions which involv e integrals over an infinitely long interval and an excellent agreement is found. The inverse Fourier transform of the ground impedance presents singu larities which complicate the numerical solution of the transmission line e quations. The order of the singularity is reduced by 1, and a careful numer ical treatment is then employed to derive an equivalent and numerically mor e appropriate form of coupling equations in which there is no longer a sing ular term. Finally, finite-difference time-domain (FDTD) solutions of the c oupling equations are presented and the theory is applied to calculate ligh tning-induced voltages on a multiconductor line. The lightning-induced volt ages are calculated for the case of lossless/lossy, single-conductor/multic onductor lines and the effect of ground losses and the presence of other co nductors on the magnitude and shape of induced voltages are illustrated.