A Spectral Formulation for the Transient Analysis of Plane-Wave Coupling to Multiconductor Transmission Lines

In this paper, a new spectral formulation for the transient analysis of plane-wave coupling to multiconductor transmission lines (MTLs) is presented. The proposed approach is fully based on a recently developed technique to represent the Green's function of the second-order telegrapher's equation in a series rational form. The use of trigonometric basis functions to model the spatial distribution of voltages allows one to analytically compute the convolution integrals describing the equivalent sources. Furthermore, the rational form of the Green's function permits one to handle MTLs with frequency-dependent per-unit-length parameters, leading to a rational form of the equivalent sources that can be easily computed and incorporated in nonlinear simulators. Hence, the proposed approach, besides avoiding the problem of mixed time/frequency simulations, provides a rigorous spectral form of the equivalent sources that is well suited for time-domain analysis. Numerical results are presented for port voltages induced on MTLs by incident plane waves, confirming the accuracy of the proposed method compared to existing techniques based on the inverse fast Fourier transform.