Time-domain analysis of lossy multiconductor transmission lines based on the Lax–Wendroff technique

Abstract

Taking advantage of the hyperbolic characteristics of the telegrapher equations, this paper applies the Lax-Wendroff technique, usually used in fluid dynamics, to transmission line analysis. A second-order-accurate Lax-Wendroff difference scheme for the telegrapher equations for both uniform and nonuniform transmission lines is derived. Based on this scheme, a new method for analyzing lossy multiconductor transmission lines which do not need to be decoupled is presented by combining with matrix operations. Using numerical experiments, the proposed method is compared with the characteristic method, the fast Fourier transform (FFT) approach, and the Lax-Friedrichs technique. With the presented method, a circuit including lossy multiconductor transmission lines is analyzed and the results are consistent with those of PSPICE. The nonlinear circuit including nonuniform lossy multiconductor transmission lines is also computed and the results are verified by HSPICE. The proposed method can be conveniently applied to either linear or nonlinear circuits which include general transmission lines, and is proved to be efficient.

The Von Neumann conditions for the upwind and Lax-Wendroff schemes of the Telegraph Equation

“…We can now derive, . This requirement is contradicted with (13). Note that as mentioned in Introduction, the reference [13], without doing stability analysis, gave a stability condition (see equation (13) there):…”

“…Those classical methods such as the Upwind and Lax-Wendroff methods should have not been well applied to deal with the Telegraph Equation. No result on the Upwind method for solving the Telegraph Equation has been reported, while we can find only one on the Lax-Wendroff method in [13] where no stability analysis was done but a stable condition (that will be further discussed later on) for the Lax-Wendroff scheme was given, see equation (13) there. This paper makes up the blank.…”

Time-domain modelling of interconnects with highly oscillatory sources

“…In addition, some frequency-domain models become complex when handling nonuniform transmission lines (Tang and Mao, 2008). Some time-domain approaches for nonuniform interconnects are the two-step perturbation technique (Chernobryvko et al, 2014), the finite-difference time-domain technique (Afrooz and Abdipour, 2012), the time-step integration method (Tang and Mao, 2008), the Lax-Wendroff difference method (Dou and Dou, 2011), the implicit Wendroff method (Bran cík and Ŝev cík, 2011;Bran cík, 2011), the finite element method (Juri c-Grgi c et al, 2015) and spectral methods COMPEL 37,1 504 (Antonini, 2012). In this paper, an approach is proposed for the case when the signals on the interconnects have wide-varying frequency content and as such present major challenges for numerical simulation.…”