Analysis of multiconductor transmission lines using the time domain method of lines

In this study, the solution of lossy multiconductor transmission lines is obtained using the numerical Time Domain Method of Lines (TDMoL). The TDMoL algorithm comprises discretizing a differential equation in the spatial dimensions and using an analytical solution in the time domain. This leads to high numerical accuracy compared with full-discretizing finite difference techniques which require a significant computational time and extensive memory. In addition, investigation of the numerical dispersion characteristics of the single and multiconductor lossy and lossless transmission lines engenders a time independent relation which proves the unconditionally stability and nondispersive property of the method. To examine the accuracy of the TDMoL, three different structures including a three-coupled uniform transmission line, a nonuniform coupled transmission line and a lossy interconnect with dynamic and functional crosstalk are evaluated. The results of the proposed methodology are validated by those of leap-frog finite difference time domain (LF-FDTD) method and ADS commercial software, and reveals up to 90% reduction in CPU time while maintaining the same degree of accuracy.