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.

在这项研究中，有损多导体传输线的解决方案是使用数字时域线法 (TDMoL) 获得的。TDMoL 算法包括在空间维度上离散化微分方程并在时域中使用解析解。与需要大量计算时间和大量内存的全离散化有限差分技术相比，这导致了高数值精度。此外，对单导体和多导体有损和无损传输线的数值色散特性的研究产生了时间无关的关系，证明了该方法的无条件稳定性和非色散特性。为了检查 TDMoL 的准确性，包括三耦合均匀传输线在内的三种不同结构，评估了非均匀耦合传输线和具有动态和功能串扰的有损互连。所提出方法的结果得到了跨越式有限差分时域 (LF-FDTD) 方法和 ADS 商业软件的验证，并显示 CPU 时间减少了 90%，同时保持相同程度的精度。