Efficient frequency-domain modelling and simulation of nonuniform coupled transmission lines: application in transient analysis of VLSI circuits

A new method of analysis of the transients in nonuniform lossy multiconductor transmission lines with frequency-dependent parameters is presented. The terminations may be nonlinear, and the interconnections networks are arbitrary. The method of the solution is based on steplines approximation of the nonuniform transmission lines and quasitransverse electromagnetic mode (quasi-TEM) assumptions. Using steplines approximation, the system of coupled nonuniform transmission lines is subdivided into an arbitrarily large number of coupled uniform lines (steplines) with different characteristics. Then, using the modal decomposition method, the system of coupled partial differential equations for each step is decomposed into a number of uncoupled ordinary telegraph equations, which are then solved in the frequency domain. Thereafter each step of the system is modelled as a linear filter with frequency-dependent coefficients. The terminations for linear and nonlinear cases are then modelled as linear or nonlinear systems. Finally, the transfer matrix of the system is obtained. Some examples from the literature are then solved to demonstrate the validity of the method. The method proposed here is very fast and can easily be implemented using general-purpose software packages like MATLAB.