Pade approximation applied to transient simulation of lossy coupled transmission lines

A new approach for transient simulation of lossy coupled transmission lines terminated in arbitrary nonlinear elements is presented. The approach is based on convolution simulation. The multiconductor lines are first decoupled to obtain modal functions. Using the Pade approximations of each modal function, the authors derive a recursive convolution formulation, which greatly reduces the computation used to perform convolutions. The approach can handle general coupling situations; no assumption on the simulated circuits is introduced. The approach was implemented in the Stepwise Equivalent Conductance MOS timing simulator, SWEC. The key feature of SWEC is that Newton-Raphson iteration is not needed for the implicit integration of a circuit even with lossy lines terminated in nonlinear elements. The comparisons with SPICE3.e indicated that SWEC can be one to two orders of magnitude faster.<>