A new algorithm, which is incorporated into the waveform relaxation analysis, for efficiently simulating the transient response of single lossy transmission lines or lossy coupled multiconductor transmission lines, terminated with arbitrary networks will be presented. This method exploits the inherent delay present in a transmission line for achieving simulation efficiency equivalent to obtaining converged waveforms with a single iteration by the conventional iterative waveform relaxation approach. To this end we propose 'line delay window partitioning' algorithm in which the simulation interval is divided into sequential windows of duration equal to the transmission line delay. This window scheme enables the computation of the reflected voltage waveforms accurately, ahead of simulation, in each window. It should be noted that the present window partitioning scheme is different from the existing window techniques which are aimed at exploiting the non–uniform convergence in different windows. In contrast, the present window technique is equivalent to achieving uniform convergence in all the windows with a single iteration. In addition our method eliminates the need to simulate the transmission line delay by the application of Branin's classical method of characteristics. Further, we describe a simple and efficient method to compute the attenuated waveforms using a particular form of lumped element model of attenuation function. Simulation examples of both single and coupled lines terminated with linear and nonlinear elements will be presented. Comparison indicates that the present method is several times faster than the previous waveform relaxation method and its accuracy is verified by the circuit simulator PSpice.

Acceleration techniques have been incorporated into the generalized method of characteristics (GMC) to perform transient analysis of uniform transmission lines, for the special case when the transmission lines are driven by digital signals. These techinques have been proved to improve the simulation speed to a great extent when the analysis is carried out using iterative waveform relaxation method. It has been identified that the load impedance connected to the transmission line has a bearing on the efficiency of one of these acceleration techniques. Examples of an RLCG line terminated with linear loads as well as nonlinear loads are given to illustrate the advantage of incorporating these acceleration techniques.

This paper describes a novel but simple method of implementing waveform relaxation technique for bipolar circuits involving ECL gates. This method performs gate level partitioning of ECL circuits not only during the cutoff state of the input transistor but also when the input transistor is in its active state. Partitioning at all times has become possible due to the favorable property of input and output stages of ECL gates. It is shown that this method is faster than direct method even when the circuits containing only few gates is simulated. Further, it is shown that the present method is applicable to the case where the interconnections between the ECL gates is treated as lossy transmission lines.

A new efficient waveform relaxation technique based on dynamically overlapped partitioning scheme is presented. This overlapped partitioning method enables the application of waveform relaxation technique to bipolar VLSI circuits. Instead of fixed overlapping, we select the depth of overlapping dynamically based on the sensitivity criteria. By minimizing the overlapped area, we could reduce the additional computational overhead which results from overlapping the partitions. This overlapped waveform relaxation method has better convergence properties due to smaller error introduced at each step compared with standard relaxation techniques. When overlapped partitioning is used in the case of digital circuits, the waveforms obtained after first iteration are nearly accurate. Therefore, by using these waveforms as initial guess waveforms for the second iterations we can reduce Newton-Raphson iterations at each time point.