This paper describes the matrix order reduction method by the nodal analysis formulation and the application of relaxation-based simulation technique to interconnect and plane networks. First, the characteristics of the power/ground plane networks are considered. Next, the formulation of the plane network by nodal analysis (NA) method is suggested. Furthermore, application and estimation results of the relaxation-based numerical analyses are shown. Finally, it is confirmed that the relaxation-based methods improved by the suggested formulation are much more efficient than the conventional direct-based methods.

This paper describes the application techniques of the latency insertion method (LIM) to CMOS circuit simulations. Though the existing LIM algorithm to CMOS circuit performs fast transient analysis, CMOS circuits are not modeled accurately. As a result, they do not provide accurate simulations. We propose a more accurate LIM scheme for the CMOS inverter circuit by adopting a more accurate model of the CMOS inverter characteristics. Moreover, we present the way to expand the LIM algorithm to general CMOS circuit simulations. In order to apply LIM to the general CMOS circuits which consist of CMOS NAND and NOR, we derive the updating formulas of the explicit form of the LIM algorithm. By using the explicit form of the LIM scheme, it becomes easy to take in the characteristics of CMOS NAND and NOR into the LIM simulations. As a result, it is confirmed that our techniques are useful and efficient for the simulations of CMOS circuits.