This paper presents a fast transient simulation method for power distribution networks (PDNs) of the PCB/Package. Because these PDNs are modeled as large-scale linear circuits consisting of a large number of RLC elements, it takes large costs to solve by conventional circuit simulators, such as SPICE. Our simulation method is based on the leapfrog algorithm, and can solve RLC circuits of PDNs faster than SPICE. Actual PDNs have frequency-dependent dispersions such as the skin-effect of conductors and the dielectric loss. To model these dispersions, more number of RLC elements are required, and circuit structures of these dispersion models are hard to solve by using the leapfrog algorithm. This paper shows that the circuit structures of dispersion models can be converted to suitable structures for the leapfrog algorithm. Further, in order to reduce the simulation time, our proposed method exploits parallel computation techniques. Numerical results show that our proposed method using single processing element (PE) enables a speedup of 20-100 times and 10 times compared to HSPICE and INDUCTWISE with the same level of accuracy, respectively. In a large-scale example with frequency-dependent dispersions, our method achieves over 94% parallel efficiency with 5PEs.

In this paper, we show the generalized method of the time-domain circuit simulation based on LIM. Our method is applicable to any structure of circuits by combination with the SPICE-like method. In order to show the validity and efficiency of our method, an example circuit is simulated and the proposed method is compared with the conventional ones.

In this paper, we propose a new method which makes transient simulation faster for the circuit including both nonlinear and linear elements. First, the method for generating the projection matrix with Krylov-subspace technique is described. The order of the circuit equation is reduced by congruence transformation with the projection matrix. Next, we suggest a method which can calculate the reduced Jacobian matrix directly in each Newton-Raphson iteration. Since this technique does not need to calculate the original size of Jacobian matrix, the calculation cost is reduced drastically. Therefore, efficient circuit simulation can be achieved. Finally, our method is applied to some example circuits and the validity of the nonlinear circuit reduction technique is verified.

With the progress of integration of circuits and PCBs (Printed Circuit Boards), novel techniques have been required for verification of signal integrity. Noise analysis of the power/ground planes is one of the most important issues. This paper describes a high-speed simulator for PCBs which contain the interconnects with nonlinear terminations. This simulator is based on the environmental tool ASSIST (Assistant System for Simulation Study) constructed for development of the circuit simulators, and is combined with PRIMA (Passive Reduced-Order Interconnect Macromodeling Algorithm). In this simulator, an efficient implementation of PRIMA is considered with using a voltage-controlled current source (VCCS) model. Finally, this simulator is applied to the analysis of power/ground planes of the simple PCBs, and the validity is verified.