Co-simulation of linear electromagnetic structures and non-linear devices in the time-domain finite-element reduction-recovery method

Abstract

The scaling of supply voltages and the increased level of integration have conspired to make the analysis and design of microelectronic systems increasingly challenging. The impact of dynamic noise due to signal switching, die-package coupling, power management techniques, substrate coupling, etc., can been seen at all levels of a power delivery network, from chip to package to mother board to the voltage regulator module. Thus, there is a critical need for the co-simulation of the integrated circuits and nonlinear devices to control the global electrical interaction and optimize performance as an integrated system. However, the co-simulation of integrated circuits and nonlinear devices results in numerical problems of ultra-large scale, requiring billions of parameters to describe them accurately. In order to address the large problem size, electromagnetic solutions have to scale favorably. In [1], a time-domain layered finite-element reduction-recovery method was developed for solving large-scale IC problems. This method can reduce the system matrix of size O(N) rigorously to that of size O(M) for any multilayered structure, with N being the number of unknowns in the entire 3D structure, and M being the number of unknowns in a single layer. Furthermore, the reduction from O(N) to O(M) was achieved without any computational cost via analytical means, and hence the CPU and memory overheads are minimal. In [2], a set of orthogonal prism vector basis functions were developed. These basis functions rendered the reduced single-layer system diagonal, and hence the reduced system can be solved readily. The method entails no approximation. It is applicable to arbitrarily-shaped 3D multilayer structures embedded in inhomogeneous media. The goal of this paper is to develop a method to co-simulate linear electromagnetic structures and non-linear circuit devices in the framework of the time-domain finite-element reduction-recovery method. The co-simulation of electromagnetic structures and circuit devices in a time-domain finite-element method has been discussed in [3–4]. The goal of this research is to perform the co-simulation without sacrificing the computational efficiency of the time-domain finite-element reduction-recovery method.