Transient Chip-Package Cosimulation of Multiscale Structures Using the Laguerre-FDTD Scheme

Transient simulation using Laguerre polynomials is unconditionally stable and is ideally suited for modeling structures containing both small and large feature sizes. The focus of this paper is on the automation of this technique and its application to chip-package cosimulation. Laguerre finite-difference time-domain (FDTD) requires using the right number of basis coefficients to generate accurate time-domain waveforms. A method for generating the optimal number of basis functions is presented in this paper. Equivalent circuit models of the FDTD grid have been developed. In addition, a method for simulation over a long time period is also presented that enables the extraction of the frequency response both at low and high frequencies. A node numbering scheme in the circuit model of the FDTD grid that is suitable for implementation has been discussed. Results from a chip-package example that shows the scalability of this technique to solve multiscale problems have been presented.