The PSTD algorithm: a fast and accurate time-domain method for electronic package characterization

Abstract

Conventional finite-difference time-domain (FDTD) methods are very inefficient for simulations of electromagnetic wave propagation in large-scale complex media. This is mainly because of the low-accuracy associated with the spatial discretization in the FDTD methods. As a result, even for a moderate size problem, a large number of cells (typically 10-20 cells per wavelength) are required to obtain reasonably accurate results. This requirement becomes much more stringent for large-scale problems since the dispersion error grows rapidly with the propagation distance. Recently a pseudospectral time-domain (PSTD) algorithm has been developed which requires only two cells per wavelength regardless of the problem size. In terms of spatial discretization, this method is an optimal time-domain solution since it has an infinite order of accuracy in the spatial representation. For a problem with structures much smaller than the smallest wavelength, the PSTD algorithm still provides high accuracy up to a much higher spatial frequency than FDTD methods. In addition, the only error introduced in the PSTD algorithm is the temporal discretization. Unlike the dispersion error in FDTD methods, this error is isotropic and does not increase with the scale of the problem. In this work, we apply the PSTD method to characterize the electrical performance of electronic packages. In particular, it is used to investigate the effects of enclosure resonance and electromagnetic interference.