Chip-package co-simulation with multiscale structures

Chip-package co-simulation is required to predict the interaction between the chip and package at the system level. The FDTD method can be used to analyze these structures but is limited by the Courant condition. In this paper, an alternate method is suggested by combining Laguerre Polynomials with the FDTD method. Since, the solution is implicit, the Courant condition is no longer an issue and therefore the method provides unconditional stability. In addition, the time domain response can be computed similar to the FDTD scheme. The formulation allows the conversion of an electromagnetic problem to a circuit representation with resistors, voltage and current sources. Such a representation is useful since a DC solution can be used to obtain the transient response. To obtain the low frequency response using an FDTD based method, computing the time domain response over long time duration is required. Due to the behavior of the Laguerre Polynomials, this can be difficult. In this paper, computing the time domain response over several micro-seconds is discussed using Laguerre Polynomials combined with the FDTD scheme. This method now can be applied to compute the frequency response from DC to very high frequencies for multiscale structures arising in chip-package co-simulation.