Modeling and transient simulation of planes in electronic packages for GHz systems

This paper presents a modeling and simulation approach for ground/power planes in high speed packages. The electrical characteristics of a plane structure are derived in terms of an impedance (Z) or scattering (S) matrix at port locations in the frequency domain by solving Maxwell's equations. Since the solution is a closed form equation, the frequency and transient response can be computed efficiently, requiring small computing time. The response of the plane structure has been captured using rational functions. These functions, which are SPICE-compatible, enable the connection of plane models to the rest of the package for simulation. The frequency and transient response computed using the analytical expression and rational functions have been compared against measurements. The simulation results show good correlation with measured data.