Modeling and transient simulation of planes in electronic packages

This paper presents a modeling and simulation approach for ground/power planes in high speed packages. A plane pair structure is first characterized in terms of its impedance (Z) matrix at arbitrary port locations in the frequency domain. This solution is then extended for multiple plane pairs under the assumption that skin effect is prominent at higher frequencies causing isolation between the layers. Since the solutions are in analytical form, the frequency and transient response can be computed efficiently requiring small computational time. To develop spice models, equivalent circuits are constructed using resonator models with passive elements using model order reduction methods. This paper also discusses a method for incorporating decoupling capacitors into the plane models. The simulation results show good correlation with measured data.