Study of Expandable Power Delivery Network Equivalent Circuit Model

Abstract

This paper introduces a modeling method to accelerate the time for estimation of resonance and antiresonance frequency based on the impedance of grid-type PDNs (power distribution networks) implemented on an interposer. 3D electro-magnetic simulations are known for their time-consuming nature when extracting results. To save the simulation time, the grid-type PDN needs to be converted into a simplified circuit model, followed by conducting spice simulations. Moreover, to ensure consistent simulation time even with a largesize PDN, a fixed equivalent circuit model can be utilized. The equations for the R, L, and C for the equivalent circuit model based on the size of the PDN are presented in this paper. Four models are proposed to predict the first resonance and antiresonance for interwire Configurations with varying Capacitance. The verification was conducted by comparing 3D EM simulation and Spice simulation. Comparing the simulation time of 3D EM simulation with Spice simulation for a 9x9 unitcell with a width of 10m and a space of 90 m, the 3D EM simulation takes 28 minutes and spice simulation takes 0.029 seconds. Each model's result graph and MAPE (mean absolute percentage error) is analyzed.