Inductance Extraction of Grid Power Distribution Network

For the package or on-chip power distribution network (PDN) design, plane metals are usually adopted. In this paper, we propose a closed-form grid metals solution to calculate the inductance of such grid PDN for the frequencies below its first antiresonant frequency. First, the grid PDN is equivalent to a plane PDN based on the equivalent circuit of their unit cells. Furthermore, the equivalent plane PDN is simplified as an RLCG lumped circuit, where {L} is the inductance of the grid PDN. Finally, the inductance of the grid PDN is obtained by the mode analysis of the equivalent plane PDN with a modified modal function. The proposed method is scalable, which can calculate the grid PDNs with the size from micrometer to centimeter. To verify the proposed method, a centimeter grid PDN is fabricated. The inductance obtained by the proposed method has a good agreement with that obtained by measurement and 3-D full-wave simulation. The proposed method can also be expanded to the case that the grid PDN has load impedances. In comparison with the numerical methods, the proposed method can give a more easy-to-understand explanation of the new antiresonant frequency produced by the load impedance.