An Integral Equation Hybrid Method for the Impedance Calculation of the Grid Power Distribution Network With an Arbitrary Shape

The grid power distribution network (PDN) is an essential component in electronic packages to provide the dc power to circuits. In this paper, an integral equation hybrid method is proposed for the efficient calculation of the impedance of the complex grid PDN. First, the original 3-D grid PDN is reduced to a simple 2-D plane PDN. Both of them have the same input and mutual parasitic impedances. After that, this equivalent plane PDN is solved by using the 2-D integral equation method to consider its arbitrary shape. By comparing between the obtained impedances from the proposed method, full-wave method, and measurement, the accuracy and efficiency of the proposed method is verified. The proposed method provides a simple and useful electronics design automation tool for the power integrity analysis of complex circuits.