Inductance Calculation for the Power Net Area Fill of Packages and PCBs Based on Plane-Pair PEEC

Abstract

The inductance of the power/ground planes is an integral contributor to the input impedance of a power delivery network for high-speed printed circuit boards (PCBs) and packages. Conventionally, differential-equation (DE) circuit and cavity type models have been applied to compute the inductive behavior of the plane-to-plane inductance. However, these methods are not suitable for the case where the structures are perforated or involve other uneven structures. In this article, a new partial-element-equivalent-circuit (PEEC)-based method is presented to compute the inductance of parallel plate-like planes and other structures. Examples are given to show that the new method can efficiently compute inductances for multiple integrated circuit power vias, power/ground planes, and multiple decoupling capacitors. The proposed model is validated with both full-wave CEM simulations as well as with measurements. Further, the speed and the accuracy for real PCB and package designs are presented to validate the efficiency as well as the accuracy of the proposed approach. An important aspect of any approach is the limitations for solving real life problems. In this article, we consider important issues related of plane-pair PEEC to power distribution evaluations. Specifically, we show that large holes in planes can accurately be modeled. This is a difficult issue for DE methods. Another surprising practical issue is the accuracy obtained even if the planes are not of the same size. We also consider the speedup, which can be obtained in comparison to solutions for other approaches. This is due to the sparsity of the coupling for the rapid coupling decrease with distance. This short-distance coupling also increases the maximum frequency for which the method can be applied.