Parallel Plate Impedance and Equivalent Inductance Extraction Considering Proximity Effect by a Modal Approach


A modal approach for parallel plate impedance and equivalent inductance extraction for power integrity analysis including ball grid arrays (BGAs) between two parallel plates is presented. Since the BGAs are placed close to each other, the current flowing through each ball is not uniformly distributed due to the proximity effect. In this paper, a modal-based cavity method is proposed to count for this proximity effect. Analytical solutions for both the parallel plate impedance and the equivalent inductances associated with the BGAs are derived from the modal-based cavity method. The proposed method is validated by finite element method simulations and the application of the proposed method for power distribution network design is demonstrated.


Electrical and Computer Engineering

Research Center/Lab(s)

Electromagnetic Compatibility (EMC) Laboratory


National Science Foundation (U.S.)


This work was supported in part by the National Science Foundation under Grant IIP-1440110.

Keywords and Phrases

Ball grid arrays; Cavity resonators; Current density; Electric conductors; Electric impedance; Electronics packaging; Extraction; Frequency modulation; Inductance; Semiconductor device testing; Soldered joints; Cavity method; Equivalent inductance; Finite element method simulation; Modal expansion; Parallel plates; Power Distribution Network Design; Power integrity; Proximity effects; Finite element method; Analytical solution; Application-specified integrated circuit (ASIC) package; Ball grid array (BGA); Equivalent ball inductances; Parallel plate impedance

International Standard Serial Number (ISSN)

0018-9375; 1558-187X

Document Type

Article - Journal

Document Version


File Type





© 2018 Institute of Electrical and Electronics Engineers (IEEE), All rights reserved.

Publication Date

01 Oct 2018