Via interconnects in multilayer substrates, such as chip scale packaging, ball grid arrays, multichip modules, and printed circuit boards (PCB) can critically impact system performance. Lumped-circuit models for vias are usually established from their geometries to better understand the physics. This paper presents a procedure to extract these element values from a partial element equivalent circuit type method, denoted by CEMPIE. With a known physics-based circuit prototype, this approach calculates the element values from an extensive circuit net extracted by the CEMPIE method. Via inductances in a PCB power bus, including mutual inductances if multiple vias are present, are extracted in a systematic manner using this approach. A closed-form expression for via self inductance is further derived as a function of power plane dimensions, via diameter, power/ground layer separation, and via location. The expression can be used in practical designs for evaluating via inductance without the necessity of full-wave modeling, and, predicting power-bus impedance as well as effective frequency range of decoupling capacitors.


Electrical and Computer Engineering

Research Center/Lab(s)

Electromagnetic Compatibility (EMC) Laboratory


United States. Army Research Office


This work was supported in part by the U.S. Army Research Office under Grant DAAG55-97-1-0001 as part of the DDR&E MURI program.

Keywords and Phrases

CEMPIE; Ball Grid Arrays; Chip Scale Packaging; Closed-Form Expression; Decoupling Capacitors; Effective Frequency Range; Element Values; Equivalent Circuits; Full-Wave Modeling; Geometries; Inductance; Lumped-Circuit Model Extraction; Multichip Modules; Multilayer Substrates; Mutual Inductances; Partial Element Equivalent Circuit Type Method; Physics-Based Circuit Prototype; Power Plane Dimensions; Power-Bus Impedance; Power/Ground Layer Separation; Printed Circuit Boards; Printed Circuit Design; Self Inductance; Surface Mount Technology; Via Diameter; Via Location; Vias; DC Power-Bus Design; Decoupling Capacitor Design; Multilayer Substrate; Via Inductance; Via Interconnects

International Standard Serial Number (ISSN)

0018-9375; 1558-187X

Document Type

Article - Journal

Document Version

Final Version

File Type





© 2003 Institute of Electrical and Electronics Engineers (IEEE), All rights reserved.

Publication Date

01 May 2003