Giuseppe Selli, Ph.D. Student, University of Missouri-Rolla
Christian Schuster, Professor, Technical University Hamburg-Harburg
Young Kwark, Research Staff Member, IBM
Mark Ritter, Research Manager, IBM
James Drewniak, Professor, University of Missouri-Rolla

At DesignCon 2006, the authors introduced the concept of "physical" or "physics-based" models for single-ended vias in printed circuit boards. Accurate measurements of hardware showed that relatively simple equivalent circuit models can be used to simulate complex via behavior up to high frequencies. The models are very concise and have a one-to-one relationship between circuit elements and real-world features. In this paper, the physical models are extended from single-ended vias with simple ground returns to more complex scenarios, including coupled and ground-return vias. Good correlation to measurements validates the proposed approach.