Unified formulation for multiple vias with or without circular pads in high speed interconnects

Zhonghai Guo, George Pan, Helen K. Pan

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


A unified full-wave characterization of massive number of vias with or without circular pads is formulated analytically by means of equivalent magnetic frill array model and Galerkin's procedure. The proposed method takes advantage of the parallel-plate structure and employs image theory and Fourier transform to simplify the problem from 3-D configuration into 2-D frame. Based on the cylindrical symmetry with Bessel's functions and addition theorem, the final matrix equation is formulated analytically which can be used immediately for sensitivity analysis in both via dimensions and pad size. As a result, the new method is simple, efficient, and accurate. Numerical examples demonstrate good agreement between our analytical solution and the results obtained by commercial software (high frequency structure simulator) over a frequency range up to 20 GHz.

Original languageEnglish (US)
Article number5958584
Pages (from-to)1226-1233
Number of pages8
JournalIEEE Transactions on Components, Packaging and Manufacturing Technology
Issue number8
StatePublished - Aug 2011


  • Galerkin's procedure
  • image theory
  • integrated circuits
  • magnetic frill

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Industrial and Manufacturing Engineering
  • Electrical and Electronic Engineering


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