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

Zhonghai Guo; George Pan; Helen K. Pan

doi:10.1109/TCPMT.2011.2149520

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 journal › Article › peer-review

3 Scopus citations

Abstract

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 language	English (US)
Article number	5958584
Pages (from-to)	1226-1233
Number of pages	8
Journal	IEEE Transactions on Components, Packaging and Manufacturing Technology
Volume	1
Issue number	8
DOIs	https://doi.org/10.1109/TCPMT.2011.2149520
State	Published - Aug 2011

Keywords

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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10.1109/TCPMT.2011.2149520

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title = "Unified formulation for multiple vias with or without circular pads in high speed interconnects",

abstract = "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.",

keywords = "Galerkin's procedure, image theory, integrated circuits, magnetic frill",

author = "Zhonghai Guo and George Pan and Pan, {Helen K.}",

note = "Funding Information: Manuscript received August 2, 2010; revised January 28, 2011; accepted March 15, 2011. Date of publication July 22, 2011; date of current version August 12, 2011. This work was supported in part by the Intel Research Laboratory, Hillsboro, under Grant DW9-1040. Recommended for publication by Associate Editor S. L. Dvorak upon evaluation of reviewers{\textquoteright} comments.",

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doi = "10.1109/TCPMT.2011.2149520",

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AU - Guo, Zhonghai

AU - Pan, George

AU - Pan, Helen K.

N1 - Funding Information: Manuscript received August 2, 2010; revised January 28, 2011; accepted March 15, 2011. Date of publication July 22, 2011; date of current version August 12, 2011. This work was supported in part by the Intel Research Laboratory, Hillsboro, under Grant DW9-1040. Recommended for publication by Associate Editor S. L. Dvorak upon evaluation of reviewers’ comments.

PY - 2011/8

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N2 - 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.

AB - 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.

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KW - image theory

KW - integrated circuits

KW - magnetic frill

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

Abstract

Keywords

ASJC Scopus subject areas

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