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Guo Z.,Apache Design Solutions | Pan G.G.,Arizona State University | Pan H.K.,Intel Corporation
IEEE Transactions on Components, Packaging and Manufacturing Technology | Year: 2011

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. © 2011 IEEE. Source


Tong M.S.,University of Illinois at Urbana - Champaign | Qian Z.-G.,University of Illinois at Urbana - Champaign | Qian Z.-G.,Apache Design Solutions | Chew W.C.,University of Illinois at Urbana - Champaign | Chew W.C.,University of Hong Kong
IEEE Transactions on Antennas and Propagation | Year: 2010

The volume integral equations (VIEs) for electromagnetic (EM) scattering by three-dimensional (3D) penetrable objects are solved by Nystrm method. The VIEs are essential and cannot be replaced by surface integral equations (SIEs) for inhomogeneous problems, but they are usually solved by the method of moments (MoM). The Nystrm method as an alternative for the MoM has shown much promise and has been widely used to solve the SIEs, but it is less frequently applied to the VIEs, especially for 3D EM problems. In this work, we implement the Nystrm method for 3D VIEs by developing an efficient local correction scheme for singular and near singular integrals over tetrahedral elements. The scheme first interpolates the unknown functions within the tetrahedral elements and then derives analytical solutions for the resultant singular or near singular integrals after singularity subtraction. The scheme is simpler and more efficient in implementation compared with those based on the redesign of quadrature rules for the singular or near singular integrands. Numerical examples are presented to demonstrate the effectiveness of the proposed scheme and its convergence feature is also studied. © 2006 IEEE. Source


Qian Z.-G.,University of Illinois at Urbana - Champaign | Qian Z.-G.,Apache Design Solutions | Chew W.C.,University of Hong Kong
IEEE Transactions on Antennas and Propagation | Year: 2010

The recently developed augmented electric field integral equation (A-EFIE) remedies the well-known low-frequency breakdown. However, it loses accuracy of current when applied to certain low-frequency applications like plane wave scattering. This paper addresses the low-frequency inaccuracy problem, and proposes a perturbation method as a remedy. A-EFIE with perturbation solves the same A-EFIE matrix system with updated right hand side vectors repeatedly to obtain the current and charge on different frequency orders as a perturbation series. This method does not require a search for the loop and tree basis, but the loop and tree currents can also be recovered. Numerical experiments validate the novel method. © 2010 IEEE. Source


Zhang L.,Arizona State University | Pan G.,Arizona State University | Guo Z.,Apache Design Solutions
2012 IEEE 21st Conference on Electrical Performance of Electronic Packaging and Systems, EPEPS 2012 | Year: 2012

We developed a full-wave formulation to model massive number of vias in high-speed printed circuit board (PCB), through silicon via (TSV) and electric band-gap (EBG) structures. This analytic method employs the equivalent magnetic frill array, Galerkin's procedure, image theory and Fourier transform to simplify the problem from a 3D configuration into a 2D frame. Based on Bessel's functions and addition theorem, the final matrix equation is formulated analytically without using any numerical techniques. The new method is purely from the boundary conditions. Consequently, it is simple, versatile, efficient and accurate. Numerical examples demonstrate good agreement between our analytical solution and commercial software (HFSS) for through silicon and PCB vias. The model is also used to study the EBG wall and cavity, for leakage fields. © 2012 IEEE. Source


Patra B.,Qualcomm | Chandak N.,Apache Design Solutions | Chakrabarti A.,University of Calcutta
Journal of Low Power Electronics | Year: 2011

ElectroMigration (EM) is becoming an increasingly important challenge in advanced process technologies due to reducing interconnect widths, increasing inter-connect lengths (increasing die-size), increasing on-die temperatures, and increasing complexity of ElectroMigration rules (provided by foundry). Hence traditional approaches of attempting to create correct by construction interconnect design is becoming increasingly inadequate and found to leave numerous real EM violations on design. Further, higher performance goals and current densities at these nodes, necessitate checking ElectroMigration not just for average currents but also peak and rms (self-heat) currents. In this paper, we review some of these challenges and then describe a practical CAD methodology for Signal ElectroMigration analysis for large SOC designs at advanced technology nodes using EDA tool RedHawk-SEM. We present results and observations from application of this methodology on some high performance large SOC designs at 45 nm. © 2011 American Scientific Publishers All rights reserved. Source

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