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In this paper, we model multiple vias with irregular antipad in arbitrarily shaped 3-D integrated circuit and packaging system based on generalized Foldy–Lax equations method, boundary integral equation method, and generalized T matrix. We first obtain the impedance matrix for finite cavity, which includes the reflection features of the cavity boundaries. Then, the scattered field from a single via and a generalized T matrix, including the wall effects, are derived. The Foldy–Lax multiple scattering equations are generalized to include the wall effects using impedance matrix and the generalized T matrix. To obtain the incident field for the case of vias in the arbitrarily shaped antipad, we calculate the exciting and scattering field coefficients based on the transformation that converts surface integration of magnetic surface currents in antipad into 1-D line integration of surface charges on the vias and ground plane. The coupling among vertical vias are solved by applying Foldy–Lax multiple scattering equations. The scattering matrix of coupling among vias is calculated to make corresponding signal/power integrity analysis. Numerical results for the method are in a good agreement with a commercial full-wave numerical tool up to 50 GHz. [ABSTRACT FROM PUBLISHER]

We consider multiple scattering among different groups of vias with each group of vias sharing one antipad in planar waveguide. A transformation is used that converts the 2-D discretization and 2-D surface integration of the product of Green's functions and magnetic surface currents into 1-D discretization and 1-D integration of surface charges on the vias and on the ground plane. This is used to calculate the incident fields onto the vias. Based on the incident fields, the Foldy–Lax equations can be solved to calculate the circuit parameters for the problem. We show that the results are superior to the previously used finite difference method. In addition, the group T-matrix method is used to represent a group of vias to account for the scattering among different groups of vias. Results are illustrated for various cases of multiple vias up to 20 GHz. Results show the accuracy of the method even to very closely spaced vias when they are separated by merely 1 mil. Numerical results are in excellent agreement with ANSOFT HFSS. [ABSTRACT FROM AUTHOR]

Three-dimensional electromagnetic simulation models are often simplified in order to reduce simulation time and memory requirements without sacrificing the accuracy of the results. A commonly adopted methodology in the simulation of complex electronic package and board designs is to truncate the size of the model, leaving only a few important features surrounding the nets of interest. In this paper we demonstrate that this simplification can have a significant impact on the simulation results if it is not performed carefully, and it can introduce spurious nonphysical resonances. The interaction between cavities and signals is first studied using a simple coupled differential via test structure. It is demonstrated that the return currents generated by these vias excite cavity resonances in power-ground plane pairs causing them to behave as parallel-plate waveguides. The role of interplane shorting vias in suppressing cavity resonances is then investigated and the impact of boundary conditions on the simulation results of package models is also shown and discussed. The focus is then shifted to PCB/package cosimulation and the impact of different truncation schemes is discussed through the simulation of test structures of varying complexity. A simulation methodology is then proposed and is verified for a combined model of a realistic complex multilayer package and board and it is demonstrated that accurate results can be obtained through proper truncation of the geometry. [ABSTRACT FROM AUTHOR]

The authors applied the method of Foldy–Lax multiple scattering equations to multiple vias in ball grid arrays and the interior layers of printed circuit boards. The method gives the scattering parameters of the array. The results are verified with Ansoft's HFSS with very little difference between the Foldy–Lax approach and the HFSS results. The CPU required for the method is only a small fraction of the time that HFSS requires. For a 16 × 16 array of vias, the method calculates all the S-parameters of the 512 ports in 4 min for 10 frequencies on a Pentium 3.2 GHz PC. © 2006 Wiley Periodicals, Inc. Microwave Opt Technol Lett 49: 225–231, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.22091 [ABSTRACT FROM AUTHOR]

Originally published in Microwave Opt Technol Lett 49: 2392–2395, 2007. © 2007 Wiley Periodicals, Inc. Microwave Opt Technol Lett 50: 263, 2008; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.23053 [ABSTRACT FROM AUTHOR]

Originally published Microwave Opt Technol Lett 49 (2007), 225–231. © 2007 Wiley Periodicals, Inc. Microwave Opt Technol Lett 50: 263, 2008; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.23005 [ABSTRACT FROM AUTHOR]