Modeling and simulation for signal and power integrity of electronic packages

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Choi, Jae Young
Swaminathan, Madhavan
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The objective of this dissertation is to develop electrical modeling and co-simulation methodologies for signal and power integrity of package and board applications. The dissertation includes 1) the application of the finite element method to the optimization for decoupling capacitor selection and placement on a power delivery network (PDN), 2) the development of a PDN modeling method effective for multidimensional and multilayer geometries, 3) the analysis and modeling of return path discontinuities (RPDs), and 4) the implementation of the absorbing boundary condition for PDN modeling. The optimization technique for selection and placement of decoupling capacitors uses a genetic algorithm (GA) and the multilayer finite element method (MFEM), a PDN modeling method using FEM. The GA is customized for the decoupling problem to enhance the convergence speed of the optimization. The mathematical modifications necessary for the incorporation of the capacitor model into MFEM is also presented. The main contribution of this dissertation is the development of a new modeling method, the multilayer triangular element method (MTEM), for power/ground planes of a PDN. MTEM creates a surface mesh on each plane-pair using dual graphs; a non-uniform triangular mesh (Delaunay triangulation) and its orthogonal counterpart (Voronoi diagram), to which electromagnetic and equivalent circuit concepts are applied. The non-uniform triangulation is especially efficient for discretizing multidimensional and irregular geometries which are common in package and board PDNs. Moreover, MTEM generates a sparse, banded, and symmetric system matrix, which enables efficient computations. For a given plane-pair, MTEM extracts an equivalent circuit that is consistent with the physics-based planar-circuit model of a plane-pair. Thus, the values of the lumped elements can be simply calculated from the physical parameters, such as material properties and mesh geometries of each unit-cell. Consequently, the modeling of MTEM is flexible and easy to modify for further extensions, such as the incorporation of external circuits, e.g. decoupling capacitors and vertical interconnects. Power and ground planes provide paths for the return current of signal traces. Typically, planes have discontinuities such as via holes, plane cutouts, and split planes that disturb flow of signal return currents. At the discontinuity, return currents have to detour or switch to different layers, causing signal and power integrity problems. Therefore, a separate analysis of signal interconnects will neglect the significant coupling with a PDN, and the result will not be reliable. In this dissertation, the co-simulation of the signal and power integrity is presented focusing on the modeling of RPDs created by split planes, apertures, and vias. Plane resonance is one of the main sources of power integrity problems in package and board PDNs. A number of techniques have been developed and published in literature to reduce or prevent the resonance of a plane-pair. One of the techniques is to surround plane-pair edges with absorbing material that effectively damps the outgoing parallel-plate wave and minimizes the reflection. To model this behavior, the boundary condition of MTEM needs to be changed from its original form, the open-circuit boundary condition. In this dissertation, the application of the 1st order absorbing boundary condition to MTEM is presented.
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