Ieee Transactions on Computer - Aided Design 111 [ 24 ]

Two optimizations to accelerated method-of-moments algorithms for signal integrity analysis of complicated 3-d packages. he was responsible for the design methodology for IBM's G4 S/390 microprocessors. Since 1997, he has been at Columbia University, where he is now Associate Professor. Number of nonzero elements in the inductance matrix. Full partial inductance extraction is shown as is the result of shell sparsification on this matrix. This compares favorably with the number of elements required in the return-limited inductance extraction. \very big" indicates that the number of nonzero elements was too large to even practically count (> 50 million). approach results in a positive-semi-deenite inductance matrix and achieves sparsity by breaking inductive couplings between the power-ground lines and signal lines and by using a set of geometry-based decomposition rules to discard \insigniicant" coupling interactions between signal lines and between power and ground lines. By taking advantage of the fail-safe availability of power-ground lines as high-frequency current returns while preserving inductive coupling between signal lines, we have demonstrated remarkable eeciency and accuracy over other sparsiication techniques. We plan to combine this technique with capacitance extraction to produce a true full-chip RLC extraction environment. As part of this work, further reenement of the shadow rules may be necessary to achieve maximum accuracy for minimum loss of eeciency. A much closer interaction with layout will also be required in analysis and extraction in order to understand current distributions in the substrate and how this might eeect interconnect response in some cases. Design methodologies and circuit design trade-oos for the HP PA 8000 processor. Coordinate-transformed Arnoldi for generating guranteed stable reduced-order models for RLC circuits. 109 returns for the horizontal segments, the discarded forward mutual inductances are more signiicant. To demonstrate this, we also ran this example in which we doubled the size of the horizontal interaction regions to include more forward mutual inductances. The results are shown in the dotted curve in Figure 14(b). Good approximation is obtained with the return-limited extraction in the near-end driving point impedance as shown in Figure 13(c). Figure 15 shows a more complex example in which two signal lines, one beginning at A and ending at D, and the other beginning at C and ending at B, are routed within the same power and ground distribution network. Nodes B and D are shorted at the far end to the power grid and the ideal de-coupling assumption is applied. Once …