Brute-force simulation approaches to estimating serial-link bit-error rates (BERs) become computationally intractable for the case when BERs are low and the interconnect electrical response is slow enough to generate intersymbol interference that spans dozens of bit periods. Electrical-level statistical simulation approaches based on superposing pulse responses were developed to address this problem, but such pulse-based methods have difficulty analyzing jitter and rise/fall asymmetry. In this paper we present a superposing-edge approach for statistical simulation, as edge-based methods handle rise/fall asymmetry and jitter in straightforward way. We also resolve a key problem in using edge-based approaches, that edges are always correlated, by deriving an efficient inductive approach for propagating the edge correlations. Examples are presented demonstrating the edge-based method's accuracy and effectiveness in analyzing combinations of uniform, Gaussian, and periodic distributed random jitter.

In [1], it was shown that an equation formulation based on mesh analysis can be combined with a GMRES-style iterative matrix solution technique to make a reasonably fast 3-D frequency dependent inductance and resistance extraction algorithm. Unfortunately, both the computation time and memory required for that approach grow faster than n/sup 2/, where n is the number of volume-filaments. In this paper, we show that it is possible to use multipole-acceleration to reduce both required memory and computation time to nearly order n. Results from examples are given to demonstrate that the multipole acceleration can reduce required computation time and memory by more than an order of magnitude for realistic packaging problems.

The combination of a mesh analysis equation formulation technique with a preconditioned GMRES matrix solution algorithm to accelerate the determination of inductances of complex three-dimensional structures is described. Addition of the preconditioner to GMRES can reduce the cost of solution to m/sup 2/ operations compared to m/sup 2/ for direct inversion. Results from FASTHENRY, a 3-D inductance extraction program, demonstrate that the iterative approach can accelerate solution times by more than an order of magnitude.>