Stochastic LIM for uncertainty characterization of fiber-weave effect on coupled transmission lines

Fiber-weave effect impacts the transmission of signal waves on printed circuit board transmission lines. The effect is especially pronounced for differential signals, since the difference in dielectric properties between glass fiber and resin can lead to different propagation velocity between two lines in the pair, which results in intra-pair skew. The fiber-weave effect is difficult to model exactly since it depends on the relative position of the etched traces with respect to the glass fiber bundles in the substrate. In this paper, we present a method to model coupled transmission line traces with uncertainties due to the fiber-weave effect. We also present a very fast and efficient stochastic transient simulator to produce time-domain waveform of the differential signal. The simulator uses finite difference scheme in combination with Stochastic Galerkin Method to quantify the results of uncertainties in the circuit with a single simulation of an expanded state-space system.