RC-in RC-out Model Order Reduction Accurate up to Second Order Moments

In this paper, we present a RC-in RC-out model order reduction method which takes RC circuits and accurate reduced models which can be realized using passive RC elements. The reduced models are accurate up to 2nd order moment and hence are more accurate than the first order moment matching based algorithm [3], [4], [ 5 ] . The runtime and reduction ratios of our method are not dependent on the number of ports, which can be very large for tightly coupled interconnects. Extensive SPICE simulations show the average accuracy of our algorithm is 5X better than first order moment based algorithms. It also significantly improves the reduction ratio by 50% comparing the first order moment based algorithm for the same accuracy. I. PATTERN MATCHING RULE-BASED REDUCTION P ROCEDU RE In this section, we present our rule-based realizable model order reduction method. We first develop marly circuit primitives which can match predetermined second order moments and then recursively search the circuits to replace such circuit patterns which can be replaced by these primitives without losing much accuracy. L2-Reduction and C2-Reduction are the rules we newly proposed. 1) L2-Reduction: ,% ~ ~ The basic primitive of L2-reduction is a 2-7r model as RI R I . . . ~ ~-~~ ~~~~ .... ~. ~~~~ ~ ,U,< , . , . . . . .. . . . . . . .~ CI . c2 ~C' :