Two-pole analysis of interconnection trees

We address the two-pole simulation of interconnect trees via the moment matching technique. We simulate the interconnect network by modeling the distributed lines with non-uniform m lumped segments and using the two-pole methodology. To this end, we derive new non-uniform equivalent circuits which match the general distributed line transfer function up to the second term. Using the recursive equation for the admittance of a tree, we give the exact expressions for the first and second moments of the transfer function of the interconnect tree. Our results show that delay estimates using our method are within 13% of SPICE-computed delays. As routing trees become bigger and interconnection lines become longer, e.g., in MCM design, our approach has advantages in both accuracy and simulation complexity.