Accurate Analysis of Interconnect Trees With Distributed<tex>$ RLC$</tex>Model and Moment Matching

Abstract

In this paper, a new method is presented for accurate analysis of interconnect trees. Based on the ABCD matrix of distributed RLC transmission lines, the new iterative method can derive the exact transfer functions of an interconnect tree with distributed RLC model. Moment matching and second-order approximation are used for fast simulation of time responses and 50% delays of interconnect trees. The new method has three advantages. First, it can calculate the exact transfer functions of an interconnect tree with any interconnect model besides distributed RLC model. Second, it can derive all leaf nodes' time-domain responses in one iterative process. Third, it runs faster than HSPICE with time complexity linearly proportional to the number of branches in an interconnect tree. Time-domain responses and 50% propagation delays of the new method are compared to the results of HSPICE, the Elmore delay for lumped RC trees, and equivalent Elmore delay for lumped RLC trees, showing that the new method is both accurate and fast.