Fast and accurate simulation of tree structured interconnect

A method is introduced to evaluate time domain signals within RLC trees with arbitrary accuracy in response to any input signal. This method depends on finding a low frequency reduced order transfer function by direct truncation of the exact transfer function at different nodes of an RLC tree. The method is numerically accurate for any order of approximation, which permits approximations to be determined with a large number of poles appropriate for approximating RLC trees with underdamped responses. The method is computationally efficient with a complexity linearly proportional to the number of branches in an RLC tree. A common set of poles are determined that characterize the responses at all of the nodes of an RLC tree which further enhances the computational efficiency. Stability is guaranteed by the DTT method for low order approximations with less than 5 poles. Such low order approximations are useful for evaluating monotone responses exhibited by RC circuits.