A sum-over-paths impulse-response moment-extraction algorithm for RLCM IC-interconnect networks

We have created a new impulse-response (IR) moment-extraction algorithm for RLCM circuit networks. It employs a Feynman sum-over-paths postulate. Our approach begins with generation of s-domain nodal-voltage equations. We then perform a Taylor-series expansion of the circuit transfer function. These expansions yield transition diagrams involving mathematical coupling constants, or weight factors, in integral powers of complex frequency s. Our sum-over-paths postulate supports stochastic evaluation of path sums within the circuit transition diagram to any desired order of s. The specific order of s in the sum corresponds, as well, to the order of IR moment we seek to extract. In developing the algorithm, importantly, we maintain computational efficiency and full parallelism. Initial verification studies of uncoupled and coupled RLCM lines furnished promising results: less than 10% 1-σ error for m1 or m2 moment, after 10 K sampled path-sum terms. In addition, we observed excellent convergence to exact, analytical moment values with increasing number of samples. Our sum-over-paths postulate, in fact, implies generality for arbitrary RLCM-interconnect network topologies, beyond those specific examples presented in this work. We believe, in conclusion, that this type of IR-moment extraction algorithm may find useful application in a massively coupled electrical system, such as a high-end digital-IC interconnect network.