Improved model-order reduction by using spacial information in moments

The new concept of multinode moment matching (MMM) is introduced in this paper. The MMM technique simultaneously matches the moments at several nodes of a circuit using explicit moment matching around = 0. As compared to the well known single-point moment matching (SMM) techniques (such as asymptotic waveform evaluation), MMM has several advantages. First, the number of moments required by MMM is significantly lower than SMM for a reduced-order model of the same accuracy, which directly translates into computational efficiency. This higher computational efficiency of MMM as compared to SMM increases with the number of inputs to the circuit. Second, MMM has much better numerical stability as compared to SMM. This characteristic allows MMM to calculate an arbitrarily high-order approximation of a linear system, achieving the required accuracy for systems with complex responses. Finally, MMM is highly suitable for parallel-processing techniques especially for higher order approximations while SMM has to calculate the moments sequentially and cannot be adapted to parallel processing techniques.