Efficient symbolic analysis of large analog circuits using sensitivity-driven ranking of matroid intersections

A new program for the generation of approximate symbolic network functions is presented. The approximation technique used in this tool is the simplification during expression generation technique, which in the general case suffers from a nonpolynomial CPU complexity. The technique makes use of the two-graph method. Using matroid intersection theory, spanning trees common to the voltage and the current graph are directly generated at selected sample frequencies. The generation of the approximate symbolic expression of a network function is driven by the sensitivity of the magnitude of the network function with respect to the different coefficients. In this way, very little terms are generated more than once. The total algorithm runs in O(Kmn³) time. Here, K is the average number of matroid intersections that must be generated for the approximation of each coefficient of the network function, n is the number of nodes in the linearized network and m is the number of circuit elements. Experimental results are presented and a comparison to previous methods based on matroid intersection theory is given