Symbolic analysis of large analog integrated circuits: the numerical reference generation problem

Symbolic analysis potentialities for gaining circuit insight and for efficient repetitive evaluations have been limited by the exponential increase of formula complexity with the circuit size. This drawback has began to be solved by the introduction of simplification before and during generation techniques. An appropriate error control in both involves the generation of a numerical reference, which implies the calculation of network functions in the complex frequency variable. The polynomial interpolation method, traditionally used for this task, is analyzed in detail, its limitations for large circuit analysis are pointed out, and an adaptive scaling mechanism is proposed to meet the efficiency and accuracy requirements imposed by the new simplification methodologies.