An evaluation of symbolic computation algorithms for the extraction of small signal parameters of a linear circuit

Using symbolic algorithms for small signal circuit parameter extraction could make possible implementing extraction programs which, unlike those based on pure numerical methods, no longer require initial (“start”) values for the parameters being extracted, thus ensuring that the final result corresponds to the true global minimum of the error function. Solving the extraction problem, in the particular case of a linear circuit, can be reduced to the math problem of determining the solutions of a system of polynomial equations. During resolution, classical mathematical algorithms used in the symbolic computing phase could generate during execution symbolic polynomials of size that could increase too fast (by a double exponential law) with the size of the input polynomials (thus making the symbolic computation useless), but in the case of specialized algorithms the size of intermediate polynomials could grow much slower (only by a polynomial law). An insight of the state of art of computational algebra can identify the main algorithms having good performance in terms of computational complexity to be used for symbolic variables elimination between the equations of a polynomial system. This paper analyzes, using a particular circuit, the performance of existing implementations for CAD math systems, which use symbolic methods based on different mathematical approaches, and compares the performances of these programs.