Algebraic representation of error bounds for describing function using Groebner base [nonlinear circuit analysis example]

This paper presents an algebraic approach to find the region where the true periodic solution of a nonlinear system or circuit lies when a describing function solution is given. Because algebraic representations of the error bounds are obtained by the Groebner base, the dependence of the bounds on parameter values becomes clear. Further, we propose an efficient method to improve the estimation. The Groebner base is shown to be applicable to the describing function method. The estimation is modified considerably.