Algebraic Approach to Ambiguity-Group Determination in Nonlinear Analog Circuits

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> In this paper, a symbolic procedure for ambiguity-group determination, based on the <emphasis emphasistype="boldital">a priori</emphasis> identifiability concept, is proposed. The method starts from the analysis of the occurrence of circuit parameters in the coefficients of the input/output relationship in order to select the potential canonical ambiguity groups. This first step allows one to strongly reduce the problem complexity. In a second step, the obtained nonlinear system that imposes the ambiguity conditions is solved, resorting to Gröbner bases theory. Both of these steps are completely symbolic, thus avoiding round-off errors. Furthermore, the method can be applied to both linear and nonlinear circuits. An alternative approach is also proposed, which extends to nonlinear circuits a method presented in the literature, which can be directly applied only to linear circuits. The methods are illustrated by means of benchmarks regarding well-known linear and nonlinear circuits. </para>