Finding All DC Operating Points of Nonlinear Circuits Based on Interval Linearization and Coordinate Transformation

Diagnosis of Analog Circuits: The Problem of Ambiguity of Test Equation Solutions

“…Robust and efficient determination of solutions to systems of nonlinear equations is a challenging problem from a theoretical and practical point of view. Calculating DC solutions is one of the most critical tasks when analyzing electronic circuits [1][2][3][4][5][6][7][8][9]. The Newton-Raphson method and its variants are used in standard simulators to compute solutions to the equations describing the analyzed circuits.…”

“…Two approaches to the problem exist in the literature. The first approach relies on methods that guarantee finding all solutions [3,5,6]. The methods usually require a specific hybrid description, can be applied to circuits belonging to a strictly defined class, and use simple models of semiconductor devices.…”

“…For reliable results, it is necessary to analyze the original nonlinear circuits. Interval methods and approaches based on the idea of successive contraction, division, and elimination of certain hyper-rectangular regions where solutions are sought can be applied here [1,3,6]. The complexity of the numerical procedures and the time-consuming aspect make the problem of finding all solutions for a large-scale circuit still unsolved.…”

“…In the meantime, many papers have highlighted potential problems in the simulation and operation of nonlinear circuits. Researchers have focused particular attention on the issue of multiple solutions and chaos [1][2][3][4][5][6][7][8][9]. Simultaneously, research was performed on the automation of testing different classes of circuits .…”