Homotopy method with a formal stop criterion applied to circuit simulation

The continuous scaling for fabrication technologies of electronic circuits demands the design of new and improved simulation techniques for integrated circuits. Therefore, this work shows a new double bounded polynomial homotopy based on a polynomial formulation with four solution lines separated by a fixed distance. The new homotopy scheme presents a bounding between the two internal solution lines and the symmetry axis, which allows to establish a stop criterion for the simulation in DC. Besides, the initial and final points on this new double bounded homotopy can be set arbitrarily. Finally, mathematical properties for the new homotopy are introduced and exemplified using a benchmark circuit.