Homotopy-based direct current analysis with formal stop criterion

Circuit simulation aids to predict and improve analog circuits performance. Direct current (DC) simulation highlights as a key tool to analyse linear and nonlinear circuits. Then, during the recent decades homotopy continuation methods (HCM) have been proposed as replacement for Newton-Raphson method (NR) to obtain operating points (OP) of nonlinear circuits. HCM has the ability to find multiple OP with global convergence, whilst NR method can only find one OP due to its characteristic of local convergence. Nonetheless, HCM lacks of a formal stop criterion to end DC simulations. Therefore, in this work, we propose a new double bounded homotopy (DBH) as a tool to find multiple OP of nonlinear circuits with a reliable mathematical stop criterion based on its property of forming closed trajectories. This kind of homotopy joins the other two reported DBH. Hence, we will show a performance comparison between the proposed method and the other two existent DBH; resulting in a better performance by the proposed HCM for a benchmark study case circuit having nine OP and containing bipolar transistors as nonlinear elements.