Passivity and no-gain properties establish global convergence of a homotopy method for DC operating points

Finding the DC operating points of transistor circuits is an important task in circuit simulation. The problem is equivalent to solving sets of nonlinear algebraic equations describing transistor circuits. Existing circuit simulators use Newton´s method, or its variants, to achieve this task. Newton´s method is local and requires a good initial guess for convergence, while its variants globally converge under restrictive conditions. Recent mathematical results guarantee the existence of constructive, globally convergent homotopy methods for finding zeros of nonlinear maps with probability one. These results are applied to the DC operating point problem by constructing various homotopies to create a simple problem that is solved before proceeding with the continuation process that will transform it into the initially stated difficult problem. It is shown that for a certain class of circuits used in the design of integrated circuits, nodal equations satisfy the conditions required by the globally convergent homotopy methods