Parameter embedding (also called continuation and homotopy) methods are robust and accurate numerical techniques for solving nonlinear algebraic equations. Past implementation of homotopy algorithms in industrial circuit simulators proved that they were viable options to resolving convergence difficulties when finding circuits' DC operating points. They also show promise in finding steady-state solutions of highly nonlinear transistor circuits.
The main drawback in using homotopy methods is their computational intensity. Therefore, they are most suitable for solving difficult nonlinear problems where initial solutions are hard to estimate or multiple solutions are desired. For circuits that fall in this category, homotopy algorithms offer a very attractive alternative.
We illustrate that successful design of such algorithms and their implementation must exploit fundamental properties of transistor circuits and should rely on thorough understanding of their nonlinear behavior.