In circuit simulation, dc operating points of nonlinear circuits are obtained by solving circuit equations. In this paper, we consider "hybrid equations" as the circuit equations and discuss the stability of dc operating points obtained by solving hybrid equations. We give a simple criterion for identifying unstable operating points from the information of the hybrid equations. We also give a useful criterion for identifying initial points from which homotopy methods coverge to stable operating points with high possibility. These results are derived from the theory of dc operating point stability developed by M. M. Green and A. N. Willson, Jr.

Tracing solution curves of nonlinear equations is an important problem in circuit simulation. In this paper, simple techniques are proposed for improving the computational efficiency of the spherical method, which is a method for tracing solution curves. These techniques are very effective in circuit simulation where solution curves often turn very rapidly. Moreover, they can be easily performed with little computational effort.