Automatic detection of Hopf bifurcations on the solution path of a parametrized nonlinear circuit

A numerical technique for the automatic detection of Hopf bifurcations on the solution path of a continuously parametrized nonlinear circuit operating in time-periodic steady state is discussed. The algorithm is based on the piecewise harmonic-balance technique, is truly general-purpose, and can be applied to any kind of nonlinear microwave subsystem without restrictions on circuit topology and device models. This method can lead to software tools for the solution of complex CAD problems, such as the detection of spurious tones in any nonlinear circuit and the analysis of the injection locking of oscillators.<>