Efficient stability analysis of free running microwave oscillators in the frequency domain

A stability analysis of free running oscillators in the frequency domain is presented. By insertion of a simple damping subnetwork, depending on one parameter, a global stability analysis starting in a Hopf bifurcation is performed. Near the bifurcation, stability of a periodic orbit is determined by studying stability of the stationary solutions. Provided turning and bifurcation points are detected, stability is thus known on the whole path connecting the Hopf bifurcation and the solution of the undamped oscillator network. It is shown that for the generation of starting values for the signal analysis by homotopy and for the stability analysis the same solution path can be utilized. Thus coupling of large-signal and stability analysis leads to an efficient algorithm where stability of oscillatory solutions is computed as a by-product of signal analysis with hardly any additional cost. The presented method is applied to a microwave oscillator at 15 GHz and to an oscillator model which has several coexisting large-signal solutions. Our method may be combined with any large-signal analysis program based on a piecewise network description. It may be fully automated and requires no sophisticated knowledge of the program user about stability analysis or bifurcation theory.