EFFICIENT STABILITY ANALYSIS OF FREE-RUNNING MICROWAVE-OSCILLATORS INTHE FREQUENCY-DOMAIN

A stability analysis of free running oscillators in the frequency doma in is presented. By insertion of a simple damping subnetwork, dependin g on one parameter, a global stability analysis starting in a Hopf bif urcation is performed. Near the bifurcation, stability of a periodic o rbit is determined by studying stability of the stationary solutions. Provided turning and bifurcation points are detected, stability is thu s known on the whole path connecting the Hopf bifurcation and the solu tion of the undamped oscillator network. It is shown that for the gene ration of starting values for the signal analysis by homotopy and for the stability analysis the same solution path can be utilized. Thus co upling of large-signal and stability analysis leads to an efficient al gorithm where stability of oscillatory solutions is computed as a by-p roduct of signal analysis with hardly any additional cost. The present ed method is applied to a microwave oscillator at 15 GHz and to an osc illator model which has several coexisting large-signal solutions. Our method may be combined with any large-signal analysis program based o n a piecewise network description. It may be fully automated and requi res no sophisticated knowledge of the program user about stability ana lysis or bifurcation theory.