Phase locking of high power microwave oscillators with large injection power ratios

An analysis of phase locking between two high power microwave oscillators with large injection power ratios has been developed by making use of the concept of a lumped circuit, which makes it possible to predict the locked relative phases more accurately and provides a more suitable phase-locking condition for most practical cases. Sample phase calculations starting from different initial conditions are presented, which show that the conventional phase-locking theory is sufficient only when the frequency difference between the oscillators is small enough, however, it must be modified when the frequency difference and the power ratios are both large. Moreover, it has also been found that a longer locked time and a wider locking bandwidth are expected by the new results than those obtained by the conventional phase-locking theory.