Four magnetron oscillator models are constructed and analyzed for the study of relativistic magnetron phase locking physics: the extended spoke model, the magnetron-specific equivalent model, the van der Pol equation, and the magnetron oscillator equation. The spoke model reproduces the magnetron specific conductance and susceptance features that are incorporated into other models. The equivalent circuit model and the magnetron oscillator equation model generate the same set of predictions concerning phase-locking condition, locking time, saturation amplitude and final phase. Both models predict a wider locking bandwidth and a shorter locking time as results of the frequency pushing effect. The van der Pol model solved in the fast time scale reveals the dependence of locking time on injection power and oscillator growth rate as well as on injection frequency.
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