Power spectrum of an injection-locked Josephson oscillator

Previous experiments have shown that a Josephson oscillator, exposed to a weak narrow-band input signal, exhibits behavior characteristic of an injection-locked oscillator. When in lock, Adler's theory of injection locking describes the experimental observations reasonably well. This paper extends the range of applicability of the theory to the out-of-lock regime where a spectrum of output frequencies is observed. Obtaining the theoretical output power spectrum requires solving a differential equation having the same form as the equation describing the resistively shunted junction model of Stewart and of McCumber. Experimental measurements of the output spectrum of a nearly locked Josephson oscillator are shown to be in reasonable agreement with the theory. Additional results discussed briefly include the observation of a frequency dependence of the locked Josephson oscillator output, and experiments in which a Josephson oscillator-mixer was injection locked by a weak signal at the if.