Mutual Pulling Between Two Oscillators

Behavior of two mutually coupled phase-locked or free-running oscillators with nearby frequencies is studied. In the case of two free-running mutually coupled oscillators, the two oscillators are either locked to a common frequency, or they undergo through a mutual pulling interaction. It is shown that center frequencies of the pulled oscillators come closer, however, they do not necessarily approach toward each other from opposite directions. It is also demonstrated that the strengths of mutual injections as well as the phase-shifts experienced by the mutually injected signals, affect locations of the two center frequencies. The paper also studies impacts of phase-locked loops on the location and magnitude of the sidebands, when the two mutually coupled oscillators are phase-locked. Effects of the phase-shifts endured by the mutually injected signals on the sidebands are also discussed.