Explicit formulation for injection-locked coupled-oscillator systems

The use of an external injection-locking source prevents undesired frequency shifts in coupled-oscillator systems. Here an explicit formulation for the analysis of these systems is presented, based on a numerical model of the oscillator elements in free-running regime, obtained with harmonic balance. It demonstrates the opposed effects of oscillator coupling and injection locking in a realistic manner and brings to light the influence of the oscillator characteristics and coupling-network parameters. The explicit expressions provide the minimum injection-locking power required for a full variation of the interstage phase shift and allow fixing and/or maximizing the locking bandwidth through a suitable choice of the coupling networks.